Nomenclature
Chapter 4 4.0 RESULTS AND DISCUSSIONS
4.1 Code Validation
4.1.1 Selection of Turbulence Models
Turbulance is of great importance in CFD. The understanding of the physics of turbulane is cretical and many different models have evolved. Sometimes the turbulance models are validated through vehacle aerodynamics. Computers have been used to solve fluid flow problems for many years. Numerous programs have been written to solve either specific problems, or specific classes of problems. From the mid-1970's, the complex mathematics required to generalize the algorithms began to be understood, and general purpose CFD solvers were developed. Recent advances in computing power, together with powerful graphics and interactive 3D manipulation of models have made the process of creating a CFD model and analyzing results much less labor intensive, reducing time and, hence, cost. Advanced solvers contain algorithms which enable robust solutions of the flow field in a reasonable time.
For the comparison purpose we have chosen
k-
s,k-
w, Shear Stress Transport (SST) and Baselinek-
co (BSL) turbulence models. The comparison is done on the basis of velocity profiles at different locations over Ahmed car body. A velocity of 40m/s, is taken in these simulations and the respective velocity profiles are compared for the different turbulence models. The experimental data of the Linhart Ct al. (2000) is also compared with the chosen turbulence models velocity profiles. A detail of these comparisons are discussed below:The origin of the Cartesian coordinate system considered is placed at the floor beneath the rear end of the body, x-axis is placed in the longitudinal direction towards outlet, y-axis is placed along the width, and z axis is along the vertical. As a result the body is at the negative side of x (A brief description of the body is given in
§-
3.2 earlier). Velocity profiles at different locations are taken but for the sake of brevity only six key locations are presented here with inlet flow velocity 40m/s. The locations are in front of the body, about the middle part of the body, close to the start of the slant, over the slant, close to the rear end and a bit away from the back. Velocity profiles of the simulations with k-c, k-o, SST and BSL turbulence models, are compared with the experimental data of Linhart etal. (2000). The velocity profiles at different locations along with the experimental data are presented in Fig 4. 1. 1 (a-f).
Velocity profiles at x= -1.062m
p.
i
C iN
0.75
0.6
0.45
0.3
0.15
1.3E-14
0
-0.15
--- --- - --- --- ---
. k-
- epsilon
k-omega:
10 20 30 40 SST
H
BSL
Velocity m/s
x = -l.062m
Figure 4.1.1(a):Velocity profiles at x= -1.062m.
In the front position (Fig 4.1.1a) the velocity profiles due to all the turbulence models matches well with the experimental value up to a certain height 0.45m. Above that height the velocity suggested by the models are more than the experimental, of them k-s, models velocity deviates more with the increase of height.
69
Velocity profiles at x= -0.862m
r 7C -
0.6
--- ---H
0.45
---
0.3---
-.-- k-epsilon
0.15 --- --- - k-omega
SST 1.3E-14
BSL
40 45
—E---Exp.val.
-0.15 Velocity rnis
• - •
1 x = -0.862m
Figure 4.1. 1(b): Velocity profiles at x- -0.862m.
Over the midpoint of the body (Fig 4. 1.1 b) all the patterns of the velocity profiles due to the different turbulence model matches well with the experimental one but differ in terms of velocities except nearer the body. Nearer the body, the shape of the experimental velocity profile mismatches with the model. Of the four, suggested velocity by k- model is closer to the experimental (little more) near the body. Its suggested velocity remains more than the experimental all through the height. Except close to the body velocity profiles of BSL remain close to the experimental.
Velocity profiles at x= -0.212m
0.75 -
0.6-
0.45- -c 0)
a)
0.3--- N
0.15 -
1.3E-14
-0.15 -
epsilon
—s--- k-omegai
SST
_____ __________ -*-- BSL
40 45 —*--Exp.val.
Velocity m/s
x = -0.212m Figure 4.1.1(c): Velocity profiles at x -0.212m
At the position near the start of the body (Fig 4.1. ic) velocity profiles suggested by k-w model is close to the experimental (near the body). Velocity produced by the k-F, model is the next, but deviates more with the increase in height.
71
7
A
Velocity profiles at x=-0.112m 0.75
0.6
0.45 - -
• - k-epsilon k-omega SST x BSL
--- Exp. val.
Fz-
0)
NJ
V x=-O.112m
Figure 4.1.1( d): Velocity profiles at x-0.1 12m.
Over the slant, near the body k-6 model's velocity is in the best match with the experimental data, BSL model suggested profile is next (Fig 4.1.1d). None of the model is showing the sharp turning as is found in the experiment.
velocity profiles at x= 0.038m 0.75
0:4&_f
0r3
N I 1. -
• k-epsilon k-omega SST BSL Exp.Val.
-
-----r -20 -10
9
10 20 30 40 50-0.15 J
Velocity rn/s
• .: ...
• •• - . •;'-\.,--L: '- -
--- çt'--- •- . -
x'0.038m
Figure 4.1.1( e): velocity profiles at x= 0.038m.
At the position after the rear end the shape prescribed by the experimental data is not found through models (Fig 4.1.1e). The models suggested shape is smooth but the experimental one is not that much. At the sharp turning performance of the k-c is close to experimental. With the increase in height k-c model's velocity differ more from the experiment.
73
C.
Velocity profiles at x=0.138m -- k-epsHonl
0.75 1 k-omega
SST
06- ---
xBSL
Exp.
E j
N
XK
_____
-20 20 40 60
Velocity m/s
- -
•'
,
x0.13 Figure 4.1.1(f): Velocity profiles at x0. 138m.
Away from the rear end the sharp turning is found in all model's velocity profile (Fig 4.1.11) but the velocities and heights of turning are different for different models. The velocity and height at the turning produced by the BSL model is close to the experimental data, though the velocity-height relationship differ from the experimental data before the free stream.
From the above discussion it may be concluded that
(a) The geometry proposed by Ahmed (1984) has been well adapted in the simulation.
The velocity profiles at different locations obtained through different turbulent models are comparable among them and also to the benchmark.
Near the body the performance of the k-a model is best among the models considered.
Hence for our further experiments purpose k-c model will be considered.