The Design of Shock-Free Compressor Cascades Including Viscous Boundary-Layer Effects

1988 ◽  
Vol 110 (3) ◽  
pp. 354-362 ◽  
Author(s):  
A. A. Hassan
Keyword(s):  
Boundary Layer ◽  
Numerical Procedure ◽  
Transition To Turbulence ◽  
Viscous Effects ◽  
Compressor Blades ◽  
Viscous Boundary Layer ◽  
Design Algorithm ◽  
Transonic Compressor ◽  
Coupling Procedure ◽  
Hodograph Plane

A numerical procedure has been developed for the design of shock-free transonic compressor cascades with an allowance for viscous effects, providing that the boundary layer is fully attached over the blade. The method described combines, in an iterative process, a modified inviscid hodograph-based inverse-design algorithm (CIDA), originally developed by the author for the design of shock-free airfoils, and the inverse boundary-layer algorithm (LTBLCEQL) of Miner et al. [22]. In the numerical procedure, the inviscid subsonic and supersonic regions of the flow are decoupled allowing the solution of either an elliptic or hyperbolic-type partial differential equation for the full stream function. For the subcritical portion of the flow, the inviscid calculation is performed in a computational plane which is obtained through a sequence of conformal and numerical transformations of the two-sheeted hodograph plane. For the supercritical portion, a characteristic calculation is carried out in the hodograph plane. The results are then mapped back to the physical plane to determine the inviscid blade configuration. Viscous effects are then incorporated via the boundary-layer displacement surface concept. The boundary-layer algorithm incorporates a two-layer eddy viscosity turbulence model and allows for gradual, rather than instantaneous, transition to turbulence. Two examples of shock-free compressor blades are given to demonstrate the capabilities of the numerical coupling procedure.

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

1990 ◽  
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.

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.

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

1987 ◽  
Vol 109 (1) ◽  
pp. 83-90 ◽  
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.

Design of Shock-Free Compressor Cascades Including Viscous Boundary Layer Effects

1983 ◽  
Author(s):  
George S. Dulikravich ◽  
Helmut Sobieczky
Keyword(s):  
Boundary Layer ◽  
Solution Process ◽  
Full Potential ◽  
Compressor Cascade ◽  
Viscous Boundary Layer ◽  
Integral Boundary ◽  
Potential Equation ◽  
Transonic Compressor ◽  
Viscosity Effects ◽  
Displacement Thickness

A computer code that generates shock-free transonic compressor cascade shapes while taking into account viscosity effects is developed. The mathematical model for the inviscid flow field is the full potential equation. The Kutta-Joukowski condition is satisfied by varying the free stream angle at downstream infinity. A boundary fitted computational grid of C-type is generated using a sequence of conformal mapping and nonorthogonal coordinate stretching and shearing transformations. The inviscid calculation is performed sequentially on up to four consecutively refined grids thereby accelerating the convergence of the solution process. The full potential equation is solved using a finite area technique and rotated, type-dependent finite differencing. Artificial viscosity of the first order is added in a fully conservative form. Shock-free cascade airfoil shapes are obtained using the fictitious gas concept of Sobieczky and the method of characteristics in the rheograph plane. Viscosity effects are incorporated via a boundary layer displacement thickness. The integral boundary layer code is based on Rotta’s turbulence model and assumes transition region of zero length.

scholarly journals Turbulence dynamics near a turbulent/non-turbulent interface

2012 ◽  
Vol 695 ◽  
pp. 257-287 ◽  
Author(s):  
M. A. C. Teixeira ◽  
C. B. da Silva
Keyword(s):  
Boundary Layer ◽  
Scaling Law ◽  
Tangential Velocity ◽  
Flow Region ◽  
Inviscid Flow ◽  
Normal Velocity ◽  
Viscous Effects ◽  
Viscous Boundary Layer ◽  
Velocity Variances ◽  
Viscous Boundary

AbstractThe characteristics of the boundary layer separating a turbulence region from an irrotational (or non-turbulent) flow region are investigated using rapid distortion theory (RDT). The turbulence region is approximated as homogeneous and isotropic far away from the bounding turbulent/non-turbulent (T/NT) interface, which is assumed to remain approximately flat. Inviscid effects resulting from the continuity of the normal velocity and pressure at the interface, in addition to viscous effects resulting from the continuity of the tangential velocity and shear stress, are taken into account by considering a sudden insertion of the T/NT interface, in the absence of mean shear. Profiles of the velocity variances, turbulent kinetic energy (TKE), viscous dissipation rate ($\varepsilon $), turbulence length scales, and pressure statistics are derived, showing an excellent agreement with results from direct numerical simulations (DNS). Interestingly, the normalized inviscid flow statistics at the T/NT interface do not depend on the form of the assumed TKE spectrum. Outside the turbulent region, where the flow is irrotational (except inside a thin viscous boundary layer),$\varepsilon $decays as${z}^{\ensuremath{-} 6} $, where$z$is the distance from the T/NT interface. The mean pressure distribution is calculated using RDT, and exhibits a decrease towards the turbulence region due to the associated velocity fluctuations, consistent with the generation of a mean entrainment velocity. The vorticity variance and$\varepsilon $display large maxima at the T/NT interface due to the inviscid discontinuities of the tangential velocity variances existing there, and these maxima are quantitatively related to the thickness$\delta $of the viscous boundary layer (VBL). For an equilibrium VBL, the RDT analysis suggests that$\delta \ensuremath{\sim} \eta $(where$\eta $is the Kolmogorov microscale), which is consistent with the scaling law identified in a very recent DNS study for shear-free T/NT interfaces.

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.

On the Importance of Transition Control at Transonic Compressor Blades

2019 ◽  
Author(s):  
A. Hergt ◽  
J. Klinner ◽  
S. Grund ◽  
C. Willert ◽  
W. Steinert ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
High Speed ◽  
Experimental Investigations ◽  
Compressor Cascade ◽  
Compressor Blades ◽  
Transition Control ◽  
Transonic Compressor ◽  
Air Jet ◽  
Loss Level

Abstract The flow through a transonic compressor cascade is characterized by high unsteadiness and a high loss level. This results from the shock waves in the blade cascade and their interaction with the blade suction side boundary layer. In the case of a laminar shock wave boundary layer interaction the loss level is higher due to the occurrence of a laminar separation bubble below the shock wave compared to the shock wave interaction with a turbulent boundary layer. In addition, the oscillation of the shock position in both cases influences the working range concerning the point of stall onset as well as leading to an unsteady interaction with the blade, called buffeting. The reduction of losses and of unsteadiness in the shock wave oscillation, connected to a decrease of the blade buffeting effect, are the aims of the current investigation. Therefore, experimental investigations using a roughness patch as well as air jet vortex generators in order to control the transition in a transonic compressor cascade have been conducted at the transonic cascade wind tunnel of DLR at Cologne. At an inflow Mach number of 1.21 a loss reduction for both transition control cases is achieved. In spite of a nearly uninfluenced fluctuation range of the passage shock wave compared to the reference cascade, the oscillation spectra of the transition control cases show a reduction of the shock movement amplitude at a frequency below 500 Hz and above 1 kHz. In the closing section of the paper a detailed discussion on the reasons for the resulting flow behaviour based on PIV and High Speed Shadowgraphy data is given. The resulting conclusion of the study is that the consideration of transition control at transonic compressor blades is very important in order to reduce losses and flow unsteadiness which directly influences blade buffeting and the numerical prediction quality of the stall onset.

EXPERIMENTAL INVESTIGATION OF FLOW RESPONSE TO STATIONARY DISTURBANCE IN ROTATING-DISK FLOW

2019 ◽  
Vol XVI (2) ◽  
pp. 13-22
Author(s):  
Muhammad Ehtisham Siddiqui
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Careful Analysis ◽  
Laboratory Frame ◽  
Transition To Turbulence ◽  
Turbulent Regime ◽  
Mean Velocity ◽  
Layer Flow

Three-dimensional boundary-layer flow is well known for its abrupt and sharp transition from laminar to turbulent regime. The presented study is a first attempt to achieve the target of delaying the natural transition to turbulence. The behaviour of two different shaped and sized stationary disturbances (in the laboratory frame) on the rotating-disk boundary layer flow is investigated. These disturbances are placed at dimensionless radial location (Rf = 340) which lies within the convectively unstable zone over a rotating-disk. Mean velocity profiles were measured using constant-temperature hot-wire anemometry. By careful analysis of experimental data, the instability of these disturbance wakes and its estimated orientation within the boundary-layer were investigated.

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