The Impact of Viscous Effects on the Aerodynamic Damping of Vibrating Transonic Compressor Blades — A Numerical Study

A parametric study which investigates the influence of viscous effects on the damping behaviour of vibrating compressor cascades is presented here. To demonstrate the dependence of unsteady aerodynamic forces on the flow viscosity, a computational study was performed for a transonic compressor cascade of which the blades underwent tuned pitching oscillations while the flow conditions extended from fully subsonic to highly transonic flow. Additionally, the reduced frequency and Reynolds number were varied. In order to check the linear behavior of the aerodynamic forces, all calculations were carried out for three different oscillation amplitudes. Comparisons with inviscid Euler results helped identify the influence of viscous effects. The computations were performed with a Navier-Stokes code, the basic features of which are the use of an AUSM upwind scheme, an implicit time integration, and the implementation of the Baldwin-Lomax turbulence model. In order to demonstrate the possibility of this code to correctly predict the unsteady behavior of strong shock-boundary layer interactions, the experiment of Yamamoto and Tanida on a self-induced shock oscillation due to shock-boundary layer interaction was calculated. A significant improvement in the prediction of the shock amplitude was achieved by a slight modification of the Baldwin Lomax turbulence model. An important result of the presented compressor cascade investigations is that viscous effects may cause a significant change in the aerodynamic damping. This behaviour is demonstrated by two cases in which an Euler calculation predicts a damped oscillation whereas a Navier-Stokes computation leads to an excited vibration. It was found that the reason for these contrary results are shock-boundary-layer interactions which dramatically change the aerodynamic damping.

The Impact of Viscous Effects on the Aerodynamic Damping of Vibrating Transonic Compressor Blades—A Numerical Study

10.1115/1.1354139 ◽

2000 ◽

Vol 123 (2) ◽

pp. 409-417 ◽

Cited By ~ 18

Author(s):

Bjo¨rn Gru¨ber ◽

Volker Carstens

Keyword(s):

Boundary Layer ◽

Turbulence Model ◽

Navier Stokes ◽

Implicit Time ◽

Compressor Cascade ◽

Viscous Effects ◽

Aerodynamic Forces ◽

Aerodynamic Damping ◽

Transonic Compressor ◽

A parametric study which investigates the influence of viscous effects on the damping behavior of vibrating compressor cascades is presented here. To demonstrate the dependence of unsteady aerodynamic forces on the flow viscosity, a computational study was performed for a transonic compressor cascade of which the blades underwent tuned pitching oscillations while the flow conditions extended from fully subsonic to highly transonic flow. Additionally, the reduced frequency and Reynolds number were varied. In order to check the linear behavior of the aerodynamic forces, all calculations were carried out for three different oscillation amplitudes. Comparisons with inviscid Euler results helped identify the influence of viscous effects. The computations were performed with a Navier-Stokes code, the basic features of which are the use of an AUSM upwind scheme, an implicit time integration, and the implementation of the Baldwin-Lomax turbulence model. In order to demonstrate the possibility of this code to correctly predict the unsteady behavior of strong shock-boundary layer interactions, the experiment of Yamamoto and Tanida on a self-induced shock oscillation due to shock-boundary layer interaction was calculated. A significant improvement in the prediction of the shock amplitude was achieved by a slight modification of the Baldwin Lomax turbulence model. An important result of the presented compressor cascade investigations is that viscous effects may cause a significant change in the aerodynamic damping. This behavior is demonstrated by two cases in which an Euler calculation predicts a damped oscillation whereas a Navier-Stokes computation leads to an excited vibration. It was found that the reason for these contrary results are shock-boundary-layer interactions which dramatically change the aerodynamic damping.

A Navier–Stokes Analysis of Airfoils in Oscillating Transonic Cascades for the Prediction of Aerodynamic Damping

10.1115/1.2841013 ◽

1997 ◽

Vol 119 (1) ◽

pp. 77-84 ◽

Cited By ~ 13

Author(s):

R. S. Abhari ◽

M. Giles

Keyword(s):

Numerical Study ◽

Three Dimensional ◽

Outer Region ◽

Navier Stokes ◽

Compressor Cascade ◽

Time Step ◽

Aerodynamic Damping ◽

Transonic Compressor ◽

Standard Configuration ◽

An unsteady, compressible, two-dimensional, thin shear layer Navier–Stokes solver is modified to predict the motion-dependent unsteady flow around oscillating airfoils in a cascade. A quasi-three-dimensional formulations is used to account for the stream-wise variation of streamtube height. The code uses Ni’s Lax–Wendroff algorithm in the outer region, an implicit ADI method in the inner region, conservative coupling at the interface, and the Baldwin–Lomax turbulence model. The computational mesh consists of an O-grid around each blade plus an unstructured outer grid of quadrilateral or triangular cells. The unstructured computational grid was adapted to the flow to better resolve shocks and wakes. Motion of each airfoil was simulated at each time step by stretching and compressing the mesh within the O-grid. This imposed motion consists of harmonic solid body translation in two directions and rotation, combined with the correct interblade phase angles. The validity of the code is illustrated by comparing its predictions to a number of test cases, including an axially oscillating flat plate in laminar flow, the Aeroelasticity of Turbomachines Symposium Fourth Standard Configuration (a transonic turbine cascade), and the Seventh Standard Configuration (a transonic compressor cascade). The overall comparison between the predictions and the test data is reasonably good. A numerical study on a generic transonic compressor rotor was performed in which the impact of varying the amplitude of the airfoil oscillation on the normalized predicted magnitude and phase of the unsteady pressure around the airfoil was studied. It was observed that for this transonic compressor, the nondimensional aerodynamic damping was influenced by the amplitude of the oscillation.

Unsteady Navier-Stokes Simulation of a Transonic Flutter Cascade Near Stall Conditions Applying Algebraic Transition Models

Volume 4: Turbo Expo 2005 ◽

10.1115/gt2005-68221 ◽

2005 ◽

Author(s):

Hans Thermann ◽

Reinhard Niehuis

Keyword(s):

Boundary Layer ◽

Stokes Equations ◽

Strong Shock ◽

Turbulence Models ◽

Navier Stokes ◽

Implicit Time ◽

Compressor Cascade ◽

Transonic Compressor ◽

Transition Models ◽

Operating Points

Due to the trend in the design of modern aeroengines to reduce weight and to realize high pressure ratios, fan and first stage compressor blades are highly susceptible to flutter. At operating points with transonic flow velocities and high incidences stall flutter might occur involving strong shock-boundary layer interactions, flow separation and oscillating shocks. In this paper, results of unsteady Navier-Stokes flow calculations around an oscillating blade in a linear transonic compressor cascade at different operating points including near stall conditions are presented. The nonlinear unsteady Reynolds-averaged Navier-Stokes equations are solved time-accurately using implicit time-integration. Different Low-Reynolds-Number turbulence models are used for closure. Furthermore, empirical algebraic transition models are applied to enhance the accuracy of prediction. Computations are performed two-dimensionally as well as three-dimensionally. It is shown that, for the steady calculations, the prediction of the boundary layer development and the blade loading can be substantially improved compared with fully turbulent computations when algebraic transition models are applied. Furthermore, it is shown that the prediction of the aerodynamic damping in the case of oscillating blades at near stall conditions can be dependent on the applied transition models.

Unsteady Navier-Stokes Simulation of a Transonic Flutter Cascade Near-Stall Conditions Applying Algebraic Transition Models

10.1115/1.2183313 ◽

2005 ◽

Vol 128 (3) ◽

pp. 474-483 ◽

Cited By ~ 4

Author(s):

Hans Thermann ◽

Reinhard Niehuis

Keyword(s):

Boundary Layer ◽

Stokes Equations ◽

Strong Shock ◽

Turbulence Models ◽

Navier Stokes ◽

Implicit Time ◽

Compressor Cascade ◽

Transonic Compressor ◽

Transition Models ◽

Operating Points

Due to the trend in the design of modern aeroengines to reduce weight and to realize high pressure ratios, fan and first-stage compressor blades are highly susceptible to flutter. At operating points with transonic flow velocities and high incidences, stall flutter might occur involving strong shock-boundary layer interactions, flow separation, and oscillating shocks. In this paper, results of unsteady Navier-Stokes flow calculations around an oscillating blade in a linear transonic compressor cascade at different operating points including near-stall conditions are presented. The nonlinear unsteady Reynolds-averaged Navier-Stokes equations are solved time accurately using implicit time integration. Different low-Reynolds-number turbulence models are used for closure. Furthermore, empirical algebraic transition models are applied to enhance the accuracy of prediction. Computations are performed two dimensionally as well as three dimensionally. It is shown that, for the steady calculations, the prediction of the boundary layer development and the blade loading can be substantially improved compared with fully turbulent computations when algebraic transition models are applied. Furthermore, it is shown that the prediction of the aerodynamic damping in the case of oscillating blades at near-stall conditions can be dependent on the applied transition models.

Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education; IGTI Scholar Award ◽

A Navier Stokes Analysis of Airfoils in Oscillating Transonic Cascades for the Prediction of Aerodynamic Damping

10.1115/95-gt-182 ◽

1995 ◽

Cited By ~ 1

Author(s):

Reza S. Abharl ◽

Michael Giles

Keyword(s):

Numerical Study ◽

Outer Region ◽

Navier Stokes ◽

Compressor Cascade ◽

Time Step ◽

Aerodynamic Damping ◽

Transonic Compressor ◽

Compressor Rotor ◽

Standard Configuration ◽

An unsteady, compressible, two dimensional, thin shear layer Navier Stokes solver is modified to predict the motion-dependent unsteady flow around oscillating airfoils in a cascade. A quasi 3-D formulation is used to account for the streamwise variation of streamtube height. The code uses Ni’s Lax-Wendroff algorithm in the outer region, an implicit ADI method in the inner region, conservative coupling at the interface, and the Baldwin-Lomax turbulence model. Computational mesh consists of an O-grid around each blade plus an unstructured outer grid of quadrilateral or triangular cells. The unstructured computational grid was adapted to the flow to better resolve shocks and wakes. Motion of each airfoil was simulated at each time step by stretching and compressing the mesh within the O-grid. This imposed motion consists of harmonic solid body translation in two directions and rotation, combined with the correct inter-blade phase angles. Validity of the code is illustrated by comparing its predictions to a number of test cases, including an axially oscillating flat plate in laminar flow, the Aeroelasticity of Turbomachines Symposium Fourth Standard Configuration (a transonic turbine cascade), the Seventh Standard Configuration (a transonic compressor cascade). The overall comparison between the predictions and the test data is reasonably good. A numerical study on a generic transonic compressor rotor was performed in which the impact of varying the amplitude of the airfoil oscillation on the normalized predicted magnitude and phase of the unsteady pressure around the airfoil was studied. It was observed that for this transonic compressor, the non-dimensional aerodynamic damping was influenced by the amplitude of the oscillation.

Proceedings of the Institution of Mechanical Engineers Part A Journal of Power and Energy ◽

Boundary layer investigations on a highly loaded transonic compressor cascade with shock/laminar boundary layer interactions

10.1243/095765003322315405 ◽

2003 ◽

Vol 217 (4) ◽

pp. 349-356 ◽

Cited By ~ 5

Author(s):

L Hilgenfeld ◽

P Cardamone ◽

L Fottner

Keyword(s):

Boundary Layer ◽

Laminar Boundary Layer ◽

Suction Side ◽

Navier Stokes ◽

Compressor Cascade ◽

Flow Solver ◽

Transonic Compressor ◽

Shock System ◽

The One ◽

Highly Loaded

Detailed experimental and numerical investigations of the flowfield and boundary layer on a highly loaded transonic compressor cascade were performed at various Mach and Reynolds numbers representative of real turbomachinery conditions. The emerging shock system interacts with the laminar boundary layer, causing shock-induced separation with turbulent reattachment. Steady two-dimensional calculations have been performed using the Navier—Stokes solver TRACE-U. The flow solver employs a modified version of the one-equation Spalart—Allmaras turbulence model coupled with a transition correlation by Abu-Ghannam/Shaw in the formulation by Drela. The computations reproduce well the experimental results with respect to the profile pressure distribution and the location of the shock system. The transitional behaviour of the boundary layer and the profile losses in the wake are properly predicted as well, except for the highest Mach number tested, where large separated regions appear on the suction side.

A Numerical Analysis of the Three-Dimensional Viscous Flow in a Transonic Compressor Rotor and Comparison With Experiment

10.1115/1.3262074 ◽

1987 ◽

Vol 109 (1) ◽

pp. 83-90 ◽

Cited By ~ 34

Author(s):

W. N. Dawes

Keyword(s):

Boundary Layer ◽

Numerical Analysis ◽

Stokes Equations ◽

Three Dimensional ◽

Axial Flow ◽

Tip Clearance ◽

Navier Stokes ◽

Viscous Effects ◽

Transonic Compressor ◽

Compressor Rotor

The numerical analysis of highly loaded transonic compressors continues to be of considerable interest. Although much progress has been made with inviscid analyses, viscous effects can be very significant, especially those associated with shock–boundary layer interactions. While inviscid analyses have been enhanced by the interactive inclusion of blade surf ace boundary layer calculations, it may be better in the long term to develop efficient algorithms to solve the full three-dimensional Navier–Stokes equations. Indeed, it seems that many phenomena of key interest, like tip clearance flows, may only be accessible to a Navier–Stokes solver. The present paper describes a computer program developed for solving the three-dimensional viscous compressible flow equations in turbomachine geometries. The code is applied to the study of the flowfield in an axial-flow transonic compressor rotor with an attempt to resolve the tip clearance flow. The predicted flow is compared with laser anemometry measurements and good agreement is found.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

Journal of Fluids Engineering ◽

10.1115/1.4024107 ◽

2013 ◽

Vol 135 (7) ◽

Cited By ~ 15

Author(s):

A. Ghidoni ◽

A. Colombo ◽

S. Rebay ◽

F. Bassi

Keyword(s):

Discontinuous Galerkin ◽

Turbulence Model ◽

Stokes Equations ◽

Time Integration ◽

High Order ◽

Transitional Flow ◽

Navier Stokes ◽

Implicit Time ◽

Turbine Cascade ◽

High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

Comparison of Inviscid Computations With Theory and Experiment in Vibrating Transonic Compressor Cascades

Volume 1: Turbomachinery ◽

10.1115/90-gt-373 ◽

1990 ◽

Cited By ~ 3

Author(s):

G. A. Gerolymos ◽

E. Blin ◽

H. Quiniou

Keyword(s):

Boundary Layer ◽

Plate Theory ◽

Strong Shock ◽

Acoustic Resonance ◽

Boundary Layer Separation ◽

Computational Method ◽

Viscous Effects ◽

Transonic Compressor ◽

Boundary Layer Interaction ◽

Interaction Regions

The prediction of unsteady flow in vibrating transonic cascades is essential in assessing the aeroelastic stability of fans and compressors. In the present work an existing computational code, based on the numerical integration of the unsteady Euler equations, in blade-to-blade surface formulation, is validated by comparison with available theoretical and experimental results. Comparison with the flat plate theory of Verdon is, globally, satisfactory. Nevertheless, the computational results do not exhibit any particular behaviour at acoustic resonance. The use of a 1-D nonreflecting boundary condition does not significantly alter the results. Comparison of the computational method with experimental data from started and unstarted supersonic flows, with strong shock waves, reveals that, notwithstanding the globally satisfactory performance of the method, viscous effects are prominent at the shock wave/boundary layer interaction regions, where boundary layer separation introduces a pressure harmonic phase shift, which is not presicted by inviscid methods.

Development of a Numerical Investigation Framework for Ground Vehicle Platooning

Fluids ◽

10.3390/fluids6110404 ◽

2021 ◽

Vol 6 (11) ◽

pp. 404

Author(s):

Charles Patrick Bounds ◽

Sudhan Rajasekar ◽

Mesbah Uddin

Keyword(s):

Turbulence Model ◽

Turbulence Models ◽

Navier Stokes ◽

Ground Vehicle ◽

Simulation Methodology ◽

Vehicle Platooning ◽

Length Separation ◽

Dynamics Simulations ◽

The Impact ◽

Far Wake

This paper presents a study on the flow dynamics involving vehicle interactions. In order to do so, this study first explores aerodynamic prediction capabilities of popular turbulence models used in computational fluid dynamics simulations involving tandem objects and thus, ultimately presents a framework for CFD simulations of ground vehicle platooning using a realistic vehicle model, DrivAer. Considering the availability of experimental data, the simulation methodology is first developed using a tandem arrangement of surface-mounted cubes which requires an understanding on the role of turbulence models and the impacts of the associated turbulence model closure coefficients on the prediction veracity. It was observed that the prediction accuracy of the SST k−ω turbulence model can be significantly improved through the use of a combination of modified values for the closure coefficients. Additionally, the initial validation studies reveal the inability of the Unsteady Reynolds-Averaged Navier-Stokes (URANS) approach to resolve the far wake, and its frailty in simulating tandem body interactions. The Improved Delayed Detached Eddy Simulations (IDDES) approach can resolve the wakes with a reasonable accuracy. The validated simulation methodology is then applied to the fastback DrivAer model at different longitudinal spacing. The results show that, as the longitudinal spacing is reduced, the trailing car’s drag is increased while the leading car’s drag is decreased which supports prior explanations of vortex impingement as the reason for drag changes. Additionally, unlike the case of platooning involving Ahmed bodies, the trailing model drag does not return to an isolated state value at a two car-length separation. However, the impact of the resolution of the far wake of a detailed DrivAer model, and its implication on the CFD characterization of vehicle interaction aerodynamics need further investigations.