Two Investigations of Compressor Stability: Spike Stall Inception and Transient Heat Transfer Effects. Andras Laszlo Andor Kiss

Transcription

1 Two Investigations of Compressor Stability: Spike Stall Inception and Transient Heat Transfer Effects by Andras Laszlo Andor Kiss S.B, Massachusetts Institute of Technology (2013) Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Masters of Science in Aerospace Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2015 c Massachusetts Institute of Technology All rights reserved. Author Department of Aeronautics and Astronautics August 19, 2015 Certified by Zoltán S. Spakovszky Professor of Aeronautics and Astronautics Thesis Supervisor Accepted by Paulo C. Lozano Associate Professor of Aeronautics and Astronautics Chair, Graduate Program Committee

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3 Two Investigations of Compressor Stability: Spike Stall Inception and Transient Heat Transfer Effects by Andras Laszlo Andor Kiss Submitted to the Department of Aeronautics and Astronautics on August 19, 2015, in partial fulfillment of the requirements for the degree of Masters of Science in Aerospace Engineering Abstract Two investigations of current problems in the field of compressor stability are presented. The first is of the formation of spike-type rotating stall precursors. Recently, high fidelity computations have attributed pre-cursor formation to a leading-edge separation and consequent shedding of vorticity near the rotor tip due to high incidence. This hypothesis is assessed via experiments in a low-speed compressor and a linear cascade, supported by unsteady computations. Fast-response pressure measurements at the blade tip show spike pre-cursors propagating in the cascade environment at a rate consistent with the low-speed compressor. The cascade design produces high incidence at the mid-span and fast-response velocity measurements show pre-cursor formation away from the tip region. Unsteady computations confirm leading-edge separation and vortex shedding in both the compressor and cascade. A single blade was instrumented with smoke injection at the leading-edge to visualize the separation and the effect of Reynolds number on pre-cursor formation was quantified to facilitate smoke visualization. The resultant visualizations confirm the leading-edge separation and propagation of shed vorticity. The second investigation is of the effects of heat transfer between the compressor structure and gas path during transient operation. A mean line model of an advanced, high pressure ratio compressor is extended to include the effects of heat transfer. Diabatic, transient calculations show a 9.9 point reduction in stall margin from the adiabatic case. 2.5 points are attributed to the effect of heat transfer on blade row deviation and the remainder is attributed to stage rematching. Heat transfer increases loading in the front stages and the stalling pressure ratio is set by front stage stall, suggesting heat transfer effects are greater for compressors with highly loaded front stages. Sensitivity studies of heat flow rate and deviation show a linear dependence of stall margin loss for ratios of heat flow rate to inlet stagnation enthalpy flux much less than unity. Thesis Supervisor: Zoltán S. Spakovszky Title: Professor of Aeronautics and Astronautics 3

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5 per aspera ad astra... 5

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7 Acknowledgments I would first and foremost like to thank my advisor Professor Zoltán Spakovszky. It is hard to believe that it s already been six years since I began working with him; the time has simply flown by. He has always pushed me to improve as a researcher and his passion, enthusiasm, and perpetual optimism have served as a source of inspiration. This research was supported and made possible by Pratt & Whitney, under the guidance of Gavin Hendricks. Also at Pratt & Whitney, I would like to thank Ding Li for his assistance with the many computations in this thesis and Brian Schuler for his support in developing the mean line model. Thanks also to Scott Jones at NASA Glenn Research Center for providing OTAC and aiding me (through countless s) in its implementation. I have made many new friends during my time at the Gas Turbine Lab. Vincent, Derek, Georgi, and Andrew you guys kept me laughing the entire time. Thanks to Jinwook for making the endless quals study sessions as fun as they could be; we did it! Special thanks to Vincent for taking over the administration of the GTL cluster while I sequestered myself in the library to write this thesis. Outside the GTL I would like to thank Matt and Taylor for the friendships of a lifetime, Steven for his boundless positivity and encouragement, and, of course, my partner Jeff; his love and unwavering support kept me going even when I thought I could not. I would like to thank all of my family for their love and encouragement. To my father, Gabor, thank you for inspiring me in the world of engineering and instilling in me a love of aviation, as well as so many other things. To my mother, Eva, your limitless love and support has made all of this possible. 7

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9 Contents 1 Introduction Background Thesis Contributions Summary of Thesis Chapters Spike-Type Rotating Stall Inception Introduction Previous Work Motivation and Objectives Technical Roadmap Experimental and Computational Setup Experimental Setup Test Compressor Linear Cascade Design Smoke Generation and Injection Instrumentation Computational Setup CFD Solver Description Mesh Generation and Validation Computational Procedure Numerical Challenges Rotor-Only Axial Compressor Computations

10 3.3.1 Validation with Experimental Data Simulation of Stall Pre-cursors Summary Experimental Assessment of Formation Mechanism Demonstration of Spike Pre-cursor in the Cascade Experiment Reynolds Number Effects on Pre-cursor Formation Visualization of Pre-cursor Formation Major Findings Transient Heat Transfer Effects on Compressor Stability Introduction Previous Work Motivation and Objectives Technical Roadmap Development and Validation of a Diabatic Mean Line Model Object-Oriented Turbomachinery Analysis Code (OTAC) Mean Line Model Input Parameters Simulation Setup of an Acceleration Transient Adiabatic Validation of the Mean Line Model Implementation of Heat Transfer Effects Diabatic Loss and Deviation Correlations Summary Assessment of Diabatic Stall Margin Loss Quantifying the Impact of Deviation Effects Heat Transfer Effects on Stage Rematching Quantifying Stall Margin Loss Sensitivity to Model Inputs Limitations and Expansion of Current Capability Major Findings

11 8 Conclusions Spike-type Rotating Stall Inception Recommendations for Future Work Transient Heat Transfer Effects Recommendations for Future Work A Guidelines for OTAC Implementation and Usage 135 B Guidelines for Smoke Visualization

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13 List of Figures 2-1 Modal and spike pre-cursors in pressure traces Criteria for stall inception type Tip-clearance flow as a mechanism for spike-type stall inception Spike pre-cursor formation process proposed by Pullan et al Technical roadmap for spike-type stall inception investigation MIT research compressor performance and pre-stall behavior Cascade design schematics Compressor and cascade parameters Velocity profile of compressor endwall boundary layer Smoke generator schematic Dual cascade top casings facilitate instrumentation and flow visualization Relationship of compressor operating point and outlet boundary condition Blade mesh at 90% span Computational domain size Limiting streamlines showing large hub separation Shape of time-averaged pressure rise characteristic in good agreement with experiment Pressure traces for compressor computation and experiment at stall in good agreement Compressor computation captures spike pre-cursor formation

14 3-14 Pre-cursor formation mechanism in compressor computations agree with that of Pullan et al Spike pre-cursor behavior with change in reference frame: up-spike leads down-spike in compressor, down-spike leads up-spike in cascade Spike pre-cursor demonstrated in cascade experiment Spike pre-cursor formation captured at lower spans Spike pre-cursor formation at 50% span for 15,000 Reynolds number Cascade computation show same pre-cursor formation mechanism at 50% span as in compressor computations Flow visualization prior to pre-cursor formation Flow visualization at t 1 : partial leading-edge separation at blade Flow visualization at t τ: blade 2 leading-edge fully separated Flow visualization at t τ: propagation of shed vorticity to adjacent passage Flow visualization at t τ: blade 2 boundary layer re-attached Unsteady component temperatures for typical acceleration transient. Differing time scales of component and main gas path temperatures drive transient heat transfer Stage pressure ratio as functions of inlet and outlet corrected flow. Stage outflow sensitive to excursions in inflow Demonstration of stage stacking behavior. Small excursions in front stages bring rear stages close to stall Stall line reduction due to heat transfer as predicted by Maccallum and Grant Results of Shah indicate impact of heat extraction on loss and deviation approximately uniform across incidence range Technical roadmap for transient heat transfer investigation BladeRow element structure

15 6-2 Compressor model execution sequence Representative loss and deviation buckets derived from reference mean line data Combined loss parameter polynomial surface Operating points for blockage calculation Blockage distribution at design corrected speed Schematic of transient calculation showing use of engine system model (ESM) data and choked HPT assumption Mean line model captures adiabatic compressor performance and agrees with reference mean line model data Stall line from diffusion factor stall criterion in agreement with reference mean line data Mean line model produces representative transient operating line, with some discrepancy due to choking assumption Schematic of BladeRow element modifications for heat transfer capability Heat transfer element reproduces Rayleigh line Heat transfer increases excursion of transient operating lines Net heat flux as a function of non-dimensional time. Maximum heat addition at 95.3% corrected speed Composite compressor maps for diabatic transient. 9.9 point reduction in stall margin between 93% and 100% corrected speed Stall margin as a function of corrected speed for adiabatic and diabatic calculations. Heat transfer results in a stall margin loss of 9.9 points Percentage of stalling events per blade row. Heat transfer increases stall frequency in front blade rows Diffusion factors at stall point for select blade rows. Heat transfer increases loading for front blade rows and reduces loading for rear blade rows

16 7-7 Loss buckets showing compressor matching at stall for 95.3% corrected speed. Incidence increases in front stages and decreases in rear stages with maximum change in incidence of Impact of heat transfer at different axial locations. Heat addition backpressures upstream blade rows Stall margin as a function of corrected speed for modified values of ζ. stall margin loss is proportional to ζ Sensitivity coefficient S ζ for deviation correlation. Stall margin loss is approximately linear with ζ Stall margin loss as a function of corrected speed for modified values of heat flux (qcomp,net). Stall margin loss is proportional to qcomp,net Sensitivity coefficient S q for heat flow. Stall margin loss is approximately linear with qcomp,net Transient operating lines from diabatic mean line model and current NPSS capability Stall margin from diabatic mean line model and current NPSS capability. Current capability understimates stall margin loss Time averaged heat flux distribution Uniform heat flow distribution captures 80% of stall margin loss

17 List of Tables 2.1 Characteristic differences of spike and modal stall pre-cursors Design parameters of MIT research compressor Reynolds number study: Pre-cursor topology and propagation rate unchanged for Reynolds number range of 30,000-60,000. Pre-cursors not observed near blade tip for 15,000 Reynolds number Heat transfer element independents and dependents Compressor block definition

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19 Nomenclature Abbreviation & Acronym AG5 AutoGrid 5 DF Diffusion factor ESM Engine system model NPSS Numerical Propulsion System Simulation OTAC Object-oriented Turbomachinery Analysis Code PR Re SM Pressure ratio Reynolds number Stall margin Greek α β δ γ κ λ Absolute frame flow angle Relative frame flow angle Deviation Ratio of specific heats Metal angle Stagger angle 19

20 ν Ω Kinematic viscosity Rotor angular velocity Φ, φ Flow coefficient Vx U t Ψ, ψ Total-to-static pressure rise coefficient po P t,i 1 2 ρu 2 t ρ σ τ θ ω ω Density Solidity Blade passing period Circumferential position Blade loss parameter Pt,o P t,i P t,i p i Vorticity, specific rate of dissipation of turbulent kinetic energy, ω r Non-dimensional radial vorticity ωr U t/r t ζ Deviation correlation sensitivity Roman A Area c p Specific heat at constant pressure c s Pre-cursor velocity in absolute frame C dq Heat flux distribution control parameter h, h t Static, total enthalpy I i k Rothalpy Incidence angle Turbulent kinetic energy 20

21 ṁ, ṁ c Physical, corrected mass flow M Mach number N, N c Physical, corrected rotor speed p, P t Static, total pressure p Q Pressure coefficient p P t,i 1 2 ρu 2 t Heat flow rate q Non-dimensional heat flux Q ṁh t,i R r S Gas constant Radius Blade pitch S ζ, S q Stall margin sensitivity coefficients to deviation correlation, net heat flux s Specific entropy T, T t Static, total temperature t Time t acc Acceleration time constant t Non-dimensional time t τ t Non-dimensional time t t acc U t Blade tip velocity U Cascade free-stream velocity V W Absolute frame velocity Relative frame velocity 21

22 Subscript 25 High pressure compressor inlet 3 Combustor inlet 4 High pressure turbine inlet design At design point i, in Inlet quantity LE m Leading-edge Meridional component o, out Outlet quantity rel θ T E x Relative frame quantity Tangential component Trailing-edge Axial component 22

23 Chapter 1 Introduction 1.1 Background With the rise of fuel prices and environmental regulation in the past two decades, the focus on the fuel efficiency of gas turbine engines has grown enormously. To improve efficiency, engine manufacturers have sought higher pressure ratios in their designs, with overall pressure ratios of 40 common today and 60 on the horizon. Rising pressure, and hence temperature, ratios increases the opportunity for compressor instability from heat transfer throughout the compressor. To enable lower fan pressure ratios, gas turbine cores have shrunk considerably in size. Such small cores present challenges in maintaining tight tip clearances, the lack of which is known to promote compressor instability. This thesis presents two investigations of current problems in the area of compressor instability: 1) the onset of spike-type rotating stall and 2) the impact of heat transfer during compressor transients on stall margin. The first investigation is of the growth and development of so-called spike stall pre-cursors. Spike stall pre-cursors are one of two forms of rotating stall inception, the other being modal stall pre-cursors. Unlike modal-type stall, which is relatively well understood and captured by existing models, the fluid mechanical mechanisms of the formation and growth of spike stall pre-cursors are still not well characterized. Recently, leading-edge vortex shedding has been hypothesized as a mechanism for the formation of spike stall pre-cursors. In this thesis, this hypothesis is further assessed 23

24 using an experimental and numerical test program. The second problem relates to heat transfer between the main gas path and the compressor blades and endwall surface during transient operation. While the detrimental effects of transient heat transfer are well known, estimation of the stall margin loss is left largely to empirical models. The heat transfer results in stall margin loss via two mechanisms: changes in the blade row performance and an alteration of the stage matching. A first-principles based model is developed to quantify the stall margin loss, as well as to characterize the mechanisms that drive stall margin loss and assess the sensitivity of the stall margin loss to heat transfer. 1.2 Thesis Contributions The contributions of this thesis can be summarized as follows: 1. First demonstration of spike pre-cursors in a non-rotating, cascade experiment 2. Identification and quantification of Reynolds number effects on the formation of spike pre-cursors 3. Visualization of spike stall pre-cursor formation and evidence of leading-edge vortex shedding as the formation mechanism 4. First-principles based quantification of transient stall margin loss due to heat transfer in a compressor of technological interest 5. Characterization of the dominant mechanisms of transient stall margin loss 6. Quantification of transient stall margin loss sensitivity to heat transfer magnitude and blade row deviation 24

25 1.3 Summary of Thesis Chapters Chapter 2 presents an introduction into compressor instability and the differences between modal-type and spike-type rotating stall inception. A literature review indicates that while tip-leakage flow has historically been considered necessary for spike stall pre-cursor formation, recent experiments have shown spike-type stall inception in the absence of tip-leakage flows. Based on an extensive numerical investigation, leading-edge separation and vortex shedding has been previously proposed as a formation mechanism for spike pre-cursors. An experimental and numerical test program is outlined to evaluate this hypothesis, utilizing smoke flow visualization in a linear rotor blade cascade and corresponding computations. Chapter 3 details the development of the elements necessary to assess the leadingedge vortex shedding hypothesis. The rotor of the MIT single-stage, low-speed compressor serves as a test geometry and details of the compressor performance are presented. The design of a linear rotor blade cascade capable of capturing the spike pre-cursor and a smoke injection mechanism to visualize pre-cursor formation are given in detail. Computations, of both the compressor and cascade, are used to support the experimental assessment. The computational setup of both calculations is discussed in detail. The chapter ends with the validation of the compressor computations with experimental data from the MIT single-stage compressor, demonstrating that the computational methodology is capable of capturing the formation of spike pre-cursors. Chapter 4 presents the experimental assessment of the leading-edge vortex shedding hypothesis. The linear cascade demonstrates pre-cursor formation at the blade tip and the propagation rate is in reasonable agreement with stall experiments in the single-stage compressor. Pre-cursor formation is demonstrated at lower spans, lending evidence to the incidence driven, leading-edge vortex shedding hypothesis. Cascade computations are performed and show the same formation mechanism is present in the cascade as in the compressor. Reynolds number is found to impact pre-cursor formation. These effects are quantified in a systematic investigation, and boundary 25

26 layer transition is hypothesized as a mechanism for the observed behavior. Informed by the Reynolds number investigation, spike pre-cursor formation and propagation is visualized using smoke flow visualization and the visualization is found to be in good agreement with both the cascade computations and the published literature. Chapter 5 introduces the investigation of transient heat transfer effects. It starts with a brief overview of the mechanisms that drive transient heat transfer and stage matching in multi-stage compressors. A literature review indicates that stall margin loss due to heat transfer is as great as 12 points, with effects of heat transfer on the blade boundary layer and stage matching of the same order of magnitude. The limited agreement of the literature with experiment, however, motivates a re-assessment of this result using higher fidelity tools and data from compressors of current technological interest. The development of a diabatic mean line model capable of capturing the effects of heat transfer is outlined. Chapter 6 details the development of the diabatic mean line model. A recently developed mean line solver for the widely used NPSS framework is utilized and a brief overview of its capabilities and design is provided. Loss, deviation, and blockage models are developed utilizing data for an advanced, high pressure ratio compressor. A procedure for the simulation of transient operation is developed and the adiabatic steady state and transient performance of the model are validated with compressor data. A stall criterion based on the Lieblein diffusion factor is developed such that the effects of heat transfer on the stall line can be assessed. The mean line model is then expanded to include heat transfer capability and correlations for the effects of heat transfer on blade loss and deviation are implemented. The heat transfer capability of the mean line model is validated with analytical results for one dimensional, compressible channel flow with heat addition. Chapter 7 presents the assessment of transient stall margin loss due to heat transfer. Heat transfer is found to reduce transient stall margin by as much as as 10 points, with 75% of the stall margin loss due to stage rematching effects. While it is found that heat transfer does increase transient operating line excursion, the majority of the stall margin loss is due to reductions in the stall line. The changes in stage match- 26

27 ing are examined and it is found that heat transfer acts to increase loading in the front stages, resulting in the stalling of the front blade rows. The sensitivity of the predicted stall margin loss to heat transfer magnitude and the deviation correlation used is assessed and the dependence of stall margin loss on both of these quantities is found to be approximately linear. Simulations representative of the current modeling capability in NPSS demonstrate that only 7% of the total stall margin loss is captured in the current capability. The chapter ends with the presentation of simplifying assumptions that can be utilized to form a first approximation of the transient stall margin loss. Chapter 8 summarizes the significant findings from both investigations and provides recommendations for future work. 27

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29 Chapter 2 Spike-Type Rotating Stall Inception 2.1 Introduction Stable compressor operation is limited by surge and rotating stall. Surge is an instability of the entire compression system resulting from interactions of the compressor and a downstream volume and throttle. During surge, the mass flow and compressor pressure rise exhibit large amplitude (relative to the mean), one-dimensional oscillations and even periods of reversed flow are possible. The onset of surge, and subsequent compressor behavior, has been well captured by one-dimensional, lumped parameter models [1, 2]. In contrast, rotating stall is a phenomenon isolated to the compressor. Similar to traditional wing stall, rotating stall is the result of a separation of the airfoil boundary layer along all or part of the span. This separation reduces the achievable pressure rise and mass flow through the passage. The re-distribution of flow around the blocked passage results in the separation propagating along the circumference in one or more stall cells at 20-70% of the rotor rotational speed [3]. During rotating stall, the compressor pressure rise and annulus-averaged mass flow are quasi-steady, however, the local flow through the blade row passages is highly unsteady. The unsteadiness of the passage flow, as well as the often three-dimensional nature of the separation, present challenges in modeling and characterizing the onset of rotating stall. Two distinct forms of rotating stall inception have been identified: modal waves 29

30 (a) Modal stall pre-cursor (b) Spike stall pre-cursor Figure 2-1: Modal and spike pre-cursors in pressure traces (reproduced from [6]) and spike-type stall pre-cursors. In both forms, small disturbances grow in magnitude to the point where the bulk flow through several blade passages breaks down, separation occurs, and the stall cell is formed. Modal pre-cursors are long-wavelength (on the order of the annulus circumference), oscillations in pressure and mass flow throughout the length of the compressor. They are typically observable revolutions prior to the onset of rotating stall and travel around the circumference at a rate between 20% and 40% of rotor speed [3, 4]. Figure 2-1a shows a typical modal pre-cursor as captured by pressure transducers distributed circumferentially on the compressor casing. The growth of the modal pre-cursor is only possible when the slope of the total-to-static pressure rise characteristic is positive and the compressor damping is negative [5]. Spike pre-cursors are short-wavelength disturbances (on the order of two to three blade pitches) that travel around the annulus at approximately 70% rotor speed [7]. The term spike pre-cursor is given to these disturbances after the sharp waveforms they produce in pressure or velocity measurements. The spike pre-cursor is a three dimensional phenomena producing a local breakdown of the flow within a blade passage. Figure 2-1b shows typical pressure traces of spike stall pre-cursors and Table 2.1 summarizes the characteristic differences between modal and spike pre-cursors. Camp and Day [8] proposed a criterion, shown schematically in Figure 2-2, for 30

31 Spike Modal Length Scale Blade Pitch Annulus Circumference Propagation Speed (% Rotor Speed) Time Prior to Stall (Rotor Revolutions) Table 2.1: Characteristic differences of spike and modal stall pre-cursors determining which form of stall inception will arise. If a critical rotor incidence angle is achieved prior to the peak of the compressor characteristic, where the characteristic is negatively sloped, then the compressor will exhibit spike-type stall inception. The damping of the compressor is positive and modal waves cannot develop. If, however, the critical rotor incidence is reached after the peak, the compressor experiences a region of negative damping, allowing modal pre-cursors to form and grow into a mature stall cell prior to the possible formation of a spike pre-cursor. From this criterion a general observation can be made: spike-type inception is likely if the compressor stalls while the characteristic is negatively sloped and modal-type inception is likely if it stalls while the characteristic is positively sloped or at the peak. Figure 2-2: Criteria for stall inception type (reproduced from [8]) 31

32 2.2 Previous Work While the work of Camp and Day provided a criterion to determine the form of stall inception, it did not identify the underlying fluid mechanisms responsible for the formation of the spike pre-cursor. This mechanism has been the subject of much study in the past decades. It has been reported that the spike pre-cursor is confined to the rotor tip region [7, 8], and as such, the tip-leakage flow was examined as a candidate mechanism. Early computational studies by Hoying [9] captured the formation of the spike pre-cursor and provided evidence that its formation was linked to the trajectory of the tip-clearance vortex. The computations showed the tip-clearance vortex grew increasingly perpendicular to the main flow as the compressor was throttled into stall (as shown in Figure 2-3a) and, at the stall point, the tip-clearance vortex moved axially upstream of the blade row. Hoying attributed the spike pre-cursor to the propagation of tip-clearance vortex upstream of the blade row. The spillage of tipclearance flow upstream of the leading edge, as well as backflow of tip-clearance flow near the trailing edge (see Figure 2-3b), were later established as a criteria for the formation of spike pre-cursors by Vo et al. [10]. The criteria of Vo et al. was later supported by full-annulus URANS computations [11]. Recent studies, however, have indicated that spike-type stall inception is possible in the absence of tip-leakage flow. Spakovszky and Rodunner [12] reported spike-type stall inception in the vaned diffuser of a centrifugal compressor. The vaned diffuser has no tip clearance (as there are no rotating components) and thus no tip-leakage flow. The spike pre-cursor propagated circumferentially at 20% of the impeller speed, however, this speed was measured in the same reference frame as the stalling blade row (the absolute frame). In a typical axial rotor, the spike pre-cursor propagates at 60%-90% of rotor speed in the absolute frame, corresponding to 40%-10% with respect to the rotor (the stalling blade row), in the relative frame. The propagation speed of 20% in the vaned diffuser is thus consistent with the behavior of spike pre-cursors in axial rotors. Brand and Kottapalli [6] reported spike-type stall inception in a shrouded axial rotor. A low-speed research compressor was re-staggered such that it exhibited 32

33 (a) Tip-clearance vortex trajectories for decreasing flow-coefficient [9] (b) Criteria for formation of spike-type stall inception by Vo et al. [10] Figure 2-3: Tip-clearance flow as a mechanism for spike-type stall inception spike-type stall inception and a metallic shroud installed to prevent tip-leakage flow. Even in the absence of tip-leakage flow, the compressor dynamic behavior was not altered and the machine still exhibited spike-type stall inception. The spike precursors observed with and without the presence of tip-leakage flow appeared identical in the pressure traces and propagated circumferentially at the same rate, indicating they had similar topologies and that similar fluid dynamic mechanisms were present. The work by Spakovszky and Rodunner and by Brand and Kottapalli suggest tip-leakage flow is not necessary for the formation of spike pre-cursors. Pullan et al. [13] proposed that spike pre-cursor formation is the result of a leading-edge flow separation, and consequent vortex shedding, near the blade tip. Close to stall, a single blade experiences an increase in incidence, resulting in a separation at the leading edge (Figure 2-4a). The vorticity once bound in the suction side boundary layer is shed and rolls up into a vortex tube (Figure 2-4b) which connects the casing and blade suction surface. 1 The casing end of the vortex tube propagates circumferentially along the leading-edge plane while the blade surface end continues downstream of the blade row. The blockage associated with the leading-edge separation results in the up-spike observed in the pressure traces, while the low-pressure core of the vortex 1 Vortex lines cannot in the fluid, and as such, the vortex tube does not end at the blade or casing surface. The vortex lines that comprise the vortex tube instead spread out along the surface and there is no longer a coherent structure 33

34 (a) Leading-edge separation due to increased incidence (b) Vortex tube structure Figure 2-4: Spike pre-cursor formation process proposed by Pullan et al. (reproduced from [13]) tube is responsible for the down-spike. The topology of the vortex tube proposed by Pullan et al. agrees well with the structures seen in the simulations of both Inoue [14] and Yamada [15]. Pullan et al. presented results from full-wheel 2D and 3D simulations that support this hypothesis. In all three simulations (2D, 3D without tip-clearance, and 3D with tip-clearance), the same mechanism of increased incidence, leading-edge separation, and shedding of vorticity was found to be responsible for the formation of the spike pre-cursor. The fluid dynamical process responsible for the increased incidence, however, was dependent on the simulation. In the case of the 2D simulation, a trailing-edge separation of the adjacent blade resulted in blockage and increased incidence on the stalling blade, whereas in the 3D case without tip-clearance it was the blockage of a growing hub-corner separation. Regardless of the cause of the increased incidence, however, it was the consequent leading-edge separation and shed vorticity that was responsible for the development of the spike pre-cursor. 34

35 2.3 Motivation and Objectives Recent experiments have shown the tip-leakage vortex is not necessary for the formation of spike pre-cursors. To explain this development, a mechanism was proposed by Pullan et al. which attributes the formation of the pre-cursor to leading-edge separation and vortex shedding, resulting from a critical incidence being exceeded. Through several computations, it was shown that this mechanism is responsible for the formation of spike pre-cursors in the absence of the tip-leakage vortex. The work of Pullan et al., however, is numerical in nature, as is much of the published literature. To date there has been limited experimental characterization of the spike pre-cursor formation and topology, likely owing to the challenges of flow characterization in the rotating environment of the compressor. Furthermore, the majority of experimental investigations have been conducted at low Reynolds numbers, typically an order of magnitude below those found in gas turbines. The impact of Reynolds number on pre-cursor formation, however, has not been characterized. This work seeks to address these limitations with the following objectives: 1. Demonstrate the formation of spike pre-cursors in a non-rotating environment 2. Experimentally assess the previously proposed incidence driven, leading-edge vortex shedding mechanism for the formation of spike pre-cursors 3. Characterize the impact of Reynolds number on pre-cursor formation 4. Visualize the pre-cursor formation process 35

36 2.4 Technical Roadmap Single-Stage Compressor Test Stall Inception Assessment in Cascade Reynolds Number Study Cascade Flow Visualization Compressor Computation Cascade Computation Figure 2-5: Technical roadmap for spike-type stall inception investigation The technical roadmap is shown in Figure 2-5. The rotor of the MIT single-stage compressor serves as the basis for this investigation. Stall ramps are used to identify the critical incidence for the rotor blade geometry. A linear cascade of the same geometry is used to capture the spike pre-cursor in a non-rotating environment. At the core of the previously proposed formation mechanism is the idea of a critical incidence resulting in a leading-edge separation. The mechanism does not, however, require this incidence be achieved at the blade tip. In theory, pre-cursor formation should be possible at any spanwise location where the critical incidence is met. To assess the incidence driven mechanism, the cascade is designed to enable large incidence changes away from the blade tip. Specifically, the blades used in the cascade are twisted, with incidence increasing from the tip to the hub. Pre-cursor formation in the cascade is first assessed at the blade tip using a combination of fastresponse pressure and velocity measurements. Velocity measurements are conducted along the span to determine if pre-cursor formation occurs at lower spans, away from the tip. Smoke flow is used to visualize pre-cursor formation. Smoke flow visualization requires low Reynolds numbers to avoid rapid diffusion of the smoke. These Reynolds numbers are typically an order of magnitude below those achieved in low speed research compressors [16]. To assess the feasibility of using smoke flow, a systematic 36

37 investigation of pre-cursor formation at lower Reynolds number is conducted. Smoke flow visualization is then performed at the lowest possible Reynolds number. The smoke flow visualization is correlated with velocity measurements to identify the structures responsible for the characteristic waveform in compressor pressure traces. The cascade experiment is supported by 3D URANS calculations. Compressor calculations are first used to develop the numerical simulation framework and focused on capturing the pre-cursor formation. The same methodology is used to assess the formation of the spike pre-cursor in the cascade. The cascade flow visualization and velocity measurements are compared with the cascade computations and the results of Pullan et al. 37

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39 Chapter 3 Experimental and Computational Setup 3.1 Experimental Setup In this section the setup of the single-stage compressor and linear rotor blade cascade tests are outlined. The cascade design, instrumentation, and smoke generation and injection are also discussed in detail Test Compressor All work in this investigation was done using the MIT single-stage, low-speed research compressor. This compressor was previously used by Brand and Kottapalli [6] to investigate spike-type stall inception in a shrouded rotor, but for all studies in this thesis the rotor was un-shrouded. Design parameters of the MIT research compressor are given in Table 3.1. The compressor was run without the stator to prevent losses in the stator from producing a positive slope of the pressure rise characteristic and promoting the growth of modal stall pre-cursors. The measured pressure rise characteristic is shown in Figure 3-1a. Six fast-response pressure transducers were installed around the circumference at 25% chord upstream of the rotor leading edge to investigate the pre-stall behavior. The resultant pressure traces are given in Figure 39

40 % Ω Ψ Φ stall = θ location ρu2 t Φ Rotor revolutions (a) Pressure rise characteristic (b) Pre-stall behavior Figure 3-1: MIT research compressor performance and pre-stall behavior 3-1b and demonstrate that the compressor exhibits spike-type stall inception. The rotor blade geometry of the compressor is a legacy design and is known to be more heavily loaded at the hub than the tip [17]. As a result, the hub separates at even high flow coefficients, the extent of the which is shown in Section While the hub separation reduces the negative slope of the measured characteristic, the slope of the local characteristic at the tip can be more negative. Ultimately the compressor exhibits spike-type stall inception, making it an appropriate test vehicle for this study. The rotor blade geometry was used for all computational studies and for the linear cascade investigation. For the computations, the rotor blade geometry was re-constructed using the information reported by Gopalakrishnan [18]. The mean cross-section is a NACA 6409 airfoil with varying leading-edge and trailing-edge metal angles along the span. The maximum camber magnitude and position, m and p in the NACA centerline polynomial respectively [19], were varied to match the metal angles, resulting in several airfoil cross-sections along the span. The cross-sections were linearly lofted to define the 3D blade geometry for computation. 40

41 Table 3.1: Design parameters of MIT research compressor Design Flow Coefficient φ 0.59 Tip Stagger Angle 60 Design Pressure Rise Coefficient ψ 0.66 Mean Radius 259 mm Hub to Tip Ratio 0.75 Chord 38 mm Solidity 1.03 Blade Count 44 Aspect Ratio 1.90 Reynolds Numbers 75, , Linear Cascade Design One objective of this work is to generate a spike pre-cursor in a non-rotating cascade experiment so as facilitate visualization of the formation process. This results in the following design requirements for the cascade: 1. Re-create rotor tip flow field at stall and capture spike pre-cursor 2. Facilitate smoke injection near the leading edge 3. Permit instrumentation with pressure transducers and a hotwire anemometer Figure 3-2 presents two schematics of the cascade design. This section discusses the design decisions to meet the first requirement. Smoke generation and instrumentation are discussed in the next two sections. The key feature of the formation mechanism proposed by Pullan et al. is a leadingedge separation resulting from a critical incidence being reached. As such, reproducing the rotor tip incidence α at stall in the cascade is of great importance. Figure 3-3 shows the relevant parameters in both the compressor and cascade. 41

42 (a) Design features (b) Top view Figure 3-2: Cascade design schematics i W β Ωr λ S Tunnel Airflow U = W β i S λ V x Compressor Cascade Figure 3-3: Compressor and cascade parameters 42

43 While the blade stagger angle is a function of the compressor geometry only, the flow angle in the compressor is a function of the flow coefficient at stall, ( 1 β = arctan, φ = φ) V x U t As the incidence angle at the blade tip is under consideration, the flow coefficient is defined using the blade speed at the tip. In the cascade, the flow angle is set by the angle between the tunnel axis (the direction of the free-stream flow) and the leading-edge plane. The pressure rise characteristic in Figure 3-1a shows that the compressor stalled at a flow coefficient of , corresponding to a blade tip flow angle of β = The flow coefficient in Figure 3-1a was determined using the axial velocity V x from a pitotstatic probe upstream of the rotor face and at the mean radius. The axial velocity at the rotor tip, however, is less than that at the mean radius due to the endwall boundary layer, resulting in a locally lower flow coefficient and thus higher flow angle and incidence. The endwall boundary layer velocity profile, shown in Figure 3-4, was previously measured by Gysling using a hotwire anenometer located 1/3 rd of a blade chord upstream of the leading-edge. The nominal stalling flow coefficient is reduced by based on the decrease in flow coefficient observed at 88.5% span, which represents the mean of the last spanwise location with a nominal flow coefficient (77% span) and the blade tip. This results in a local stalling flow coefficient of at the tip, corresponding to a flow angle of β = The flow angle sets the angle between the tunnel axis and the leading-edge plane during construction of the cascade. The blade stagger angle ( γ) and pitch (S) are taken from the compressor geometry and are 60 and 31.8 mm respectively. The blade with smoke injection is staggered an additional 5 to promote pre-cursor formation at the location of smoke injection. One goal of this work is to assess whether pre-cursor formation can occur at locations below the tip span. This requires the incidence at lower spans to be equal to, or greater than, that at the tip. Such a setup can be achieved by using twisted blades 43

44 Percent Span [ ] Φ [ ] Figure 3-4: Velocity profile of compressor endwall boundary layer (from [17]) in which the incidence increases from tip to hub. This is the case for compressor blades, and the same physical blades from the compressor were used in the cascade. Using the compressor blades offered two additional benefits. First, the large number of pre-fabricated blades enabled a high blade count of 20 in the cascade. This eliminated the need for boundary layer control along the sidewalls to maintain periodicity. Furthermore, the cascade could serve as a test bed for smoke visualization techniques for future use in the compressor. The cascade was fabricated of optically clear polycarbonate to permit visual access and the sidewalls were machined to produce the same average tip clearance as in the compressor. Poor tolerance control during the manufacture of the blades, however, prevented the precise control of tip clearances. The tip clearances varied by as much as 1.0% of chord, with the average tip clearance being 1.3% of chord. This is comparable to that of the single-stage compressor which has tip clearance variations of up to 1.3% chord. A trip strip was installed upstream of the rotor blades on the top and bottom casing to force transition of the endwall boundary layer. The trip strip was installed parallel to the leading-edge plane such that the boundary layer thickness was approximately the same at each blade. 44

45 3.1.3 Smoke Generation and Injection Smoke has long been used as a tool for flow visualization in experimental aerodynamics. In typical wind tunnel experiments, smoke is injected upstream of the object under study. Such setups use large contractions downstream of injection to reduce the velocity, and hence Reynolds number, at the smoke injection point. Lower Reynolds numbers reduce the mixing and diffusion of the smoke, producing more coherent streaklines downstream. The Reynolds numbers of smoke flow experiments are typically an order of magnitude lower than those found in research compressors [16]. Constraints on the size of the smoke generating apparatus are also less severe as the injection occurs well upstream of the object being studied. This work seeks to visualize the leading-edge separation of the suction surface boundary layer and consequent vortex shedding. To improve the visualization, it is desirable to inject smoke directly into the suction side boundary layer. Once injected, the smoke would remain with the boundary layer fluid throughout the formation process. This, however, requires injection at the test velocity rather than at the reduced velocity upstream of a contraction, resulting in higher Reynolds numbers and increased diffusion. Furthermore, the injection apparatus must be small relative to the blade to reduce its aerodynamic influence. While the Reynolds number in the cascade can be made small by reducing the free-stream velocity, the impact of low Reynolds number on pre-cursor formation is unknown. A study of pre-cursor formation at low Reynolds number was performed prior to flow visualization and is discussed in Section 4.2. The study identified the lowest Reynolds number for which visualization is feasible while spike stall pre-cursors are still formed. No commercial smoke generator was suitable for the current study due to their size relative to the blade, and a miniaturized smoke generator was instead developed. It was found that the best visualization was achieved when the smoke was made in-situ, rather than being piped from an external location. The smoke generator was originally designed to be placed into a modified blade for use in the compressor, however, it could also be used detached from the blade. As the modified blade was 45

46 Heated Nichrome Wire Fed Through Outer Bores Enamel Seals Outer Bores Mineral Oil Flows Through Inner Bores + V - Ceramic Thermocouple Tube Plastic Tubing Figure 3-5: Smoke generator schematic ultimately not used in this study, the details are not given here and can be found in [20]. The smoke generator, shown in Figure 3-5, consists primarily of a quad-bore, ceramic thermocouple tube. The tube has a diameter of 1.6 mm, corresponding to 4% of the blade chord and 46% of the maximum blade thickness. Mineral oil is pumped through two of the bores. A nichrome wire runs through the remaining two bores and the mineral oil is heated to the point of evaporation via conductive heat transfer through the walls of the thermocouple tube. The two bores carrying the nichrome wire are sealed with high temperature enamel to prevent oil leakage. While a dual-bore design in which the nichrome is directly submerged in the oil would be more efficient and produce greater volumes of smoke, it was found that such a design produced excessive oil leakage Instrumentation There are three types of data to be acquired in the cascade experiment: fast-response static pressure and velocity measurements to capture the spike pre-cursor, high-speed video of the smoke visualization, and total and static pressure from a pitot probe to set the cascade operating point. Kulite model XCQ PSI fast-response pressure transducers were installed in the top casing to record the unsteady static pressure field. Two different top casings were used. The first, shown in Figure 3-6a, had an array of possible Kulite locations available. The first row of Kulite holes were placed 10% chord upstream of the leading-edge plane, aligned with the path of the leading-edge vortex. They were spaced at one third of a blade pitch apart for three passages downstream 46

47 Blade with Smoke Injection Blade with Smoke Injection K1 K2 K3 K4 K5 = Installed Kulite (a) Casing with Kulite array Hotwire (b) Casing with reduced instrumentation for flow visualization Figure 3-6: Dual cascade top casings facilitate instrumentation and flow visualization of the blade with smoke injection. Holes with the same pitchwise spacing were also placed within the passage to provide flexibility, in case the leading-edge vortex were to convect down a passage. They proved to be unnecessary and were covered with Kaptan tape during operation to prevent leakage. While this top casing provides the required spatial resolution of the unsteady static pressure field, the installed Kulites and unused holes obscured the smoke visualization when viewing the cascade from the top. A top-down perspective is preferable as it provides resolution of both the pitchwise and axial positions of any visualized structures. A second top casing, shown in Figure 3-6b, was manufactured with only two Kulites. The first is located two thirds of a blade pitch upstream of the blade with smoke injection. The second is located two blade pitches downstream, at the same location as K5 in Figure 3-6a. The upstream Kulite is used to ensure that the visualized structure did not convect from upstream and the downstream Kulite is used to assess whether the observed structures produce the characteristic up-down waveform of spike pre-cursors. A TSI Model 1210 hotwire was also used to record unsteady velocity measurements. It was placed in the leading-edge plane, with the shaft running axially through the passage to the trailing-edge. The hotwire offered greater sensitivity than the Kulites and could be placed at any span. Voltage signals from both the Kulites and the hotwire were amplified and sampled at 10 khz, approx- 47

48 imately 10 times the equivalent blade passing frequency, by a National Instruments 9215 A/D converter. The smoke visualization was recorded using a Photron Fastcam SA5 high-speed video camera. A Unilux 1xF strobe was used to provide illumination, providing a maximum bandwidth of 833 Hz and a short flash duration of 100 µs to reduce motion blur. Due to the bandwidth limitations of the strobe, the SA5 was operated at a frame rate of 750 Hz. The rate at which the pre-cursor propagates one blade pitch is on the order of 35% of blade passing frequency, or 154 Hz for the fastest equivalent rotor speed tested with smoke injection. For this case, the flow structure would propagate only 0.2 passages per frame. The camera and strobe were synchronized using a voltage pulse output by the camera. The voltage pulse was also recorded by the A/D converter to allow synchronization of the video frames and the pressure and velocity measurements from the Kulites and hotwire. The free-stream total and static pressure from the pitot probe were recorded using a Scanivalve DSA3217 1PSID pressure transducer. In summary, the linear cascade described is designed to match the blade tip incidence of the compressor at stall in order to generate a spike pre-cursor. The use of twisted blades allows investigating spike pre-cursor formation at lower spans, away from the tip. To facilitate flow visualization, a miniaturized smoke generator was designed to inject smoke directly into the suction surface boundary layer. Finally, the cascade incorporates the necessary instrumentation to capture the unsteady pressure and velocity field. 3.2 Computational Setup A brief description of the solver is provided and turbulence modeling, inlet and outlet boundary conditions, and time-stepping for unsteady calculations are discussed. Mesh generation and validation are discussed next and the procedure for performing a simulated throttle ramp is outlined. While the specific blade geometry presents some numerical challenges, which will be described in detail, the computational methodol- 48

49 ogy described below will be shown to be capable of capturing the spike pre-cursor CFD Solver Description All computations in this thesis were produced using a proprietary Reynolds Averaged Navier-Stokes (RANS) solver. The solver is a finite-volume code designed specifically for the simulation of turbomachinery flows and utilizes a structured hexahedral mesh. The equations are solved in the frame of reference of the blade row, i.e. the rotating frame for compressor computations and the stationary frame for cascade computations. Details of the solver settings and models are given below. Turbulence Modeling The k ω turbulence model is used for all computations in this thesis. It is a two equation model used to provide closure for the RANS equations. In this model, two transport equations are used to determine the turbulent kinetic energy k and the specific rate of dissipation ω. The turbulent eddy viscosity is then formed from these two quantities as ν t = k. The k ω model has been shown to capture flows with ω adverse pressure gradients [21], making it particularly suitable for compressor flows. Further details on the k ω model can be found in [22]. Both high and low Reynolds number treatments for near-wall modeling are available in the k ω model. In the high Reynolds number treatment, the first cell is placed in the log-layer and the log-law is used to model the velocity profile within the boundary layer. In the low Reynolds number treatment, the first cell is placed in the viscous sub-layer and the boundary layer is fully resolved. Low Reynolds number treatments are more accurate in capturing and predicting separation than high Reynolds number treatments, but require very fine meshes near the wall, increasing computational cost. The low Reynolds number treatment is required in this work as separation is fundamental to the hypothesized pre-cursor formation mechanism. The flow results were examined to ensure the first cell is located at y + 1 and that the mesh met the requirements for the low Reynolds number treatment. 49

50 Inlet Boundary Conditions For all computations, total pressure, total temperature, and flow angle were specified at the inlet. Total temperature was held at the standard day value (288.15K). Axial inlet flow was used for all compressor computations. For cascade computations, the inlet flow angle (β in Figure 3-3) was varied to set the incidence angle. Both total temperature and velocity direction were set to be spatially uniform. In compressor computations, a radial total pressure profile was used to simulate the inlet boundary layer as the inlet of the computational domain was shorter than the compressor inlet. The axial velocity profile at the rotor inlet was set to that measured by Gopalakrishnan [18]. This approach was not necessary for the cascade computations as the inlet of the domain was of the same length as the inlet in the cascade experiment and the boundary layer could develop naturally. Outlet Boundary Conditions During a typical stall inception experiment, a compressor is driven into stall by closing the downstream throttle. The compressor operating point is set by the intersection of the resultant throttle line, shown in Figure 3-7, and the pressure rise characteristic. While the behavior of a throttle can be modeled numerically (e.g. [23]), this requires the implementation of an actuator disk or the added computational cost of meshing a variable area nozzle. It is more common to set the operating point by either specifying the outlet mass flow or static pressure. Given a specified mass flow at the outlet of the domain, the solver varies the outlet static pressure until the appropriate operating point is found. The mass flow boundary condition was used for all steady simulations. For time-accurate unsteady simulations, however, this type of boundary condition is not suitable as the timevarying backpressure introduces an artificial source of unsteadiness. A constant static pressure boundary condition was used instead for all unsteady computations. As can be seen for the lower chained line in Figure 3-7, two valid solutions can exist for a given pressure boundary condition, one on the negatively sloped side of the characteristic and the other on the positively sloped side. The lack of a unique 50

51 Ψ Mass Flow B.C. p out Pressure B.C. Throttle Lines ṁ Figure 3-7: Relationship of compressor operating point and outlet boundary condition Φ solution can lead to numerical divergence, especially near the peak of the characteristic. This is less of a concern for this work, however, as compressors that exhibit spike-type stall inception typically stall on the negatively sloped side of the characteristic. The calculation also diverges if an exit pressure above the maximum pressure rise of the compressor is imposed, as in the upper chained line in Figure 3-7. As the compressor characteristic is not known a-priori, the back pressure must be increased by small increments and in many calculations to prevent such a condition, increasing the computational cost. The details of the computational procedure for the unsteady computations are given in Section A non-reflecting method of characteristics formulation of the mass flow and static pressure boundary conditions were used in all cases. While this serves only to reduce computational time for steady calculations, as the solution is driven to the time-average and any waves are damped, it is of greater importance for unsteady calculations. A constant pressure boundary condition can reflect unsteady pressure waves emanating from the blade row back into the computational domain. These reflections would interact with the blade row, artificially changing its behavior. The non-reflecting formulation seeks to prevent these reflections, however, some amount of reflection always occurs. An extended outlet 51

52 domain and cell-stretching were also used to further damp reflections and prevent any coupling between the blade row and the outlet boundary condition. Details of the computational mesh are given in section Temporal Resolution All unsteady compressor computations were performed with 100 physical time steps per blade passing period. This is consistent with the temporal resolution of other numerical work on spike-type stall inception (e.g. [13, 15]). Unsteady cascade computations were performed with 100 physical time steps per equivalent blade passing period, i.e. the blade passing period for the equivalent compressor rotational speed such that the same temporal resolution is maintained between cascade and compressor calculations Mesh Generation and Validation All meshes used in this work were produced using Numeca AutoGrid 5 (AG5). AG5 is a tool designed specifically for the rapid meshing of turbomachinery geometries and offers great control of the meshing process. All meshes were of an O4H topology and contained 1.2 million cells per blade passage. The blade mesh at 90% span is shown in Figure 3-8. Single passage calculations were performed with increased refinement (1.6 million cells per blade passage) and the pressure rise characteristic was unchanged, indicating the mesh was converged. The tip gap was meshed with additional blocks in an OH topology with 17 points in the tip gap. The blade stagger was set to that of the compressor (60 at the tip) and was uniform for all blades. The computational domain, shown in Figure 3-9, extends 0.8 tip radii upstream and 1.5 tip radii downstream of the blade row, 10.5 and 18 axial chords respectively, and is similar in size to that of Pullan et al. [13]. Cell-stretching has been reported to damp reflections from the outlet boundary and was utilized by Everitt [24] in an investigation of spike-type stall inception in centrifugal compressors. The cellstretching domain began 8 axial chords downstream of the blade row with a stretching factor of The stretching factor is 4 times less than that used by Everitt, however, 52

53 the base cell size prior to stretching was several times larger than those for Everitt due to the large outlet domain. The final cell of the outlet domain is approximately one axial chord long and further stretching was found to be unnecessary. The same mesh refinement and topology were used for the compressor and cascade computations to maintain consistency. Figure 3-8: Blade mesh at 90% span 1.5x Tip Radius 0.8x Tip Radius Cell Stretching Domain Figure 3-9: Computational domain size 53

54 3.2.3 Computational Procedure To reduce computational cost, steady computations were carried out as close to the stall point as possible. The first steady computations were initialized from a uniform flow field and run at an operating point that presented the least separation to the flow solver to aid in convergence, e.g. at high flow for the compressor computations or at low incidence for the cascade computations. Consequent steady calculations were initialized using the results from the previous calculation and were driven towards the stall point by decreasing the mass flow or increasing the inlet flow angle. The steady computations diverged for even relatively moderate operating conditions, likely due to the large amounts of separation expected from this blade geometry, at which point unsteady computations were used to further approach the stall point. The first unsteady computations were initialized with the results of the last converged steady computations. Consequent calculations were driven to the stall point with step increases in the outlet static pressure or incidence angle. A step increase was only performed after physical quantities such as mass flow or inlet static pressure reached steady levels for 1.5 rotor revolutions. In other words, when the computation had settled at the new operating point. These step changes were initially large to reduce the computational cost, on the order of a change in flow coefficient of 0.05, but were decreased in size as the operating point approached stall Numerical Challenges This rotor geometry is known to exhibit hub separation, even at high flow coefficients near the design point. The hub separation was further exacerbated by the blade twist in the cascade configuration. Figure 3-10 shows the limiting streamlines on a single blade both near design and near stall. Even near design, the hub is separated and the separation continues to mid-span. Close to stall, the separation has grown significantly and exists along the entire span. The unsteadiness of this separation posed a challenge to the steady flow solver, resulting in the steady computations diverging at a higher flow coefficient. The lim- 54

55 (a) Near design (b) Near stall Figure 3-10: Limiting streamlines showing large hub separation ited utility of the steady computations necessitated a greater number of unsteady computations. To reduce computational cost, only four passages, or an eleventh of an annulus, were simulated. It was found that the limited domain of the computations was capable of capturing the spike pre-cursor, as will be shown in the next section. 3.3 Rotor-Only Axial Compressor Computations In this section, the results of the rotor-only compressor computations are shown and the steady-state performance and unsteady stalling behavior of the computations are validated with experimental data. The computations capture the formation of the spike pre-cursor and the formation process is consistent with that proposed by Pullan et al. [13] Validation with Experimental Data Capturing the shape of the pressure rise characteristic is a primary requirement of the compressor computations as this governs the stalling behavior. Figure 3-11 shows 55

56 Experiment Rotor Only Ψ Computation Rotor Only Φ Figure 3-11: Shape of time-averaged pressure rise characteristic in good agreement with experiment the time-averaged pressure rise characteristic of the compressor computations and experiment. The shape of the characteristic from the computations agrees well with that of experiment. The characteristic from the computations, however, is shifted to lower flow coefficients. RANS calculations have known limitations in quantifying the impact of large separations. It is believed that the large hub separation results in an over-prediction of the overall blockage, resulting in the shift of the characteristic. As the shape of the characteristic is the primary concern, and this was in good agreement with experiment, the discrepancy in blockage was considered acceptable for the present study Simulation of Stall Pre-cursors The first unsteady computation was initialized at a flow coefficient of φ = The operating point was brought to stall via step changes in the back pressure, as detailed in Section Figure 3-12a shows pressure traces for the stalling calculation at six locations uniformly distributed across the four passages and 10% chord upstream of 56

57 % Ω % Ω θ Location ρu2 t θ location ρu2 t Rotor revolutions Rotor revolutions (a) Compressor computation, rotor-only (b) Compressor experiment, rotor-only Figure 3-12: Pressure traces for compressor computation and experiment at stall in good agreement the blade row. The equivalent pressure traces for the experimental stall ramps are shown in Figure 3-12b. The abscissa in Figure 3-12a has been scaled such that an angled line represents the same propagation speed on both plots. The stalling behavior of the compressor computation is in good agreement with the experiment. The characteristic up-down waveform of the spike pre-cursor is first observed in the computation at t 1 = 1.48 rotor revolutions and grows in magnitude. The propagation rate of the pre-cursor in the computation is 76% of rotor speed and agrees with the measured 77% in the experiment. It should be noted that the stall in the computation was not triggered by an imposed perturbation or a re-staggered blade. While the step change in back pressure used to change the operating point does produce a large perturbation to the flow field, the calculation had settled at the new operating point and continued for one rotor revolution without any significant behavior prior to the stall event. The stalling behavior was likely triggered by numerical turbulence inherent to the calculation. Figure 3-13a shows a contour plot of non-dimensional radial vorticity ω r at t 1 = 57

58 1.48 for a 90% span slice. The two lines above the contour plot show the pressure coefficient p across the domain and 10% chord upstream of the blade row (corresponding to the dotted line in the contour plot). The solid line is the pressure coefficient for the time presented while the dashed line is the steady pressure coefficient prior to the stall event. p 1 2 ρu 2 t p 1 2 ρu 2 t ω r ω r (a) t 1 = (b) t 2 = t 1 + 7τ = 1.64 Figure 3-13: Compressor computation captures spike pre-cursor formation At time t 1 the leading-edge of blade 3 has separated, producing blockage and a corresponding increase in static pressure upstream. The shed vorticity from the leading-edge separation propagates to the adjacent passages. Seven blade passing passing periods later, at t 2 = 1.64, a finite vortex is seen at blade 1 in Figure 3-13b. The core of the vortex produces a region of low static pressure corresponding to the down-spike seen in the pressure trace. Blade 4, while beginning to recover, is still separated. The separation blocks the passage between blades 1 and 4, producing a region of high static pressure, corresponding to the up-spike. Figure 3-14a compares the leading-edge separation with that found by Pullan et al. and Figure 3-14b compares the resulting leading-edge vortex. The two flow fields are in good agreement, further supporting the proposed mechanism. 58

59 (a) Leading-edge separation (b) Roll-up of vorticity into vortex core Figure 3-14: Pre-cursor formation mechanism in compressor computations agree with that of Pullan et al. To summarize, the compressor rotor-only computations capture the performance of the compressor and the formation of the spike pre-cursor in the compressor environment. The shape of the pressure rise characteristic is in agreement with experiment, as are the unsteady static pressure measurement at the rotor tip during stall. This demonstrates that the computational methodology, including the limited domain of four passages, is capable of characterizing the formation mechanism of spike-type stall pre-cursors and that this methodology can be used to characterize spike pre-cursor formation in the cascade. Furthermore, the formation mechanism is in agreement with the hypothesis of Pullan et al. and provides further numerical evidence in support of the hypothesis. 59

60 3.4 Summary In this chapter, all the elements necessary to assess the leading-edge vortex shedding hypothesis have been developed. The cascade design reproduces the incidence of the blade tip in the compressor at stall. Furthermore, the use of twisted blades to produce a range of incidences enables the investigation of pre-cursor formation at lower spans, in accordance with the incidence driven mechanism of Pullan et al. A miniaturized smoke generator has been developed to visualize the formation process and the cascade is instrumented with fast-response pressure transducers and a hotwire anemometer to capture the unsteady pressure and velocity field. 3D URANS calculations of both the compressor and cascade are used to support the experiment. The computational methodology is capable of capturing the spike pre-cursor formation in the compressor computation, indicating its applicability for simulating pre-cursor formation in the cascade. 60

61 Chapter 4 Experimental Assessment of Formation Mechanism In this chapter it is shown that the cascade captures the spike pre-cursor at the blade tip. The pre-cursor topology and propagation rate in the cascade is in agreement with that of the compressor experiment. Spanwise traverses of the hotwire are performed and demonstrate pre-cursor formation at lower spans, supporting the previously proposed incidence driven mechanism. To assess the feasibility of smoke flow visualization, a study of the impact of Reynolds number on pre-cursor formation is performed. The study found no changes in pre-cursor formation for Reynolds numbers between 90,000 (the same as that in the compressor experiment) and 30,000. At a Reynolds number of 15,000, however, pre-cursor formation was observed only at mid-span and not at the blade tip. From this result, pre-cursor formation was visualized at mid-span for a Reynolds number of 15,000 and a corresponding cascade computation was performed. The visualization is in good agreement with the cascade computation and both indicate the pre-cursor formation mechanism in the compressor and the cascade are identical. 61

62 4.1 Demonstration of Spike Pre-cursor in the Cascade Experiment Given the change of reference frame, it is useful to first consider the expected behavior of a spike pre-cursor in the cascade. In the pressure traces from the compressor experiment, an up-spike, associated with the blockage from the leading-edge separation, leads the down-spike, associated with the low pressure region in the vortex core. In the compressor experiment, pressure transducers are mounted on the casing and are in the stationary frame. In this frame, the spike pre-cursor propagates in the direction of rotor rotation, but at a rate less than rotor speed. Thus in the rotating frame, i.e. the blade relative frame, the spike pre-cursor propagates opposite the direction of rotor rotation. A pressure transducer in the blade relative frame, as is the case for the the cascade experiment, thus observes a down-spike followed by an up-spike. The change in behavior is shown schematically in Figure 4-1 Compressor Cascade dp dp time time x Ωr θ Transducer Absolute Frame c s Ωr c s Transducer Relative Frame Figure 4-1: Spike pre-cursor behavior with change in reference frame: up-spike leads down-spike in compressor, down-spike leads up-spike in cascade Pressure traces from the cascade and compressor experiments are given in Figure 4-2. The cascade is operated at a blade chord Reynolds number of 90,000, corresponding to the same conditions as the single-stage compressor experiment. The characteristic sharp waveform of the spike pre-cursor is observed in the cascade pres- 62

63 sure traces, with the down-spike leading the up-spike as expected from the previous discussion. The waveform propagates in the pitchwise direction at 37% of equivalent rotor speed, corresponding to 63% of rotor speed when viewed in the absolute frame. While this propagation rate is less than the 77% observed in the compressor experiment, it is within the range of observed spike pre-cursor propagation rates in the literature % Ω θ location ρu2 t 77% Ω Θ position (deg, Θ opp. rotor direction) ρu 2 t Rotor revolutions Rotor revolutions (a) Compressor experiment (b) Linear cascade experiment Figure 4-2: Spike pre-cursor demonstrated in cascade experiment The cascade experiment captured the spike pre-cursor at the blade tip, meeting the first objective of this work. Another objective is to assess the incidence driven mechanism. The mechanism does not limit pre-cursor formation to the blade tip and suggests that pre-cursor formation should be possible at any location where the critical incidence is met. The cascade design incorporated twisted blades, with increasing incidence at lower spans, specifically to assess this hypothesis. Figure 4-3 presents the recorded velocities of a spanwise hotwire traverse at 10% chord upstream of the leading-edge plane. As only one hotwire was available, the data at each spanwise location was recorded at different moments in time, but are presented together on a single plot. Figure 4-3 is meant only to evaluate the formation 63

64 of pre-cursors at different spans and should not be viewed as coherent in time. Note that the cascade operating point during the hotwire traverse resulted in a Reynolds number of 30,000, as opposed to the Reynolds number of 90,000 in Figure 4-2b. The role of Reynolds number on pre-cursor formation is discussed later in Section U t Spanwise Position Rotor revolutions Figure 4-3: Spike pre-cursor formation captured at lower spans. Data shown is for a Reynolds number of 30,000 and is not coherent in time The characteristic up-down waveform of the spike pre-cursor is observed at 90% span, for example at t = 6.2, as expected from the cascade pressure traces. The same waveform can also be seen at 70% and 60% span at t = 3.0, indicating pre-cursor formation at these spans. At even lower spans, such as 30%, large magnitude turbulence is observed and no coherent structures are discernible. The incidence at this span is sufficiently high to produce continuous separation and is more representative of of a blade row in rotating stall. In fact, the velocity trace at 30% span is similar to those recorded in a compressor in rotating stall (such as in [7]). The observed formation of spike pre-cursors at lower span provides experimental evidence for the incidence driven mechanism of Pullan et al. Furthermore, it is another example of pre-cursor formation in the absence of the tip-leakage vortex. 64

65 4.2 Reynolds Number Effects on Pre-cursor Formation Low-speed testing is common in the investigation of compressor stall, and specifically spike-type stall inception. The Reynolds numbers of these low speed experiments are typically on the order of 100,000 and an order of magnitude below those seen in gas turbine engines. The impact of Reynolds number on pre-cursor formation, however, has yet to be characterized. Pre-cursor formation at low Reynolds number is of particular interest in this work as an objective is to visualize the formation with smoke. Smoke visualization at high Reynolds number is challenging due to the rapid diffusion of smoke and operating at lower Reynolds numbers is desirable to improve visualization quality. Pre-cursor formation in the cascade was demonstrated at a Reynolds number of 90,000, the same as that in the compressor. Such a Reynolds number, however, is too high to perform smoke visualization. To characterize any changes from this baseline condition, pressure and velocity measurements were taken at successively lower Reynolds numbers, from 60,000 to 15,000 in increments of 15,000, and are shown in Table 4.1. The first column presents the casing pressure traces from the same configuration used to produce Figure 4-2b. The second column presents results produced from a configuration similar to that shown in Figure 3-6b. The hotwire was placed at 85% span and located at the same pitchwise location as the downstream Kulite in Figure 3-6b. The hotwire trace is used to assist in evaluating the pre-cursor topology, as the signal to noise ratio of the Kulites degrades at low Reynolds numbers (i.e. low free-stream velocities). The results shown in Table 4.1 are for representative events at each of the Reynolds number and many such events were observed in each data set. 65

66 Table 4.1: Reynolds number study: Pre-cursor topology and propagation rate unchanged for Reynolds number range of 30,000-60,000. Pre-cursors not observed near blade tip for 15,000 Reynolds number Reynolds # Propagation (Pressure Perturbations) Topology (Velocity Perturbations) 30 65% Ω 60,000 Θ position (deg, Θ opp. rotor direction) ρu 2 t Rotor revolutions Θ position (deg, Θ opp. rotor direction) U t, 1 2 ρu 2 t Rotor revolutions 30 60% Ω 45,000 Θ position (deg, Θ opp. rotor direction) ρu 2 t Rotor revolutions Θ position (deg, Θ opp. rotor direction) U t, 1 2 ρu 2 t Rotor revolutions 30 64% Ω 30,000 Θ position (deg, Θ opp. rotor direction) ρu 2 t Rotor revolutions Θ position (deg, Θ opp. rotor direction) U t, 1 2 ρu 2 t Rotor revolutions Continued on next page 66

67 Table 4.1: Continued from previous page Reynolds # Propagation (Pressure Perturbations) Topology (Velocity Perturbations) 30 15,000 Not shown due to poor signal to noise ratio Θ position (deg, Θ opp. rotor direction) U t, 1 2 ρu 2 t Rotor revolutions Pre-cursor formation is observed for Reynolds numbers of 60,000, 45,000, and 30,000. The same characteristic waveform is found in the pressure and velocity traces as in the baseline case. Furthermore, the propagation rates for the three cases are within three percentage points of the baseline (63% rotor speed). These results suggest that pre-cursor formation and topology is unchanged when the Reynolds number is reduced from 90,000 to 30,000. At a Reynolds number of 15,000, however, precursor formation was not observed throughout the 5,000 rotor revolutions of data acquired. No activity is observed beyond a periodic oscillation in the hotwire signal at approximately five times rotor frequency. It is believed this oscillation is associated with unsteadiness of the tip-leakage flow and was masked in the results at higher Reynolds number by frequent pre-cursor formation. In the previous section it was demonstrated that pre-cursor formation occurred at lower spans. Given the absence of pre-cursor formation at the blade tip for a Reynolds number of 15,000, it was of interest to assess whether this was also true at lower spans. Figure 4-4 shows the results of a spanwise traverse at a Reynolds number of 15,000. Pre-cursor formation can be observed at 50% span, such as at t = 3.1 and t = 4.0. The oscillation discussed prior is observed at 90% span but not at 80% span, providing evidence that it is due to unsteadiness in the tip-leakage flow. 67

68 U t Spanwise Position Rotor revolutions Figure 4-4: Spike pre-cursor formation at 50% span for 15,000 Reynolds number. Data not coherent in time Even at these low Reynolds numbers, airfoils of similar design and loading have demonstrated transition of the suction surface boundary layer [25]. Furthermore, the rotor blades used were built with a leading-edge radius to maximum thickness ratio of only Such sharp leading-edges have been shown to promote transition [26]. Given these two factors, it is likely that the suction surface boundary layer is undergoing transition. Counter to the observed trend, however, turbulent boundary layers generally grow less resistant to separation as the Reynolds number decreases [27]. Movement of the transition location is one possible mechanism for this behavior. The incidence at any span is set only by the cascade geometry and is not a function of free-stream velocity (and hence Reynolds number). For a constant incidence, the transition location moves further aft along the suction surface as the Reynolds number decreases [27]. Thus as the Reynolds number decreases, the transition location at all spans moves aft. For a given Reynolds number, however, the transition location moves forward as incidence increases [27]. As the mid-span operates at an incidence 15 68

69 greater than the blade tip (from the blade twist), at any given Reynolds number the mid-span transitions earlier than the blade tip. The absence of pre-cursor formation at the tip suggests there may be a threshold transition location, beyond which precursor formation is affected. It is hypothesized that at even lower Reynolds numbers, pre-cursor formation would be absent from the mid-span as well. The discussion above suggests that the role of transition and transition location are valuable topics for future work, especially as pre-cursor formation near the laminar regime has yet to be characterized. While the Reynolds numbers of future small-core compressors are estimated to be an order of magnitude larger than in the present study [28], these compressors will likely experience later transition as well, further motivating characterization of spike pre-cursor formation at low Reynolds number. 4.3 Visualization of Pre-cursor Formation The Reynolds number study indicated that pre-cursor formation occurs at 50% span for a Reynolds number of 15,000. Given the constraints of smoke flow visualization, this Reynolds number and location was chosen for visualization. A cascade computation was first performed to characterize the pre-cursor formation mechanism. Figure 4-5 shows contours of non-dimensional radial vorticity at 50% span from the cascade computation. In Figure 4-5a the leading-edge of blade 2 is separated and the vorticity from the suction side boundary layer can be seen along the leading-edge plane between blades 2 and 3. In Figure 4-5b, 1.2 blade passing periods later, the shed vorticity from the leading-edge separation has propagated to the adjacent passage, between blades 3 and 4. The cascade computation shows the same pre-cursor formation mechanism as in the compressor computations. It should be noted that while the cascade experiment showed periods of precursor formation interspersed with periods of little activity, pre-cursor formation was continuous in the computation. This is attributed to the lack of non-uniformities in the computation, e.g. each blade is geometrically the same, the tip-clearance is uniform, the inlet condition is uniform etc. In the cascade experiment there are 69

70 ω r (a) Leading-edge separation on blade 2, t = t τ = 0 ω r (b) Propagation of vorticity to adjacent passage, t = 1.2 Figure 4-5: Cascade computation show same pre-cursor formation mechanism at 50% span as in compressor computations inherent non-uniformities not present in the computation. Prior to examining the flow visualization results, it is valuable to consider what is to be expected to be seen. Vorticity convects with the fluid, i.e. vortex lines are fluid lines. Smoke particles also convect with the fluid into which they are released. As the smoke is injected directly into the suction surface boundary layer, it is expected that the smoke particles will mark the bound vorticity. For example, consider the leadingedge separation of blade 3 shown in Figure 4-5a. The suction surface boundary layer is separated and the bound vorticity can be seen within the passage, along the leadingedge plane. In the experiment, it is expected that the smoke trail would lift off from the suction surface and become parallel to the leading-edge plane. The smoke would then propagate along the leading-edge plane, as the shed vorticity does in Figure 4-5b. Figures 4-7 to 4-10 show a series of direct comparisons of the flow visualization and computation, each separated in time by 1.2 blade passing periods. At the top of each comparison is a contour plot of non-dimensional radial vorticity at 50% span 70

71 from the cascade computation. Inset in the top left is a velocity trace for the location marked on the contour plot with a cross. Directly below the contour plot is a frame showing the smoke flow visualization. To assist the reader, the suction surface at mid-span is outlined with red lines. Smoke is injected at the leading-edge of blade 2. The hotwire is located approximately 10% chord upstream of the leading-edge plane in the adjacent passage (between blades 3 and 4) and the velocity measured by the hotwire is inset in the top left of the frame. For reference, Figure 4-6 shows the flow visualization before pre-cursor formation, at a time of little activity. The suction surface boundary layer of blade 2 is attached. All the smoke convects down the passage between blades 2 and 3, with no smoke visible in the adjacent passage. Ṽ U t Rotor Revolutions Suction side boundary layer attached Smoke convects down passage Figure 4-6: Flow visualization prior to pre-cursor formation 71

72 Ṽ U t t Rotor Revolutions Ṽ U t Rotor Revolutions t Boundary layer beginning to separate Some smoke visible near leading-edge of blade Figure 4-7: Flow visualization at t 1 : partial leading-edge separation at blade 2 72

73 Ṽ U t Rotor Revolutions Ṽ U t Rotor Revolutions Smoke seen connecting leading-edges and is visible upstream of blade 3 leading-edge Boundary layer fully separated Figure 4-8: Flow visualization at t τ: blade 2 leading-edge fully separated 73

74 Ṽ U t Rotor Revolutions Ṽ U t Rotor Revolutions Boundary layer beginning to reattach Smoke convects from within passage to leading-edge of blade 3 due to backflow Smoke from blade 2 separation visible in adjacent passage Figure 4-9: Flow visualization at t τ: propagation of shed vorticity to adjacent passage 74

75 Ṽ U t Rotor Revolutions Ṽ U t Rotor Revolutions Boundary layer re-attached and smoke follows suction surface contour Some smoke visible adjacent blade 4, but most has dissipated Figure 4-10: Flow visualization at t τ: blade 2 boundary layer re-attached 75