# Journal of Turbomachinery

Published by American Society of Mechanical Engineers

Print ISSN: 0889-504X

Published by American Society of Mechanical Engineers

Print ISSN: 0889-504X

Publications

In this paper, the surge and rotating stall post instability behaviors of axial flow compressors are investigated from a bifurcation-theoretic perspective. A sequence of local and global bifurcations of the nonlinear system dynamics is uncovered. This includes a previously unknown global bifurcation of a pair of large amplitude periodic solutions. Resulting from this bifurcation are a stable oscillation ("surge") and an unstable oscillation ("antisurge"). The latter oscillation is found to have a deciding significance regarding the particular post-instability behavior experienced by the compressor. These results are used to reconstruct Greitzer's (1976) findings regarding the manner in which post-instability behavior depends on system parameters. Moreover, the results provide significant new insight deemed valuable in the prediction, analysis and control of stall instabilities in gas turbine jet engines.

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Measurements, made with laser Doppler velocimetry, about a double-circular-arc compressor blade in a cascade are presented for -1.5 and -8.5 degree incidence angles and a chord Reynolds number near 500,000. Comparisons between the results of the current study and those of an earlier work at a 5.0 degree indicence are made. It is found that, in spite of the relative sophistication of the measurement techniques, transition on the pressure surface at the -1.5 degree incidence is dominated by a separation 'bubble' too small to be detected by the laser Doppler velocimeter. The development of the boundary layers at -1.5 and 5.0 degrees are found to be similar. In contrast to the flow at these two incidence angles, the leading edge separation 'bubble' is on the pressure surface for the -8.5 degree incidence.

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A computational method for performing aeroelastic analysis using either a time-linearized or an unsteady time-accurate solver for the compressible Reynolds averaged Navier-Stokes (RANS) equations is described. The time-linearized solver employs the assumption of small time-harmonic perturbations and is implemented via finite differences of the nonlinear flux routines of the time-accurate solver. The resulting linear system is solved using a parallelized Generalized Minimal Residual
(GMRES) method with block-local preconditioning. The time accurate solver uses a dual time stepping algorithm for the solution of the unsteady RANS equations on a periodically moving computational grid. For either solver, and both flutter and forced response problems, a mapping algorithm has been developed to map structural eigenmodes, obtained from finite element structural analysis, from the surface mesh of the finite element structural solver to the surface mesh of the finite volume flow solver. Using the surface displacement data an elliptic mesh deformation algorithm, based on linear elasticity theory, is then used to compute the grid deformation vector field. The developed methods are validated first using standard configuration ten. Finally, for an ultra high bypass ratio fan the results of the timelinearized and the unsteady module are compared. The gain in prediction time using the linearized methods is highlighted.

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A centrifugal impeller which was initially designed for a pressure ratio of approximately 5.5 and a mass flow rate of 0.959 kg/sec was tested with a vaneless diffuser for a range of design point impeller area ratios from 2.322 to 2.945. The impeller area ratio was changed by successively cutting back the impeller exit axial width from an initial value of 7.57 mm to a final value of 5.97 mm. In all, four separate area ratios were tested. For each area ratio a series of impeller exit axial clearances was also tested. Test results are based on impeller exit surveys of total pressure, total temperature, and flow angle at a radius 1.115 times the impeller exit radius.
Results of the tests at design speed, peak efficiency, and an exit tip clearance of 8 percent of exit blade height show that the impeller equivalent pressure recovery coefficient peaked at a design point area ratio of approximately 2.748 while the impeller aerodynamic efficiency peaked at a lower value of area ratio of approximately 2.55. The variation of impeller efficiency with clearance showed expected trends with a loss of approximately 0.4 points in impeller efficiency for each percent increase in exit axial tip clearance for all impellers tested. The data also indicated that the impeller would probably separate at design area ratios greater than 2.748. An analysis was performed with a quasi-three-dimensional inviscid computer code which confirmed that a minimum velocity ratio was attained near this area ratio thus indicating separation. This data can be used to verify impeller flow models which attempt to account for very high diffusion and possible separation.

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This paper presents the numerical results of a code for computing the unsteady transonic viscous flow in a two-dimensional cascade of harmonically oscillating blades. The flow field is calculated by a Navier-Stokes code, the basic features of which are the use of an upwind flux vector splitting scheme for the convective terms (Advection Upstream Splitting Method), an implicit time integration and the implementation of a mixing length turbulence model.
For the present investigations two experimentally investigated test cases have been selected in which the blades had performed tuned harmonic bending vibrations. The results obtained by the Navier-Stokes code are compared with experimental data, as well as with the results of an Euler method.
The first test case, which is a steam turbine cascade with entirely subsonic flow at nominal operating conditions, is the fourth standard configuration of the “Workshop on Aeroelasticity in Turbomachines”. Here the application of an Euler method already leads to acceptable results for unsteady pressure and damping coefficients and hence this cascade is very appropriate for a first validation of any Navier-Stokes code. The second test case is a highly-loaded gas turbine cascade operating in transonic flow at design and off-design conditions. This case is characterized by a normal shock appearing on the rear part of the blades’s suction surface, and is very sensitive to small changes in flow conditions. When comparing experimental and Euler results, differences are observed in the steady and unsteady pressure coefficients. The computation of this test case with the Navier-Stokes method improves to some extent the agreement between the experiment and numerical simulation.

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The tip clearance flows of transonic compressor rotors are important because they have a significant impact on rotor and stage performance. While numerical simulations of these flows are quite sophisticated. they are seldom verified through rigorous comparisons of numerical and measured data because these kinds of measurements are rare in the detail necessary to be useful in high-speed machines. In this paper we compare measured tip clearance flow details (e.g. trajectory and radial extent) with corresponding data obtained from a numerical simulation. Recommendations for achieving accurate numerical simulation of tip clearance flows are presented based on this comparison. Laser Doppler Velocimeter (LDV) measurements acquired in a transonic compressor rotor, NASA Rotor 35, are used. The tip clearance flow field of this transonic rotor was simulated using a Navier-Stokes turbomachinery solver that incorporates an advanced k-epsilon turbulence model derived for flows that are not in local equilibrium. Comparison between measured and simulated results indicates that simulation accuracy is primarily dependent upon the ability of the numerical code to resolve important details of a wall-bounded shear layer formed by the relative motion between the over-tip leakage flow and the shroud wall. A simple method is presented for determining the strength of this shear layer.

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The aerodynamics of a biconvex airfoil cascade oscillating in torsion is investigated using the unsteady aerodynamic influence coefficient technique. For subsonic flow and reduced frequencies as large as 0.9, airfoil surface unsteady pressures resulting from oscillation of one of the airfoils are measured using flush-mounted high-frequency-response pressure transducers. The influence coefficient data are examined in detail and then used to predict the unsteady aerodynamics of a cascade oscillating at various interblade phase angles. These results are correlated with experimental data obtained in the traveling-wave mode of oscillation and linearized analysis predictions. It is found that the unsteady pressure disturbances created by an oscillating airfoil excite wind tunnel acoustic modes which have detrimental effects on the experimental data. Acoustic treatment is proposed to rectify this problem.

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A radial compressor stage has been investigated experimentally for
aerodynamic stage optimization. The rotor consists of a profiled axial
inducer and a conventionally designed radial impeller. Inducer and
impeller can be locked at different circumferential positions relative
to each other thus, forming a tandem wheel with adjustable geometry.
Conventional and laser-2-focus system measurements for the tandem-rotor
and the stage were performed at different operating points to study the
influence of the circumferential clearance geometry between inducer and
impeller with respect to compressor characteristics and performance.
Furthermore, 3D Navier-Stokes calculations are being developed at design
point condition to analyze the flow field. Small influence of the
inducer adjustment on the rotor characteristics is observed. The maximum
rotor efficiency of 93.5 percent varies in a range of less than 1
percent depending on the different inducer positions.

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A high performance compressor airfoil at a low Reynolds number condition (Re = 1.3×105 ) has been developed using evolutionary algorithms in order to improve the performance of the outlet guide vane (OGV), used in a single low pressure turbine (LPT) of a small turbofan engine for business jet aircrafts. Two different numerical optimization methods, the Evolution Strategy (ES) and the Multi-Objective Genetic Algorithm (MOGA), were adopted for the design process to minimize the total pressure loss and the deviation angle at the design point at low Reynolds number condition. Especially, with respect to the MOGA, robustness against changes of the incidence angle is considered. The optimization process includes the representation of the blade geometry, the generation of a numerical grid and a blade-to-blade analysis using a quasi-three-dimensional (Q3D) Navier-Stokes solver with a k-ω turbulence model including a newly implemented transition model to evaluate the performance. Overall aerodynamic performance and boundary layer properties for the two optimized blades are discussed numerically. The superior performance of the two optimized airfoils is demonstrated by a comparison with conventional controlled diffusion airfoils (CDA). The advantage in performance has been confirmed by detailed experimental investigations, which are presented in Part 2 of this paper.

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High performance compressor airfoils at a low Reynolds number condition at (Re = 1.3 × 10 5) have been developed using evolutionary algorithms in order to improve the performance of the outlet guide vane (OGV), used in a single low pressure turbine (LPT) of a small turbofan engine for business jet aircrafts. Two different numerical optimization methods, the evolution strategy (ES) and the multi-objective genetic algorithm (MOGA), were adopted for the design process to minimize the total pressure loss and the deviation angle at the design point at low Reynolds number condition. Especially, with respect to the MOGA, robustness against changes of the incidence angle is considered. The optimization process includes the representation of the blade geometry, the generation of a numerical grid and a blade-to-blade analysis using a quasi-three-dimensional Navier-Stokes solver with a κ-ω turbulence model including a newly implemented transition model to evaluate the performance. Overall aerodynamic performance and boundary layer properties for the two optimized blades are discussed numerically: The superior perfbrmance of the two optimized airfoils is demonstrated by a comparison with conventional controlled diffusion airfoils (CDA). The advantage in performance has been confirmed by detailed experimental investigations, which are presented in Part II of this paper.

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Modern methods for axial compressor design are capable of shaping the blade surfaces in a three dimensional way. Linking these methods with automated optimization techniques provides a major benefit to the design process. The application of non-axisymmetric contoured endwalls is considered to be very successful in turbine rotors and vanes. Concerning axial compressors non-axisymmetric endwalls are still a field of research. This two-part paper presents the recent development of a novel endwall design. An aerodynamic separator, generated by a non-axisymmetric endwall groove, interacts with the passage vortex. This major impact on the secondary flow results in a significant loss reduction because of load redistribution, reduction of recirculation areas and suppressed corner separation. The first paper deals with the development of the initial endwall design using a linear compressor cascade application. A brief introduction of the design methods is provided, including the automated optimization, the 3D process chain with a focus on the endwall contouring tool. Hereafter the resulting flow phenomena and physics due to the modified endwall surface are described and analyzed in detail. Additionally, the endwall design principal is transferred to an axial compressor stage. The endwall groove is applied to the hub and casing endwalls of the stator and the initial numerical investigation is presented. For highly loaded operating points the flow behaviour at the hub region can be improved in accord with the cascade results. Obviously, the casing region is dominated by the incoming tip vortex generated by the rotor and still remains an area for further investigations concerning non-axisymmetric endwall contouring.

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Part 1 of this paper describes the design and optimization of two high turning subsonic compressor cascades operating as an outlet guide vane (OGV) behind a single stage low pressure turbine at low Reynolds number condition (Re = 1.3×105 ). In the numerical optimization algorithm, the design point and off-design performance has been considered in an objective function to achieve a wide low loss incidence range. The objective of the present paper is to examine some of the characteristics describing the new airfoils as well as to prove the reliability of the design process and the applied flow solver. Some aerodynamic characteristics for the two new airfoils and a conventional controlled diffusion airfoil (CDA), have been extensively investigated in the cascade wind tunnel of DLR Cologne. For an inlet Mach number of 0.6 the effect of Reynolds number and incidence angle on each airfoil performance is discussed, based on experimental and numerical results. For an interpretation of the airfoil boundary layer behavior, results of some boundary layer calculations are compared to oil flow visualization pictures. The design goal of an increased low loss incidence range at low Reynolds number condition could be confirmed without having a negative effect on the high Reynolds number region.

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The development of high performance turbine airfoils has been investigated under the condition of a supersonic exit Mach number. In order to obtain a new aerodynamic design concept for a high loaded turbine rotor blade, we employed an evolutionary algorithm for numerical optimization. The target of the optimization method, which is called evolution strategy (ES), was the minimization of the total pressure loss and the deviation angle. The optimization process includes the representation of the airfoil geometry, the generation of the grid for a blade-to-blade CFD analysis, and a 2D Navier-Stokes solver with a low-Re k-ƒÕ turbulence model in order to evaluate the performance. Some interesting aspects, for example, a double shock system and an early transition observed in the optimized airfoil are discussed. The increased performance of the optimized blade has been confirmed by detailed experimental investigation, using conventional probes, hot films and L2F system.

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Modern methods for axial compressor design are capable of shaping the blade surfaces in a three dimensional way. Linking these methods with automated optimization techniques provides a major benefit to the design process. The application of non-axisymmetric contoured endwalls is considered to be very successful in turbine rotors and vanes. Concerning axial compressors non-axisymmetric endwalls are still a field of research. This two-part paper presents the recent development of a novel endwall design. A vortex created by a nonaxisymmetric endwall groove acts as an aerodynamic separator, preventing the passage vortex from interacting with the suction side boundary layer. This major impact on the secondary flow results in a significant loss reduction by means of load redistribution, reduction of recirculation areas and suppressed corner separation. Part I of this paper deals with the endwall design and its compressor application. The resulting flow phenomena and physics are described and analysed in detail. The second paper presents the detailed experimental and numerical investigation of the developed endwall groove. The measurements carried out at the transonic cascade wind tunnel of DLR in Cologne, demonstrated a considerable influence on the cascade performance. A loss reduction and redistribution of the cascade loading were achieved at the aerodynamic design point as well as near the stall condition of the cascade. This behaviour is well predicted by the numerical simulation. The combined analysis of experimental and numerical flow patterns allows a detailed interpretation and description of the resulting flow phenomena. In this context high fidelity 3D-RANS flow simulations are required to analyse the complex blade and endwall boundary layer interaction.

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Increased emphasis on sustained supersonic or hypersonic cruise has revived interest in the supersonic throughflow fan as a possible component in advanced propulsion systems. Use of a fan that can operate with a supersonic inlet axial Mach number is attractive from the standpoint of reducing the inlet losses incurred in diffusing the flow from a supersonic flight Mach number to a subsonic one at the fan face. The design of the experiment using advanced computational codes to calculate the components required is described. The rotor was designed using existing turbomachinery design and analysis codes modified to handle fully supersonic axial flow through the rotor. A two-dimensional axisymmetric throughflow design code plus a blade element code were used to generate fan rotor velocity diagrams and blade shapes. A quasi-three-dimensional, thin shear layer Navier-Stokes code was used to assess the performance of the fan rotor blade shapes. The final design was stacked and checked for three-dimensional effects using a three-dimensional Euler code interactively coupled with a two-dimensional boundary layer code. The nozzle design in the expansion region was analyzed with a three-dimensional parabolized viscous code which corroborated the results from the Euler code. A translating supersonic diffuser was designed using these same codes.

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The development of high performance turbine airfoils has been investigated under the condition of a supersonic exit Mach number. In order to obtain a new aerodynamic design concept for a high loaded turbine rotor blade, we employed an evolutionary algorithm for numerical optimization. The target of the optimization method, which is called evolution strategy (ES), was the minimization of the total pressure loss and the deviation angle. The optimization process includes the representation of the airfoil geometry, the generation of the grid for a blade-to-blade CFD analysis, and a 2D Navier-Stokes solver with a low-Re k-eps turbulence model in order to evaluate the performance. Some interesting aspects, for example, a double shock system and an early transition observed in the optimized airfoil are discussed. The increased performance of the optimized blade has been confirmed by detailed experimental investigation, using conventional probes, hot films and L2F system.

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The aerodynamic performance of a scale model, counter-rotating unducted fan has been determined and the results are discussed. Experimental investigations were conducted using the scale model propulsor simulator and uniquely shaped fan blades. The blades, designed for a high disk loading at Mach 0.72 at 35,000 feet altitude maximum climb condition are aft-mounted on the simulator in a pusher configuration. Data are compared with analytical predictions at the design point and show good agreement.

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A mathematical model developed to predict the enhanced coupled bending-torsion unstalled supersonic flutter stability due to alternate circumferential spacing aerodynamic detuning of a turbomachine rotor. The translational and torsional unsteady aerodynamic coefficients are developed in terms of influence coefficients, with the coupled bending-torsion stability analysis developed by considering the coupled equations of this aerodynamic detuning on coupled bending-torsion unstalled supersonic flutter as well as the verification of the modeling are then demonstrated by considering an unstable 12 bladed rotor, with Verdon's uniformly spaced Cascade B flow geometry as a baseline. However, with the elastic axis and center of gravity at 60 percent of the chord, this type of aerodynamic detuning has a minimal effect on stability. For both uniform and nonuniform circumferentially space rotors, a single degree of freedom torsion mode analysis was shown to be appropriate for values of the bending-torsion natural frequency ratio lower than 0.6 and higher 1.2. When the elastic axis and center of gravity are not coincident, the effect of detuning on cascade stability was found to be very sensitive to the location of the center of gravity with respect to the elastic axis. In addition, it was determined that when the center of gravity was forward of an elastic axis located at midchord, a single degree of freedom torsion model did not accurately predict cascade stability.

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An aeroelastic analysis is presented which accounts for the effect of steady aerodynamic loading on the aeroelastic stability of a cascade of compressor blades. The aeroelastic model is a two degree of freedom model having bending and torsional displacements. A linearized unsteady potential flow theory is used to determine the unsteady aerodynamic response coefficients for the aeroelastic analysis. The steady aerodynamic loading was caused by the addition of airfoil thickness and camber and steady flow incidence. The importance of steady loading on the airfoil unsteady pressure distribution is demonstrated. Additionally, the effect of steady loading on the tuned flutter behavior and flutter boundaries indicates that neglecting either airfoil thickness, camber or incidence could result in nonconservative estimates of flutter behavior.

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As a part of an innovative aerodynamic design concept for a single stage low pressure turbine, a high turning outlet guide vane is required to remove the swirl from the hot gas. The airfoil of the vane is a highly loaded compressor airfoil that has to operate at very low Reynolds numbers (Re ∼ 120,000). Recently published numerical design studies and experimental analysis on alternatively designed airfoils showed that blade profiles with an extreme front loaded pressure distribution are advantageous for low Reynolds number conditions. The advantage even holds true for an increased inlet Mach number at which the peak Mach number on the airfoils reaches and exceeds the critical conditions (Mss > 1.0). This paper discusses the effect of the inlet Mach number and Reynolds number on the cascade performance for both a controlled diffusion airfoil (CDA) (called baseline) and a numerically optimized front loaded airfoil. The results show that it is advantageous to design the profile with a fairly steep pressure gradient immediately at the front part in order to promote early transition or to prevent too large laminar — even shock induced — separations with the risk of a bubble burst. Profile Mach number distributions and wake traverse data are presented for design and off-design conditions. The discussion of Mach number distributions and boundary layer behavior is supported by numerical results obtained from the blade-to-blade flow solver MISES.

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A computational method, based on a theory for turbomachinery blading design in three-dimensional inviscid flow, is applied to a parametric design study of a radial inflow turbine wheel. As the method requires the specification of swirl distribution, a technique for its smooth generation within the blade region is proposed. Excellent agreements have been obtained between the computed results from this design method and those from direct Euler computations, demonstrating the correspondence and consistency between the two. The computed results indicate the sensitivity of the pressure distribution to a lean in the stacking axis and a minor alteration in the hub/shroud profiles. Analysis based on Navier-Stokes solver shows no breakdown of flow within the designed blade passage and agreement with that from design calculation; thus the flow in the designed turbine rotor closely approximates that of an inviscid one. These calculations illustrate the use of a design method coupled to an analysis tool for establishing guidelines and criteria for designing turbomachinery blading.

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Inlet guide vanes (IGV) of high-temperature gas turbines require an effective trailing edge cooling. But this cooling significantly influences the aerodynamic performance caused by the unavoidable thickening of the trailing edge and the interference of the cooling flow with the main flow. As part of a comprehensive research program, an inlet guide vane was designed and manufactured with two different trailing edge shapes. The results from the cascade tests show that the flow behavior upstream of the trailing edge remains unchanged. The homogeneous values downstream show higher turning and higher losses for the cut-back blade, especially in the supersonic range. Additional tests were conducted with carbon dioxide ejection, in order to analyze the mixing process downstream of the cascade.

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A parametric study which investigates the influence of viscous effects on the damping behavior of vibrating compressor cascades is presented here. To demonstrate the dependence of unsteady aerodynamic forces on the flow viscosity, a computational study was performed for a transonic compressor cascade of which the blades underwent tuned pitching oscillations while the flow conditions extended from fully subsonic to highly transonic flow. Additionally, the reduced frequency and Reynolds number were varied. In order to check the linear behavior of the aerodynamic forces, all calculations were carried out for three different oscillation amplitudes. Comparisons with inviscid Euler results helped identify the influence of viscous effects. The computations were performed with a Navier-Stokes code, the basic features of which are the use of an AUSM upwind scheme, an implicit time integration, and the implementation of the Baldwin-Lomax turbulence model. In order to demonstrate the possibility of this code to correctly predict the unsteady behavior of strong shock-boundary layer interactions, the experiment of Yamamoto and Tanida on a self-induced shock oscillation due to shock-boundary layer interaction was calculated. A significant improvement in the prediction of the shock amplitude was achieved by a slight modification of the Baldwin Lomax turbulence model. An important result of the presented compressor cascade investigations is that viscous effects may cause a significant change in the aerodynamic damping. This behavior is demonstrated by two cases in which an Euler calculation predicts a damped oscillation whereas a Navier-Stokes computation leads to an excited vibration. It was found that the reason for these contrary results are shock-boundary-layer interactions which dramatically change the aerodynamic damping.

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Thermodynamic and aerodynamic measurements were carried out in a linear turbine ascade ith transonic flow field. Heat transfer and adiabatic film-cooling effectiveness resulting from the interaction of the flow field and the ejected coolant at the endwall were measured and will be discussed in two parts. The investigations were performed in the Windtunnel for Straight Cascades (EGG) at DLR, Goettingen. The film-cooled NGV endwall was operated at representative nondimensional engine conditions regarding Mach and Reynolds number (Ma_2=1.0, Re_2=850,000). Part I of the investigations discusses the aerodynamic measurements. Detailed aerodynamic measurements were carried out in the vicinity of a turbine stator endwall using conventional pressure measurements and a Laser-2-Focus (L2F) device. The L2F served as a velocimeter measuring 2D-velocity vectors and turbulence quantities and as a tool to determine the concentration of coolant ejected through a slot and through holes at the endwall. Pressure distribution measurements provided information on the endwall pressure field and its variation with coolant flow rate. Pressure probe measurements delivered cascade performance data. Oil flow visualization and Laser velocimetry gave a picture of the near endwall flow field and its interference with the coolant. A strikingly strong interaction of coolant air and secondary flow field could be identified. The measurement of coolant concentration downstream of the ejection locations provided a detailed picture of the coolant flow convection and its mixing with the main flow. The relative coolant concentration in the flow field is directly comparable to the adiabatic film-cooling effectiveness measured by thermal methods at the wall.

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As part of a European research project, the aerodynamic and thermodynamic performance of a high pressure turbine cascade with different trailing edge cooling configurations was investigated in the wind tunnel for linear cascades at DLR in Göttingen. A transonic rotor profile with a relative thick trailing edge was chosen for the experiments. Three trailing edge cooling configurations were applied, first central trailing edge ejection, second a trailing edge shape with a pressure side cut-back and slot equipped with a diffuser rib array, and third pressure side film cooling through a row of cylindrical holes. For comparison aerodynamic investigations on a reference cascade with solid blades (no cooling holes
or slots) were performed. The experiments covered the subsonic, transonic and supersonic exit Mach number range of the cascade while varying cooling mass flow ratios up to 2 %.
This paper analyzes the effect of coolant ejection on the airfoil losses. Emphasis was given on separating the different loss contributions due to shocks, pressure and suction side boundary layer, trailing edge and mixing of the coolant flow. Employed measurement techniques are schlieren
visualization, blade surface pressure measurements and traverses by pneumatic probes in the cascade exit flow field and around the trailing edge.
The results show that central trailing edge ejection ignificantly reduces the mixing losses and therefore decreases the overall loss. Higher loss levels are obtained when applying the configurations with pressure side blowing. In particular the cut-back geometry reveals strong mixing losses due to the low momentum coolant fluid which is decelerated by the diffuser rib array inside the slot. The influence of coolant flow rate on the trailing edge loss is tremendous, too. Shock and boundary layer losses are major contributions to the overall loss but are less affected by the coolant. Finally a parameter variation changing the temperature ratio of coolant to main flow was performed, resulting in increasing losses with decreasing coolant temperature.

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A method is presented for the quick and accurate prediction of the stability of aerodynamically excited turbomachinery using real eigenvalue/eigenvector data obtained from a rotordynamics model. An expression is presented which uses the modal data and the transmitted torque to provide a numerical value of the relative stability of the system. This approach provides a powerful design tool to quickly ascertain the effects of squeeze-film damper bearings, bearing location, and support changes on system stability.

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Fundamental experiments are performed in the NASA Lewis Research Center Transonic Oscillating Cascade Facility to investigate and quantify the aerodynamics of a cascade of bioconvex airfoils executing torsion mode oscillations at realistic reduced frequency values. Both steady and unsteady airfoil surface pressures are measured at two inlet Mach numbers, 0.65 and 0.80, and two incidence angles, 0 and 7 deg, with the harmonic torsional airfoil cascade oscillations at realistic high reduced frequency and unsteady data obtained at several interblade phase angle values. The time-variant pressures are analyzed by means of discrete Fourier transform techniques, with these unique data compared with predictions from a linearized unsteady cascade model. The experimental results indicate that the interblade phase angle has a major effect on the chordwise distributions of the airfoil surface unsteady pressure, with the effect of reduced frequency, incidence angle, and Mach numbers somewhat less significant.

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Splitter plates usable as aeroelastic detuner devices for supersonic flutter in turbomachinery, through the introduction of both aerodynamic and structural detuning to enhance aeroelastic stability, are presently considered by a mathematical model. The model demonstrates that aerodynamic detuning is due to both the alternate circumferential spacing of the full chord airfoils and the variable circumferentially spaced splitters between each pair of full chord airfoils. Structural detuning is based on the lower natural frequencies of the splitters, by comparison with the full chord airfoils. The model's application to two unstable rotors demonstrates enhanced torsion mode flutter stability through the incorporation of splitters, where the critical parameters are chord length and the circumferential and axial locations of the splitters.

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A numerical simulation of a transonic mixed flow turbine stage has been carried out using an average passage Navier-Stokes analysis. The mixed flow turbine stage considered here consists of a transonic nozzle vane and a highly loaded rotor. The simulation was run at the design pressure ratio and is assessed by comparing results with those of an established throughflow design system. The three-dimensional aerodynamic loads are studied as well as the development and migration of secondary flows and their contribution to the total pressure loss. The numerical results indicate that strong passage vortices develop in the nozzle vane, mix out quickly, and have little impact on the rotor flow. The rotor is highly loaded near the leading edge. Within the rotor passage, strong spanwise flows and other secondary flows exist along with the tip leakage vortex. The rotor exit loss distribution is similar in character to that found in radial inflow turbines. The secondary flows and non-uniform work extraction also tend to significantly redistribute a non-uniform inlet total temperature profile by the exit of the stage.

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An experimental study was made to obtain heat transfer and air temperature data for a simple three-leg serpentine test section that simulates a turbine blade internal cooling passage with trip strips and bleed holes. The objectives were to investigate the interaction of ribs and various bleed conditions on internal cooling and to gain a better understanding of bulk air temperature in an internal passage. Steady-state heat transfer measurements were obtained using a transient technique with thermochromic liquid crystals. Trip strips were attached to one wall of the test section and were located either between or near the bleed holes. The bleed holes, used for film cooling, were metered to simulate the effect of external pressure on the turbine blade. Heat transfer enhancement was found to be greater for ribs near bleed holes compared to ribs between holes, and both configurations were affected slightly by bleed rates upstream. Air temperature measurements were taken at discrete locations along one leg of the model. Average bulk air temperatures were found to remain fairly constant along one leg of the model.

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Turbofan noise generation and suppression in aircraft engines are reviewed. The chain of physical processes which connect unsteady flow interactions with fan blades to far field noise is addressed. Mechanism identification and description, duct propagation, radiation, and acoustic suppression are discussed. The experimental techniques of fan inflow static tests are discussed. Rotor blade surface pressure and wake velocity measurements aid in the determination of the types and strengths of the generation mechanisms. Approaches to predicting or measuring acoustic mode content, optimizing treatment impedance to maximize attenuation, translating impedance into porous wall structure, and interpreting far field directivity patterns are illustrated by comparisons of analytical and experimental results. The interdependence of source and acoustic treatment design to minimize far field noise is emphasized. Areas requiring further research are discussed, and the relevance of aircraft turbofan results to quieting other turbomachinery installation is addressed.

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An accurate numerical analysis of the flows associated with rotor-stator configurations in turbomachinery can be extremely helpful in optimizing the performance of turbomachinery. In this study the unsteady, thin-layer, Navier-Stokes equations in two spatial dimensions are solved on a system of patched and overlaid grids for a rotor-stator configuration from an axial turbine. The governing equations are solved using a finite-difference, upwind algorithm that is set in an iterative, implicit framework. Results in the form of pressure contours, time-averaged pressures, unsteady pressure amplitudes and phase are presented. The numerical results are compared with experimental data and the agreement is found to be good. The results are also compared with those of an earlier study which used only one rotor and one stator. The current study uses multiple rotors and stators and a pitch ratio that is much closer to the experimental ratio. Consequently the results of this study are found to be closer to the experimental data.

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Similar to jet engine development, modern design methods are used today to improve the performance of industrial compressors. In order to verify the loading limits, a cascade profile representative for the first rotor hub section of an industrial compressor has been designed by optimizing the suction surface velocity distribution using a direct boundary layer calculation method. The experimental results confirmed the design intent and resulted in a low loss coefficient of 1.8% at design condition and an incidence range of nearly 12 degrees (4% loss level) at an inlet Mach number of 0.62. (from authors' abstract)

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Tests of transonic compressor cascades require special measuring techniques to determine the inlet flow angle around sonic inlet flow conditions. One of the main requirements for these methods is the ability to adjust the inlet flow angle during the test to a prescribed value. A method has been successfully applied that relies on theoretically determined suction surface velocities. The described method was applied in testing cascades at inlet Mach numbers between M1 = 0.75-1.18. The test results confirmed the practicability of this method.

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The naphthalene sublimation technique is used to investigate the heat transfer characteristics of turbulent air flow in a two-pass channel. A test section that resembles the internal cooling passages of gas turbine airfoils is employed. The local Sherwood numbers on the ribbed walls were found to be 1.5-6.5 times those for a fully developed flow in a smooth square duct. Depending on the rib angle-of-attack and the Reynolds number, the average ribbed-wall Sherwood numbers were 2.5-3.5 times higher than the fully developed values.

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Detailed measurement of the flow field in the tip region of a compressor rotor was carried out using LDV. The axial and tangential components of relative velocities were measured upstream, inside the passage, and at the exit of the rotor, up to about 20 percent of the blade span from the blade tip. The annulus-wall boundary layer is well behaved at the leading edge and far downstream of the rotor. But inside the passage, complex interactions between the leakage flow and the annulus-wall boundary layer result in unconventional profiles with wide deviations from models employed for analyses.

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A frequency domain linearized unsteady aerodynamic analysis is presented for three-dimensional unsteady vortical flows around a cascade of loaded airfoils. The analysis fully accounts for the distortion of the impinging vortical disturbances by the mean flow. The entire unsteady flow field is calculated in response to upstream three-dimensional harmonic disturbances. Numerical results are presented for two standard cascade configurations representing turbine and compressor bladings for a reduced frequency range from 0.1 to 5. Results show that the upstream gust conditions and blade sweep strongly affect the unsteady blade response.

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An experimental investigation was conducted to characterize a symmetrical horseshoe vortex system in front of and a around a single large-diameter right cylinder centered between the sidewalls of a wind tunnel. Surface flow visualization anad surface static pressure measurements as well as extensive mean velocity and pressure measurements in and around the vortex system were acquired. The results lend new insight into the formation and development of the vortex system. Contrary to what has been assumed previously, a strong vortex was not identified in the streamwise plane of symmetry, but started a significant angular distance away from it. Rather than the multiple vortex systems reported by others, only a single primary vortex and saddle point were found. The scale of the separation process at the saddle point was much smaller than the scale of the approaching bundary layer thickness. Results of the present study not only shed light on such phenomena as the nonsymmetrical endwall flow in axial turbomachinery but can also be used as a test case for three-dimensional computational fluid mechanics computer codes.

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Experimental results from the present study show substantial, independent Mach number effects (as the Reynolds number is held constant) for an array of impinging jets. The present discharge coefficients, local and spatially averaged Nusselt numbers, and local and spatially averaged recovery factors are unique because (i) these data are obtained at constant Reynolds number as the Mach number is varied, and at constant Mach number as the Reynolds number is varied, and (ii) data are given for jet impingement Mach numbers up to 0.74, and for Reynolds numbers up to 60,000. As such, results are given for experimental conditions not previously examined, which are outside the range of applicability of existing correlations.

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A transonic compressor stage has been designed for the Naval Postgraduate School Turbopropulsion Laboratory. The design relied heavily on CFD techniques while minimizing conventional empirical design methods. The low aspect ratio (1.2) rotor has been designed for a specific head ratio of .25 and a tip relative inlet Mach number of 1.3. Overall stage pressure ratio is 1.56. The rotor was designed using an Euler code augmented by a distributed body force model to account for viscous effects. This provided a relatively quick-running design tool, and was used for both rotor and stator calculations. The initial stator sections were sized using a compressible, cascade panel code. In addition to being used as a case study for teaching purposes, the compressor stage will be used as a research stage. Detailed measurements, including non-intrusive LDV, will be compared with the design computations, and with the results of other CFD codes, as a means of assessing and improving the computational codes as design tools.

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The experimental investigation of an aspirated fan stage designed to achieve a pressure ratio of 3.4:1 at 1500 ft/sec is presented in this paper. The low-energy viscous flow is aspirated from diffusion-limiting locations on the blades and flowpath surfaces of the stage, enabling a very high pressure ratio to be achieved in a single stage. The fan stage performance was mapped at various operating speeds from choke to stall in a compressor facility at fully simulated engine conditions. The experimentally determined stage performance, in terms of pressure ratio and corresponding inlet mass flow rate, was found to be in good agreement with the three-dimensional viscous computational prediction, and in turn close to the design intent. Stage pressure ratios exceeding 3:1 were achieved at design speed, with an aspiration flow fraction of 3.5 percent of the stage inlet mass flow. The experimental performance of the stage at various operating conditions, including detailed flowfield measurements, are presented and discussed in the context of the computational analyses. The sensitivity of the stage performance and operability to reduced aspiration flow rates at design and off design conditions are also discussed.

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This paper describes the development of a new analysis to predict the onset of flow instability for an axial compressor operating in a circumferentialy distorted inlet flow. A relatively simple model is used to examine the influence of various distortions in setting this instability point. It is found that the model reproduces known experimental trends for the loss of stability margin with increasing distortion amplitude and with changes in reduced frequency. In particular, there is a recognizable 'critical sector angle' which characterizes loss of stability margin. To the authors' knowledge, this is the first time the effects described herein have been theoretically demonstrated as the direct result of a fluid dynamic stability.

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Fluid dynamics of turbomachines are complicated due to aerodynamic interactions between rotors and stators. It is necessary to understand the aerodynamics associated with these interactions in order to design turbomachines that are both light and compact as well as reliable and efficient. The current study uses an unsteady, thin-layer Navier-Stokes zonal approach to investigate the unsteady aerodynamics of a multi-stage compressor. Relative motion between rotors and stators is made possible by use of systems of patched and overlaid grids. Results have been computed for a 2 1/2-stage compressor configuration. The numerical data compares well with experimental data for surface pressures and wake data. In addition, the effect of grid refinement on the solution is studied.

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Heat transfer measurements have been made in the stagnation region of a flat plate with a circular leading edge. Electrically heated aluminum strips placed symmetrically about the leading edge stagnation region were used to measure spanwise averaged heat transfer coefficients. The maximum Reynolds number obtained, based on leading edge diameter, was about 100,000. The model was immersed in the flow field downstream of an approximately half scale model of a can-type combustor from a low NOx, ground based power-generating turbine. The tests were conducted with room temperature air; no fuel was added. Room air flowed into the combustor through six vane type fuel/air swirlers. The combustor can contained no dilution holes.
The fuel/air swirlers all swirled the incoming airflow in a counter clockwise direction (facing downstream). A 5-hole probe flow field survey in the plane of the model stagnation point showed the flow was one big vortex with flow angles up to 36° at the outer edges of the rectangular test section. Hot wire measurements showed test section flow had very high levels of turbulence, around 28.5%, and had a relatively large axial-length scale-to-leading edge diameter ratio of 0.5. X-wire measurements showed the turbulence to be nearly isotropic. Stagnation heat transfer augmentation over laminar levels was around 77% and was about 14% higher than predicted by a previously developed correlation for isotropic grid generated turbulence.

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A numerical automation procedure has been developed to be used in conjunction with an inverse hodograph method for the design of controlled diffusion blades. With this procedure a cascade of airfoils with a prescribed solidity, inlet Mach number, inlet air flow angle, and air flow turning can be produced automatically. The trailing edge thickness of the airfoil, an important quantity in inverse methods, is also prescribed. The automation procedure consists of a multidimensional Newton iteration in which the objective design conditions are achieved by acting on the hodograph input parameters of the underlying inverse code. The method, although more general in scope, is applied in this paper to the design of axial flow compressor blade sections, and a wide range of examples is presented.

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Time-averaged Stanton number and surface-pressure distributions are reported for the first-stage vane row and the first-stage blade row of the Rocketdyne Space Shuttle Main Engine two-stage fuel-side turbine. These measurements were made at 10 percent, 50 percent, and 90 percent span on both the pressure and suction surfaces of the component. Stanton-number distributions are also reported for the second-stage vane at 50 percent span. A shock tube is used as a short-duration source of heated and pressurized air to which the turbine is subjected. Platinum thin-film gages are used to obtain the heat-flux measurements and miniature silicone-diaphragm pressure transducers are used to obtain the surface pressure measurements. The first-stage vane Stanton number distributions are compared with predictions obtained using a quasi-3D Navier-Stokes solution and a version of STAN5. This same N-S technique was also used to obtain predictions for the first blade and the second vane.

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Flow-field measurements of unsteady turbulent flow downstream of a rotating spoked-wheel wake generator were performed in a short-duration light-piston tunnel, and the instantaneous-velocity data were phase averaged based on a signal synchronized with the bar-passing frequency. Mean axial velocities were found to agree well with those obtained from measurements behind a stationary cylinder and to be independent of both Reynolds and bar-passing Strouhal numbers. Reynolds stresses were found to be consistent with related cylinder-wake measurements, but were significantly higher than corresponding measurements obtained in large-scale research turbomachines. Phase-averaged triple velocity correlations were calculated from the digital velocity records, revealing the sign and the magnitude of skewness in the velocity probability density distributions for the two components.

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Blade measurements of time-averaged flux distribution are obtained with and without gas injection for a full-stage rotating turbine. Results are presented along the blade in the flow direction at 10, 50, and 90 percent span locations for both the pressure and suction surfaces; enough measurements were obtained to present spanwise distributions as well. The results suggest that the suction surface laminar flat plate prediction is in reasonable agreement with the data from the stagnation point up to about 10 percent of the wetted distance. The influence of upstream nozzle guide vane injection is to significantly increase the local blade heat flux in the immediate vicinity of the leading edge.

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Calculations were performed to assess the effect of the tip leakage flow on the rate of heat transfer to blade, blade tip and casing. The effect on exit angle and efficiency was also examined. Passage geometries with and without casing recess were considered. The geometry and the flow conditions of the GE-E 3 first stage turbine, which represents a modem gas turbine blade were used for the analysis. Clearance heights of 0%, 1%, 1.5% and 3% of the passage height were considered. For the two largest clearance heights considered, different recess depths were studied. There was an increase in the thermal load on all the heat transfer surfaces considered due to enlargement of the clearance gap. Introduction of recessed casing resulted in a drop in the rate of heat transfer on the pressure side but the picture on the suction side was found to be more complex for the smaller tip clearance height considered. For the larger tip clearance height the effect of casing recess was an orderly reduction in the suction side heat transfer as the casing recess height was increased. There was a marked reduction of heat load and peak values on the blade tip upon introduction of casing recess, however only a small reduction was observed on the casing itself. It was reconfirmed that there is a linear relationship between the efficiency and the tip gap height. It was also observed that the recess casing has a small effect on the efficiency but can have a moderating effect on the flow underturning at smaller tip clearances.

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An application of a simple aeroelastic model to an advanced supersonic axial flow fan is presented. Lane's cascade theory is used to determine the unsteady aerodynamic loads. Parametric studies are performed to determine the effects of mode coupling, Mach number, damping, pitching axis location, solidity, stagger angle, and mistuning. The results show that supersonic axial flow fan and compressor blades are susceptible to a strong torsional mode flutter having critical reduced velocities which can be less than one.

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