Multistage Axial Flow Compressor Research Articles

Analysis of Unsteady Blade Row Interaction Using Nonlinear Harmonic Approach

An efficient non-linear harmonic methodology has been developed for predicting unsteady blade row interaction effects in multistage axial flow compressors. Flow variables are decomposed into time averaged variables and unsteady perturbations, resulting in time averaged equations with deterministic stress terms depending on the unsteady perturbation. The non-linear interaction between the time averaged flow field and the unsteady perturbations are included by a simultaneous pseudotime integration approach, leading to a strongly coupled solution. The stator/rotor interface treatment follows a flux averaged characteristic based mixing plane approach and includes the deterministic stress terms due to upstream running potential disturbances and downstream running wakes, resulting in the continuous nature of all parameters across the interface. The basic computational methodology is applied to the three-dimensional Navier-Stokes equations and validated against several cases. Results show that this method is much more efficient than the non-linear time-marching methods while still modeling the nonlinear unsteady blade row interaction effects.Copyright © 2000 by ASME

Performance prediction of axial flow compressors using stage characteristics and simultaneous calculation of interstage parameters

A new method for predicting performance of multistage axial flow compressors is proposed that utilizes stage performance curves. The method differs from the conventional sequential stage-stacking method in that it employs simultaneous calculation of all interstage variables (temperature, pressure and flow velocity). A consistent functional formulation of governing equations enables this simultaneous calculation. The method is found to be effective, i.e. fast and stable, in obtaining solutions for compressor inlet and outlet boundary conditions encountered in gas turbine analyses. Another advantage of the method is that the effect of changing the angles of movable stator vanes on the compressor's operating behaviour can be simulated easily. Accordingly, the proposed method is very suitable for complicated gas turbine system analysis. This paper presents the methodology and performance estimation results for various multistage compressors employing both fixed and variable vane setting angles. The effect of interstage air bleeding on compressor performance is also demonstrated.

Influence of deterministic stresses on flow prediction of a low-speed axial flow compressor rear stage

Deterministic stresses are used to describe the unsteady effects on the flow field in multistage axial flow compressors. In this paper, a circumferentially non-uniform mixing plane method implemented with deterministic stresses is used for the flow prediction inside the rear stage of an axial flow compressor in a multistage environment. The deterministic stress field is calculated with an overlapped solution approach for the same flow passage and implemented with the Navier-Stokes equations in order to provide continuous interfaces. The aerodynamic boundary condition is simplified with the application of a repeating stage model where only the mass flowrate and stage exit average static pressure are required. Two computational cases for the third stage of the Cranfield low-speed research compressor, one with the mixing plane model and the second with the mixing plane model in combination with deterministic stresses, are examined and compared with each other and also with corresponding experimental data. It is shown that the implementation of the deterministic stresses is beneficial for the flow prediction but the improvement in accuracy for low-speed axial flow compressor rear stages is not significant.

Three-dimensional flow field downstream of an embedded stator in a multistage axial flow compressor: Part 1: Steady and unsteady flow fields

A comprehensive investigation of the three-dimensional unsteady flow and thermal field downstream of an embedded stator in a multistage compressor, acquired with a high-response hot-film probe and aspirating probe, is presented and analysed. Some of the earlier data (from a five-hole probe and a high-response Kulite probe) from the same compressor is used with the present data to provide an integrated interpretation of the flow and thermal fields. Part 1 includes a brief description of the facility, the development of the hot-film technique for the multistage flow field measurement and an interpretation of the various flow field features, such as the hub clearance flow and the suction surface-casing end-wall corner region. Part 2 covers velocity-velocity and velocity-temperature correlations and the assessment of their magnitudes in the average-passage equations. The results presented in this part of the paper (Part 1) indicate that major blockage in the stator hub end wall is caused by leakage flow and its possible subsequent roll-up into a vortex. Similar features exist in the suction surface casing end-wall corner due to secondary flow and its interaction with the upstream rotor end-wall flow. These are also the regions with the highest levels of unsteadiness. The transport of rotor wake towards the pressure side of the stator is confirmed. Both the revolution and the blade periodic velocity fluctuations are found to be significantly greater than the aperiodic fluctuations.

Three-dimensional flow field downstream of an embedded stator in a multistage axial flow compressor: Part 2: Deterministic stress and heat flux distribution and average-passage equation system

The results from the area traverse measurements of the unsteady velocity and total temperature downstream of the second stator of a three-stage axial flow compressor have been correlated to derive various deterministic stress and heat flux terms. These terms are consistent with those arising from the average-passage equation system of Adamczyk. The deterministic periodic stress and heat flux terms were found to be larger than the aperiodic terms for both the normal and the shear components. Consequently the terms involving the aperiodic components in the average-passage equations could be neglected for stator exit and rotor inlet flow modelling. The deterministic periodic normal and shear stresses were seen to be most significant in the stator wakes away from the end-wall regions. The most significant shear stress correlation was between the axial and the tangential velocity components. Since the correlations involving the radial component were small, it is postulated that the dominant mechanism for mixing (in the radial direction) is due to the steady deterministic radial velocity. All three components of deterministic heat flux were found to be significant in this flow field, especially in the wakes. The dominant terms in the average-passage equation system away from the end walls were due to the tangential gradient compared with the radial gradient terms and both the terms were found to be of equal importance in the hub and casing end-wall regions.

Viscous-Flow Two-Dimensional Analysis Including Secondary Flow Effects

During the last few decades extremely powerful Quasi-three-dimensional (3D) codes and fully 3D Navier-Stokes solvers have been developed and successfully utilized in the design process and optimization of multistage axial-flow compressors. However, most of these methods proved to be difficult in handling and extremely time consuming. Due to these disadvantages, the primary stage design and stage matching as well as the off-design analysis is nowadays still based on fast 2D methods incorporating loss-, deviation- and end wall modeling. Only the detailed 3D optimization is normally performed by means of advanced 3D methods. In this paper a fast and efficient 2D calculation method is presented, which already in the initial design phase of multistage axial flow compressors, considers the influence of hub leakage flows, tip clearance effects, and other end wall flow phenomena. The method is generally based on the fundamental approach by Howard and Gallimore (1992). In order to allow a more accurate prediction of skewed and nondeveloped boundary layers in turbomachines, an improved theoretical approach was implemented. Particularly the splitting of the boundary layers into an axial and tangential component proved to be necessary in order to account for the change between rotating and stationary end walls. Additionally, a new approach is used for the prediction of the viscous end wall zones including hub leakage effects and strongly skewed boundary layers. As a result, empirical correlations for secondary flow effects are no longer required. The results of the improved method are compared with conventional 2D results including 3D loss- and deviation-models, with experimental data of a three-stage research compressor of the Institute for Jet Propulsion and Turbomachinery of the Technical University of Aachen and with 3D Navier-Stokes solutions of the V84.3A compressor and of a multistage Siemens research compressor. The results obtained using the new method show a remarkable improvement in comparison with conventional 2D methods. Due to the high quality and the extremely short computation time, the new method allows an overall viscous design of multistage compressors for heavy duty gas turbines and aeroengine applications.

Effective Performance Prediction of Axial Flow Compressors Using a Modified Stage-Stacking Method

In this work, a modified stage-stacking method for the performance prediction of multi-stage axial flow compressors is proposed. The method is based on a simultaneous calculation of all interstage variables (temperature, pressure, flow velocity) instead of the conventional sequential stage-by-stage scheme. The method is also very useful in simulating the effect of changing angles of the inlet guide vane and stator vanes on the compressor operating characteristics. Generalized stage performance curves are used in presenting the performance characteristics of each stage. General assumptions enable determination of flow path data and stage design performance. Performance of various real compressors is predicted and comparison between prediction and field data validates the usefulness of the present method.

The Influence of Shrouded Stator Cavity Flows on Multistage Compressor Performance

Experiments were performed on a low-speed multistage axial-flow compressor to assess the effects of shrouded stator cavity flows on aerodynamic performance. Five configurations, which involved systematic changes in seal-tooth leakage rates and/or elimination of the shrouded stator cavities, were tested. Rig data indicate increasing seal-tooth leakage substantially degraded compressor performance. For every 1 percent increase in seal-tooth clearance-to-span ratio, the decrease in pressure rise was 3 percent and the reduction in efficiency was 1 point. These observed performance penalties are comparable to those commonly reported for rotor and cantilevered stator tip clearance variations. The performance degradation observed with increased leakage was brought about in two distinct ways. First, increasing seal-tooth leakage directly spoiled the near-hub performance of the stator row in which leakage occurred. Second, the altered stator exit flow conditions, caused by increased leakage, impaired the performance of the next downstream stage by decreasing the work input of the rotor and increasing total pressure loss of the stator. These trends caused the performance of downstream stages to deteriorate progressively. Numerical simulations of the test rig stator flow field were also conducted to help resolve important fluid mechanic details associated with the interaction between the primary and cavity flows. Simulation results show that fluid originating in the upstream cavity collected on the stator suction surface when the cavity tangential momentum was low and on the pressure side when it was high. The convection of cavity fluid to the suction surface was a mechanism that reduced stator performance when leakage increased.

The nature of wakes in multistage axial flow compressors

This paper describes the measurement and processing of unsteady turbulence data from a multistage low-speed compressor. In this study, a two-element hot-wire probe was traversed along a circumferential path downstream of the third rotor row of a large-scale low-speed four-stage facility. Simultaneous circumferential and axial velocity measurements were made. Three flow conditions were measured: peak efficiency with blade Re = 200000. peak efficiency with blade Re = 55 000 and close to stall with blade Re = 200 000. Ensemble averaging has been used to deduce the periodic components of the velocity. In addition, measurements have been made of turbulence intensity, turbulence length scale and turbulent shear stress (Reynolds stress).

Search for compromise solution of the multistage axial compressor’s stochastic optimization problem

The aim of this paper is to discuss a method of the compromise region determination for the multistage axial flow compressor stochastic optimization problems. This method is based on the 2-D axisymmetrical mathematical model of the compressor and on the new multicriteria optimization procedure. A specific feature of the multicriteria optimization procedure is a possibility to obtain a set of the Edgeworth-Pareto optimal solutions within the frame of single optimization task. The paper presents some examples of the compressor’s geometrical parameters multicriteria optimization.

Numerical optimization of a stator vane setting in multistage axial-flow compressors

This paper presents a numerical methodology for optimizing a stator stagger setting in a multistage axial-flow compressor environment. The method involves simultaneous resetting of several blade rows, which influences overall performance in a complex manner. The paper is presented in four parts: modelling the effect of stagger setting on individual stage performance, overall performance including surge point prediction, stagger setting optimization and numerical examples. The stage performance model is a one-dimensional meanline method where correlations are used to introduce real flow effects. The method uses (experimental or predicted) stage characteristics at design (nominal) setting to generate characteristics at other settings. A stage-by-stage model is used to ‘stack’ the stages together with a dynamic surge prediction model. A direct search method incorporating a sequential weight increasing factor technique (SWIFT) was then used to optimize stagger setting. The objective function in this optimization is penalized externally with an updated factor which helped to accelerate convergence. The methodology has been incorporated into a FORTRAN program and validated using data from a seven-stage aircraft compressor with hypothetical variable stagger vanes. Results have demonstrated that variable stagger is a powerful method to rematch stages which can be used to improve desired overall performance. Parametric studies on the optimization algorithm have also been conducted where it showed numerical stability and fast convergence.

Aspirating Probe Measurements of the Unsteady Total Temperature Field Downstream of an Embedded Stator in a Multistage Axial Flow Compressor

The results from the area traverse measurements of the unsteady total temperature using a high-response aspirating probe downstream of the second stator of a three-stage axial flow compressor are presented. The measurements were conducted at the peak efficiency operating point. The unsteady total temperature data are resolved into deterministic and unresolved components. Hub and casing regions have high levels of unsteadiness and consequently high levels of mixing. These regions have significant levels of shaft resolved and unresolved unsteadiness. Comparisons are made between the total temperature and the total pressure data to examine the rotor 2 wake characteristics and the temporal variation of the stator exit flow. Isentropic efficiency calculations at the midpitch location show that there is about a 4 percent change in the algebraically averaged efficiency across the blades of the second rotor and if all the rotor 2 blades were behaving as a “best” blade, the improvement in efficiency would be about 1.3 percent. An attempt is made to create a composite flow field picture by correlating the unsteady velocity data with temperature and pressure data.

Unsteady Total Pressure Field Downstream of an Embedded Stator in a Multistage Axial Flow Compressor

The results from measurements of the unsteady total pressure field downstream of an embedded stage of a three stage axial flow compressor are presented in this paper. The measurements include area traverses of a high response kulite total pressure probe and a pneumatic five hole probe downstream of stator 2 at the peak efficiency operating point for the compressor. These data indicate that both the shaft-resolved and unresolved fluctuations contribute to the unsteadiness of the total pressure field in multistage compressors. Specifically, regions associated with high levels of unsteadiness and, consequently, high levels of mixing including both the hub and casing end walls and the airfoil wakes have significant levels of shaft resolved and unresolved unsteadiness. Temporal variations of stator exit flow are influenced by both shaft resolved and unresolved unsteadiness distributions. The limitations of state-of-the-art instrumentation for making measurements in moderate and high speed turbomachinery and the decomposition used to analyze these data are also discussed.

Analysis of Instability Inception in High-Speed Multistage Axial-Flow Compressors

A nonlinear, two-dimensional, compressible dynamic model has been developed to study rotating stall/surge inception and development in high-speed, multistage, axial flow compressors. The flow dynamics are represented by the unsteady Euler equations, solved in each interblade row gap and inlet and exit ducts as two-dimensional domains, and in each blade passage as a one-dimensional domain. The resulting equations are solved on a computational grid. The boundary conditions between domains are represented by ideal turning coupled with empirical loss and deviation correlations. Results are presented comparing model simulations to instability inception data of an eleven stage, high-pressure-ratio compressor operating at both part and full power, and the results analyzed in the context of a linear modal analysis.

Exit Flowfield of an Embedded Stator in a Multistage Axial Flow Compressor

A complete area traverse downstream of the second stator of the Pennsylvania State University Multistage Compressor Facility has been carried out at the peak efŽ ciency and peak pressure ratio operating conditions using a miniature (1.07-mm-diam) Ž ve-hole probe and a thermocouple probe. Axial velocity, total pressure, and total temperature contours are presented and discussed at both operating conditions. Blade-to-blade proŽ les of total velocity and absolute  ow angle presented at three representative radii show the effect of loading on the wake structure between the two operating conditions. The stator clearance  ow and hub rotation result in  ow underturning (from design), which persists up to 10% of the span from the hub. A region of low  uid momentum develops on the suction side of the stator blade endwall (casing region) corner at both operating conditions. The low  uid momentum region in the suction side casing endwall corner is identiŽ ed as the dominant source of  ow unsteadiness to the downstream rotor at both compressor operating conditions. This is seen in the distribution of apparent stresses, which are conŽ ned to the wake region along most of the span, with the exception of the low  uid momentum core in the endwall region where signiŽ cant levels are reached across a substantial portion of the passage at both operating conditions.

Active Control of Surge in Multi-Stage Axial-Flow Compressors

This paper deals with a theoretical study of the active control of purely axial 1D instabilities in multi-stage axial-flow compressors. The paper briefly considers the development of a suitable surge model and continues with the derivation of a controller using linear optimal control theory. The controller is specifically designed to suppress the instabilities predicted by the linearised form of the surge model. The control technique involves a bleed being dynamically varied in response to fluctuations of variables. It is found that a stabilising optimal controller can always be obtained. The second part of the paper presents a non-linear simulation of the surge prediction model with the linear controller, using a 4th order Runge-Kutta scheme. This demonstrates how some non-linearities in the flow model can affect the controller operation. It is also shown that, the amplitudes and the frequency response required of the actuator to retain stability can exceed the practical limitations.Copyright © 1993 by ASME

Stability Analysis of Axial Flow Compressor Based Lyapunov Method.

The multistage axial flow compressor is modeled by the lumped cascade model of interconnected subsystems. Dynamics for each stage of the compressor are established with a state vector which has three state variables of flow rate, pressure and temperature. Compressor characteristics are estimated using the stage stacking method. Lyapunov stability analysis is applied to such a model for each decoupled linear subsystem. A degree of stability is derived from the eigenvalues of symmetric matrices as solutions of the Lyapunov matrix equations. Physically the degree of stability corresponds to the damping coefficient of the Lyapunov function defined at each stage. The degree of stability represents quantitatively the margin between the surge line and the steady state operating lines. The results allow specification of the stage from which the surge will occur when the compressor becomes unstable. The degree of stability is classified into three distribution patterns according to the rotational speed of compressor operation.

Experimental Investigation of the Flow Field in a Multistage Axial Flow Compressor

The nature of the flow field in a three stage axial flow compressor, including a detailed survey at the exit of an embedded stator as well as the overall performance of the compressor is presented and interpreted in this paper. The measurements include area traverse of a miniature five hole probe (1.07 mm dia) downstream of stator 2, radial traverses of a miniature five hole probe at the inlet, downstream of stator 3 and at the exit of the compressor at various circumferential locations, area traverse of a low response thermocouple probe downstream of stator 2, radial traverses of a single sensor hot‐wire probe at the inlet, and casing static pressure measurements at various circumferential and axial locations across the compressor at the peak efficiency operating point. Mean velocity, pressure and total temperature contours as well as secondary flow contours at the exit of the stator 2 are reported and interpreted. Secondary flow contours show the migration of fluid particles toward the core of the low pressure regions located near the suction side casing endwall corner.

Active Control of Surge in Multi-Stage Axial-Flow Compressors

Non-linear simulations of a surge model with and without control are investigated using a Runge-Kutta scheme. This shows how some non-linearities in the flow model can affect the normal operation of a linear controller and the problem of actuatop sensor locations. Also, the amplitudes and frequency response required of the actuator to retain stability can sometimes be found to exceed the practical limitations.

Secondary Flow in Repeating Stages of Axial Turbomachines

In a well-designed multi-stage axial flow compressor, the flow settles down to a repeating condition, in which the axial velocity profile does not deteriorate further; it is more or less unchanged between the entry and the exit of a deeply embedded stage. However, experimental data also show that the flow angles repeat, and it is this flow phenomenon that is discussed in the paper. Secondary flow analysis, coupled with empirical data on clearance flows, is used to give a description of the flow in such a repeating stage. The secondary flow at exit from a row involves both the streamwise vorticity generated in that row and the vorticity that exists at entry—the so-called ‘skew’ vorticity due to a non-uniform velocity from a stator being received by a moving rotor (and a similar effect from the rotor to the stator). However, clearance vorticity—shed from the rotor tip (casing) section and the stator root (hub) section—is also present and can be taken into account. Calculations made using the analyses are compared with some limited experimental data drawn from the published literature. Predicted underturning at rotor tip (casing) sections is confirmed by experiments; similarly, predicted underturning at stator tip (casing) sections accords with observations in one compressor but not in another. However, no universal conclusion (on whether underturning or overturning usually occurs) can be drawn for the flow through the rotor and stator root (hub) sections, as either entry or generated secondary vorticity may dominate.