Spatial optimal growth in three-dimensional compressible boundary layers

2012 ◽  
Vol 704 ◽  
pp. 251-279 ◽  
Author(s):  
David Tempelmann ◽  
Ardeshir Hanifi ◽  
Dan S. Henningson
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Optimal Growth ◽  
Flat Plates ◽  
Curvature Effects ◽  
Physical Mechanisms ◽  
Compressible Boundary Layers ◽  
Incompressible Boundary

AbstractThis paper represents a continuation of the work by Tempelmann et al. (J. Fluid Mech., vol. 646, 2010b, pp. 5–37) on spatial optimal growth in incompressible boundary layers over swept flat plates. We present an extension of the methodology to compressible flow. Also, we account for curvature effects. Spatial optimal growth is studied for boundary layers over both flat and curved swept plates with adiabatic and cooled walls. We find that optimal growth increases for higher Mach numbers. In general, extensive non-modal growth is observed for all boundary layer cases even in subcritical regions, i.e. where the flow is stable with respect to modal crossflow disturbances. Wall cooling, despite stabilizing crossflow modes, destabilizes disturbances of non-modal nature. Curvature acts similarly on modal as well as non-modal disturbances. Convex walls have a stabilizing effect on the boundary layer whereas concave walls have a destabilizing effect. The physical mechanisms of optimal growth in all studied boundary layers are found to be similar to those identified for incompressible flat-plate boundary layers.

Correlated incompressible and compressible boundary layers

1949 ◽  
Vol 200 (1060) ◽  
pp. 84-100 ◽  
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Boundary Layers ◽  
Absolute Temperature ◽  
Stream Velocity ◽  
Main Stream ◽  
Boundary Layer Equations ◽  
Compressible Boundary Layers ◽  
Incompressible Boundary ◽  
Similar Solutions

The boundary-layer equations for a compressible fluid are transformed into those for an incompressible fluid, assuming that the boundary is thermally insulating, that the viscosity is proportional to the absolute temperature, and that the Prandtl number is unity. Various results in the theory of incompressible boundary layers are then taken over into the compressible theory. In particular, the existence of ‘similar’ solutions is proved, and Howarth’s method for retarded flows is applied to determine the point of separation for a uniformly retarded main stream velocity. A comparison with an exact solution is used to show that this method gives a closer approximation than does Pohlhausen’s.

scholarly journals Entrainment of short-wavelength free-stream vortical disturbances in compressible and incompressible boundary layers

2016 ◽  
Vol 797 ◽  
pp. 683-728 ◽  
Author(s):  
Xuesong Wu ◽  
Ming Dong
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Free Stream ◽  
Base Flow ◽  
Bypass Transition ◽  
Leading Order ◽  
Compressible Boundary Layers ◽  
Characteristic Wavelength ◽  
Incompressible Boundary ◽  
Edge Layer

The fundamental difference between continuous modes of the Orr–Sommerfeld/Squire equations and the entrainment of free-stream vortical disturbances (FSVD) into the boundary layer has been investigated in a recent paper (Dong & Wu, J. Fluid Mech., vol. 732, 2013, pp. 616–659). It was shown there that the non-parallel-flow effect plays a leading-order role in the entrainment, and neglecting it at the outset, as is done in the continuous-mode formulation, leads to non-physical features of ‘Fourier entanglement’ and abnormal anisotropy. The analysis, which was for incompressible boundary layers and for FSVD with a characteristic wavelength of the order of the local boundary-layer thickness, is extended in this paper to compressible boundary layers and FSVD with even shorter wavelengths, which are comparable with the width of the so-called edge layer. Non-parallelism remains a leading-order effect in the present scaling, which turns out to be more general in that the equations and solutions in the previous paper are recovered in the appropriate limit. Appropriate asymptotic solutions in the main and edge layers are obtained to characterize the entrainment. It is found that when the Prandtl number $\mathit{Pr}<1$, free-stream vortical disturbances of relatively low frequency generate very strong temperature fluctuations within the edge layer, leading to formation of thermal streaks. A composite solution, uniformly valid across the entire boundary layer, is constructed, and it can be used in receptivity studies and as inlet conditions for direct numerical simulations of bypass transition. For compressible boundary layers, continuous spectra of the disturbance equations linearized about a parallel base flow exhibit entanglement between vortical and entropy modes, namely, a vortical mode necessarily induces an entropy disturbance in the free stream and vice versa, and this amounts to a further non-physical behaviour. High Reynolds number asymptotic analysis yields the relations between the amplitudes of entangled modes.

Boundary Layer Calculation Including the Prediction of Transition and Curvature Effects

1989 ◽  
Author(s):  
B. Guyon ◽  
T. Arts
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Convex Surface ◽  
Turbine Blades ◽  
Operating Conditions ◽  
Detailed Knowledge ◽  
Flat Plates ◽  
Transfer Rates ◽  
Curvature Effects

The calculation of surface temperature on gas turbine blades in severe operating conditions requires a detailed knowledge of boundary layers behaviour. The prediction of laminar to turbulent transition as to existence and location, as well as the evaluation of heat transfer rates are major concerns. The program developed by SNECMA for this purpose is presented, in which models are introduced to take into account the main effects occuring on blades without film-cooling. The algorithm and discretisation scheme for boundary layer equations is Patankar and Spalding’s, with profiles initialization by Pohlhausen’s method. The turbulence and transition model, after Mc Donald and Fish, was improved in search for more stability and to have a better detection of the beginning of the transition. Adams and Johnston’s model for curvature, including propagation effects, was adapted to a transitional boundary layer. The validation tests of this program are described, which are based on numerous experimental data taken from a bibliography of tests over flat plates and blades. Other tests use heat transfer rate measurements conducted by SNECMA, together with VKI, on vanes and blades in non-rotating grids. The calculation results are further compared to the STAN5 program results; they show a superiority in predicting the transfer rates on a convex surface and for transitional boundary layers.

A Theory for Boundary Layer Growth on the Blades of a Radial Impeller Including Endwall Influence

1983 ◽  
Vol 105 (3) ◽  
pp. 403-411
Author(s):  
H. Ekerol ◽  
J. W. Railly
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Prediction Method ◽  
Suction Side ◽  
Layer Growth ◽  
Secondary Flows ◽  
Curvature Effects ◽  
Momentum Integral ◽  
Boundary Layer Growth

Experimental data on the wall shear stress of a turbulent boundary layer on the suction side of a blade in a two-dimensional radial impeller is compared with the predictions of a theory which takes account of rotation and curvature effects as well as the three-dimensional influence of the endwall boundary layers. The latter influence is assumed to arise mainly from mainstream distortion due to secondary flows created by the endwall boundary layers, and it appears as an extra term in the momentum integral equation of the blade boundary layer which has allowance, also for the Coriolis effect; an appropriate form of the Head entrainment equation is derived to obtain a solution and a comparison made. A comparison of the above theory with the Patankar-Spalding prediction method, modified to include the effects of Coriolis (including mixing length modification, MLM), is also made.

A Theory for Boundary Layer Growth on the Blades of a Radial Impeller Including End Wall Influence

1982 ◽  
Author(s):  
H. Ekerol ◽  
J. W. Railly
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Prediction Method ◽  
Suction Side ◽  
Layer Growth ◽  
Secondary Flows ◽  
Curvature Effects ◽  
Wall Boundary ◽  
End Wall

Experimental data on the wall shear stress of a turbulent boundary layer on the suction side of a blade in a two-dimensional radial impeller is compared with the predictions of a theory which takes account of rotation and curvature effects as well as the three-dimensional influence of the end-wall boundary layers. The latter influence is assumed to arise mainly from mainstream distortion due to secondary flows created by the end-wall boundary layers and it appears as an extra term in the momentum integral equation of the blade boundary layer which has allowance, also for the Coriolis effect; an appropriate form of the Head entrainment equation is derived to obtain a solution and a comparison made. A comparison of the above theory with the Patankar-Spalding prediction method, modified to include the effects of Coriolis (including mixing length modification, MLM) is also made.

Transonic and Boundary Layer Similarity Laws in Dense Gases

1996 ◽  
Vol 118 (3) ◽  
pp. 481-485 ◽  
Author(s):  
M. S. Cramer ◽  
S. T. Whitlock ◽  
G. M. Tarkenton
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Transonic Flow ◽  
Scaling Laws ◽  
Scaling Law ◽  
Small Disturbance ◽  
Physical Mechanisms ◽  
Dense Gases ◽  
Compressible Boundary Layers ◽  
Similarity Laws

We discuss the validity of similarity and scaling laws for transonic flow and compressible boundary layers when dense gas effects are important. The physical mechanisms for the failure of each class of scaling law are delineated. In the case of transonic flow, a new similitude based on a modified small disturbance equation is presented.

Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers

1995 ◽  
Vol 291 ◽  
pp. 369-392 ◽  
Author(s):  
Ronald D. Joslin
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simulation Results ◽  
Dimensional Simulation ◽  
Attachment Line

The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier–Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic-source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in flat-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.

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.

scholarly journals On the role of acoustic feedback in boundary-layer instability

2014 ◽  
Vol 372 (2020) ◽  
pp. 20130347 ◽  
Author(s):  
Xuesong Wu
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Acoustic Waves ◽  
Feedback Loop ◽  
Peak Frequency ◽  
S Wave ◽  
Flat Plates ◽  
Acoustic Coupling ◽  
Acoustic Feedback ◽  
Roughness Elements

In this paper, the classical triple-deck formalism is employed to investigate two instability problems in which an acoustic feedback loop plays an essential role. The first concerns a subsonic boundary layer over a flat plate on which two well-separated roughness elements are present. A spatially amplifying Tollmien–Schlichting (T–S) wave between the roughness elements is scattered by the downstream roughness to emit a sound wave that propagates upstream and impinges on the upstream roughness to regenerate the T–S wave, thereby forming a closed feedback loop in the streamwise direction. Numerical calculations suggest that, at high Reynolds numbers and for moderate roughness heights, the long-range acoustic coupling may lead to absolute instability, which is characterized by self-sustained oscillations at discrete frequencies. The dominant peak frequency may jump from one value to another as the Reynolds number, or the distance between the roughness elements, is varied gradually. The second problem concerns the supersonic ‘twin boundary layers’ that develop along two well-separated parallel flat plates. The two boundary layers are in mutual interaction through the impinging and reflected acoustic waves. It is found that the interaction leads to a new instability that is absent in the unconfined boundary layer.

scholarly journals An Application of Octant Analysis to Turbulent and Transitional Flow Data

1993 ◽  
Author(s):  
Ralph J. Volino ◽  
Terrence W. Simon
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Boundary Layer Transition ◽  
Transitional Flow ◽  
Heated Wall ◽  
Turbulent Shear ◽  
Stream Velocity ◽  
Turbulent Heat ◽  
Flat Plates

A technique called “octant analysis” was used to examine the eddy structure of turbulent and transitional heated boundary layers on flat and curved surfaces. The intent was to identify important physical processes that play a role in boundary layer transition on flat and concave surfaces. Octant processing involves the partitioning of flow signals into octants based on the instantaneous signs of the fluctuating temperature, t′; streamwise velocity, u′; and cross-stream velocity, v′. Each octant is associated with a particular eddy motion. For example, u′<0, v′>0, t′>0 is associated with an ejection or “burst” of warm fluid away from a heated wall. Within each octant, the contribution to various quantities of interest (such as the turbulent shear stress, −u′v′, or the turbulent heat flux, v′t′) can be computed. By comparing and contrasting the relative contributions from each octant, the importance of particular types of motion can be determined. If the data within each octant is further segregated based on the magnitudes of the fluctuating components so that minor events are eliminated, the relative importance of particular types of motion to the events that are important can also be discussed. In fully-developed, turbulent boundary layers along flat plates, trends previously reported in the literature were confirmed. A fundamental difference was observed in the octant distribution between the transitional and fully-turbulent boundary layers, however, showing incomplete mixing and a lesser importance of small scales in the transitional boundary layer. Such observations were true on both flat and concave walls. The differences are attributed to incomplete development of the turbulent kinetic energy cascade in transitional flows. The findings have potential application to modelling, suggesting the utility of incorporating multiple length scales in transition models.

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