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At least 127 records · Page 7

An unconditionally stable Runge-Kutta method for unsteady flows

A quasi-three dimensional analysis was developed for unsteady rotor-stator interaction in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body fitted coordinate system. It accounts for the effects of rotation, radius change, and stream surface thickness. The Baldwin-Lomax eddy viscosity model is used for turbulent flows. The equations are integrated in time using a four stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing was employed to accelerate the solution of the time accurate computations. The scheme is described and accuracy analyses are given. Results are shown for a supersonic through-flow fan designed for NASA Lewis. The rotor:stator blade ratio was taken as 1:1. Results are also shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Here the blade ratio is 2:3. Implicit residual smoothing was used to increase the time step limit of the unsmoothed scheme by a factor of six with negligible differences in the unsteady results. It is felt that the implicitly smoothed Runge-Kutta scheme is easily competitive with implicit schemes for unsteady flows while retaining the simplicity of an explicit scheme.

Jorgenson, Philip C. E.↗

An unconditionally stable Runge-Kutta method for unsteady flows

A quasi-three-dimensional analysis was developed for unsteady rotor-stator interaction in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stream surface thickness. The Baldwin-Lomax eddy viscosity model is used for turbulent flows. The equations are integrated in time using a four-stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing was employed to accelerate the solution of the time accurate computations. The scheme is described and accuracy analyses are given. Results are shown for a supersonic through-flow fan designed for NASA Lewis. The rotor:stator blade ratio was taken as 1:1. Results are also shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Here the blade ratio is 2:3. Implicit residual smoothing was used to increase the time step limit of the unsmoothed scheme by a factor of six with negligible differences in the unsteady results. It is felt that the implicitly smoothed Runge-Kutta scheme is easily competitive with implicit schemes for unsteady flows while retaining the simplicity of an explicit scheme.

Jorgenson, Philip C. E.↗

Fluid mechanics of dynamic stall. I - Unsteady flow concepts

Advanced military aircraft 'supermaneuverability' requirements entail the sustained operation of airfoils at stalled flow conditions. The present work addresses the effects of separated flow on vehicle dynamics; an analytic method is presented which employs static experimental data to predict the separated flow effect on incompressible unsteady aerodynamics. The key parameters in the analytic relationship between steady and nonsteady aerodynamics are the time-lag before a change of flow conditions can affect the separation-induced aerodynamic loads, the accelerated flow effect, and the moving wall effect.

Ericsson, L. E.↗

Measurements of the unsteady flow field within the stator row of a transonic axial-flow fan. II - Results and discussion

Unsteady velocity field measurements made within the stator row of a transonic axial-flow fan are presented. Measurements were obtained at midspan for two different stator blade rows using a laser anemometer. The first stator row consists of double circular-arc airfoils with a solidity of 1.68. The second features controlled-diffusion airfoils with a solidity of 0.85. Both were tested at design-speed peak efficiency conditions. In addition, the controlled-diffusion stator was also tested at near stall conditions. The procedures developed here are used to identify the rotor wake generated and unresolved unsteadiness from the velocity measurements (rotor wake generated unsteadiness refers to the unsteadiness generated by the rotor wake velocity deficit and unresolved unsteadiness refers to all remaining unsteadiness which contributes to the spread in the distribution of velocities such as vortex shedding, turbulence, etc.). Auto and cross correlations of these unsteady velocity fluctuations are presented to show their relative magnitude and spatial distributions. Amplification and attenuation of both rotor wake generated and unresolved unsteadiness are shown to occur within the stator blade passage.

Hathaway, M. D.↗

Effects of Unsteady Flow Interactions on the Performance of a Highly-Loaded Transonic Compressor Stage

The primary focus of this paper is to investigate the loss sources in an advanced GE transonic compressor design with high reaction and high stage loading. This advanced compressor has been investigated both experimentally and analytically in the past. The measured compressor efficiency is significantly lower than the efficiency calculated with various existing tools based on RANS and URANS. The general understanding is that some important flow physics in this modern compressor design are not represented in the current tools. To pinpoint the source of the efficiency miss, an advanced test with detailed flow traverse was performed for the front one and a half stage at the NASA Glenn Research Center. In the present paper, a Large Eddy Simulation (LES) is employed to determine whether a higher-fidelity simulation can pick up any additional flow physics that can explain past efficiency miss with RANS and URANS. The results from the Large Eddy Simulation were compared with the NASA test results and the GE interpretation of the test data. LES calculates lower total pressure and higher total temperature on the pressure side of the stator, resulting in large loss generation on the pressure side of the stator. On the other hand, existing tools based on the RANS and URANS do not calculate this high total temperature and low total pressure on the pressure side of the stator. The calculated loss through the stator from LES seems to match the measured data and the GE data interpretation. Detailed examination of the unsteady flow field from LES indicates that the accumulation of high loss near the pressure side of the stator is due to the interaction of the rotor wake with the stator blade. The strong rotor wake interacts quite differently with the pressure side of the stator than with the suction side of the stator blade. The concave curvature on the pressure side of the stator blade increases the mixing of the rotor wake with the pressure side boundary layer significantly. On the other hand, the convex curvature on the suction side of the stator blade decreases the mixing and the suction side blade boundary layer remains thin. The jet velocity in the rotor wake in the stator frame seems to magnify the curvature effect in addition to inviscid redistribution of wake fluid toward the pressure side of the blade.

LES↗

Solutions to Kuessner's integral equation in unsteady flow using local basis functions

The computational procedure and numerical results are presented for a new method to solve Kuessner's integral equation in the case of subsonic compressible flow about harmonically oscillating planar surfaces with controls. Kuessner's equation is a linear transformation from pressure to normalwash. The unknown pressure is expanded in terms of prescribed basis functions and the unknown basis function coefficients are determined in the usual manner by satisfying the given normalwash distribution either collocationally or in the complex least squares sense. The present method of solution differs from previous ones in that the basis functions are defined in a continuous fashion over a relatively small portion of the aerodynamic surface and are zero elsewhere. This method, termed the local basis function method, combines the smoothness and accuracy of distribution methods with the simplicity and versatility of panel methods. Predictions by the local basis function method for unsteady flow are shown to be in excellent agreement with other methods. Also, potential improvements to the present method and extensions to more general classes of solutions are discussed.

Fromme, J. A.↗

Bifurcations In Unsteady Flows

Report discusses various types of bifurcations occurring between steady and unsteady aerodynamic flows. Provides examples to illustrate ways bifurcations influence results of experiments. Recommends experimenters take bifurcation phenomena into account in interpretation of measurements.

Chapman, Gary T.↗

Measurements of the unsteady flow field within the stator row of a transonic axial-flow fan. 1: Measurement and analysis technique

This two-part paper presents laser anemometer measurements of the unsteady velocity field within the stator row of a transonic axial-flow fan. The objective is to provide additional insight into unsteady blade-row interactions within high speed compressors which affect stage efficiency, energy transfer, and other design considerations. Part 1 describes the measurement and analysis techniques used for resolving the unsteady flow field features. The ensemble-average and variance of the measured velocities are used to identify the rotor wake generated and unresolved unsteadiness, respectively. (Rotor wake generated unsteadiness refers to the unsteadiness generated by the rotor wake velocity deficit and the term unresolved unsteadiness refers to all remaining contributions to unsteadiness such as vortex shedding, turbulence, mass flow fluctuations, etc.). A procedure for calculating auto and cross correlations of the rotor wake generated and unresolved unsteady velocity fluctuations is described. These unsteady-velocity correlations have significance since they also result from a decomposition of the Navier-Stokes equations. This decomposition of the Navier-Stokes equations resulting in the velocity correlations used to describe the unsteady velocity field will also be outlined in this paper.

Suder, K. L.↗

Measurements of the unsteady flow field within the stator row of a transonic axial-flow fan. I - Measurement and analysis technique

This two-part paper presents laser anemometer measurements of the unsteady velocity field within the stator row of a transonic axial-flow fan. The objective is to provide additional insight into unsteady blade-row interactions within highspeed compressors which affect stage efficiency, energy transfer, and other design considerations. Part 1 describes the measurement and analysis techniques used for resolving the unsteady flow field features. The ensemble-average and variance of the measured velocities are used to identify the rotor wake generated and unresolved unsteadiness, respectively. (Rotor wake generated unsteadiness refers to the unsteadiness generated by the rotor wake velocity deficit and the term unresolved unsteadiness refers to all remaining contributions to unsteadiness such as vortex shedding, turbulence, mass flow fluctutions, etc.). A procedure for calculating auto and cross correlations of the rotor wake generated and unresolved unsteady velocity fluctuations is described. These unsteady-velocity correlations have significance since they also result from a decomposition of the Navier-Stokes equations. This decomposition of the Navier-Stokes equations resulting in the velocity correlations used to describe the unsteady velocity field will also be outlined in this paper.

Suder, K. L.↗

Computation of Separated and Unsteady Flows with One- and Two-Equation Turbulence Models

The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. The two-equation turbulence models are discretized in space with an upwind-biased, second order accurate total variation diminishing scheme. One and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading edge and where natural transition was allowed to occur naturally are considered. The more recently developed field-equation turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are obtained. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading edge transitional flow region in order to capture the correct physical mechanism that leads to dynamic stall.

Ekaterinaris, John A.↗

Visualization of quasi-periodic unsteady flows

A self-synchronizing schlieren flow visualization technique has been developed to study unsteady periodic flows which may result from aeroelastic effects. The technique allows the experimentalist to stroboscopically 'freeze' the streak line pattern at any phase in one period of the motion by driving the schlieren light source with an electronically processed synchronizing signal that is derived by measuring a periodic flow variable with a convenient sensor. Results for the visualization of the near-wake behind an oscillating airfoil at low speeds which show an ordered series of discrete vortices and a curious short-wave-length wake disturbance are examined. Results are also presented for edge tone sound generation.

Kadlec, R. A.↗

Application of a generalized minimal residual method to 2D unsteady flows

A generalized minimum residual scheme (GMRES), previously developed for solving nonlinear and linear systems of equations, has been applied to the numerical solution of 2D unsteady compressible flows. It is found that the use of GMRES significantly increases the time step that may be used, compared to noniterative implicit schemes. The feasibility of reducing the memory requirements of the GMRES scheme using a multigrid strategy has also been explored. Several sample steady and unsteady viscous flow applications are presented.

Hixon, Ray↗

Some aspects on unsteady flow past airfoils and cascades

The unsteady boundary layer due to a gust propagating past an isolated airfoil and on airfoils in cascade was measured with a hot wire anemometer in a low speed gust tunnel. Coherent signals were obtained by a phase lock averaging technique that was implemented in an on-line analysis using a PDP 12 computer. Changes in a boundary layer shape factor, noise level, and pressure gradient were correlated over a complete gust cycle. It is concluded that the character of the boundary layer changes from laminar to turbulent and back to laminar during the course of a gust cycle at certain chordwise positions. These measurements help explain certain anomalies that were observed during a previous study of the pressure fluctuations due to gust loadings on airfoils and cascades.

Satyanarayana, B.↗

Fast-dynamo action in unsteady flows and maps in three dimensions

Unsteady fast-dynamo action is obtained in a family of stretch-fold-shear maps applied to a spatially periodic magnetic field in three dimensions. Exponential growth of a mean field in the limit of vanishing diffusivity is demonstrated by a numerical method which alternates instantaneous deformations with molecular diffusion over a finite time interval. Analysis indicates that the dynamo is a coherent feature of the large scales, essentially independent of the cascade of structure to small scales.

Bayly, B. J.↗

Unsteady Flows in a Single-Stage Transonic Axial-Flow Fan Stator Row

Measurements of the unsteady velocity field within the stator row of a transonic axial-flow fan were acquired using a laser anemometer. Measurements were obtained on axisymmetric surfaces located at 10 and 50 percent span from the shroud, with the fan operating at maximum efficiency at design speed. The ensemble-average and variance of the measured velocities are used to identify rotor-wake-generated (deterministic) unsteadiness and turbulence, respectively. Correlations of both deterministic and turbulent velocity fluctuations provide information on the characteristics of unsteady interactions within the stator row. These correlations are derived from the Navier-Stokes equation in a manner similar to deriving the Reynolds stress terms, whereby various averaging operators are used to average the aperiodic, deterministic, and turbulent velocity fluctuations which are known to be present in multistage turbomachines. The correlations of deterministic and turbulent velocity fluctuations throughout the axial fan stator row are presented. In particular, amplification and attenuation of both types of unsteadiness are shown to occur within the stator blade passage.

Hathaway, Michael D.↗

A first-order time-domain Green's function approach to supersonic unsteady flow

A time-domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. The Green's function method is employed in order to convert the potential-flow differential equation into an integral one. This integral equation is then discretized, in space through standard finite-element technique, and in time through finite-difference, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. Consistent with the spatial linear (first-order) finite-element approximations, the potential and co-normalwash are assumed to vary linearly in time. The long range goal of our research is to develop a comprehensive theory for unsteady supersonic potential aerodynamics which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range.

Freedman, M. I.↗

Nonlinearities in analyses of unsteady flow around oscillating wings

An analysis of nonlinearities involved in unsteady subsonic viscous flow around wings at high Reynolds numbers is presented. The finite element method was applied for the numerical integration of the vorticity transport equations. Physical and numerical aspects of the nonlinearities are discussed. Magnification of nonlinearities in the convection terms near wing surfaces due to changing geometry at leading and trailing edges of the wing chord is determined. As a bubble is generated near the leading edge, the timewise variation of vorticity and pressure distributions over the surface is shown. The different procedures for the integration of the vorticity transport equations in three dimensions along spanwise, chordwise, and normal directions are discussed.

Bratanow, T.↗