5. A priori simulation results of the flow in the CSPD duct
5.1. CFD study with fully developed turbulent flow in rectangular duct as inlet boundary condition
5.1.5. Results
Five different cases were investigated:
Table 5.1. The cases investigated.
Case Number of cells Turbulence modell
1 650000 realizable k-epsilon
2 1400000 realizable k-epsilon
3 2000000 realizable k-epsilon
4 2000000 SST k-omega
5 3000000 SST k-omega
A PRIORI SIMULATION RESULTS OF THE FLOW IN THE CSPD DUCT
The results shown will be:
− velocity isosurfaces and wall streamlines at the last third (20 nozzles) of the duct,
− contours of the static pressure and the velocity on the symmetry plane,
− lineplots of the axial velocity, the velocity in the y direction, the static pressure and the turbulence kinetic energy from five different lines, which are on the symmetry plane,
− flow rates on the nozzles.
The locations of the lines are presented in Fig. 5.4.
Fig. 5.4. The locations of the lines.
To better understand the fluid dynamics in the CSPD duct, in some cases results for a duct with constant cross sectional area will be shown as well. The mesh (number of cells: 2000000) and the geometry for this duct were created similarly to the CSPD duct. The turbulence model for this case was the SST k-omega model.
5.1.5.1. VELOCITY ISOSURFACES
The visualisation of velocity isosurfaces helps to qualitatively analyse the flow. In addition to the isosurfaces, the regions, where the wall shear stress is 0, will be shown with black. At these locations the flow is separated from the wall. Fig. 5.5 shows the results for the duct with constant cross sectional area.
Fig. 5.5. Velocity isosurfaces for (coloured) and regions where τw=0 (black) in the duct with constant cross sectional area.
Fig. 5.6 shows the results for all the cases in the CSPD duct. It can be observed, that the separation bubble is much bigger for the non-CSPD case, and it is very similar for the
A PRIORI SIMULATION RESULTS OF THE FLOW IN THE CSPD DUCT
different cases in the CSPD duct. In Subchapter 3.5 (Possible deficiencies of the 1D modelling), it was also mentioned, that if separation occurs, the validity of the equations used to predict the friction factor is questionable, so this can be one of the culprits for the measured lower air flow rates at the end of the duct.
Case 1. Case 2.
Case 3. Case 4.
Case 5.
Fig. 5.6. Velocity isosurface for umag=2 m/s (red) and regions where τw=0 (black) in the CSPD duct.
5.1.5.2. WALL STREAMLINES
The wall shear stress vectors are tangential to the wall streamlines. By visualising them, the regions where separation occurs - the wall shear stress is close to zero- can be found more easily. Fig. 5.7 shows the duct with constant cross sectional area. The trace of the same complex flow structures can be observed as in Fig. 5.5. The black areas show the locations where the wall shear stress is zero. The streamlines are coloured by the magnitude of the wall shear stress, so these black regions are not necessary but help in finding the separation regions.
A PRIORI SIMULATION RESULTS OF THE FLOW IN THE CSPD DUCT
Fig. 5.7. Wall streamlines in the duct with constant cross sectional area.
The front plate with the nozzles is removed
Fig. 5.8 shows the wall streamlines in the CSPD duct. For the coarsest mesh with the epsilon model, the wall shear stress is lower than in Cases 2 and 3, but it is closer to the k-omega results (Case 4 and 5). For these results basically the same conclusion can be drawn as above (point 5.1.5.1).
Case 1. Case 2.
Case 3. Case 4.
Case 5.
A PRIORI SIMULATION RESULTS OF THE FLOW IN THE CSPD DUCT
5.1.5.3. CONTOURS OF THE STATIC PRESSURE
The contours of the static pressure can show, if the CSPD geometry results in flow which complies with the boundary condition used (constant static pressure in the main duct). Fig.
5.9 shows the results for the duct with non-CSPD geometry.
Fig. 5.9. Contours of the static pressure in the duct with constant cross sectional area.
Fig. 5.10 shows the contours of the static pressure in the CSPD duct. For Case 1, the inlet pressure is around 50 Pa, whereas for Case 2 it is 54 Pa, and for Cases 3-5 it is 60 Pa. As it can be seen, the static pressure is almost constant in all the cases, which means, that the real flow in the duct complies with the boundary condition used in Chapter 3. For the non-CSPD duct, the pressure is changing from 40 Pa to 60 Pa until the end of the duct.
A PRIORI SIMULATION RESULTS OF THE FLOW IN THE CSPD DUCT
Case 1. Case 2.
Case 3. Case 4.
Case 5.
Fig. 5.10. Contours of the static pressure in the CSPD duct.
5.1.5.4. CONTOURS OF THE VELOCITY MAGNITUDE
Fig. 5.11 shows the results for the duct with non-CSPD geometry. The trace of separation can be also seen, as at the end there is a region where the velocity magnitude is really low.
A PRIORI SIMULATION RESULTS OF THE FLOW IN THE CSPD DUCT
On the other hand, as Fig. 5.12 shows, the results in the CSPD duct are quite different, as there are not any similar regions. It should be also mentioned, that the results are basically the same for each case.
Case 1. Case 2.
Case 3. Case 4.
Case 5.
Fig. 5.12. Contours of the velocity magnitude in the CSPD duct.
5.1.5.5. VELOCITY LINEPLOTS FROM THE SYMMETRY PLANE
This point presents the results from the five lines (Fig. 5.4) for the axial (x) velocity and the y velocity. Fig. 5.13 shows the axial velocity profiles. These diagrams confirm what was seen in the contour plots. There are slight differences between the profiles, the results of Case 2-3 and Case 1,4 and 5 are close to each other, except the last location, where Case 5 is different from the four other cases.
A PRIORI SIMULATION RESULTS OF THE FLOW IN THE CSPD DUCT
x=0.51 m x=1.01 m
x=1.51 m x=2.01 m x=2.51 m
Fig. 5.13. Axial velocity profiles at five locations from the symmetry plane.
Fig. 5.14 shows the profiles of the y velocity.
A PRIORI SIMULATION RESULTS OF THE FLOW IN THE CSPD DUCT
x=0.51 m x=1.01 m
x=1.51 m x=2.01 m x=2.51 m
Fig. 5.14. y velocity profiles at five locations from the symmetry plane.
Here, above y=0 there are no noticeable differences between the profiles, but for y<0, the different meshes and models produced different results.
5.1.5.6. STATIC PRESSURE LINEPLOTS FROM THE SYMMETRY PLANE
With these diagrams it is easier to compare the results seen in the contour plots. Fig. 5.15 shows static pressure profiles from the five locations selected. With the coarser meshes (Case 1. and 2.) the predicted static pressures are lower. Also, as the axial distance gets higher, the differences between the two turbulence models become more significant.
A PRIORI SIMULATION RESULTS OF THE FLOW IN THE CSPD DUCT
x=0.51 m x=1.01 m
x=1.51 m x=2.01 m x=2.51 m
Fig. 5.15. Static pressure profiles at five locations from the symmetry plane.
5.1.5.7. TURBULENCE KINETIC ENERGY LINEPLOTS FROM THE SYMMETRY PLANE
Fig. 5.16 show the turbulence kinetic energy from the lines selected. The results of the two turbulence models are quite different.
A PRIORI SIMULATION RESULTS OF THE FLOW IN THE CSPD DUCT
x=0.51 m x=1.01 m
x=1.51 m x=2.01 m x=2.51 m
Fig. 5.16. Turbulence kinetic energy profiles at five locations from the symmetry plane.
5.1.5.8. FLOW RATE DISTRIBUTION ON THE NOZZLES
Fig. 5.17 shows the flow rate distributions for the different cases and for the duct with constant cross sectional area. From the chart it is obvious that the CSPD is much better, except for the last ~10 nozzles and there are no significant differences between the different cases.
A PRIORI SIMULATION RESULTS OF THE FLOW IN THE CSPD DUCT
Fig. 5.17. Flow rates on the nozzles non-dimensionalised with the ideal flow rate.