A Numerical Study on Performances of Centrifugal Compressor Stages With Different Radial Gaps

A three-dimensional unsteady compressible viscous flow solver has been developed, and applied to a low speed centrifugal compressor configuration. Good agreement with experiments have been obtained for a compressor tested at NASA Lewis Research Center. Comparisons with measured surface pressures, and performance data are given. For this compressor, stall was found to occur in the diffuser region. It is demonstrated that this stall may be eliminated, and stable operation may be restored by the use of bleed valves located on the diffuser walls. INTRODUCTION In many army applications (tanks and rotorcraft) small gas turbine engines are often used. The mass flow rate in these engines is small (below 10 Ibs/sec). The compression is provided by one or two centrifugal compressor stages, sometimes in combination with an axial compressor stage. Centrifugal compressors are well suited for handling such low mass flow rates. They are rugged and compact. However, the geometric complexity of the blades and the twisting blade passages give rise to a host of aerodynamic problems such as unsteadiness, establishment of cross flows, flow separation at the trailing edge of the compressor blade, separation over diffuser guide vanes, and unsteady meandering motion of a 'tip vortex' that originates in the vicinity of the gap between the rotor and the casing. In many instances, this unsteadiness leads to rotating stall and surge. Considerable interest exists in the engine community in understanding and eventually controlling these phenomena, particularly compressor stall and surge. Computational fluid dynamics methods provide an efficient way of studying the complex flow phenomena within centrifugal compressors. Thanks to the availability of post-processing and scientific visualization software, the computed flow fields can be extensively analyzed. It is also convenient to test within a numerical model various control strategies such as bleeding, energizing of incoming flow using jets, excitation /wiggling of guide vanes, etc. Passive mechanisms such as slots, slats and flaps can also be easily studied within the scope of a numerical method. These simulations are thus a useful and economical first step to detailed flow control experiments. Finally, CFD simulations provide a wealth of numerical and flow physics information which are useful in developing reduced order models. For these reasons, a 3-D CFD code capable of analyzing centrifugal compressor configurations has been developed by the present investigators. Rather than solving the flow equations in a rotating coordinate system, the present calculations are carried out in an inertial system, with grid velocity terms used to simulate a rotor. Inflow and outflow boundary conditions appropriate for internal flows in general and centrifugal compressors in particular are used. This paper is organized as follows. The flow solution algorithm is first described. Next, results in the form of velocity fields, surface pressure data and performance map are presented for a NASA low-speed centrifugal compressor. The performance of this compressor for off-design low mass flow ratio conditions is subsequently studied. Methods for improving the compressor performance during such conditions are discussed. NUMERICAL FORMULATION The 3-D unsteady compressible Reynolds averaged Navier-Stokes equations are solved numerically using a time marching scheme. This involves solving the governing equations at each time step by marching in time from an initial flow condition with appropriate boundary conditions. The governing equations are cast in a curvilinear body-fitted coordinate system (£,T|,£) and solved using an Alternating Direction Implicit (ADI) scheme 1. This implicit scheme has been validated for a number of fixed wing and rotary wing configurations both in steady and unsteady flight conditions^'*. The partial derivatives in the governing equations are calculated using finite difference approximations. The Graduate Research Assistant, Student Member AIAA. * Regents' professor, Associate Fellow AIAA. Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc. inviscid flux terms are calculated using a third order upwind scheme and the viscous stress terms are calculated using standard central difference representations. The details of the upwind formulation are given by Roe. The time derivative is approximated using a two point first order backward difference. The finite difference representation of the governing Navier-Stokes equations at time level 'n' is components at the inflow boundary were set to zero, assuming that there was no swirl at the inlet. It is possible within the framework of the present boundary conditions to prescribe swirl, non-uniform total pressure and total temperature at the inlet. At every time step, the speed of sound a and the normal component of velocity un were found at the inflow boundary from the relations: AT 2a 2a — u = n — u n = I 8 f R + S S + S , T (1) Interior where Aq* is the change in the flow property vector q during adjacent time levels and At is the time step. The operators 8£, 5r| and 8^ are the standard central difference operators. The viscous terms are evaluated explicitly and the inviscid flux vectors F, G and H are calculated implicitly at time level n+1. A three factor approximate factorization is used to factorize the implicit coefficient matrix operator into block tri-diagonal matrices. The factorized system of equations is solved using the Thomas algorithm. Turbulence effects are modeled using the SpalartAllmaras model. INITIAL AND BOUNDARY CONDITIONS The centrifugal compressor is shown in figure 1. The boundary grids are also shown for a single blade passage. The volume grid is made of three segments: inlet region, the rotor, and the diffuser. The following boundary conditions were applied: Periodicity: In the present study, the flow through only a single blade passage has been studied, assuming blade-toblade periodicity. At the periodic boundaries, the flow properties are computed by averaging the properties on either side of the periodic boundary. Solid walls: At the solid walls, the no slip boundary condition was used. The velocity on the walls of the inlet and the diffuser were set to zero, while the velocity for grid points on the compressor blades and the shaft were set equal to Q x r. The pressure, density and temperature values at the solid surfaces were extrapolated from the interior using relationships such as 9p/3n=dT/9n=3p/3n=0, where n represents the direction normal to the solid surface. Inflow Boundary: At this boundary, the stagnation temperature T0 and the total pressure p0 were assumed known. In the simulation of a compressor drawing the air from the atmosphere, these quantities may be set based on ambient conditions. In a multistage compressor analysis, these quantities will be known at the downstream boundary of the previous stage. The tangential (vand w-) (2)

An innovative lightweight compression system presented could push the limits and ramp up the capabilities of modern gas turbines. This system integrates the two established multi-stage compressor architectures. Firstly, the widely prevalent axial-centrifugal compressor is the configuration with several axial compressor stages with a back-end centrifugal impeller. Secondly, the contra-rotating compressor is a stator-less configuration with two sets of counter-rotating rotors. In the present study, this configuration is adopted for a small and compact compressor stage with three rotors. These are two counter-rotating front and rear axial-flow rotors and one back end centrifugal impeller rotating in the same direction as the rear axial-flow rotor. Moreover, two special annular duct arrangements, i.e. inter-stage connecting duct and centrifugal diffuser-duct were configured for aerodynamic matching of the stage and effective diffusion of flow respectively. The challenges of the present problem are manifold which comprises components such as axial-flow compressors, a centrifugal compressor, an inter-stage connecting annular duct, and a curved diffuser-duct along with the concept of contra-rotation. Multiple design innovations were performed to create an overall lightweight and compact compression system. In this work, the design approach to the proposed compressor stage and its components operating at low-speed and low-mass flow is presented. Subsequently, the numerical results performed with Computational fluid dynamics (CFD) analysis to improve the design performance iteratively are discussed. The baseline design of the contra-rotating axial compressor was configured with a higher aerodynamic loading of the front rotor and lower aerodynamic loading of the rear rotor, the rear rotor rotating at a higher design speed than the front rotor and low aspect-ratio blades. The baseline design of the backend centrifugal compressor was configured with diffusing passage shape of the diffuser-duct with a critical hub surface modification producing overall improved flow characteristics.

The performance of radial diffusers in centrifugal compressor stages is influenced by the impeller exit flow characteristics as well as the vaneless and semi-vaneless space flow characteristics. Both steady and unsteady flow interactions are present due to the propagation of pressure fields upstream and downstream between the impeller and diffuser. Furthermore, unsteady flow interactions occur when the impeller moving wakes developed due to secondary and tip clearance flows propagate through the diffuser passages. The present study aims at presenting a model that describes the unsteady wake propagation in the centrifugal compressor diffuser using vorticity principles. 3D unsteady Reynolds-Averaged Navier Stokes simulations are performed for both a vaned and a vaneless diffuser centrifugal stage. The simulations are used to examine the mechanism for the unsteady wake flow interactions in the diffuser. The unsteady streamwise vortical structures present in the impeller wakes and their propagation through the diffuser flow field is presented. The effect of the unsteady flow on loss production in the compressor stage is investigated. The velocity perturbations due to these vortical structures are presented. The present study indicates that the impeller wake propagation in the diffuser can be represented by a series of unsteady streamwise vortices superimposed on a uniform flow field. These vortices result in velocity perturbations that take the form of both positive and negative jets in the diffuser.

The interaction between impeller and diffuser is considered to have strong influence on the flow in centrifugal compressors. However, the knowledge about this influence is still not satisfying. This two-part paper presents an experimental investigation of the effect of impeller-diffuser interaction on the unsteady and the time averaged flow field configuration in impeller and diffuser and the performance of these components. The flat wedge vaned diffuser of the investigated compressor allows an independent adjustment of diffuser vane angle and radial gap between impeller exit and diffuser vane inlet. Attention is mainly directed to the radial gap, as it determines the intensity of the impeller-diffuser interaction. Part I deals with the integral flow losses and the diffusion in impeller, diffuser and the entire compressor. An extensive test series with steady probe measurements at impeller exit and diffuser exit was performed at 10 different diffuser geometries and different operating points. The results show that in most cases smaller radial gaps are leading to a more homogeneous flow field at diffuser vane exit and to a higher diffuser pressure recovery resulting in a higher compressor efficiency. On the other hand, impeller efficiency is hardly affected by the radial gap. In Part II, measurements with a laser-2-focus velocimeter are presented illuminating the reasons for the effects found. The experimental results are published as an open CFD test case under the name “Radiver.”

This study numerically and experimentally examines the effects of applying curvilinear element blades to fully shrouded centrifugal impellers on the performance of the centrifugal compressor stages. The curvilinear element blades we developed for centrifugal turbomachinery were defined by the coordinate transformations between a revolutionary flow-coordinate system and a cylindrical coordinate system. All the blade sections in the transferred cylindrical coordinate system were moved and stacked spanwise in accordance with the given “lean profile,” which meant the spanwise distribution profile of movement of the blade sections, to form a new leaned blade surface. The effects of the curvilinear element blades on the impeller flowfield were investigated using numerical simulations, and the optimum design guidelines for impellers with curvilinear element blades were considered. Then, a new impeller using these design guidelines was designed and the performance improvement of a new compressor stage was evaluated by numerical simulations. As mentioned in several papers, we numerically confirmed that curvilinear element blades with a negative tangential lean (TGL) profile improved the velocity distribution and stage efficiency because they help to suppress the secondary flows in the impeller. The negative TGL mentioned in this paper represents the lean profile in which the blade hub end leans forward in the direction of the impeller rotation compared to the blade shroud end. At the same time, we also found that the stall margin of these impellers deteriorated due to the increase in relative velocity deceleration near the suction surface of the shroud in the forward part of the impeller. Therefore, we propose new design guidelines for impellers with the curvilinear element blades by applying a negative TGL to line element blades in which the blade loading of the shroud side in the forward part of the impeller is reduced. We confirmed from the numerical simulation results that the performance of the new compressor stage improved compared to that in the corresponding conventional one. The new design guidelines for the curvilinear element blades were experimentally verified by comparing the performance of the new compressor stage with the corresponding conventional one. The measured efficiency of the new compressor stage was 2.4% higher than that of the conventional stage with the stall margin kept comparable. A comparison of the measured velocity distributions at the impeller exit showed that the velocity distribution of the new impeller was much more uniform than that of the conventional one.

Rotating stall is a well-known aerodynamic instability in compressors that limits the operating envelope of aircraft gas turbine engines. An innovative method for delaying the most common form of rotating stall inception using an annular dielectric barrier discharge (DBD) plasma actuator had been proposed. A DBD plasma actuator is a simple solid-state device that converts electricity directly into flow acceleration through partial air ionization. However, the proposed concept had only been preliminarily evaluated with numerical simulations on an isolated axial rotor using a relatively basic CFD code. This paper provides both an experimental and a numerical assessment of this concept for an axial compressor stage as well as a centrifugal compressor stage, with both stages being part of a low-speed two-stage axial-centrifugal compressor test rig. The two configurations studied are the two-stage configuration with a 100 mN/m annular casing plasma actuator placed just upstream of the axial rotor leading edge (LE) and the single-stage centrifugal compressor with the same actuator placed upstream of the impeller LE. The tested configurations were simulated with a commercial RANS CFD code (ansys cfx) in which was implemented the latest engineering DBD plasma model and dynamic throttle boundary condition, using single-passage multiple blade row computational domains. The computational fluid dynamics (CFD) simulations indicate that in both types of compressors, the actuator delays the stall inception by pushing the incoming/tip clearance flow interface downstream into the blade passage. In each case, the predicted reduction in stalling mass flow matches the experimental value reasonably well.

The fundamental analysis in the first report was extended to calculate the unsteady flow induced by the interaction between impeller blades and diffuser vanes/volute casing in a diffuser pump. The unsteady flow in the diffuser vane passage, as well as the volute casing, is assumed to be induced by the five kinds of singularities—the bound vortices distributed on the impeller blades, diffuser vanes and volute casing wall, the sources at volute outlet, and the free vortices shed from the trailing edge of diffuser vanes. Calculated unsteady pressures agree with the corresponding experimental data. And the calculated results showed the effects of the flow rate, volute casing and the radial gaps between impeller blade trailing edge and diffuser vane leading edge on the magnitude of unsteady pressure downstream of impeller.

Steady Reynolds-averaged Navier-Stokes (RANS) simulation with the mixing-plane approach is the most common procedure to obtain the performance of a centrifugal compressor in an industrial development process. However, the accurate prediction of complicated flow fields in centrifugal compressors is the most significant challenge. Some phenomena such as the impeller-diffuser flow interaction generates the unsteadiness which can affect the steady assumption. The goal of this study is to investigate the differences between the RANS and URANS simulation results in a centrifugal compressor stage. Simulations are performed at three operating points: near surge (NS), design point (DP), and near choke (NC). The results show that the RANS simulation can predict the overall performance with reasonable accuracy. However, the differences between the RANS and URANS simulation are quite significant especially in the region that the flows are highly unsteady or nearly separated. The RANS simulation is still not very accurate to predict the time-dependent quantities of the flow structure. It shows that the URANS calculations are necessary to predict the detailed flow structures and performance. The phenomena and mechanisms of the complex and highly unsteady flow in the centrifugal compressor with a vaned diffuser are presented and analyzed in detail.

A three-dimensional unsteady, viscous aerodynamic analysis has been developed for the flow inside a transonic, high-through-flow, single stage compressor. The compressor stage is comprised of a low-aspect-ratio rotor and a closely coupled stator. The analysis is based on a numerical method for solving the three-dimensional Navier-Stokes equation for unsteady viscous flow through multiple turbomachinery blade rows. The method solves the fully three-dimensional Navier-Stokes equation with an implicit scheme. A two-equation turbulence model with a low-Reynolds-number modification is applied for the turbulence closure. A third-order accurate upwinding scheme is used to approximate convection terms while a second-order accurate central difference scheme is used for the discretization of the viscous terms. A second-order accurate scheme is employed for the temporal discretization. The numerical method is applied to study the unsteady flow field inside a transonic, high-through-flow, axial compressor stage. The numerical results are compared with available experimental data.

Adjustable diffuser vanes offer an attractive design option for centrifugal compressors applied in industrial applications. However, the knowledge about the impact on compressor performance of a diffuser vane clearance between vane and diffuser wall is still not satisfying. This two-part paper summarizes results of experimental investigations performed with an industrial-like centrifugal compressor. Particular attention was directed toward the influence of the diffuser clearance on the operating behavior of the entire stage, the pressure recovery in the diffuser, and on the diffuser flow by a systematic variation of the parameters diffuser clearance height, diffuser vane angle, radial gap between impeller exit and diffuser inlet, and rotor speed. Compressor map measurements provide a summary of the operating behavior related to diffuser geometry and impeller speed, whereas detailed flow measurements with temperature and pressure probes allow a breakdown of the losses between impeller and diffuser and contribute to a better understanding of relevant flow phenomena. The results presented in Part I show that an one-sided diffuser clearance does not necessarily has a negative impact on the operation and loss behavior of the centrifugal compressor, but instead may contribute to an increased pressure ratio and improved efficiency as long as the diffuser passage is broad enough with respect to the clearance height. The flow phenomena responsible for this detected performance behavior are exposed in Part II, where the results of detailed measurements with pressure probes at diffuser exit and particle image velocimetry (PIV) measurements conducted inside the diffuser channel are discussed. The experimental results are published as an open computational fluid dynamics (CFD) testcase “Radiver 2.”

The operational envelope of gas turbine engines such as employed in the Army Blackhawk helicopter is constrained by the stability limit of the compression system. Stall control technologies developed at the ARL Vehicle Technology Directorate and NASA Glenn Research Center to improve the stable operating range of compressors lack fundamental understanding beneficial to design guidance. Improved understanding of the stall inception process and how stall control technologies mitigate such will provide compressors with increased tolerance to stall, thereby expanding the operational envelope of military gas turbine engines. To provide improved understanding, time accurate CFD simulations are being computed at full-scale actual engine conditions using the parallel solver, TURBO, developed at Mississippi State University (MSU) with support from NASA, DoD, and industry. As a compressor nears stall the flow field is no longer periodic from passage to passage, therefore full-annulus (i.e., all blade passages of every blade row) must be computed. For a typical multistage compressor this becomes a formidable computational challenge requiring access to massively parallel machines in order to meet the computational and memory demands of the problem. Unsteady full-annulus simulations of both a single stage axial and centrifugal compressor, for which detailed experimental data are available, provide validation of the TURBO code for subsequent use in predicting the stall inception processes in an axicentrifugal multistage compressor employed in the Army Blackhawk helicopter. The simulations show the inception of stall and subsequent evolution into a fully developed stall cell. Also, shown are the predictions of range extension with stall control and comparison to measurements. Finally, a status of the unsteady fullannulus simulations of the compression system components of the U.S. Army Helicopter Gas Turbine Engine is presented. All military and commercial gas turbine engine systems can benefit from the proposed work. In the future, this work could lead to new gas turbine engine designs with resistance to compressor stall and thus improved combat capability. This work will provide the first-ever 3-dimensional viscous time-accurate simulation of the stall inception process in a multistage compressor, providing insight into the causal link between compressor blade design parameters and the stable operating limit, which will be used to guide new design practices leading to compressor designs with increased tolerance to stall. This paper presents final-year progress on this challenge project.

This study investigates the unsteady shear flow patterns and their relation with the aerodynamic instability of a shrouded supercritical carbon dioxide (SCO2) centrifugal compressor impeller using the dynamic mode decomposition method combined with detached eddy simulation. The results demonstrate that discrete shedding vortex array in the blade tip region is the dominant mode of the SCO2 shrouded centrifugal compressor impeller, with a frequency of 0.5 times the blade passing frequency. In contrast, the main flow structures in the identical impeller using ideal air consist of small-scale shedding vortices near the suction surface and the separated secondary flow. Further analysis of flow field details indicates that the shedding vortex structure inside the shrouded centrifugal impeller originates from the Kelvin–Helmholtz instability generated on the shear interface between the mainstream and the recirculation flow. The greater shear intensity within the SCO2 centrifugal impeller is the reason for the evident occurrence of vortex shedding phenomena in its flow field. Additionally, during the transition from near-stall to stall, vortex pairing phenomena happens at the throat of the centrifugal impeller due to evolutional behaviors of the vortexes. The occurrence of vortex pairing leads to faster blockage of the blade tip region and then the secondary flow spillage over to adjacent passage, ultimately resulting in reverse flow in the blade tip region and extensive blockage at the impeller inlet. The unsteady shear flow evolution clearly demonstrates the processes of stall in SCO2 shrouded impellers.

This paper introduces a new test case for compressor aerodynamics. The dataset is provided for the Dresden four-stage Low-Speed Research Compressor (LSRC), which was put into operation in 1995. The compressor consists of four identical stages, which are preceded by an inlet guide vane. The data set will be provided for the reference blading of the compressor with cantilevered stator vanes. This blading was developed on the basis of the profiles of a middle stage of a high-pressure compressor of a jet engine. This paper makes available the blading geometry as well as a variety of flow field measurement results. This includes the compressor map, selected pressure distributions and other results of flow field measurements with conventional techniques (e.g. Pitot probes, 5-hole probes). Furthermore different aspects of blade row interactions were addressed in this compressor within recent years. The periodical unsteady flow field within a selected rotor blade row was investigated using Laser-Doppler-Anemometry. Further results on the unsteady profile pressures and profile boundary layers will be provided. Supplementary, numerical results will be compared to the experiments. Results are available for several stages of the compressor and different operating points. With this test case a unique database for the aerodynamics in a multistage axial compressor will be provided that can be used for the validation of numerical codes.

In the present paper a computational analysis of the interactions between a backswept impeller and its downstream vaned diffuser in a high-speed centrifugal compressor is presented. Both steady and unsteady simulations are carried out at the peak efficiency point. Geometry scaling was used in the unsteady simulation in order to deal with the problem of unequal pitch. For the steady simulation, an averaging approach is used at the interface between the impeller and the diffuser. A detailed comparison between the time averaged unsteady results and the steady simulation results is performed and some unsteady phenomena are also discussed in order to advance the understanding of the flow physics involved. One important conclusion is that the unsteady simulation is important since the difference between the time averaged unsteady results and steady simulation results is quite significant especially in the velocity field and the stage efficiency. From the comparisons of the predicted results with available experimental data in terms of velocity vectors and isentropic efficiency, it can be concluded that the geometry scaling method used in the current unsteady simulation is reasonable and successful and the computational model employed for the predictions consists a reliable computational tool. In general, the contours of different flow variables for the averaged unsteady simulation results are more uniform than the steady ones, especially in the vaneless space. In the static pressure field, there are relatively small differences. The main differences occur in the region of the vaneless space and downstream of the throat area, and in general the difference is found to be quite small. In the velocity field, the differences are large compared with the ones occurring in the pressure field. The area with the largest differences extends from the vaneless space into the semi-vaneless and vaned diffuser channel. The unsteadiness also modifies the flow angle and hence the incidence angle at the leading edge of the vaned diffuser, the maximum difference can reach 3 degrees. The difference in the stage isentropic efficiency can reach above 1 per cent, which is considered to be quite high. The results also indicate that the larger differences between the time-averaged unsteady and steady state simulation results usually occurred in the area that flows are highly unsteady or nearly separated. Consequently the steady state simulation is still not very accurate to predict highly unsteady flow and separated flows.

In this paper a 3D optimization process for the aerodynamic design of a centrifugal multistage compressor stage is presented using the commercial software NUMECA/Design3D. The exercise, starting from a given single stage configuration with vaned diffuser, consists in the automatic design of the vaned diffuser with a return channel in order to obtain a repetitive compressor stage for multistage compressor architecture. The design process uses the meta-model approach coupled to 3D Navier-Stokes simulations; the optimization algorithm drives the automatic design process to minimize a prescribed goal function. Only the design condition has been considered and the effect of the starting DoE population on the optimization process has been investigated. In the paper a critical analysis on the design process using the meta-model approach is performed and the most crucial issues to set up a best practice for the effective use of such technology are discussed in some detail.