The time-dependent Reynolds averaged Navier-Stokes equations, are solved with the finite volume flow solver EURANUS of the FINE/TURBO environment, with either the algebraic turbulence model of Baldwin-Lomax or two-equation k-ε models for the turbulence closure. The flow solver is based on a structured multiblock, multigrid approach, including non-matching block boundaries and incorporates various numerical schemes, based on either a central or an upwind space discretization.
For the present calculations, the Baldwin-Lomax algebraic turbulence model and the linear k-ε model of Yang and Shih [1993], modified by Khodak and Hirsch [1996], are selected. In Yang and Shih 's model, the wall damping function used in the eddy viscosity is based on Ry = (k1/2y/ν). The calcula-tions were performed with a second-order centered scheme, with second and fourth order artificial dissipation terms and a W-cycle multigrid technique. The numerical procedure applied a four-stage Runge-Kutta scheme, coupled to a local time stepping and implicit residual smoothing for conver-gence acceleration.
The Reynolds number is based on the tip radius (1.524 m) and tip speed (153 m/s) and is equal to Re=1.610+7 whereas the Prandtl number is set to Pr=0.7. Thermodynamic properties are defined by Cp=1004.5 J/kg/oK and γ=1.4.
For all computations, the convergence criteria is based on a mass flow error less than 0.1% and 4 to 5 order of magnitude reduction in the RMS residual.
9.8.5. Results
Table 1 lists the cases of CFD results presented in this report. There are three different meshes, Mesh-1, Mesh-2 and Mesh-3, two different tip gap sizes, Design Gap and 50% Design Gap, and two turbulence models, Baldwin-Lomax (B-L) and linear k-ε models.
Mesh-1 Mesh-2 Mesh-3
Table 1: Test cases definition
k T V and
At design flow rate of 30 kg/s, there are four calculated operating points for the design gap case, one computed with Mesh-2, two points computed with Mesh-1 and one point computed with Mesh-3, while for the 50% gap case, there is only one point computed with Mesh-1 and the Baldwin-Lomax turbu-lence model. At off-design flow rate, there are two calculated operating points for the design gap case with the k-ε turbulence model respectively on Mesh-1 and Mesh-2. On the coarser mesh Mesh-3, a single k-ε computation is carried on at design flow rate and tip gap.
In many radial compressor simulations there is some considerable uncertainty in the running tip clear-ance of the blades, due to the effects of centrifugal and bending stresses in the blades, temperature distortions of the casing and manufacturing tolerances. The sensitivity to these effects have been ex-amined by running a single simulation with a smaller tip gap. For the design gap case, the gap height is constant from the leading edge to the trailing edge while for the 50% design gap case the gap height is linearly reduced from the design height at the leading edge to half of it at the trailing edge.
Figure 2 shows the effect of grid density, geometry and turbulence models on overall absolute total pressure ratio. We notice that the CFD data obtained with the k-ε model on Mesh-2 is in excellent agreement with the experimental data. For the coarser mesh, Mesh-1, the k-ε solution underpredicts slightly the pressure ratio. Reducing the tip gap size by 50% at the trailing edge, the pressure ratio in-creases about 0.4%. The computation on the coarse mesh Mesh-3 gives the lowest pressure ratio prediction with an underestimation of about 1%.
The effect of turbulence model is shown at the design flow rate of 30 kg/s where the Baldwin-Lomax model gives a lower pressure ratio than the k-ε model on Mesh-1 and Mesh-2, putting the calculated operating point further away from the experiments.
Figure 3 presents grid density (Mesh-1 and Mesh-2) and geometry influence for the k-ε model at the design flow rate. A comparison of reduced static pressure measured at six sections from 5% to 98%
span is shown. As seen, in all the computations, with different meshes and different gaps, apparent difference in the predicted pressure at the spanwise sections can only be found downstream of the mid-chord. The best agreement with the experimental data is obtained on the fine mesh, Mesh-2. The 98% spanwise distribution clearly shows an effect of gap size.
Figure 4 shows the effect of grid density, and turbulence model on the throughflow velocity at design conditions. A comparisons of computed throughflow isolines and the experimental results at the ex-perimental station 165 are presented. This station is located at 6% of meridional shroud length up-stream of the impeller exit. The throughflow velocity is normalized with the exit tip speed. We observe on Mesh-1 that the k-ε model reproduces better the isolines trend and in particular the location of the maximum throughflow velocity near the suction side. As expected, the Mesh-2 computation gives bet-ter results than those obtained on the coarser mesh, Mesh-1, showing the necessity to have sufficient grid density in the spanwise and circumferential directions. This grid density effect is also seen from the computation on Mesh-3 where the maximum velocity location is shifted towards the hub, showing a flow pattern similar to the prediction of the Baldwin-Lomax model on Mesh-1.
9.8.6. Conclusions
The 3D viscous flow in the NASA LSCC impeller has been computed with different meshes, different tip gap sizes, and different turbulence models to demonstrate the sensitivity of the simulations to these effects. It is shown that compared to a low Reynolds k-ε turbulence model, the algebraic Baldwin-Lomax turbulence model underpredicts the global pressure ratio and is not able to predict the flow pat-tern with the same accuracy, showing the necessity to use precise turbulence models for quantitative simulations in turbomachines. It is also shown that grid density in the spanwise and circumferential di-rections play an important role in the accuracy of the global performance data such as the pressure ra-tio as well as on local flow features. The sensitivity to the uncertainties in the geometry is demon-strated by a 50% tip gap reduction where the gap height is linearly reduced from the design height at the leading edge to half of it at the trailing edge. The tip gap reduction slightly increases the global pressure ratio and affects the pressure distribution mainly on the pressure side near the shroud (in the region where a tip leakage vortex could be expected to lie).
9.8.7. References
Chriss, R. M., Hathaway, M. D., and Wood, J. R., (1996), "Experimental and Computational Results from the NASA Lewis Low-Speed Centrifugal Impeller at Design and Part-Flow Conditions", J. of Tur-bomachinery, Vol. 118, pp.55-65.
Hathaway, M. D., Chriss R. M., Wood, J. R., and Strazisar, A. J., (1993), "Experimental and Com-putational Investigation of NASA Low-Speed Centrifugal Compressor Flow Field", J. of Turbomachin-ery, Vol. 115, pp.527.
Khodak, A., and Hirsch, Ch., (1996), "Second Order Non-Linear k-e Models with Explicit Effect of Curvature and Rotation", Computational Fluid Dynamics'96, Proceeding of the Third ECCOMAS Com-putational Fluid Dynamics Conference, 690-696.
Yang, Z., and Shih, T. H., (1993), "New Time Scale Based on k-e Model for Near-Wall Turbulence", AIAA J., Vol. 31, No.7, pp.1191-1198.
S. Kang and Hirsch Ch., (1999) “Effect of flow rate on the development of three-dimensional flow in NASA LSCC impeller, based on numerical solutions, ISABE Paper No. 99-7225.
Figure 1: Geometry and grid for the LSCC impeller
Figure 2: Effect of grid density, geometry and turbulence model on total pressure ratio
Figure 3: Effect of grid density and geometry on static pressure distribution at six sections from 5% to 98% span
(circle: experiments; Full line: Mesh2, Design Gap; Dashed line: Mesh1, Design gap; Dashed dotted line: Mesh1, 50% gap)
Baldwin-Lomax Mesh-1 K-E Mesh-1
K-E Mesh-2 K-E Mesh-3
Experiments
Figure 4: Comparisons of computed throughflow isolines with the experimental results at the station located at 6% of meridional shroud length upstream of the impeller exit