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.

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.

Turbulent boundary-layer structure in supersonic flow

1991 ◽  
Vol 336 (1641) ◽  
pp. 81-93 ◽  
Keyword(s):  
Experimental Data ◽  
Supersonic Flow ◽  
Boundary Layers ◽  
Large Scale ◽  
Layer Structure ◽  
Turbulent Boundary Layers ◽  
Recent Experimental Data ◽  
Physical Mechanisms ◽  
Compressible Boundary Layers ◽  
Reynolds Number Dependence

A summary is given of the recent experimental data on the structure of turbulent boundary layers in supersonic flow. The physical mechanisms differentiating incompressible and compressible boundary layers are discussed, and a simple model for the Mach and Reynolds number dependence of the decay of the large-scale motions is proposed.

Numerical Verification of Scaling Laws for Shock-Boundary Layer Interactions in Arbitrary Gases

1997 ◽  
Vol 119 (1) ◽  
pp. 67-73 ◽  
Author(s):  
M. S. Cramer ◽  
S. H. Park ◽  
L. T. Watson
Keyword(s):  
Boundary Layer ◽  
Scaling Laws ◽  
Plate Boundary ◽  
Strong Support ◽  
Ideal Gas ◽  
Numerical Verification ◽  
Dense Gases ◽  
Ideal Gas Law ◽  
Dimensional Interaction ◽  
Wide Range

The steady, two-dimensional interaction of an oblique shock with a laminar flat-plate boundary layer has been examined through use of the Beam-Warming implicit scheme. A wide range of fluids is considered as are freestream pressures corresponding to dense gases, i.e., gases at pressures which are so large that the ideal gas law is no longer accurate. The results, when combined with the triple-deck theory of Kluwick (1994), provides strong support for the idea that the classical scaling laws can be extended to dense gases.

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.

Classical Boundary-Layer Theory

2018 ◽  
Author(s):  
Anatoly I. Ruban
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Boundary Layer Theory ◽  
Laminar Jet ◽  
Compressible Boundary Layers ◽  
Wedge Surface ◽  
Blasius Boundary Layer ◽  
Classical Boundary ◽  
Fast Rotating

Chapter 1 discusses the flows that can be described in the framework of Prandtl’s 1904 classical boundary-layer theory, including the Blasius boundary layer on a flat plate and the Falkner–Skan solutions for the boundary layer on a wedge surface. It presents Schlichting’s solution for the laminar jet and Tollmien’s solution for the viscous wake. These are followed by analysis of Chapman’s shear layer performed with the help of Prandtl’s transposition theorem. It also considers the boundary layer on the surface of a fast rotating cylinder with the purpose of linking the circulation around the cylinder with the speed of its rotation. It concludes discussion of the classical boundary-layer theory with analysis of compressible boundary layers, including the interactive boundary layers in hypersonic flows.

scholarly journals Separated rows structure of vortex streets behind triangular objects

2019 ◽  
Vol 862 ◽  
pp. 216-226
Author(s):  
Ildoo Kim
Keyword(s):  
Boundary Layer ◽  
Thin Layer ◽  
Boundary Layers ◽  
Experimental Studies ◽  
Soap Film ◽  
Separation Distance ◽  
Two Dimensional ◽  
Spatial Structures ◽  
Physical Mechanisms ◽  
Vortex Streets

We discuss two distinct spatial structures of vortex streets. The ‘conventional mushroom’ structure is commonly discussed in many experimental studies, and the exotic ‘separated rows’ structure is characterized by a thin layer of irrotational fluid between two rows of vortices. In a two-dimensional soap film channel, we generate the exotic vortex arrangement by using triangular objects. This setting allows us to vary the thickness of boundary layers and their separation distance independently. We find that the separated rows structure appears only when the boundary layer is thinner than 40 % of the separation distance. We also discuss two physical mechanisms of the breakdown of vortex structures. The conventional mushroom structure decays due to the mixing, and the separated rows structure decays because its arrangement is hydrodynamically unstable.

scholarly journals Direct numerical simulation of Taylor–Couette flow with grooved walls: torque scaling and flow structure

2016 ◽  
Vol 794 ◽  
pp. 746-774 ◽  
Author(s):  
Xiaojue Zhu ◽  
Rodolfo Ostilla-Mónico ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Couette Flow ◽  
Boundary Layer Thickness ◽  
Scaling Laws ◽  
Scaling Law ◽  
Smooth Wall ◽  
Secondary Circulations ◽  
Taylor Couette ◽  
Taylor Couette Flow

We present direct numerical simulations of Taylor–Couette flow with grooved walls at a fixed radius ratio ${\it\eta}=r_{i}/r_{o}=0.714$ with inner cylinder Reynolds number up to $Re_{i}=3.76\times 10^{4}$, corresponding to Taylor number up to $Ta=2.15\times 10^{9}$. The grooves are axisymmetric V-shaped obstacles attached to the wall with a tip angle of 90°. Results are compared to the smooth wall case in order to investigate the effects of grooves on Taylor–Couette flow. We focus on the effective scaling laws for the torque, flow structures, and boundary layers. It is found that, when the groove height is smaller than the boundary layer thickness, the torque is the same as that of the smooth wall cases. With increasing $Ta$, the boundary layer thickness becomes smaller than the groove height. Plumes are ejected from the tips of the grooves and secondary circulations between the latter are formed. This is associated with a sharp increase of the torque, and thus the effective scaling law for the torque versus $Ta$ becomes much steeper. Further increasing $Ta$ does not result in an additional slope increase. Instead, the effective scaling law saturates to the ‘ultimate’ regime effective exponents seen for smooth walls. It is found that even though after saturation the slope is the same as for the smooth wall case, the absolute value of torque is increased, and more so with the larger size of the grooves.

Unsteady heat transfer in compressible boundary layers

1965 ◽  
Vol 61 (2) ◽  
pp. 555-567 ◽  
Author(s):  
N. Riley
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Steady State ◽  
Boundary Layers ◽  
Laminar Boundary Layer ◽  
Wall Temperature ◽  
Sudden Change ◽  
General Boundary ◽  
Unsteady Heat Transfer ◽  
Compressible Boundary Layers

AbstractThe flow following a sudden change in the wall temperature in a laminar boundary layer, which was originally incompressible and steady, is studied. The temperature to which the wall is raised is supposed large enough to bring about density changes in the boundary layer. The details of the flow immediately after the change in wall temperature are analysed for a general boundary layer. Two specific examples are considered and for these the manner in which the new steady state is achieved is also investigated.

Momentum Thickness Measurements for Thick Axisymmetric Turbulent Boundary Layers

2003 ◽  
Vol 125 (3) ◽  
pp. 569-575 ◽  
Author(s):  
Kimberly M. Cipolla ◽  
William L. Keith
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Boundary Layers ◽  
Control Volume ◽  
Scaling Law ◽  
Reynolds Numbers ◽  
Momentum Thickness ◽  
Spatial Growth ◽  
Thickness Measurements

Experimental measurements of the mean wall shear stress and boundary layer momentum thickness on long, thin cylindrical bodies are presented. To date, the spatial growth of the boundary layer and the related boundary layer parameters have not been measured for cases where δ/a (a=cylinder radius) is much greater than one. Moderate Reynolds numbers 104<Reθ<105 encountered in hydrodynamic applications are considered. Tow tests of cylinders with diameters of 0.61, 0.89, and 2.5 mm and lengths ranging from approximately 30 meters to 150 meters were performed. The total drag (axial force) was measured at tow speeds up to 17.4 m/sec. These data were used to determine the tangential drag coefficients on each test specimen, which were found to be two to three times greater than the values for the corresponding hypothetical flat-plate cases. Using the drag measurements, the turbulent boundary layer momentum thickness at the downstream end of the cylindrical bodies is determined, using a control volume analysis. The results show that for the smallest diameter cylinders, there is no indication of relaminarization, and a fully developed turbulent boundary layer exists. A scaling law for the momentum thickness versus length Reynolds number is determined from the data. The results indicate that the spatial growth of the boundary layers over the entire length is less than for a comparable flat-plate case.

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