DEGREE PROJECT IN MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS
STOCKHOLM, SWEDEN 2019
Experimental validation of a
periodic heat transfer CFD model
of a vertical shell and tube heat
exchanger
PATRIK BENGTSSON
DILIP KUMAR VELLORE SAIKUMAR
KTH ROYAL INSTITUTE OF TECHNOLOGY
SCHOOL OF INDUSTRIAL ENGINEERING AND MANAGEMENT
TRITA-ITM-EX 2019:100
SE-100 44 STOCKHOLM
Abstract Flow obstructions are used as a passive design element in heat exchangers to enhance heat
transfer. Further, a change in flow structure can also have a positive effect on the heat transfer. A
vertical shell and tube heat exchanger, used to recover heat in the greywater stream, is
investigated in this study. The heat exchanger consists of flow obstructions such as annular
grooves and a helical string. The flow structure can be modified to a swirling film flow by
adding a passive design element, called a Cyclone generator. This study aims to experimentally
validate a periodic heat transfer CFD model of a shell and tube heat exchanger, with uniform
flow at steady-state laminar conditions. The study further analyses the heat transfer
characteristics of the annular grooves and the helical string, and the modified flow due to a
swirling film.
A calibrated test rig is constructed to consist of a heat source and a heat sink, as well as a means
for measuring the flow and temperature of a vertical heat exchanger at elevated temperatures.
The experimental results were evaluated using the Ɛ -NTU method and uncertainty analysis of
one standard deviation. The heat exchanger geometry had periodically repeating sections
between the inlet and the outlet. Hence the large geometry was simplified to a smaller periodic
module. The module was subjected to periodic boundary conditions and was simulated using a
pressure-based coupled algorithm on ANSYS Fluent. Further, the distribution of pressure and
velocity flow fields are examined for uniform flow in CFD. The experiment investigated the heat
transfer of a swirling flow at a wide range of flow rates.
The CFD model could not be validated by the experiment due to a difference between the overall
heat transfer coefficients, calculated in the model and the experiment. The error in validation
could be pointed to an ambiguous energy result in one of the streams. However, the model could
simulate real-life pressure drop conditions. It was found that the helical string contributed to a
substantial increase in the local turbulence, which translates to an increase in heat transfer. The
heat transfer was also increased in the presence of the annular grooves.
From the experiment, a higher heat transfer is noticed at the entrance region of the heat
exchanger compared to the middle section. The heat transfer characteristics of the swirling film
were found to be significantly higher than that of the uniform flow. Finally, for uniform and
swirling flows, the heat exchanger effectiveness, Ɛ, can be described as a single logarithmic
function of the NTU.
Acknowledgment We want to thank our KTH supervisor, Dr. Joachim Claesson, for his constant support with his
expertise and knowledge in the field of CFD, experimental procedure, and heat exchangers. We
are also grateful to Ian Hostetter, our supervisor from CONSAT SES, for giving us the
opportunity to perform this study. Without his vision and positive spirit, this master thesis would
not be possible. Further, we appreciate the assistance provided by Peter Hill and Benny Sjöberg
in the SEU Lab. Lastly, we would like to convey a special thanks to our supportive and loving
families.
Table of Contents Introduction ................................................................................................................................................... 1
Literature Review .......................................................................................................................................... 1
Heat transfer theory ................................................................................................................................... 1
Conductive heat transfer ....................................................................................................................... 1
Convective heat transfer ........................................................................................................................ 1
Radiative heat transfer .......................................................................................................................... 1
Fluid flow .................................................................................................................................................. 2
Viscosity of fluids ................................................................................................................................. 2
Steady vs unsteady flow ........................................................................................................................ 2
Uniform vs non-uniform flow ............................................................................................................... 2
Flow profile within fluids flow ............................................................................................................. 2
Compressible vs incompressible flow ................................................................................................... 3
Inviscid vs viscous flow ........................................................................................................................ 3
Flow structure ....................................................................................................................................... 3
Nusselt number ..................................................................................................................................... 3
Heat exchanger.......................................................................................................................................... 4
Thermal Resistance ............................................................................................................................... 4
Ɛ -NTU method ..................................................................................................................................... 4
Design Parameters................................................................................................................................. 5
Passive design ....................................................................................................................................... 5
Active design ........................................................................................................................................ 6
Wastewater Heat exchanger .................................................................................................................. 6
Potential of greywater in Sweden ......................................................................................................... 7
Description of the heat exchanger ......................................................................................................... 7
Measurement ............................................................................................................................................. 9
Statistical method .................................................................................................................................. 9
Calibration ............................................................................................................................................. 9
Computational Fluid Dynamics .............................................................................................................. 10
Numerical technique in fluid dynamics .............................................................................................. 10
CFD role in fluid dynamics ................................................................................................................. 10
Fluid modeling techniques – Finite control volume............................................................................ 11
Governing Equations ........................................................................................................................... 12
Accuracy of CFD ................................................................................................................................ 13
Periodic Heat Transfer ........................................................................................................................ 13
Methodology ............................................................................................................................................... 14
Experiment .............................................................................................................................................. 14
Experimental Setup ............................................................................................................................. 14
Experimental procedure ...................................................................................................................... 16
Assumptions/Remarks ........................................................................................................................ 17
Computational Fluid Dynamics .............................................................................................................. 17
Modelling of Geometry ....................................................................................................................... 17
Mesh Generation ................................................................................................................................. 19
Physical Problem Setup ...................................................................................................................... 20
Simulation Settings ............................................................................................................................. 22
Results & Discussion .................................................................................................................................. 23
Experiment .............................................................................................................................................. 23
Computational fluid dynamics ................................................................................................................ 30
Validation of Periodic model .................................................................................................................. 37
Conclusion .................................................................................................................................................. 38
Future studies .............................................................................................................................................. 39
Bibliography ............................................................................................................................................... 40
Appendix – Calibration ............................................................................................................................... 44
Appendix - Calibration Raw Data ............................................................................................................... 51
Appendix – Data from experiment .............................................................................................................. 59
Appendix – CFD ......................................................................................................................................... 62
Nomenclature 𝑎 − 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 [𝑚/𝑠2]
𝐴 − 𝐴𝑟𝑒𝑎 [𝑚2]
𝐶 − 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑟𝑎𝑡𝑖𝑜 [−]
𝐶𝑛 − ℎ𝑒𝑎𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑚𝑒𝑑𝑖𝑢𝑚 𝑛 [𝐽/𝑘𝑔𝑠]
𝐶𝑝 − 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 ℎ𝑒𝑎𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 [𝐽/𝐾𝑘𝑔]
𝑑 − 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 [𝑚]
𝐷ℎ − 𝐻𝑦𝑑𝑟𝑎𝑢𝑙𝑖𝑐 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 [𝑚]
Ɛ − 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑛𝑒𝑠𝑠 [−]
𝐹 − 𝐹𝑜𝑟𝑐𝑒 [𝑘𝑔𝑚/𝑠2]
ℎ − 𝐶𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑣𝑒 ℎ𝑒𝑎𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 [𝑊/𝐾𝑚2]
𝑘 − 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 [𝑊/𝐾𝑚]
𝐿 − 𝐿𝑒𝑛𝑔𝑡ℎ [𝑚]
𝐿𝑀𝑇𝐷 − 𝐿𝑜𝑔𝑎𝑟𝑖𝑡𝑚𝑖𝑐 𝑚𝑒𝑎𝑛 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 [𝐾]
𝑚 − 𝑚𝑎𝑠𝑠 [𝑘𝑔]
𝑚 − 𝑚𝑎𝑠𝑠𝑓𝑙𝑜𝑤 [𝑘𝑔/𝑠]
𝑁𝑇𝑈 − 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑢𝑛𝑖𝑡𝑠 [−]
𝜌 − 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 [𝑘𝑔/𝑚3]
𝑝 − 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 [𝑃𝑎]
𝑃𝑟 − 𝑃𝑟𝑎𝑛𝑑𝑡𝑙 𝑛𝑢𝑚𝑏𝑒𝑟[−]
𝑄 − 𝐻𝑒𝑎𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑟𝑎𝑡𝑒 [𝑊]
𝑟 − 𝑅𝑎𝑑𝑖𝑢𝑠 [𝑚]
𝑅 − 𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 [𝐾/𝑊]
𝑅𝑒 − 𝑅𝑒𝑦𝑛𝑜𝑙𝑑𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 [−]
𝑇 − 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 [K]
𝜇 − 𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 [𝑘𝑔/𝑚𝑠]
𝑢 − 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 [𝑚/𝑠]
𝑈𝐴 − 𝑂𝑣𝑒𝑟𝑎𝑙𝑙 ℎ𝑒𝑎𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 [𝑊/𝐾]
𝑣 − 𝑘𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 [𝑚2/𝑠]
1
Introduction The energy consumption of all the buildings in the world is 30 to 40 percent of the global energy
demand [1]. Therefore, any energy-efficient improvements done within this field might have a
significant impact on the environment. In Sweden, the residential and service sector represents
40 percent of the total energy use; where the household energy accounts for 59 percent [2].
Despite the overall reduction of energy demand in a passive or ultra-low energy building;
historically the reduction in energy consumption for water heating has been overlooked. From a
compilation of statistics presented in a previous study, it is evident that the fraction of energy
used for hot tap water in a building will rise as buildings become more efficient [3]. With the
new energy policies in Sweden, regarding the requirement of lower energy consumption, more
focus might turn into reducing the energy needed for hot tap water. In order to reduce energy
consumed in hot tap water, the focus is often towards the change in user behavior or usage of
more efficient water consuming devices [4] [5]. By the introduction of a heat exchanger on the
wastewater, a previous experiment has shown an approximate energy recovery of 30 % [6].
However, by neglecting the low valued toilet water, products show an energy saving potential of
50 % [7] [8] [9].
Literature Review Heat exchangers are widely used and exist in a vast number of types, which often depends on the
area of usage. However, the purpose of a heat exchanger remains the same; to increase the
temperature of one fluid and reduce the temperature of another.
Heat transfer theory
Heat transfer can be defined as the thermal energy exchange between two objects, where heat is
transferred from an object at a higher temperature towards an object with lower temperature by
the Second Law of Thermodynamics. Hence, the temperature difference is the driving force in a
heat exchanger. The exchange of heat between two objects can occur in three transportation
principles; conductive, convective and radiative heat transfer [10].
Conductive heat transfer
The conductive heat transfer is an exchange of thermal energy which takes place in solid
materials or stationary liquids or gases. The transportation of energy occurs due to interaction,
through collision or movement of electrons, between particles with different levels of energy
[11].
Convective heat transfer
Convective heat transfer applies to liquids and gases in motion, where the mechanism of the
energy transportation is due to diffusion, the random movement of individual particles, and the
movement of the fluid itself [11].
Radiative heat transfer
All objects, with a higher temperature than the absolute zero, transfer heat by electromagnetic
waves. These electromagnetic waves are created due to the movement of the particles or the
atoms within an object. An essential feature of radiative heat transfer, differing from conductive
2
and convective heat transfer, is: that heat is transferred between two elements separated by a cold
medium [11].
Fluid flow
To be able to predict, understand and evaluate fluid flow, the flow must be dissected into several
aspects, where some of the aspects aim to describe the movement of fluid, and the rest try to
describe the physical properties of the fluid. Further, these aspects can be applied to the three
conservation laws for the region of interest. The conservation laws are the conservation of
energy, momentum, and mass. The following section presents the aspects regarded in this study.
Viscosity of fluids
Viscosity is a measure on how fluid is deformed due to the stresses acting within a fluid. Further,
viscosity can be described as the amount of resistance against the fluid moving through a path. A
fluid can be categorized as a Newtonian and non-Newtonian fluid depending on the physical
behavior of viscosity. In a Newtonian fluid, the deformation is proportional to the amount of
stresses, while for a non-Newtonian fluid the behavior is not proportional and can vary.
According to a previous study, a Newtonian fluid has a higher heat transfer coefficient than the
investigated non-Newtonian fluid under certain conditions. The study concludes that a higher
viscosity creates larger boundary layers and this, in turn, corresponds to an increase of thermal
resistance of the fluid [12].
Steady vs. unsteady flow
A steady flow is a flow were the fluid properties remains constant over time. In contrary to the
steady flow, the unsteady flow properties vary over a time period. An element, at a point in time,
can have a specific path or temperature, which can change direction or magnitude for the next
point in time.
Uniform vs. non-uniform flow
Like steady flow, the properties for a fluid remain constant, but with regards to the relationship
of the elements in the flow. Hence, the properties for the different elements in the flow is equal,
and variation of properties can only occur by time. Whereas in a non-uniform flow, the
properties between the elements will vary [13].
Flow profile within a fluid’s flow
The movement within a fluid’s flow can be categorized either as laminar, transitional or
turbulent flow. Laminar flow indicates that there is no recirculation, mixing or random behavior
within the flow, while the opposite applies for a flow categorized as turbulent. Transitional flow
is a combination of laminar and turbulent flow, with turbulent flow in a part of the flow and the
rest is laminar. The categorization of a fluid’s flow is set by the dimensionless Reynolds number,
which is dependent on the geometry and the kinetic energy of the flow, as well as the physical
properties of the fluid.
𝑅𝑒 = 𝐷ℎ𝑢
𝑣
Where: 𝐷ℎ is the hydraulic diameter, 𝑢 is the average velocity and 𝑣 is the kinematic viscosity of
the fluid.
3
A Reynolds number below 2300 is defined as laminar flow, while a number above 4000 is
defined as turbulent flow. In the range of 2300 to 4000, transitional flow occurs. In a turbulent
flow, the heat transfer is higher compared to a laminar flow. The higher heat transfer is due to the
randomness of the flow, where the randomness enhances the transport of energy within the
medium [14].
Compressible vs. incompressible flow
All flows are compressible to some extent, which means that the elements within the flow
change density along the direction of travel, due to interference or contact with other elements in
the flow. When the Mach number of flow is less than 0,3, the flow is incompressible, and the
density is assumed to be constant.
Inviscid vs. viscous flow
The difference between an inviscid flow and a viscous flow is that the inviscid flow neglects the
viscous forces, which occur due to the viscosity of the fluid. Hence an inviscid flow assumes
zero viscosity in the fluid. However, the selection of an inviscid flow is often made by
investigating the Reynolds number, since Reynolds number is defined as the ratio between
inertial and viscous forces. A high Reynolds number indicates a lower influence of the viscous
forces. In contrast to the inviscid flow, the boundary layer of the viscous flow is non- uniform
due to the inclusion of viscous forces.
Flow structure
When a fluid is exposed to a change in geometry or boundary conditions, the flow is not
considered to be fully developed until a constant velocity profile is regained. This region with a
spatial variance within the flow also results in a discrepancy of the temperature profile, which
has higher heat and energy transfer characteristics, compared to the fully developed flow [14].
Fully develop laminar flow may be assumed to be obtained after the distance x from [15]:
𝑥 ≈ 0,05𝑅𝑒𝐷ℎ
For turbulent flow, the following thumb rule can be applied for when the fully developed flow is
occurring [16]:
𝑥 ≈ 10𝐷ℎ
Nusselt number
The Nusselt number is a dimensionless parameter that characterizes convective heat transfer. It is
the ratio of convection to conduction in heat transfer. The theoretical equation states that the heat
transfer coefficient is a function of pipe diameter, viscosity, velocity, specific heat, thermal
conductivity, and density, arranged in dimensionless groups [17]. Nusselt can be defined as:
ℎ𝐷ℎ 𝑁𝑢 =
𝑘
where h is the convective heat transfer coefficient.
4
𝑖 𝑖
Further, the Nusselt number is a function of the Reynolds number and Prandtl number. It is also
a function of the length of the tube when the fluid is still in the entrance region. However, when
the fluid is fully developed, the Nusselt number is constant in the laminar regime. If the value of
the Nusselt number is one, then the heat transfer is purely conduction. If the turbulence increases,
this will translate to an increase in the heat transfer due to convection, and hence an increase in
Nusselt number. In the turbulent regime, the Nusselt number is usually 100 to 1000 [18].
Heat exchanger
The primary design criterion of a heat exchanger is to have two media separated by solid
material, for the exchange of heat between the two media. These fluids can either be liquid, such
as water, or gases, such as air. Heat exchangers which transfer heat between either gas and gas,
gas and liquid or liquid and liquid, use the same order of transportation principle. When
navigating from the hot fluid towards the cold fluid; the heat is transferred by convection from
the hot fluid to the solid wall’s inner boundary. Further the heat is transferred by conduction
between the solid wall’s inner and outer boundaries, and finally, the heat is transferred to the
cold fluid by convection.
Thermal Resistance
Like electric resistance, heat transfer in a heat exchanger considers thermal resistance. A small
thermal resistance is preferred for an efficient heat transfer. For a shell and tube heat exchanger
the following equation can be used to break down the resistance into different segments:
1 1 ln(𝑟𝑜/𝑟𝑖) 1 𝑅𝑡𝑜𝑡 =
𝑈𝐴 = ℎ A
+ + 2𝜋𝐿𝑘 ℎ𝑜 A𝑜
+ 𝑅
Where 1
ℎ𝑖∗A𝑖
and 1
ℎ𝑜∗A𝑜
is the convection resistance of the different mediums. The term ln(𝑑𝑜−𝑑𝑖) 2∗ 𝜋∗𝐿∗𝑘
is the conduction resistance of the solid separating the mediums. The R is the sum of additional
resistance due to fouling or rough surfaces between two solids [11].
Ɛ -NTU method
The relation between how much is put into and gain from a system can be measured by
effectiveness, which indicates the performance of the system. The most commonly used methods
are Ɛ -NTU, which gives the number of transfer units, and LMTD, which means the log mean
temperature difference. In a scenario where the temperatures are not accessible, the Ɛ -NTU
method must be used over the LMTD method. The foundation in the Ɛ -NTU method is the
effectiveness expression [19]:
𝑄 𝑎𝑐𝑡𝑢𝑎𝑙 𝐶𝑛|𝑇𝑛,𝑖𝑛 − 𝑇𝑛,𝑜𝑢𝑡| 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑛𝑒𝑠𝑠 = Ɛ =
𝑄 𝑜𝑝𝑡𝑖𝑚𝑎𝑙
= 𝐶𝑚𝑖𝑛 (𝑇ℎ𝑜𝑡,𝑖𝑛 − 𝑇𝑐𝑜𝑙𝑑,𝑖𝑛)
Where 𝑄 𝑎𝑐𝑡𝑢𝑎𝑙, is the actual heat transfer rate between the media and 𝑄 𝑜𝑝𝑡𝑖𝑚𝑎𝑙 is the maximum
heat transfer rate based on physical limitations of the fluid media. These physical limitations are
the driving force of the temperature difference, the maximum temperature difference, and the
5
media’s possibility to store energy. The medium with the smallest storage capability is denoted
as; 𝐶𝑚𝑖𝑛 and the one with the largest storage capability is 𝐶𝑚𝑎𝑥. The definition of heat capacity
rate for a fluid can be stated as:
𝐶𝑛 = 𝑚 𝑛𝐶𝑝,𝑛
Where, 𝑚 𝑛, is the mass flow of the medium n and 𝐶𝑝,𝑛 is the specific heat capacity. Other
concepts needed for the Ɛ -NTU method are the definitions of NTU and C, capacity ratio, which
are defined as:
𝑁𝑇𝑈 =
𝑈𝐴
𝐶𝑚𝑖𝑛
𝐶 =
𝐶𝑚𝑖𝑛
𝐶𝑚𝑎𝑥
Where, NTU, is a dimensionless number of transfer units. The 𝑈𝐴, overall heat transfer
coefficient, can be explained as a function of R, overall thermal resistance [20]:
1
Where R can be expressed as:
𝑅 =
𝑈𝐴
moreover, LMTD as:
𝑅 =
𝐿𝑀𝑇𝐷
𝐶𝑛 ∗ |𝑇𝑛,𝑖𝑛 − 𝑇𝑛,𝑜𝑢𝑡|
𝐿𝑀𝑇𝐷 = (𝑇ℎ𝑜𝑡,𝑖𝑛 − 𝑇𝑐𝑜𝑙𝑑,𝑜𝑢𝑡) − (𝑇ℎ𝑜𝑡,𝑜𝑢𝑡 − 𝑇𝑐𝑜𝑙𝑑,𝑖𝑛)
𝑙𝑛(𝑇ℎ𝑜𝑡,𝑖𝑛 − 𝑇𝑐𝑜𝑙𝑑,𝑜𝑢𝑡) − 𝑙𝑛(𝑇ℎ𝑜𝑡,𝑜𝑢𝑡 − 𝑇𝑐𝑜𝑙𝑑,𝑖𝑛)
Design Parameters
There are many techniques in order to enhance the effectiveness of a heat exchanger. Increased
performance of a heat exchanger can be implemented either in a passive or active approach with
the focus on either increasing; the heat transfer coefficient, U, or the surface area between the
two mediums and last the opposing temperature difference [21].
Passive design
The passive design of a heat exchanger is the structure as well as the physical properties of the
material and fluids. Previous studies have described the different effect of passive techniques on
a tube, such as introducing a rough surface instead of a smooth and the variation of the pitch
angle of a helically coiled tube.
It was concluded in the investigation of the rough and smooth surface, for specific preset
condition; the heat transfer coefficient did increase when switching from a smooth pipe to a
rough. However, a rougher surface has a more substantial friction factor between the surface and
6
fluid. The higher friction factor has a negative impact on the pumping power, due to the
increased pressure drop [22].
The numerical evaluation of a helically coiled tube brings forward that with a lower pitch angle
of the helical, the heat exchanger effectiveness increases. It states that the increased coil surface
area also increases the heat exchanger effectiveness [23]. The same study also investigated the
impact on the effectiveness of changing volume to surface ratio of the medium. The results were
that a larger volume to surface ratio reduces the effectiveness of the heat exchanger.
Another key aspect regarding passive design is the configuration of the inlets, were as a counter
flow heat exchanger has theoretical higher heat exchanger effectiveness compare to parallel
flow. In an infinitely long counter flow heat exchanger that is perfectly insulated against the
surrounding theoretically the exergy of the system will switch between the fluids. Hence the
outlet temperature of the cold fluid will correspond to the inlet temperature of the hot fluid.
Another configuration, which is more common in a gas-to-fluid heat exchanger, is the crossflow
configuration with theoretical effectiveness between counterflow and parallel configuration.
These inlet and outlet configurations can be combined in various hybrids, such as a multi-pass
flow heat exchanger [24].
Copper is the most used material for the construction of tube in previous studies. The reason is
copper´s thermal properties, with high heat transfer capabilities, as well as priceworthy. A
previous study has investigated aluminum as a potential substitute from the copper material, due
to the lower material cost and simplified manufacturing process. In the same study, fouling´s
influence on heat transfer and thermal resistance was investigated. Fouling is a summary of new
surface properties, such as surface corrosion or additional surface material, which segregates
overtime from water [25]. A change in surface structure will affect the flow pattern, interrupting
previous flow path.
Active design
An active design requires external power in order to enhance the heat transfer, hence requires
maintenance and becoming a lesser viable option than the passive design. These active design
methods can be to for example introduce the heat exchanger to vibration, rotating motion or
electromagnetic field [26]. Previously studies have investigated an active system, with a heat
pump and thereby increasing the driving force in the heat exchanger with heat pump solution
[27]. This solution can transport the energy directly to an appropriate temperature but is still
constrained by the heat exchanger on the wastewater side.
Wastewater Heat exchanger
Wastewater from a building can be divided into two main categories, blackwater, and greywater.
Blackwater is defined as wastewater from toilets, and greywater consists of water from showers,
laundry machine, and faucets. Depending on which type of wastewater and as well as placement
in the water system, the layout of heat exchanger variates. The heat exchanger can either be
placed locally, in the sewage or at the treatment plant. With a heat exchanger, not placed locally,
the transport distance becomes longer. More heat can be lost to the surroundings due to the
impact of long distances. However, the benefits of a centralized system is a more abundant and
7
stable heat source due to a continuous flow. These heat exchangers are horizontal configured,
which increase the number of residuals getting trapped on performance enhancement surfaces. In
order to maintain efficient heat transfer, additional cleaning is required corresponding to a
shutdown of a sewage system [27]. A similar solution can be found locally, where space is
limited. A study investigating a horizontal heat recovery solution, using a pipe in pipe design,
concluded efficiency of 50 %. However, sediment stacking up remains a problem and requires
attention [28] [29]. Previous studies have investigated vertically configured heat exchanger.
These heat exchangers have used a gravity falling film of the greywater flow within a tube, while
the freshwater is transported in a helical coil attached to the outside of the tube [29] [30]. Similar
or higher effectiveness has been obtained in these studies compared to the horizontal configured.
The helical coil requires a large amount of material, increasing the investment cost as well as
increasing the ecological footprint of the product. Due to the manufacturing process, tightness
between the helical coil and the tube is problematic to achieve, creating small air gaps. These air
gaps increase the thermal resistance between the coil and the tube surface, reducing the heat
transfer [29].
Potential of greywater in Sweden
From a summary of other studies, the temperature of greywater in Sweden is in the range 18 to
38 C. Further, most of the data showed an average temperature of 30 °C [31]. Regarding the
freshwater temperature, the yearly average temperature has been recorded for the two largest
sanitary plants to be 6,9 respectively 8,7 °C, for the region of Stockholm [32] [33]. Stockholm’s
freshwater is supplied by surface water extraction as most of Sweden [34]. In the summary of
several case studies, the average Swede consumes approximate 100 liters of greywater per day
[31]. Corresponding to an untapped source of energy of approximate 3 MWh per person a year,
neglecting the fraction of heat recovery performed centralized.
Description of the heat exchanger
This study investigates the copper heat exchanger QB1-21, where Figure 1 & 2 shows the
geometries of the heat exchanger. The heat exchanger is a shell and tube heat exchanger, where
double walls separate the two water streams. These double walls divide the two streams and are a
safety precaution in order to avoid mixing of the two fluids. Figure 1 presents the passive
enhancement device, a cyclone generator. This generator was attached to a part of the experiment
and created a swirling falling flow in the heat exchanger. Figure 2 shows some other passive
enhancements implemented into the main design of the heat exchanger. The greywater stream, in
the inner tube, is subject to annular grooves. Theses grooves purpose is to create disturbances to
the fluid and create additional mixing of the flow. Hence increase the heat transfer. In the
construction of these annular grooves, an annular air gap is created, in the space between the
double walls. In the same space, there exist three vertical air gaps along the entire heat
exchanger, due to the manufacturing process. These air gaps will increase thermal resistance. In
the freshwater stream, the outer fluid, there are two copper strings. One copper string is helically
attached in the freshwater stream and held in place by a vertical copper string. The primary
purpose of the helical string’s is the same as for the annular grooves, to create disturbances.
8
Figure 1. The geometrical configuration of the heat exchanger, installation guide [35].
Figure 2. Cross-section of the heat exchanger.
The heat exchanger has been certified by Netherlands Kiwa, which is a company performing
testing and certification. Kiwa measured the pressure drop in the freshwater stream of the QB1-
21. Figure 3 presents the certified pressure drop.
Figure 3. Measured pressure drop in the freshwater stream by Kiwa [35].
9
Measurement
When doing measurements with an instrument, there is always an error occurring between the
measurement and the actual value. This error can be categorized into, random error, and
systematic error. Random errors can occur due to fluctuation in the surrounding environment or
within the system. Systematic error is a continuous error which is due to a biased measurement
instrument [36].
Statistical method
The uncertainty in an experiment can be evaluated by statistical methods, in order to approve or
reject a hypothesis or an experiment. When testing an experiment, a level of confidence and
distribution of the outcome must be chosen. A t-distribution shall be applied, for an experiment
with up to 30 measurements. Above 30 measurements a normal distribution can be applied.
However, a test can be applied to validate the distribution. The decision of confidence interval or
significance level is for a normal distribution, dependent on a standard deviation. One standard
deviation has a confidence interval of 68 % of all data, two standard deviations contain 95 %,
and three standard deviations contains 99,7 %. The standard deviation of the mean, standard
uncertainty of repeated measurement, is defined as:
√ 1 ∑𝑛
(𝑥 2 − 𝑥 )
𝑢(𝑥)𝐴 = 𝑛 − 1 𝑗=1 𝑗
√𝑛
Where 𝑛 is the number of measurements, 𝑥𝑗 is the value of measurement j and 𝑥 is the average
value of all measurement. Further uncertainty to consider in an experiment, is the assumed
systematic errors, 𝑢(𝑥)𝐵, from for example a measuring device. Typical calibration data. These
assumed systematic error, must be considered with an assumed distribution. Such as a
rectangular, triangular or u-shape distribution, depending on the function of the measuring
device. These uncertainties can be combined using the RSS, Root-Sum-Square, method. Where
the combined standard uncertainty is:
𝑢(𝑥) 𝑁
2 = ∑ ( 𝜕𝑓 2 )
𝑢(𝑥)
𝑁 2
+ ∑ ( 𝜕𝑓 2 ) 𝑢(𝑥) 2
𝐶
𝑖=1
𝜕𝑥𝑖 𝐴
𝑖=1
𝜕𝑥𝑖 𝐵
Where 𝜕𝑓 is the sensitivity coefficient, which is the derivation of the function to be considered 𝜕𝑥𝑖
by the measured parameter.
Calibration
The purpose of conducting a calibration process is to trim the systematic errors of a measuring
device, hence increasing the trueness of measurement by reducing the difference between the
measurement and the reference standard. Hence reducing the uncertainty of the experiment [37].
In the construction of the calibration process, criteria shall be taken forward individually for each
experiment. These criteria are due to the vast number of parameters that affect the process, such
as, time, cost and test environment. However, there are a few guidelines for the construction of a
suitable calibration process such as having a degree of freedom greater than three. Where the
10
degree of freedom is the number of independent parameters, in calibration, correspond to each
measurement at a point. Further, at least five equally spaced measuring points should be
considered. The measuring points in the operating range should have two measurements on each
point. However, if the measuring device is only supposed to operate in a small interval, two
measuring points are required [37].
When constructing a calibration curve over a regime, it is necessary to validate the model of the
calibration curve. The F-statistic is an approach to validate if an additional term is required in the
equation of the calibration curve, in order to more accurately describe the data. An F-stat value
of lower that one suggests, that the calibration curve requires no additional term. The formula for
the F-stat value can be calculated using the following equation [38]:
(𝑆𝑆𝐸1 − 𝑆𝑆𝐸2)((𝑑𝑓2 − 𝑑𝑓1)
where:
𝐹 − 𝑠𝑡𝑎𝑡 =
MSE2
• 𝑆𝑆𝐸1is the sum of squares for the residuals of a linear model or the lower-level of a
polynomial model.
• 𝑆𝑆𝐸2 is the sum of squares for the residuals of the higher-level polynomial model.
• 𝑑𝑓1 is the degree of freedom of the residuals of a linear model or the lower-level of a
polynomial model.
• 𝑑𝑓2is the degree of freedom of the residuals of the higher-level polynomial model.
• MSE2 is the mean square of the residuals of the higher-level polynomial model.
Computational Fluid Dynamics
Numerical technique in fluid dynamics
There are two methods of solving a problem in fluid dynamics, the Analytical method and the
Numerical method. Analytical methods result in exact solutions since the problem at hand is
analyzed at every point in the medium. However, analytical methods are restricted to the solution
of governing equations that are differential. Real-life problems involve convoluted geometries,
accompanied by complicated boundary conditions and variable properties. Such problems
consume an immense amount of time and resources when solved analytically. These problems
lead to engineers making crude approximations of the model.
Numerical techniques involve results, generated in a computer environment that is sufficiently
accurate with appropriate model approximations. This technique usually defined as CFD,
Computational Fluid Dynamics. Partial differential equations govern fluid flow. With the advent
of computers with high processing speeds and powerful software packages that are incredibly
convenient, the partial differential equations can be solved with relative ease. Fluid flow can be
modeled close to reality, just by comprehending the physical nature of the problem, and the
variation of its results. "Approximate" solutions of a "realistic" model are often more accurate
than "exact" solutions of a "crude" model [39].
CFD role in fluid dynamics
Fluid flow can be defined physically by three elementary principles:
11
1) Mass is conserved
2) Newton's second law, 𝐹 = 𝑚𝑎 3) Energy is conserved.
These principles are represented in partial differential equations. CFD is a technique of replacing
these partial differential equations by numbers, and further advancing these numbers in time and
space, to obtain a numerical prediction of the fluid flow [40].
CFD serves as the third element in fluid dynamics, as it can either support or complement either
pure theory or pure experiment. CFD can be used to compute the governing equations in their
exact form, with the inclusion of various other physical phenomena. It is impossible to solve the
governing partial differential equations through theoretical analyses.
Today, CFD plays a vital role in engineering design. Recently, CFD has excelled in the subject
of wind tunnel testing, as the computational costs have decreased, and while the wind tunnel
costs have increased. It is economical to calculate the aerodynamic characteristics of aero-plane
designs in CFD, rather than in a wind tunnel. Moreover, CFD can be used to obtain detailed
information on the flow fields, which is very difficult to measure in a wind tunnel. CFD can be
used to handle a significant share of the design process, and wind tunnels can be used to fine-
tune the design.
CFD has become a staple in preliminary and primary levels of research. It is particularly useful
in either replicating or replacing laboratory experiments. Despite its advantages, CFD falls short
in reproducing physics that are not included in the problem formulation. One such problem is
turbulence. Most of the turbulent flow solutions available today are just approximations of the
real-life explanations since a bulk of the models still use empirical values of constants. These
approximations lead to inaccurate and unreliable solutions. Moreover, CFD cannot accurately
compute chemically reacting flows, since the mechanisms of kinetic rate and the magnitudes of
the rate constants are very uncertain [40]. Experiments can significantly assist in validating a
CFD model and hence gauging the level of accuracy.
Fluid modeling techniques – Finite control volume
When a solid object is moving, the velocity of every single part is the same, and hence it is
simple to define. However, when a fluid is moving, the velocity might be different in different
parts of the flow-field. These differences in velocities, lead to significant changes in the
modeling technique. Assuming that the fluid is a continuum medium, we can approach the
modeling process using several techniques.
One such technique is the finite control volume approach. A control volume, V, bound by a
control surface, S, is either stationary or in motion within the flow field. In both cases, the
control volume is finite, and the focus is directed to the fluid inside the finite space. With this
concept, fundamental physics can be applied to the fluid within the control volume and at the
control surface. The integral or partial differential equations obtained by considering the finite
control volume to be stationary within the fluid, where the fluid particles flow into and out of the
control volume are called the Conservation form of Governing Equations. Illustrated in Figure 4.
On the other hand, the Non-conservation form of Governing Equations is obtained by
12
considering the control volume to flow with the fluid, where the fluid particles in the control
volume are fixed. Depicted in Figure 5. The distinction between conservative and non-
conservative forms can make little difference in theoretical fluid dynamics. However, they are
vital in CFD as the application of the right form makes a difference in some cases [40].
Figure 4. Finite control volume approach, the control volume is stationary within the fluid field [40].
Figure 5. Finite control volume approach, the control volume is in motion within the fluid field [40].
Governing Equations
The fundamental governing equations of fluid dynamics are the continuity, momentum and
energy equations.
For steady state-incompressible flows in non-conservation form, the governing equations are as
follows:
• The Continuity Equation
The conservation of mass is the physical principle used in the Continuity Equation.
∇. �� = 0
Where �� is the velocity vector
• The Momentum Equation (The Navier-Stokes Equation)
Newton's second law is the physical principle used in the Momentum Equation. The governing
momentum equations are known as the Navier-Stokes Equations.
𝜌[(�� . ∇)�� ] = −∇𝑝 + 𝜇∇2�� + 𝜌𝑓
Where 𝜌 is the density, 𝑝 is the pressure, 𝜇 is the constant dynamic viscosity, 𝑓 is the body force
per unit mass. The body force is the external force applied to the body, such as the gravitational
force.
• The Energy Equation
13
The conservation of energy is the physical principle used in the Energy Equation.
𝜌𝐶𝑝[(�� . ∇)𝑇] = 𝑘∇2𝑇 + 𝜙
Where 𝜙 is the dissipation function representing the work done against viscous forces. This work
is irreversibly converted into internal energy.
Accuracy of CFD
It is essential to ensure that CFD models are accurate and cost-effective. CFD are prone to large
values of error, as the results are entirely dependent on the physical models used to represent the
governing equations and boundary conditions. Each algorithm used will have its related
truncation error; this coupled with round-off errors, can severely compromise the accuracy of
CFD models [40]
Periodic Heat Transfer
Despite the advent of fast and efficient computing resources, modeling fully developed flow and
heat transfer in large heat exchangers can still prove to be very demanding; in terms of
computational time and cost. However, if the heat exchanger's geometry is periodically repeating
in the flow direction, the flow and heat transfer characteristics in the periodically repeating
sections can be generalized over the entire geometry. Modeling the flow and heat transfer in just
the periodically repeating section requires a fraction of the time when compared to the entire
model. If the velocity components or the pressure drop is found to be periodic across the model,
the entrance and exit regions can be avoided [41].
There are two types of periodic heat transfers, namely, periodic heat transfer without a pressure
drop across the planes, and periodic heat transfer with a pressure drop across periodic boundary
conditions that are translational. The latter can enable the modeling the fully developed flows.
This model is known as "streamwise periodic heat transfer". The streamwise flow conditions can
be considered when the flow pattern recurs over a certain length, with constant pressure drop in
each section. The periodic flow conditions can be predicted after a certain entrance length of the
flow. The entrance length is dependent on the flow profile and the geometric configuration.
The delimitations of the streamwise periodic heat transfer are,
1) The flow must be incompressible
2) Net mass additions through the inlets and exits are not allowed
3) Reacting flows cannot be modeled
4) The particles should have complete trajectories, to model the steady particle tracks
5) Only the pressure-based solver can be used
6) The thermal boundary conditions must either be of a constant wall temperature type or a
specified heat flux type. A zero-heat-flux model can be used with constant temperature
walls, but temperature profiles cannot be used.
7) The fluid's thermodynamic and transport properties do not vary as a function of
temperature. However, the transport properties change spatially with the turbulence field,
and the periodic flows can have effective transport properties varying with the turbulence
field.
14
Methodology
Experiment
The experimental part of the study was divided into two parts. Part 1 with a uniform flow on
both greywater and freshwater, while for Part 2 the flow on the greywater is modified to enter as
a falling swirling flow.
Experimental Setup
The test rig was constructed with the purpose of maintaining two separate inlet temperature
levels of both streams and be able to supply a similar inlet temperature into the heat exchanger
for the different flow rates. Other chosen criteria were to monitor the inlet and outlet
temperatures of the heat exchanger, measure the surface temperature on the outer freshwater
tube, as well as to be able to vary and measure the flow entering the heat exchanger.
Furthermore, the test rig was designed to be able to switch the flow direction easily.
Description of the test rigs
The test rig can be viewed as two systems, a warm system, and a cold system, separated by the
heat exchanger. Figure 6 & 7 illustrates the layout of the test rig with the different principal
components.
Figure 6. Layout sketch of test rigs setup for Part 1.
15
Figure 7. Layout sketch of test rigs setup for Part 2.
Main components
Figure 6 & 7 shows that the test rig consists of two water tanks. These uninsulated tanks,
“Strömsnäspannan TS 750”, had a capacity of 750 liters each. These tanks acted as heat and cold
storage of the test rig. Further, to remove excess heat on the freshwater side, a dry cooler “Alfa
Laval DGL.501.1AS4V” with room temperature as the heat sink, was used. The dry cooler was
controlled by setting a desired outlet temperature of the medium leaving the dry cooler. For the
greywater side of the test rig, in order to keep an energy balance within the system, heat must be
generated. An electric heater, “Backer IU 3R”, was attached to the greywater tank with a
capacity of 12 kW. This heater controlled the temperature of the greywater tank with a
thermostat. The flow rate through the heat exchanger was controlled by setting the pump speed
and manually control the rotary wheel valve. The used pump on the greywater side was a “WILO
Stratos 25/1-8”, with variable speed. On the freshwater side, a “WILO TOP-S30/10 KTL” pump
was used for the circulation into the heat exchanger, while a “GRUNDFOS MAGNA 25-80 180”
circulate water through the dry cooler.
The test rig’s piping was mainly constructed using 22 mm copper tubes. However, some flexible
hoses and 50 mm PVC pipes were also used to create flexibility of the test rig. The equipment on
the greywater side was insulated using different sizes of “Armaflex” insulation, to reduce heat
loss to the surrounding environment.
Measurement devices
The test rig involved 18 T-thermocouples, both for measurement and monitoring purposes. Two
of these T-thermocouples, which was measuring the inlet and outlet temperature of the
16
greywater, were of an unknown model. Due to a problem with the fit of the rig; the type T-
thermocouples, of an unknown model, were used. This model was of a smaller size and
unshielded. However, the other T-thermocouples were “OMEGA TT-T-24-TWSH-SLE", which
is a twisted and shielded thermocouple model.
The T-thermocouples were connected to a 4- Wire RTD logger with an insulated pt100 reference
temperature. Further, the data was stored and retrieved through the software Agilent-Benchlink
Data Logger 3.
Two heat meters attached to the rig, were of the type Brunata HGQ3-R0, with a high-resolution
screen. Only the magnetic inductive flow sensor of the heat meter was used, which had been
modified to send a pulse every 0,1 liter instead of the previous value of one liter. The high-
resolution screens were recorded using a laptop camera, and the software VLC were used to
retrieve data.
Experimental procedure
The first step conducted in the procedure after the construction of the test rig was the calibration
process of the measurement instrument. The 4 T-thermocouples, which measured the inlet and
outlet temperature of the heat exchanger, were calibrated using “Fluke 1551A Ex”, with an
accuracy of ± 0,05 °C, as the reference thermometer. An Isotech thermal bath container
controlled the surrounding temperature of the thermoelements. The T-thermocouple was
calibrated for the range of 25°C and 55°C for seven temperature levels. On every level, after
reaching steady state, 30 measurements were recorded. On the outer wall of the heat exchanger
and insulation, 10 T-thermocouples were mounted with a distance of 20 cm between one another,
using a ruler. These T-thermocouples were calibrated against the two T-thermocouples on the
freshwater side, measuring the outlet and inlet temperature, when only the freshwater was
running through the heat exchanger. The calibration was performed for three temperature levels
and with 30 measurements on each level.
The flowmeters were calibrated using the gravimetric weighing method, using a scale with an
accuracy of ± 0,01 kg. The flowmeters were mounted in series. Ten pipe diameters were the
distance between the two flowmeters as well as the distance between the first flowmeter and the
entrance. Three levels of flow rates were considered for Part 1, whereas for Part 2 an additional
two levels were considered. Each flow rate level was repeated and by recording the high-
resolution screen, 30 measured flow rates were recorded from each run at equally spaced time
window for each flowmeter. For example, every five or ten seconds, which was dependent on
the fill time of the 25-liter bucket.
After the data collection from the T-thermocouples and flowmeters, the data were analyzed using
the software Excel, and its Data Analysis tool: “Regression”. The deviations from the reference
temperature were plotted and used in the “Regression” tool in order to obtain values for the F-
statistic method. Further, a model for the calibration curve could be chosen by the F-statistic
method. The same procedure was conducted for the flowmeters.
In Part 1, the heat exchanger was supplied with greywater from the bottom, in order to create the
uniform flow, using the principal of a water lock. Since the freshwater is a closed system, the
17
freshwater was supplied from the top for the counterflow configuration. The considered flow
rates were approximately 1, 2, 3, 4, 5, and 6 l/min for C equal to 1, at an elevated temperature of
approximately 30 °C on the freshwater and 50 °C on the greywater. After reaching steady state,
the temperatures and flow rates were recorded for 10 minutes. The flow rates were recorded
every 10 seconds and T-thermocouple every second.
In Part 2, both the flow direction were changed to be able to use gravity to create the falling film
on the greywater stream. Further, the cyclone generator was attached and insulated to the rig,
creating a swirling flow on the greywater. The test region was increased, to 12 l/min, with the
same steps. Other parameters from Part 1 were carried on to this scenario.
Assumptions/Remarks
During the calibration, it is assumed that there is no fluctuation or change in the temperatures as
well as in the supply flow rate from the district water treatment plant. Hence there is no
fluctuation of the reference measuring device or method. The uncertainties in the gravimetric
method are assumed to have a time accuracy of ± 1 s. In the attachment of the T-thermocouples,
the ruler had an accuracy of ± 0,001 m. For correction of flow in order to achieve equal heat
storage capacity for the experiment, the temperature dependent properties such as density and
viscosity were considered constant for the freshwater temperature of 30 °C, and greywater
temperature 50 °C.
When the temperature of the inlet and outlet T-thermocouples were visually stable from the
graph in the software “Agilent”, it was assumed that steady-state conditions were obtained. The
results from the experiment were presented with an uncertainty of one standard deviation.
Computational Fluid Dynamics
Modeling of Geometry
The heat exchanger’s geometry was measured using a Vernier caliper with a least count of 0,05
mm. The data was used to model the heat exchanger on Solid Edge. The length of the entire heat
exchanger is 2100 mm. The length of the section between the freshwater inlet and outlet, that is
periodic, is 1836 mm. The length of one periodic element is 25,5 mm. The heat exchanger
consists of five parts, namely, the greywater part, the inner pipe, the air gap, the freshwater part,
and the outer pipe. Figure 8 & 9 depicts the solid parts of the heat exchanger. The inner pipe
consists of annular grooves to increase the turbulence and hence increase the heat transfer.
Further, in Figure 9, the annular grooves which extend 0,85 mm from the surface of the inner
pipe, can be seen. The inner and outer diameter of the inner pipe is 47,5 mm respectively 50 mm.
The annular groove geometry is not translated to the interior part of the outer pipe, and hence this
results in an air gap between the inner pipe and the outer pipe. The interior part of the outer pipe
has three longitudinal air gaps. These are inherited after the outer pipe is pressed against the
inner pipe during manufacturing. The inner and outer diameter of the interior part of the outer
pipe is 50 mm and 51 mm respectively. The inner and outer diameter of the exterior part of the
outer pipe is 54 and 56 mm, respectively.
18
Outer
pipe –
exterior
part
Outer
pipe –
Interior
part
Inner
pipe
Figure 8. Overview of the geometries for the three main solid parts used in the simulation.
Figure 9. Cross-section view of the geometries for the three main solid parts used in the simulation
The greywater and freshwater parts are modeled as fluids, where Figure 10 portrays the
geometry of the periodic freshwater. The outer pipe consists of a helical copper string with a
diameter of 0,6 mm. This string can be seen in Figure 11 and has an approximated pitch angle of
12,75 mm per leap. The heat transfer implications of the copper wire are ignored due to its
relatively small effect on heat transfer and its requirement of a highly resolved mesh. Instead, the
model uses a hollow helical tube of diameter 0,6 mm.
Outer
pipe –
Interior
part
Inner
pipe
Outer
pipe –
exterior
part
19
Figure 10. Overview of the freshwater geometry
used in the simulation
Figure 11. Side view of the helical string in the
freshwater.
Helical tubes with a circular cross-section are meshed using the NURBS, non-uniform rational
basis spline, model. This model consumes a vast resource of computational time and capacity.
An octagonal cross-section replaced the circular cross-section since a study shows that an
octagon is the closest approximation to a circle in two-dimensional flow behavior [42]. Figure 12
depicts the geometry of the helical string.
Figure 12. Cross-section view of the octagonal helical string in the freshwater.
Mesh Generation
Since a periodic modeling technique does not allow two or more streams of fluids in the same
simulation environment. Hence, the geometric model was divided into two modules, namely, the
“Greywater module” and the “Freshwater module”. The two modules were simulated separately.
The Greywater module includes the parts, Greywater, Inner pipe, and the Air gap. The
Freshwater module includes the Outer pipe – exterior, Outer pipe – interior, and the Freshwater.
20
The match control function was used to match the two end faces of a part that preserved its form
in the translational direction. The match control function would later assist in the application of
“conformal periodic boundary condition” in the “Problem Setup” stage. Match control was
applied to the following parts, Air gap, Outer pipe – interior, Outer pipe – exterior, and
Freshwater. An unstructured mesh was used for the other remaining parts, namely, Greywater
and Inner pipe. A “Proximity and Curvature” size function was used for better accuracy when
meshing the helical string and the annular groove.
Physical Problem Setup
A laminar model was used to analyze the viscosity in the flow.
Material selection
The solid and liquid parts of the heat exchanger were modeled using Copper and Water
respectively. The heat exchanger has an inherent air gap which inhibits heat transfer. Using three
streams of fluids, i.e., air stream in the air gap, the greywater stream, and the freshwater stream,
would consume a lot of computational time and resources. Hence, the air was modeled as a solid
with the following properties:
1. Specific heat – 1006,43 J/kgK
2. Thermal conductivity – 0,0242 W/mK
3. Density – 1,225 kg/m³
Cell Zone Conditions
The greywater module of the heat exchanger consisted of the following cell zones:
1. Air gap
2. Greywater
3. Inner pipe
The freshwater module of the heat exchanger consisted of the following cell zones:
1. Outer pipe – exterior part
2. Outer pipe – interior part
3. Freshwater
Since the model is simulated in two modules, the surface heat flux obtained in the results of the
Graywater module served as an input for the Freshwater module.
Boundary conditions
Periodic boundary conditions were applied to the model to minimize the computational time. The
two types of periodic boundary conditions used were, conformal and non-conformal. The
conformal periodic boundary conditions were used for the cell zones that preserved their form in
the translational direction, i.e., Air gap, Outer pipe – exterior, Outer pipe – interior, Freshwater.
The other cell zones were not symmetric in the translational direction due to the annular rings.
Hence, non-conformal periodic boundary conditions were used for the cell zones, Greywater,
and Inner pipe. Both the greywater and freshwater streams were set up as uniform flows, where
21
the elements at the inlets share the same properties and conditions. The inlets and outlets of the
greywater and freshwater were configured in accordance with Part 1 of the experiment.
Mesh Interfaces
A mapped and coupled interface wherever the mesh interfaces were between a solid and fluid,
namely, Greywater to Inner pipe, Freshwater to Outer pipe – exterior, Freshwater to outer pipe –
interior.
Solution Method
A pressure-based coupled algorithm is used to solve the model.
The pressure-based coupled algorithm involves a sequence of
steps to solve the model. Figure 13 shows a visualization of the
pressure-based coupled algorithm. The steps of the model are:
1. All the properties of the fluid are input into the solver.
2. The pressure-based coupled algorithm solves the
problem by coupling the momentum and continuity
equations.
3. The initial values of the pressure and the velocity field
are updated with the new values obtained after the
continuity equation.
4. Then the energy equation is solved using the new values
to obtain convergence.
Pseudo Transient under-relaxation is used to vary the under-
relaxation factors, using a pseudo time step size, for faster
convergence of the simulation [43].
Initialization of Solution
A hybrid initialization is used to set up the solution. The
Figure 13. Workflow of pressure-
based coupled algorithm [48].
initialization is followed by patching temperatures to improve the convergence. The patched
values are 51°C for greywater and 30 °C for freshwater.
22
Simulation Settings
In Table 1, a summary of the used simulation setting in Ansys, are depicted.
Table 1. Summary of simulation setting used in Ansys. Function Specification
Solver Pressure-based (solver type); Absolute (velocity formulation); Steady-state (time)
Models Laminar (viscous model); Energy enabled
Materials Water-liquid (density – 998,2 kg/m³, specific heat – 4182 J/kgK, thermal conductivity – 0,6 W/mK,
viscosity – 0,001003);
Copper (density – 8978 kg/m³, specific heat – 381 J/kgK, thermal conductivity – 387,6 W/mK); Air-solid (density – 1,225 kg/m³, specific heat – 1006,43 J/kgK, thermal conductivity – 0,0242 W/mK)
Periodic
conditions Mass flow specification (input type); Upstream bulk temperature = 51 °C for greywater & 30 °C for
freshwater; Relaxation factor = 0,5
Solution
method
Coupled (pressure-velocity coupling); Segregated (continuity-energy calculation); Second order
(pressure discretization); Second order upwind (momentum and energy discretization); Pseudo-transient
enabled; Relaxation factor = 0,25
Solution
controls
Pseudo transient explicit relaxation factors: Pressure = 0,5; Momentum = 0,5; Density = 1;
Body forces = 1; Energy = 0,75
Convergence
conditions
Absolute criteria of residuals: Continuity = 1e-03; X-Velocity = 1e-03; Y-Velocity = 1e-03;
Z-Velocity = 1e-03; Energy = 1e-06
23
Results & Discussion For the calibration results and discussion, see Appendix - Calibration.
Experiment
The constructed test rig can be seen in Figure 14, configured for part 2. This rig can easily be
configured for testing other vertical heat exchangers. One change that could be useful for future
tests is to introduce a motorized valve to automate the flow rate control. The motorized valves
would make it possible to run the test without supervision as well as reducing the time window
for a test range.
Figure 14. Setup of the test rig configured for Part 2.
24
Table 2 shows the average temperature and flow results from both parts of the experiments.
From the data, the difference in temperature between outlet and inlet increases, with a lower flow
rate. The phenomenon applies to both parts of the experiment. Further, the swirling flow on the
greywater side has a more substantial temperature difference compared to the same flow rate
from part 1. The larger temperature difference is occurring even though the maximum
temperature of the system is smaller, due to an incorrect setting of the heater, which occurred
after the adjustment of the rig to part 2. A similar error in adjustment, also occurred on the
freshwater side for higher flow rates, when the cooling capacity of the rig was not enough. The
dry cooler’s capacity was low due to the high surrounding room temperature above 25 °C. The
lower temperature on the greywater results in the reduction of turbulence, as the viscosity of
water, increases at lower temperatures. The temperature change will also have an impact on the
heat transfer, as heat transfer coefficient will slightly increase for the greywater side. It is vice
versa for the heat transfer coefficient of the freshwater side, with the increase in inlet
temperature.
Table 2. Measured mean temperatures and flow rates for both parts of the test.
Part Measure Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Run 11 Run 12
1
102 [°C] 38,27 40,56 42,04 43,75 43,85 44,17 - - - - - -
103 [°C] 50,88 51,39 51,69 51,66 51,5 51,01 - - - - - -
104 [°C] 29,40 29,64 29,8 30,97 30,25 30,35 - - - - - -
105 [°C] 41,42 40,08 39,24 38,89 37,82 37,23 - - - - - -
2 Grey
[m3/s] 0,060 0,120 0,180 0,239 0,299 0,360 - - - - - -
3 Fresh
[m3/s] 0,060 0,120 0,180 0,241 0,301 0,360 - - - - - -
2
102 [°C] 50,38 50,91 50,9 50,5 50,66 48,97 47,98 48,03 47,51 47,11 46,28 46,33
103 [°C] 34,61 34,55 35,28 35,92 36,44 36,44 37,05 37,56 37,71 37,71 38,68 38,98
104 [°C] 44,63 45,19 45,07 44,85 44,79 43,26 42,48 42,35 41,87 41,44 41,65 41,67
105 [°C] 29,39 29,57 30,11 30,87 31,14 31,27 31,96 32,3 32,48 32,44 34,35 34,55
2 Grey
[m3/s] 0,060 0,119 0,180 0,239 0,301 0,359 0,420 0,481 0,541 0,600 0,660 0,722
3 Fresh [m3/s]
0,059 0,119 0,179 0,239 0,301 0,359 0,421 0,482 0,541 0,604 0,663 0,721
With a measurement of the four outlets and inlets temperature, the temperature difference
between T-thermocouples, 102 & 103 and 104 & 105 should be equal in order to maintain
energy balance, due to the equal heat storage capacity used for both media. For the major part of
Part 1, as well as Part 2, was the higher temperature difference on the greywater compared to the
freshwater side. The difference in temperature indicates that there is an uneven ratio of the heat
storage capacity, a measuring error or an external heat source or sink. The heat exchanger is
wrapped by insulation; hence no significant heat loss or gain should occur due to the surrounding
environment. Table 3 shows the measured heat capacity and their uncertainties at one standard
deviation. Error due to uneven heat storage capacities can be neglected. The uncertainty cannot
confirm the energy balance due to measuring error. However, the data showed a more substantial
energy reduction on the greywater compared to the energy-addition on the freshwater. Hence,
25
there must be a heat loss to the surroundings despite the presence of insulation. Henceforth, the
best estimate of the results is an average of the freshwater and greywater results, with the
maximum uncertainties as the extreme limits.
An increase in heat transfer effect for an increased flow rate can be noticed in both parts of the
experiment, which is due to the increase in exergy of the system as well as an increase in the
driving force. The increased driving force is due to the smaller temperature difference between
the entry and exit of the media, or higher outlet temperatures of the greywater as the flow rate
increases. However, the increase in exergy is not proportional to the heat transfer effect,
suggesting a difference in heat recovery. In a comparison of both parts, there is a larger heat
transfer effect between the media in Part 2, indicating that a swirling flow has a higher heat
transfer coefficient compared to uniform flow.
Table 3. Measured heat capacity at one standard deviation for the greywater measurement and freshwater
measurement.
Part
Measure
Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run
10
Run
11
Run
12
1
QGrey [W] 876 1499 2013 2190 2649 2851 - - - - - -
Uncertainty [W] ± 26 ± 24 ± 24 ± 25 ± 29 ± 33 - - - - - -
QFresh [W] 831 1449 1956 2202 2631 2859 - - - - - -
Uncertainty [W] ± 24 ± 23 ± 24 ± 25 ± 29 ± 33 - - - - - -
Difference [W] -5 4 9 -38 -39 -57 - - - - - -
ReFresh 249 502 753 1035 1274 1527
2
QGrey [W] 1102 2254 3246 4037 4949 5212 5323 5837 6136 6534 5806 6149
Uncertainty [W] ± 73 ± 76 ± 73 ± 70 ± 70 ± 65 ± 61 ± 62 ± 63 ± 66 ± 65 ± 69
QFresh [W] 1042 2152 3098 3859 4740 4967 5111 5596 5868 6278 5593 5934
Uncertainty [W] ± 76 ± 78 ± 76 ± 72 ± 72 ± 75 ± 63 ± 64 ± 65 ± 67 ± 66 ± 69
Difference [W] -89 -52 -1 36 66 106 88 115 140 124 82 78
ReFresh 246 498 757 1024 1297 1548 1844 2124 2396 2671 3046 3328
Presented in Figure 15 is the vertical temperature gradient along the surface of the heat
exchanger for Part 1. The temperature gradient indicates a non-equal heat capacity rate, as the
curve is polynomial. The temperature gradient indicates higher temperature changes at the inlet
and the outlet of the heat exchanger. A constant vertical temperature gradient should be observed
if the heat capacity rate was equal. However, in the entrance regions, the flow is not fully
developed. With a smaller thickness of the boundary layer, the heat transfer increases, giving a
more considerable temperature change along the surface.
The side with greywater inlet and freshwater outlet, between V1 and V2, indicates that there is a
lower flow rate of the freshwater compared to the greywater. Hence, one of the flowmeters must
be faulty with a varying output, or it must be subject to an installation error. Further, the T-
thermocouple 114, measuring the point V4, appears to give lower values as it might be
misplaced. Figure 16 & 17 shows the same pattern.
26
[l/min]
[l/min]
[l/min]
[l/min]
[l/min]
[l/min]
Figure 15. Vertical temperature gradient of the heat exchanger outer surface, Part 1.
Figure 16 and Figure 17 shows the vertical temperature gradient along the surface of the heat
exchanger for Part 2. The temperature gradient is larger on the side where greywater is entering
the heat exchanger, and a swirling film is present. A larger vertical temperature gradient in this
region indicates that the heat transfer coefficient of swirling falling film is more significant
compared to the uniform flow. The region of larger temperature gradients increases with lower
flow rates, which indicates that the swirling falling film is extended at lower flow rates.
Figure 16. Vertical temperature gradient of the heat exchanger outer surface, Part 2 higher regime.
Temperature gradient between thermocouples
10
9
8
7
6
5
4
3
2
1
0
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
Thermocouple
Run 6 [l/min]
Run 5 [l/min]
Run 4 [l/min]
Run 3 [l/min]
Run 2 [l/min]
Run 1 [l/min]
Uncertainty: ± 0,37 °[C/m]
Vertical temperature gradient - Part 2
12
10
8
6
4
2
0
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
T-thermocouple
Run 12
Run 11
Run 10
Run 9
Run 8
Run 7
Uncertainty: ± 0,37 °[C/m]
Tem
per
atu
re g
rad
ien
t [°
C/m
] Te
mp
erat
ure
gra
die
nct
[°C
/m]
27
[l/min]
[l/min]
[l/min]
[l/min]
[l/min]
[l/min]
Figure 17. Vertical temperature gradient of the heat exchanger outer surface, Part 2 lower regime.
Figure 18 presents the overall heat transfer coefficient correlation with the investigated flow
rates. The solid lines correspond to the interval of uncertainties. When the flow is evolving from
laminar towards turbulent, the heat transfer coefficient increases, the phenomenon exists in
previous studies [29] [44]. At approximately 3 liters per minute, the greywater in Part 1 evolved
to turbulent flow. However, the heat transfer coefficient did not increase drastically. A Wilson
plot experiment could have identified the impact of turbulence on the heat transfer coefficient.
The Wilson plot experiment investigates the different heat transfer coefficients of both media. It
seems that the swirling falling film has a higher heat transfer coefficient compared to the
freshwater side. The larger overall heat transfer coefficient, in Part 2 compared to Part 1 at lower
flow rates, confirms the higher heat transfer coefficient for the swirling falling film. At lower
flow rates the Reynolds number and the flow type remain approximately the same between Part
1 and 2 on the freshwater side.
Vertical temperature gradient - Part 2
16
14
12
10
8
6
4
2
0
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
T-thermocouple
Run 6
Run 5
Run 4
Run 3
Run 2
Run 1
Uncertainty: ± 0,37 °[C/m]
Tem
per
atu
re g
rad
ien
ct [
°C/m
]
28
Figure 18. Overall heat transfer coefficient for Part 1 and Part 2 at the entire test range.
From Figure 19, it is evident, that the falling swirling flow has a higher heat transfer coefficient
compared to the uniform flow, as the other factors such as heat transfer coefficient of the
freshwater, the tube walls, and the air gap, will remain constant between the two parts of the
experiment. At 4 liters per minute, shown in Figure 17, the slope of the difference is decreasing,
which might be due to the impact of the falling film breaking down earlier.
Figure 19. Overall heat transfer coefficient for the lower flow rates of Part 1 and the difference between
Part 2 & Part 1.
Figure 20 presents the measured effectiveness correlation with NTU, where the solid line is the
uncertainty of the experiment. Even though the overall heat transfer coefficient increases with a
higher flow rate in Figure 18, the heat exchanger effectiveness decreases in Figure 20. For the
Volume flow [l/min]
12 10 8 6 4 2 0
1600
1400
1200
1000
800
600
400
200
0
Overall heat transfer coefficient at different flow rates
Part 1
Part 2
Volume flow [l/min]
7 6 5 4 3 2 1 0
900
800
700
600
500
400
300
200
100
0
Overall heat transfer coefficient of the lower regime
Part 1
Part 2 - Part 1
UA
-val
ue
[W/K
] U
A-v
alu
e [W
/K]
29
lower flow rate, the number of transfer units increases, reaching maximum effectiveness of 74,9
± 2,1 % for Part 2. The effectiveness follows the same curve for both parts. The difference
between Part 1 and Part 2 is the region which gives a different range of the number of transfer
units for similar flow rates. The swirling falling flow of greywater in Part 2 increases the NTU
from the regime 0,5-1,3 to 2,2-3,0. The following equation gives the heat exchanger
effectiveness for a system with equal heat capacity rates:
𝜀 = 0,2359 ∗ ln(𝑁𝑇𝑈) + 0,4991
From a previous study, an increase in effectiveness can occur by changing the ratio of the heat
capacity rates [45]. A heat capacity ratio of one has the lowest effectiveness compared to uneven
heat capacity ratios. The more uneven the heat capacity ratio is, the higher the effectiveness can
be. In realistic operating conditions of a greywater heat exchanger, the greywater flow is often
lower compared to the freshwater. Hence the realistic operating conditions would have higher
effectiveness. However, further studies should be performed, investigating the impact of
different heat capacity ratios.
Figure 20. Correlation between Heat exchanger effectiveness and NTU for both parts of the experiment.
Higher NTU corresponds to a lower flow rate.
Figure 21 presents the variation of the ratio between overall heat transfer coefficient and pressure
drop in the freshwater stream. At a lower flow rate, the amount of external pumping power is
lower compared to the amount of heat transfer occurring within the heat exchanger. The same
applies to the effectiveness of the heat exchanger. These results can be used to compare other
greywater heat exchangers when pumping power is limited. Further, with the investigated
regions and with the shapes in Figure 18, 20, & 21, an optimum operating condition cannot be
suggested, without performing a Life Cycle Assessment. However, it can be concluded that the
heat exchanger is more efficient at lower flow rates, with higher effectiveness as well as lower
pumping power.
Heat exchanger effectivness
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
0 0,5 1 1,5 2 2,5 3 3,5
NTU [-]
Part 1
Part 2 Effe
ctiv
ne
ss [
-]
30
Figure 21. The ratio of the overall heat transfer coefficient and pressure drop for Part 2. Pressure drop
data is based on the documented values from Kiwa.
The unquantifiable error of the experiment can be reduced by using T-thermocouples from the
same batch, to make sure all the thermocouples have the same material properties. Using
thermocouples from the same batch would ensure that the test environment has the same
influence on all the thermocouples. The flowmeter should be calibrated using a more accurate
flowmeter, rather than the assumption of constant conditions in the district water supply. Further,
the flowmeter should be mounted on the test rig during calibration, to reduce installation error.
Computational fluid dynamics
A grid independence study is conducted to make sure that the obtained results are dependent on
the resolution of the mesh. The surface heat transfer coefficient is tracked to indicate grid
independency between various mesh resolutions at an inlet flow rate of 6 liters per minute on the
two modules. Table 4 presents the results of the grid independence study. The Greywater module
is grid independent at 290 002 elements and 127 439 nodes, and the Freshwater module is grid
independent at 1 999 921 elements and 696 003 nodes.
Volume flow [l/min]
13 12 11 10 9 8 7 6
45
40
35
30
25
20
15
10
5
0
Ratio of overall heat transfer coefficient and pressure drop
Part 2
UA
/Pre
ssu
re d
rop
[W
/K*k
Pa]
31
Table 4. Grid Independence Study for the Greywater and Freshwater modules.
Greywater
Module
Number of
elements
20 181 180 920 264 339 290 002 378 125
Surface heat
transfer coeff
[W/m²K]
246,35 225,17 207,49 205,86 205,45
Difference in
result [%]
- 8,60 7,85 0,78 0,20
Freshwater
Module
Number of
elements
514 366 1 413 329 1 999 921 4 000 231 -
Surface heat
transfer coeff
[W/m²K]
565,56 535,80 535,29 535,23 -
Difference in
result [%]
- 5,26 0,10 0,01 -
The Greywater and Freshwater modules were simulated for mass flow rates in the laminar
regime at a 1:1 proportion. According to Reynolds number calculation, the flow is transitional at
approximately 3 liters per minute on the greywater and 9 liters per minute on the freshwater.
Therefore, flow rates of 1 and 2 liters per minute, can be related to the experiment. To have a
better resolution of results and the corresponding behavior, five flow rates, namely, 0,5, 1,0, 1,5,
2 and 2,5 liters per minute were simulated. Table 5 & 6 portrays the simulation results for the
greywater and freshwater modules.
Table 5. Greywater module’s simulated and calculated data, for the respective flow rates.
Flow
rate
[l/min]
Mass flow rate
[kg/s]
Reynolds
number
Velocity [m/s] Surface heat
transfer
coefficient
[W/m²K]
Nusselt
number
Outgoing
total
surface
heat flux
[W/m²] 0,5 0,0083 410 0,0047 279,68 22,1 5507,72
1 0,0166 820 0,0094 246,22 19,5 5100,12
1,5 0,0250 1230 0,0141 221,01 17,5 4761,23
2 0,0333 1639 0,0188 194,08 15,4 4368,28
2,5 0,0416 2049 0,0235 205,88 16,3 4574,42
Table 6. Freshwater module’s simulated and calculated data, for the respective flow rates.
Flow
rate
[l/min]
Mass flow rate
[kg/s]
Reynolds
number
Velocity [m/s] Surface heat
transfer
coefficient
[W/m²K]
Nusselt
number
Total
Pressure
drop [Pa]
0,5 0,0083 126 0,0337 635,41 3,2 4712
1 0,0166 252 0,0674 603,43 3,0 1404
1,5 0,0249 379 0,1011 574,25 2,9 2930
2 0,0333 505 0,1347 535,29 2,7 5072
2,5 0,0416 631 0,1684 550,25 2,8 7679
32
The graph in Figure 22 depicts the variation of the simulated Nusselt number at different flow
rates for both the modules as well as the theoretical values. The greywater module was simulated
as a smooth pipe without the grooves. The simulation resulted in a Nusselt number of 3,88. The
Nusselt number of a fully developed flow in a circular tube, in the laminar region, is constant at a
value of 3,66 for constant heat flux [46]. Hence, the presence of the annular groove could
augment the convective heat transfer in the greywater, which translates to a larger Nusselt
number of 15 to 22.
The simulated Nusselt number of greywater decreases with the increase in the volume flow rate,
between 0,5 to 2 liter per minute, which is counter-intuitive to theory. However, a previous study
observes a similar drop in Nusselt number and heat transfer coefficient at lower volume flow
rates [47]. The study believed the reason for this behavior of unstable heat transfer was due to
irregular geometries of the heat exchanger. However, at flow rates higher than 2 liters per
minute, the heat transfer coefficient and consequently the Nusselt number increases until the
flow becomes transitional at 3 liters per minute. The simulations were still converging after this
point, but these results will not be reliable. A suitable turbulent model must be used in the future
to examine the flow development in the turbulent region.
A concentric annular duct with a ratio of the radius that is similar to the Freshwater module has a
Nusselt number approximately equal to 7,25 at constant heat flux condition [46]. The simulated
Nusselt number were of the range 2,5 to 3,5 as seen in Table 6. The simulated Nusselt number
indicates that the helical string might hinder the convective heat transfer.
Figure 22. Theoretical and simulated Nusselt number for Greywater and Freshwater module at various
flow rates.
Figure 23 shows the effect of the helical string through the temperature contours of two different
sections of the freshwater stream. The fluid encounters the helical string at the entrance of the
pipe in the cross-section 1. In the cross-section 2, the fluid encounters the string at the mid-
25 Theoretical vs simulated Nusselt number
20
15
10
5
0
0 0,5 1 Volume flow [l/min]
1,5 2 2,5 3
Theoretical value of a smooth tube, constant heat flux Greywater module
Greywater module smooth
Theoretical value of concentric duct, constant heat flux Freshwater module
Nu
[-]
33
section of the pipe. The fluid is observed to mix closer to the entrance in cross-section 2 when
compared to the cross-section 1, as the temperature increases faster in the streamline. The
reduction in temperature suggests that the helical string delays the heat transfer through
convection.
Figure 23. Temperature contour at two cross-sections, 1 & 2, for the volume flow rates; (a) 0,5
liter/minute (b) 1 liter/minute (c) 1,5 liter/minute (d) 2 liter/minute. Flow direction is downwards.
1(a) 2(a)
1(c) 2(c)
1(b) 2(b)
1(d) 2(d)
34
However, the velocity and pressure contours of the Freshwater module indicate opposite
regarding the convective heat transfer in Figure 24 & 25. Figure 24 below portrays the velocity
contour at 2 liters per minute at three different cross sections of the Freshwater module. The
helical string is located either at the straight section of the annular tube or at the bump. The
straight section is smaller than the bump. The stream has a higher local velocity at the straight
section and lower local velocity at the bump. The higher local velocity indicates that the helical
string has a positive influence on the turbulence and hence the convective heat transfer should be
larger in the helix’s presence.
Figure 24. Velocity contour at three different cross-sections for 2 liters per minute. Flow direction is
downwards.
The pressure contours also support the fact that the helical string augments the turbulence. Figure
25 illustrates the pressure contour at 2 liters per minute in the Freshwater module. The local
pressure drop is higher when the helix passes through the straight section when compared to the
helix passing through the bump. The high local pressure drop also indicates a positive influence
on the turbulence and hence the convective heat transfer.
35
Figure 25. Pressure contour at three different cross-sections for 2 liters per minute. Flow direction is downwards.
Figure 26 compares the pressure drop over the entire heat exchanger from the simulation results of the
Freshwater module and the experimental results from Kiwa [35]. The pressure drop is linear between
0,5 and 2,5 liter per minute in the simulation results, and hence the pressure drop was extrapolated for
higher flow rates. The simulation results are similar to the experimental results until 9 liters per minute.
Above 9 liters per minute, the simulation results diverge from the experimental results, since the slope
of the experimental pressure drop increases. The divergence is true since the flow is transitional at 9,2
liter per minute. This demands for a turbulent and transitional simulation in the future.
Figure 26. Pressure drop in the freshwater stream based on the simulation results and the pressure drop recorded
by Kiwa [35].
70 Pressure drop in freshwater stream
60
50
40 Data from Kiwa
30
20
Simulated & extrapolated results
10
0
0 2 4 Vol6ume flow [l/m8 in] 10 12 14
Pre
ssu
re d
rop
[kP
a]
36
Figure 27 & 28 illustrate the pressure distribution in the Greywater module. The figures depict a
pressure drop at the annular groove. The pressure drop increases with increase in the flow rate. The
influence of this pressure drop spreads towards the flow particles at the center of the tube as the flow
rate increases. For more flow rates or enhanced illustrations, see Appendix – CFD.
Figure 27. Pressure contour of Greywater module at
0,5 liters per minute. Flow Direction is upwards.
Figure 28. Pressure contour of Greywater module at 2
liters per minute. Flow Direction is upwards.
Figure 29 portrays the pressure distribution in the freshwater module. As expected, the pressure drop
increases with the increase in flow. For more flow rates or enhanced illustrations, see Appendix – CFD.
Figure 29. Pressure contour of Freshwater module at flow rates 0,5 (left) & 2 (right) liters per minute. Flow
direction is downwards.
Figure 30 shows the velocity distribution in the greywater module. The flow velocities are fully
developed at the center and close to zero at the walls. The annular grooves do not have any significant
37
effect on the flow. The flow contour does not change with the flow rate. For more flow rates or
enhanced illustrations, see Appendix – CFD.
Figure 30. Velocity contour of Graywater module at flow rates 0,5(left) & 2(right) liters per minute. Flow
direction is downwards.
Figure 31 indicates the velocity distribution in the freshwater module. The helical string causes an
increase in the velocity in the flow direction. The flow is relatively stationary at the wake of the helical
string. The velocity vector diagram shows that the vectors are almost non-existent at the wake of the
helical string. For more flow rates or enhanced illustrations, see Appendix – CFD.
Figure 31. Velocity contour of Freshwater module at flow rates 0,5(left) & 2(middle) liter per minute and velocity
vector diagram at 0,5(right) liter per minute. Flow direction is downwards.
Validation of Periodic model
From the above discussion, it is evident that the modeled Pressure-velocity coupling of the
periodic heat transfer is true. However, the segregated energy model is predicting a lower heat
transfer coefficient and a lower Nusselt number on the freshwater. The faulty energy model also
resulted in a failed validation with the experiment. Figure 32 represents the overall heat
38
coefficient obtained in the simulations against the experimental values. The percentage of error is
59%, which says that the simulated values are 69 W/K lower than the experimental values. The
other probable factors that lead to the error are:
1. Measurement error – The heat exchanger was measured using a Vernier caliper with a least
count of 0,05 mm, which could have a significant error in measurement. The measured
difference between the inner and outer radius of the outer pipe annulus was 3 mm, and the
thickness of the helical string was 0,6 mm. A small error in the radius of the annulus would
change the hydraulic diameter, which will correspond to an error in the Nusselt number. The heat
exchanger also has a complicated geometry with the annular groove in the inner pipe, the two air
gaps, and the bump in the outer pipe. These features were modeled by approximation.
2. Oscillation in the helical string – The helical string was loosely suspended inside the outer
pipe as it was only attached at the ends of the heat exchanger. The loosely attached string could
cause oscillation of the string which in turn leads to turbulence in the freshwater stream. Hence
increased heat transfer. However, this phenomenon is hard to detect or measure and is ignored by
the simulation.
Figure 32. Overall heat transfer coefficient from CFD and Experimental results.
Conclusion The CFD model could not be validated by the experiment as the overall heat transfer coefficient
in CFD was almost half of the experimental results. The overall heat transfer coefficient
increases with an increase in the uniform flow rate for the experiment in the laminar regime. The
overall heat transfer coefficient varied from 90 to 130 W/K. However, it is rather constant in the
CFD simulation at 50 W/K for equal flow rates.
3 2,5 2 1,5
Volume flow [l/min]
1 0,5 0
0
50
100
150
200
250
Overall heat transfer coefficient
Experiment
CFD
UA
-val
ue
[W/K
]
39
The difference in overall heat transfer coefficient could be due to the ambiguous effect of the
helical string, in the freshwater pipe. The simulated Nusselt number of the freshwater pipe, with
helical string, was approximately half than the theoretical Nusselt number of a pipe without
obstructions.
However, the simulated pressure drop in the freshwater pipe could be validated with a third-party
experiment. The pressure drop increased linearly with the laminar flow rate. The CFD also
showed that the presence of the string augments the local velocity and pressure drop and hence
increasing the turbulence.
The annular grooves in the greywater pipe showed a marked increase in the heat transfer when
compared with a simulated as well as the theoretical smooth pipe. The Nusselt number was
almost five times larger than a smooth pipe.
Within the heat exchanger, heat transfer is more substantial in the entrance region compared to
the middle section for both types of flow. With an increase in flow rates the swirling falling film
is attached for a shorter length; however, the heat transfer coefficient for the swirling flow
increases.
The overall heat transfer coefficient and hence the NTU of a swirling flow is larger compared to
that of a uniform flow for the same flow rates. The heat exchanger effectiveness varied from 33
to 57% for the uniform flow and 69 to 75% for the swirling flow in the same flow regime. For
both uniform flow and swirling flow, the heat exchanger effectiveness can be described as a
single logarithmic function of the NTU for a capacity ratio of one; with higher effectiveness at
lower flow rates.
Despite the tedious periodic heat transfer setup, the model was very efficient in terms of
computational time and resources. Periodic heat transfer simplified the huge geometry into a
small module, which allows for faster product development in the future.
Future studies Some question marks for further studies to be investigated:
• The transient behavior of the heat exchanger, such as response time and fouling build up
within the heat exchanger.
• The impact when subject to different water composition, such as toothpaste, shower gel
and chemicals in the water stream can be investigated.
• Investigation of the effect of different heat capacity ratios.
• Performing Cost and Environmental Life Cycle Assessment.
• A different approach for energy modeling of the freshwater side.
• The heat exchanger’s turbulent and transitional behavior.
• Comparison of heat transfer augmentation by various other geometries
40
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44
Appendix – Calibration
T-thermocouples – Inlet/Outlet
The 4 type T-thermocouples that were to record the inlet and outlet temperature of the heat
exchanger was named: 102, 103, 104 & 105. The average deviation of these T-thermocouples
against the reference thermometer, for the 30 samples at every temperature level, can be seen in
Figure A1.
Figure A1. Deviation of average temperature given by inlet/outlet T-thermocouple and reference, at
different temperature levels.
From Figure A1. It can be seen that there is an offset between 0,15 to 0,4 °C. This is within the
range of expected results of an uncalibrated T-thermocouple. The appearance of the offset is a
polynomial, which comprehends to that a thermocouple applies a 9th-degree polynomial.
In Table A1, the result from the regression tool in excel is presented. From the data, it can be
seen that the Hexic model, for all the T-thermocouples, has no residual and is a perfect fit.
Deviation of average temperature of 102-105 vs reference
0,45
0,4
0,35
0,3
0,25
0,2
0,15
0,1
0,05
0
20 25 30 35 40 45 50 55 60
Fluke 1551A Ex Temperature [°C]
102
103
104
105
Dev
iati
on
of
tem
pe
ratu
re [
°C]
45
Table A1. Number of residuals for an applied calibration curve for different models. Results from
regression tool in Excel. T-thermocouple Model Degree of Freedom SSE MSE
102 Linear 5 0,024656 0,004931
Quadratic 4 0,005355 0,001339
Cubic 3 0,005178 0,001726
Quartic 2 0,000534 0,000267
Quintic 1 2,83E-05 2,83E-05
Hexic 0 0 65535
103 Linear 5 0,024626 0,004925
Quadratic 4 0,005228 0,001307
Cubic 3 0,005002 0,001667
Quartic 2 0,000555 0,000277
Quintic 1 0,000189 0,000189
Hexic 0 0 65535
104 Linear 5 0,025104 0,005021
Quadratic 4 0,005388 0,001347
Cubic 3 0,005288 0,001763
Quartic 2 0,00076 0,00038
Quintic 1 0,000301 0,000301
Hexic 0 0 65535
105 Linear 5 0,024764 0,004953
Quadratic 4 0,005131 0,001283
Cubic 3 0,005003 0,001668
Quartic 2 0,00017 8,48E-05
Quintic 1 9,82E-05 9,82E-05
Hexic 0 0 65535
In Table A2, an F-statistic test matrix has been taken forward, based on the data from Table A1.
The matrix is showing the significance of increasing the model towards a higher polynomial. For
all of the T-thermocouples, a linear model should be replaced with a quadratic model. The
quadratic model has a lower lack of fit compared to the linear model, as the F-value of
approximate 15 is way greater than 1. Regarding further analyses of the quadratic model for all
of the T-thermocouples, it can be concluded that is has a better fit than the cubic and Hexic
model. However, a quadratic and quintic model is better describing the data to be corrected.
Between the quadratic and quintic model, it is not necessary for T-thermocouple 105, to apply
the quintic model. However, for the other, it should be applied. For simplification, the quartic
model is used as a calibration curve for T-thermocouple 102-105. Due to that the quintic
polynomial only affects the five decimal on a temperature.
46
Table A2. F-statistic test matrix. Showing the F value between different models. T-thermocouple Model Linear Quadratic Cubic Quartic Quintic
102 Quadratic 14,41598965 - - - -
Cubic 5,642647513 0,102802574 - - -
Quartic 30,11513315 9,028828337 17,39310304 - -
Quintic 217,4468159 62,7124061 182,3706923 17,85935345 -
Hexic 7,52461E-08 2,04295E-08 2,63369E-08 4,07416E-09 4,32058E-10
103 Quadratic 14,84332048 - - - -
Cubic 5,885257699 0,135437921 - - -
Quartic 28,93158085 8,424532437 17,39310304 - -
Quintic 32,40945069 8,910458766 26,0334958 1,942467065 -
Hexic 7,51538E-08 1,99418E-08 2,63369E-08 4,23188E-09 2,87642E-09
104 Quadratic 14,28371876 - - - -
Cubic 5,485727981 0,056589558 - - -
Quartic 20,92862729 6,086729208 16,03486341 - -
Quintic 20,18444343 5,62736316 17,0510213 1,523320555 -
Hexic 7,51538E-08 2,05521E-08 2,63369E-08 5,80017E-09 4,59725E-09
105 Quadratic 15,19701097 - - - -
Cubic 5,883356022 0,076877347 - - -
Quartic 96,09416147 29,2424669 11,91105166 - -
Quintic 62,41329678 17,07584823 50,42261291 0,726960465 -
Hexic 7,51538E-08 1,95743E-08 2,63369E-08 1,29449E-09 1,49916E-09
In Table A3 the calibration curve and the fossilized uncertainty at one standard deviation are presented for
thermocouple 102-105. Where the fossilized uncertainty contains the lack of fit and the maximum
uncertainty of repeated measurement, random error, as well as a systematic error from the fluke reference
thermometer, it can be seen in Table A3; the uncertainty of the T-thermocouples are low, which is
compared to uncertainty given from a manufacturer, between 0,5 to 1 °C for a thermocouple of type t.
Table A3. The applied calibration curve and new systematic uncertainty for T-thermocouple 102-105 at
one standard deviation. T-thermocouple Calibration Curve Fossilized uncertainty,
𝑢(𝑥)𝐵 , [°C]
102 -0,0000055785*x^4 + 0,0008754029*x^3 - 0,0508632273*x^2 +
2,2969401054*x - 11,9250153963
0,0502
103 -0,0000054411*x^4 + 0,0008527624*x^3 - 0,0494965845*x^2 +
2,2604702584*x - 11,5607028302
0,0504
104 -0,0000055516*x^4 + 0,0008732704*x^3 - 0,0508838304*x^2 +
2,303483736*x – 12,0970164302
0,0504
105 -0,0000056864*x^4 + 0,0008922498*x^3 - 0,0518319952*x^2 +
2,3209034804*x - 12,0748453929
0,0505
47
Avereage temperature of 110-115 vs reference
0,5
0,45
0,4
0,35
0,3
0,25
0,2
0,15
0,1
0,05
0
25 30 35 40 45
Average temperature of 104 & 105 [°C]
110
112
113
114
115
T-thermocouples – Surface The ten surface T-thermocouples had been mounted in place before the calibration process, in order to
reduce the installation losses. By mounting these in advance, the calibration process took longer, since the
cold storage tank took longer to adjust in temperature than the previously used thermal bath container.
Hence the three temperature levels. With the three temperature levels, a linear model must be applied.
Which is due to the lacking amount of degree of freedom.
In Figure A2 & A3, the deviation between the average temperature of the surface T-thermocouples and
the average temperature of 104 & 105, is presented. It can be seen, that with higher temperature the offset
increases. However, the results are similar to the scale of the offset found in Figure A1.
Figure A2. Deviation of average temperature given by T-thermocouple 110-115 and 104 & 105, at
different temperature levels.
Figure A3. Deviation of average temperature given by T-thermocouple 116-120 and 104 & 105, at
different temperature levels.
Average temperature of 104 & 105 [°C]
45 40 35 30 25
0,6 0,5
0,4
0,3
0,2
0,1
0
Average temperature of 116-120 vs reference
116
117
118
119
120
Dev
iati
on
of
tem
pe
ratu
re [
°C]
Dev
iati
on
of
tem
pe
ratu
re [
°C]
48
In Table A4 the calibration curve and the fossilized uncertainty at one standard deviation is presented for
T-thermocouple 110-120. Where the fossilized uncertainty contains the lack of fit and the maximum
uncertainty of repeated measurement for the T-thermocouple, random error, as well as fossilized and
random uncertainty of T-thermocouple 104 & 105, by comparing Table A4 to Table A3, it can be seen
that the fossilized uncertainty from thermocouple 104 & 105, remains the most significant contributor
towards the uncertainty. The impact of poor curve fit and random error is not significant.
Table A4. The applied calibration curve and new systematic uncertainty for T-thermocouple 110-120 at
one standard deviation. T-thermocouple Calibration Curve Fossilized uncertainty,
𝑢(𝑥)𝐵 , [°C]
110 1,0074x + 0,0540 0,0508
112 1,0053x + 0,1079 0,0510
113 1,0051x + 0,2068 0,0508
114 1,0066x - 0,0101 0,0514
115 1,0046x + 0,2040 0,0508
116 1,0080x - 0,0969 0,0530
117 1,0053x + 0,1746 0,0515
118 1,0070x + 0,1777 0,0511
119 1,0061x + 0,1869 0,0508
120 1,0075x + 0,1928 0,0525
Flowmeter Figure A4 shows the deviation of the average flow from the high-resolution screens of the flowmeters
compared to flow gain from the gravimetric method. Due to similar constraints as for surface T-
thermocouples, a linear model must be applied. The data was further used in the experiment as run
parameters, to adjust the inlet flow for Part 1. Seen in Figure A4, the behavior of the flowmeter is the
opposite of each other. Flowmeter 3 is increasing its offset as the flow rates increases, while the
flowmeter 2 is reducing the offset. Further, it can be seen that the distances of the two similar measuring
levels increases, in the same portion between both flowmeters. The reason might be to the assumption of
district water supply being constant through the time of the calibration process. Since during the
calibration process, both flowmeters were attached in series, with a valve controlling the flow. At high
flow rates, the district pressure becomes more vital, compared to a lower flow rate. Hence the possible
reason for the increasing gap between the two measuring levels.
49
Figure A4. Deviation of average flow given by flowmeter 2 & 3 at different flow rates levels, part 1.
In Figure A5, similar data as Figure A4 is presented and the data was used in the same procedure for Part
2. It can be seen, that flowmeter two offset is increasing with higher flow rates, rather than decreasing as
from Figure A4. However, flowmeter three is following the same behavior as from Figure A4, but with an
increased slope of the offset.
Figure A5. Deviation of average flow given by flowmeter 2 & 3 at different flow rates levels, part 2.
In Table A5, the calibration curve and the fossilized uncertainty at one standard deviation are presented
for flowmeter 2 & 3. Where the fossilized uncertainty contains the random and systematic errors from the
gravimetric method and the lack of fit as well as the maximum random error from repeated measurement
at a flow rate, it can be seen that the fossilized uncertainty increases drastically between Part 1 and Part 2
calibration process. The reason for this is with higher flow rate the fluctuations from the reading of the
high-resolution screens increases. Further, the lack of fit also plays a vital part in the increased
Gravimetric flow [m3/h]
0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4
0,007
0,006
0,005
0,004
0,003
0,002
0,001
0,000
-0,001 0
-0,002
Deviation of flowmeter 2 & 3 vs reference
3
2
Gravimetric flow [m3/h] -0,002
0,8 0,7 0,5 0,6 0,4 0,2 0,3 0,1 0
0,014
0,012
0,010
0,008
0,006
0,004
0,002
0,000
Deviation of flowmeter 2 & 3 vs reference
3
2
Dev
iati
on
of
flo
w [
m3 /
h]
Dev
iati
on
of
flo
w [
m3/h
]
50
uncertainty. The right model with an F – test should have been investigated, but due to time constrain the
linear model was applied. In Figure A6, the impact of a higher order polynomial as a calibration curve for
flowmeter 2, can be seen. The quintic model would possibly be the outcome of an F – test. However, it is
not possible that these fluctuations would occur.
Table A5. The applied calibration curve and new systematic uncertainty for flowmeter 2 & 3 at one
standard deviation. Flowmeter Calibration Curve Fossilized uncertainty,
𝑢(𝑥)𝐵 , [m3/h]
3 (Part 1) 1,0075x + 0,0016 0,0017
2 (Part 1) 0,9962x + 0,0012 0,0017
3 (Part 2) 1,0139x + 0,0006 0,0043
2 (Part 2) 1,0036x + 0,0000 0,0040
Figure A6. Example of a quintic model calibration curve for flowmeter 2, Part 2.
Deviation of flowmeter 2 vs reference, quintic model
0,020
0,010
0,000
-0,010 0
-0,020
-0,030
-0,040
-0,050
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
Gravimetric flow [m3/h]
2
Dev
iati
on
of
flo
w [
m3 /
h]
51
Appendix - Calibration Raw Data Table B1. Raw data used for calibration of T-thermocouple 102-105
Reference
[°C]
102
[°C]
103
[°C]
104
[°C]
105
[°C]
Reference
[°C]
102
[°C]
103
[°C]
104
[°C]
105
[°C]
25,1 24,86 24,847 24,9 24,809 39,93 39,645 39,614 39,739 39,559
25,1 24,893 24,868 24,922 24,82 39,93 39,619 39,648 39,643 39,564
25,1 24,895 24,863 24,903 24,83 39,93 39,633 39,633 39,646 39,565
25,1 24,9 24,892 24,932 24,822 39,93 39,616 39,618 39,644 39,579
25,1 24,901 24,909 24,933 24,836 39,93 39,629 39,644 39,652 39,569
25,1 24,892 24,889 24,935 24,833 39,93 39,608 39,621 39,626 39,555
25,1 24,891 24,899 24,947 24,837 39,93 39,602 39,618 39,644 39,432
25,1 24,889 24,886 24,924 24,833 39,93 39,64 39,634 39,626 39,553
25,1 24,895 24,912 24,949 24,85 39,93 39,623 39,62 39,641 39,56
25,1 24,888 24,891 24,945 24,837 39,93 39,626 39,631 39,647 39,563
25,1 24,89 24,901 24,925 24,831 39,93 39,614 39,612 39,64 39,565
25,1 24,905 24,894 24,94 24,862 39,93 39,62 39,633 39,633 39,575
25,1 24,9 24,879 24,943 24,847 39,93 39,633 39,63 39,622 39,562
25,1 24,885 24,891 24,947 24,824 39,93 39,614 39,629 39,627 39,556
25,1 24,893 24,887 24,949 24,842 39,93 39,618 39,626 39,647 39,568
25,1 24,891 24,888 24,942 24,853 44,82 44,491 44,478 44,476 44,402
25,1 24,912 24,886 24,926 24,832 44,82 44,497 44,508 44,481 44,432
25,1 24,899 24,883 24,947 24,813 44,82 44,481 44,505 44,497 44,436
25,1 24,903 24,895 24,935 24,827 44,82 44,494 44,513 44,5 44,426
25,1 24,906 24,893 24,931 24,845 44,82 44,486 44,486 44,486 44,441
25,1 24,897 24,878 24,942 24,837 44,82 44,479 44,494 44,502 44,426
25,1 24,883 24,878 24,945 24,835 44,82 44,483 44,441 44,496 44,512
25,1 24,906 24,89 24,927 24,825 44,82 44,504 44,499 44,502 44,441
25,1 24,879 24,906 24,925 24,844 44,82 44,506 44,508 44,493 44,422
25,1 24,884 24,895 24,946 24,833 44,82 44,482 44,508 44,501 44,425
25,1 24,884 24,887 24,933 24,831 44,82 44,48 44,506 44,495 44,43
25,1 24,897 24,886 24,948 24,835 44,82 44,51 44,516 44,576 44,416
25,1 24,892 24,892 24,956 24,827 44,82 44,488 44,502 44,496 44,423
25,1 24,91 24,888 24,926 24,835 44,82 44,497 44,51 44,484 44,424
25,1 24,909 24,882 24,966 24,829 44,82 44,505 44,508 44,495 44,432
30,07 29,751 29,735 29,759 29,689 44,82 44,495 44,51 44,489 44,413
30,07 29,74 29,743 29,78 29,673 44,82 44,501 44,49 44,488 44,433
30,07 29,761 29,764 29,782 29,686 44,82 44,504 44,496 44,486 44,428
30,07 29,745 29,764 29,793 29,699 44,82 44,509 44,514 44,48 44,417
30,07 29,75 29,739 29,798 29,709 44,82 44,502 44,499 44,489 44,426
30,07 29,747 29,755 29,785 29,701 44,82 44,497 44,502 44,489 44,428
30,07 29,768 29,757 29,803 29,717 44,82 44,52 44,504 44,478 44,421
30,07 29,765 29,77 29,787 29,695 44,82 44,481 44,499 44,491 44,423
52
30,07 29,759 29,772 29,805 29,574 44,82 44,505 44,484 44,492 44,432
30,07 29,772 29,756 29,786 29,684 44,82 44,506 44,532 44,496 44,409
30,07 29,765 29,741 29,806 29,696 44,82 44,518 44,492 44,489 44,416
30,07 29,766 29,78 29,788 29,699 44,82 44,488 44,48 44,506 44,428
30,07 29,775 29,762 29,789 29,687 44,82 44,506 44,495 44,503 44,411
30,07 29,762 29,754 29,797 29,713 44,82 44,508 44,493 44,493 44,43
30,07 29,764 29,761 29,788 29,694 44,82 44,48 44,506 44,472 44,42
30,07 29,77 29,767 29,781 29,703 49,7 49,344 49,362 49,349 49,18
30,07 29,756 29,753 29,78 29,543 49,7 49,345 49,394 49,34 49,294
30,07 29,759 29,761 29,802 29,683 49,7 49,337 49,375 49,352 49,288
30,07 29,758 29,769 29,793 29,691 49,7 49,362 49,369 49,446 49,305
30,07 29,752 29,76 29,787 29,704 49,7 49,349 49,374 49,339 49,295
30,07 29,762 29,762 29,791 29,703 49,7 49,359 49,397 49,346 49,293
30,07 29,755 29,763 29,763 29,71 49,7 49,355 49,404 49,366 49,343
30,07 29,763 29,761 29,798 29,696 49,7 49,347 49,375 49,355 49,306
30,07 29,76 29,768 29,795 29,73 49,7 49,364 49,339 49,364 49,318
30,07 29,769 29,766 29,804 29,704 49,7 49,357 49,368 49,357 49,306
30,07 29,763 29,744 29,795 29,698 49,7 49,352 49,362 49,35 49,296
30,07 29,754 29,767 29,786 29,7 49,7 49,345 49,296 49,365 49,396
30,07 29,757 29,746 29,799 29,714 49,7 49,353 49,373 49,358 49,304
30,07 29,75 29,756 29,807 29,686 49,7 49,358 49,445 49,363 49,309
30,07 29,752 29,768 29,809 29,704 49,7 49,365 49,378 49,358 49,301
35 34,637 34,637 34,647 34,569 49,7 49,385 49,385 49,362 49,308
35 34,661 34,666 34,672 34,599 49,7 49,362 49,38 49,357 49,311
35 34,642 34,664 34,685 34,605 49,7 49,374 49,435 49,353 49,313
35 34,669 34,65 34,671 34,609 49,7 49,368 49,358 49,36 49,314
35 34,675 34,672 34,683 34,602 49,7 49,367 49,388 49,357 49,395
35 34,659 34,621 34,683 34,629 49,7 49,351 49,356 49,353 49,292
35 34,663 34,668 34,676 34,604 49,7 49,373 49,373 49,353 49,314
35 34,653 34,642 34,669 34,602 49,7 49,364 49,369 49,359 49,3
35 34,659 34,665 34,662 34,592 49,7 49,384 49,377 49,364 49,31
35 34,675 34,654 34,667 34,595 49,7 49,373 49,381 49,286 49,317
35 34,654 34,724 34,662 34,606 49,7 49,374 49,39 49,374 49,32
35 34,657 34,665 34,668 34,593 49,7 49,373 49,385 49,373 49,298
35 34,66 34,655 34,673 34,595 49,7 49,363 49,381 49,376 49,315
35 34,661 34,669 34,685 34,602 49,7 49,353 49,374 49,376 49,31
35 34,667 34,664 34,683 34,621 49,7 49,365 49,373 49,367 49,314
35 34,67 34,667 34,672 34,603 54,45 54,216 54,239 54,193 54,165
35 34,661 34,658 34,674 34,594 54,45 54,243 54,258 54,23 54,205
35 34,645 34,663 34,677 34,615 54,45 54,234 54,27 54,239 54,203
35 34,637 34,666 34,685 34,623 54,45 54,251 54,279 54,236 54,18
53
35 34,667 34,664 34,664 34,592 54,45 54,271 54,271 54,245 54,212
35 34,657 34,662 34,676 34,592 54,45 54,248 54,271 54,256 54,195
35 34,656 34,653 34,672 34,615 54,45 54,25 54,266 54,238 54,217
35 34,66 34,679 34,719 34,601 54,45 54,266 54,281 54,24 54,22
35 34,665 34,657 34,676 34,622 54,45 54,261 54,291 54,261 54,204
35 34,671 34,662 34,668 34,593 54,45 54,251 54,28 54,257 54,198
35 34,669 34,663 34,677 34,612 54,45 54,28 54,285 54,249 54,21
35 34,677 34,647 34,685 34,615 54,45 54,272 54,3 54,252 54,213
35 34,664 34,673 34,702 34,613 54,45 54,281 54,284 54,241 54,207
35 34,681 34,665 34,668 34,614 54,45 54,272 54,297 54,251 54,2
35 34,688 34,667 34,696 34,608 54,45 54,274 54,289 54,246 54,215
39,93 39,611 39,645 39,706 39,556 54,45 54,279 54,284 54,238 54,223
39,93 39,61 39,628 39,62 39,557 54,45 54,278 54,283 54,248 54,204
39,93 39,618 39,636 39,618 39,55 54,45 54,258 54,289 54,253 54,207
39,93 39,622 39,68 39,619 39,567 54,45 54,265 54,273 54,255 54,232
39,93 39,613 39,613 39,637 39,563 54,45 54,275 54,285 54,267 54,218
39,93 39,608 39,624 39,618 39,566 54,45 54,279 54,294 54,248 54,205
39,93 39,613 39,616 39,611 39,577 54,45 54,271 54,289 54,251 54,19
39,93 39,593 39,627 39,627 39,549 54,45 54,269 54,3 54,251 54,19
39,93 39,616 39,629 39,613 39,566 54,45 54,271 54,281 54,258 54,212
39,93 39,618 39,612 39,633 39,578 54,45 54,258 54,281 54,25 54,202
39,93 39,604 39,612 39,628 39,57 54,45 54,262 54,288 54,267 54,206
39,93 39,622 39,628 39,62 39,565 54,45 54,276 54,284 54,243 54,207
39,93 39,612 39,638 39,635 39,573 54,45 54,275 54,28 54,249 54,178
39,93 39,619 39,632 39,629 39,566 54,45 54,268 54,281 54,253 54,22
39,93 39,622 39,619 39,624 39,577 54,45 54,268 54,276 54,255 54,197
Table B1. Raw data used for calibration of T-thermocouple 110-120
110
[°C]
112
[°C]
113
[°C]
114
[°C]
115
[°C]
116
[°C]
117
[°C]
118
[°C]
119
[°C]
120
[°C]
104 –
Corrected
[°C]
105 –
Corrected
[°C]
29,024 29,057 28,965 29,143 28,981 29,186 28,963 28,938 28,963 28,89 29,305 29,323
29,064 29,053 28,964 29,147 28,967 29,187 28,978 28,927 28,948 28,905 29,323 29,319
29,054 29,067 28,984 29,151 28,998 29,199 28,995 28,925 28,968 28,901 29,305 29,331
29,057 29,043 28,968 29,153 28,973 29,196 28,976 28,949 28,957 28,893 29,321 29,312
29,063 29,065 28,963 29,159 29,006 29,192 28,985 28,947 28,963 28,907 29,324 29,340
29,063 29,082 28,99 29,168 28,982 29,208 29,001 28,942 28,966 28,918 29,338 29,332
29,064 29,069 28,986 29,166 28,994 29,206 29,013 28,935 28,97 28,916 29,320 29,346
29,066 29,064 28,991 29,147 28,997 29,203 29,007 28,932 28,964 28,908 29,331 29,351
29,049 29,073 28,982 29,157 28,996 29,194 28,998 28,947 28,955 28,912 29,330 29,342
29,062 29,043 28,976 29,143 29,008 29,199 28,984 28,952 28,965 28,917 29,345 29,347
29,074 29,064 28,978 29,158 28,986 29,201 29,01 28,945 28,97 28,905 29,333 29,343
54
29,057 29,063 28,979 29,159 28,985 29,216 28,979 28,95 28,963 28,872 29,312 29,315
29,056 29,064 28,997 29,15 28,994 29,214 28,988 28,959 28,972 28,897 29,311 29,338
29,071 29,066 28,961 29,136 29,009 29,208 28,996 28,958 28,969 28,915 29,338 29,348
29,061 29,058 28,98 29,152 28,972 29,201 28,98 28,929 28,962 28,908 29,316 29,319
29,039 29,042 28,961 29,147 28,983 29,198 28,999 28,937 28,956 28,902 29,313 29,305
29,041 29,065 28,966 29,138 28,974 29,202 29,004 28,944 28,955 28,907 29,307 29,315
29,048 29,056 28,962 29,166 28,975 29,182 28,975 28,94 28,956 28,911 29,319 29,302
29,052 29,057 28,969 29,135 28,982 29,216 28,998 28,926 28,958 28,91 29,323 29,321
29,071 29,073 28,982 29,159 28,985 29,205 28,982 28,95 28,971 28,91 29,321 29,326
29,079 29,068 28,977 29,165 29,004 29,202 28,987 28,958 28,969 28,915 29,318 29,321
29,076 29,079 28,993 29,175 29,001 29,229 29,014 28,961 28,977 28,931 29,330 29,358
29,081 29,097 29,003 29,178 29,019 29,231 29,019 28,968 29,006 28,947 29,345 29,366
29,079 29,087 28,996 29,181 29,022 29,243 29,028 28,987 28,996 28,942 29,346 29,356
29,088 29,082 28,999 29,179 29,01 29,233 29,034 28,959 28,996 28,948 29,376 29,356
29,119 29,076 29,012 29,175 29,025 29,253 29,028 28,974 28,99 28,953 29,359 29,350
29,084 29,103 29,009 29,192 29,039 29,237 29,036 28,974 28,99 28,942 29,373 29,380
29,089 29,099 29,008 29,183 29,021 29,236 29,029 28,984 29,005 28,96 29,358 29,382
29,08 29,08 29 29,191 29,027 29,226 28,992 28,973 28,986 28,927 29,345 29,382
29,075 29,078 28,992 29,18 29,019 29,215 29,013 28,952 28,989 28,917 29,355 29,347
29,091 29,088 28,999 29,152 29,007 29,222 29,013 28,98 28,975 28,932 29,336 29,349
36,774 36,821 36,737 36,866 36,761 36,9 36,787 36,709 36,74 36,698 37,114 37,116
36,776 36,828 36,718 36,883 36,755 36,904 36,773 36,702 36,71 36,684 37,119 37,126
36,785 36,837 36,73 36,884 36,743 36,916 36,745 36,709 36,725 36,698 37,125 37,151
36,804 36,844 36,744 36,872 36,778 36,893 36,76 36,713 36,734 36,684 37,113 37,134
36,799 36,836 36,715 36,896 36,755 36,893 36,762 36,707 36,71 36,665 37,118 37,113
36,802 36,836 36,723 36,873 36,758 36,904 36,763 36,7 36,726 36,676 37,116 37,121
36,796 36,825 36,731 36,88 36,752 36,924 36,78 36,71 36,731 36,675 37,118 37,123
36,819 36,83 36,727 36,879 36,769 36,905 36,756 36,704 36,733 36,685 37,131 37,135
36,804 36,827 36,73 36,877 36,754 36,911 36,764 36,725 36,722 36,648 37,123 37,154
36,792 36,826 36,737 36,886 36,734 36,909 36,763 36,695 36,718 36,676 37,129 37,126
36,807 36,846 36,734 36,904 36,739 36,912 36,768 36,705 36,715 36,681 37,121 37,126
36,803 36,821 36,734 36,886 36,74 36,91 36,763 36,671 36,708 36,677 37,127 37,116
36,797 36,833 36,736 36,88 36,776 36,899 36,768 36,708 36,718 36,676 37,106 37,139
36,809 36,817 36,72 36,882 36,762 36,906 36,772 36,691 36,723 36,675 37,107 37,130
36,795 36,829 36,734 36,892 36,766 36,884 36,774 36,708 36,727 36,69 37,117 37,166
36,793 36,84 36,717 36,887 36,751 36,885 36,775 36,709 36,707 36,683 37,139 37,122
36,791 36,827 36,725 36,874 36,749 36,919 36,762 36,691 36,717 36,681 37,120 37,128
36,798 36,827 36,725 36,876 36,769 36,89 36,756 36,709 36,704 36,672 37,125 37,140
36,78 36,827 36,722 36,887 36,759 36,921 36,785 36,688 36,725 36,691 37,122 37,132
36,8 36,834 36,719 36,873 36,758 36,9 36,779 36,703 36,724 36,663 37,133 37,124
36,795 36,829 36,727 36,876 36,753 36,895 36,766 36,709 36,711 36,685 37,130 37,122
36,795 36,831 36,719 36,876 36,75 36,891 36,771 36,698 36,721 36,682 37,127 37,132
55
36,795 36,821 36,727 36,871 36,75 36,905 36,745 36,706 36,69 36,669 37,135 37,140
36,793 36,814 36,707 36,88 36,741 36,908 36,777 36,694 36,704 36,691 37,139 37,112
36,824 36,842 36,732 36,868 36,735 36,916 36,766 36,677 36,727 36,666 37,112 37,117
36,797 36,839 36,716 36,873 36,755 36,907 36,776 36,692 36,726 36,679 37,111 37,129
36,791 36,83 36,715 36,891 36,739 36,891 36,762 36,707 36,726 36,678 37,118 37,115
36,802 36,815 36,723 36,881 36,75 36,896 36,773 36,697 36,723 36,668 37,113 37,123
36,799 36,812 36,725 36,872 36,733 36,893 36,759 36,691 36,697 36,648 37,126 37,120
36,786 36,796 36,718 36,872 36,749 36,893 36,757 36,702 36,71 36,662 37,110 37,097
36,786 36,825 36,697 36,872 36,739 36,906 36,744 36,673 36,707 36,678 37,105 37,097
44,696 44,738 44,662 44,811 44,664 44,837 44,672 44,607 44,625 44,554 45,083 45,089
44,709 44,738 44,662 44,827 44,678 44,843 44,672 44,602 44,623 44,536 45,102 45,102
44,705 44,752 44,64 44,805 44,7 44,833 44,666 44,595 44,637 44,558 45,103 45,098
44,716 44,742 44,661 44,813 44,682 44,855 44,69 44,588 44,622 44,564 45,088 45,106
44,678 44,731 44,668 44,796 44,681 44,841 44,665 44,581 44,623 44,555 45,079 45,066
44,696 44,735 44,662 44,808 44,672 44,84 44,675 44,578 44,625 44,559 45,083 45,083
44,694 44,725 44,647 44,807 44,686 44,851 44,67 44,6 44,621 44,547 45,076 45,092
44,702 44,746 44,644 44,801 44,668 44,848 44,657 44,602 44,642 44,55 45,082 45,082
44,7 44,75 44,658 44,805 44,698 44,844 44,682 44,598 44,611 44,551 45,096 45,085
44,696 44,735 44,657 44,78 44,672 44,837 44,667 44,589 44,638 44,547 45,089 45,073
44,694 44,731 44,655 44,812 44,681 44,838 44,673 44,603 44,621 44,548 45,090 45,090
44,707 44,744 44,65 44,796 44,707 44,846 44,658 44,582 44,637 44,561 45,098 45,087
44,701 44,727 44,641 44,809 44,691 44,832 44,678 44,596 44,617 44,541 45,099 45,089
44,708 44,724 44,64 44,823 44,677 44,847 44,674 44,59 44,63 44,527 45,075 45,088
44,71 44,728 44,647 44,817 44,686 44,833 44,663 44,582 44,629 44,55 45,074 45,074
44,702 44,728 44,647 44,812 44,673 44,844 44,663 44,595 44,624 44,558 45,082 45,085
44,674 44,714 44,635 44,81 44,672 44,826 44,659 44,596 44,622 44,53 45,075 45,101
44,692 44,739 44,647 44,81 44,671 44,828 44,66 44,597 44,634 44,532 45,074 45,085
44,685 44,721 44,643 44,787 44,659 44,837 44,653 44,591 44,611 44,554 45,075 45,070
44,684 44,713 44,637 44,791 44,642 44,794 44,629 44,576 44,603 44,527 45,058 45,058
44,688 44,712 44,615 44,777 44,62 44,79 44,633 44,56 44,586 44,521 45,042 45,042
44,67 44,702 44,628 44,77 44,623 44,783 44,636 44,56 44,612 44,518 45,052 45,050
44,673 44,704 44,631 44,78 44,636 44,796 44,649 44,568 44,592 44,521 45,052 45,055
44,682 44,719 44,617 44,771 44,651 44,805 44,622 44,556 44,617 44,536 45,046 45,057
44,674 44,697 44,611 44,768 44,647 44,784 44,619 44,564 44,574 44,496 45,030 45,054
44,647 44,682 44,608 44,757 44,627 44,768 44,606 44,54 44,574 44,498 45,027 45,022
44,646 44,675 44,589 44,762 44,62 44,791 44,597 44,526 44,578 44,505 45,029 45,034
44,659 44,706 44,627 44,761 44,627 44,782 44,617 44,551 44,583 44,501 45,049 45,036
44,653 44,701 44,609 44,758 44,617 44,774 44,63 44,536 44,593 44,504 45,046 45,039
44,647 44,676 44,608 44,765 44,624 44,789 44,611 44,53 44,574 44,501 45,038 45,033
44,641 44,69 44,607 44,751 44,599 44,785 44,614 44,531 44,557 44,491 45,031 45,036
56
Table B3. Gravimetric measurement of the flow rate.
Weight [kg] 5,78 6,8 21,56 23,36 22,96 24,56 25,72 26,02 26,9 27,58
Time [s] 335 392 377 407 230 245 177 179 130 133
Mass flow [kg/s] 0,017254 0,017347 0,057188 0,057396 0,099826 0,100245 0,145311 0,145363 0,206923 0,207368
Volume flow [m3/s] 1,73E-05 1,74E-05 5,73E-05 5,75E-05 1E-04 0,0001 0,000146 0,000146 0,000207 0,000208
Volume flow[m3/h] 0,062212 0,062549 0,206206 0,206954 0,359947 0,361457 0,523953 0,524142 0,746111 0,747717
Table B4. Readings from flowmeter 2 & 3 during gravimetric measurement. Reference 3 2 Reference 3 2 Reference 3 2
0,0622 0,060 0,062 0,2070 0,204 0,207 0,5240 0,512 0,512
0,0622 0,061 0,062 0,2070 0,204 0,206 0,5240 0,519 0,519
0,0622 0,060 0,061 0,2070 0,203 0,207 0,5240 0,510 0,517
0,0622 0,060 0,061 0,2070 0,203 0,206 0,5240 0,516 0,525
0,0622 0,060 0,061 0,2070 0,200 0,203 0,5240 0,515 0,522
0,0622 0,061 0,062 0,2070 0,200 0,208 0,5240 0,520 0,532
0,0622 0,060 0,061 0,2070 0,201 0,206 0,5240 0,504 0,509
0,0622 0,060 0,061 0,2070 0,203 0,205 0,5240 0,511 0,518
0,0622 0,061 0,062 0,2070 0,204 0,205 0,5240 0,509 0,515
0,0622 0,060 0,062 0,2070 0,202 0,205 0,5240 0,520 0,524
0,0622 0,061 0,062 0,2070 0,203 0,206 0,5241 0,516 0,514
0,0622 0,061 0,062 0,2070 0,204 0,206 0,5241 0,515 0,520
0,0622 0,061 0,062 0,2070 0,206 0,208 0,5241 0,521 0,527
0,0622 0,061 0,062 0,2070 0,203 0,205 0,5241 0,518 0,524
0,0622 0,061 0,062 0,2070 0,205 0,207 0,5241 0,516 0,518
0,0622 0,061 0,062 0,2070 0,201 0,203 0,5241 0,519 0,531
0,0622 0,061 0,062 0,2070 0,206 0,208 0,5241 0,518 0,521
0,0622 0,060 0,061 0,2070 0,204 0,206 0,5241 0,521 0,528
0,0622 0,060 0,061 0,2070 0,203 0,204 0,5241 0,520 0,524
0,0622 0,060 0,061 0,2070 0,203 0,206 0,5241 0,516 0,526
0,0622 0,061 0,062 0,3599 0,356 0,364 0,5241 0,517 0,525
0,0622 0,060 0,061 0,3599 0,360 0,361 0,5241 0,521 0,531
0,0622 0,059 0,061 0,3599 0,357 0,361 0,5241 0,515 0,521
0,0622 0,060 0,062 0,3599 0,359 0,362 0,5241 0,519 0,525
0,0622 0,060 0,061 0,3599 0,357 0,362 0,5241 0,519 0,519
0,0622 0,060 0,061 0,3599 0,356 0,359 0,5241 0,512 0,521
0,0622 0,060 0,061 0,3599 0,358 0,359 0,5241 0,523 0,526
0,0622 0,060 0,061 0,3599 0,361 0,362 0,5241 0,514 0,512
0,0622 0,060 0,061 0,3599 0,358 0,364 0,5241 0,509 0,522
0,0622 0,060 0,061 0,3599 0,358 0,364 0,5241 0,518 0,524
0,0625 0,062 0,062 0,3599 0,355 0,363 0,5241 0,514 0,519
0,0625 0,059 0,062 0,3599 0,357 0,361 0,5241 0,513 0,514
0,0625 0,060 0,062 0,3599 0,361 0,366 0,5241 0,516 0,514
57
0,0625 0,060 0,062 0,3599 0,354 0,357 0,5241 0,516 0,520
0,0625 0,060 0,062 0,3599 0,359 0,364 0,5241 0,516 0,521
0,0625 0,061 0,062 0,3599 0,357 0,359 0,5241 0,514 0,512
0,0625 0,060 0,061 0,3599 0,358 0,360 0,5241 0,510 0,509
0,0625 0,061 0,062 0,3599 0,356 0,360 0,5241 0,517 0,516
0,0625 0,061 0,061 0,3599 0,358 0,362 0,5241 0,518 0,523
0,0625 0,060 0,062 0,3599 0,359 0,358 0,5241 0,515 0,520
0,0625 0,060 0,061 0,3599 0,356 0,360 0,7461 0,731 0,738
0,0625 0,060 0,061 0,3599 0,357 0,360 0,7461 0,727 0,737
0,0625 0,060 0,061 0,3599 0,357 0,364 0,7461 0,736 0,737
0,0625 0,060 0,061 0,3599 0,355 0,360 0,7461 0,743 0,756
0,0625 0,061 0,062 0,3599 0,359 0,364 0,7461 0,728 0,744
0,0625 0,061 0,061 0,3599 0,356 0,359 0,7461 0,731 0,748
0,0625 0,060 0,061 0,3599 0,350 0,357 0,7461 0,736 0,748
0,0625 0,060 0,061 0,3599 0,357 0,362 0,7461 0,737 0,751
0,0625 0,060 0,062 0,3599 0,356 0,361 0,7461 0,748 0,756
0,0625 0,061 0,062 0,3599 0,355 0,359 0,7461 0,729 0,735
0,0625 0,060 0,061 0,3615 0,356 0,361 0,7461 0,739 0,739
0,0625 0,060 0,060 0,3615 0,357 0,363 0,7461 0,737 0,745
0,0625 0,060 0,061 0,3615 0,358 0,361 0,7461 0,741 0,745
0,0625 0,061 0,061 0,3615 0,354 0,359 0,7461 0,728 0,739
0,0625 0,060 0,061 0,3615 0,361 0,363 0,7461 0,742 0,746
0,0625 0,060 0,061 0,3615 0,354 0,355 0,7461 0,744 0,746
0,0625 0,060 0,061 0,3615 0,354 0,362 0,7461 0,729 0,741
0,0625 0,061 0,062 0,3615 0,357 0,365 0,7461 0,745 0,750
0,0625 0,060 0,062 0,3615 0,360 0,364 0,7461 0,739 0,750
0,0625 0,060 0,061 0,3615 0,356 0,362 0,7461 0,730 0,730
0,2062 0,203 0,205 0,3615 0,357 0,362 0,7461 0,740 0,753
0,2062 0,205 0,207 0,3615 0,352 0,359 0,7461 0,729 0,733
0,2062 0,205 0,209 0,3615 0,358 0,362 0,7461 0,728 0,735
0,2062 0,204 0,206 0,3615 0,355 0,362 0,7461 0,741 0,755
0,2062 0,202 0,206 0,3615 0,358 0,362 0,7461 0,742 0,752
0,2062 0,204 0,207 0,3615 0,357 0,358 0,7461 0,746 0,752
0,2062 0,204 0,207 0,3615 0,353 0,361 0,7461 0,743 0,749
0,2062 0,202 0,205 0,3615 0,354 0,357 0,7461 0,732 0,740
0,2062 0,205 0,207 0,3615 0,358 0,362 0,7461 0,728 0,737
0,2062 0,205 0,208 0,3615 0,354 0,359 0,7461 0,744 0,748
0,2062 0,202 0,205 0,3615 0,356 0,361 0,7477 0,742 0,750
0,2062 0,205 0,207 0,3615 0,354 0,363 0,7477 0,745 0,756
0,2062 0,203 0,206 0,3615 0,355 0,361 0,7477 0,723 0,732
0,2062 0,204 0,207 0,3615 0,356 0,361 0,7477 0,726 0,735
0,2062 0,202 0,203 0,3615 0,352 0,359 0,7477 0,743 0,749
0,2062 0,204 0,207 0,3615 0,355 0,360 0,7477 0,731 0,739
58
0,2062 0,203 0,205 0,3615 0,354 0,360 0,7477 0,742 0,753
0,2062 0,201 0,204 0,3615 0,355 0,356 0,7477 0,735 0,739
0,2062 0,202 0,205 0,3615 0,359 0,361 0,7477 0,730 0,739
0,2062 0,203 0,205 0,3615 0,354 0,359 0,7477 0,735 0,747
0,2062 0,205 0,208 0,5240 0,520 0,524 0,7477 0,727 0,738
0,2062 0,206 0,207 0,5240 0,516 0,515 0,7477 0,740 0,747
0,2062 0,206 0,207 0,5240 0,515 0,520 0,7477 0,727 0,744
0,2062 0,202 0,205 0,5240 0,516 0,524 0,7477 0,744 0,753
0,2062 0,203 0,204 0,5240 0,510 0,523 0,7477 0,729 0,731
0,2062 0,204 0,205 0,5240 0,520 0,533 0,7477 0,742 0,752
0,2062 0,202 0,206 0,5240 0,512 0,515 0,7477 0,735 0,742
0,2062 0,203 0,206 0,5240 0,516 0,523 0,7477 0,739 0,741
0,2062 0,201 0,207 0,5240 0,515 0,524 0,7477 0,735 0,736
0,2062 0,203 0,205 0,5240 0,517 0,523 0,7477 0,725 0,734
0,2070 0,204 0,207 0,5240 0,515 0,523 0,7477 0,735 0,741
0,2070 0,205 0,207 0,5240 0,512 0,523 0,7477 0,736 0,747
0,2070 0,206 0,209 0,5240 0,518 0,529 0,7477 0,747 0,758
0,2070 0,205 0,207 0,5240 0,511 0,522 0,7477 0,745 0,759
0,2070 0,200 0,207 0,5240 0,512 0,521 0,7477 0,739 0,745
0,2070 0,204 0,207 0,5240 0,518 0,524 0,7477 0,732 0,739
0,2070 0,203 0,204 0,5240 0,513 0,516 0,7477 0,731 0,736
0,2070 0,202 0,205 0,5240 0,513 0,518 0,7477 0,736 0,747
0,2070 0,205 0,207 0,5240 0,516 0,519 0,7477 0,729 0,738
0,2070 0,204 0,208 0,5240 0,514 0,525 0,7477 0,740 0,752
59
Appendix – Data from the experiment Table C1. Measured mean temperatures of T-thermocouples, attached to the outer surface of the heat
exchanger.
Part T-thermocouple Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Run 11 Run 12
1
110, V1 40,2 39,13 38,3 37,95 36,85 36,28 - - - - - -
112, V2 38,43 37,67 37,01 36,89 35,83 35,35 - - - - - -
113, V3 37,18 36,7 36,12 36,19 35,16 34,75 - - - - - -
114, V4 35,73 35,48 35,09 35,34 34,38 34,05 - - - - - -
115, V5 34,86 34,61 34,34 34,73 33,81 33,55 - - - - - -
116, V6 33,88 33,72 33,58 34,12 33,26 33,04 - - - - - -
117, V7 32,8 32,87 32,89 33,55 32,72 32,6 - - - - - -
118, V8 31,99 31,81 32,06 32,9 32,13 32,08 - - - - - -
119, V9 30,73 30,65 31,04 32,07 31,34 31,35 - - - - - -
120, V10 29,43 29,7 29,85 31,01 30,28 30,38 - - - - - -
2
110, V1 29,4 29,55 30,09 30,84 31,11 31,24 31,93 32,26 32,43 32,38 34,34 34,54
112, V2 29,74 29,89 30,73 31,73 32,11 32,1 32,66 33,01 33,16 33,11 35,11 35,3
113, V3 30,71 31,14 32,17 33,17 33,48 33,27 33,73 34,05 34,19 34,08 35,93 36,11
114, V4 31,9 32,4 33,39 34,34 34,62 34,24 34,59 34,87 34,99 34,86 36,59 36,74
115, V5 33,42 33,88 34,9 35,87 36,11 35,48 35,65 35,92 36,05 35,87 37,41 37,54
116, V6 35,06 35,23 36,34 37,36 37,48 36,65 36,62 36,88 36,96 36,77 38,15 38,26
117, V7 36,13 36,69 37,95 39,2 39,19 38,05 37,81 37,98 38,05 37,86 39,04 39,12
118, V8 37,46 38,55 39,79 41,37 41,33 39,82 39,21 39,24 39,17 38,92 39,9 40,03
119, V9 39,53 41,09 41,94 43,62 43,88 42,14 41,18 41,02 40,72 40,36 40,97 41,07
120, V10 42,3 43,8 43,74 44,52 45 43,48 42,61 42,45 42,01 41,57 41,88 41,93
60
Table C2. Combined and separated uncertainties for each sensor at each run.
2
1
Part
12
0 [°C
]
11
9 [°C
]
11
8 [°C
]
11
7 [°C
]
11
6 [°C
]
11
5 [°C
]
11
4 [°C
]
11
3 [°C
]
11
2 [°C
]
11
0 [°C
]
2 [m
3/h]
3 [m
3/h]
10
5 [°C
]
10
4 [°C
]
10
3 [°C
]
10
2 [°C
]
12
0 [°C
]
11
9 [°C
]
11
8 [°C
]
11
7 [°C
]
11
6 [°C
]
11
5 [°C
]
11
4 [°C
]
11
3 [°C
]
11
2 [°C
]
11
0 [°C
]
2 [m
3/h]
3 [m
3/h]
10
5 [°C
]
10
4 [°C
]
10
3 [°C
]
10
2 [°C
]
Sen
sor
0,0
525
0,0
508
0,0
512
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
040
0,0
043
0,0
505
0,0
505
0,0
505
0,0
502
0,0
525
0,0
508
0,0
511
0,0
515
0,0
530
0,0
508
0,0
514
0,0
508
0,0
510
0,0
508
0,0
017
0,0
017
0,0
505
0,0
505
0,0
504
0,0
503
Ru
n 1
Total U
ncertain
ty, 𝑢
(𝑥)𝑐
0,0
525
0,0
508
0,0
512
0,0
516
0,0
531
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
040
0,0
043
0,0
505
0,0
505
0,0
505
0,0
503
0,0
525
0,0
508
0,0
511
0,0
515
0,0
530
0,0
508
0,0
514
0,0
508
0,0
510
0,0
508
0,0
017
0,0
017
0,0
505
0,0
505
0,0
504
0,0
503
Ru
n 2
0,0
525
0,0
509
0,0
512
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
040
0,0
043
0,0
505
0,0
505
0,0
504
0,0
505
0,0
525
0,0
508
0,0
511
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
017
0,0
017
0,0
505
0,0
505
0,0
505
0,0
503
Ru
n 3
0,0
525
0,0
508
0,0
512
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
040
0,0
043
0,0
506
0,0
505
0,0
504
0,0
503
0,0
525
0,0
508
0,0
511
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
017
0,0
017
0,0
506
0,0
505
0,0
505
0,0
503
Ru
n 4
0,0
526
0,0
509
0,0
512
0,0
515
0,0
530
0,0
508
0,0
514
0,0
508
0,0
510
0,0
508
0,0
040
0,0
043
0,0
505
0,0
506
0,0
504
0,0
505
0,0
525
0,0
508
0,0
511
0,0
515
0,0
530
0,0
508
0,0
514
0,0
508
0,0
510
0,0
508
0,0
017
0,0
017
0,0
505
0,0
505
0,0
504
0,0
503
Ru
n 5
0,0
526
0,0
509
0,0
512
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
040
0,0
050
0,0
505
0,0
506
0,0
504
0,0
505
0,0
525
0,0
508
0,0
511
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
017
0,0
017
0,0
506
0,0
505
0,0
505
0,0
503
Ru
n 6
0,0
525
0,0
508
0,0
512
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
040
0,0
043
0,0
505
0,0
505
0,0
504
0,0
503
- - - - - - - - - - - - - - - -
Ru
n 7
0,0
525
0,0
508
0,0
512
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
040
0,0
043
0,0
505
0,0
505
0,0
504
0,0
503
- - - - - - - - - - - - - - - -
Ru
n 8
0,0
525
0,0
508
0,0
512
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
040
0,0
043
0,0
505
0,0
505
0,0
504
0,0
503
- - - - - - - - - - - - - - - -
Ru
n 9
0,0
525
0,0
000
0,0
512
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
040
0,0
043
0,0
506
0,0
505
0,0
504
0,0
503
- - - - - - - - - - - - - - - -
Ru
n 1
0
0,0
525
0,0
508
0,0
511
0,0
515
0,0
530
0,0
508
0,0
514
0,0
508
0,0
510
0,0
508
0,0
040
0,0
043
0,0
505
0,0
505
0,0
504
0,0
502
- - - - - - - - - - - - - - - -
Ru
n 1
1
0,0
525
0,0
508
0,0
511
0,0
515
0,0
530
0,0
508
0,0
514
0,0
509
0,0
510
0,0
508
0,0
040
0,0
043
0,0
506
0,0
505
0,0
504
0,0
502
- - - - - - - - - - - - - - - -
Ru
n 1
2
61
0,0
015
0,0
018
0,0
014
0,0
015
0,0
014
0,0
014
0,0
013
0,0
014
0,0
013
0,0
012
0,0
001
0,0
001
0,0
012
0,0
015
0,0
026
0,0
012
0,0
006
0,0
008
0,0
008
0,0
008
0,0
008
0,0
009
0,0
008
0,0
009
0,0
008
0,0
008
0,0
000
0,0
000
0,0
008
0,0
006
0,0
006
0,0
016
Ru
n 1
Ran
do
m u
ncertain
ty, 𝑢
(𝑥)𝐴
0,0
021
0,0
024
0,0
029
0,0
033
0,0
031
0,0
027
0,0
023
0,0
018
0,0
009
0,0
007
0,0
001
0,0
001
0,0
007
0,0
021
0,0
028
0,0
021
0,0
009
0,0
010
0,0
009
0,0
010
0,0
000
0,0
011
0,0
010
0,0
011
0,0
011
0,0
011
0,0
001
0,0
001
0,0
011
0,0
010
0,0
019
0,0
024
Ru
n 2
0,0
026
0,0
028
0,0
025
0,0
023
0,0
020
0,0
019
0,0
018
0,0
018
0,0
018
0,0
009
0,0
001
0,0
001
0,0
009
0,0
027
0,0
017
0,0
056
0,0
009
0,0
010
0,0
011
0,0
011
0,0
012
0,0
012
0,0
011
0,0
012
0,0
013
0,0
013
0,0
001
0,0
001
0,0
012
0,0
009
0,0
032
0,0
026
Ru
n 3
0,0
020
0,0
020
0,0
019
0,0
018
0,0
020
0,0
019
0,0
016
0,0
017
0,0
017
0,0
016
0,0
002
0,0
001
0,0
017
0,0
022
0,0
016
0,0
028
0,0
006
0,0
008
0,0
008
0,0
009
0,0
009
0,0
011
0,0
011
0,0
013
0,0
014
0,0
017
0,0
001
0,0
001
0,0
020
0,0
006
0,0
035
0,0
035
Ru
n 4
0,0
035
0,0
034
0,0
027
0,0
023
0,0
018
0,0
015
0,0
012
0,0
011
0,0
010
0,0
009
0,0
001
0,0
001
0,0
009
0,0
036
0,0
016
0,0
055
0,0
008
0,0
009
0,0
009
0,0
009
0,0
009
0,0
009
0,0
009
0,0
010
0,0
012
0,0
012
0,0
001
0,0
001
0,0
011
0,0
008
0,0
012
0,0
022
Ru
n 5
0,0
032
0,0
030
0,0
024
0,0
020
0,0
017
0,0
015
0,0
014
0,0
014
0,0
014
0,0
009
0,0
001
0,0
025
0,0
009
0,0
033
0,0
014
0,0
052
0,0
007
0,0
008
0,0
009
0,0
010
0,0
010
0,0
010
0,0
011
0,0
014
0,0
015
0,0
016
0,0
001
0,0
002
0,0
014
0,0
007
0,0
029
0,0
030
Ru
n 6
0,0
016
0,0
014
0,0
014
0,0
013
0,0
013
0,0
013
0,0
012
0,0
012
0,0
011
0,0
009
0,0
001
0,0
003
0,0
009
0,0
017
0,0
012
0,0
020
- - - - - - - - - - - - - - - -
Ru
n 7
0,0
013
0,0
013
0,0
012
0,0
012
0,0
012
0,0
011
0,0
012
0,0
012
0,0
014
0,0
012
0,0
001
0,0
002
0,0
012
0,0
014
0,0
012
0,0
018
- - - - - - - - - - - - - - - -
Ru
n 8
0,0
014
0,0
013
0,0
012
0,0
012
0,0
013
0,0
012
0,0
012
0,0
012
0,0
011
0,0
011
0,0
002
0,0
003
0,0
011
0,0
014
0,0
014
0,0
019
- - - - - - - - - - - - - - - -
Ru
n 9
0,0
019
0,0
018
0,0
015
0,0
014
0,0
015
0,0
013
0,0
012
0,0
012
0,0
013
0,0
012
0,0
002
0,0
002
0,0
013
0,0
019
0,0
014
0,0
029
- - - - - - - - - - - - - - - -
Ru
n 1
0
0,0
010
0,0
010
0,0
010
0,0
010
0,0
010
0,0
011
0,0
011
0,0
011
0,0
011
0,0
011
0,0
002
0,0
003
0,0
011
0,0
010
0,0
010
0,0
013
- - - - - - - - - - - - - - - -
Ru
n 1
1
0,0
012
0,0
012
0,0
012
0,0
012
0,0
012
0,0
012
0,0
012
0,0
012
0,0
013
0,0
013
0,0
003
0,0
003
0,0
013
0,0
012
0,0
011
0,0
013
- - - - - - - - - - - - - - - -
Ru
n 1
2
0,0
525
0,0
508
0,0
511
0,0
515
0,0
530
0,0
508
0,0
514
0,0
508
0,0
510
0,0
508
0,0
040
0,0
043
0,0
505
0,0
504
0,0
504
0,0
502
0,0
525
0,0
508
0,0
511
0,0
515
0,0
530
0,0
508
0,0
514
0,0
508
0,0
510
0,0
508
0,0
017
0,0
017
0,0
505
0,0
504
0,0
504
0,0
502
Sy
stematic
un
certainty
,
fozzilied
, 𝑢
(𝑥)
62
Appendix – CFD
Greywater module
Note: Flow direction is upwards in all the results from greywater module simulations.
Pressure contour
Figure D1. Pressure contour at 0,5 liters per minute for Greywater module.
Figure D2. Pressure contour at 1 liter per minute for Greywater module.
63
Figure D3. Pressure contour at 1,5 liters per minute for Greywater module.
Figure D4. Pressure contour at 2,0 liters per minute for Greywater module.
64
Velocity contour
Figure D5. Velocity contour at 0,5 liters per minute for Greywater module.
Figure D6. Velocity contour at 1,0 liter per minute for Greywater module.
65
Figure D7. Velocity contour at 1,5 liters per minute for Greywater module.
Figure D8. Velocity contour at 2,0 liters per minute for Greywater module.
Directional velocity contours
Axial orientation of directional velocities:
• velocity u is in the X - direction, the cross-section of the heat
exchanger
• velocity v is in the Y – direction, along the heat exchanger, in main
flow direction
• velocity w is in the Z – direction. cross-section of the heat exchanger
66
Figure D9. Velocity u contour at 0,5 liters per minute for Greywater module.
Figure D10. Velocity u contour at 1,0 liter per minute for Greywater module.
67
Figure D11. Velocity u contour at 1,5 liter per minute for Greywater module.
Figure D12. Velocity u contour at 2,0 liters per minute for Greywater module.
68
Figure D13. Velocity v contour at 0,5 liters per minute for Greywater module.
Figure D14. Velocity v contour at 1,0 liter per minute for Greywater module.
69
Figure D15. Velocity v contour at 1,5 liters per minute for Greywater module.
Figure D16. Velocity v contour at 2,0 liters per minute for Greywater module.
70
Figure D17. Velocity w contour at 0,5 liters per minute for Greywater module.
Figure D18. Velocity w contour at 1,0 liter per minute for Greywater module
71
Figure D19. Velocity w contour at 1,5 liters per minute for Greywater module
Figure D20. Velocity w contour at 2,0 liters per minute for Greywater module
72
Velocity vector
Figure D21. Velocity vectors at 0,5 liter per minute in the Greywater module.
Figure D22. Velocity vectors around the annular groove in the Greywater module for 0,5 liter per minute.
73
Freshwater module
Note: Flow direction is downwards in all the results from freshwater module simulations.
Pressure contour
Figure D23. Pressure contour at cross-section 1 in freshwater stream for flow rates 0,5, 1, 1,5 & 2 liters per
minute. Presented in the same order.
Figure D24. Pressure contour at cross-section 2 in freshwater stream for flow rates 0,5, 1, 1,5 & 2 liters per
minute. Presented in the same order.
74
Figure D25. Pressure contour at cross-section 3 in freshwater stream for flow rates 0,5, 1, 1,5 & 2 liters per
minute. Presented in the same order.
Velocity contour
Figure D26. Velocity contour at cross-section 1 in freshwater stream for flow rates 0,5, 1, 1,5 & 2 liters
per minute. Presented in the same order.
75
Figure D27. Velocity contour at cross-section 2 in freshwater stream for flow rates 0,5, 1, 1,5 & 2 liters
per minute. Presented in the same order.
Figure D28. Velocity contour at cross-section 3 in freshwater stream for flow rates 0,5, 1, 1,5 & 2 liters per minute. Presented in the same order.
76
Directional velocity contour
Axial orientation of directional velocities:
• velocity u is in the X - direction, the cross-section of the heat
exchanger
• velocity v is in the Y – direction, along the heat exchanger, in main
flow direction
• velocity w is in the Z – direction. cross-section of the heat exchanger
Figure D29. Velocity v contour at cross-section 2 in freshwater stream for flow rates 0,5, 1, 1,5 & 2 liters per minute. Presented in the same order.
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