scholarly journals Deterministic Stress Modeling of Hot Gas Segregation in a Turbine

1999 ◽  
Author(s):  
Judy Busby ◽  
Doug Sondak ◽  
Brent Staubach ◽  
Roger Davis
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Three Dimensional ◽  
Design Tool ◽  
Source Terms ◽  
Flow Equations ◽  
Flow Solution ◽  
Viscous Solution ◽  
Hot Streak ◽  
Gas Segregation

Simulation of unsteady viscous turbomachinery flowfields is presently impractical as a design tool due to the long run times required. Designers rely predominantly on steady-state simulations, but these simulations do not account for some of the important unsteady flow physics. Unsteady flow effects can be modeled as source terms in the steady flow equations. These source terms, referred to as Lumped Deterministic Stresses (LDS), can be used to drive steady flow solution procedures to reproduce the time-average of an unsteady flow solution. The goal of this work is to investigate the feasibility of using inviscid lumped deterministic stresses to model unsteady combustion hot streak migretion effects on the turbine blade tip and outer air seal heat loads. The LDS model is obtained from an unsteady inviscid calculation. The inviscid LDS model is then used with a steady viscous computation to simulate the time-averaged viscous solution. The feasibility of the inviscid LDS model is demonstrated on a single stage, three-dimensional, vane-blade turbine with a hot streak entering the vane passage at mid-pitch and mid-span. The steady viscous solution with the LDS model is compared to the time-averaged viscous, steady viscous and time-averaged inviscid computations. The LDS model reproduces the time-averaged viscous temperature distribution on the outer air seal to within 2.3%, while the steady viscous has an error of 8.4%, and the time-averaged inviscid calculation has an error of 17.2%. The solution using the LDS model is obtained at a cost in CPU time that is 26% of that required for a time-averaged viscous computation.

scholarly journals Deterministic Stress Modeling of Hot Gas Segregation in a Turbine

1999 ◽  
Vol 122 (1) ◽  
pp. 62-67 ◽  
Author(s):  
J. Busby ◽  
D. Sondak ◽  
B. Staubach ◽  
R. Davis
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Three Dimensional ◽  
Design Tool ◽  
Source Terms ◽  
Flow Equations ◽  
Flow Solution ◽  
Viscous Solution ◽  
Hot Streak ◽  
Gas Segregation

Simulation of unsteady viscous turbomachinery flowfields is presently impractical as a design tool due to the long run times required. Designers rely predominantly on steady-state simulations, but these simulations do not account for some of the important unsteady flow physics. Unsteady flow effects can be modeled as source terms in the steady flow equations. These source terms, referred to as Lumped Deterministic Stresses (LDS), can be used to drive steady flow solution procedures to reproduce the time-average of an unsteady flow solution. The goal of this work is to investigate the feasibility of using inviscid lumped deterministic stresses to model unsteady combustion hot streak migration effects on the turbine blade tip and outer air seal heat loads. The LDS model is obtained from an unsteady inviscid calculation. The inviscid LDS model is then used with a steady viscous computation to simulate the time-averaged viscous solution. The feasibility of the inviscid LDS model is demonstrated on a single-stage, three-dimensional, vane-blade turbine with a hot streak entering the vane passage at midpitch and midspan. The steady viscous solution with the LDS model is compared to the time-averaged viscous, steady viscous, and time-averaged inviscid computations. The LDS model reproduces the time-averaged viscous temperature distribution on the outer air seal to within 2.3 percent, while the steady viscous has an error of 8.4 percent, and the time-averaged inviscid calculation has an error of 17.2 percent. The solution using the LDS model is obtained at a cost in CPU time that is 26 percent of that required for a time-averaged viscous computation. [S0889-504X(00)00601-2]

Three-Dimensional Non-Reflecting Boundary Condition for Linearized Flow Solvers

2010 ◽  
Author(s):  
Paul J. Petrie-Repar
Keyword(s):  
Boundary Condition ◽  
Unsteady Flow ◽  
Steady Flow ◽  
Three Dimensional ◽  
Far Field ◽  
Two Dimensional ◽  
Flow Equations ◽  
Flow Simulations ◽  
Unsteady Aerodynamic ◽  
2D And 3D

A three-dimensional (3D) non-reflecting boundary condition for linearized flow solvers is presented. The unsteady aerodynamic modes at the inlet and outlet (far-field) are numerically determined by solving an eigen problem for the semi-discretized flow equations on a two-dimensional mesh. Unlike previous methods the shape of the far-field can be general and the non-uniformity of the steady flow across the far-field is considered. The calculated unsteady modes are used to decompose the unsteady flow at the far-field into modes. The direction of each mode is determined, and incoming modes are prescribed and outgoing modes are extrapolated. The results of 2D and 3D inviscid linearised flow simulations using the new boundary condition are presented.

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.

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

1998 ◽  
Vol 120 (3) ◽  
pp. 508-514 ◽  
Author(s):  
W. Ning ◽  
L. He
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Nonlinear Effects ◽  
Euler Method ◽  
Time Averaging ◽  
Strongly Coupled ◽  
Flow Equations ◽  
Perturbation Equations

A 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 modeled by the nonlinear harmonic method.

A Three-Dimensional Viscous Transonic Inverse Design Method

2000 ◽  
Author(s):  
W. T. Tiow ◽  
M. Zangeneh
Keyword(s):  
Design Method ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Viscous Effects ◽  
Flow Equations ◽  
Flow Solution ◽  
Turbomachinery Blades ◽  
A Cell ◽  
Inverse Design Method ◽  
Euler Solver

The development and application of a three-dimensional inverse methodology is presented for the design of turbomachinery blades. The method is based on the mass-averaged swirl, rV~θ distribution and computes the necessary blade changes directly from the discrepancies between the target and initial distributions. The flow solution and blade modification converge simultaneously giving the final blade geometry and the corresponding steady state flow solution. The flow analysis is performed using a cell-vertex finite volume time-marching algorithm employing the multistage Runge-Kutta integrator in conjunction with accelerating techniques (local time stepping and grid sequencing). To account for viscous effects, dissipative forces are included in the Euler solver using the log-law and mixing length models. The design method can be used with any existing solver solving the same flow equations without any modifications to the blade surface wall boundary condition. Validation of the method has been carried out using a transonic annular turbine nozzle and NASA rotor 67. Finally, the method is demonstrated on the re-design of the blades.

Paper 20: Application of Non-Steady Flow in a Rotating Duct to Pulsating Flow in a Centrifugal Compressor

1967 ◽  
Vol 182 (8) ◽  
pp. 184-196 ◽  
Author(s):  
R. S. Benson ◽  
A. Whitfield
Keyword(s):  
Boundary Condition ◽  
Steady Flow ◽  
Centrifugal Compressor ◽  
Pressure Loss ◽  
Pressure Ratio ◽  
Computer Calculation ◽  
Design Tool ◽  
Centrifugal Impeller ◽  
Vaneless Diffuser ◽  
Flow Equations

This paper deals with a theoretical approach to study the non-steady flow and wave action in a centrifugal impeller and vaneless diffuser, and also to predict the non-steady flow performance of a centrifugal compressor. This was carried out by replacing the compressor unit by a model which consisted of a simplified rotating duct, a vaneless diffuser, and a cone-shaped pipe which replaced the scroll. A theoretical technique using the method of characteristics and the development of the non-steady flow equations to a rotating duct and radial diffuser is given. The development of the theory and the difficulties encountered are described. In particular, the techniques developed for starting a computer calculation are described. In order to maintain homentropic flow in the impeller and diffuser all losses were assumed to occur at the impeller inlet. A pressure loss boundary condition was developed to enable the steady pressure ratio-mass flow characteristics to be computed. When these values agreed with the experimentally determined characteristics, the boundary condition at the rotor inlet was such that the pressure loss terms allowed for the impeller and diffuser losses. The theoretical results obtained are compared with corresponding experimental results, and the possibility of using this theoretical technique as a design tool is discussed.

scholarly journals Three Dimensional Unsteady Flow for an Oscillating Turbine Blade and the Influence of Tip Leakage

1998 ◽  
Author(s):  
D. L. Bell ◽  
L. He
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Turbine Blade ◽  
Test Data ◽  
Three Dimensional ◽  
Unsteady Aerodynamics ◽  
Blade Loading ◽  
Tip Leakage ◽  
Unsteady Pressure ◽  
Reduced Frequency

The results of two investigations, conducted on the aerodynamic response of a turbine blade oscillating in a three dimensional bending mode, are presented in this paper. The first is an experimental and computational study, designed to produce detailed three dimensional test cases for aeroelastic applications and examine the ability of a 3D time-marching Euler method to predict the relevant unsteady aerodynamics. Extensive blade surface unsteady pressure measurements were obtained for a range of reduced frequency, from a test facility with clearly defined boundary conditions, Bell & He (1997). The test data exhibits a significant three dimensional effect, whereby the amplitude of the unsteady pressure response at different spanwise positions is largely insensitive to the local bending amplitude. The inviscid numerical scheme successfully captured this behaviour, and a good qualitative and quantitative agreement with the test data was achieved for the full range of reduced frequency. In addition, the issue of linearity is addressed and both experimental and numerical tests demonstrate a linear behaviour of the unsteady aerodynamics. The second, an experimental investigation, considers the influence of tip leakage on the unsteady pressure response of an oscillating turbine blade. Results are provided for three tip clearances. The steady flow measurements show marked increases in the size and strength of the tip leakage vortex for the larger tip gaps and deviations in the blade loading towards the tip section. The changes in tip gap also caused distinct trends in the amplitude of the unsteady pressure at 90% span, which were consistent with those observed for steady flow blade loading. It is the authors opinion, that the existence of these trends in unsteady pressure warrants further investigation into the influence of tip leakage upon the local unsteady flow and aerodynamic damping.

Numerical Investigations About the Aerodynamic Performance of the Cascade in Unsteady Environment

2003 ◽  
Author(s):  
L. C. Ji ◽  
J. Chen ◽  
J. Z. Xu
Keyword(s):  
Unsteady Flow ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Wave Structure ◽  
The Other ◽  
Linear Cascade ◽  
Average Value ◽  
Edge Matching ◽  
Cascade Flow ◽  
Hot Streak

The paper presents detailed parametric simulations about the unsteady flow in the cascade passageways. The studies focus on two aspects of unsteady cascade flow. One is two dimensional (2D), which describes unsteady flow characteristics only in blade-to-blade surfaces. The other is three-dimensional (3D, a linear cascade), in which more attentions are paid to the stacking of the unsteady flow of 2D cascades along all spanwise positions. In the former aspect, two different types of unsteadiness are applied at the inlet. One is an azimuthal wave structure that processes through the cascade. The other unsteadiness is spatially uniform and oscillates in time. Using each type of unsteadiness, inflow oscillations of total pressure, total temperature and inflow angle are studied for one turbine and one compressor cascades. The emphasis is focused on the aerodynamic effects of the time-average value, the amplitude and the frequency of the unsteady flow. Results show that the unsteady cascade flow produces more losses than a steady one. Some potentials towards engineering applications are also described. Finally, unsteady flow in 3D linear cascade is studied. A design freedom that can not be used under steady flow frame, Edge-Matching, is put forward. It is essentially to match phase angle of unsteady flow along the whole span so that aerodynamic, aeroelastic, aeroacoustic and heat transfer performances of turbomachinery can be optimized and compromised. With a comprehensive viewpoint, case treatment, hot streak/blade interaction, clocking and even calming effects all belong to Edge-Matching technique. It may eventually promote the daily use of unsteady design.

Linearized Unsteady Viscous Turbomachinery Flows Using Hybrid Grids

2001 ◽  
Vol 123 (3) ◽  
pp. 568-582 ◽  
Author(s):  
L. Sbardella ◽  
M. Imregun
Keyword(s):  
Unsteady Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Laplacian Operator ◽  
Finite Volume Scheme ◽  
Test Case ◽  
Flow Equations ◽  
Mixed Element

The paper describes the theory and the numerical implementation of a three-dimensional finite volume scheme for the solution of the linearized, unsteady Favre-averaged Navier–Stokes equations for turbomachinery applications. A further feature is the use of mixed element grids, consisting of triangles and quadrilaterals in two dimensions, and of tetrahedra, triangular prisms, and hexahedra in three dimensions. The linearized unsteady viscous flow equations are derived by assuming small harmonic perturbations from a steady-state flow and the resulting equations are solved using a pseudo-time marching technique. Such an approach enables the same numerical algorithm to be used for both the nonlinear steady and the linearized unsteady flow computations. The important features of the work are the discretization of the flow domain via a single, unified edge-data structure for mixed element meshes, the use of a Laplacian operator, which results in a nearest neighbor stencil, and the full linearization of the Spalart–Allmaras turbulence model. Four different test cases are presented for the validation of the proposed method. The first one is a comparison against the classical subsonic flat plate cascade theory, the so-called LINSUB benchmark. The aim of the second test case is to check the computational results against the asymptotic analytical solution derived by Lighthill for an unsteady laminar flow. The third test case examines the implications of using inviscid, frozen-turbulence, and fully turbulent models when linearizing the unsteady flow over a transonic turbine blade, the so-called 11th International Standard Configuration. The final test case is a rotor/stator interaction, which not only checks the validity of the formulation for a three-dimensional example, but also highlights other issues, such as the need to linearize the wall functions. Detailed comparisons were carried out against measured steady and unsteady flow data for the last two cases and good overall agreement was obtained.

scholarly journals APPLICATION OF AN EULER SOLVER TO SELECTED PROBLEMS IN FLIGHT DYNAMICS

Aviation ◽  
2007 ◽  
Vol 11 (2) ◽  
pp. 13-22
Author(s):  
Janusz Sznajder ◽  
Jerzy Zółtak
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Vortex Breakdown ◽  
Delta Wing ◽  
Flow Analysis ◽  
Vortical Flow ◽  
Flow Equations ◽  
Euler Solver ◽  
Unsteady Flow Analysis

Several applications of a Euler solver with the formulation of the flow equations in the noninertial reference system with steady and unsteady flow analysis are presented. The steady‐flow applications include determination of aerodynamic derivatives with respect to angular velocity and analysis of vortical flow over a delta wing at high angles of attack with the determination of aerodynamic coefficients and analysis of vortex breakdown. The unsteady flow analysis is applied in the simulation of a rapid manoeuvre for the determination of unsteady forces. The results of this simulation are compared with results of simulations using steady‐flow approximation in order to assess the advantages of unsteady flow analysis in the simulation of aircraft manoeuvres.

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