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Numerical study of a ventilation system based on wallconfluent jetsSetareh Janbakhshab & Bahram Moshfeghab

a Department of Management and Engineering, Linköping University, SE 581 83 Linköping,Swedenb Department of Building, Energy and Environmental Engineering, University of Gävle, SE80176 Gävle, SwedenAccepted author version posted online: 31 Aug 2014.Published online: 05 Nov 2014.

To cite this article: Setareh Janbakhsh & Bahram Moshfegh (2014) Numerical study of a ventilation system based on wallconfluent jets, HVAC&R Research, 20:8, 846-861, DOI: 10.1080/10789669.2014.957111

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HVAC&R Research (2014) 20, 846–861Copyright C© 2014 ASHRAE.ISSN: 1078-9669 print / 1938-5587 onlineDOI: 10.1080/10789669.2014.957111

Numerical study of a ventilation system based on wallconfluent jets

SETAREH JANBAKHSH1,2,∗ and BAHRAM MOSHFEGH1,2

1Department of Management and Engineering, Linkoping University, SE 581 83 Linkoping, Sweden2Department of Building, Energy and Environmental Engineering, University of Gavle, SE 80176 Gavle, Sweden

This study presents numerical investigation of an air supply device based on wall confluent jets in a ventilated room. Confluent jetscan be described as multiple round jets issuing from supply device apertures. The jets converge, merge, and combine at a certaindistance downstream from the supply device and behave as a united jet, or so-called confluent jet. The numerical predictions ofthe velocity flow field of isothermal confluent jets with three Reynolds-averaged Navier–Stokes turbulence models (renormalizationgroup k-ε, realizable k-ε, and shear stress transport k-ω) are reported in the present study. The results of the numerical predictionsare verified with detailed experimental measurements by a hot wire anemometer and constant temperature anemometers for twoairflow rates. The box method is used to provide the inlet boundary conditions. The study of the airflow distribution shows that aprimary wall jet (wall confluent jet) exists close to the supply device along the wetted wall, and a secondary wall jet is created afterthe stagnation region along the floor. It is presented that the flow field of the primary and secondary wall jet predicted by turbulencemodels is in good agreement with the experimental data. The current study is also compared with the literature in terms of velocitydecay and the spreading rate of the primary and secondary wall jet, the results of which are consistent with each other. Velocity decayand the spreading rate of the secondary wall jet in vertical and lateral directions were studied for different inlet airflow rates andinlet discharge heights. The comparative results demonstrate that the flow behavior is nearly independent of the inlet flow rate. Inletdischarge height is found to have impact close to the inlet, where the velocity decays faster when the jet discharges at higher level. Thedecay tendency is similar as the jet enters into the room for all discharge heights.

Introduction

During the past two decades, the global demand for primaryenergy has doubled, and during the same time, the demand forelectrical energy has tripled. As a result, the need for choos-ing the right energy conservation measures to reduce electricalenergy usage in the built environment is very crucial. Ventila-tion systems, thermal comfort, and air quality within the builtenvironment are important issues as they are related to bothenergy conservation and the health of the occupants. Poor in-door environment conditions, e.g., in offices and classrooms,cost large amounts of money in healthcare and have an effecton users’ sustained cognitive functioning, administration, andlost productivity; see, e.g., Wargocki and Seppanen (2007). Itis obvious that proper distribution of air is an important issuefor the comfort and air quality of indoor spaces. Supply air-flow from an improper supply device can cause drafts in theoccupied zone. To overcome the problems related to the healthof the occupants and to reduce energy usage, a new ventilation

Received September 23, 2013; accepted March 7, 2014Setareh Janbakhsh, Student Member ASHRAE, is a PhD Stu-dent. Bahram Moshfegh, PhD, is a Professor.∗Corresponding author e-mail: setareh.janbakhsh@liu.seColor versions of one or more of the figures in the article can befound online at www.tandfonline.com/uhvc.

system—confluent jets—has been proposed (Cho et al. 2008;Janbakhsh and Moshfegh 2014). In ventilation, confluent jetscan be described as multiple round jets issuing from supplydevice apertures. The jets converge, merge, and combine at acertain distance downstream and behave as a united jet, orso-called confluent jet.

Recently the flow behavior of the multiple interacting jets(confluent jets) was investigated with different techniques,both numerically and experimentally, in the region close tothe nozzle exits by Ghahremanian and Moshfegh (2014a,2014b) and Ghahremanian et al. (2014a, 2014b). In 2008,Cho et al. (2008) experimentally and numerically investigatedthe characteristic of the wall confluent jets (WCJ). Cho et al.(2008) claimed that the flow behavior of the WCJ can beclassified as the combination of three regions: the free jetregion, Coanda effect region, and wall region. Within thefree jet region, due to entrainment, the maximum velocityat the jet centerline is higher than that for the near wallregion. In the Coanda effect region, the maximum velocityfor the centerline is lower for the near wall region. Withinthe Coanda effect region, the combined jets behave as a walljet with a tendency to attach to the wall, where the confluentpattern also starts from this region onward. Finally the wallregion consists of two sub-regions: a wall jet region and animpingement region, where the maximum velocity decay forboth regions is similar in specific range (Cho et al. 2008).The authors (Janbakhsh and Moshfegh 2014) experimentally

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investigated the flow behavior of isothermal and non-isothermal WCJ in a mock-up office environment. In the lastdecade, the WCJ ventilation system has been used in differentbuildings (Cho et al. 2008; Janbakhsh and Moshfegh 2014;Janbakhsh et al. 2010; Karimipanah et al. 2007). It was foundthat the air from ventilation systems based on confluent jetscan reach a longer distance due to the low decay of velocity.

The prediction of room air movement began in 1970, andlater research studies have been presented by using compu-tational fluid dynamics (CFD) in an enclosed environment,some of which are cited here (Awbi 1989; Baker et al. 1994;Cho et al. 2008; Janbakhsh and Moshfegh 2014; Jones andWhittle 1992; Karimipanah et al. 2007; Karimipanah andMoshfegh 2007; Nielsen 1975, 1998; Williams et al. 1994a,1994b; Zhai 2006). In the current investigation, the CFD tech-nique, a cost-effective tool, is employed to predict the air dis-tribution issuing from the supply device into the room, andthe numerical results are then compared with the detailed ex-perimental data.

Turbulence models, the numerical scheme, and boundaryconditions are the most important factors to achieve accurateCFD simulation results. Zhai et al. (2007) and Zhang et al.(2007) evaluated different turbulence models in predictingairflow and turbulence in an enclosed environment, andthe results were compared with experimental data fromprevious literature. Most of the numerical studies on ven-tilation flows for indoor environment have been done withReynolds-averaged Navier–Stokes (RANS) equations. RANSturbulence models are divided into the Reynolds stress model(RSM) and eddy-viscosity models with two equations. In1996, Chen compared the eddy-viscosity standard k-ε modeland the RSM for room air motion. It was concluded that thedifference between the results of numerical prediction for thesetwo turbulence models are small, while the great concern ofRSM is its high computational cost. The different k-ε modelsfor prediction of indoor airflow were also examined by Chen(1995). The results showed that all turbulence models couldaccurately predict the mean velocity. He also recommendedthe use of the renormalization group (RNG) k-ε model. Thestudy by Rohdin and Moshfegh (2007) indicated that the RNGk-ε model is one of the most concurrent with the measuredresult of the airflow pattern and temperature distribution inlarge industrial premises. In 2004, the prediction of the wall jetflow was analyzed by Luo and Roux (2004), where the resultspredicted by the RNG k-ε showed good consistency with themeasurements. They also found that the RNG k-ε model isvery robust and that calculation converges smoothly for thestudied supply device. Stamou and Katsiris (2006) showedthat the main qualitative feature of the flow can satisfactorilybe predicted by the two-equation eddy-viscosity models. Theyalso presented that the shear stress transport (SST) k-ω modelcan predict slightly better results of velocity and temperaturedistributions in a model office. Rohdin and Moshfegh (2007)predicted the flow pattern in a large industrial facility andan office, respectively, with the realizable k-ε model, withgood agreement with the experiment. Thus, in the currentstudy, three two-equation eddy-viscosity models (RNG k-ε,realizable k-ε, and SST k-ω) are used for numerical prediction

of the airflow inside a ventilated model room by a WCJ supplydevice.

In the simulation of a supply device with complex geom-etry, a preferred method is to mimic the model with a lesscomplicated geometry that replicates supply device perfor-mance (Chen and Srebric 2001; Hawkins et al. 1995; Nielsen2004). A proper simplification of the supply device configura-tion can significantly reduce the computational cost. Previousstudies (Gosman et al. 1980; Nielsen 1992, 1997; Skovgaardand Nielsen 1991; Srebric and Chen 2002) described differentmethods, such as momentum, box, prescribed, and direct, allof which are used to specify the inlet boundary conditions fora complex geometry. Chen and Srebric (2001) recommendedthe box method for inlet boundary conditions of the nozzlesupply device. The box method is chosen for the present studybased on the previous investigations on wall jets (Nielsen 1992,1997; Srebric and Chen 2002).

The aim of this article is to investigate numerically theairflow pattern created from the WCJ supply device. The pre-dicted result by three RANS turbulence models (RNG k-ε,realizable k-ε, and SST k-ω) are verified with the experimentaldata. The results of the investigation explore the jet velocityprofile and flow field of the jet below the inlet wall as well asover the floor. The velocity decay and spreading rate of thejet are also compared with the experimental results from theliterature. Finally, the effect of the inlet airflow rate and inletdischarge height are investigated in terms of the velocity decayand spreading rate of the jet over the floor.

This is an on-going research project, and the authors’ in-tention is to investigate not only the nonisothermal WCJ ven-tilation but also the performance of WCJ ventilation withother conventional ventilation systems. The configuration ofthe WCJ, e.g., the diameter, number, and the shape of the noz-zles, will be investigated in detail to explore the optimal designof the present WCJ supply device.

Physical model

Room configuration

Measurements were carried out in a well-insulated test roomwith the same dimensions as the numerical model, located inthe Laboratory of Ventilation and Air Quality at the Centre forBuilt Environment, University of Gavle, Sweden. The roomhas the dimensions length (L) of 4.2 m (13.77 ft), width (W ) of3.6 m (11.81 ft), and height (H) of 2.5 m (8.20 ft). Concerningthe test room, it is a climate chamber designed for experimentalstudy of indoor environment for an office module. Air entersthe room through the WCJ supply device or the computationalbox and exits from the exhaust with an area of 0.062 m2 (0.66ft2); see Figure 1a. The exhaust was located on the same wallas the inlet at the upper corner.

Configuration of supply device for experimental study

The air issues from the 92 round jets that are placed in astaggered array of 4 × 23. Each nozzle has a diameter ofd = 0.0056 m (0.22 in.) and spacing between center to center

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Fig. 1. Physical model. a. Sketch of the test room, WCJ supplydevice, and computational box. b. WCJ supply device with sketchof the array. c. Computational grid.

of each nozzle in the same row is 17 mm (0.67 in.) and betweentwo parallel rows is 18 mm (0.70 in.). The schematic of thesupply device and details of the spacing between nozzles canbe seen in Figures 1a and 1b. The air supply device based onWCJ was mounted at height 1.9 m (6.23 ft) above the floorwith jets issuing downward. The z-axis is parallel to the axialdirection of the jets in which its positive direction is orientedtoward the floor. The x-axis is normal to the inlet wall towardthe test room, and the y-axis is parallel to the inlet wall where

the positive direction is toward the exhaust. The center of thecoordinate system (0, 0, 0) is located on the middle of the inletwall (y = 0) at the nozzle exit height (z = 0) and where it isattached to the inlet wall (x = 0). The nozzle plate is 0.4 m (1.31ft) wide (in the y-direction) and sticks out into the room by0.08 m (0.26 ft) (in the x-direction). The Cartesian coordinatesystem is sketched in Figures 1a and 1b.

Configuration of supply device for computational study

The box method was used to replace the actual diffuser with asimple geometry, in order to collect inlet boundary conditions.Based on the ASHRAE standard (ASHRAE 2009, p. 6), “thebox method does not require as fine a grid as fully numericalprediction of the wall jet development.” The suitable box sizewould be found where the jets merged. The box size mustbe small enough to avoid the effect of room dimensions, andplumes and must be larger than the domain with entrainment.In this study, the suitable distance was chosen at the combinedregion of the confluent jets (Ghahremanian and Moshfegh2014b; Ghahremanian et al. 2014a). Visualization andvelocity measurement were carried out to find the suitabledistance of the inlet plane from the nozzle exit. Two differentbox sizes were studied for Q = 0.015 m3/s (0.52 ft3/s): thesmall box (x = 0.10 m (0.32 ft), y = 0.53 m (1.73 ft), z =0.09 m (0.29 ft)) and the large box (x = 0.10 m (0.32 ft), y =0.53 m (1.73 ft), z = 0.29 m (0.95 ft)). The results of numericalprediction for both boxes were in good agreement; therefore,the small box (x = 0.10 m (0.32 ft), y = 0.53 m (1.73 ft), z =0.09 m (0.29 ft)) was chosen in this study; see Figure 1a.

Computational setup and numerical procedure

Governing equations

A steady state three-dimensional model is considered for ana-lyzing the flow in the whole room. The airflow is assumed to beincompressible. Based on these assumptions, RANS equationsare given by

∂Ui

∂xi= 0, (1)

∂(ρUj Ui

)∂xj

= −∂ P∂xi

+ μ∇2Ui + ∂

∂xj

(−ρu ′

i u′j

), (2)

where u′i u

′j is the Reynolds stress. The term (u′

i u′j ) must be

modeled to close the system of equations. The most popularmodel to approximate Reynolds stress is based on the Boussi-nesq hypothesis:

ρu ′i u

′j = −2μt Si j + 2

3δi jρk, (3)

Si j = 0.5(

∂Ui

∂xj+ ∂Uj

∂xi

), (4)

where k is the turbulent kinetic energy and μt is the eddyviscosity. The most common method to derive μt is to combine

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turbulence kinetic energy k and its dissipation rate ε by μt =Cμρ k2

εor, with specific dissipation rate ω, by μt = k

ω. Thus,

two additional transport equations for k, ε, or ω need to besolved.

Turbulence modeling

Two turbulence models based on k-ε and one model based onk-ω are used for the numerical prediction of the airflow insidethe test room.

The models can be written in a general form as follows:

ρ∂φ

∂t+ ρu j

∂φ

∂xj− ∂

∂xj

[�φ,e f f

∂φ

∂xj

]= S∅, (5)

where φ represents a variable, �φ,e f f the effective diffusioncoefficient, and S∅ the source term. The mathematical expres-sion, constant, and coefficient for the turbulence models usedin this study are summarized in Table 1. The table introducessome variables and coefficients, such as P is the turbulenceproduction, S is the rate of strain, Y is the dissipation term inthe k and ω equation, F1 and F2 are blending functions, Dω

is produced from the transformed k-ε model, and σ denotessthe turbulence Prandtl numbers.

The RNG k-ε model was presented by Yakhot andOrszag (1986). The model was derived from the instantaneousNavier–Stokes equations, using the mathematical techniquecalled the RNG method (ANSYS 2010a). The RNG k-ε modelimproves the accuracy of the prediction of k by employing anadditional term in the ε equation. The low Reynolds numbereffects for flow treatment near the wall regions is included inthe RNG k-ε. The RNG k-ε shows the best accuracy for mix-ing and forced convection with low turbulence levels (Zhanget al. 2007). Details about the RNG k-ε model can be foundin Moshfegh and Nyiredy (2004).

The realizable k-ε model was developed by Shih et al.(1995). Realizable means that the model satisfies certain math-ematical constraints on the Reynolds stresses (ANSYS 2010a).The model included two important developments: a new for-

mula for eddy viscosity and a transport equation for modelingε (ANSYS 2010a; Shih et al. 1995). The realizable k-ε model isuseful for predicting the spreading rate of both round jets andplanar jets and can also provide good result for flows involvingrotation and recirculation (ANSYS 2010a).

In this study, the enhanced wall treatment (EWT) has beenused. The EWT subdivides the near wall region into a viscoussub-layer and a fully turbulent flow.

The SST k-ω model was developed by Menter (1994). Themodel is formulated based on the standard k-ω and the k-εmodel. The blending functions are designed for switching be-tween the standard k-ε model in the bulk flow and the standardk-ω model near the wall.

Boundary conditions

Velocity component w in the z-direction was measured andthen used for the inlet boundary condition (Figure 2). Velocitywas measured at plane xy below the WCJ supply device wherethe jet is dominating in the z-direction (Figure 1a), while theother box surfaces use a free boundary with zero gradientsfor flow parameters (Nielsen 1997). The turbulent kineticenergy and its dissipation are obtained by using the followingequations:

k = 32

(wTu)2, (6)

ε = C3/4μ k3/4

l, (7)

where Tu is the turbulence intensity of the measured w, Cμ isan empirical constant (0.09), and l is the length scale (ANSYS2010b; ASHRAE 2009). Specific dissipation rate was deter-mined in the k-ω turbulence model from equation ω = ε/k. Apressure outlet was chosen as for outlet boundary condition.The internal and external walls were assumed adiabatic withno-slip conditions.

Table 1. Coefficient and Constant for two equation models.

φ �φ,e f f S∅ Constant and coefficients

RNG k-ε k, ε μ + μt/σk,μ + μt/σε

Pk − ρε,Cε1 Pκε/k − C∗

ε2ρε2/kμt = Cμρ k2

ε, Pk = μt S2, S ≡ √

2Si j Si j ,

C∗ε2 ≡ Cε2 + Cμη3

(1−η/η0

)1+βη3 , Cε1 = 1.42, Cε2 = 1.68,

Cμ = 0.0845, η = Skε, η0 = 4.38, β = 0.012,

σk = σε = 0.7194

Realizable k-ε k, ε μ + μt/σk,μ + μt/σε

Pk − ρε,ρC1Sε − ρC2

ε2

k+√νε

μt = Cμρ k2

ε, C1 = max

[0.43,

η

η+5

], η = Sk

ε,

S ≡ √2Si j Si j , C2 = 1.9, σk = 1.0, σε = 1.2

SST k-ω k, ω μ + μtσk

,μ + μt/σω

Pk − Yk, Pω − Yω + Dω μt = ρkω

1max[1/α∗,SF2/a1ω] , Pk = min (Pk, 10ρβ∗kω),

Pω = ραPkμt

, Yk = ρβ∗kω, Yω = ρβω2,

Dω = 2 (1 − F1) ρσω21ω

∂k∂xj

∂ω∂xj

, σk1 = 1.176,σω1 = 2.0, σk2 = 1.0, σω2 = 1.168, α1 = 0.31,βi,1 = 0.075, βi,2 = 0.0828, β∗ = 0.090

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Fig. 2. Contour of measured velocity w (m/s) and turbulence intensity Tu (%) at z = 0.09 for Q = 0.015 m3/s (0.52 ft3/s). a and b.0.0195 m3/s (0.68 ft3/s). c and d. 1 m = 3.28 ft (1 m/s = 3.28 ft/s).

Numerical details

The finite-volume solver Fluent 13.0 (ANSYS 2010a) wasused to numerically predict the governing equations with asegregated scheme. The pressure–velocity coupling was con-trolled by the SIMPLE algorithm. The governing equationswere discretized spatially with a second-order upwind schemefor nonlinear terms and second-order central scheme for vis-cous terms. The under-relaxation factors for pressure and mo-mentum were set to 0.7 and 0.3, respectively. The solutionswere considered converged when the relative change of anylocal variable between two consecutive iterations was below10−5.The predictions were performed on a high-performancecluster with two processors, each of which consisted of fourcores and 32 GB of system memory.

Grid resolution

In this study, three-dimensional hexahedral cells have beenprovided by ANSYS meshing 13.0 (ANSYS 2010c). Mesh in-dependency has been achieved by using a refined grid (1.4,4.5, 6.3, and 7.3 million) in areas with sharp gradients. Thelast two grids presented fairly similar results; therefore, thegrid consisting of 6.3 million (Figure 1c) structured hexahe-dral cells was chosen to be used in this article. It must also beaddresed that one advantage of structured hexahedral meshis providing a smooth converge solution. The grid is refinedenough near the solid walls to solve all boundary layers withthe two-layer model. y+ was kept less than one near the walls.

Experimental procedure

A 55P11 constant temperature hot wire anemometer (HWA)made by Dantec was placed on a 3D traversing system forcapturing velocity profiles below the supply device and over

the floor. The single wire probe has a 5-μm (0.0002-in.) diam-eter and is 1.25 mm (0.05 in.) long. The calibration was doneby low- and high-speed open-loop wind tunnels. Velocity cali-bration data were fit to a fourth-order polynomial least squareregression. National Instrument NI USB-6215 was used forcontrol data. The HWA measured air velocity with a samplingrate of 100 Hz with 18,000 samples with accuracy ±0.04 m/s(0.13 ft/s). The velocity in the z-direction was measured atdifferent lines below the WCJ supply device by the HWA. Thevelocity in the x-direction was also measured over the floor bythe HWA. The velocity profile at a different location from theinlet wall was recorded along the z-direction by the HWA. Asummary of the measurement lines and the flow pattern in theprimary and secondary regions developed by the WCJ can beseen in Figure 3.

Analyzing the wall jet behavior along the floor (x-direction)has also been obtained by using an omnidirectional con-stant temperature anemometer (CTA; Lundstrom et al. 1990).The CTA probes were connected to a multichannel system,which easily interfaces to a PC. The CTA probes used inthis study can measure the low-velocity airflow with an ac-curacy of ±0.05 m/s (0.16 ft/s). The CTA velocity measure-ment was carried out at 2-sec intervals for a total of 150samples. The CTA probes were calibrated within the rangebetween 0.05–1.2 m/s (0.16–3.93 ft/s). The temperature ofthe calibration room was kept constant during the calibrationperiod.

During the measurement, the temperature difference be-tween the inlet and the test room was less than 1◦C(33.8◦F). The room temperature was controlled by 80 type-T thermocouples (copper-constantan) with an accuracy of±0.1◦C (32.18◦F). The thermocouples were connected to adata acquisition device (Agilent 34970), which is controlledby computer to register the data. All measurements werecarried out when the test room reached the steady-statecondition.

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Fig. 3. Measured lines and flow pattern in primary and secondary regions of WCJ ventilation.

The velocity measurements by the HWA and CTA wererepeated for some lines, and the recorded data were matchedtogether.

Case studies

Two verification cases with different airflow rates are numer-ically predicted and compared with the measurement data inthis study. Six more different cases are also modeled to findthe dependency of the WCJ on inlet air flow rate and inlet dis-

Table 2. Case studies.

CaseInlet airflow rate

(m3/s)Inlet height above

the floor (m)

Verification 0.015 1.810.0195

Effect of airflow rate 0.0125 1.810.0150.01750.0195

Effect of dischargeheight

0.015 2.01

1.811.61

charge height. The details of this investigation are presentedin Table 2.

Results and discussion

Verification with experimental studies

Profile and velocity decay of the jetThe velocity profile and jet velocity decay predicted from thethree RANS turbulence models (RNG k-ε, realizable k-ε, andSST k-ω) are compared with the measured lines below theinlet (z-direction) and along the floor (x-direction) in the ver-tical mid-plane (see Figures 4, 6, and 7, presented later). Thedetail of the measured lines can be seen in Figure 3. The studyof the flow field confirms the existence of three-dimensionalflow characteristics of the jet. A primary and a secondarythree-dimensional wall jet are revealed in the test room, wherethe former main axis is along the inlet wall (z-direction) andthe latter centerline is along the floor (x-direction). The gen-eral flow pattern of the presented WCJ can be summerized inFigure 3.

Figure 4 shows the nondimensional velocity profiles in thex-direction. The velocity of the primary WCJ has been nondi-mensioned by the local maximum velocity, wmax. Distancefrom the wall x has been also nondimensioned by x0.5, i.e.,the point where the velocity has fallen to half of its maximum

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Fig. 4. Measured and predicted nondimensional velocity profile in mid-plane at different measured lines in z-direction below the inlet(the primary WCJ) for Q = 0.015 and 0.0195 m3/s (0.52 and 0.68 ft3/s).

value. Figure 4 presents the results for two airflow rates, Q =0.015 m3/s (0.52 ft3/s) and Q = 0.0195 m3/s (0.68 ft3/s). Asshown in Figure 4, the predictions from the three turbulencemodels are quite similar to each other and are also in goodagreement with the measurement results for all lines in thez-direction (z = 0.12 up to z = 1.45). The achieved results

show that the high velocity region appears near the wall, andthe jet remains attached to the wall due to the Coanda ef-fect and moves downward as a WCJ. The maximum velocityin the z-direction occurred about 0.012 m (0.039 ft) from theinlet wall. It can be found that the maximum velocity of theWCJ decreases by moving toward the floor (z), and the WCJ

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Fig. 5. Decay of maximum velocity along z-direction for casesQ = 0.015 and 0.0195 m3/s (0.52 and 0.68 ft3/s).

becomes thicker due to entrainment with the surrounding air.By increasing the distance from the inlet wall (x), the velocitydecreases after reaching local maximum value (wmax) at eachline. The maximum WCJ velocity dropped to less than 1 m/s(3.28 ft/s) about z = 1.45 m (4.75 ft) for Q = 0.015 m3/s (0.52ft3/s). It is worth mentioning that the maximum recordedvelocity is 2.48 and 3.27 m/s (8.13 and 10.72 ft/s) at z =0.12 m (0.39 ft) and x = 0.012 m (0.039 ft) for Q = 0.015 and0.0195 m3/s (0.52 and 0.68 ft3/s), respectively.

The decay of nondimensional maximum velocity (wmax/Ub)in the z-direction is shown in Figure 5 for airflow rates 0.015and 0.0195 m3/s (0.52 and 0.68 ft3/s) in the primary region. Ub

is the bulk velocity (the average velocity of the nozzles basedon the airflow rates), and A is the area of the inlet profile atz = 0.09 m (0.29 ft). As shown in Figure 5, the predictions fromthe three turbulence models are quite similar to each otherand are in good agreement with the measurement results. Thedecay of the maximum velocity is similar for the two airflowrates.

To further validate the wall jet behavior with numericalpredictions by different turbulence models along the floor, thedecay of the velocity magnitude U of the secondary wall jetfor three different heights—0.01, 0.03, and 0.2 m (0.032, 0.098,and 0.65 ft)—above the floor is depicted in Figure 6. The resultfrom the two different measuring techniques (HWA and CTA)and numerical predictions are consistent with each other. Itis worth mentioning that at z = 1.87 and 1.89 (height 0.03and 0.01 m (0.098 and 0.032 ft) above the floor), the predictedand measured velocity decays from the three turbulence mod-els show a discrepancy near the inlet wall in the stagnationregion. The realizable k-ε and SST k-ω models overpredictthe maximum velocity magnitude at z = 1.87 (height 0.03 m(0.098 ft) above the floor). Farther away from the inlet wall,x at about 1 m (3.287 ft), all turbulence models slightly over-predict the magnitude velocity at z = 1.87 and 1.89 (height0.03 and 0.01 m (0.098 and 0.032 ft) above the floor). Themaximum velocity is still attached to the inlet wall at z = 1.7(height 0.2 m (0.65 ft) above the floor). However by movingtoward the floor, the WCJ bends, and the maximum velocityof the WCJ is placed at z = 1.89 and x = 0.3 m (0.98 ft).

Nondimensional measured and predicted velocity pro-files at four different locations from the inlet wall along the

Fig. 6. Measured and predicted velocity decay U at measured lines along the floor (secondary wall jet), Q = 0.015 m3/s (0.52 ft3/s)(1 m = 3.28 ft; 1 m/s = 3.28 ft/s).

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Fig. 7. Measured and predicted nondimensional velocity profile at different locations from inlet wall (secondary wall jet), Q =0.015 m3/s (0.52 ft3/s).

z-direction (x = 0.3, 0.6, 1, and 1.25) are presented in Figure 7for the secondary wall jet. Velocity magnitude U is nondimen-sioned by the local maximum velocity Umax, and the distancefrom the floor in the z-direction is nondimensioned by thejet half width z0.5. Rather good agreement has been observedbetween the results from the two experimental measurements(HWA and CTA) and the predicted results by the three tur-bulence models. At different locations from the inlet wall, themaximum difference between the velocity predicted by CFDand measured by HWA is less than 30%. Moving farther awayfrom the floor, a slight discrepancy between measurement andpredicted results is observed at x = 1 m (3.28 ft). It has beenfound that the velocity magnitude is underpredicted from aheight of 0.2 m (0.65 ft) above the floor. It is worth mention-ing that close to the floor at x ≈ 1.25 m (4.1 ft), the maximumvelocity is close to 0.4 m/s (1.31 ft/s).

Base on the result presented above, all three turbulencemodels (RNG k-ε, realizable k-ε, and SST k-ω) show rathergood performance on the prediction of the isothermal WCJ inthe room studied. Since the predicted results are quite similarto each other, RNG k-ε was used for further investigations,as the use of this model was recommended in previous studies(Chen 1995; Luo and Roux 2004; Rohdin and Moshfegh 2007,2011).

Flow field of the jetThe measured and predicted horizontal velocity profile of theWCJ is shown in Figure 8 with different airflow rates (Q =0.015 and 0.0195 m3/s (0.52 and 0.68 ft3/s)) at the xy-plane

z = 0.29. It is observed that the footprint of WCJ has a saddle-back shape in the vicinity of the supply device.

A contour plot of measured and predicted velocity in theprimary and secondary wall jet region is depicted in Figure 9for airflow rate 0.015 m3/s (0.52 ft3/s) at mid-plane. The pre-dicted velocity contour plot exhibits good consistency in com-parison to the measurement results. Figure 9 shows that thejet produced by the supply device remains attached to the walldue to the Coanda effect. The jet velocity decreases near thewall, and the boundary of the jet becomes thick by increas-ing the distance in the z-direction. Low velocity and dynamicpressure can be seen in the stagnation area of the wall jetin the predicted result, which is not distinguishable from themeasurement.

The contour plots of the predicted velocity magnitude(m/s) by the three turbulence models are compared at twoplanes for Q = 0.015 m3/s (0.52 ft3/s); see Figure 10. As shownin Figure 10a, rather similar flow patterns have been capturedfor the mid-plane. The large recirculation is predicted in threeturbulence models in the middle of the room. The SST k-ωmodel shows recirculation at the top right corner, while thiseffect is not fully predicted in the contour plot of the velocityfor the RNG k-ε and the realizable k-ε models. In Figure 10b,the flow patterns predicted by the three turbulence models arequite similar at 0.1 m above the floor, except for the flow closeto the opposite wall. Slightly higher velocity is captured inthe impinging region by the SST k-ω model. The recircula-tion flows are predicted in the corners of the xy-plane 0.1 m(0.32 ft) above the floor by the SST k-ω model. However, thisflow pattern cannot be seen for the RNG k-ε and realizable

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Fig. 8. Contour plot of predicted and measured velocity (m/s) for xy-plane at z = 0.29 with Q = 0.0195 m3/s (0.68 ft3/s). a and b.Q = 0.015 m3/s (0.52 ft3/s). c and d. (1 m = 3.28 ft; 1 m/s = 3.28 ft/s).

k-ε models. A more detailed study needs to be carried outto validate the predicted result by turbulence models in thelow-velocity regions.

The contour plot of iso-velocities 1, 0.4, 0.2, and 0.1 m/s(3.28, 1.31, 0.65, and 0.32 ft/s) is shown for Q = 0.015 m3/s

(0.52 ft3/s) in Figure 11. The iso-velocity of 1 m/s (3.28 ft/s)is attached to the inlet wall and appears in limited volume. Bylooking at iso-velocity at 0.4 m/s (1.31 ft/s), it can be foundthat the air with velocity 0.4 m/s (1.31 ft/s) reaches the floorand very shortly afterward spreads in both x- and y-directions

Fig. 9. Contour plot of predicted and measured velocity (m/s) below the supply device and over the floor (primary and secondarywall jet) for Q = 0.015 m3/s (0.52 ft3/s) (1 m = 3.28 ft; 1 m/s = 3.28 ft/s).

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Fig. 10. Contour plot of the predicted velocity (m/s) by three different turbulence models with Q = 0.015 m3/s (0.52 ft3/s) (1 m/s =3.28 ft/s). a. In mid-plane. b. In xy-plane 0.1 m over the floor.

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Fig. 11. Iso-velocity for case RNG k-ε, Q = 0.015 m3/s (0.52 ft3/s).

over the floor. As shown in iso-velocity 0.1 m/s (0.32 ft/s), thesecondary wall jet spreads across the floor, covers the wholefloor, and reaches the opposite wall.

Comparison with the previous studiesTo further validate the current study, the decay of the maxi-mum velocity and the spreading rate of the wall jets in both theprimary and secondary regions from the RNG k-ε model arecompared with the experimental results by Sforza and Herbst(1970), Hassani et al. (1997), and Tornstrom and Moshfegh(2006). A nozzle for producing a three-dimensional wall jetwas used in the above-mentioned studies with aspect ratios of10, 74, and 10, respectively. The case based on the inlet dis-charge height 1.81 m (5.93 ft) above the floor with airflow rate0.015 m3/s (0.52 ft3/s) was used in this study. Table 3 showsthe decay of the maximum velocity magnitude Umax in two re-gions, a characteristic decay (CD) region, or transition zone,and a radial decay (RD) region, called the fully establishedturbulence zone (Equation 8; Sforza and Herbst, 1967). The

Table 3. Comparison of decay and spreading rates.

α

CD RD β �

Sforza and Herbst(1970)

0.16 1.09 0.07 0.11

Hassani et al. (1997) 0.56 1.03Tornstrom and

Moshfegh (2006)0.35 0.98 0.053

Primary wall jet in thisstudy (CFD)

0.18 0.52 0.096 0.02

Primary wall jet(this study)

0.18 0.56 0.087

Secondary wall jet inthis study (CFD)

0.34 0.93 0.06 0.71

Secondary wall jet(this study)

0.51 1.09 0.093

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Fig. 12. Effect of supply airflow rate and jet discharge height. a and d. On spreading rate of the wall jet in vertical direction. b and e.On spreading rate of wall jet in lateral direction. c and f. On maximum velocity decay across the floor in secondary wall jet region.(z∗

0.5 = 1.9 – z0.5; 1 m3/s = 35.31ft3/s).

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spreading rate of the wall jets in two directions (z and x) wasobtained for both zones together by Equations 9 and 10:

Umax/Ub

= (m∗/A0.5

)−α, (8)

z∗0.5

/A0.5 = β

(m∗/A0.5

), (9)

y0.5/

A0.5 = �(m∗/

A0.5), (10)

where for the WCJ in the primary region, m∗ = z and z∗0.5 =

x0.5, and for the secondary wall jet region, m∗ = x and z∗0.5 =

1.9 − z0.5. A is the area of the inlet box.The vertical spreading rate of the jet from the literature

gives results similar to the current study. The prediction ofthe maximum velocity magnitude decay of the current studycaptured results that were similar to the characteristic andradial regions by previous studies.

Parametric studies

Effect of airflow rateFour isothermal cases with different airflow rates, Q = 0.0125,0.015, 0.0175, and 0.0195 m3/s (0.44, 0.52, 0.61, and 0.68ft3/s), are presented for more detailed analysis. The inlet boxwas positioned at a height of 1.8 m (5.93 ft) above the floorfor all cases. The spreading rates of the wall jet in vertical(z) and lateral (y) directions across the floor are presented innondimensional form z∗

0.5/A0.5 and y0.5/A0.5 against x/A0.5,respectively. Decay of maximum velocity magnitude, Umax,across the floor is normalized by maximum velocity magnitudeUmax|in in the inlet box.

The spreading rates of the wall jet in vertical and lateraldirection along x-direction for different airflow rates are de-picted in Figures 12a and 12b. The figure represents that allwall jets spread at a similar rate and flow behavior is nearlyindependent of the airflow rates. It can be noticed that at a cer-tain distance from the inlet wall, x/A0.5 ≈ 10 (Figure 12b), thelateral spreading rate of the wall jet reaches to the side walls ina plateau shape for all airflow rates. Figure 12c shows by theeffect of the airflow rate on the velocity decay that no appre-ciable influence can be observed. However, in the region closeto the inlet wall, x/A0.5 ≈ 1.3, the effect of the airflow rate isslightly detected. In general, the flow behavior (the spreadingrate and maximum velocity decay of the wall jet) over the floor(secondary region) is nearly independent of the airflow rate inthis study.

Effect of discharge heightTo investigate the impact of the inlet discharge height, threedifferent inlet heights above the floor (2.01, 1.81, and 1.61 m(6.59, 5.93, and 5.28 ft)) with an identical airflow rate (Q =0.015 m3/s (0.52 ft3/s)) were studied. According to Figure 12d,the spreading rate of the wall jet in the vertical direction forthree discharge heights has similar behavior along the center-line of the floor (the x-direction). The effect of the dischargeheight on the spreading rate of the wall jet in lateral directiony0.5/A0.5 across the floor is also interesting, as shown in Figure12e. The graphs for the three cases follow each other closely.

It can also be seen that at a sufficient distance from the inletwall at x/A0.5 ≈ 10, the spreading rate of the wall jet in thelateral direction reaches to the side walls (in a plateau shapefor all three discharge heights).

A comparison of velocity decay (Figure 12f) shows thatclose to the floor, the wall jet tends to decay faster for the casewhere the inlet box is placed at the higher level (2.01 m (6.59ft)), but as wall jet enters into the room, the decay tendenciesare similar for all three case studies. As mentioned above, themomentum of the wall jet has the potential to conserve morewhen the jet issues at a lower height.

Conclusion

The velocity flow field of isothermal WCJ is numerically pre-dicted (RNG k-ε, realizable k-ε, and SST k-ω models) andcompared with the measurement data (HWA and CTA). Theverification between measurement and numerical prediction iscarried out for two different airflow rates. The box method isused to specify the inlet boundary conditions for the numericalprediction of the WCJ.

In this study, a primary and a secondary wall jet are foundin the test room, where the former main axis is along theinlet wall (z-direction) and the latter centerline is along thefloor (x-direction). The velocity profiles along the x-directionand the flow field of the predicted primary WCJ up to thefloor are in good agreement with the experimental data. Theresults also confirm that a high velocity region appears nearthe wall and that the WCJ remains attached to the wall dueto the Coanda effect and moves downward. The WCJ supplydevice has low velocity decay due to quite slow diffusion. Thepredicted secondary wall jet is also verified with the measuredvelocity along both the x- and z-directions. Due to the ratherhigh momentum, the wall jet spreads across the floor, coversnearly the whole floor, and reaches to the opposite wall. Tofurther validate the current study, the decay of the maximumvelocity and the spreading rate of the wall jet in the primaryand secondary regions are compared with the literature, wherethe results are consistent with each other.

The effect of the four inlet airflow rates and three inletdischarge heights of the supply device are investigated in termsof the maximum velocity decay and the spreading rate of thewall jet in the vertical and lateral directions over the floor. Theimpact of the inlet airflow rate showed that the flow behavioris nearly independent of the inlet flow rate in this study. Thevelocity decays faster for the case where the WCJ dischargeis at a higher level, but as wall jet enters the room, the decaytendencies are similar for three discharge heights.

Finally, the results revealed that the ventilation systembased on WCJ has enough momentum to spread and covernearly the whole floor and reach to the opposite wall.

Acknowledgment

The authors are thankful for the assistance received byMr. Hans Lundstrom at the Laboratory of Ventilation and

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Air Quality at the Center of Built Environment, University ofGavle, Gavle, Sweden.

Funding

The authors would like to acknowledge financial support fromUniversity of Gavle and Stravent AB, Finland.

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