Endwall Boundary Layer Research Articles

Endwall boundary layer separation in a single-stage axial-flow low-speed compressor and a high-stagger compressor cascade

Endwall boundary layer separation in a single-stage axial-flow low-speed compressor and a high-stagger compressor cascade

A Loosely Coupled Unsteady Flow Simulation of a Single Stage Compressor

A steady/unsteady, three-dimensional Navier- Stokes solver that utilizes a semi-implicit, pressure-based solution procedure is developed to simulate the three-dimensional, incompressible flow through a single stage compressor. The present numerical scheme features the implementation of a second-order plus fourth-order artificial dissipation formulation to prevent the numerical oscillation due to central differencing schemes. A low-Reynolds-number form of the two-equation turbulence model is used to account for the turbulence effects. For unsteady flow computations, the coupling between the mean flow properties and the turbulence is enhanced by an inner-iteration procedure during each time step. The steady flow field in the rotor passage is computed first. This is used as input for the computation of the unsteady flow in the subsequent stator. The predicted unsteady pressure on the stator blades and unsteady velocities at several locations inside the passage are compared with the experimental data. The unsteady pressures on the stator blade surfaces are in good agreement with the experimental data. The predicted unsteady velocity components at various locations inside the stator blade rows are generally smaller than the measured values in the endwall regions. The phase, angle variations of the unsteady velocity are in good agreement with the measured values. The effects of the rotor wake, secondary and tip clearance flows on the unsteady flow through the subsequent stator are studied. An attempt is also made to quantify the contributions of incoming tip leakage flows and the endwall boundary layers on the unsteady flow through the downstream stator. It was found that the endwall boundary layers and tip leakage flows have a much stronger influence on the unsteady flow development than the wake.

Simulation and Validation of Mach Number Effects on Secondary Flow in a Transonic Turbine Cascade Using a Multigrid, k–ε Solver

An existing three-dimensional Navier–Stokes flow solver with an explicit Runge–Kutta algorithm and a low-Reynolds-number k–ε turbulence model has been modified in order to simulate turbomachinery flows in a more efficient manner. The solver has been made to converge more rapidly through use of the multigrid technique. Stability problems associated with the use of multigrid in conjunction with two-equation turbulence models are addressed and techniques to alleviate instability are investigated. Validation for the new code was performed with a transonic turbine cascade tested by Perdichizzi. In the fully three-dimensional turbulent cascade, real convergence (i.e., CPU time) was improved nearly two times the original code. Robustness was enhanced with the full multigrid initialization procedure. The same test case was then used to perform a series of simulations that investigated the effect of different exit Mach numbers on secondary flow features. This permitted an in-depth study into the mechanisms of secondary flow formation and secondary losses at high Mach numbers. In this cascade, it was found that secondary losses and secondary flow deviation, which are fairly constant in incompressible flows with similar geometries, underwent a large reduction in the compressible flow range. The structure of the trailing edge shock system and the reduced end wall boundary layer at supersonic exit conditions were shown to be very significant in reducing the amount of secondary flow and losses.

Studies of Secondary Flow at Endwall of a Supersonic Compressor Cascade

A combined experimental and numerical study was conducted to investigate the endwall secondary flow in a linear supersonic compressor cascade. The experiment was carried out in a supersonic wind tunnel, with Mach and Reynolds numbers (based on the blade chord) of 2.36 and 4.8 X 106, respectively. A three-dimensional viscous computational fluid dynamics (CFD) calculation was performed to simulate the endwall boundary layer and the three-dimensional secondary flows. The experimental and computational analyses presented are all at the design incidence angle. Experimental measurements include multiple-color surface oil flow visualization applied to the endwall and blade surfaces, blade-to-blade pitot pressure contours at the 90% chordwise position, and upstream and downstream static pressures at the endwall. All of these measurements compare favorably with the CFD calculation. Results from the CFD analysis show that endwall total-pressure losses in this supersonic compressor cascade are a significant contributor to the overall losses and can account for one-third of the overall flowfield loss.

Flow Visualization in a Linear Turbine Cascade of High Performance Turbine Blades

Multiple smoke wires are used to investigate the secondary flow near the endwall of a plane cascade with blade shapes used in high-performance turbine stages. The wires are positioned parallel to the endwall and ahead of the cascade, within and outside the endwall boundary layer. The traces of the smoke generated by the wires are visualized with a laser light sheet illuminating various cross sections around the cascade. During the experiment, a periodically fluctuating horseshoe vortex system of varying number of vortices is observed near the leading edge of the cascade. A series of photographs and video tapes was taken in the cascade to trace these vortices. The development and evolution of the horseshoe vortex and the passage vortex are clearly resolved in the photographs. The interation between the suction side leg of the horseshoe vortex and the passage vortex is also observed in the experiment. A vortex induced by the passage vortex, starting about one-fourth of the curvilinear distance along the blade on the suction surface, is also found. This vortex stays close to the suction surface and above the passage vortex in the laminar flow region on the blade. From this flow visualization, a model describing the secondary flows in a cascade is proposed and compared with previous published models. Some naphthalene mass transfer results from a blade near an endwall are cited and compared with the current model. The flows inferred from the two techniques are in good agreement.

Stability of stationary endwall boundary layers during spin-down

Since Bödewadt's (1940) seminal work on the boundary layer flow produced by a fluid in solid-body rotation over a stationary disk of infinite radius there has been much interest in determining the stability of such flows. To date, it appears that there is no theoretical study of the stability of Bödewadt's self-similar solution to perturbations that are not self-similar. Experimental studies have been compromised due to the difficulty in establishing these steady flows in the laboratory. Savaç (1983, 1987) has studied the endwall boundary layers of flow in a circular cylinder following impulsive spin-down. During the first few radians of rotation, the endwall boundary layers have a structure very similar to Bödewadt layers. For certain conditions, SavaÇ has observed a series of axisymmetric waves travelling radially inwards in the endwall boundary layers. The conjecture is that these waves represent a mode of instability of the Bödewadt layer. Within a few radians of rotation however, the centrifugal instability of the sidewall layer dominates the spin-down process and the endwall waves are difficult to examine further.Here, the impulsive spin-down problem is examined numerically for Savaç’ (1983, 1987) conditions and good agreement with his experiments is achieved. New experimental results are also presented, which include quantitative space-time information regarding the axisymmetric waves. These agree well with both the numerics and the earlier experimental work. Further, a related problem is considered numerically. This flow is also initially in solid-body rotation, but only the endwalls are impulsively stopped, keeping the sidewall rotating. This results in a flow virtually identical to the usual spin-down flow for the first few radians of rotation, except in the immediate vicinity of the sidewall. The sidewall layer is no longer centrifugally unstable and the circular waves on the endwalls are observed without the influence of the sidewall instability.

Heat Transfer and Fluid Mechanics Measurements for the Endwall Boundary Layer Downstream of a Streamlined Strut

Heat Transfer and Fluid Mechanics Measurements for the Endwall Boundary Layer Downstream of a Streamlined Strut

Experimental and Computational Results From the NASA Lewis Low-Speed Centrifugal Impeller at Design and Part-Flow Conditions

The NASA Lewis Low-Speed Centrifugal Compressor (LSCC) has been investigated with laser anemometry and computational analysis at two flow conditions: the design condition as well as a lower mass flow condition. Previously reported experimental and computational results at the design condition are in the literature (Hathaway et al., 1993). In that paper extensive analysis showed that inducer blade boundary layers are centrifuged outward and entrained into the tip clearance flow and hence contribute significantly to the throughflow wake. In this report results are presented for a lower mass flow condition along with further results from the design case. The data set contained herein consists of three-dimensional laser velocimeter results upstream, inside, and downstream of the impeller. In many locations data have been obtained in the blade and endwall boundary layers. The data are presented in the form of throughflow velocity contours as well as secondary flow vectors. The results reported herein illustrate the effects of flow rate on the development of the through flow momentum wake as well as on the secondary flow. The computational results presented confirm the ability of modern computational tools to model the complex flow in a subsonic centrifugal compressor accurately. However, the blade tip shape and tip clearance must be known in order to properly simulate the flow physics. In addition, the ability to predict changes in the throughflow wake, which is largely fed by the tip clearance flow, as the impeller is throttled should give designers much better confidence in using computational tools to improve impeller performance.

The Flow in a Second-Stage Nozzle of a Low-Speed Axial Turbine and Its Effect on Tip Clearance Loss Development

The flow field in a one-and-a-half-stage low-speed axial turbine with varying levels of rotor tip clearance was measured in order to compare the behavior of the second nozzle with the first and to identify the manner in which the second nozzle responds to the complex tip clearance dependent flow presented to it and completes the formation of tip clearance loss. The tangentially averaged flow relative to the rotor blade in the tip clearance region was found to differ radically from that found in cascade and is not underturned with a high axial velocity. There is evidence rather of overturning caused by secondary flow. The axial velocity follows an almost normal endwall boundary layer pattern with almost no leakage jet effect. The cascade tip clearance model is therefore not accurate. The reduction in second-stage nozzle loss was shown to occur near the hub and tip, which confirms that it is probably a reduction in secondary flow loss. The nozzle exit loss contours showed that leakage suppressed the formation of the classical secondary flow pattern and that a new tip clearance related loss phenomenon exists on the suction surface. The second-stage nozzle reduced the hub endwall boundary layer below that of both the first nozzle and that behind the rotor. It also rectified secondary and tip clearance flows to such a degree that a second-stage rotor would experience no greater flow distortion than the first-stage rotor. Radial flow angles behind the second-stage nozzle were much smaller than found in a previous study with low-aspect-ratio untwisted blades.

An Experimental Investigation of the Flow Through an Axial-Flow Pump

The high Reynolds number pump (HIREP) facility at ARL Penn State has been used to perform a low-speed, large-scale experiment of the incompressible flow of water through a two-blade-row turbomachine. The objectives of this experiment were to provide a database for comparison with three-dimensional, turbulent flow computations, to evaluate engineering models, and to improve our physical understanding of many of the phenomena involved in this complex flow field. This summary paper briefly describes the experimental facility, as well as the experimental techniques—such as flow visualization, static-pressure measurements, laser Doppler velocimetry, and both slow- and fast-response pressure probes. Then, proceeding from the inlet to the exit of the pump, the paper presents highlights of experimental measurements and data analysis, giving examples of measured physical phenomena such as endwall boundary layers, separation regions, wakes, and secondary vortical structures. In conclusion, this paper provides a synopsis of a well-controlled, larger scope experiment that should prove helpful to those who wish to use the database.

An experimental study on 3-D flow in an annular cascade of high turning angle turbine blades

This paper presents an experimental study of the three-dimensional turbulent flow fields in a low-speed annular cascade of high turning angle turbine blades. Detailed measurements were performed on the blade surfaces and mid-streamsurface in the passage and at three axial planes downstream of the cascade by using wall static pressure taps, a five-hole probe and a hot-wire anemometer. The test data include static pressure distribution on blade surfaces, total pressure loss coefficient, mean flow velocity components, radial flow angle, turbulence intensity and Reynolds shear stress. Analyses of the three-dimensional cascade flow characteristics were made on the onset location of high loss vortices, the variation of pressure gradient inside the cascade passage and the properties of endwall boundary layers, total pressure loss distributions, secondary vortex turbulent dissipation and wake decay downstream of the cascade. These experimental results are valuable for revealing the details of the complex vortex flow structure in modern highly loaded axial turbomachines and validating the three-dimensional flow numerical computation codes.

Calculation of a three-dimensional turbulent cascade flow

A three-dimensional steady incompressible viscous flow through a plane cascade of turbine blades has been analyzed through a numerical method based on the Navier-Stokes equation. Particular attention is paid to the prediction of secondary flows occurring due to the endwall boundary layer and the blade geometry. A standard k-e model is used for the modelling of Reynolds stress and boundary-fitted coordinates are adopted to represent the complex blade geometry accurately. Two differencing schemes are applied to the convective terms to investigate the effect of numerical diffusion. Experimental data obtained for the flows through the Langston cascade are selected for code validation. Computed results for the velocity vectors and static pressure distributions are in good agreement with presious measurements and provide validity of this numerical method. Three-dimensional viscous flow phenomena and the distribution of total pressure loss caused by secondary flows are also reasonably well predicted.

Generation of ring vortices in axisymmetric spin-down: A numerical investigation

In this paper the sequence of finite-amplitude events that occurs prior to the onset of Taylor–Görtler (TG) vortices in axisymmetric spin-down to rest is described. It is conjectured that the TG vortices are induced by these events, which include internal waves that propagate along the axis of rotation and transient vortex breakdown. The cascade of events is led by an internal ‘‘solitary wave’’ from each end wall. These waves are induced by the end-wall (Bödewadt) boundary layers with concomitant Ekman ‘‘blowing.’’ The passage of the solitary wave causes a transient vortex breakdown followed by a train of internal waves. The combined effect of these phenomena induces disturbances in the sidewall boundary layer that grow and lead to the formation of TG vortices. The TG vortices that originate adjacent to the midplane of the cylinder in the sidewall (Rayleigh) boundary layer dominate the flow field at an intermediate time interval following the onset of spin-down. Favorable comparisons with computationally determined onset times and subsequent evolution of TG vortices reported in the literature support the prediction that naturally occurring finite-amplitude phenomena induce these vortices.

A Method for Calculating Axial Turbomachine End Wall Turbulent Boundary Layers

Based on two families of relative stream surface theory, the differential and integral equations of the endwall boundary layer in the S2 stream surface (hub to tip stream surface ) have been established in the orthogonal curvilinear coordinate system in the present paper. By directly associating the blade force defects with the warping of 32 stream surface near the endwall, we have proposed a new method for predicting the endwall boundary layer.. � This method can be used to conduct the interactions of the end wall boundary layer with the 32 stream surface potentisl flow, in order to get the iterative solution of the end wall boundary layer flow with the potential flow in $2 stream surface. The predicted results � have

Endwall Losses and Flow Unsteadiness in a Turbine Blade Cascade

The purpose of this paper is to describe an investigation of the flow within and downstream of a turbine blade cascade of high aspect ratio. A detailed experimental investigation into the changes in the endwall boundary layer in the cascade (100 deg camber angle) and total pressure loss downstream of the cascade was carried out. Flow visualization was used in order to obtain detailed photographs of the flow patterns on the endwall and for exhibiting the trailing edge vortices. Pressure measurements were carried out using a miniature cranked Kiel probe for three planes downstream of the cascade, with two levels of turbulence intensity of the free stream. Pressure distributions on the blade were measured at three spanwise locations, namely 4, 12, and 50 percent of the full span from the wall. Hot-wire anenometry combined with a spectrum analyzer program was used to determine the frequencies of the flow oscillations. The change in turbulence level of the free stream has a significant influence on all three pressure distributions. The striking difference between two of the pressure distributions is in the aft half of the suction side where the distribution with the lower turbulence intensity has the larger lift. The oil flow visualization reveals what appear to be two separation lines within the passage and are believed to originate from the horseshoe vortex. The pitchwise-averaged total pressure loss coefficient increases with the distance of the measurement plane downstream of the cascade blades. A substantial part of this loss increase close to the wall is caused by the high rate of shear of the new boundary layer on the endwall.

Three-Dimensional Relief in Turbomachinery Blading

The leading edge region of turbomachinery blading in the vicinity of the endwalls is typically characterized by an abrupt increase in the inlet flow angle and a reduction in total pressure associated with endwall boundary layer flow. Conventional two-dimensional cascade analysis of the airfoil sections at the endwalls indicates large leading edge loadings, which are apparently detrimental to the performance. However, experimental data exist that suggest that cascade leading edge loading conditions are not nearly as severe as those indicated by a two-dimensional cascade analysis. This discrepancy between two-dimensional cascade analyses and experimental measurements has generally been attributed to inviscid three-dimensional effects. This article reports on two and three-dimensional calculations of the flow within two axial-flow compressor stators operating near their design points. The computational results of the three-dimensional analysis reveal a significant three-dimensional relief near the casing endwall that is absent in the two-dimensional calculations. The calculated inviscid three-dimensional relief at the endwall is substantiated by airfoil surface static pressure measurements on low-speed research compressor blading designed to model the flow in the high-speed compressor. A strong spanwise flow toward the endwall along the leading edge on the suction surface of the airfoil is responsible for the relief in the leading edge loading at the endwall. This radial migration of flow results in a more uniform spanwise loading compared to that predicted by two-dimensional calculations.

Numerical analysis of three-dimensional viscous internal flows

A 3-D Navier-Stokes code has been developed for analysis of turbomachinery blade rows and other internal flows. The Navier-Stokes equations are written in a Cartesian coordinate system rotating about the x-axis, and then mapped to a general body-fitted coordinate system. Streamwise viscous terms are neglected using the thin-layer assumption, and turbulence effects are modeled using the Baldwin-Lomax turbulence model. The equations are discretized using finite differences on stacked C-type grids and are solved using a multistage Runge-Kutta algorithm with a spatially-varying time step and implicit residual smoothing. Calculations have been made of a horseshoe vortex formed in front of a flat plate with a round leading edge standing in a turbulent endwall boundary layer. Comparisons are made with experimental data taken by Eckerle and Langston for a circular cylinder under similar conditions. Computer and measured results are compared in terms of endwall flow visualization pictures and total pressure loss contours and vector plots on the symmetry plane. Calculated details of the primary vortex show excellent agreement with the experimental data. The calculations also show a small secondary vortex not seen experimentally.

Effect of Boundary Conditions on Mass Transfer Near the Base of a Cylinder in Crossflow

The mass (heat) transfer pattern near the base of a cylinder in crossflow, at Re{sub d} of 10,000-80,000, was described by Goldstein and Karni and Karni and Goldstein. Two small, intense vortices within the horseshoe vortex system produce high values and steep gradients of the transport coefficient over a narrow strip extending from the cylinder base to about 0.07d above it. The studies also indicate the effects of cylinder diameter and endwall boundary layer thickness on these phenomena. In the present study a portion of the endwall and the test cylinder placed normal to it are coated with naphthalene. Local mass transfer measurements are conducted on both surfaces and the results are compared to earlier data by Karni and Goldstein. Thus, the effect of changing the endwall boundary conditions from inactive to active on the mass (heat) transfer pattern is investigated.

Stall Inception in Axial Compressors

Detailed measurements have been made of the transient stalling process in an axial compressor stage. The stage is of high hub-casing ratio and stall is initiated in the rotor. If the rotor tip clearance is small stall inception occurs at the hub, but at clearances typical for a multistage compressor the inception is at the tip. The crucial quantity in both cases is the blockage caused by the endwall boundary layer. Prior to stall, disturbances rotate around the inlet flow in sympathy with rotating variations in the endwall blockage; these can persist for some time prior to stall, rising and falling in amplitude before the final increase, which occurs as the compressor stalls.

LDA Measurement of the Passage Flow Field in an Annular Airfoil Cascade

Models to predict the complex three-dimensional flow through turbomachine blade rows are being developed. To verify these models and direct necessary refinements, it is necessary that predictions be correlated with data obtained in experiments which model the fundamental three-dimensional blade row flow phenomena. This paper describes a series of experiments performed in a large scale, subsonic, annular cascade facility specifically designed to provide such data. In particular, the effect of incidence angle on the three-dimensional passage flow field through an annular cascade of cambered airfoils is investigated and quantified, accomplished by obtaining detailed and expensive LDA data. These data demonstrate and quantify the development of the passage vortices through the airfoil passage and their strong interaction with the endwall boundary layers.