# Low-speed centrifugal compressor

## Comparison of Test data and CFD

The computations presented in this section have been done by S. Kang and Ch. Hirsch (1999a,b) with the FINE/TurboTM finite volume code developed by NUMECA International, Hirsch et al. (1992).

Table-I lists the cases of CFD results. 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 consists of 422,735 points in total with 13 lines over the gap height whereas the second mesh, named Mesh-2 hereafter has more points in the pitchwise and hub to shroud directions with a total number of points equal to 616,739.

Particular care has been taken in order to ensure sufficient resolution in the end walls and blade boundary layers by controlling the position of the mesh points close to the solid surfaces. The grid location near the blade surfaces for Mesh-1 and for Mesh-2 produces a y+ value for the first cell center less than 1. A third mesh named Mesh-3, coarser than the two first counts178201 mesh points. The y+ value at the first inner cell is about y+ =2.

 Mesh-1 Mesh-2 Mesh-3 Design flow rate B-L ${\displaystyle \kappa -\varepsilon }$ ${\displaystyle \kappa -\varepsilon }$ ${\displaystyle \kappa -\varepsilon }$ Design Gap * * * * 50% Design Gap * Off-design flow rate ${\displaystyle {(78.8\%m_{d})}}$ Design gap * * Off-design flow rate ${\displaystyle {(133\%m_{d})}}$ Design gap *

## Table I: Test cases definition

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 points computed with Mesh-3, while for the 50% gap case, there is only one point computed with Mesh-1 and the Baldwin-Lomax turbulence model. At the low 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. For the high off-design flow rate, a single calculation with the design gap and the k-ε model on Mesh-2 is carried out. 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 clearance 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 examined 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(2.54mm) 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 (the blade height is linearly growing from leading edge to trailing edge).

Figure 8 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 increases about 0.4%. The computation on the coarse mesh Mesh-3 gives the lowest pressure ratio prediction with an underestimation of about 1%. The efficiency presented in figure 9 shows that for both Mesh 1 and Mesh 2, the efficiency is higher than the data at both design and off-design flow rate. Reducing the gap size results in an increase in the efficiency

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 Mesh2, putting the calculated operating point further away from the experiments.

Figure 10 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 11 shows the effect of grid density, and turbulence model on the absolute throughflow velocity normalized by the impeller tip speed at design conditions. A comparisons of computed throughflow isolines and the experimental results at the experimental station 165 are presented. This station is located at 6% of meridional shroud length upstream 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 better 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.

Figure 8: Effect of grid density, geometry and turbulence model on total pressure ratio

Figure 9: Effect of grid density, geometry and turbulence model on the global efficiency

Figure 10: 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 11:Comparison of contour plots of the absolute throughflow velocity normalized by impeller tip speed with the experimental results at the station located at 6% of meridional shroud length upstream of the impeller exit It is shown that grid density in the spanwise and circumferential directions play an important role in the accuracy of the global performance data such as the pressure ratio as well as on local flow features.

The presented computations show that the algebraic Baldwin-Lomax turbulence model is sufficiently accurate for most engineering cases. However, if detailed flow patterns want to be captured accurately then the use of more precise turbulence models such as low Reynolds two equation models are recommended.