The Aerodynamic Significance of Fillet Geometry in Turbocompressor Blade Rows

1980 ◽  
Vol 102 (4) ◽  
pp. 984-993 ◽  
Author(s):  
L. L. Debruge
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Three Dimensional ◽  
Momentum Equation ◽  
Polyhedral Approximation ◽  
Corner Flow ◽  
Fillet Radius ◽  
Dimensional Boundary ◽  
Modified Power Law

This paper describes a theoretical investigation of the influence of fillet radius on the aerodynamic behavior of turbocompressors. The fillet is that found at the intersection of an airfoil and a hub or shroud where no relative motion or gap is present. A modified power law velocity is used in conjunction with experimental estimates of the three-dimensional corner boundary layer extent to obtain values of the interference displacement and friction coefficient for the 90 deg corner flow which are in fair agreement with Gersten’s experimental results. Likewise, interference displacement and friction coefficient are obtained in the case of a corner flow in a dihedral > 150 deg for which experimental data is unavailable but where the low curvature of the stream surfaces allows the three-dimensional boundary layer extent to be calculated from Bertotti’s integral momentum equation. The boundary layer characteristics thus obtained are then applied, by means of a polyhedral approximation, in the evaluation of the influence of 90 deg corner fillet on corner flow separation. Some guidelines are provided relating the fillet radius to physical dimensions of the blading.

Secondary instability of crossflow vortices and swept-wing boundary-layer transition

1999 ◽  
Vol 399 ◽  
pp. 85-115 ◽  
Author(s):  
MUJEEB R. MALIK ◽  
FEI LI ◽  
MEELAN M. CHOUDHARI ◽  
CHAU-LYAN CHANG
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Secondary Instability ◽  
Boundary Layer Transition ◽  
Swept Wing ◽  
Layer Transition ◽  
Transition Prediction ◽  
Dimensional Boundary

Crossflow instability of a three-dimensional boundary layer is a common cause of transition in swept-wing flows. The boundary-layer flow modified by the presence of finite-amplitude crossflow modes is susceptible to high-frequency secondary instabilities, which are believed to harbinger the onset of transition. The role of secondary instability in transition prediction is theoretically examined for the recent swept-wing experimental data by Reibert et al. (1996). Exploiting the experimental observation that the underlying three-dimensional boundary layer is convectively unstable, non-linear parabolized stability equations are used to compute a new basic state for the secondary instability analysis based on a two-dimensional eigenvalue approach. The predicted evolution of stationary crossflow vortices is in close agreement with the experimental data. The suppression of naturally dominant crossflow modes by artificial roughness distribution at a subcritical spacing is also confirmed. The analysis reveals a number of secondary instability modes belonging to two basic families which, in some sense, are akin to the ‘horseshoe’ and ‘sinuous’ modes of the Görtler vortex problem. The frequency range of the secondary instability is consistent with that measured in earlier experiments by Kohama et al. (1991), as is the overall growth of the secondary instability mode prior to the onset of transition (e.g. Kohama et al. 1996). Results indicate that the N-factor correlation based on secondary instability growth rates may yield a more robust criterion for transition onset prediction in comparison with an absolute amplitude criterion that is based on primary instability alone.

Generation of steady longitudinal vortices in hypersonic boundary layer

2013 ◽  
Vol 729 ◽  
pp. 702-731 ◽  
Author(s):  
A. I. Ruban ◽  
M. A. Kravtsova
Keyword(s):  
Boundary Layer ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Viscosity Coefficient ◽  
Momentum Equation ◽  
The Body ◽  
Nonlinear Behaviour ◽  
Hypersonic Boundary Layer ◽  
Stagnation Temperature ◽  
Characteristic Distance

AbstractIn this paper we study the three-dimensional perturbations produced in a hypersonic boundary layer by a small wall roughness. The flow analysis is performed under the assumption that the Reynolds number, $R{e}_{0} = {\rho }_{\infty } {V}_{\infty } L/ {\mu }_{0} $, and Mach number, ${M}_{\infty } = {V}_{\infty } / {a}_{\infty } $, are large, but the hypersonic interaction parameter, $\chi = { M}_{\infty }^{2} R{ e}_{0}^{- 1/ 2} $, is small. Here ${V}_{\infty } $, ${\rho }_{\infty } $ and ${a}_{\infty } $ are the flow velocity, gas density and speed of sound in the free stream, ${\mu }_{0} $ is the dynamic viscosity coefficient at the ‘stagnation temperature’, and $L$ is the characteristic distance the boundary layer develops along the body surface before encountering a roughness. We choose the longitudinal and spanwise dimensions of the roughness to be $O({\chi }^{3/ 4} )$ quantities. In this case the flow field around the roughness may be described in the framework of the hypersonic viscous–inviscid interaction theory, also known as the triple-deck model. Our main interest in this paper is the nonlinear behaviour of the perturbations. We study these by means of numerical solution of the triple-deck equations, for which purpose a modification of the ‘skewed shear’ technique suggested by Smith (United Technologies Research Center Tech. Rep. 83-46, 1983) has been used. The technique requires global iterations to adjust the viscous and inviscid parts of the flow. Convergence of such iterations is known to be a major problem in viscous–inviscid calculations. In order to achieve improved stability of the method, both the momentum equation for the viscous part of the flow, and the equations describing the interaction with the flow outside the boundary layer, are treated implicitly in this study. The calculations confirm the fact that in this sort of flow the perturbations are capable of propagating upstream in the boundary layer, resulting in a perturbation field which surrounds the roughness on all sides. We found that the perturbations decay rather fast with the distance from the roughness everywhere except in the wake behind the roughness. We found that if the height of the roughness is small, then the perturbations also decay in the wake, though much more slowly than outside the wake. However, if the roughness height exceeds some critical value, then two symmetric counter-rotating vortices form in the wake. They appear to support themselves and grow as the distance from the roughness increases.

An Assessment of Three-Dimensional Turbulent Boundary Layer Prediction Methods

1973 ◽  
Vol 95 (3) ◽  
pp. 415-421 ◽  
Author(s):  
A. J. Wheeler ◽  
J. P. Johnston
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Eddy Viscosity Model ◽  
Separating Flow ◽  
Dimensional Boundary ◽  
Stress Models

Predictions have been made for a variety of experimental three-dimensional boundary layer flows with a single finite difference method which was used with three different turbulent stress models: (i) an eddy viscosity model, (ii) the “Nash” model, and (iii) the “Bradshaw” model. For many purposes, even the simplest stress model (eddy viscosity) was adequate to predict the mean velocity field. On the other hand, the profile of shear stress direction was not correctly predicted in one case by any model tested. The high sensitivity of the predicted results to free stream pressure gradient in separating flow cases is demonstrated.

Experimental and Theoretical Investigation of the Supersonic Boundary Layer Stability on the Swept Wing

2008 ◽  
Vol 3 (3) ◽  
pp. 34-38
Author(s):  
Sergey A. Gaponov ◽  
Yuri G. Yermolaev ◽  
Aleksandr D. Kosinov ◽  
Nikolay V. Semionov ◽  
Boris V. Smorodsky
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Supersonic Boundary Layer ◽  
Mean Flow ◽  
Swept Wing ◽  
Wing Model ◽  
Dimensional Boundary ◽  
The Stability ◽  
Good Agreement

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

Review: Laminar-to-Turbulent Transition of Three-Dimensional Boundary Layers on Rotating Bodies

1994 ◽  
Vol 116 (2) ◽  
pp. 200-211 ◽  
Author(s):  
Ryoji Kobayashi
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Speed Ratio ◽  
Stream Velocity ◽  
Turbulent Transition ◽  
Centrifugal Instability ◽  
Crossflow Instability ◽  
Dimensional Boundary ◽  
Axisymmetric Bodies

The laminar-turbulent transition of three-dimensional boundary layers is critically reviewed for some typical axisymmetric bodies rotating in still fluid or in axial flow. The flow structures of the transition regions are visualized. The transition phenomena are driven by the compound of the Tollmien-Schlichting instability, the crossflow instability, and the centrifugal instability. Experimental evidence is provided relating the critical and transition Reynolds numbers, defined in terms of the local velocity and the boundary layer momentum thickness, to the local rotational speed ratio, defined as the ratio of the circumferential speed to the free-stream velocity at the outer edge of the boundary layer, for the rotating disk, the rotating cone, the rotating sphere and other rotating axisymmetric bodies. It is shown that the cross-sectional structure of spiral vortices appearing in the transition regions and the flow pattern of the following secondary instability in the case of the crossflow instability are clearly different than those in the case of the centrifugal instability.

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