Nonlinear eddy viscosity modeling and experimental study of jet spreading rates

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Nonlinear eddy viscosity modeling and experimental study of jet

spreading rates

Abstract Indoor airflow pattern is strongly influenced by turbulent shear andturbulent normal stresses that are responsible for entrainment effects andturbulence-driven secondary motion Therefore an accurate prediction of roomairflows requires reliable modeling of these turbulent quantities The mostwidely used turbulence models include RANS-based models that provide quicksolutions but are known to fail in turbulent free shear and wall-affected flowsIn order to cope with this deficiency this study presents a nonlinear k-eturbulence model and evaluates it along with linear k-e models for an indoorisothermal linear diffuser jet flow measured in two model rooms using PIV The

results show that the flow contains a free jet near the inlet region and a wall-affected region downstream where the jet is pushed toward the ceiling byentrainment through the well-known Coanda effect The CFD results show thatan accurate prediction of the entrainment process is very important and that thenonlinear eddy viscosity model is able to predict the turbulence-drivensecondary motions Furthermore turbulence models that are calibrated for highReynolds free shear layer flows were not able to reproduce the measuredvelocity distributions and it is suggested that the model constants of turbulencemodels should be adjusted before they are used for room airflow simulations

C Heschl1 K Inthavong2 W Sanz3 J Tu2

1Fachhochschule Burgenland University of Applied

Science Pinkafeld Austria 2Platform Technologies

Research Institute School of Aerospace Mechanical

and Manufacturing Engineering RMIT University

Bundoora Victoria Australia 3 Institute for Thermal

Turbomachinery and Machine Dynamics Graz University

of Technology Graz Austria

Key words Linear diffuser Jet flow Turbulent models

Reynolds Averaged Navier Stokes equations Nonlinear

RANS Spreading rate

Prof J Tu

School of Aerospace Mechanical and Manufacturing

Engineering

RMIT University PO Box 71 Plenty Road Bundoora

Victoria 3083 Australia

e-mail jiyuanturmiteduau

Received for review 18 November 2012 Accepted for

publication 8 May 2013

Practical ImplicationsA nonlinear version of the standard k-e turbulence model is proposed to improve its performance for the jet spreadingfound in linear diffusers The model is evaluated against new measured PIV experimental data that serve as a bench-mark for future evaluations of turbulence modeling in indoor airflows The PIV measurements provide insight intothe flow behavior from linear diffusers The results will help users choose the appropriate default turbulence modelsthat are readily available in commercial CFD software to suit the indoor air simulation

Introduction

Indoor airflows subjected to linear jet diffusers feature

a rich variety of fluid dynamics These flow characteris-tics also exert significant influence on the distributionof contaminant particles suspended in the air andtherefore the accurate prediction of such airflows playsan important role in the design process of ventilationsystems for both occupant comfort and contaminantremoval (Chang et al 2006 He et al 2005 Inthavonget al 2012) Computational fluid dynamics (CFD) is apromising tool to capture such flow phenomena Dueto the lower computational effort most airflowsimulations are based on the Reynolds AveragedNavier Stokes equations (RANS) with a first-order-

closure turbulence model While its use has been prom-inent in recent years as reviewed by Chen and Zhai(2004) and Zhai et al (2007) the accuracy and reliabil-

ity of the simulation significantly depend on the imple-mentation of the turbulence model to account for theflow behavior

Early numerical investigations of two-dimensionalroom airflows (Nielsen 1990 Soslashrensen and Nielsen2003 Voigt 2002) showed that isotropic turbulencemodels (eg a linear eddy viscosity model) were suffi-cient in predicting the room airflows However thestandard Boussinesq approach used relies on a linearcorrelation between the Reynolds stress tensor and thestrain rate tensor which is not able to reproduce theturbulent normal stresses sufficiently For this reason

1

Indoor Air 2013 copy 2013 John Wiley amp Sons AS Published by John Wiley amp Sons Ltd wileyonlinelibrarycomjournalinaPrinted in Singapore All rights reserved INDOOR AIR

doi101111ina12050



this approach fails in the prediction of turbulence-driven secondary motions (Demuren and Rodi 1984Heschl et al 2013 van Hooff et al 2013) For roomairflows this scenario can be observed at air diffusersor inlets that are mounted near a wall so that a three-dimensional wall jet is encountered The large lateral tonormal spreading rates caused by the redistribution of

the turbulent normal stresses near the wall are not cap-tured by linear correlation turbulence models leadingto poor predictions in downstream flow (Abrahams-son 1997 Craft and Launder 2001 Leuroubcke amp ThRung 2003) A further difficulty in CFD modeling of indoor airflows is the low inlet velocities that produceReynolds numbers in the range of Re 102 104 Inthis range transitional effects influence the entrainmentof the inlet jet Studies have shown that the jet spread-ing rate is dependent on the Re number (Deo et al2007) The importance of the turbulent normal stressesand the transitional effects indicates that a nonlineareddy viscosity turbulence model (EVM) calibrated withregard to normal stresses and flow entrainment is indis-pensable for an accurate prediction of room airflows

Therefore the purpose of this study is the develop-ment of a nonlinear eddy viscosity model capable to sim-ulate the room flow phenomena described previouslyStarting from the investigation of the performance of k-e turbulence models in the prediction of the lateralspreading rate of isothermal three-dimensional wall jetsa nonlinear eddy viscosity modification is made to thestandard k-e model and its model constants are cali-brated based on experimental data (isothermal case)For this reason two model rooms with different widths

and heights and a linear diffuser inlet producing a wall jet flow across the ceiling are investigated experimentallyusing particle image velocimetry (PIV) and used to eval-uate the k-e turbulence models

Experimental setup

The test setup consists of an air supply duct system amodel room made of plexiglass in an air-conditioned

test room and a PIV measurement system (Figure 1)The test rig is equipped with a frequency-controlledfan unit which feeds the air via an orifice plate a recti-fier a mass flow measurement unit temperature sen-sors and seeding mixing chamber to the plexiglass testmodel The plexiglass model is placed inside a black-coated test room to allow optimum illumination while

thermal influences are minimized by placing the laserenergy supply and the computer equipment outside of the test room During the measurements temperaturesof the inlet outlet and surrounding walls the relativehumidity and the ambient pressure are logged so thatthe air properties can be determined to ensure anisothermal case

Plexiglass models

The two plexiglass model rooms with their dimensionsare shown in Figure 2 They differ in their length-to-height and length-to-width ratios and in their outletsBoth models have an inlet air supply duct with evenlydistributed holes The supply ducts are fed from bothend sides over a flow rectifier For Room-1 the air sup-ply extends over a length of 666 mm and contains 222holes (2-mm diameter) evenly spaced along the ductThe mean inlet velocity is 1484 ms (air change rateACH = 84) and the inlet angle is 16deg downwards fromthe horizontal direction The air leaves the model roomthrough a small channel of 12 mm height and the samelength of 666 mm at the opposite wall of the roomAdditional parameters are as follows H = 400 mm DH = 0001 WH = 20 LH = 30

The air supply of the second model room containsseven groups of 32 holes with a diameter of 13 mmover an overall length of 4408 mm The distancebetween the holes is 15 mm and between the seven-hole groups 135 mm The mean inlet velocity is3688 ms (ACH = 84) and the inlet angle is 275degdownwards from the horizontal direction The outlet isa duct at the opposite wall which has the same hole dis-tribution as the inlet air supply duct

Fig 1 Schematic of experimental setup for the room flow investigation

2

Heschl et al



PIV measurement setup

The light sheet optic and the two cameras are mountedon a two-dimensional traverse system so that only onecalibration is needed for all PIV measurements Thetwo cameras are mounted on top of each other so thatthe complete height of the model room can be coveredThe field of view of one camera is 155 9 200 mm983218 sothat in x-direction 294 in y-direction 110 and inz-directions 39 measured positions were obtained Thisyields in a measured domain ranging from x = 110 to1200 mm y = 0 to 400 mm and z = 0 to 800 mm

which consists of about 1300000 vectors To eliminatethe turbulent fluctuations the measuring data are aver-aged over a measuring period of 30 s with a samplerate of 4 Hz

The field of view of one camera was155 9 200 mm983218 so that the complete height of themodel room could be measured at the same time forevery position For all PIV measurements two cameraswith a resolution of 1344 9 1024 pixels are used Theinterrogation areas are defined with 32 9 32 pixels andan overlapping of 25 In the z-direction the lightsheet probe and cameras were traversed in steps of

20 mm to determine the x and y velocity componentsin about 40 measurements planes normal to the z-axisMeasurement uncertainty analysis was performed

following Coleman amp Steele (1995) The accuracy of velocity measurement is limited by the accuracy of thesub-pixel interpolation of the displacement correlationpeak In this study the cross-correlation is performedusing the adaptive correlation method (Dantec 2002)Based on the size of the interrogation area the adap-tive correlation is used to calculate the instantaneousvector maps and the large number of instantaneousvector maps is used to calculate the mean velocity Forour data this leads to an uncertainty in the streamwise

and wall-normal mean velocities at 95 confidencelevel of 23 and 29 respectively

Numerical method

In the CFD model the inlet consisting of individualholes was simplified to a single slot with the hole diam-eter as its height Due to the larger inlet area the inletvelocity was reduced to achieve the same mass flow Toobtain the same momentum a small volume in the inletarea of the slot was created where a momentum sourcewas defined to match the original supply duct This

technique is known as the momentum method (Srebricand Chen 2002) Preliminary CFD simulations wereperformed and compared with the PIV measurementsprior to performing the full room simulations

The steady-state continuity and momentum RANSequations for incompressible fluids and isothermal floware as follows

u j

x j

frac14 0 eth1THORN

u j

ui

x j

frac14 1

q

p

xi

thorn

x j

v

ui

x j

u0

i u0 j

x j

eth2THORN

To close the equation system the Reynolds stressesqu0

i u0 j must be modeled Typically this is achieved by

the linear eddy viscosity concept where the turbulentstress tensor is expressed by a linear correlationbetween the strain rate tensor S ij and the Reynoldsstress tensor

qu0i u

0 j frac14 qC lLtU tS ij 2

3qkdij eth3THORN

where C micro is a model constant U t and Lt are turbulentvelocity and length scales respectively and k is the tur-bulence kinetic energy

Model Room-1 Model Room-2

(a) Schematic of the two plexiglass model rooms

Fig 2 Geometry of the plexiglass model rooms Dimensions are in mm

3

Nonlinear turbulence model for indoor airflow



Standard k -e turbulence model and its modifications

To close the linear eddy viscosity turbulence model theturbulent velocity scale and the turbulent length or timescale must be determined For the standard k-e turbu-lence model two additional transport equations for theturbulence kinetic energy k and the rate of dissipation eare used to achieve this The equations are given as

qu j

k

x j

frac14

xi

l thorn lt

rk

k

xi

thorn Pk qe eth4THORN

qu j

e

x j

frac14

xi

l thorn lt

re

e

xi

thorn C e1Pk C e2qe

T eth5THORN

The time scale T frac14 Lt

U t and the velocity scale are deter-

mined by T = ke and U t frac14 ffiffiffi

kp

respectively and theturbulent viscosity is expressed as

lt frac14

qC lk2

e

eth6THORN

The standard empirical model constants areC l = 009 C ɛ 1 = 144 and C ɛ 2 = 192

The standard k-e model is a semi-empirical modelderived primarily for high Reynolds number flows andthus valid for flow regions far from wall boundaries(turbulent core flow) For low Reynolds number flowssuch as those found near walls wall functions(Launder and Spalding 1974) are typically used toconnect the turbulent core flow with the near-wall flowIn this study an enhanced wall function is used whichimplies a fine near-wall mesh where the first node from

the wall is placed around y+ = 1 to resolve the viscoussublayer Modifications to improve the standard k-e(SKE) model include the Realizable k-e model (RKE)by Shih et al (1995) and the Renormalization Groupk-e model (RNG) by Yakhot and Orszag (1986)

Nonlinear k -e turbulence model

Nonlinear turbulence models include nonlinear termsof the strain rate for the definition of the Reynoldsstresses so that the Reynolds stresses can be based onthe Reynolds stress anisotropy tensor bij as

bij frac14u0

i u0 j

2k 1

3dij eth7THORN

In principle nonlinear eddy viscosity models assumethat the anisotropy tensor depends on the local velocitygradients vorticity and the turbulent time scale whichcan be summarized in the following form

bij frac14Xk

Gk T kij T ij frac14 T ij S ij Xij T t eth8THORN

where

S ij frac14 ui

x j

thorn u j

xi

Xij frac14 ui

x j

u j

xi

eth9THORN

where Gk are model constants T ij is a nonlinear func-tion of the local velocity gradients expressed by theshear rate tensor S ij and the vorticity tensor Ωij and T tis the turbulent time scale for a nonlinear k-e model

T t = ke For the modeling of the Reynolds stressanisotropy tensor bij the approach of Gatski andSpeziale (1992) is used where

bij frac14 G1T tS ij thorn G2T 2t S ikS kj 1

3S kl S kl dij

thorn G3T 2t XikS kj X jkS ki

eth10THORN

With the model constants

G1 frac14 C l G2 frac14 C 1 G3 frac14 C 2 eth10THORN

For calibration of the model constants C 1 and C 2existing experimental and DNS data from simple shearflows are used [Kim et al (1987) Tavoularis and Kar-nik (1989) Tavoularis and Corrsin (1981) De Souzaet al (1995)] and plotted in Figure 3 as these flows cor-respond well to jet flows The dimensionless invariantsg and ξ are used to characterize the flow parametersand are defined as

g frac14 T ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2 S ij S ij p

n frac14 T ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2Xij Xij

p eth11THORN

For homogeneous shear and boundary layer flows theanisotropy coefficient b12 is proportional to g and ξ and the anisotropy coefficient bii to g983218 and ξ 983218 It is notedthat only the values for b11 and b22 are shown becausefor simple shear flows the terms S ikS kj 1

3S kl S kl dij

and XikS kj X jkS ki

in Equation 10 are close to zero

for i = 1 and j = 2 This makes b12 mainly dependenton C micro (ie the influence of C 1 and C 2 becomes negligi-

Fig 3 Dependence of the model constants C 1 and C 2 on thedimensionless parameter c

4

Heschl et al



ble) A dimensionless invariant c is introduced to deter-mine the model constants C 1 and C 2 and is defined as

C i frac14 C i c2

c frac14

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi05 g2 thorn n2

q eth12THORN

The dependence of the model constants C 1 and C 2 onthe dimensionless invariant c is shown in Figure 3

where the data points are DNS and experimental datafound in literature cited previously The solid black linerepresents the corresponding approximation equationfound as

C 1 frac14 C 2 frac14 0171

09 thorn c2 eth13THORN

The dashed lines in Figure 3 show the limits forsimple shear stress flows (homogeneous shear flowstwo-dimensional channel flow boundary layer flowsetc) where the turbulent normal stresses u02

2 [ 0 andu

02

3 [ 0 are positive The comparison between the

approximation in Equation 13 and the limit linesshows that the proposed nonlinear model always pre-dicts positive turbulent normal stresses so that arobust and stable numerical solution can be expected

The computations were performed with the commer-cial CFD code ANSYS Fluent (Fluent 2007) The SIM-PLE-based segregated solver is used for the convectiveterms the second order upwind discretization is appliedBeside the included turbulence models (SKE RKERNG) the proposed nonlinear eddy viscosity modifica-tion was imposed to the SKE model leading to theSKE-NL (nonlinear) model The implementation into

Fluent was performed through UDF (user-defined func-tion) routines where the simulation time of the nonlin-ear model is 13-times longer than with the defaultmodels For both model rooms a structured mesh withhigh resolution in the near wall to satisfy the require-ments for low-Re turbulence models that is y+ of firstgrid point lt1 was used consisting of 35 million cells forRoom-1 and 25 million for Room-2 The turbulenceproperties defined at the inlet boundary to define thesupply jet were chosen in such a way so that the flowprofiles in the near inlet region obtained from the exper-imental data were matched For Room-1 a turbulence

intensity of 40 corresponding to a turbulent kineticenergy of 112 m2s2 and a dissipation of 42152 m2s3

was used while for Room-2 the turbulence intensitywas 20 corresponding to a turbulent kinetic energyof 20 m2s2 and the dissipation was 162264 m2s3

Results and discussion

Nonlinear EVM calibration

Any individual tuning of model constants should be con-sistent to the log-law layer (Wilcox 2006) A simpleoption is to adapt the proportionality factor of the pro-

duction and dissipation term in the e equation in such away that both the measured spreading rate and the loga-rithmic wall law are fulfilled For the k-e-based turbulencemodels it is shown in (Pope 2000) that the followingrelations for the model parameters are constrained by

j2

frac14 C e2

C e1

eth THORNre ffiffiffiffiffiffiC lp eth

14

THORNwhere j (kappa) is the von Karman constant If thespreading rate is known a specific calibration of themodel constants based on the Equations 14 can beachieved The measurement data obtained in this studyprovide the mean inlet velocity and the specific jetspreading rate for the two room flows

For the air supply duct of Room-1 a constantspreading rate of d y12dx = 0110 and of Room-2 of d y12dx = 0108 was determined The proposed cali-bration procedure yields C e1 = 142 re = 123 for theSKE-NL The other model constants comply with their

default values

Velocity distribution

A comparison of the measured and predicted velocitydistribution is shown in Figure 4 for Room-1 and inFigure 5 for Room-2 In both cases the flow is charac-terized by a free jet at the inlet region and a wall-affected region downstream The latter region is drivenby the Coanda effect that pushes the jet toward theceiling The measurement of Room-1 exhibits a nearsymmetric flow whereas the airflow in Room-2 isasymmetric This asymmetry may be caused by the

smaller room size and its confinement effect whichinfluences the rate of entrainment of ambient air intothe jet For Room-1 the flow behavior is reproducedby all turbulence models except for the RKE modelwhich partly predicts an asymmetric airflow The RKEmodel overpredicts the dissipative turbulence interac-tion so that the entrainment is significantly underpre-dicted (the measured spreading rate in the inlet area isabout dy12dx = 011 while the RKE predicts (dy12dx = 009) This leads to a lower entrainment in theshear layer flow and consequently a smaller jet profilewith a higher centerline velocity This behavior of the

RKE model can also be observed in Room-2 It under-predicts the entrainment so that a complete attachmentof the jet to the wall is suppressed In contrast thestandard model SKE with a computed spreading rateof dy12dx = 011 predicts the flow pattern and thevelocity distribution clearly better than the RKE andalso RNG model The computed flow pattern indicatesthat an accurate prediction of the entrainment processis very important Because of the low inlet velocity atransitional flow behavior which leads to a highentrainment effect can be expected Consequently lin-ear turbulence models that are calibrated for high Rey-nolds free shear layer flows are not able to reproduce

5




the observed velocity distribution and therefore itsmodel constants should be adjusted before they areused for room airflow simulations

The effect of the nonlinear modifications consideringthe influence of the anisotropy based on strain rate androtation rate can be seen in the velocity contours Thecomparison of the velocity distribution for Room-1(Figure 4) between the SKE and the SKE-NL modelshows that the nonlinear model provides better agree-

ment with the experimental findings particularly fur-ther downstream at xL = 075 where the turbulenceeffects are more distinct and are evident through thewall jet attaching to the ceiling the flow is more realis-tically reproduced by the SKE-NL model Interest-ingly the influence of the turbulent normal stresses isnot noticeable in Room-2 This may be due to the lar-ger inlet angle so that a hardly visible wall jet arises

Jet development downstream

The development of the wall jet as it progresses down-stream is visualized through a contour plot of the

streamwise u-velocity component for both rooms(Figures 6 and 7) The experimental results show alarge core region dominated by the jet in the upper half of the room with a positive axial velocity For Room-1 all turbulence models predict the qualitative jetdevelopment fairly well although the SKE-NL modelproduces a thinner high velocity region downstreamThe development of the wall jet in Room-2 shows agreater jet plume created by the increased inlet angle of

the jet The flow is entrained rapidly and the jet reat-taches to the ceiling at approximately x = 200 mmThe SKE and RKE model predictions show the jetvelocity decaying rapidly and at x = 900 mm theinfluence of the jet is diminished

Velocity profiles for Room-1

Additional quantitative analyses are performed forRoom-1 because the flow pattern shows some symme-try and therefore values at specific locations shouldprovide a good reflection of the flow characteristicsThe u-velocity along the room height at mid-section is

umag u0

00 035

x = 300 mm x L = 025

umag u0

00 020

x = 600 mm x L = 050

umag u0

00 018

x = 900 mm x L = 075

E

x p

S K E - N L

S K E

R K E

R N G

Fig 4 Comparison of velocity contours in three planes normal to the x-axis in Room-1 The diagrams show the complete cross-section

6

Heschl et al



depicted in Figure 8 for three locations (x = 300 mm600 mm and 900 mm as depicted in Figure 6) The tur-bulence models are able to capture the peak velocitiesreasonably along the height at x = 300 mm Howeverthe reverse flow region below the jet flow is not cap-

tured at all by any of the linear k-e models The flowaxial velocity remains positive no recirculation isfound As the flow develops downstream the linearmodels eventually produce the recirculation in thelower half of the room (x = 900 mm) The proposed

umag u0

000 018

x = 182 mm x L = 0206

umag u0

000 015

x = 304 mm x L = 0344

umag u0

000 009

x = 608 mm x L = 0688

E x p

S K E - N L

S K E

R K E

R N G

Fig 5 Comparison of velocity contours in three planes normal to the x-axis in Room-2 Measurement region is a height of 195 mm(from ceiling) and a width of 608 mm (full width of the room)

u-veluo x = 300 mm x = 600 mm x = 900 mm

Experiment

SKE-NL SKE

RNG RKE

Fig 6 Comparison of the u-velocity contours in the mid z-plane of Room-1 The measurement region is the complete cross-section

7




SKE-NL model shows significant improvements incapturing not only the recirculation but also the veloc-ity profiles quantitatively The improved prediction of the normal stress distribution by the nonlinear modelenables the turbulence-driven secondary motion thatenhances the prediction of the lateral spreading rate of the three-dimensional wall jet at the ceiling

The turbulent kinetic energy (TKE) taken along thevertical lines x = 300 mm 600 mm and 900 mm aregiven in Figure 9 to highlight the differences in each of

the k-e-based turbulence models The In the near inlet jet region the TKE profiles are similar for all modelsgiven that the flow development is not fully realizedFurther downstream where the entrainment and turbu-lence-driven secondary motions become more influen-tial greater variation between the linear k-e modelswith the nonlinear is much more evident The nonlin-ear model provides has the ability to capture the sec-ondary flow motions and turbulent normal stresseswhereas the linear models cannot


Experiment

SKE-NL SKE

RNG RKE

Fig 7 Comparison of u-velocity contours in the mid z-plane for Room II The measurement region shows a height of 195 mm fromceiling and the complete room length 8831 mm

x = 300 mm x = 600 mm x = 900 mm

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

RNG

RKE

SKE

SKE-NL

Exp

Fig 8 Axial velocity (u-component) profiles in the vertical coordinate in the z-midplane (PIV measurement data determined with mov-

ing-average validation) taken at x = 300 mm x = 600 mm and x = 900 mm of Room-1

8

Heschl et al





van Hooff T Blocken B and van Heijst

GJ (2013) On the suitability of steady

RANS CFD for forced mixing ventila-

tion at transitional slot Reynolds num-

bers Indoor Air 23 236 ndash 249

Inthavong K Ge QJ Li XD and Tu

JY (2012) Detailed predictions of parti-

cle aspiration affected by respiratory

inhalation and airflow Atmos Environ

62 107 ndash

117

Kim J Moin P and Moser R (1987) Tur-

bulence statistics in fully developed chan-

nel flow at low Reynolds number J Fluid

Mech 177 133 ndash 166

Launder BE and Spalding DB (1974)

The numerical computation of turbulent

flows Comput Methods Appl Mech

Eng 3 269 ndash 289

Leuroubcke HM and Th Rung FT (2003)

Prediction of the spreading mechanism of

3D turbulent wall jets with explicit Rey-

nolds-stress closure Int J Heat Fluid

Flow 24 434 ndash 443

Nielsen PV (1990) Specification of a Two-

Dimensional Test Case Book Specifica-

tion of a Two-Dimensional Test Case Aal-

borg University IEA Annex 20 Air Flow

Patterns within Buildings

Pope SB (2000) Turbulent Flows New

York Cambridge University Press

Shih TH Liou WW Shabbir A Yang

Z and Zhu J (1995) A new k-e eddy vis-

cosity model for high Reynolds number

turbulent flows Comput Fluids 24 227 ndash

238

Soslashrensen DN and Nielsen PV (2003)

Quality control of computational fluid

dynamics in indoor environments Indoor

Air 13 2 ndash 17

Srebric J and Chen Q (2002) Simplified

numerical models for complex air

supply diffusers HVACampR Res 8

277 ndash 294

Tavoularis S and Corrsin S (1981) Experi-

ments in nearly homogenous turbulent

shear flow with a uniform mean tempera-

ture gradient Part 1 J Fluid Mech 104

311 ndash 347

Tavoularis S and Karnik U (1989) Further

experiments on the evolution of turbulent

stresses and scales in uniformly sheared

turbulence J Fluid Mech 204 457 ndash 478

Voigt LK (2002) Validation of Turbulence

Models using Topological Aspects

Proceeding of ROOMVENT 2002

173 ndash

176

Wilcox DC (2006) Turbulence Modeling for

Cfd DCW Industries Incorporated La

Canada CA

Yakhot V and Orszag SA (1986) Renor-

malization group analysis of turbulence

I Basic theory J Sci Comp 1 3 ndash 51

Zhai ZJ Zhang Z Zhang W and Chen

QY (2007) Evaluation of various turbu-

lence models in predicting airflow and

turbulence in enclosed environments by

CFD Part 1 mdash Summary of prevalent

turbulence models HVACampR Res 13

853 ndash 870

10

Heschl et al



this approach fails in the prediction of turbulence-driven secondary motions (Demuren and Rodi 1984Heschl et al 2013 van Hooff et al 2013) For roomairflows this scenario can be observed at air diffusersor inlets that are mounted near a wall so that a three-dimensional wall jet is encountered The large lateral tonormal spreading rates caused by the redistribution of

the turbulent normal stresses near the wall are not cap-tured by linear correlation turbulence models leadingto poor predictions in downstream flow (Abrahams-son 1997 Craft and Launder 2001 Leuroubcke amp ThRung 2003) A further difficulty in CFD modeling of indoor airflows is the low inlet velocities that produceReynolds numbers in the range of Re 102 104 Inthis range transitional effects influence the entrainmentof the inlet jet Studies have shown that the jet spread-ing rate is dependent on the Re number (Deo et al2007) The importance of the turbulent normal stressesand the transitional effects indicates that a nonlineareddy viscosity turbulence model (EVM) calibrated withregard to normal stresses and flow entrainment is indis-pensable for an accurate prediction of room airflows

Therefore the purpose of this study is the develop-ment of a nonlinear eddy viscosity model capable to sim-ulate the room flow phenomena described previouslyStarting from the investigation of the performance of k-e turbulence models in the prediction of the lateralspreading rate of isothermal three-dimensional wall jetsa nonlinear eddy viscosity modification is made to thestandard k-e model and its model constants are cali-brated based on experimental data (isothermal case)For this reason two model rooms with different widths

and heights and a linear diffuser inlet producing a wall jet flow across the ceiling are investigated experimentallyusing particle image velocimetry (PIV) and used to eval-uate the k-e turbulence models

Experimental setup

The test setup consists of an air supply duct system amodel room made of plexiglass in an air-conditioned

test room and a PIV measurement system (Figure 1)The test rig is equipped with a frequency-controlledfan unit which feeds the air via an orifice plate a recti-fier a mass flow measurement unit temperature sen-sors and seeding mixing chamber to the plexiglass testmodel The plexiglass model is placed inside a black-coated test room to allow optimum illumination while

thermal influences are minimized by placing the laserenergy supply and the computer equipment outside of the test room During the measurements temperaturesof the inlet outlet and surrounding walls the relativehumidity and the ambient pressure are logged so thatthe air properties can be determined to ensure anisothermal case

Plexiglass models

The two plexiglass model rooms with their dimensionsare shown in Figure 2 They differ in their length-to-height and length-to-width ratios and in their outletsBoth models have an inlet air supply duct with evenlydistributed holes The supply ducts are fed from bothend sides over a flow rectifier For Room-1 the air sup-ply extends over a length of 666 mm and contains 222holes (2-mm diameter) evenly spaced along the ductThe mean inlet velocity is 1484 ms (air change rateACH = 84) and the inlet angle is 16deg downwards fromthe horizontal direction The air leaves the model roomthrough a small channel of 12 mm height and the samelength of 666 mm at the opposite wall of the roomAdditional parameters are as follows H = 400 mm DH = 0001 WH = 20 LH = 30

The air supply of the second model room containsseven groups of 32 holes with a diameter of 13 mmover an overall length of 4408 mm The distancebetween the holes is 15 mm and between the seven-hole groups 135 mm The mean inlet velocity is3688 ms (ACH = 84) and the inlet angle is 275degdownwards from the horizontal direction The outlet isa duct at the opposite wall which has the same hole dis-tribution as the inlet air supply duct

Fig 1 Schematic of experimental setup for the room flow investigation

2

Heschl et al










Numerical method




u j

x j

frac14 0 eth1THORN

u j

ui

x j

frac14 1

q

p

xi

thorn

x j

v

ui

x j

u0

i u0 j

x j

eth2THORN




qu0i u


3qkdij eth3THORN





3






qu j

k

x j

frac14

xi

l thorn lt

rk

k

xi


qu j

e

x j

frac14

xi

l thorn lt

re

e

xi

thorn C e1Pk C e2qe

T eth5THORN




kp


lt frac14

qC lk2

e

eth6THORN






bij frac14u0

i u0 j

2k 1

3dij eth7THORN


bij frac14Xk


where

S ij frac14 ui

x j

thorn u j

xi

Xij frac14 ui

x j

u j

xi

eth9THORN




3S kl S kl dij


eth10THORN





2 S ij S ij p


2Xij Xij

p eth11THORN


3S kl S kl dij





4

Heschl et al




C i frac14 C i c2

c frac14


q eth12THORN



C 1 frac14 C 2 frac14 0171



2 [ 0 andu

02











j2

frac14 C e2

C e1


14



default values





5













umag u0

00 035

x = 300 mm x L = 025

umag u0

00 020

x = 600 mm x L = 050

umag u0

00 018

x = 900 mm x L = 075

E

x p

S K E - N L

S K E

R K E

R N G


6

Heschl et al





umag u0

000 018

x = 182 mm x L = 0206

umag u0

000 015

x = 304 mm x L = 0344

umag u0

000 009

x = 608 mm x L = 0688

E x p

S K E - N L

S K E

R K E

R N G



Experiment

SKE-NL SKE

RNG RKE


7








Experiment

SKE-NL SKE

RNG RKE


x = 300 mm x = 600 mm x = 900 mm

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

RNG

RKE

SKE

SKE-NL

Exp



8

Heschl et al














62 107 ndash

117








Eng 3 269 ndash 289

















238




Air 13 2 ndash 17




277 ndash 294





311 ndash 347








173 ndash

176



Canada CA










853 ndash 870

10

Heschl et al










Numerical method




u j

x j

frac14 0 eth1THORN

u j

ui

x j

frac14 1

q

p

xi

thorn

x j

v

ui

x j

u0

i u0 j

x j

eth2THORN




qu0i u


3qkdij eth3THORN





3






qu j

k

x j

frac14

xi

l thorn lt

rk

k

xi


qu j

e

x j

frac14

xi

l thorn lt

re

e

xi

thorn C e1Pk C e2qe

T eth5THORN




kp


lt frac14

qC lk2

e

eth6THORN






bij frac14u0

i u0 j

2k 1

3dij eth7THORN


bij frac14Xk


where

S ij frac14 ui

x j

thorn u j

xi

Xij frac14 ui

x j

u j

xi

eth9THORN




3S kl S kl dij


eth10THORN





2 S ij S ij p


2Xij Xij

p eth11THORN


3S kl S kl dij





4

Heschl et al




C i frac14 C i c2

c frac14


q eth12THORN



C 1 frac14 C 2 frac14 0171



2 [ 0 andu

02











j2

frac14 C e2

C e1


14



default values





5













umag u0

00 035

x = 300 mm x L = 025

umag u0

00 020

x = 600 mm x L = 050

umag u0

00 018

x = 900 mm x L = 075

E

x p

S K E - N L

S K E

R K E

R N G


6

Heschl et al





umag u0

000 018

x = 182 mm x L = 0206

umag u0

000 015

x = 304 mm x L = 0344

umag u0

000 009

x = 608 mm x L = 0688

E x p

S K E - N L

S K E

R K E

R N G



Experiment

SKE-NL SKE

RNG RKE


7








Experiment

SKE-NL SKE

RNG RKE


x = 300 mm x = 600 mm x = 900 mm

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

RNG

RKE

SKE

SKE-NL

Exp



8

Heschl et al














62 107 ndash

117








Eng 3 269 ndash 289

















238




Air 13 2 ndash 17




277 ndash 294





311 ndash 347








173 ndash

176



Canada CA










853 ndash 870

10

Heschl et al





qu j

k

x j

frac14

xi

l thorn lt

rk

k

xi


qu j

e

x j

frac14

xi

l thorn lt

re

e

xi

thorn C e1Pk C e2qe

T eth5THORN




kp


lt frac14

qC lk2

e

eth6THORN






bij frac14u0

i u0 j

2k 1

3dij eth7THORN


bij frac14Xk


where

S ij frac14 ui

x j

thorn u j

xi

Xij frac14 ui

x j

u j

xi

eth9THORN




3S kl S kl dij


eth10THORN





2 S ij S ij p


2Xij Xij

p eth11THORN


3S kl S kl dij





4

Heschl et al




C i frac14 C i c2

c frac14


q eth12THORN



C 1 frac14 C 2 frac14 0171



2 [ 0 andu

02











j2

frac14 C e2

C e1


14



default values





5













umag u0

00 035

x = 300 mm x L = 025

umag u0

00 020

x = 600 mm x L = 050

umag u0

00 018

x = 900 mm x L = 075

E

x p

S K E - N L

S K E

R K E

R N G


6

Heschl et al





umag u0

000 018

x = 182 mm x L = 0206

umag u0

000 015

x = 304 mm x L = 0344

umag u0

000 009

x = 608 mm x L = 0688

E x p

S K E - N L

S K E

R K E

R N G



Experiment

SKE-NL SKE

RNG RKE


7








Experiment

SKE-NL SKE

RNG RKE


x = 300 mm x = 600 mm x = 900 mm

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

RNG

RKE

SKE

SKE-NL

Exp



8

Heschl et al














62 107 ndash

117








Eng 3 269 ndash 289

















238




Air 13 2 ndash 17




277 ndash 294





311 ndash 347








173 ndash

176



Canada CA










853 ndash 870

10

Heschl et al




C i frac14 C i c2

c frac14


q eth12THORN



C 1 frac14 C 2 frac14 0171



2 [ 0 andu

02











j2

frac14 C e2

C e1


14



default values





5













umag u0

00 035

x = 300 mm x L = 025

umag u0

00 020

x = 600 mm x L = 050

umag u0

00 018

x = 900 mm x L = 075

E

x p

S K E - N L

S K E

R K E

R N G


6

Heschl et al





umag u0

000 018

x = 182 mm x L = 0206

umag u0

000 015

x = 304 mm x L = 0344

umag u0

000 009

x = 608 mm x L = 0688

E x p

S K E - N L

S K E

R K E

R N G



Experiment

SKE-NL SKE

RNG RKE


7








Experiment

SKE-NL SKE

RNG RKE


x = 300 mm x = 600 mm x = 900 mm

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

RNG

RKE

SKE

SKE-NL

Exp



8

Heschl et al














62 107 ndash

117








Eng 3 269 ndash 289

















238




Air 13 2 ndash 17




277 ndash 294





311 ndash 347








173 ndash

176



Canada CA










853 ndash 870

10

Heschl et al












umag u0

00 035

x = 300 mm x L = 025

umag u0

00 020

x = 600 mm x L = 050

umag u0

00 018

x = 900 mm x L = 075

E

x p

S K E - N L

S K E

R K E

R N G


6

Heschl et al





umag u0

000 018

x = 182 mm x L = 0206

umag u0

000 015

x = 304 mm x L = 0344

umag u0

000 009

x = 608 mm x L = 0688

E x p

S K E - N L

S K E

R K E

R N G



Experiment

SKE-NL SKE

RNG RKE


7








Experiment

SKE-NL SKE

RNG RKE


x = 300 mm x = 600 mm x = 900 mm

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

RNG

RKE

SKE

SKE-NL

Exp



8

Heschl et al














62 107 ndash

117








Eng 3 269 ndash 289

















238




Air 13 2 ndash 17




277 ndash 294





311 ndash 347








173 ndash

176



Canada CA










853 ndash 870

10

Heschl et al





umag u0

000 018

x = 182 mm x L = 0206

umag u0

000 015

x = 304 mm x L = 0344

umag u0

000 009

x = 608 mm x L = 0688

E x p

S K E - N L

S K E

R K E

R N G



Experiment

SKE-NL SKE

RNG RKE


7








Experiment

SKE-NL SKE

RNG RKE


x = 300 mm x = 600 mm x = 900 mm

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

RNG

RKE

SKE

SKE-NL

Exp



8

Heschl et al














62 107 ndash

117








Eng 3 269 ndash 289

















238




Air 13 2 ndash 17




277 ndash 294





311 ndash 347








173 ndash

176



Canada CA










853 ndash 870

10

Heschl et al







Experiment

SKE-NL SKE

RNG RKE


x = 300 mm x = 600 mm x = 900 mm

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

ndash2 0 2

0

005

01

015

02

025

03

035

04

H e i g h t [ m ]

u-velocity [ms]

RNG

RKE

SKE

SKE-NL

Exp



8

Heschl et al














62 107 ndash

117








Eng 3 269 ndash 289

















238




Air 13 2 ndash 17




277 ndash 294





311 ndash 347








173 ndash

176



Canada CA










853 ndash 870

10

Heschl et al














62 107 ndash

117








Eng 3 269 ndash 289

















238




Air 13 2 ndash 17




277 ndash 294





311 ndash 347








173 ndash

176



Canada CA










853 ndash 870

10

Heschl et al












62 107 ndash

117








Eng 3 269 ndash 289

















238




Air 13 2 ndash 17




277 ndash 294





311 ndash 347








173 ndash

176



Canada CA










853 ndash 870

10

Heschl et al

Documents

Nonlinear eddy viscosity modeling and experimental study of jet spreading rates