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

1997 ◽  
Vol 119 (1) ◽  
pp. 77-84 ◽  
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 ◽  
The Impact

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.

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

1995 ◽  
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 ◽  
The Impact

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.

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

2000 ◽  
Vol 123 (2) ◽  
pp. 409-417 ◽  
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 ◽  
The Impact

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.

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

2000 ◽  
Author(s):  
Björn Grüber ◽  
Volker Carstens
Keyword(s):  
Boundary Layer ◽  
Turbulence Model ◽  
Navier Stokes ◽  
Implicit Time ◽  
Compressor Cascade ◽  
Viscous Effects ◽  
Aerodynamic Forces ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
The Impact

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.

scholarly journals Darmstadt Rotor No. 2, II: Design of Leaning Rotor Blades

2003 ◽  
Vol 9 (6) ◽  
pp. 385-391
Author(s):  
Jörg Bergner ◽  
Dietmar K. Hennecke ◽  
Martin Hoeger ◽  
Karl Engel
Keyword(s):  
Mechanical Stability ◽  
Three Dimensional ◽  
Stability Limit ◽  
Operating Conditions ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Structural Constraints ◽  
Transonic Compressor ◽  
Aero Engines ◽  
The Impact

For Darmstadt University of Technology's axial singlestage transonic compressor rig, a new three-dimensional aft-swept rotor was designed and manufactured at MTU Aero Engines in Munich, Germany. The application of carbon fiber–reinforced plastic made it possible to overcome structural constraints and therefore to further increase the amount of lean and sweep of the blade. The aim of the design was to improve the mechanical stability at operation that is close to stall.To avoid the hazard of rubbing at the blade tip, which is found especially at off-design operating conditions close to the stability limit of the compression system, aft-sweep was introduced together with excessive backward lean.This article reports an investigation of the impact of various amounts of lean on the aerodynamic behavior of the compressor stage on the basis of steady-state Navier-Stokes simulations. The results indicate that high backward lean promotes an undesirable redistribution of mass flow and gives rise to a basic change in the shock pattern, whereas a forward-leaning geometry results in the development of a highly back-swept shock front. However, the disadvantage is a decrease in shock strength and efficiency.

Analytical Maps of Aerodynamic Damping as a Function of Operating Condition for a Compressor Profile

2006 ◽  
Author(s):  
Paul J. Petrie-Repar ◽  
Andrew McGhee ◽  
Peter A. Jacobs ◽  
Rowan Gollan
Keyword(s):  
Inviscid Flow ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Operating Condition ◽  
Flow Solver ◽  
Aerodynamic Damping ◽  
Wide Range ◽  
Contour Plots ◽  
Standard Configuration

In this paper, analytical maps of aerodynamic damping for a two-dimensional compressor cascade (Standard Configuration 10) are presented. The maps are shown as contour plots of the aerodynamic damping as a function of operating condition. The aerodynamic dampings were calculated by a linearized Navier-Stokes flow solver. The flutter boundaries over a wide range of operating conditions are clearly shown on the damping maps and were found to be strongly dependent on the mode frequency and the mode shape. Extremely low values of negative aerodynamic damping were predicted for some off-design operating conditions where flow separation occurred. A damping map was also constructed based on inviscid flow simulations. There were differences in the viscous and inviscid flutter boundaries particularly at off-design inflow angles. The extremely low values of negative aerodynamic damping were only predicted by the viscous simulations and not the inviscid simulations.

Blade Aerodynamic Damping Variation With Rotor-Stator Gap: A Computational Study Using Single-Passage Approach

2003 ◽  
Vol 127 (3) ◽  
pp. 573-579 ◽  
Author(s):  
H. D Li ◽  
L. He
Keyword(s):  
Computational Study ◽  
Three Dimensional ◽  
Forced Response ◽  
Navier Stokes ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
Single Passage ◽  
Finite Volume Discretization ◽  
Shape Correction ◽  
Gap Spacing

One of the outstanding issues in turbomachinery aeromechanic analysis is the intrarow interaction effects. The present work is aimed at a systematic examination of rotor-stator gap effects on blade aerodynamic damping by using a three-dimensional (3D) time-domain single-passage Navier-Stokes solver. The method is based on the upwind finite volume discretization and the single-passage shape-correction approach with enhanced accuracy and efficiency for unsteady transonic flows prediction. A significant speedup (by a factor of 20) over to a conventional whole annulus solution has been achieved. A parametric study with different rotor-stator gaps (56%–216% rotor tip chord) for a 3D transonic compressor stage illustrates that the reflection from an adjacent stator row can change rotor aerodynamic damping by up to 100% depending on the intrarow gap spacing. Furthermore, this rotor aerodamping dependency on the intrarow gap seems also to be affected by the number of stator blades. The predicted nonmonotonic relationship between the rotor blade aerodynamic damping and the gap spacing suggests the existence of an optimum gap regarding rotor flutter stability and/or forced response stress levels.

Inviscid-Viscous Interaction Analysis of Compressor Cascade Performance

1990 ◽  
Author(s):  
M. Barnett ◽  
D. E. Hobbs ◽  
D. E. Edwards
Keyword(s):  
Interaction Analysis ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Interaction Technique ◽  
Transonic Compressor ◽  
Viscous Interaction ◽  
Pressure Distributions

An inviscid-viscous interaction technique for the analysis of quasi-three-dimensional turbomachinery cascades has been developed. The inviscid flow is calculated using a time-marching, multiple-grid Euler analysis. An inverse, finite-difference viscous-layer analysis, which includes the wake, is employed so that boundary-layer separation can be modeled. This analysis has been used to predict the performance of a transonic compressor cascade over the entire incidence range. The results of the numerical investigation in the form of cascade total pressure loss, exit gas angle and blade pressure distributions are compared with existing experimental data and Navier-Stokes solutions for this cascade, and show that this inviscid-viscous interaction procedure is able to accurately predict cascade loss and airfoil pressure distributions. Several other aspects of the present interaction analysis are examined, including transition and wake modeling, through comparisons with data.

Inviscid-Viscous Interaction Analysis of Compressor Cascade Performance

1991 ◽  
Vol 113 (4) ◽  
pp. 538-552 ◽  
Author(s):  
M. Barnett ◽  
D. E. Hobbs ◽  
D. E. Edwards
Keyword(s):  
Interaction Analysis ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Interaction Technique ◽  
Transonic Compressor ◽  
Viscous Interaction ◽  
Pressure Distributions

An inviscid-viscous interaction technique for the analysis of quasi-three-dimensional turbomachinery cascades has been developed. The inviscid flow is calculated using a time-marching, multiple-grid Euler analysis. An inverse, finite-difference viscous-layer analysis, which includes the wake, is employed so that boundary layer separation can be modeled. This analysis has been used to predict the performance of a transonic compressor cascade over the entire incidence range. The results of the numerical investigation in the form of cascade total pressure loss, exit gas angle, and blade pressure distributions are compared with existing experimental data and Navier–Stokes solutions for this cascade, and show that this inviscid-viscous interaction procedure is able to predict cascade loss and airfoil pressure distributions accurately. Several other aspects of the present interaction analysis are examined, including transition and wake modeling, through comparisons with data.

scholarly journals Three-Dimensional Numerical Study of the Effect of Protective Barrier on the Dispersion of the Contaminant in a Building

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1125
Author(s):  
Chemseddine Maatki
Keyword(s):  
Rayleigh Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vorticity Vector ◽  
Volume Method ◽  
The Impact ◽  
Buoyancy Ratio

The finite volume method and potential-vorticity vector formalism in their three-dimensional form were used to numerically study the impact of an adiabatic and impermeable vertical barrier on the dispersion of a local aero-contaminant due to the double-diffusive Rayleigh–Benard convection inside a cubic container. Different governing parameters such as the Rayleigh number, buoyancy ratio and barrier height were analyzed for Le = 1.2 and Pr = 0.7, representing an air-contaminant mixture. The potential-vector-vorticity formalism in the three-dimensional form allowed the elimination of the pressure terms appearing in the Navier–Stokes equations. It was found that the heat and mass transfer as well as the effectiveness of the barrier in reducing contaminant dispersion are strongly influenced by the buoyancy ratio, the barrier size and the Rayleigh number. In addition, the barrier effectiveness is more than 70% for a height of half the building height.

Viscous Flow Computations on a Smooth Cylinders: A Detailed Numerical Study With Validation

2007 ◽  
Author(s):  
Guilherme Vaz ◽  
Christophe Mabilat ◽  
Remmelt van der Wal ◽  
Paul Gallagher
Keyword(s):  
Experimental Data ◽  
Viscous Flow ◽  
Numerical Study ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Detached Eddy Simulation ◽  
Time Step ◽  
Drag Forces

The objective of this paper is to investigate several numerical and modelling features that the CFD community is currently using to compute the flow around a fixed smooth circular cylinder. Two high Reynolds numbers, 9 × 104 and 5 × 105, are chosen which are in the so called drag-crisis region. Using a viscous flow solver, these features are assessed in terms of quality by comparing the numerical results with experimental data. The study involves grid sensitivity, time step sensitivity, the use of different turbulence models, three-dimensional effects, and a RANS/DES (Reynolds Averaged Navier Stokes, Detached Eddy Simulation) comparison. The resulting drag forces and Strouhal numbers are compared with experimental data of different sources. Major flow features such as velocity and vorticity fields are presented. One of the main conclusions of the present study is that all models predict forces which are far from the experimental values, particularly for the higher Reynolds numbers in the drag-crisis region. Three-dimensional and unsteadiness effects are present, but are only fully captured by sophisticated turbulence models or by DES. DES seems to be the key to better solve the flow problem and obtain better agreement with experimental data. However, its considerable computational demands still do not allow to use it for engineering design purposes.

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