Numerical Study of the Different
Turbulence Models for Wind Barriers
Allah Rakha
August 2014
Allah Rakha
SoHPC-2014
Mentor: Dr. Marijo Telenta
(marijo.telenta@lecad.fs.uni-lj.si) University
Mechanical Engineering, Slovenia
of
Ljubljana,
Faculty
of
Coordinator: Dr. Leon Kos
(Leon.kos@lecad.fs.uni-lj.si) University of Ljubljana, Faculty of Mechanical
Engineering, Slovenia
1. Abstract
The flow near and behind the porous barrier is studied here numerically at a detailed level.
The unsteady Reynolds-averaged Navier-Stokes (URANS) computation is applied here to
investigate and compare two different turbulence models because flow here is not statistically
stationary. The comparison of these two turbulent models RNG-KE and RKE is done by
assessment of turbulent kinetic energies and velocities. The barrier model comprised of
horizontal bars with inclination angle of 900 is applied in this study. Our results show that
RKE model can simulate for fluid velocity and turbulent kinetic energy up to higher heights
of the barriers. In addition, the drag force is different by 0.068 % and 2.93 % for RNG-KE
and RKE models respectively.
2. Introduction
There are many turbulence models for the study of these wind barriers in order to generate
shelter for desired purposes. In this project we are testing three of those theoretical turbulence
models for bar type wind barrier configuration with inclination angle of 900 . Numerical
simulations are performed using the finite volume method based in ANSYS Fluent
Computational Fluid Dynamics code. The models are Realizable 𝜅 − 𝜖(𝑅𝐾𝐸) and RNG-KE
Model.
The complex flow near and through the openings of a porous wind barrier is the cutting edge
research for various applications. The flow characteristics of the turbulent wake behind the
barrier are experimentally and numerically investigated. In this study, the wind barrier is
accurately geometrically represented with a three- dimensional model in the numerical
simulation. The unsteady Reynold -averaged Navier Stokes (URANS) computation is applied
since the flow is not statistically stationary.
A deeper understanding of turbulent structure dynamics is required to evaluate the sheltering
effect. Previous studies used the Reynolds averaging method with turbulence closure for a
two- dimensional fluid flow simulation in which the porous barrier was represented as a
momentum sink. As stated in Bourdin and Wilson (2008), numerical methods utilizing the
momentum sink approach for wind barrier modeling treat complex unresolved flow near and
through the gaps at a superficial level. The goal of this work is to compare different fluid
models and numerically simulate fluid flow through a geometrically accurate
three-dimensional barrier model and resolve the flow near and through the porous barrier. In
particular, the objective is to investigate the interaction between bleed flow and reverse flow
for different barrier configurations.
3. Barrier Model
Mostly used wind barriers are of two types, solid and porous. Porous wind barriers are mainly
used as turbulence manipulators and are exploited for many practical applications. There are
a variety of porous barrier constructions, such as upright, horizontal and screened. Up right
and horizontal wind barriers are usually made from bars and are widely used because their
construction is simple and economical. In this work, the porous bar barrier model is used with
inclination angle of 900 [1].
4. Fluent
The numerical simulation was set to represent the scaled wind tunnel experiment. The
commercial CFD code Ansys Fluent 14.5 was used to solve the equations of fluid motion.
Ansys Fluent is general- purpose, proprietary software that is well-known and a standard flow
solver. It uses cell-centered numerics, in this simulation, a segregated approach, on a
collocated, unstructured grid. The three-dimensional finite volume method was used for
RANS equation discretization. The second-order accurate central discretization for the
diffusion terms, the second-order accurate up wind discretization for the advection terms, and
the second order accurate time discretization were used. The PISO algorithm was applied for
pressure velocity coupling because it is recommended for transient calculations. Unsteady
Reynolds-averaged Navier Stokes (URANS) modeling was utilized. URANS relies on RANS
models but are unsteady even with steady boundary conditions, and therefore vortex shedding
is allowed past a bluff body. If massive separation is found in the flow, the numerical
simulation cannot find a steady state and the only course is to operate in a time-accurate
mode and analyze an unsteady solution (Spalart, 2000). Proper RANS simulation must be
time - dependent when the flow is periodic in time. Steady computations produce an
erroneously long wake since they omit an important component of the averaged flow field,
the periodic vortex shedding. The unsteady computations reproduce essential physics of
three- dimensional and massively separated flows (Iaccarino et al., 2003).
4. 1. Parallel Computing
High performance computing (HPC) was utilized for numerical simulations on a Prelog
cluster (2011) with 756 processor cores with 4 GBytes of RAM each. The computer code was
parallelized applying the message passing interface (MPI) technique for communication
between processes. Each numerical simulation was solved on 72 processor cores for a total
duration of 360 hours.
4. 2. Mathematical Model
The fluid was described by incompressible Navier Stokes equations.
𝜕𝑢𝑖
𝜕𝑢𝑖
1 𝜕𝑝
+ 𝑢𝑗
=−
+ 𝜈𝛻 2 𝑢𝑖 𝑖 = 1,2,3
𝜕𝑡
𝜕𝑥𝑗
𝜌 𝜕𝑥𝑖
𝜕𝑢𝑖
=0
𝜕𝑥𝑖
(1)
(2)
Where 𝑢𝑖 is the i-component of the velocity, 𝑥𝑖 is the i-direction, t is the time, p is the
pressure, 𝜌 is the density and 𝜈 is the kinematic viscosity. Eq. (1) represents the
momentum equations, and Eq. (2) represents the continuity equation.
4. 3. Meshing
The ICEM-CFD commercial grid generator software was utilized to create the numerical
grid. Tetrahedral grids were created due to the geometric complexity. Hyperbolic stretching
was used to make a finer grid near the wall boundary condition of the wind tunnel and the
barrier. Strong clustering was applied close to the wall boundary conditions to capture the
near-wall turbulent regions. The stretching ratio between two adjacent cells was a maximum
of 1.08.
4. 4. Boundary Conditions
The dimensions of the computational domain were set to simulate the wind tunnel and are
shown in Fig. 1.
Figure 1. Extension of the computational domain with boundary conditions [1]
The inlet was placed 3H upstream of the barrier, and the flow outlet was placed 14H
downstream. The tunnel height was 0.407m.Based on the experiments; solid walls were used
to simulate the barrier’s surface and the floor, roof and lateral walls of the wind tunnel.
No-slip boundary conditions were applied on all these surfaces. Thus, the appropriate
boundary layer and blockage ratio were used in the wind tunnel cross section. At the domain
inflow, the upstream face, a velocity inlet boundary condition with a uniform velocity profile
was specified. A small turbulence intensity of 0.1% was imposed at the inlet and
corresponded to the experimental case. A pressure outlet was applied at the domain
outflow.A slip wall boundary condition was applied on all four sides along a distance H from
the inlet boundary condition. This is done in order to correctly simulate the flow at the
leading edge.
5. Convergence Criteria
Computations were calculated until the maximum continuity residual dropped five orders of
magnitude. The barrier drag was monitored during the iterative numerical procedure. Because
the unsteady RANS (URANS) method was used, the simulation was run until the transient
flow field became statistically steady. Monitoring the integral value, in this case, the barrier
drag, helped determine if this condition was met. The size of the time step was 3e-05s. The
ANSYS Fluent temporal formulation was fully implicit. Thus, there was no stability criterion
that needed to be met in determining the size of the time step. The choice of the size of the
time step was based on the number of iterations at each time step. The number of iterations
per time step was around the recommended5–10.Furthermore, the Courant Friedrichs Lewy
(CFL) number was monitored. It was kept at CFL≈ 1.In addition, there were much more than
the suggested 20 time steps per period for vortex shedding.A smaller time step size did not
alter the numerical results.
6. Turbulence Modeling
The governing equations due to the Reynolds averaging procedure have additional unknown
variables, known as Reynolds stresses. Thus, the governing equations need a turbulence
model to be solved. The turbulence models used in this study are RNG 𝜅 − 𝑠𝑖𝑙𝑜𝑛 (𝑅𝑁𝐺 −
𝐾𝐸) Model and Realizable 𝜅 − 𝜖 (𝑅𝐾𝐸).
6. 1. RNG 𝛋 − 𝛜 (𝐑𝐍𝐆 − 𝐊𝐄) Model
The RNG 𝜅 − 𝜖 model has a similar form to the standard 𝜅 − 𝜖 model. The turbulence
kinetic energy,𝜅 and its rate of dissipation, 𝜖 are obtained from the following transport
equations:
𝜕𝑘
𝜕
𝜕
𝜕
(𝜌 𝑘) +
(𝜌 𝑘 𝑢𝑖 ) =
(𝛼𝑘 𝜇𝑒 𝑓𝑓 𝜕𝑥 ) + 𝐺𝑘 + 𝐺𝑏 − 𝜌 𝜖 − 𝑌𝑀 + 𝑆𝑘 (3)
𝜕𝑡
𝜕𝑥𝑖
𝜕𝑥𝑗
𝑗
𝜕
𝜕
(𝜌 𝜖) +
(𝜌 𝜖 𝑢𝑖 )
𝜕𝑡
𝜕𝑥𝑖
𝜕𝜖
𝜕
𝜖
=
(𝛼𝜖 𝜇𝑒 𝑓𝑓
) + 𝐶1 𝑜𝑛 (𝐺𝑘 + 𝐶3 𝜖 𝐺𝑏 )
𝜕𝑥𝑗
𝜕𝑥𝑗
𝑘
2
𝜖
− 𝐶2 𝜖 𝜌 + −𝑅𝜖 𝑆𝜖
𝑘
(4)
where, constants are defined as follows,
𝐺𝑘 = Generation of turbulence kinetic energy due to the mean velocity gradients.
𝐺𝑏 = Generation of turbulence kinetic energy due to buoyancy.
𝑌𝑀 = Contribution of the fluctuating dilatation in compressible turbulence to the overall
dissipation rate.
𝛼𝑘 and 𝛼𝜖 = Inverse effective Prandtl numbers for 𝜅 and 𝜖, respectively.
𝑆𝑘 and 𝑆𝜖 = User-defined source terms.
𝐶1 𝜖 𝐶2 𝜖 𝐶3 𝜖 = Model Constants.
6. 2. Realizable 𝛋 − 𝛜 (𝐑𝐊𝐄) Model
The realizable 𝜅 − 𝜖 (𝑅𝐾𝐸) model differs from the standard 𝜅 − 𝜖 (𝑆𝐾𝐸) model in two
important ways.
1) It has an alternative formulation for the turbulent viscosity.
2) A modified transport equation for the dissipation rate 𝜖, has been derived from an exact
equation for the transport of the mean-square vorticity fluctuation.
The term realizable means that the model satisfies the constraints on Reynolds stresses,
consistent with the physics of turbulent flows.
The modeled transport equations for 𝜅 and 𝜖 in the realizable 𝜅 − 𝜖 model are,
𝜕
𝜕
(𝜌 𝑘) +
(𝜌 𝑘 𝑢𝑗 )
𝜕𝑡
𝜕𝑥𝑗
𝜇𝑡 𝜕𝑘
𝜕
(5)
=
[(𝜇 + 𝜎 )
] + 𝐺𝑘 + 𝐺𝑏 − 𝜌 𝜖 − 𝑌𝑀
𝜕𝑥𝑗
𝑘 𝜕𝑥𝑗
+ 𝑆𝑘
and
𝜕
𝜕
(𝜌 𝜖) +
(𝜌 𝜖 𝑢𝑗 )
𝜕𝑡
𝜕𝑥𝑗
𝜇𝑡
𝜕𝜖
𝜕
=
[(𝜇 + 𝜎 )
] + 𝜌 𝐶1 𝑆 𝜖
𝜕𝑥𝑗
𝜖 𝑟𝑡𝑖𝑎𝑙𝑥𝑗
𝜖2
𝜖
− 𝜌 𝐶2 + 𝐶1 𝜖 𝐶3 𝜖 𝐺𝑏 + 𝑆𝜖
𝑘
𝑘 + √𝜈 𝜖
𝜂
𝑘
Where, 𝐶1 = 𝑀𝑎𝑥 [0.43, 𝜂+5], 𝜂 = 𝑆 𝜖 , , 𝑆 = √𝑆𝑖𝑗 𝑆𝑖𝑗
Where all these constants are defined in section(3.6.1)
(6)
5. Results
The simulation results for these models for turbulent kinetic energy and velocity are given
here for the comparison. While comparing the stream line velocity for these two models, both
models have three maxima and minima and for turbulent kinetic energy, both models have
two maxima and minima with ranges.
5. 1. Results of RNG
𝜿 − 𝝐 Model
For RNG-KE model Fig. 2 the minima are at 0.03 𝑚, 0.06 𝑚 and 0.16 𝑚 with
streamline velocity 2𝑚 𝑠 −1 ,2𝑚 𝑠 −1 and 9𝑚 𝑠 −1 respectively and maxima are at
0.0𝑚 ,0.13𝑚 and 0.20𝑚 with streamline velocity 29𝑚 𝑠 −1 ,16𝑚 𝑠 −1 and 28𝑚 𝑠 −1 respectively. The RKE model Fig. 6 has minima at 0.03𝑚 ,0.11𝑚 and 0.18𝑚 with
streamline velocity 8𝑚 𝑠 −1 ,2𝑚 𝑠 −1 and 2𝑚 𝑠 −1 respectively and maxima at
0.0𝑚 ,0.06𝑚 ,0.13𝑚 and 0.20𝑚 with streamline velocity 23𝑚 𝑠 −1 ,16𝑚 𝑠 −1 ,7𝑚 𝑠 −1 and 25𝑚 𝑠 −1 respectively.
Figure 2. Velocity profile from the numerical simulations at 1H position
On the other hand from contour plots, the velocity for RNG-KE model Fig. 3, it is higher at
the top and very low at the lower end of the barrier and behind the porous part, it has medium
values with very low turbulence. On the contrast, for the RKE model Fig. 7, it has very high
values above and very low the barrier and very low values at the upper edge of the barrier.
Behind the porous part of the barrier it has medium values with nearly zero turbulence.
Figure 3. Contour plot of velocity profile from the numerical simulations
For model (RNG-KE) Fig. 4 the minima are at 0.07𝑚 and 0.11𝑚 above the barrier with
13 𝑚2 𝑠 −2 𝑎𝑛𝑑 11 𝑚2 𝑠 −2 of turbulent kinetic energy. And maxima are at the height of
0.02𝑚 and 0.16𝑚 with turbulent kineticenergy of the 33 𝑚2 𝑠 −2 and 25 𝑚2 𝑠 −2. For
model (RKE) Fig. 8 the minima of turbulent kinetic energy are 15 𝑚2 𝑠 −2 and 17 𝑚2 𝑠 −2
at the height of 0.07𝑚 and 0.14 𝑚 and maxima are at the 0.01𝑚 and 0.19𝑚 with
turbulent kinetic energy of the 41 𝑚2 𝑠 −2 and 58 𝑚2 𝑠 −2.
Figure 4. Turbulent kinetic energy profile from the numerical simulations at 1H position
This model also has a medium value of the turbulent kinetic energy 30 𝑚2 𝑠 −2 𝑎𝑡 0.10 𝑚
which is higher than the RNG-KE model i.e 14 𝑚2 𝑠 −2 at 0.08𝑚
Figure 5. Contour plot of turbulent kinetic energy profile from the numerical simulations
5. 2. Results of Realizable 𝜿 − 𝝐 (𝑹𝑲𝑬) Model
These results show that RKE model has higher values of the turbulent kinetic energy as
compared to RNG-KE model at nearly same heights of barrier. Finally, most important, in
RNG-KE Model the turbulent kinetic energy is zero above 0.20 m of barrier however, in the
RKE model its value is 33 𝑚2 𝑠 −2. This shows that RKE Model simulates results up to
higher heights from barrier.
Figure 6. Velocity profile from the numerical simulations at 1H position
Figure 7. Contour plot of velocity profile from the numerical simulations
From contour plots for RNG-KE model Fig. 5, the turbulent kinetic energy is higher at both
lower and upper end and behind the porous part of the barrier. The turbulence is less at lower
end and higher at upper edge of the barrier, however the eddies behind porous part of the
barrier give rise to small range of turbulence in order to produce strong reverse flow. While
for RKE model Fig. 9, the turbulent kinetic energy is higher at the top barrier and turbulent
flow is also higher behind the barrier with short range strong reverse flow.
Figure 8. Turbulent kinetic energy profile from the numerical simulations at 1H position
Figure 9. Contour plot of turbulent kinetic energy profile from the numerical simulations
Finally, the drag force, for the RNG-KE model we calculate is 29.31𝑁 and for RKE model
is 30.15𝑁, while experimental value is 29.29𝑁. Thus the difference between the RNG-KE
model and experimental is 0.068 % and RKE has 2.93 % with experimental value.
6. Acknowledgment
This work was supported by PRACE-3IP under the grant of SoHPC-2014, program with
University of Ljubljana, faculty of Mechanical Engineering, Slovenia.
7. References
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using the Fluent Code. DSTO-TR-1731, DSTO Platforms Sciences Laboratory, Australia.
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unsteady separated flow. Int.J.Heat Fluid Flow 24, 147-156.
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