A New Analytical Model of a Centrifugal Compressor and Validation by Experiments

Gas turbine has broad applications in variety of industries. The developing gas turbine efficiency is of great engineering concern. This appeals to more precise modeling as somewhat inevitable. Modeling plays a decisive and essential role not only in all design phases, but also in development and manufacturing process to investigate performance of an engine. In this research, components of a gas turbine including air intake, axial and centrifugal compressors, combustion chamber and axial turbine are investigated. A novel dimensionless modeling approach is introduced and then, the engine performance parameters are predicted. Setting up a systematic series of experiments on the existing engine in Gas Turbine Laboratory at Sharif University of Technology, functional parameters of the components are obtained. The comparison of theoretical results with experimental results shows very good compliance.

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A nozzle is a variable cross sectional area used to accelerate the flow. As the fluid flows through the nozzle, the kinetic energy of the fluid is increased at the expense of pressure energy. The main use of nozzle is to produce a jet of steam (or gas) of high velocity to produce thrust for the propulsion of rocket motors and jet engines and to drive steam or gas turbines. Nozzle has many applications in industry of turbo machinery, separation systems, the jet propulsion units, geo-environmental techniques, air conditioning, thermal ejectors, wind tunnels and many others. The present work incorporates the detail study about subsonic and supersonic nozzles. The concept of method of characteristics is used in designing of nozzle. The program is developed in the language C++, which generates the profile of both the subsonic and supersonic nozzle. To study the performance and characteristics of the nozzles, the experimentation is carried out at different back pressures. These experimental results are compared with the theoretical, isentropic one dimensional flow for variable area passages. The geometry of the nozzle is created in modeling software GAMBIT 2.4.6 and the numerical simulation is carried out in FLUENT 6.3.26. The numerical results are compared with experimental results at design and off-design conditions. The results indicate that, there is good agreement between the graph of experimental and numerical results. In both the analysis at design condition, the flow gets accelerated throughout the nozzle length. At the design condition, the phenomenon of flow through the nozzle is changed with variation in back pressure value. For very high value of back pressure, compared to design pressure, the convergent part of the nozzle accelerate the flow and the divergent part of the nozzle act as a diffuser and decelerate the flow. On further reduction in the back pressure, the shock phenomenon is observed in the divergent portion of the nozzle. This shock position shifts downward from the throat to exit of the nozzle, with the reduction of back pressure.

Turbochargers are widely used to help reduce the environmental impact of automotive engines. However, a limiting factor for turbochargers is compressor surge. Surge is an instability that induces pressure and flow oscillations that often damages the turbocharger and its installation. Most predictions of the surge limit are based on low-order models, such as the Moore–Greitzer model. These models tend to rely on a characteristic curve for the compressor created by extrapolating the constant speed lines of a steady-state compressor map into the negative mass flow region. However, there is little validation of these assumptions in the public literature. In this article, we develop further the first-principles model for a compressor characteristic presented in Powers, K., Brace, C., Budd, C., Copeland, C., & Milewski, P., 2020, “Modeling Axisymmetric Centrifugal Compressor Characteristics From First Principles,” J. Turbomachinery, 142(9), with a particular emphasis on reverse flow. We then perform experiments using a 58 mm diameter centrifugal compressor provided by Cummins Turbo Technologies, where we feed air in the reverse direction though the compressor while the impeller is spinning in the forward direction to obtain data in the negative mass flow region of the compressor map. This demonstrated experimentally that there is a stable operating region in the reverse flow regime. The recorded data showed a good match with the theoretical model developed in this article. We also identified a change in characteristic behavior as the impeller speed is increased, which, to the authors’ knowledge, has not been observed in any previously published experimental work.

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)

This paper describes in detailed flow field in a centrifugal compressor with a vaned diffuser at off design point. Especially, we conducted both the experimental and numerical analysis in order to investigate the evolution process of a diffuser stall. At the stall point, the diffuser stall was initiated and rotated near the shroud side in the vaneless space. Furthermore, the diffuser stall was developed to a stage stall cell, as the mass flow was decreased. The developed stall cell was rotated within both the impeller and diffuser passages. The evolution process of the diffuser stall had three stall forms. First, the diffuser stall was rotating near the shroud side. Then, the diffuser stall shifted to the hub side and moved into the impeller passages. Finally, a stage stall was generated. From computational fluid dynamics (CFD) analysis, a tornado-type vortex was generated first, near the hub side of the diffuser leading edge, when the diffuser stall was shifted to the hub side. Next, a throat area blockage was formed near the hub side because of the boundary layer separation in the vaneless space. Finally, the blockage within the diffuser passages expanded to the impeller passages and developed into a stage stall. From the pressure measurements along the impeller and diffuser passages, the magnitude of pressure fluctuation on the casing wall of the diffuser throat area also suddenly increased when the diffuser stall shifted to the hub side. Therefore, the evolution area of the diffuser stall was caused by the evolution of the blockage near the throat area of the diffuser passage.

Rotating stall waves that travel against the direction of rotor rotation are reported for the first time and a new, low-order analytical approach to model centrifugal compressor stability is introduced. The model is capable of dealing with unsteady radially swirling flows and the dynamic effects of impeller-diffuser component interaction as it occurs in centrifugal compression systems. A simple coupling criterion is developed from first principles to explain the interaction mechanism important for system stability. The model findings together with experimental data explain the mechanism for first-ever observed backward traveling rotating stall in centrifugal compressors with vaned diffusers. Based on the low-order model predictions, an air injection scheme between the impeller and the vaned diffuser is designed for the NASA Glenn CC3 high-speed centrifugal compressor. The steady air injection experiments show an increase of 25% in surge-margin with an injection mass flow of 0.5% of the compressor mass flow. In addition, it is experimentally demonstrated that this injection scheme is robust to impeller tip-clearance effects and that a reduced number of injectors can be applied for similar gains in surge-margin. The results presented in this paper firmly establish the connection between the experimentally observed dynamic phenomena in the NASA CC3 centrifugal compressor and a first principles based coupling criterion. In addition, guidelines are given for the design of centrifugal compressors with enhanced stability. Winner of the “Best Paper Award,” Turbomachinery Committee

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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.

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Compressor maps of aero engines show the relation between corrected inlet mass flow and total pressure ratio for various engine speeds. Different speed lines represent different operating conditions of the compressor, where especially operating bounds like surge and choke are important for the design process. Typically, 3D CFD compressor maps are computed with the so called hot geometry given for the aerodynamic design point. However, in reality airfoil shapes will change for different engine speeds and gas loads resulting in twisted airfoils and changed tip clearances. Thus, using the nominal hot geometry for the whole compressor map is not fully correct. In order to obtain higher quality performance maps these effects need to be considered. The paper shows a process for computing compressor maps with 3D CFD, where strucural deformations of the blade due to varying speeds and gas loads are taken into account by blade morphing. This process is applied to a 1.5-stage compressor showcase.

Integrally geared multistage centrifugal compressors have been widely used in many industries. The design of the new compressor is very complicated and needs a reliable design process. This paper discussed the development of a high efficiency integrally geared driven centrifugal compressor for industrial applications. An inhouse program was used to design the centrifugal compressor through aerodynamic and structural optimization. CFD (Computational Fluid Dynamics) is a very important tool for centrifugal compressor design. CFD can help compressor design and perform three-dimensional optimization to further optimize the compressor. The compressor stage matching is also impact the overall compressor performance. The good stage match is very important to make the design success. The Finite Element Analysis (FEA) was used to verify the structure integrity. The CFD and FEA (Finite Element Analysis) analysis are performed to obtain a final compressor performance and to make sure to have a robust operation. The centrifugal compressor has the characteristics of high efficiency, no resonance, and low noise. The designed compressor prototype was built and performance tests were conducted. The performance test results demonstrated that the analytical are fairly agreed with experimental results. The development process and tools are successfully used in the compressor design. The design process can be used for future compressor development.

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.”

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