Modifications to RANS Turbulence Model for Use in Urban ... · Urban Wind Resource Assessment Rif...

Modifications to RANS Turbulence Model for Use inUrban Wind Resource Assessment

Rif Mohamed

University of Calgary

8th June 2015

The people’s choice: The k − ε model

CFD seen as a pecuniary palliative for wind resource assessment.Why the k − ε? Tabrizi et al. (2013) Van Hoof and Blocken (2010),etc.

stagnation regionst e rr a i n

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 2 / 16



stagnation regions

t e rr a i n




stagnation regionst e rr a i n


The modeled terms in k − ε model

Production of k

∂k∂t

+ Uj∂k∂xj

= 2νtSijSij +∂

∂xj

((ν + νt)

∂k∂xj

)+ ε

Turbulent diffusionDissipation rate of k

Go to Strain Rate

νt = Cµk2

ε



Production of k

∂k∂t

+ Uj∂k∂xj

= 2νtSijSij +∂

∂xj

((ν + νt)

∂k∂xj

)+ ε

Turbulent diffusion

Dissipation rate of k

Go to Strain Rate

νt = Cµk2

ε



Production of k

∂k∂t

+ Uj∂k∂xj

= 2νtSijSij +∂

∂xj

((ν + νt)

∂k∂xj

)+ ε

Turbulent diffusionDissipation rate of k

Go to Strain Rate

νt = Cµk2

ε


Deficiency 1 of k − ε model

Over-prediction of k instagnation region

Is the dissipation rate ofk unable to catch upwith the production of k?Is the production of knot modeled correctly?Is the gradient diffusionmodel not valid?



Over-prediction of k instagnation regionIs the dissipation rate ofk unable to catch upwith the production of k?

Is the production of knot modeled correctly?Is the gradient diffusionmodel not valid?



Over-prediction of k instagnation regionIs the dissipation rate ofk unable to catch upwith the production of k?Is the production of knot modeled correctly?

Is the gradient diffusionmodel not valid?



Over-prediction of k instagnation regionIs the dissipation rate ofk unable to catch upwith the production of k?Is the production of knot modeled correctly?Is the gradient diffusionmodel not valid?


Meanwhile, at the inlet ...

Production of k is balanced by its dissipation rate.When and to what extent is this valid?What about buoyancy?

Neutrally-Stratified Atmosphere

U =uτκ

ln

(z − y0

z0

), (1)

k =u2τ√Cµ

(2)

ε =u3τ

κz(3)


The stubbornness of k − ε modelers. Part 1.

Over-prediction of k in stagnation regions. ⇒ Buildings.

k − ε SST



Negative normal stresses. ⇒ Realizability.



Over-prediction of k and under-prediction of recirculation region atthe lee of hills . ⇒ Terrain.


Previous works

Durbin’s Model

νt = min

(Cµ

k2

ε,

k√6S

). (4)

Yaps’s Model

Sε = 0.83ε2

k

(k1.5

εle− 1

)(k1.5

εle

)2

(5)

where le is C−0.75µ κyn with yn being the normal distance to the nearest

wall and κ is the Karman constant in the logarithmic law for the meanvelocity.


Strain rate immediately upstream of a building.

0 2000 4000 6000 8000 10000 120000

1

2

3

4

5

6

SijS

ij (s−2)

z/h b

k−ε Turbulence Model

Figure: The computed SijSij at x/b=-0.75 using the k − ε turbulence model.

Go to Production of k

νt = Cµk

SijSij|∑

Sij |, Gk = 2Cµk |∑

Sij | (6)

The birth of the MW turbulence model!



0 2000 4000 6000 8000 10000 120000

1

2

3

4

5

6

SijS

ij (s−2)

z/h b




νt = Cµk

SijSij|∑


Sij | (6)

The birth of the MW turbulence model!



0 2000 4000 6000 8000 10000 120000

1

2

3

4

5

6

SijS

ij (s−2)

z/h b




νt = Cµk

SijSij|∑


Sij | (6)

The birth of the MW turbulence model!Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 10 / 16


0 2000 4000 6000 8000 10000 120000

1

2

3

4

5

6

SijS

ij (s−2)

z/h b




νt = Cµk

SijSij|∑


Sij | (6)

The birth of the MW turbulence model!Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 10 / 16

Prediction of k .

0 0.02 0.04 0.06 0.080

1

2

3

4

5

6

k/U02

z/h b

Standard k−εMW modelDurbin’s ModelYap CorrectionExperiments

x/b =−0.75

(a) k profile at positionx/b = −0.75

0 0.05 0.1 0.15 0.20

1

2

3

4

5

6

k/U02

z/h b


x/b =−0.5

(b) k profile at positionx/b = −0.5

0 0.02 0.04 0.06 0.08 0.10

1

2

3

4

5

6

k/U02

z/h b


x/b =−0.25

(c) k profile at positionx/b = −0.25

0 0.02 0.04 0.06 0.080

1

2

3

4

5

6

k/U02

z/h b


x/b =0

(d) k profile at positionx/b = −0.25


Hills

Will the MW work in the lee of a hill?Re-circulation region.Production of k smears out the steep velocity profile resulting in ashorter attachment length.


2D ridges. The Rushil experiments.

(a) Originalk − ε.

(b) Modifiedk − ε.

(c) MW. (d) SST.

Re-attachment point

Measured:x/a=2.2Standard k − ε:x/a=1.09Modified k − ε:x/a=1.58MW:x/a=2.58SST k − ω:x/a=2.18


3D hill

0 0.005 0.01 0.015 0.02 0.0250

0.5

1

1.5

2

2.5

3

k/U 2

h

y/hc

Standard k−εSSTMWExperiments

Figure: Profile of k at the crest.


Conclusions

Development of a RANS turbulence model to reduce k instagnation region.Re-formulation of the eddy viscosity.Tested on an isolated building and achieved good results relativeto other conventional modelsModel applied to complex topography. Extended re-circulationregion compared to the k − ε.Computationally less expensive than the SST.


Thank you. ñïàñèáî.

This study reports on work sponsored by the Natural Science andEngineering Research Council and the ENMAX Corporation under theNSERC Industrial Research Chairs scheme.

Questions?


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