# Low-speed centrifugal compressor

Application Challenge 6-02 © copyright ERCOFTAC 2004

## Best Practice Advice for the AC

1. Key Fluid Mechanics

The LSCC Application Challenge (AC) is a state-of-the-art flow problem that addresses the essential flow physics of high-speed subsonic centrifugal compressor in a large size, low-speed machine. The Design Or Assessment Parameters (DOAPs) that have been retained for this Application Challenge are the overall pressure ratio and the adiabatic efficiency. Both are strongly influenced by the tri-dimensional flow structure present within this centrifugal impeller.

Indeed, the accumulation of low energy fluid in the shroud area is due to the radial transport of the boundary layer material along the blade surface. Its location results from a balance between the various secondary vortices, and the tip leakage flow (see Figure 1). The secondary vortices that are concerned are essentially the end-wall passage vortex (generated by the end-wall boundary layers and the blade-to-blade streamline curvature), the blade surface vortex (due to the meridional curvature of the flow channels and the blade surface boundary layers), and the Coriolis passage vortex (due to the Coriolis force and the end-wall boundary layer in the radial parts).

Figure 1. Combination of passage and blade surface vortices, after Kang and Hirsch (1999). PVH and PVS denote passage vortices at shroud and hub. BVS and BVP denote blade surface vortices at suction side and pressure side. CV denotes Coriolis passage vortex

Therefore Underlying Flow Regimes that have been considered in order to define the Best Practice Advices for this Application Challenge are the followings:

• 1-02: Blade tip and tip clearance vortex flow.

• 3-03: 2D Boundary layers with pressure gradient.

• 3-08: 3D boundary layers under various pressure gradients, including severe adverse pressure gradient causing separation.

• 4-05: Curved passage flow (accelerating).

2. Application Uncertainities

Uncertainties that are related to this Application Challenge are the followings:

• No experimental data is provided for the turbulent Reynolds stresses. Therefore, assumptions have to be made for the definition of turbulent quantities (such as turbulent kinetic energy and dissipation) at the computational domain entrance.

• Solid wall are assumed smooth and adiabatic.

• As in many radial compressor simulations there is uncertainty in the running tip clearance of the blade, due to the effects of the centrifugal and bending stresses in the blade, temperature distortions of the casing and manufacturing tolerances. The sensitivity of DOAPs to these effects has already been examined by running a simulation at the design point with a smaller tip gap (Kang and Hirsch, 1999). This induces an increase of both the computed pressure ratio and efficiency of about 0.4% and 1%, respectively.

• Design Or Assessment Parameters obtained from measurements are not necessarily identical to those derived from numerical experiment. On the one hand, for the LSCC test case, both pressure ratio and adiabatic efficiency where inferred from 26 and 22 measurement points from the hub to the shroud at station 1 and 2, respectively. On the other hand, computed DOAPs derived from an integration on all grid cells from hub to shroud. For the LSCC test case at design point, Rautaheimo et al. (2001) have identified that when using the same points as in the experiment, the pressure ratio increases by about 0.8%. No big difference has been identified for the efficiency.

Computational Domain and Boundary Conditions

The LSCC Application Challenge requires the use of a tri-dimensional mesh that encompasses at least one blade passage. The computational domain extends from 40% meridional shroud length upstream of the impeller, to 15% impeller tip radius downstream in the radial direction. A blunt blade tip can be used, even though the real tested blade tips are rounded.

At the inlet plane, measured profiles of absolute flow angles, total pressure and an uniform total temperature are imposed. Static pressure is extrapolated from the interior. For one- equation (or more) turbulence models, boundary conditions should be specified on the turbulent quantities. It is suggest to impose a turbulent intensity of 1% together with a turbulent to laminar viscosity ratio of 10.

At the radial outlet mass flow is imposed.

Solid walls are assumed smooth and adiabatic.

Discretisation and Grid Resolution

In order to accurately predict the DOAPs the following recommendations on the discretisation and grid resolution are made:

• A second order (or above) numerical scheme is advised.

• An adequate resolution in the spanwise and pitchwise directions is required. Computations have been performed with 73 and 61 grid points in the radial and pitchwise direction, respectively (total number of points: about 600,000). The pressure ratio is particularly sensitive to this choice.

• The grid resolution in the boundary layer needs to be sufficient to capture the details of the boundary layer flows.

• The mesh should also be refined outside of the near-wall region.

• As suggested in BPAs for AC1-02, a minimum of 15 to 20 grid points across the vortices cores is necessary in order to resolve the high velocity gradients.

Physical Modelling

In order to accurately predict the DOAPs the following recommendations on the physical models used are made:

• A value of y+ at the first grid points near solid walls should be defined in accordance with the requirements of the turbulence model used. A value close to unity is required for Low-Reynolds models.

• The algebraic Baldwin-Lomax turbulence model is sufficiently accurate for a qualitative prediction of the flow patterns and for an estimate of the DOAPs.

• However, a more accurate prediction of the DOAPs and of the details aspects of the flow patterns requires the use of more precise Low-Reynolds turbulent models based on transport equations for turbulent quantities.

Recommendations for Future Work

In order to improve the quality of the BPAs, several recommendations for future work could be provided.

• To perform a new computation of this AC with a higher number of grid points in the spanwise direction (at least 81).

• To make a sensitivity study of the DOAPs to the number of grid points used in the streamwise direction.

• To perform new calculations with more recent turbulence models such as Spalart-Allmaras, SST, v2-f, and Reynolds Stress models.

• To make a sensitivity study of the DOAPs to the inlet boundary condition used for the turbulent quantities.

## 7. References

S. Kang, Ch. Hirsch, 1999, “Numerical investigation of the three-dimensional flow in NASA low-speed centrifugal compressor impeller”. 4th International Symposium on Aerothermodynamics of internal flows. Sept. 1999, Dresden.

P. Rautaheimo, E. Salminen, and T. Siikonen, 2001, “Numerical simulation of the flow in the NASA Low-Speed Centrifugal Compressor”. Submitted to ASME Journal of Turbomachinery. 2001.