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

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 regions

t e rr a i n

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

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

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

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 3 / 16

The modeled terms in k − ε model

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

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 3 / 16

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

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 3 / 16

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?

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 4 / 16

Deficiency 1 of k − ε model

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?

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 4 / 16

Deficiency 1 of k − ε model

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?

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 4 / 16

Deficiency 1 of k − ε model

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?

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 4 / 16

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)

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 5 / 16

The stubbornness of k − ε modelers. Part 1.

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

k − ε SST

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 6 / 16

The stubbornness of k − ε modelers. Part 2.

Negative normal stresses. ⇒ Realizability.

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 7 / 16

The stubbornness of k − ε modelers. Part 3.

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

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

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.

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 9 / 16

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!

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 10 / 16

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!

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 10 / 16

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!Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 10 / 16

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!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

Standard k−εMW modelDurbin’s ModelYap CorrectionExperiments

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

Standard k−εMW modelDurbin’s ModelYap CorrectionExperiments

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

Standard k−εMW modelDurbin’s ModelYap CorrectionExperiments

x/b =0

(d) k profile at positionx/b = −0.25

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 11 / 16

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.

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 12 / 16

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

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 13 / 16

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.

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 14 / 16

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.

Rif Mohamed (UCalgary) NAWEA 2015 Graduate Student Symposium 8th June 2015 15 / 16

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?

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