In GENUS, the calculations are performed for the Standard k-ε Model and the Reynolds Stress Model with the 3D sector only. In the FLUENT solver there is a graphical user interface where all the parameters are speci-fied. When a calculation is started in GENUS, a setup-file has to be loaded.
In the setup-file, the user specifies what is to be solved, what kind of models are to be used, values of the model constants and solver parameters and so on. The setup-file also calls other files, such as, species, domain, mesh and boundary conditions, see figure 8.4.
Figure 8.4. Structure of files.
The species file contains information about elements, viscosity and stream composition. JANAF polynomials are used to calculate all the thermo-chemical data necessary. The domain file initialises the field and the mesh file contains information about the grid. Every file contains short notes to help the user to set the problem correctly. The domain B. C. file calls files that contain information about boundary conditions. It is possible to create for example a velocity profile, this is done in separate files. One or more of the B. C. files, shown in figure 8.4 call these files.
GENUS Solver
Species Mesh
Domain B. C.
Domain
B. C.
Profile
Setup
As a starting point, a simulation with the Standard k-ε Model was per-formed. This simulation was similar to the 3D sector in FLUENT, it is just to set the case and run. As a start up, UDS was used to get an initial field.
This code uses a blend factor for the interpolation, 0.0 is UDS and 1.0 is CDS (UDS and CDS are discussed in chapter 6.4.1 and 6.4.2 respectively).
After a while the blend factor was changed to 0.5 to avoid numerical diffu-sion. The GENUS code is fully transient and therefore time steps must be used. In the setup file, the user specifies an initial time step, a maximum and a minimum time step and they were set to 10-6, 5 and 10-7 seconds. The time step is automatically adjusted during the calculation to optimise the per-formance. Due to the fact that this is a transient code, it is not possible to set a steady state convergence criterion as in the FLUENT simulation. A con-vergence criterion is used for each time step and this is set to 10-4. The Standard k-ε Model needed approximately 20000 iterations to converge.
Tecplot 8 is used as post-processor. For the Reynolds Stress Model, the so-lution with the Standard k-ε Model was used as an initial field. Because of this, the blend factor was 0.5 during the entire simulation. The Reynolds Stress Model needed 24000 iterations to reach steady state. Note that in the GENUS code, there are 4 different Reynolds Stress Models. The one that is used is the Generalised Langevin Model proposed by Haworth and Pope. It would be nice to try all of them on this case to see the differences.
Available measurements are axial velocity, swirl velocity, RMS axial velocity and RMS swirl velocity at three different positions [16] and axial and swirl velocities at five different positions [15]. Unlike FLUENT, the RMS velocities are automatically calculated and therefore, no user-defined functions have to be defined.
8.5.1 Results
Experimental data show that the central air injection should penetrate fully through the reverse flow created by the swirling flow. The Standard k-ε Model does predict penetration similar to the result for the 2D axisymmet-ric case with FLUENT using Reynolds Stress Model, see figure 8.5 and compare with figures 8.2, 8.3 and A3.1, A3.2 in appendix 3.
The axial and swirl velocities agree well with experimental data close to the inlet. Farther downstream the prediction accuracy decreases and the ve-locities are in general too high. The poor agreement is probably a conse-quence of the fact that anisotropic effects are not taken into account by this model. If the results are compared with the results from the 3D FLUENT simulation one can see that the velocities farther downstream are better pre-dicted by FLUENT. This is a direct consequence of the fact that FLUENT does not predict the flow qualitatively correct, showing no penetration. No penetration leads to lower velocities farther downstream.
Due to the fact that the Standard k-ε Model predicted penetration of the jet in GENUS, but not in FLUENT, false convergence was suspected. The convergence criterion in FLUENT was then set to 10-6 to investigate if the jet penetrated, but this was not the case. The solution was almost unaffected by further iteration. The Results obtained with the Reynolds Stress Model is similar to those obtained with FLUENT. But with the big difference that in FLUENT, reverse flow on the outlet is present. See figure 8.6 and compare with figures 8.2, 8.3 and A3.1, A3.2 in appendix 3. See also appendix 4 where both turbulence models are compared with experimental data. In ap-pendix 5, the results from FLUENT and GENUS are compared. There is no
doubt that the Reynolds Stress Model predicts the swirling flow more cor-rect despite some discrepancies between measured and predicted values.
X
Y
0 0.2 0.4 0.6 0.8 1
-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
0.6 UVel: -1.2797 -0.959775 -0.63985 -0.319925 1.00009E-12
Figure 8.5. 3D sector with GENUS. Reverse axial velocity (m/s) for the Standard k-ε Model that shows full penetration.
X
Y
0 0.5 1 1.5
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
UVel: -1.39391 -1.04543 -0.696955 -0.348478 -5.55112E-17
Figure 8.6. 3D sector with GENUS. Reverse axial velocity (m/s) for the Reynolds Stress Model that shows penetration to x = 0.6 m.
9 Simulation of test case 2
The purpose of this test case is to see how the different CFD codes pre-dict the turbulent burning velocity in a frozen turbulence field. The turbulent burning velocity is defined [9] in analogy with the laminar burning velocity.
This is the speed at which a unstretched planar steadily propagating laminar flame moves, perpendicular to itself, into a stationary combustible mixture.
Comparison with experimental data [5] makes it possible to check the ac-curacy of predictions from theoretical combustion models.
9.1 Geometry
This is a really simple geometry, it is basically a plate, the length is 2 m and the height is 0.1 m. Split the plate, 1.5 m downstream in the x-direction, into two domains, to make the domain prepared for the initial conditions.
The idea is to have only reactants in the first domain and only products in the second domain. See figure 9.1.
Figure 9.1. The geometry for test case 2.
GENUS is a pure 3D code and therefore a similar geometry was used in three dimensions. To save computational time, the length of the domain is 1 m instead of 2 m. The height and width are 0.5 m, this does not matter be-cause the case is 1D. In GENUS, the domains are divided at x = 0.9 m.
9.2 Grid
This is a one-dimensional case and therefore, a grid containing 2000 quadrilateral cells in the x-direction and only one cell in the y-direction is used in FLUENT. All cells are equally spaced. The grid and the geometry are created in GAMBIT. In GENUS, a grid containing 1000 quadrilateral cells in the x-direction and only one cell in the y and z-directions respec-tively is used.