Xiaofeng Sun

Constructing spectral schemes of the immersed interface method via a global description of discontinuous functions

A global description of discontinuous functions is introduced in this paper. By expressing a discontinuous function as the sum of a smooth function and a correction term determined by jump conditions, we turn the unknown function from a discontinuous one into a sufficiently smooth one when solving a differential equation. Spectral schemes are developed based on this concept with the intention of eliminating or reducing the Gibbs oscillation. Finite difference schemes are also constructed as an alternative of the current immersed interface methods. Both spectral and finite difference schemes are tested on one- and two-dimensional cases.

A General Theory of Flow-Instability Inception in Turbomachinery

A general eigenvalue theory on flow stability in turbomachinery is proposed with the emphasis on flow-instability onset. Based on this theory, a stall-inception model including the effects of complex solid geometry is developed for a multistage fan/compressors system. The capacity of the present model to predict the stall-inception point is assessed against experimental data of both a low-speed and transonic single rotor. Comparisons with a simplified two-dimensional model are performed to identify the nonnegligible effects of spanwise distribution of flowfield in a general configuration on the unstable mode of the concerned fan/compressors. It is verified that this model is capable of predicting mass flow at the stall-onset point of both subsonic and transonic flow with a reasonable accuracy, and it is sustainable in terms of computation cost for industrial application.

Further Investigation on Transonic Compressor Stall Margin Enhancement With Stall Precursor-Suppressed Casing Treatment

A kind of casing treatment, named as stall precursor-suppressed (SPS), has been developed recently, which was proved to be able to effectively improve stall margin (SM) without significant efficiency loss in low-speed axial flow compressors and a transonic compressor rotor. In this paper, the effectiveness of the SPS casing treatment is investigated in a single-stage transonic compressor. Based on an extended stall inception model, the quantitative evaluation of the SM enhancement by the SPS casing treatment is presented for the transonic compressor stage. The model predicts that a 2.5–6.8% of stall margin improvement (SMI), which is defined in terms of mass flow rate at stall inception, can be achieved at the design rotational speed. The experimental results show that the SPS casing treatment can achieve 3.5–9.3% of the SMI at 95% design rotational speed. Due to the fact that the distributions of the total pressure ratio along the spanwise direction are kept the same as those of the solid wall casing at the same mass flow rate, the SPS casing treatments with a small open area ratio and large backchamber enhance the SM without a recognizable efficiency loss and a migration of the pressure-rise characteristics. Furthermore, the mechanism of SMI with the SPS casing treatment is investigated in the experiments. In comparison with the solid wall casing, the emergence and the evolution of the stall inception waves are suppressed and the nonlinear development of the stall process is delayed with the SPS casing treatment.

Effects of Rotating Inlet Distortion on Compressor Stability With Stall Precursor-Suppressed Casing Treatment

This paper conducts an experimental research of rotating inlet distortion on a low-speed large size test compressor with emphasis on the stability problem of axial fan/compressors, and the stall margin enhancement with a kind of stall precursor-suppressed (SPS) casing treatment. Some results on compressor stall margin and prestall behavior under the restriction of rotating inlet distortion are presented. The experimental results show that whether the inlet distortion is co-rotating or counter-rotating, the SPS casing treatment can still improve the stall margin without leading to additional efficiency loss caused by such configuration. The experiment results also show that the mechanism of the stall margin improvement with such casing treatment is associated with delaying the nonlinear development of the stall precursor waves and weakening the unsteady flow disturbances in a compression system.

An Evaluation Approach for the Stall Margin Enhancement With Stall Precursor-Suppressed Casing Treatment

It is known that a kind of stall precursor-suppressed (SPS) casing treatment can be used to enhance compressor stall margin (SM) without recognizable efficiency loss. The further requirement in this regard is to develop an effective way to determine the variation range of the SM improvement during the design of such SPS casing treatment. In this investigation, based on the extrapolation hypothesis and the existing work, an extended stall inception model for quantitative evaluation of the SM enhancement is presented for both subsonic and transonic compressors with the SPS casing treatment. The capability of the extended model to quantitatively evaluate the SM enhancement with the SPS casing treatment is validated against the experimental data. The quantitative evaluation results show that the SPS casing treatments with different geometric parameters can improve the SM by a diverse percentage. In particular, for the facilities used in the present investigation, the experiments show that the SPS casing treatments can cause relevant increases of the SM. The change trend of the SM enhancement with various design parameters of the SPS casing treatment is in line with the corresponding theoretical results.

Multi-domain Spectral Immersed Interface Method for Solving Elliptic Equation with a Global Description of Discontinuous Functions

Abstract This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed interface method(IIM) divides the whole computation domain into the smooth and discontinuous parts. Fewer points on the smooth domains are used via taking advantage of the high accuracy property of the spectral method, but more points on the discontinuous domains are employed to enhance the resolution of the calculation. Two discontinuous problems are tested to verify the present method. The results show that the domain decomposition technique can reduce the error of the spectral IIM, especially when more collocation points are placed around the discontinuity. The present method is favorable for the reason that the same level of the accuracy can be reached, in spite of the enlarged computational domain.

Flow Instability Inception Model of Compressors based on Eigenvalue Theory

An eigenvalue theory on flow stability in turbomachinery is proposed with the emphasis on flow instability onset. Based on this theory, a stall inception model including the effects of complex solid geometry is developed for multi-stage fan/compressors system. The capacity of the present model to predict the stall inception point is assessed against experimental data of both low speed and transonic single rotor. Comparisons with a simplified two-dimensional model are performed to identify the nonnegligible effects of spanwise distribution of flow field in a general configuration on the unstable mode of the concerned fan/compressors. It is verified that this model is capable of predicting stall onset point of both subsonic and transonic flow with a relative error of less than 1.8%, and it is sustainable in terms of computation cost for industrial application.

A Theoretical Model for Flow Instability Inception in Transonic Fan/Compressors

This paper applies a theoretical model, which has been developed recently, to calculate the flow instability inception of axial transonic fan/compressors system. After the mean flow field is computed by steady CFD simulation, a body force approach, which is a function of flow field data, is taken to represent the effects of discrete blades on the flow field and duplicate the physical sources of flow turning and loss. Further by applying appropriate boundary conditions and spectral collocation method, a group of homogeneous equations will yield from which the stability equation can be derived. The singular value decomposition method is adopted over a series of fine grids in frequency domain to solve the resultant eigenvalue problem, and the onset point of flow instability can be judged by the imaginary part of the resultant eigenvalue. The present investigation is to validate the feasibility of calculating the stall onset point for single stage transonic compressor. It is shown that this model is capable of predicting instability inception point of transonic flow with reasonable accuracy, and it is sustainable in terms of computational cost for industrial application. It is shown that this model can provide an unambiguous judgment on stall inception without numerous requirements of empirical relations of loss and deviation angle. It provides a possibility to check overpredicted stall margin during the design phase of new high speed fan/compressors. In addition, the effect of flow compressibility on the stall onset point calculation for transonic rotor is studied.

Stall-Warning Approach Based on Aeroacoustic Principle

In a fan/compressor, the pass of the blade is a periodic event and this periodicity deteriorates when rotating stall is gradually approached. The present work studies this periodicity of the pressure signal and explains when and why this periodicity deterioration happens from the perspective of the aeroacoustic principle. A theoretical analysis shows that the change of blade circulation has a close association with rotating stall and can be reflected on the periodicity deterioration of pressure signals sampled by a near-field dynamic pressure sensor located on the casing wall. A defined parameter Rc, which can revalue this periodicity, has the potential to be a stall-warning criterion. Then, a stall-warning approach is developed in terms of this feature. The values of Rc are calculated by the pressure signals of several blade pitches based on the current and the previous shaft periods. Statistical estimations are conducted on Rc within statistical windows by calculating the probabilities of Rc less than a...

Calculation of Flow Instability Inception in High Speed Axial Compressors

This paper applies a theoretical model developed recently to calculate the flow instability inception point in axial high speed compressors system. After the mean flow field is computed by steady CFD simulation, a body force approach, which is a function of flow field data and comprises of one inviscid part and the other viscid part, is taken to duplicate the physical sources of flow turning and loss. Further by applying appropriate boundary conditions and spectral collocation method, a group of homogeneous equations will yield from which the stability equation can be derived. The singular value decomposition method is adopted over a series of fine grid points in frequency domain, and the onset point of flow instability can be judged by the imaginary part of the resultant eigenvalue. The first assessment is to check the applicability of the present model on calculating the stall margin of one single stage transonic compressors at 85% rotational speed. The reasonable prediction accuracy validates that this model can provide an unambiguous judgment on stall inception without numerous requirements of empirical relations of loss and deviation angle. It could possibly be employed to check over-computed stall margin during the design phase of new high speed fan/compressors. The following validation case is conducted to study the nontrivial role of tip clearance in rotating stall, and a parameter study is performed to investigate the effects of end wall body force coefficient on stall onset point calculation. It is verified that the present model could qualitatively predict the reduced stall margin by assuming a simplified body force model which represents the response of a large tip clearance on the unsteady flow field.Copyright