Unsteady Flow Development and Reynolds Stress Measurements in a Centrifugal Compressor Vaned Diffuser

As modern computational fluid dynamics (CFD) capabilities continue to improve, their role in the turbomachinery design process continues to take a more prominent position. Traditionally, pitchline or throughflow codes were used to approximate the performance of a stage, and then, limited additional computations would be performed with 3D CFD to analyze more detailed design changes. Modern computational abilities have made it commonplace to perform full-stage CFD simulations and reduce the number of rig tests needed in the development of a novel design. As designs are pushed to higher levels of performance, they will exceed the capabilities of historical correlations, and CFD will become even more critical.

The first successful simulation of flow within a centrifugal compressor was performed by Moore and Moore [1]. This model was highly simplified as it neglected compressibility effects, tip leakage flows, and unsteadiness, but it was the beginning of flow simulations in a centrifugal compressor. As computational tools have improved over time, it has become possible to incorporate more features of a physical compressor stage such as surface roughness, heat transfer, and unsteady flow effects. The inclusion of such effects results in more realistic predictions of the flow within a centrifugal compressor stage [2].

The Reynolds stress tensor consists of six independent components, which represent the average correlation of the fluctuations in two velocity components. The continuity equation along with the three momentum equations from Eq. (1) represents a system of four equations with ten unknowns. This situation is known as the turbulence closure problem, which has led to the creation of turbulence models to relate flow properties to the Reynolds stress tensor [3].

Numerous turbulence models have been developed for different applications, and each contains unique strengths and weaknesses. The shear stress transport (SST) model is a two-equation model that blends the k–ε and k–ω models to more adequately predict both freestream and near-wall flows [4]. However, the SST model has difficulties predicting flows with strong secondary flows and streamline curvature, which presents a challenge for centrifugal compressors [3]. In an attempt to improve predictions for flows with these characteristics, the explicit algebraic Reynolds stress models (EARSM) can be implemented. These EARSM turbulence models can more accurately capture secondary flows and the effects of streamline curvature because they generalize the constitutive relation by allowing turbulence anisotropy [5,6]. Turbulence models are often calibrated for canonical flow environments; therefore, it is necessary to exercise caution when implementing these models in complex flow environments such as in a centrifugal compressor analysis. To ensure that high-performing stages can be designed with these computational tools, it is imperative that models are calibrated with experimental turbomachinery data.

Traditionally, conventional measurement techniques for compressors consist of installing an array of static pressure ports, total temperature rakes, and total pressure rakes as well as various other probes to measure flow angles. Centrifugal compressors have relatively small blade and vane passages, and thus, placement of these measurement devices can adversely affect the flow field. These probes can be intrusive to the flow and create a blockage that is usually the same order of magnitude as the passage area, bringing to question the legitimacy of those measurements for this application [7,8]. Additionally, the blockage introduced by these intrusive probes for centrifugal compressor testing causes performance instabilities [9]. To reduce the impact of instrumentation on the flow field and to improve the quality of measurements, nonintrusive measurement techniques can be utilized.

Vaned diffusers for aeroengine centrifugal compressors can feature small vane passages, which make them a prime candidate for the implementation of these nonintrusive measurement techniques. Examples of nonintrusive measurement techniques commonly used in turbomachinery include flow visualization methods such as particle image velocimetry and laser Doppler velocimetry (LDV). LDV was first developed by Cummins et al. [10]. This technique allows for velocity measurement through the Doppler effect, which is the apparent shift in frequency due to the motion between an observer and the signal source [11]. Several investigations have implemented LDV to study the aerodynamics of centrifugal compressor stages.

Early investigations relied on acquiring data for one component of velocity in each measurement. Adler and Levy [12] conducted a study on a pump-style impeller which showed a uniform exit flow. Fagan and Fleeter [13] showed that a low-velocity region developed along the shroud surface in an unshrouded impeller. Two studies conducted by NASA were the first to resolve the three-dimensional flow by measuring two velocity components and ensemble averaging the results [14,15]. The first LDV studies of a vaned diffuser for a high-speed centrifugal compressor were conducted by Stahlecker et al. [16], Stahlecker and Gyarmathy [17], and Cattanei et al. [18].

Understanding the flow through a vaned diffuser is critical to maximizing the performance of a centrifugal compressor stage. The purpose of the vaned diffuser is to maximize the pressure rise of the stage by recovering static pressure from kinetic energy in the impeller exit flow [19]. The diffuser inlet flow (or impeller exit flow) is highly unsteady and nonuniform, which adds to the difficulty of designing a high-performance stage. Several attempts have been made to measure and understand impeller exit flow, but it is regarded as an open area of research. Most studies have supported the original theory presented by Dean and Senoo, known as the jet/wake model. This model proposed that there is a region of high relative velocity jet flow exiting the impeller adjacent to the pressure surface of the blade and a region of low relative velocity wake flow between the suction surface of the blade and the jet flow [20]. The jet/wake flow structure was first experimentally observed by Eckardt using Laser-2-Focus Velocimetry. Eckardt's results showed that the wake region was focused near the shroud instead of present across the full span, as proposed by the original model [21]. A study conducted by Krain on a more modern impeller design showed that the wake region was spread across much of the entire passage along the shroud [22]. Although the studies on impeller exit flow present conflicting conclusions on the location of flow structures, they do result in the same conclusion that the flow is nonuniform.

This unsteady and nonuniform impeller exit flow presents a challenging inlet condition for diffuser designs. The jet/wake flow structure results in significantly varying diffuser vane incidence through each impeller blade pass period. Early investigations concluded that the unsteadiness of the impeller exit flow had very little effect on overall stage performance because it mixed out quickly [23–25]. However, as modern centrifugal compressor designs are pushed beyond traditional design limits to maximize stage efficiency and minimize size, this may no longer be a valid conclusion.

Although previous LDV studies in centrifugal compressors present results for the three-dimensional flow field, the open literature does not include any studies that feature three-component coincident data. To the authors' knowledge, this is the first three-component, coincident laser Doppler velocimetry study conducted in a vaned diffuser for a high-speed centrifugal compressor. Previous LDV studies acquired one or two velocity components at a time, and the data would be ensemble averaged together to obtain all three components at an instance during the blade-passing period. This study acquired the data in a coincident procedure, meaning all three velocity components were measured simultaneously. In addition to studying the velocity vector field of the diffuser vane passage, the coincident nature of this study allows for the determination of the full Reynolds stress tensor at several locations. These data are used to calculate local levels of TKE within the passage and elucidate the turbulent structures of the flow, which could be used to improve computational turbulence models.

The experiments were conducted in the Centrifugal Stage for Aerodynamic Research (CSTAR) facility at the Maurice J. Zucrow laboratories of Purdue University. This facility houses a low-specific-speed centrifugal compressor designed for an axi-centrifugal aeroengine compressor configuration. Full details of this compressor facility are documented in Ref. [26]. The stage, depicted in Fig. 1, consists of an impeller with 15 main blades and 15 splitter blades, which discharges to a vaned diffuser that contains 35 wedge-shaped vanes. The diffuser vane leading edges are located at an impeller exit radius ratio of 1.08. Flow from the diffuser exits into a turn-to-axial deswirl component, which exhausts into a circumferential exhaust collector. The design speed of the stage is 22,500 rpm, and it achieves a total pressure ratio of approximately 3.

The compressor stage is densely instrumented to obtain temperature and pressure data throughout the flow path. Total pressures are measured at the impeller inlet, diffuser inlet, diffuser exit, and within the turn-to-axial component. Total temperatures are measured at the impeller inlet, diffuser inlet, and at the exit of the turn-to-axial component. Static pressures are measured along the shroud surface throughout the flow path.

Several modifications to the hardware were made to facilitate the LDV study discussed herein. The diffuser shroud has been modified to allow optical access for nonintrusive measurements. A clear, fused silica window is installed in the shroud over the diffuser passage and vaneless space. A fast-curing room temperature vulcanizing (RTV) rubber is applied at the vane tips before each test to seal between the vanes and the glass window. The hub surface has been coated with an antireflective coating that reduces reflections, which contribute noise to the signal measured by the probes.

Performance maps of the stage for both the modified LDV configuration and the baseline compressor stage have been shown to match well [27]. All velocity and turbulence data presented in this work were acquired at the aerodynamic design point for this centrifugal compressor stage. This operating point was set as a ratio, referred to as the loading ratio, of the stage total pressure ratio to the inlet corrected mass flowrate. While operating at 100% Nc, the throttle valve in the exhaust system was gradually closed to adjust the operating point to achieve a loading ratio of 0.875. This value was verified every 5 min through each test period in the experimental campaign.

This investigation utilized a commercially available LDV system from Dantec Dynamics. A Coherent, Inc., 5.0-Watt Argon-Ion laser head outputs a single beam which is split, and one beam is passed through a Bragg cell to produce a 40-MHz frequency shift. The three primary wavelengths of these two beams (514.5 nm, 488.0 nm, and 476.5 nm) are then separated and sent to the probe heads in the compressor test cell via fiber optic cables. Two pairs of beams are output through one probe, while the third pair is output through a second probe. The six beams are aligned through a pinhole with a diameter of 50 µm to ensure data are acquired at the same geometric location for each pair of beams. Both probes are mounted to a traverse system with a resolution of 6.25 µm, which allows for a detailed grid of points to be acquired through the diffuser vane passage. The intersection of the six beams, or the measurement volume, is aligned to the compressor by mounting a 100-µm pinhole in the passage, and that is used to set the “origin” for the grid of measurement points.

The flow is locally seeded at the impeller inlet with a traversable injection nozzle. The seed fluid is di-ethyl-hexyl-sebacate, which flows through a six-jet atomizer before injection into the impeller inlet. The seed particle diameter distribution for this fluid and atomizer was determined in a laboratory and is illustrated in Fig. 2. The cutoff frequency for 5% and 1% slip are also depicted with the particle diameter distribution. For this investigation, 95% of the seed particles are expected to follow velocity fluctuations of 57 kHz at 5% slip and 25 kHz at 1% slip. The impeller blade-passing frequency for this compressor is 11.25 kHz, so these seed particles are expected to adequately follow the flow.

The Dantec Dynamics model F80 BSA operates with a sampling frequency of 180 MHz and a bandwidth of 120 MHz. This allows for measurements of flow up to supersonic velocities with high turbulence intensities. The uncertainty analysis applied in this investigation is detailed in Ref. [28]. This analysis yields uncertainty in flow angle of ±1 deg, ±2% in spanwise (axial) velocity, and ±1% in pitchwise and streamwise velocities. However, these values can nearly triple where the signal-to-noise ratio decreases, such as in areas adjacent to walls and in regions of separated flow. For much of the flow field, the uncertainty in the Reynolds stress component magnitude was maintained within ±20 m²/s² as calculated by the methodology outlined in Ref. [29]. For more information on the LDV system and setup for this application, see Ref. [30].

All data presented in this work were acquired at the aerodynamic design point for the compressor stage. The LDV data were coincident: acquired at the same instance in time in the same measurement volume. Data were acquired at each geometric point for a minimum of 60 s, but this acquisition time increased to 300 s for the points where the TKE was calculated. During data acquisition, data rates of greater than 750 Hz in each channel were targeted, but 1 kHz was often achieved in two of the three laser Doppler anemometer (LDA) channels. The acquired data were separated into blade passages based on the rotational speed of the impeller and a once-per-revolution signal from the impeller. The averaged signal for the individual passages was then ensemble-averaged to generate a mean-passage representation of the velocity signal. Details of the velocity vector and Reynolds stress calculations based on these signals are detailed subsequently.

Velocity components are measured for each seed particle that passes through the measurement volume within the diffuser blade passage. These velocity components are then transformed into the coordinate system for the CSTAR research compressor, using a rotation matrix based on the angle of the LDV probes' orientations. For the purposes of this discussion, the cartesian velocity components have been transformed into cylindrical polar coordinates. The axial velocity (V_Z) component represents the spanwise flow direction between the diffuser hub and shroud. The pitchwise velocity (V_ϴ) component represents flow in the blade-to-blade direction. The bulk flow velocity upstream of the diffuser throat is represented as the radial velocity (V_R) component, which is the velocity directed radially outward from the axis of rotation. The bulk flow velocity downstream of, and including, the diffuser throat is defined as the streamwise velocity (V_S), which is the velocity vector projected onto the plane bisecting two adjacent diffuser vanes.

The turbulent kinetic energy and velocity components will be used as the primary metrics for the analysis of the diffuser flow in this investigation.

Time-transient CFD simulations have been conducted on this compressor stage to see how well the turbulence models are able to predict the turbulent quantities from the experimental LDV results. The commercial, pressure-based solver, ansys cfx 19.1, was used for all simulations. This solver uses an element-based finite volume method and a nonlinear advection scheme. ansys turbogrid was used to generate structured meshes for both the impeller and diffuser domains. The domain for this computational work is illustrated in Fig. 3.

Due to the unequal pitch ratio between the impeller and diffuser, the time transformation method was used to obtain the time-transient solutions presented in this work. The time transformation method was applied with 120 time steps per blade pass period and ten inner coefficient loops. The solution was advanced in time using a fully implicit, second-order, backward Euler scheme. To obtain an impeller-to-diffuser pitch ratio compatible with this method, the impeller domain consisted of one main blade and one splitter blade passage, or one-fifteenth of the entire impeller. The diffuser domain consisted of two diffuser vane passages. Both grids utilized a structured topology with O, C, and H blocks. The impeller grid consisted of 16.1 million elements, and the diffuser domain consisted of 14.8 million. The y+ value was maintained below 10 along all solid surfaces. The stage inlet boundary conditions applied were total pressure and total temperature. The stage exit boundary condition was static pressure. This value was adjusted to match the loading condition used in the experiment.

Previous computational work with this centrifugal compressor stage has informed modeling decisions that were implemented for the results included in this investigation. These model features include isothermal shroud boundary conditions, surface roughness representative of the experimental stage, and hub-side diffuser vane fillets. Each of these features yields more accurate flow structures when included in the computational model [2]. Surface temperature measurements on the shroud of the compressor stage were acquired during the experimental component of this work. These temperatures were then mapped to the correct meridional locations along the shroud model to implement the isothermal boundary condition. Surface roughness values were acquired for the experimental stage hardware and converted to sand-grain roughness values. These were applied in the model definition file to incorporate the effects of machined hardware. A uniform profile of 5% turbulence intensity was applied at the inlet plane of the computational domain.

The CFD results were obtained with the SST and the ansys baseline k–ω explicit algebraic Reynolds stress model (BSL-EARSM) turbulence models. The SST model was utilized for its prevalence in the turbomachinery industry, and the BSL-EARSM model was previously shown to more accurately predict flow structures in this stage [2].

The results presented in this section follow a sequence that matches the flow path in the compressor stage. The flow development will be tracked from the impeller exit through the diffuser passage to understand the origins of the downstream flow structures. Traditionally, the Reynolds stress tensor is discussed in the context of the RANS equation and modeling the turbulence in these solutions. The results presented here use TKE as a tool to highlight the differences between the experimental flow and the simulations at the same loading condition. Experimental and computational results are compared simultaneously to highlight the differences in each region of the stage. Additionally, this dataset allows for analysis of the unsteady flow field as it develops through the impeller blade-passing period. Figure 4 highlights the key measurement locations that will be used in this discussion of the flow field. This figure shows the regions of the vaneless space and diffuser passage that were accessible for LDV measurements. Each circle represents one of the test matrix points, and specific points that are relevant to the included discussion are labeled. The vaneless space portion of the test matrix consists of eight arcs of twelve points, with the first arc at r/r₂ = 1.0125 and the last at r/r₂ = 1.08. The rest of the matrix consists of planes of points from the semivaneless space through the diffuser passage. Specific points discussed in this paper are labeled by number in the adjacent yellow boxes. The geometric locations that are discussed as planes are filled with the same color as their label's color. In these location labels, planes are labeled with a letter and percentage. The percentage represents what fraction of the diffuser passage (from throat to passage exit) the plane crosses. Computational results are extracted from the compressor flow field at the same geometric locations where experimental data were acquired.

The figures in the following sections will illustrate the flow field development in terms of the blade-passing period, where t represents a time in the period, and t_BP represents the full period. In these figures, full impeller blade denotes the approximate location of the full impeller blade, and impeller splitter blade denotes the approximate location of the impeller splitter blade. For each of the contour plots, the experimental data are presented in the top row, computational results using the SST turbulence model are illustrated in the middle row, and the computational results from the BSL-EARSM model are depicted in the bottom row. The contour plots from the simulation results only show velocities at spans where experimental data were acquired.

The data in this investigation were acquired in the stationary reference frame. The measurements described as the impeller exit flow field were acquired at an impeller radius radio (r/r₂) of 1.0125. The impeller exit flow is the inlet condition for the stationary diffusion system, beginning with the vaneless space. The initial mixing of the impeller jet and wake begins the process of vortex generation as the flow proceeds downstream.

The radial velocity contours at point 37, as defined in Fig. 4, at the impeller exit are depicted in Fig. 5. These contours illustrate qualitative agreement between the two computational models and the experimental results in terms of the jet and wake structure. The general shape of the jet and wake and the large velocity deficit directly behind each blade on the hub surface are captured by both models. However, both models predict a larger deficit along the shroud surface and a lower velocity magnitude within the wake flow. The BSL-EARSM simulation more correctly predicts the flow structure, as the SST model predicts a larger radial velocity deficit within the wake flow.

A key difference between the experimental data and the computational results is the magnitude of the axial velocity. Contours illustrating axial velocity for the experimental, SST model, and BSL-EARSM model are presented in Fig. 6. Both models predict a band of axial velocity toward the hub surface behind each blade in the wake. Outside of these bands, the predicted axial velocity is nearly zero, contrary to the experimental results. The experimental data indicate the flow is moving toward the shroud surface through the entire blade-passing period. This phenomenon is not clearly linked to the jet, wake, or tip leakage flow. The discrepancy in axial velocity at the impeller exit will propagate through the remainder of the diffuser passage and influence the flow accordingly. The effect of the axial velocity on the downstream flow structures will be discussed in subsequent sections.

Reynolds stress measurements were acquired at the impeller exit for spans of 90%, 95%, and 98% and are presented in Fig. 7. These measurements were used to calculate the TKE for several instances in the blade pass period. Similar to the velocity contours, this figure compares the experimental results with those from both computational models. The results from both turbulence models indicate similar magnitudes of TKE across the period and the local minima and maxima occur at approximately the same time during the period. The data indicate narrow peaks that are not represented in the simulation results, however, but the general trend across the blade pass period qualitatively agrees. The spanwise TKE will be an important metric to monitor as the flow develops downstream.

Further downstream in the compressor stage, the radial velocity contours maintain the qualitative agreement originally presented at the impeller exit. Figure 8 illustrates the radial velocity contours for the three comparisons at an impeller radius ratio of 1.05. The data presented were acquired at point 8. Both models still predict a larger shroud-side velocity deficit, similar to the impeller exit flow predictions, which are not observed experimentally. Additionally, both models predict higher radial velocity magnitudes within the jet flow regions than measured experimentally. While the predicted jet and wake flow velocity magnitudes are greater than the data indicate, the relative difference in velocity between the jet and wake is similar between both models and the data.

Reynolds stress measurements were acquired at 50%, 70%, and 95% span at this vaneless space location. These measurements were used to calculate the TKE for several instances in the blade pass period (Fig. 9). Unlike the radial velocity contours, the computational TKE results start to vary from the experimental data at this location, just past halfway through the vaneless space.

The results at 50% span indicate a general qualitative agreement between experiment and computation, with the exception of the short-term doubling of TKE at approximately 1/3 t_BP. Throughout the period, the models both exhibit smaller ranges between minimum and maximum TKE than observed experimentally. Additionally, there is an increasing phase shift between the TKE peaks in the models from the experiment at the higher spans. When comparing the TKE levels from a radius ratio of 1.0125 to a radius ratio of 1.05, the experimental data indicate an increase, while the models predict almost no change. This indicates the models are not accurately capturing the production of turbulence within the vaneless space. The difference in TKE at higher spans becomes apparent when studying the flow further downstream as the larger TKE facilitates spanwise mixing.

Downstream from the 1.05 impeller radius ratio plane, the spanwise incidence profile is calculated at the diffuser vane leading edge (Fig. 10). This point is located at an impeller exit radius ratio of 1.08. Incidence is defined as the difference between the absolute flow angle and the diffuser inlet metal angle, where the flow angle is measured from the radial direction to the absolute flow vector. A negative incidence indicates more radial flow and a positive incidence indicates more tangential flow.

Incidence profiles are depicted for the jet flow, wake flow, and the time average across the blade pass period. For all three profiles, both computational models predict the same profile qualitatively. Through the midspan region, 10–70% span, the experimental data indicate a more positive incidence by about 3–5 deg. The largest difference between the experimental results and the computational models occurs between 70% span and the shroud surface. Both models predict a strong increase in positive incidence above 70% span, but the experimental data indicate a more radial flow angle, leading to a lower incidence. This trend is especially prevalent in the wake flow region and is again represented in the time-averaged incidence profile.

The difference between experimental and computational incidence profiles can be explained by the difference in axial velocity magnitudes that was observed as far upstream as the impeller exit, Fig. 5. Axial velocity induces spanwise mixing between the midspan flow and the flow adjacent to the shroud wall. The flow along the shroud is dominated by tip leakage flow and the shroud boundary layer, leading to a strong gradient between that and the midspan flow. The low axial velocity magnitude predicted by both the SST and BSL-EARSM models would lead to a low rate of spanwise mixing and cause the observed gradient in the incidence near the shroud. On the contrary, the experimental data indicated a stronger axial velocity component, which would lead to more spanwise mixing between the midspan flow and shroud-wall flow. This would allow for a more uniform incidence between the midspan and shroud-adjacent flow.

This observation is further substantiated by analyzing the turbulent kinetic energy at this location in the flow path, as illustrated in Fig. 11. The experimental TKE values indicate an increase in magnitude from 50% through 95% span, whereas the computational results indicate almost no change from 50% to 70% span and a large increase to 95% span. This is associated with the increased transport of TKE experimentally by the higher axial velocity component. The larger axial velocity component induces spanwise mixing of the TKE.

The average TKE level is higher in the experimental data than for both models at 50% and 70% span, while they are nearly equivalent at 95% span. At 50% span, the transient trend of TKE through the blade pass period matches well between the data and the model. However, at the higher spans, there is a phase shift between the peaks in the experimental and computational results, which has been observed at the locations upstream in the flow path. This phase shift is likely a result of different rates of spanwise mixing of the jet and wake flows from midspan toward the shroud, which is caused by the lower axial velocities observed in the computational models.

The flow passes through the semivaneless space and enters the diffuser passage through the throat region, which is considered a 0% vane passage. The streamwise velocity contours presented through the diffuser passage compare the experimental results (left column), SST model results (middle column), and BSL-EARSM model results (right column). The top row represents the instance in time when the jet flow passes through the diffuser throat, and the middle row represents the instance when the wake flow passes through the throat. The bottom row is the time average of the flow through the throat through the entire impeller blade pass period. For each of the contours, the velocities are presented as the difference between an individual measurement, V_S,i, and the mean value across the entire passage at that location, $VS¯$⁠. In the following figures, empty space in the contours for the experimental results represents regions of the passage where strong beam reflections or probe access prevented data acquisition.

Streamwise velocity at the diffuser throat is depicted by the contours in Fig. 12. The throat is the first region in the stage where major discrepancies begin to arise between the experimental data and both computational models. The clearest difference between the data and the models is the high-velocity region within the wake flow. The data indicate a core flow region adjacent to the shroud surface above 60% span, but both computational models predict a core flow region adjacent to the diffuser vane pressure surface. Both models also overpredict low momentum regions adjacent to the shroud and the vane suction surface. While there are significant differences between the experimental and computational results, both computational models predict streamwise velocity profiles that are nearly identical. The secondary flow vectors overlaid on the velocity contours indicate that both computational models qualitatively predict the secondary flow structure within the diffuser throat.

Reynolds stress measurements were acquired at the diffuser throat plane and used to calculate the transient turbulent kinetic energy at this location. Figure 13 illustrates the comparison of experimental TKE with the computational results for both the SST and BSL-EARSM models. The average level of TKE is approximately double the values predicted by both computational models. At 50% and 70% spans, the models capture the qualitative trend of TKE through the impeller blade pass period. While they predict the transient trend of TKE, there is a significant discrepancy in the predicted level of TKE. This indicates some errors in the ability of the turbulence models to predict the convection and production of turbulence in the diffuser inlet region.

Downstream of the diffuser throat, the streamwise velocities are compared at two planes within the diffuser passage. Planes DSTM B and DSTM G, as defined in Fig. 4, are used for this comparison to study the development of the flow through the diffusion process. The streamwise velocity contours are presented in the same manner as the contours for the diffuser throat, depicting contours for experimental data and both computational models. At these locations downstream of the throat, the differences between each computational model and the experimental results become more apparent.

The streamwise velocity contours for the plane located at 10% vane passage are illustrated in Fig. 14. Both computational models still predict regions of low momentum flow along the shroud wall, which was also predicted at the throat. However, the experimental data indicate higher streamwise velocities near the shroud, and in the wake flow, there is a core flow region adjacent to the shroud. The largest discrepancy between results is the flow separation predicted in the pressure surface corner adjacent to the shroud. Streamwise velocity values beyond the limits of the color bar were predicted, which resulted in the white contour in this region. Flow separation is apparent in this location through the jet flow, wake flow, and time-averaged flow. This separated flow is not predicted by the BSL-EARSM model or observed experimentally. The secondary flow vectors reflect this separation as they indicate flow toward the hub around the separated flow region.

The experimental streamwise velocity indicates a narrow band of core flow along the diffuser vane suction surface within the jet flow. This band is still present, though less prominently, in the time-averaged velocity contour. The secondary flow vectors illustrate a general pitchwise flow from the vane suction surface toward the pressure surface. The data indicate significant differences in streamwise velocity between jet and wake flow periods. Both computational models do indicate differences between the jet and wake flow, so they accurately capture the unsteadiness of the flow at this point in the passage. However, neither the jet structure nor the wake structure from either computational model resembles the measured velocity profile. The differences between the jet flow and wake flow instances suggest that the jet and wake have not fully mixed out through the first 10% of the passage, so the unsteady effects of the flow are still affecting the diffusion process.

As the flow proceeds downstream through the diffuser passage, the small differences between the computational models and experimental results continue to grow. The streamwise velocity contours for the plane located at 40% diffuser vane passage are depicted in Fig. 15. These streamwise velocity contours are presented in the same manner as Figs. 12 and 14. The small, separated flow region along the pressure surface (PS) shroud corner that was predicted by the SST model at 10% passage has grown considerably by 40% passage. It now extends from the PS to nearly midpitch at the shroud, and from about 60% span along the PS to the shroud. This separation was not observed experimentally nor predicted by the BSL-EARSM model.

The low momentum regions predicted along the vane surfaces and endwalls by the BSL-EARSM model further upstream have grown to include a larger extent of the passage at this location. This model does not predict any large regions of flow separation at 40% passage. It predicts a nearly symmetric velocity profile with a rectangular-shaped core flow surrounded by boundary layer regions.

Neither the SST nor BSL-EARSM models accurately predicted the experimental streamwise velocity profile. The experimental profile is characterized by a large region of high streamwise velocity between 50% span and the shroud, accompanied by a region of low streamwise velocity in the PS hub corner. The secondary flow structure computed with the BSL-EARSM model qualitatively matches the experimental flow with low spanwise velocity and a general suction surface-to-PS flow direction. The SST model predicts this general secondary flow direction, as well at spans below about 50%, but the large separation region in the PS shroud corner induces a spanwise component to the flow, which alters the secondary flow structure at higher spans.

Both models indicate a relatively steady flow between the jet and wake instances, which is also supported by the experimental data. The region of separated flow predicted by the SST model is stationary in time between the jet, wake, and time-averaged flows. The symmetric velocity profile from the BSL-EARSM model retains the same shape and low momentum regions at the extent of the passage through the entire impeller blade pass period. In the experimental profile, the large region of core flow adjacent to the shroud and the low-velocity region in the PS hub corner are both present in the jet and wake flow instances. This indicates the jet and wake have fully mixed out by 40% through the passage, resulting in mostly steady flow through the remainder of the passage. This trend observed in the experimental data is accurately captured by both computational models.

Spanwise profiles of time-averaged turbulent kinetic energy have been extracted from both computational models at midpitch from the diffuser throat through 40% of the passage. Reynolds stress data were acquired at point 34, the diffuser throat, and at midpitch of the DSTM B plane (see Fig. 4), and thus, experimental values of TKE are included with these spanwise profiles. Figure 16 depicts these spanwise profiles of TKE through the diffuser passage, where the streamwise direction is from left to right.

These profiles of spanwise TKE reflect the changes in streamwise velocity observed through the diffuser throat. At 40% through the passage, the SST model predicted a large region of separated flow along the vane PS shroud corner. This is reflected by a large increase in the TKE levels predicted by the SST model above the 60% span. Outside this region of separated flow, both computational models are consistent with their predictions of TKE, as their predicted flow structures at midpitch are relatively similar. However, in both locations where spanwise profiles of TKE could be acquired experimentally, the models underpredicted the levels at almost every point. At the diffuser throat, the models accurately predicted the qualitative spanwise trend of TKE even though the levels varied. This difference in predicted levels of TKE through the passage indicates the turbulence models used in CFD simulations have difficulty predicting the convection, dissipation, and production of turbulence in a vaned diffuser for a centrifugal compressor.

The purpose of this investigation was to gain a detailed understanding of the unsteady flow field in a vaned diffuser for an aeroengine centrifugal compressor by acquiring unique, three-component, coincident LDV data. The turbulent quantities were measured, and the capabilities of current computational models to predict these quantities were also investigated. Previous investigations of vaned diffusers suggest the unsteady flow effects are negligible, but this study leads to a different conclusion.

From the impeller exit through the vaneless space, there is very little dissipation of the jet and wake flows. The radial velocity contours indicate clear regions of jet and wake flows through the vaneless space, which is also reflected in the spanwise incidence profile at the diffuser vane leading edge. These unsteady flow fluctuations due to the impeller jet and wake flows persist until about 40% through the diffuser passage. Most of the dissipation occurred in the semivaneless space as a result of the diffuser vane potential field turning the flow into the diffuser passage. These features were also supported by the transient computational models using the SST and BSL-EARSM turbulence models. Both models predicted the presence of flow unsteadiness due to the impeller jet and wake up to 40% of the vane passage.

The six components of the Reynolds stress tensor were directly measured and used to compute the turbulent kinetic energy at multiple locations in the compressor stage. These data depicted an increase in turbulence intensity through the vaneless space, meaning turbulence is not just generated in the impeller and convected through the diffuser. The turbulent kinetic energy levels were also extracted from computational models using the SST and BSL-EARSM turbulence models for comparison with the experimental results. At the diffuser throat, the models accurately predicted the qualitative trend of spanwise TKE. However, throughout the vaneless space and diffuser passage, both models underpredicted the levels of TKE. This indicates that the models are not accurately predicting the convection and production of turbulence as the flow develops.

Future centrifugal compressor stage performance will be limited by the capabilities of the CFD solvers used by designers. One step to improve the capabilities of these solvers, and thus improve the accuracy of flow prediction, would be to calibrate the turbulence models with experimental turbulent kinetic energy data. This would allow for small flow structures to propagate through the passage more realistically, and more effectively understand the effects of design choices. Future investigations will focus on acquiring a similar LDV data set at other loading conditions to understand how the turbulent characteristics change with loading.

The authors would like to thank Rolls-Royce Corporation for its funding and permission to publish this work. Additionally, the technical expertise of Cliff Weissman of Dantec Dynamics was critical to the success of this investigation.

There are no conflicts of interest.

The authors attest that all data for this study are included in the article.

i =

Incidence angle

t =

Time in period

P =

Static pressure

t_BP =

Blade-passing period

R_ij =

Reynolds stress tensor

S_ji =

Rate of strain tensor

U₂ =

Impeller exit tip speed

V_R =

Radial velocity component

V_S =

Streamwise velocity component

$VS¯$ =

Average planar streamwise velocity

V_S,i =

Streamwise location at a point

V_Z =

Axial velocity component

V_θ =

Pitchwise velocity component

CFD =

Computational fluid dynamics

EARSM =

Explicit algebraic Reynolds stress model

Exp =

Experimental results

LDV =

Laser Doppler velocimetry

PS =

Pressure surface

RANS =

Reynolds-averaged Navier–Stokes

r/r₂ =

Impeller radius ratio

SST =

Shear stress transport

TKE =

Turbulent kinetic energy

μ =

Dynamic viscosity

ρ =

Density