The Effect of the Turbulence Model and Finite Differencing Scheme on the Accuracy of the CFD Solution.

Due to turbulent flow in the Turbosep, the key to success in CFD lies with the accurate description of the turbulent behaviour. A number o f turbulence models are available (described in Table 3.2) ranging from the industry standard k-s model to the more complex Reynolds Stress model. However, the k-s model has shown to be inadequate

for the calculations of flows with swirl (Boysan et al, 1982) because it leads to

excessive levels of turbulent viscosity and unrealistic tangential velocity distributions.

Chapter 3. CFD Theory and Model Development (/) E c CD c R E 8 o 0 Q) >

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Figure 3.3 The effect of number of control volumes on the CFD predicted axial air velocities across the radius of the Turbosep at a simulated air flow rate of 500 Lmin ‘. The vortex finder is positioned at a radius of 4 mm.

The Reynolds Stress model perfonns much better than the k-e model in swirling flows, but it has the disadvantage of being computationally expensive. Turbulence models

based on statistical rather than continuum mechanics such as the RNG k- 8 model

(Yakhot and Smith, 1992) have been reported to have the mathematical simplicity of the k-G model whilst having the accuracy of the Reynolds Stress model. The main difference between the k-s model and the standard one is in the calculation of the turbulent viscosity, which in the case of the RNG k-s model uses an ordinary differential equation, which includes the effect of rotation.

To select the most suitable turbulence model for describing the turbulent behaviour in the Turbosep a series of comparative simulations were performed using both the standard and RNG k-s models. Due to the high computational demand of the Reynolds Stress model and the limited computer power available, the model wasn’t utilised during the course of the project, the increased computational time required to achieve a converged solution being prohibitively long.

Chapter 3. CFD Theory and Model Development r ît #11 fiiiiiiiiini ÎÎÎT Tr u it

Figure 3.4 A two-dimensional representation of the computational grid employed. The grid was composed of 91000 control volumes.

Figure 3.5 shows a comparison of the experimentally measured and CFD predicted

pressure drops across the Turbosep. The RNG k- 8 model was found to provide an

excellent correlation with the experimental data. The standard k-s model performed less well, the false predictions being attributed to the generation of anisotropic Reynolds stresses caused by the swirling motion of the fluid (see Table 3.2). Moreover, the sudden deviation of the k-s model from the experimental data at a flow rate of 500 Lmin ' can be explained by the development of increased swirl at the vanes resulting in a greater level of anisotropy throughout the computational domain.

Chapter 3. CFD Theory and Model Development 2 5 -1 2 0- 1 5 - Q- 1 0- 100 200 300 400 500

A eration rate (Lmin'^)

Figure 3.5 Comparison of the experimental (see figure 4.5) and predicted pressure drops across the Turbosep, ( • ) experimental, (■) RNG k-e turbulence model and (A ) k-e turbulence model.

The finite differencing scheme has been reported to have an effect upon the accuracy of a CFD simulation, although the more accurate schemes tend to be less robust or slower. Indeed when the unmodified QUICK and CCCT schemes were used the solution diverged. However as grid independence had been achieved the hybrid differencing scheme would be expected to have only a minimal effect on solution accuracy. This is evident in Figure 3.5 where the hybrid scheme used in combination with the RNG k-s turbulence model was able to accurately predict the pressure drop across the Turbosep. Based on the previous discussions, all further CFD simulations used a computational grid composed of 91000 control volumes, the RNG k-s turbulence model, a hybrid treatment for convection and the default SIMPLEC algorithm (Van Doormal and Raithby, 1984) to couple pressure and velocity. A high level of under relaxation (see Section 3.1.4) was also required for the models to converge adequately.

Chapter 3. CFD Theory and Model Development

3.2.1.4 CFD Predictions of the Air Flow in the Turbosep.

Figure 3.6 shows a vector plot of the flow field generated from the CFD model at a simulated air flow rate of 500 Lmin'% the maximum rated flow capacity of the Turbosep used (for clarity the azimuthal components of velocity have been suppressed). The flow field is also presented as a velocity contour plot is figure 3.7. It can been seen that the flow forms descending and ascending streams which flow parallel to one another before leaving the Turbosep through the vortex finder. This behaviour is expected and is due to the fact that swirling flows have a tendency to resist radial motion.

21.55 ms 10.7 ms

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Figure 3.6 Velocity vector plot of the flow field generated from the CFD model at a simulated air flow rate of 500 Lmin '.

Chapter 3. CFD Theory and Model Development

After entering the Turbosep, the main body of the flow passes through the vanes which impart a swirling motion. The flow then streamlines along the outer wall towards the bottom of the Turbosep. The acceleration of the flow as it passes along the outer wall of the vortex finder is due to area reduction. Upon reaching the vortex arrester, this stream changes direction and moves upward towards the vortex finder.

m 21.55 m s^

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