Axially Symmetric Laminar Free Mixing With Large Swirl

1962 ◽  
Vol 84 (4) ◽  
pp. 370-374 ◽  
Author(s):  
Martin H. Steiger ◽  
Martin H. Bloom
Keyword(s):  
Boundary Layer ◽  
Compressible Flow ◽  
Free Stream ◽  
A Priori ◽  
Radial Pressure ◽  
Pressure Gradients ◽  
Axially Symmetric ◽  
Axial Pressure ◽  
Integral Methods ◽  
Special Case

Viscous laminar axially symmetric free mixing with large swirl is investigated by a boundary-layer type of analysis with integral methods. Large swirl generates axial pressure gradients as well as large radial pressure gradients, and therefore alters the streamwise flow. Examples calculated for both incompressible and compressible flow show that the wake may be significantly lengthened by large swirl. However, this effect is shown to be diminished in the compressible case where higher free-stream Mach numbers lead to decreased densities, and to decreased centrifugal effects, decreased radial pressure gradients, and decreased axial pressure gradients. In the limiting special case of small or moderate swirl the results agree with those previously obtained by Steiger and Bloom [1] in analysis wherein the induced pressure gradients were neglected a priori.

Boundary Layer Effects in the Turbulent Spiral Vortex Flow of a Compressible Fluid

1968 ◽  
Vol 183 (1) ◽  
pp. 179-188 ◽  
Author(s):  
B. F. Scott
Keyword(s):  
Boundary Layer ◽  
Vortex Flow ◽  
Free Stream ◽  
Three Dimensional ◽  
Cross Flow ◽  
Radial Pressure ◽  
Vortex Chamber ◽  
Adiabatic Wall ◽  
Spiral Vortex ◽  
Momentum Integral

Because of the characteristically narrow impeller tip width in a proposed supersonic centrifugal compressor design, boundary layer effects in the vortex chamber are likely to be significant. The radial pressure gradient in the chambers sweeps retarded fluid towards the centre of curvature of the streamlines, thereby creating a ‘cross-flow’ in the boundary layer which is three-dimensional. Although the flow geometry has axial symmetry, the cross-flow is not independent of the streamwise flow. The momentum—integral method is adopted, together with assumptions concerning the velocity profiles; the energy equation is solved with the assumption of an adiabatic wall. Simultaneous solution of the free stream and boundary layer equations yields results emphasizing the critical dependence of the transverse deflection and growth of the boundary layer on the whirl component of the velocity. Separation cannot be predicted, but effects in the free stream can be estimated when the perturbations are small. Although the results are related to compressor performance, the method is generally applicable in situations where the idealizing assumption of spiral vortex flow is acceptable.

Boundary Layer Receptivity to Unsteady Free-Stream Pressure Gradients

1990 ◽  
pp. 426-439
Author(s):  
Roland A. E. Heinrich ◽  
Thomas B. Gatski ◽  
Edward J. Kerschen
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Pressure Gradients

Free-Stream Turbulence and Pressure Gradient Effects on Heat Transfer and Boundary Layer Development on Highly Cooled Surfaces

1985 ◽  
Vol 107 (1) ◽  
pp. 54-59 ◽  
Author(s):  
K. Rued ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Stream ◽  
Boundary Layer Transition ◽  
Pressure Gradients ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
Boundary Layer Development ◽  
Gradient Effects ◽  
Layer Development

Heat transfer and boundary layer measurements were derived from flows over a cooled flat plate with various free-stream turbulence intensities (Tu = 1.6–11 percent), favorable pressure gradients (k = νe/ue2•due/dx = 0÷6•10−6) and cooling intensities (Tw/Te = 1.0–0.53). Special interest is directed towards the effects of the dominant parameters, including the influence on laminar to turbulent boundary layer transition. It is shown, that free-stream turbulence and pressure gradients are of primary importance. The increase of heat transfer due to wall cooling can be explained primarily by property variations as transition, and the influence of free-stream parameters are not affected.

scholarly journals Similarity Behavior in Transitional Boundary Layers Over a Range of Adverse Pressure Gradients and Turbulence Levels

1990 ◽  
Author(s):  
J. P. Gostelow ◽  
G. J. Walker
Keyword(s):  
Boundary Layer ◽  
Form Factor ◽  
Velocity Profile ◽  
Transition Region ◽  
Boundary Layers ◽  
Free Stream ◽  
Local Equilibrium ◽  
Pressure Gradients ◽  
Lag Effects ◽  
Free Stream Turbulence

Boundary layer transition has been investigated experimentally under low, moderate and high free-stream turbulence levels and varying adverse pressure gradients. Under high turbulence levels and adverse pressure gradients a pronounced subtransition was present. A strong degree of similarity in intermittency distributions was observed, for all conditions, when the Narasimha procedure for determination of transition inception was used. Effects of free-stream turbulence on the velocity profile are particularly strong for the laminar boundary layer upstream of the transition region. This could reflect the influence of the turbulence on the shear stress distribution throughout the layer and this matter needs further attention. The velocity profiles in wall coordinates undershoot the turbulent wall layer asymptote near the wall over most of the transition region. The rapidity with which transition occurs under adverse pressure gradients produces strong lag effects on the velocity profile; the starting turbulent boundary layer velocity profile may depart significantly from local equilibrium conditions. The practice of deriving integral properties and skin friction for transitional boundary layers by a linear combination of laminar and turbulent values for equilibrium layers is inconsistent with the observed lag effects. The velocity profile responds sufficiently slowly to the perturbation imposed by transition that much of the anticipated drop in form factor will not have occurred prior to the completion of transition. This calls into question both experimental techniques which rely on measured form factor to characterize transition and boundary layer calculations which rely on local equilibrium assumptions in the vicinity of transition.

scholarly journals A Bypass Transition Model for Boundary Layers

1993 ◽  
Author(s):  
Mark W. Johnson
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Free Stream ◽  
Transition Model ◽  
Wall Region ◽  
Bypass Transition ◽  
Pressure Gradients ◽  
Turbulence Level ◽  
Velocity Fluctuations ◽  
Laminar Boundary Layers

Experimental data for laminar boundary layers developing below a turbulent free stream shows that the fluctuation velocities within the boundary layer increase in amplitude until some critical level is reached which initiates transition. In the near wall region, a simple model, containing a single empirical parameter which depends only on the turbulence level and length scale, is derived to predict the development of the velocity fluctuations in laminar boundary layers with favourable, zero or adverse pressure gradients. A simple bypass transition model which considers the streamline distortion in the near wall region brought about by the velocity fluctuations suggests that transition will commence when the local turbulence level reaches approximately 23%. This value is consistent with experimental findings. This critical local turbulence level is used to derive a bypass transition prediction formula which compares reasonably with start of transition experimental data for a range of pressure gradients (λθ = −0.01 to 0.01) and turbulence levels (Tu = 0.2% to 5%). Further improvement to the model is proposed through prediction of the boundary layer distortion, which occurs due to Reynolds stresses generated within the boundary layer at high free stream turbulence levels and also through inclusion of the effect of turbulent length scale as well as turbulence level.

scholarly journals Boundary Layer Transition of Strongly Concave Surfaces

1989 ◽  
Author(s):  
Stephen Riley ◽  
Mark W. Johnson ◽  
John C. Gibbings
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Boundary Layer Transition ◽  
Radius Of Curvature ◽  
Pressure Gradients ◽  
Flat Plates ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
Surface Data ◽  
Correlation Techniques

Boundary layer transition has been studied on two blades of constant 0.5 and 1 metre radius of curvature with free stream turbulence levels of 0.7%, 2.6% and 7.2%. Zero pressure gradients were used throughout. Strong Gortler vortices developed in the boundary layer which led to growth rates of up to ten times the flat plate rate. The boundary layer profile was also highly distorted by the vortices. Transition correlation techniques for flat plates proved totally inadequate for the concave surface data, but a method of obtaining correlations for these surfaces was suggested by considering the inner critical region of the boundary layer alone.

The Magnification of Roughness Drag by Pressure Gradients

1967 ◽  
Vol 71 (673) ◽  
pp. 44-46 ◽  
Author(s):  
J. F. Nash ◽  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Roughness Element ◽  
Dynamic Pressure ◽  
Subsequent Development ◽  
Adverse Pressure Gradient ◽  
Initial Boundary ◽  
Stream Velocity ◽  
Pressure Gradients ◽  
Roughness Elements

SummaryA simplified analysis indicates that the increase in profile drag of an aerofoil due to an isolated roughness element is, in general, different from the drag of the element measured on a flat plate with the same free-stream velocity. This “magnification” effect is caused chiefly by the effect of the pressure gradients on the boundary layer downstream of the roughness element.The degree of magnification is not closely approximated by the ratio of local to free-stream dynamic pressure and, in many typical cases, the contribution to the drag due to roughness elements may be seriously under-estimated in this way.Measurements of the effect of the initial boundary-layer thickness on the subsequent development of a turbulent boundary-layer in an adverse pressure gradient support the theoretical conclusions.

The Boundary Layer Inside a Conical Surface Due to Swirl

1956 ◽  
Vol 23 (4) ◽  
pp. 587-592
Author(s):  
H. E. Weber
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Free Stream ◽  
Swirl Flow ◽  
Conical Surface ◽  
Axially Symmetric ◽  
Dust Separator ◽  
Potential Vortex ◽  
Particle Paths ◽  
Theory And Experiment

Abstract An analysis of the axially symmetric boundary layer on the inside of a conical surface due to swirl flow about the conical axis is presented. The momentum integrals of the boundary layer are derived, and both the laminar and turbulent boundary-layer solutions are obtained numerically. In the free stream the flow is assumed to be a potential vortex. A comparison between theory and experiment is made by using the particle paths on the conical surface of a cyclone dust separator.

Bypass Transition Modelling: A New Method Which Accounts for Free-Stream Turbulence Intensity and Length Scale

2000 ◽  
Author(s):  
Paul E. Roach ◽  
David H. Brierley
Keyword(s):  
Boundary Layer ◽  
Turbulence Intensity ◽  
Free Stream ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Test Surface ◽  
Length Scale ◽  
Pressure Gradients ◽  
Layer Transition ◽  
Free Stream Turbulence

The publication of the present authors’ boundary layer transition data in 1992 (now widely known as the ERCOFTAC test case T3) has led to a spate of new experimental and modelling efforts aimed at improving our understanding of this problem. This paper describes a new method of determining boundary layer transition with zero mean pressure gradient. The approach examines the development of a laminar boundary layer to the start of transition, accounting for the influences of free-stream turbulence and test surface geometry. It is presented as a “proof of concept”, requiring a significant amount of work before it can be considered as a practically applicable model for transition prediction. The method is based upon one first put forward by G.I. Taylor in the 1930’s, and accounts for the action of local, instantaneous pressure gradients on the developing laminar boundary layer. These pressure gradients are related to the intensity and length scale of turbulence in the free-stream using Taylor’s simple isotropic model. The findings demonstrate the need to account for the separate influences of free-stream turbulence intensity and length scale when considering the transition process. Although the length scale has less of an effect than the intensity, its influence is, nevertheless, significant and must not be overlooked. This fact goes a long way towards explaining the large scatter to be found in simple correlations which involve only the turbulence intensity. Intriguingly, it is demonstrated that it is the free-stream turbulence at the leading edge of the test surface which is important, not that found locally outside the boundary layer. The additional influence of leading edge geometry is also shown to play a major role in fixing the point at which transition begins. It is suggested that the leading edge geometry will distort the incident turbulent eddies, modifying the effective “free-stream” turbulence properties. Consequently, it is shown that the scale of the eddies relative to the leading edge thickness is a further important parameter, and helps bring together a large number of test cases.

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