Investigation of Mixed Micro-Compressor Casing Treatment Using Non-Matching Mesh Interface

Abstract

In this paper, a non conservative interpolation boundary condition, for the non-matching mesh blocks, was developed and validated for the micro compressor casing treatment. The conservative variables were interpolated in the halo layers of nonmatching mesh interface using Finite Element Method (FEM) type linear interpolation shape functions, instead of using overset grids. Using this new boundary condition, the effect of casing treatment on stall margin and compressor performance is investigated for a mixed flow type micro-compressor. The computed compressor performance map for the casing treatment case is compared with the experimental results and shows good agreement except in the region close to stall. With the application of the casing treatment, improvement in the stall margin is observed without the loss of efficiency over the operating range. NOMENCLATURE Lre f Reference length dw Wall normal distance ρ∞ Freestream density U∞ Freestream velocity μ∞ Freestream dynamics viscosity Ω Vorticity Wt Tangential velocity in relative frame ∗Ph.D. Student †Professor, ASME Fellow Vt Tangential velocity in absolute frame Vm Meridional velocity β Relative flow angle= tan(−Wt/Vm) α Absolute flow angle= tan(Vt/Vm) Re Reynolds number SS Suction Surface PS Pressure Surface SA Spalart-Allmaras B.C. Boundary Condition CT Casing Treatment MUSCL Monotonic Upwind Scheme for Conservation Laws CFD Computational Fluid Dynamics FEM Finite Element Method INTRODUCTION Aviation industry is constantly striving to increase the aerodynamic efficiency of aircraft and thereby reducing the fuel consumption and its emission pollution. High lift and low drag wing design is one of the crucial requirements of aircraft design. Active flow control is considered as a promising direction to improve the airfoil performance. Zha et al. [1–4] have developed Co-Flow Jet active flow control airfoil, which is demonstrated to achieve very high lift coefficient, reduce drag, and also improve the cruise efficiency. One of the vital component of Co-Flow Jet technology is the micro-compressor actuator to draw a mass flow near the trailing edge, pressurize it and eject the flow near 1 Copyright c © 2019 by ASME the leading edge. As this compressor needs to work under various operating conditions during take-off, cruise and landing, its design needs to encompass wide operating range with high efficiency. Over the last two decades, aircraft engine compressors and fans are designed with increased loading to reduce the size and weight. This brings more attention to the study of effects of increased blade tip loading. Blade tip loading plays an important role to the tip vortex, which is one of the primary source of stall inception. The tip vortex trajectory normal to the main flow is considered as near stall operating point. Low-momentum tip vortex near the rotor tip leading edge causes flow spillage and leads to stall inception [5]. It is observed that the extraction of this low axial momentum flow and reinjection of the same in the main flow with Casing Treatment (CT) helps to improve the stall margin of compressors [6, 7]. Various designs of Casing Treatment (CT) are devised, including circumferential grooves CT [8], non-axisymmetric slottype CT [9], honeycomb CT [10], self-recirculating flow channels [6, 11], ported shroud casing treatment [7] and multiple cylindrical hole casing treatment (MHCT) [12]. In the early development, researchers found that apart from enhancing operating range, they brought penalty mostly in the form of efficiency. In order to mitigate the efficiency penalty, over the time various CT designs have been proposed and investigated to understand their effect on the tip leakage flow and thereby its influence on the main passage flow. Based on Khalid [10], the use of flow aligned honeycomb casing treatment gives higher stall margin than the circumferential grooves as it helps to absorb tangential energy in the flow and enhances streamwise flow momentum by aligning flow more axially. Hathaway [6] showed the concept of the self-recirculating casing treatment to increase the stall margin with minimal or no decrement to efficiency, where pressure difference across the CT acts as a driving force for fluid movement and the direction of flow in CT is determined by high pressure side of CT. Chen et al. [7] demonstrated that the use of ported CT design for centrifugal compressor can enhance stall margin by reducing the strength of shock on the blade suction surface and removal of low momentum flow due to recycling it by port CT. Yang et al. [12] investigated the effect of extraction hole area and its location on transonic axial compressor stability margin. Based on their findings, penalty on the compressor pressure ratio and efficiency is influenced by the amount of recirculation flow governed by the size of extraction hole and its location. In general, CT design needs to reduce accumulation of low momentum area and move the trajectory of tip vortex from circumferential to axial in order to delay stall inception. Most of the previous CT studies are focused on aircraft engine compressors with high Reynolds number. Recently, with the growing importance of active flow control for aircraft performance, micro-compressors used as actuators for active flow control open a new area of research and applications [13]. The micro-compressors usually have the diameters in the order of less than 8cm, which brings the Reynolds number in the order of 50,000 or less. The small Reynolds number make the flow prone to separation and make the compressor prone to stall. Casing treatment to extend the operating range of micro-compressors are hence very important. The other feature of micro-compressors is that they are often designed as mixed type to take the advantage of the compactness of centrifugal compressors and high mass flow rate of axial compressors. Few casing treatment studies for mixed micro-compressors are seen in literatures. In the present research, the casing treatment of a mixed micro-compressor is simulated and investigated. The casing treatment comprises of multiple cylindrical channels to extract flow from casing and collection chamber. Numerical investigation of such CT design requires generation of high quality grid. Grid clustering and proper smoothness have remained nettlesome task for the solution of 3D Navier-Stokes equations. With the increasing geometric complexity, creating structured conformal mesh is becoming increasingly difficult and sometimes prohibitive. This leads to the development of gridembedding or overset grid technique. Benek et al. [14] developed chimera grid-embedding method allowing more flexibility to generate boundary-conforming grids on components part of geometry, refining mesh in the region of interest, and allowing different flow model solution on different grid. This method in the original form uses non-conservative trilinear interpolation scheme. Kao et al. [15] developed Dragon grid, which is a hybrid grid scheme preserving the strength of Chimera grid, and at the same time preserving conservation of conservative properties by embedding unstructured grid in the hole region of Chimera grid. Fenwick et al. [16] implemented FEM like halo layer interpolation. This paper is intended to develop a general numerical strategy to simulate any type of compressors casing treatments. A mixed micro-compressor casing treatment is investigated due to the scarcity of the research in this area and its extremely high importance for active flow control. The objective of this paper is to introduce a new FEM type interpolation boundary condition across the interface between the CT channel and compressor flow path with non-matching mesh, which is non-conservative. The advantage of this method is its convenience to treat casing treatment without matching mesh across interface for flux conservation, but it still achieves a fairly good accuracy as to be demonstrated. The major difference between Fenwick’s implementation and the present one lies in the way of searching halo cells position and determining their associated weights, which are mentioned later on. The present implementation is validated with the experimental results of a mixed micro-compressor with self recirculating casing treatment. Using this non-matching mesh interface treatment, the effect of the self-recirculating casing treatment on the mixed 2 Copyright c © 2019 by ASME micro-compressor stability and its performance is studied. GOVERNING EQUATIONS IN GENERALIZED COORDINATES The in-house CFD solver, originally developed by the CFD and Aerodynamics lab at the University of Miami, is used in the present research. The Favre-averaged RANS equation along with one equation Spalart-Allmaras (SA) turbulence model are solved in fully coupled manner using an implicit unfactored Gauss-Seidel line iteration to achieve high convergence rate. The Favre-averaged RANS equations are nondimensionalized using Lre f , ρ∞, U∞ and μ∞ and their differential form in generalized coordinates are given by: ∂Q ∂ t + ∂E ∂ξ + ∂F ∂η + ∂G ∂ζ = 1 Re [ ∂R ∂ξ + ∂S ∂η + ∂T ∂ζ ] +Sv (1)