Experimental validation of a periodic heat transfer CFD model ...

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]

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

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

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

Where: 𝐷ℎ is the hydraulic diameter, 𝑢 is the average velocity and 𝑣 is the kinematic viscosity of

the fluid.

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 =

where h is the convective heat transfer coefficient.

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

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

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]:

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

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

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.

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].

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

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

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 =

• 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:

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

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

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.

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.

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

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

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.

pipe –

exterior

pipe –

Interior

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.

pipe –

Interior

pipe –

exterior

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.

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

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.

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

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.

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

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 - - - - - -

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,

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.

Measure

Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run

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

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.

[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

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

V1 V2 V3 V4 V5 V6 V7 V8 V9 V10

T-thermocouple

Run 12

Run 11

Run 10

[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

V1 V2 V3 V4 V5 V6 V7 V8 V9 V10

T-thermocouple

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

Overall heat transfer coefficient at different flow rates

Part 1

Part 2

Volume flow [l/min]

7 6 5 4 3 2 1 0

Overall heat transfer coefficient of the lower regime

Part 1

Part 2 - Part 1

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 0,5 1 1,5 2 2,5 3 3,5

NTU [-]

Part 1

Part 2 Effe

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

Ratio of overall heat transfer coefficient and pressure drop

Part 2

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.

[l/min]

Mass flow rate

[kg/s]

Reynolds

number

Velocity [m/s] Surface heat

transfer

coefficient

[W/m²K]

Nusselt

number

Outgoing

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.

[l/min]

Mass flow rate

[kg/s]

Reynolds

number

Velocity [m/s] Surface heat

transfer

coefficient

[W/m²K]

Nusselt

number

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

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

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

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)

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.

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

40 Data from Kiwa

Simulated & extrapolated results

0 2 4 Vol6ume flow [l/m8 in] 10 12 14

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

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

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

Overall heat transfer coefficient

Experiment

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

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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

20 25 30 35 40 45 50 55 60

Fluke 1551A Ex Temperature [°C]

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.

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

Avereage temperature of 110-115 vs reference

25 30 35 40 45

Average temperature of 104 & 105 [°C]

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

Figure A3. Deviation of average temperature given by T-thermocouple 116-120 and 104 & 105, at

Average temperature of 104 & 105 [°C]

45 40 35 30 25

0,6 0,5

Average temperature of 116-120 vs reference

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.

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

-0,001 0

-0,002

Deviation of flowmeter 2 & 3 vs reference

Gravimetric flow [m3/h] -0,002

0,8 0,7 0,5 0,6 0,4 0,2 0,3 0,1 0

Deviation of flowmeter 2 & 3 vs reference

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

-0,010 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]

Appendix - Calibration Raw Data Table B1. Raw data used for calibration of T-thermocouple 102-105

Reference

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

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

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

104 –

Corrected

105 –

Corrected

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

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

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

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

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

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

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

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 - - - - - -

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

Table C2. Combined and separated uncertainties for each sensor at each run.

0 [°C

9 [°C

8 [°C

7 [°C

6 [°C

5 [°C

4 [°C

3 [°C

2 [°C

0 [°C

5 [°C

4 [°C

3 [°C

2 [°C

0 [°C

9 [°C

8 [°C

7 [°C

6 [°C

5 [°C

4 [°C

3 [°C

2 [°C

0 [°C

5 [°C

4 [°C

3 [°C

2 [°C

Total U

ncertain

ty, 𝑢

(𝑥)𝑐

- - - - - - - - - - - - - - - -

ncertain

ty, 𝑢

(𝑥)𝐴

- - - - - - - - - - - - - - - -

stematic

certainty

fozzilied

, 𝑢

(𝑥)

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.

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.

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

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.

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.

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.

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

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

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.

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.

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.

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.

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.

Figure D30. Velocity w 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.

Velocity Vector

Figure D31. Velocity vector at the helical string in the freshwater stream at 0,5 liters per minute.

Experimental validation of a periodic heat transfer CFD model ...

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