Numerical Investigation of the Unsteady Flow Fields in Centrifugal Compressor Diffusers

The present work forms part of a research project of the Institute of Jet Propulsion and Turbomachinery at the RWTH Aachen University in collaboration with GE Aviation. The subject is the detailed numerical analysis of the unsteady flow field, focusing on the interaction between the impeller and the passage diffuser of a close-coupled transonic centrifugal compressor used in an aero engine. The centrifugal compressor investigated is characterized by a close-coupled impeller and passage diffuser with a radial gap of only 3.6%. The close coupling tends to provide a high aerodynamic efficiency but simultaneously cause a high unsteady interaction between the impeller and the diffuser. These unsteady effects can have a significant impact on the performance of both components and present a challenge to state-of-the-art numerical methods. With increasing compressor efficiency, the more important it is to have an understanding of the detailed unsteady flow physics. Experimental data was obtained from a state-of-the art centrifugal compressor test rig located at the Institute of Jet Propulsion. Steady and unsteady pressure measurements within the impeller and diffuser are used to gain detailed information on the temporal, time-averaged, and spectral pressure distributions within the stage to validate the CFD. The work presented here shows the unsteady phenomena caused by the interaction and the location and propagation of these phenomena within the centrifugal stage. Within the impeller, the exducer is in first order excited by the blade passing frequency (BPF) of the diffuser, whereas in the diffuser both the BPF and the passage passing frequency (PPF), are present up until the end of the pipe-diffuser. Significant effects on the integral component performance could only be identified for the impeller. Special focus is paid to evaluate the diffuser upstream pressure field, since this is the major source of unsteadiness within the impeller. The performance of the rotor decreases due to the unsteady interaction. This effect is traced back to the unsteady tip-clearance flow, in which the time-averaged mass transport decreases, whereas the specific entropy production increases in a nonlinear way. Within the diffuser, local effects counteracting with respect to the integral performance are found. In front of the throat, there is less decay in the total pressure as a result of tangentially expanding pressure waves. Within the passage a decrease in flow uniformity in the unsteady flow is identified as the reason for the lower diffusion up until the throat and higher losses within the downstream diffuser passage.

This paper presents results of unsteady viscous flow calculations and corresponding cold flow experiments of a three-stage low-pressure turbine. The investigation emphasizes the study of unsteady flow interaction. A time-accurate Reynolds-averaged Navier–Stokes solver is applied for the computations. Turbulence is modeled using the Spalart–Allmaras one-equation turbulence model and the influence of modern transition models on the unsteady flow predictions is investigated. The integration of the governing equations in time is performed with a four-stage Runge–Kutta scheme, which is accelerated by a two-grid method in the viscous boundary layer around the blades. At the inlet and outlet, nonreflecting boundary conditions are used. The quasi-three-dimensional calculations are conducted on a stream surface around midspan, allowing a varying stream tube thickness. In order to study the unsteady flow interaction, a three-stage low-pressure turbine rig of a modern commercial jet engine is built up. In addition to the design point, the Reynolds number, the wheel speed, and the pressure ratio are also varied in the tests. The numerical method is able to capture important unsteady effects found in the experiments, i.e., unsteady transition as well as the blade row interaction. In particular, the flow field with respect to time-averaged and unsteady quantities such as surface pressure, entropy, and skin friction is compared with the experiments conducted in the cold air flow test rig. [S0889-504X(00)02004-3]

In this effort, 3D CFD simulations are carried out for real gas flow in a refrigeration centrifugal compressor. Both commercial and the in-house CFD codes are used for steady and unsteady simulations, respectively. The impact on the compressor performance with various volute designs and diffuser modifications are investigated with steady simulations and the analysis is focused on both the diffuser and the volute loss, in addition to the flow distortion at impeller exit. The influence of the tongue, scroll diffusion ratio, diffuser length, and cross sectional area distribution is examined to determine the impact on size and performance. The comparisons of total pressure loss, static pressure recovery, through flow velocity, and the secondary flow patterns for different volute designs show that the performance of the centrifugal compressor depends upon how well the scroll portion of the volute collects the flow from the impeller and achieves the required pressure rise with minimum flow losses in the overall diffusion process. Finally, the best design is selected based on compressor stage pressure rise and peak efficiency improvement. An unsteady simulation of the full wheel compressor stage was carried out to further examine the interaction of impeller, diffuser and the volute. The unsteady flow interactions are shown to have a major impact on the performance of the centrifugal stage.

This paper describes the unsteady flow analysis in a centrifugal compressor stage using a three dimensional CFD algorithm. The flow unsteadiness arising from the interaction between the impeller and the diffuser has been analysed using an algorithm suitable for equal or multiple number of rotor and diffuser blades. The multi-block, structured grid CFD code TASCflow was used as a basis and algorithm development was undertaken to provide the required capability of modelling the unsteady interactions of the impeller and the diffuser. The centrifugal compressor stage studied consists of an impeller with splitters and a vaned diffuser. The results presented are for off-design flow conditions where some experimental results were available for comparison. The results obtained for the steady-state model show a good agreement with the measurements. In general the unsteady flow field obtained show a reasonable agreement with experimental data and demonstrates significant differences when compared to the steady state results especially in terms of the velocity field. A detailed analysis of the unsteady flow field is carried out using Fourier transforms of velocity and pressure at various locations of the flow field and the level of unsteadiness is determined as distributed to various frequencies. The unsteadiness in the impeller passage is much less than in the diffuser where a strong coupling is predicted in the vaneless space.

The present work forms part of a research project of the Institute of Jet Propulsion and Turbomachinery at the RWTH Aachen University in collaboration with GE Aviation. The subject is the detailed numerical analysis of the unsteady flow field focusing on the interaction between the impeller and the passage diffuser of a close-coupled transsonic centrifugal compressor used in an aero engine. The centrifugal compressor investigated is characterized by a close-coupled impeller and passage diffuser with a radial gap of only 3.6%. The close coupling tends to provide a high aerodynamic efficiency but simultaneously cause a high unsteady interaction between the impeller and the diffuser. These unsteady effects can have a significant impact on the performance of both components [1,2] and present a challenge to state-of-the-art numerical methods. With increasing compressor efficiency, the more important it is to have a understanding of the detailed unsteady flow physics. Experimental data was obtained from a state-of-the art centrifugal compressor test rig located at the Institute of Jet Propulsion [3]. Steady and unsteady pressure measurements within the impeller and diffuser are used to gain detailed information on the temporal, time-averaged and spectral pressure distributions within the stage to validate the CFD. The work presented shows the unsteady phenomena caused by the interaction as well as the location and propagation of these phenomena within the centrifugal stage. Within the impeller, the exducer is in first order excited by the BPF of the diffuser, whereas in the diffuser both the BPF, as well as the PPF, are present up until the end of the pipe-diffuser. Significant effects on the integral component performance could only be identified for the impeller. Special focus is paid to evaluate the diffuser upstream pressure field, since this is the major source of unsteadiness within the impeller. The performance of the rotor decreases due to the unsteady interaction. This effect is traced back to the unsteady tip-clearance flow, in which the time-averaged mass transport decreases, whereas the specific entropy production increases in a nonlinear way. Within the diffuser, local effects counteracting with respect to the integral performance are found. In front of the throat, there is less decay in total pressure, as a result of tangentially expanding pressure waves. Within the passage an decrease in flow uniformity in the unsteady flow is identified as the reason for the lower diffusion up until the throat and higher losses within the downstream diffuser passage.

This paper, the second of two parts, presents an experimental investigation of the unsteady flow field evolving in a two-stage two-spool test turbine facility. The experimental setup, which was designed to reproduce the operating condition of modern commercial aero-engines, consists of a high-pressure turbine (HPT) stage followed by a turbine center frame (TCF) with non-turning struts, and a co-rotating low-pressure turbine (LPT) stage. Measurements carried out with a fast-response aerodynamic pressure probe (FRAPP) were post-processed to describe the unsteady evolution of the flow downstream of the HPT rotor, through the TCF duct, and at the exit of the LPT stage. The time-resolved results presented in the first part of this paper show that deterministic fluctuations due to both rotors characterize the flow field downstream of the LPT. In order to characterize the deterministic unsteadiness induced by all the components constituting the turbine facility (HPT, TCF and LPT) and their interactions, measurements were carried out in three different planes located downstream of the HPT, at the exit of the TCF and downstream of the LPT stage. The unsteady results obtained in the plane located at the exit of the LPT are discussed in more details in this second part of this paper, providing information about the interactions between the two rotors. A proper phase-average procedure, known as rotor synchronic averaging (RSA), which takes into account the rotorrotor interaction, was adopted to capture the unsteadiness due to both rotors. Proper Orthogonal Decomposition (POD) was also applied to provide a characterization of the major contributors in terms of energy to the deterministic unsteadiness occurring in the test turbine facility. At the exit of the LPT rotor, the perturbations induced by the HPT stage and the interactions between the two rotors were found to dominate over the unsteadiness due to the LPT only.

The unsteady convective flow effects in a transonic compressor rotor with a circumferential-groove casing treatment are investigated in this paper. Experimental results show that the circumferential-groove casing treatment increases the compressor stall margin by almost 50% for the current transonic compressor rotor. Steady flow simulation of the current casing treatment, however, yields only a 15% gain in stall margin. The flow field at near-stall operation is highly unsteady due to several self-induced flow phenomena. These include shock oscillation, vortex shedding at the trailing edge, and interaction between the passage shock and the tip clearance vortex. The primary focus of the current investigation is to assess the effects of flow unsteadiness and unsteady flow convection on the circumferential-groove casing treatment. Unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) techniques were applied in addition to steady Reynolds-averaged Navier-Stokes (RANS) to simulate the flow field at near-stall operation and to determine changes in stall margin. The current investigation reveals that unsteady flow effects are as important as steady flow effects on the performance of the circumferential grooves casing treatment in extending the stall margin of the current transonic compressor rotor. The primary unsteady flow mechanism is unsteady flow injection from the grooves into the main flow near the casing. Flows moving into and out of the grooves are caused due to local pressure difference near the grooves. As the pressure field becomes transient due to self-induced flow oscillation, flow injection from the grooves also becomes unsteady. The unsteady flow simulation shows that this unsteady flow injection from the grooves is substantial and contributes significantly to extending the compressor stall margin. Unsteady flows into and out of the grooves have as large a role as steady flows in the circumferential grooves. While the circumferential-groove casing treatment seems to be a steady flow device, unsteady flow effects should be included to accurately assess its performance as the flow is transient at near-stall operation.

Modern aeroengine designers face the challenge of reducing fuel consumption, which is pushing compressor technology into new design spaces. To optimize these design spaces, high-fidelity computational models are crucial to the compressor design process. It is important to validate these models with experimental data. Nonintrusive measurement techniques allow for the acquisition of data well suited for this comparison, as they do not lead to local disruptions of the flow field. This investigation utilized three-component laser Doppler velocimetry to acquire a unique dataset of detailed unsteady velocity measurements in the vaned diffuser of an aeroengine centrifugal compressor. These measurements allowed for a thorough study of the flow development in the vaneless and semivaneless space of the diffuser as well as through the diffuser passage. The components of the Reynolds stress tensor were also determined at multiple locations in the diffuser flow field. These data are used to study the jet and wake propagation from the impeller exit flow field into the diffuser passage and the resulting secondary flow structures. Predictions from unsteady computational fluid dynamics (CFD) simulations using the shear stress transport (SST) and baseline k–ω explicit algebraic Reynolds stress model (BSL-EARSM) turbulence models are also compared with these experimental data. Both turbulence models yielded results that qualitatively agreed with the experimental radial velocity profile through the vaneless and semivaneless space. With the experimentally determined Reynolds stress tensor, the turbulent kinetic energy (TKE) is calculated at multiple points through the flow field and is compared to the TKE at the same geometric locations in the computational flow field. This comparison highlights the difference in dissipation and production of turbulence between the experimental data and the computational predictions. Investigating the differences in TKE throughout the diffuser helps elucidate the differences in predicted flow structures in the diffuser passage.

Heat and mass transfer characteristics on the first-stage gas turbine blade under unsteady wake flow

Unsteady blade row interactions play an important role in the performance of the compressor stages. However, due to the large cost of the unsteady flow simulation, most aerodynamic optimizations of the compressor are based on the steady flow simulation. This paper adopts the time spectral method to reduce the cost of the unsteady flow simulation and a discrete adjoint solver based on the unsteady flow solver has been developed. The unsteady flow equations and the adjoint equations are solved using an in-house code. The in-house code is based on the finite volume method and solves the URANS (Unsteady Reynolds Averaged Navier-Stokes) equations on the multi-block structured mesh. For spatial discretization the 3rd order WENO (Weighted Essentially Nonoscillatory) upwind scheme is used for reconstruction and the convective flux is computed with Roe’s approximate Riemann solver. The widely used one-equation Spalart-Allmaras turbulence model is adopted for the flow simulation. For the adjoint solution, the constant-eddy viscosity assumption is adopted and only the main flow adjoint equations are solved. The adjoint equations are formed in a discrete manner, which leads to more accurate discrete objective function sensitivity than the continuous adjoint method. The present work serves as an essential part of the system for efficient unsteady aerodynamic optimization of turbomachinery.

A numerical study of 3D unsteady flows in centrifugal compressor stages solving the Navier-Stokes equations is presented. The emphasis is on the effect of the radial gap between blade rows on the aerodynamic performance. In the numerical tests, Krain’s centrifugal impeller was combined with a DCA (Double Circular Arc) type radial vaned diffuser. The compressor stages with three settings of radial gap ranging from 5 to 15 percent of the impeller trailing edge radius are configured and unsteady flow simulations are carried out to compare the time-averaged efficiencies. The performance predictions show that the efficiency is deteriorated if the radial gap between blade rows is reduced with intensified blade row interaction, which is in contradiction to the general trend for axial compressor stages. In the centrifugal compressors tested, wake chopping by diffuser vanes, which usually benefits efficiency in axial compressor stages, causes unfavourable wake compression through the diffuser passages to deteriorate the efficiency.

The effect of tip clearance to the centrifugal compressor diffuser flow fields and stage overall performance are studied experimentally. The relative tip clearance (tip clearance divided by the impeller exit blade height) is increased by shimming the shroud side casing of a high-speed variable speed driven industrial centrifugal compressor. Four different relative tip clearances are studied: 0.027, 0.053, 0.082, and 0.106. The stage efficiency and pressure ratios are measured, as well as the diffuser flow fields. The diffuser flow fields are measured both at the diffuser inlet and outlet. The total pressure and flow angle are measured with a cobra probe, and the total pressure and temperature with three Kiel probes. Static pressures are measured adjacent to the probe measurements. As expected, increasing the tip clearance leads to lower stage efficiency and pressure ratios. The decrement in the efficiency due to the increasing of the tip clearance is higher with higher mass flows, and at lower rotational speeds. Increasing tip clearance increases the size of the secondary flow region present at the impeller outlet near the shroud.

Recent research has revealed positive effects of unsteady flow on the development of boundary layers in turbine cascades, especially at conditions with a laminar suction side separation bubble at low Reynolds-numbers. Compared to steady flow a reduction of total pressure loss coefficient over a broad range of Reynolds-numbers has been shown. Taking into account the positive effects of wake-induced transition already during the design process, new high lift bladings with nearly the same low losses at unsteady inlet flow conditions could be achieved. This leads to a reduction of weight and cost of the whole turbine module for a constant stage loading. Unsteady flow in turbomachines is caused by the relative motion of rotor and stator rows. For simulating a moving blade row upstream of a linear cascade in the High Speed Cascade Wind Tunnel of the Universität der Bundeswehr München, a wake generator has been designed and built. The wakes are generated with bars, moving with a velocity of up to 40 m/s in the test section upstream of the cascade inlet plane. Unsteady flow causes the transition on the surface of the suction side of a low pressure turbine blade to move upstream whenever an incoming wake is present on the surface, moreover a laminar separation bubble can be diminished or even suppressed. In order to detect the effects of wakes on the boundary layer development a new hot-wire data acquisition system is required. Due to the fact that hot-wires give a good insight into boundary layer development a new hot-wire data acquisition system has been set up. The anemometry system is able of acquiring four channels simultaneously, therefore being capable of logging a triple hot-wire sensor and a bar trigger simultaneously. One further channel is utilised for a once-per revolution trigger. The once-per revolution trigger is used to start the measurement of one data block. Using the well established ensemble averaging technique, 300 ensembles each consisting of 5 wake passing periods have been acquired. Ensemble averaging can be directly performed without any data reduction. The adaptation of this new hot-wire anemometry data acquisition system to the High Speed Cascade Wind Tunnel of the Universität der Bundeswehr München is pointed out. First results on unsteady periodic boundary layer development of a highly loaded low pressure turbine cascade under unsteady inlet flow conditions are presented. During the present investigation four boundary layer traverses, ranging from x/lax = 0.82 to x/lax = 0.99 (suction side), at steady and unsteady inlet flow conditions (Ubar = 10 m/s) at an outlet Reynolds-number of Re2th = 100000 have been conducted.

The unsteady behaviour of delta wing vortical flows is still a subject which is a challenge for numerical methods, such as computational fluid dynamics. New approaches to turbulence modelling, such as detached eddy simulation (DES) have been proposed which allow for greater accuracy of the numerical predictions. However, this increase in accuracy comes with a considerable increase in computational expense compared to traditional turbulence modelling. This investigation considers the use of both DES and unsteady Reynolds averaged Navier-Stokes (URANS) turbulence methods in the prediction of unsteady vortical flows. Calculations using DES are initially considered for two test cases and the predicted behaviour and resolution of the flow are considered. These results are then validated against existing experimental data, before the URANS calculations are considered with respect to the DES results. From this investigation it is determined that URANS turbulence models are able to predict the dominant features of the low frequency phenomenon present in the vortex system and in the post-breakdown region. Consideration is also given to the effect of grid refinement for both methods and the effect of temporal resolution for the DES calculations.

The subject of this work is the development of a nonlinear model of the interaction of an unsteady fluid flow with a structure and finding analytical solutions for the system of equations that correspond to the specified model. The convection effect of the fluid velocity field was already considered in the previous works of the authors of this paper. These studies are devoted to the water hammer without considering the "flow-structure" interaction. This work expands the possibilities of modeling and considers four equations instead of two equations of the theory of the water hammer (equations of conservation of mass and momentum), two of which relate to the motion of particles of a solid body (pipes or structures). The novelty of this work lies in the consideration of the model that describes the interaction of the flow with the structure, the convection in the velocity field, and the effect, together with the friction of the fluid against the solid wall, on the dynamics of the shock pulse propagation process both in the fluid and in the solid body. It should be noted that the solution of the nonlinear system of differential equations as a whole is carried out by an analytical method, which makes it possible to obtain an exact (rather than numerical) solution of the problem. Since the effects of various factors should be evaluated by comparison with the main components, dimensionless equations containing six parameters (dimensionless combinations) were obtained in this study. Two of these parameters were named after scientists – Darcy and Weisbach (steady friction) and Bruno (unsteady friction). Particular cases of the general (full) model were considered, and the effects of various factors on the dynamics of the interaction of the flow with the structure during the propagation of the shock pulse were determined. Research methods are purely theoretical. The concepts of a self-similar equation and a system of equations, balances of forces acting on particles of a fluid and a solid body, and a standard method of reducing a system of equations to a single equivalent equation are used. Conclusions. An extended model of the interaction between the unsteady fluid flow and the structure is proposed. The transition to a self-similar variable makes it possible to solve a nonlinear system of differential equations and obtain an analytical (exact) solution. The functions of longitudinal stress in a solid body, pressure disturbance, and velocity of motion of particles in a solid body (pipe) are linearly expressed by the velocity of shock pulse propagation in the fluid. It should also be noted that the results for the particular case of the linear model completely agree with the already known ones. The advantage of using a self-similar solution is that it is easy to obtain. The results of previous studies on the water hammer problem were qualitatively consistent. As the fluid viscosity increases, the shock pulse domain becomes more concentrative.