A Time-Linearized Navier–Stokes Analysis of Stall Flutter

1999 ◽  
Vol 122 (3) ◽  
pp. 467-476 ◽  
Author(s):  
William S. Clark ◽  
Kenneth C. Hall
Keyword(s):  
Unsteady Flow ◽  
Turbulence Modeling ◽  
Unsteady Aerodynamics ◽  
Computational Method ◽  
Navier Stokes ◽  
Integration Scheme ◽  
Mean Flow ◽  
Viscous Effects ◽  
Computational Mesh ◽  
Stall Flutter

A computational method for predicting unsteady viscous flow through two-dimensional cascades accurately and efficiently is presented. The method is intended to predict the onset of the aeroelastic phenomenon of stall flutter. In stall flutter, viscous effects significantly impact the aeroelastic stability of a cascade. In the present effort, the unsteady flow is modeled using a time-linearized Navier–Stokes analysis. Thus, the unsteady flow field is decomposed into a nonlinear spatially varying mean flow plus a small-perturbation harmonically varying unsteady flow. The resulting equations that govern the perturbation flow are linear, variable coefficient partial differential equations. These equations are discretized on a deforming, multiblock, computational mesh and solved using a finite-volume Lax–Wendroff integration scheme. Numerical modeling issues relevant to the development of the unsteady aerodynamic analysis, including turbulence modeling, are discussed. Results from the present method are compared to experimental stall flutter data, and to a nonlinear time-domain Navier–Stokes analysis. The results presented demonstrate the ability of the present time-linearized analysis to model accurately the unsteady aerodynamics associated with turbomachinery stall flutter. [S0889-504X(00)00203-8]

scholarly journals A Time-Linearized Navier-Stokes Analysis of Stall Flutter

1999 ◽  
Author(s):  
William S. Clark ◽  
Kenneth C. Hall
Keyword(s):  
Unsteady Flow ◽  
Unsteady Aerodynamics ◽  
Computational Method ◽  
Navier Stokes ◽  
Integration Scheme ◽  
Mean Flow ◽  
Viscous Effects ◽  
Computational Mesh ◽  
Unsteady Viscous Flow ◽  
Stall Flutter

A computational method for accurately and efficiently predicting unsteady viscous flow through two-dimensional cascades is presented. The method is intended to predict the onset of the aeroelastic phenomenon of stall flutter. In stall flutter, viscous effects significantly impact the aeroelastic stability of a cascade. In the present effort, the unsteady flow is modeled using a time-linearized Navier-Stokes analysis. Thus, the unsteady flow field is decomposed into a nonlinear spatially varying mean flow plus a small-perturbation harmonically varying unsteady flow. The resulting equations that govern the perturbation flow are linear, variable coefficient partial differential equations. These equations are discretized on a deforming, multi-block, computational mesh and solved using a finite-volume Lax-Wendroff integration scheme. Numerical modelling issues relevant to the development of the unsteady aerodynamic analysis, including turbulence modelling, are discussed. Results from the present method are compared to experimental stall flutter data, and to a nonlinear time-domain Navier-Stoke analysis. The results presented demonstrate the ability of the present time-linearized analysis to model accurately the unsteady aerodynamics associated with turbomachinery stall flutter.

Rotational and Quasiviscous Cold Flow Models for Axisymmetric Hybrid Propellant Chambers

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Joseph Majdalani ◽  
Michel Akiki
Keyword(s):  
Rocket Engine ◽  
Navier Stokes ◽  
Mathematical Treatment ◽  
Hybrid Rocket ◽  
Mean Flow ◽  
Viscous Effects ◽  
Navier Stokes Equation ◽  
Flow Models ◽  
Hybrid Rocket Engine ◽  
Wall Injection

In this work, we present two simple mean flow solutions that mimic the bulk gas motion inside a full-length, cylindrical hybrid rocket engine. Two distinct methods are used. The first is based on steady, axisymmetric, rotational, and incompressible flow conditions. It leads to an Eulerian solution that observes the normal sidewall mass injection condition while assuming a sinusoidal injection profile at the head end wall. The second approach constitutes a slight improvement over the first in its inclusion of viscous effects. At the outset, a first order viscous approximation is constructed using regular perturbations in the reciprocal of the wall injection Reynolds number. The asymptotic approximation is derived from a general similarity reduced Navier–Stokes equation for a viscous tube with regressing porous walls. It is then compared and shown to agree remarkably well with two existing solutions. The resulting formulations enable us to model the streamtubes observed in conventional hybrid engines in which the parallel motion of gaseous oxidizer is coupled with the cross-streamwise (i.e., sidewall) addition of solid fuel. Furthermore, estimates for pressure, velocity, and vorticity distributions in the simulated engine are provided in closed form. Our idealized hybrid engine is modeled as a porous circular-port chamber with head end injection. The mathematical treatment is based on a standard similarity approach that is tailored to permit sinusoidal injection at the head end.

scholarly journals Modeling the 3-d flow around a cylinder using the SAS hybrid model

2014 ◽  
Vol 16 (5) ◽  
pp. 901-918 ◽  
Keyword(s):  
Turbulence Modeling ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Cross Flow ◽  
Numerical Code ◽  
Navier Stokes ◽  
Computational Domain ◽  
Mean Flow ◽  
Unstable Flow ◽  
Vortex Size

<div> <p>Three-dimensional calculations were performed to simulate the flow around a cylindrical vegetation element using the Scale Adaptive Simulation (SAS) model; commonly, this is the first step of the modeling of the flow through multiple vegetation elements. SAS solves the Reynolds Averaged Navier-Stokes equations in stable flow regions, while in regions with unstable flow it goes unsteady producing a resolved turbulent spectrum after reducing eddy viscosity according to the locally resolved vortex size represented by the von Karman length scale. A finite volume numerical code was used for the spatial discretisation of the rectangular computational domain with stream-wise, cross-flow and vertical dimensions equal to 30D, 11D and 1D, respectively, which was resolved with unstructured grids. Calculations were compared with experiments and Large Eddy Simulations (LES). Predicted overall flow parameters and mean flow velocities exhibited a very satisfactory agreement with experiments and LES, while the agreement of predicted turbulent stresses was satisfactory. Calculations showed that SAS is an efficient and relatively fast turbulence modeling approach, especially in relevant practical problems, in which the very high accuracy that can be achieved by LES at the expense of large computational times is not required.</p> </div> <p>&nbsp;</p>

scholarly journals A Numerical Model of the Onset of Stall Flutter in Cascades

1995 ◽  
Author(s):  
William S. Clark ◽  
Kenneth C. Hall
Keyword(s):  
Unsteady Flow ◽  
Stokes Equations ◽  
Fluid Dynamic ◽  
Computational Fluid Dynamic Model ◽  
Navier Stokes ◽  
Aeroelastic Stability ◽  
Blade Vibration ◽  
Navier Stokes Equations ◽  
The Mean ◽  
Stall Flutter

In this paper, we present a computational fluid dynamic model of the unsteady flow associated with the onset of stall flutter in turbomachinery cascades. The unsteady flow is modeled using the laminar Navier-Stokes equations. We assume that the unsteadiness in the flow is a small harmonic disturbance about the mean or steady flow. Therefore, the unsteady flow is governed by a small-disturbance form of the Navier-Stokes equations. These linear variable coefficient equations are discretized on a deforming computational grid and solved efficiently using a multiple-grid Lax-Wendroff scheme. A number of numerical examples are presented which demonstrate the destabilizing influence of viscosity on the aeroelastic stability of airfoils in cascade, especially for torsional modes of blade vibration.

Concurrent Blade Aerodynamic-Aero-elastic Design Optimization Using Adjoint Method

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
L. He ◽  
D. X. Wang
Keyword(s):  
Unsteady Flow ◽  
Solution Method ◽  
Stokes Equations ◽  
Adjoint System ◽  
Elastic Stability ◽  
Adjoint Equations ◽  
Navier Stokes ◽  
Simple Extension ◽  
Mean Flow ◽  
Elastic Design

Increasing aerothermal and aero-elastic performance requirements and constraints are closely linked in modern blading designs. There is thus a need for more concurrent interaction between the disciplines at earlier stages of a design process. Presented in this paper are the development, validation, and demonstration of the adjoint approach to concurrent blading aerodynamic and aero-elastic design optimizations. A nonlinear harmonic phase solution method is adopted to solve the unsteady Reynolds-averaged Navier–Stokes equations. The flow field response in terms of both the mean aerothermal performance and aero-elastic stability to a geometrical perturbation can be obtained by three “steadylike” flow solutions at three distinctive temporal phases. This unsteady flow solution method is computationally very efficient and provides a convenient and consistent base for formulating the corresponding adjoint equations. The adjoint system for the unsteady flow solver is solved effectively by a relatively simple extension of the method and techniques previously developed for a steady flow adjoint solver. As a result, the sensitivities of both the steady (time-mean) flow loss and the aerodynamic damping/forcing to detailed blade geometry changes can be very efficiently obtained by solving equivalently three steadylike adjoint equations. Several case studies are presented to illustrate the validity and effectiveness of this new concurrent approach.

scholarly journals Physics of Airfoil Clocking in Axial Compressors

1997 ◽  
Author(s):  
Karen L. Gundy-Burlet ◽  
Daniel J. Dorney
Keyword(s):  
Unsteady Flow ◽  
Thin Layer ◽  
Relative Motion ◽  
Unsteady Aerodynamics ◽  
Flow Fields ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Low Speed ◽  
Axial Compressors ◽  
Potential Interactions

Axial compressors have inherently unsteady flow fields because of relative motion between rotor and statnr airfnils. This relative motion leads to viscous and inviscid (potential) interactions between blade rows. As the number of stages increases in a turbomachine, the buildup of convected wakes can lead in progressively more complex wake/wake and wake/airfnil interactions. Variations in the relative circumferential positions of stators or rotors can change these interactions, leading to different unsteady forcing functions on airfoils and different compressor efficiencies. The current study uses an unsteady, two-dimensional thin-layer Navier-Stokes zonal approach to investigate the unsteady aerodynamics of stator clocking in a low-speed 2 ½-stage compressor. Relative motion between rotors and stators is made possible by the use of systems of patched and overlaid grids. Results include surface pressures instantaneous forces and efficiencies for a 2 ½-stage compressor configuration.

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.

A Navier-Stokes Analysis of the Stall Flutter Characteristics of the Buffum Cascade

2000 ◽  
Author(s):  
Stefan Weber ◽  
Max F. Platzer
Keyword(s):  
Mach Number ◽  
Turbulence Modeling ◽  
Separation Bubble ◽  
Leading Edge ◽  
Navier Stokes ◽  
Implicit Time ◽  
Fully Implicit ◽  
High Incidence ◽  
Stall Flutter ◽  
Good Agreement

Numerical stall flutter prediction methods are highly needed as modern jet engines require blade designs close to the stability boundaries of the performance map. A Quasi-3D Navier-Stokes code is used to analyze the flow over the oscillating cascade designed and manufactured by Pratt & Whitney, and studied at the NASA Glenn Research Center by Buffum et al. The numerical method solves for the governing equations with a fully implicit time-marching technique in a single passage by making use of a direct-store, periodic boundary condition. For turbulence modeling the Baldwin-Lomax model is used. To account for transition, the criterion to predict the onset location suggested by Baldwin and Lomax is incorporated. Buffum et al. investigated two incidence cases for three different Mach numbers. The low-incidence case at a Mach number of 0.5 exhibited the formation of small separation bubbles at reduced oscillation frequencies of 0.8 and 1.2. For this case the present approach yielded good agreement with the steady and oscillatory measurements. At high-incidence at the same Mach number of 0.5 the measured steady-state pressure distribution and the separation bubble on the upper surface was also found in good agreement with the experiment. But computations for oscillations at high-incidence failed to predict the negative damping contribution caused by the leading edge separation.

scholarly journals Turbulence Modeling Insights into Supercritical Nitrogen Mixing Layers

Energies ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1586
Author(s):  
Leandro Magalhães ◽  
Francisco Carvalho ◽  
André Silva ◽  
Jorge Barata
Keyword(s):  
Turbulence Modeling ◽  
Turbulence Models ◽  
Variable Density ◽  
Computational Method ◽  
Model Complexity ◽  
Navier Stokes ◽  
Rocket Engines ◽  
Liquid Rocket ◽  
Conventional Behavior ◽  
The Cost

In Liquid Rocket Engines, higher combustion efficiencies come at the cost of the propellants exceeding their critical point conditions and entering the supercritical domain. The term fluid is used because, under these conditions, there is no longer a clear distinction between a liquid and a gas phase. The non-conventional behavior of thermophysical properties makes the modeling of supercritical fluid flows a most challenging task. In the present work, a Reynolds Averaged Navier Stokes (RANS) computational method following an incompressible but variable density approach is devised on which the performance of several turbulence models is compared in conjunction with a high accuracy multi-parameter equation of state. In addition, a suitable methodology to describe transport properties accounting for dense fluid corrections is applied. The results are validated against experimental data, making it clear that there is no trend between turbulence model complexity and the quality of the produced results. For several instances, one- and two-equation turbulence models produce similar results. Finally, considerations about the applicability of the tested turbulence models in supercritical simulations are given based on the results and the structural nature of each model.

Simulation of Flow-Induced Oscillations of a Rectangular Bluff Body in Incompressible, Turbulent Flow

2002 ◽  
Author(s):  
Ulf Bunge ◽  
Andreas Gurr ◽  
Frank Thiele
Keyword(s):  
Bluff Body ◽  
Turbulence Modeling ◽  
Flow Direction ◽  
Oscillatory Behavior ◽  
The Body ◽  
Navier Stokes ◽  
Mean Flow ◽  
Time Step ◽  
Numeric Simulation ◽  
Linear Spring

The incompressible flow around a rectangular body with a length to height ratio of L/H = 2 and its flow–induced oscillatory behavior is numerically investigated at different Re–numbers in a range between 1 to 6 · 104. The body has one degree of freedom perpendicular to the mean–flow direction with a linear spring and linear damping. To compute the flow a finite–volume based Navier–Stokes CFD-code is used, which is enhanced by a finite–difference based algorithm to solve the vibration differential equation. Target is the numeric simulation of a incident flow velocity where resonance occurs and the exact determination of the physical mechanisms especially in the flowing medium. Particular substantial parameters of the total model, e.g. turbulence modeling, time step or grid, which exert influence on the quality of the simulation are examined. To achieve this aim simulations with steady and oscillating body are compared with experimental data and deviations are analyzed.

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