Calculation of Three-Dimensional Unsteady Flows in Turbomachinery Using the Linearized Harmonic Euler Equations

1993 ◽  
Vol 115 (4) ◽  
pp. 800-809 ◽  
Author(s):  
K. C. Hall ◽  
C. B. Lorence
Keyword(s):  
Unsteady Flow ◽  
Euler Equations ◽  
Small Perturbation ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Large Error ◽  
Surface Boundary ◽  
Mean Flow ◽  
Airfoil Surface ◽  
Acceleration Techniques

An efficient three-dimensional Euler analysis of unsteady flows in turbomachinery is presented. The unsteady flow is modeled as the sum of a steady or mean flow field plus a harmonically varying small perturbation flow. The linearized Euler equations, which describe the small perturbation unsteady flow, are found to be linear, variable coefficient differential equations whose coefficients depend on the mean flow. A pseudo-time time-marching finite-volume Lax-Wendroff scheme is used to discretize and solve the linearized equations for the unknown perturbation flow quantities. Local time stepping and multiple-grid acceleration techniques are used to speed convergence. For unsteady flow problems involving blade motion, a harmonically deforming computational grid, which conforms to the motion of the vibrating blades, is used to eliminate large error-producing extrapolation terms that would otherwise appear in the airfoil surface boundary conditions and in the evaluation of the unsteady surface pressure. Results are presented for both linear and annular cascade geometries, and for the latter, both rotating and nonrotating blade rows.

Calculation of Three-Dimensional Unsteady Flows in Turbomachinery Using the Linearized Harmonic Euler Equations

1992 ◽  
Author(s):  
Kenneth C. Hall ◽  
Christopher B. Lorence
Keyword(s):  
Unsteady Flow ◽  
Euler Equations ◽  
Small Perturbation ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Large Error ◽  
Surface Boundary ◽  
Mean Flow ◽  
Airfoil Surface ◽  
Acceleration Techniques

An efficient three-dimensional Euler analysis of unsteady flows in turbomachinery is presented. The unsteady flow is modelled as the sum of a steady or mean flow field plus a harmonically varying small perturbation flow. The linearized Euler equations, which describe the small perturbation unsteady flow, are found to be linear, variable coefficient differential equations whose coefficients depend on the mean flow. A pseudo-time time-marching finite-volume Lax-Wendroff scheme is used to discretize and solve the linearized equations for the unknown perturbation flow quantities. Local time stepping and multiple-grid acceleration techniques are used to speed convergence. For unsteady flow problems involving blade motion, a harmonically deforming computational grid which conforms to the motion of the vibrating blades is used to eliminate large error-producing extrapolation terms that would otherwise appear in the airfoil surface boundary conditions and in the evaluation of the unsteady surface pressure. Results are presented for both linear and annular cascade geometries, and for the latter, both rotating and nonrotating blade rows.

scholarly journals Experimental and Computational Study of the Unsteady Flow in a 1.5 Stage Axial Turbine With Emphasis on the Secondary Flow in the Second Stator

1998 ◽  
Author(s):  
Ralf E. Walraevens ◽  
Heinz E. Gallus ◽  
Alexander R. Jung ◽  
Jürgen F. Mayer ◽  
Heinz Stetter
Keyword(s):  
Unsteady Flow ◽  
Secondary Flow ◽  
Computational Study ◽  
Three Dimensional ◽  
Cross Flow ◽  
Axial Flow ◽  
Time Dependent ◽  
Flow Structures ◽  
Mean Flow ◽  
Dependent Flow

A study of the unsteady flow in an axial flow turbine stage with a second stator blade row is presented. The low aspect ratio blades give way to a highly three-dimensional flow which is dominated by secondary flow structures. Detailed steady and unsteady measurements throughout the machine and unsteady flow simulations which include all blade rows have been carried out. The presented results focus on the second stator flow. Secondary flow structures and their origins are identified and tracked on their way through the passage. The results of the time-dependent secondary velocity vectors as well as flow angles and Mach number distributions as perturbation from the time-mean flow field are shown in cross-flow sections and azimuthal cuts throughout the domain of the second stator. At each location the experimental and numerical results are compared and discussed. A good overall agreement in the time-dependent flow behaviour as well as in the secondary flow structures is stated.

Unsteady Flow Behavior due to Breakdown of Tip Leakage Vortex in an Axial Compressor Rotor at Near-Stall Condition

2000 ◽  
Author(s):  
Masato Furukawa ◽  
Kazuhisa Saiki ◽  
Kazutoyo Yamada ◽  
Masahiro Inoue
Keyword(s):  
Unsteady Flow ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Surface Boundary ◽  
Pressure Side ◽  
Suction Surface ◽  
Tip Leakage Vortex ◽  
Tip Leakage ◽  
Pressure Surface ◽  
Compressor Rotor

The unsteady flow nature caused by the breakdown of the tip leakage vortex in an axial compressor rotor at near-stall conditions has been investigated by unsteady three-dimensional Navier-Stokes flow simulations. The simulations show that the spiral-type breakdown of the tip leakage vortex occurs inside the rotor passage at the near-stall conditions. Downstream of the breakdown onset, the tip leakage vortex twists and turns violently with time, thus interacting with the pressure surface of the adjacent blade. The motion of the vortex and its interaction with the pressure surface are cyclic. The vortex breakdown causes significant changes in the nature of the tip leakage vortex, which result in the anomalous phenomena in the time-averaged flow fields near the tip at the near-stall conditions: no rolling-up of the leakage vortex downstream of the rotor, disappearance of the casing wall pressure trough corresponding to the leakage vortex, large spread of the low-energy fluid accumulating on the pressure side, and large pressure fluctuation on the pressure side. As the flow rate is decreased, the movement of the tip leakage vortex due to its breakdown becomes so large that the leakage vortex interacts with the suction surface as well as the pressure one. The interaction with the suction surface gives rise to the three-dimensional separation of the suction surface boundary layer.

Inviscid-Viscous Coupled Solution for Unsteady Flows Through Vibrating Blades: Part 2—Computational Results

1993 ◽  
Vol 115 (1) ◽  
pp. 101-109 ◽  
Author(s):  
L. He ◽  
J. D. Denton
Keyword(s):  
Unsteady Flow ◽  
Transonic Flow ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Computational Results ◽  
Flow Conditions ◽  
Viscous Effects ◽  
Blade Flutter ◽  
Coupled Solution

A quasi-three-dimensional inviscid-viscous coupled approached has been developed for unsteady flows around oscillating blades, as described in Part 1. To validate this method, calculations for several steady and unsteady flow cases with strong inviscid-viscous interactions are performed, and the results are compared with the corresponding experiments. Calculated results for unsteady flows around a biconvex cascade and a fan tip section highlight the necessity of including viscous effects in predictions of turbomachinery blade flutter at transonic flow conditions.

scholarly journals A Linearized Euler Analysis of Unsteady Transonic Flows in Turbomachinery

1993 ◽  
Author(s):  
Kenneth C. Hall ◽  
William S. Clark ◽  
Christopher B. Lorence
Keyword(s):  
Unsteady Flow ◽  
Three Dimensional ◽  
Computational Method ◽  
Shock Capturing ◽  
Flow Conditions ◽  
Mean Flow ◽  
Transonic Flows ◽  
Linearized Euler Equations ◽  
Volume Equations

A computational method for efficiently predicting unsteady transonic flows in two- and three-dimensional cascades is presented. The unsteady flow is modelled using a linearized Euler analysis whereby the unsteady flow field is decomposed into a nonlinear mean flow plus a linear harmonically varying unsteady flow. The equations that govern the perturbation flow, the linearized Euler equations, are linear variable coefficient equations. For transonic flows containing shocks, shock capturing is used to model the shock impulse (the unsteady load due to the harmonic motion of the shock). A conservative Lax-Wendroff scheme is used to obtain a set of linearized finite volume equations that describe the harmonic small disturbance behavior of the flow. Conditions under which such a discretization will correctly predict the shock impulse are investigated. Computational results are presented that demonstrate the accuracy and efficiency of the present method as well as the essential role of unsteady shock impulse loads on the flutter stability of fans.

Numerical Solutions for Unsteady Subsonic Vortical Flows Around Loaded Cascades

1993 ◽  
Vol 115 (4) ◽  
pp. 810-816 ◽  
Author(s):  
J. Fang ◽  
H. M. Atassi
Keyword(s):  
Flow Field ◽  
Unsteady Flow ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Frequency Range ◽  
Mean Flow ◽  
Vortical Flows ◽  
Unsteady Aerodynamic ◽  
Reduced Frequency ◽  
The Mean

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.

Simulation of the Piston Driven Flow Inside a Cylinder With an Eccentric Port

1998 ◽  
Vol 120 (2) ◽  
pp. 319-326 ◽  
Author(s):  
Adrin Gharakhani ◽  
Ahmed F. Ghoniem
Keyword(s):  
Unsteady Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Vortex Method ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Solid Boundary ◽  
Surface Boundary ◽  
Time Varying ◽  
Stroke Length

A grid-free Lagrangian approach is applied to simulate the high Reynolds number unsteady flow inside a three-dimensional domain with moving boundaries. For this purpose, the Navier-Stokes equations are expressed in terms of the vorticity transport formulation. The convection and stretch of vorticity are obtained using the Lagrangian vortex method, while diffusion is approximated by the random walk method. The boundary-element method is used to solve a potential flow problem formulated to impose the normal flux condition on the boundary of the domain. The no-slip condition is satisfied by a vortex tile generation mechanism at the solid boundary, which takes into account the time-varying boundary surfaces due to, e.g., a moving piston. The approach is entirely grid-free within the fluid domain, requiring only meshing of the surface boundary, and virtually free of numerical diffusion. The method is applied to study the evolution of the complex vortical structure forming inside the time-varying semi-confined geometry of a cylinder equipped with an eccentric inlet port and a harmonically driven piston. Results show that vortical structures resembling those observed experimentally in similar configurations dominate this unsteady flow. The roll-up of the incoming jet is responsible for the formation of eddies whose axes are nearly parallel to the cylinder axis. These eddies retain their coherence for most of the stroke length. Instabilities resembling conventional vortex ring azimuthal modes are found to be responsible for the breakup of these toroidal eddies near the end of the piston motion. The nondiffusive nature of the numerical approach allows the prediction of these essentially inviscid phenomena without resorting to a turbulence model or the need for extremely fine, adaptive volumetric meshes.

A Simplified Theory of Oscillating Aerofoils in Transonic Flow: Review and Extension

1980 ◽  
Vol 31 (4) ◽  
pp. 252-284
Author(s):  
E.H. Dowell
Keyword(s):  
Boundary Condition ◽  
Unsteady Flow ◽  
Flow Separation ◽  
Transonic Flow ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Bernoulli’S Equation ◽  
Surface Boundary Condition

SummarySignificant new results are presented to show to what extent a simplified theory for transonic flow may be used. Solutions are obtained by classical techniques and compared with experiment. Results are given for two-dimensional and three-dimensional, steady and unsteady flow. The effects of flow separation and improvements in Bernoulli’s equation and the surface boundary condition are also briefly discussed.

scholarly journals Computation of Unsteady Flows Around Oscillating Blades Using Linear and Nonlinear Harmonic Euler Methods

1997 ◽  
Author(s):  
Wei Ning ◽  
Li He
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Nonlinear Effects ◽  
Euler Method ◽  
Time Averaging ◽  
Strongly Coupled ◽  
Flow Equations ◽  
Perturbation Equations

An quasi three-dimensional time-linearized Euler method has been developed to compute unsteady flows around oscillating blades. In the baseline method, unsteady flow is decomposed into a steady flow plus a linear harmonically varying unsteady flow. Both the steady flow equations and the unsteady perturbation equations are solved using a pseudo time-marching method. Based upon this method, a novel nonlinear harmonic Euler method has been developed. Due to the nonlinearity of the aerodynamic governing equations, time-averaging generates extra “unsteady stress” terms. These nonlinear effects are included by a strongly coupled approach between the perturbation equations and the time-averaged equations. Numerical results demonstrate that nonlinear effects are very effectively modelled by the nonlinear harmonic method.

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