Effect of free stream vorticity on spatial stability of incompressible boundary layers with nonparallel effects

1976 ◽  
Vol 19 (3) ◽  
pp. 362
Author(s):  
A. R. Wazzan
Keyword(s):  
Boundary Layers ◽  
Free Stream ◽  
Spatial Stability ◽  
Incompressible Boundary

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.

Effects of Embedded Vortices on Film-Cooled Turbulent Boundary Layers

1989 ◽  
Vol 111 (1) ◽  
pp. 71-77 ◽  
Author(s):  
P. M. Ligrani ◽  
A. Ortiz ◽  
S. L. Joseph ◽  
D. L. Evans
Keyword(s):  
Heat Transfer ◽  
Boundary Layers ◽  
Film Cooling ◽  
Free Stream ◽  
Flow Behavior ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Longitudinal Vortices

Heat transfer effects of longitudinal vortices embedded within film-cooled turbulent boundary layers on a flat plate were examined for free-stream velocities of 10 m/s and 15 m/s. A single row of film-cooling holes was employed with blowing ratios ranging from 0.47 to 0.98. Moderate-strength vortices were used with circulating-to-free stream velocity ratios of −0.95 to −1.10 cm. Spatially resolved heat transfer measurements from a constant heat flux surface show that film coolant is greatly disturbed and that local Stanton numbers are altered significantly by embedded longitudinal vortices. Near the downwash side of the vortex, heat transfer is augmented, vortex effects dominate flow behavior, and the protection from film cooling is minimized. Near the upwash side of the vortex, coolant is pushed to the side of the vortex, locally increasing the protection provided by film cooling. In addition, local heat transfer distributions change significantly as the spanwise location of the vortex is changed relative to film-cooling hole locations.

Recent Developments in Calculation Methods for Turbulent Boundary Layers With Pressure Gradients and Heat Transfer

1966 ◽  
Vol 33 (2) ◽  
pp. 429-437 ◽  
Author(s):  
J. C. Rotta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Distribution ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Calculation Methods ◽  
Recent Developments ◽  
Incompressible Boundary

A review is given of the recent development in turbulent boundary layers. At first, for the case of incompressible flow, the variation of the shape of velocity profile with the pressure gradient is discussed; also the temperature distribution and heat transfer in incompressible boundary layers are treated. Finally, problems of the turbulent boundary layer in compressible flow are considered.

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.

On the transient response of the turbulent boundary layer inception in compressible flows

2018 ◽  
Vol 850 ◽  
pp. 1117-1141 ◽  
Author(s):  
J. Saavedra ◽  
G. Paniagua ◽  
S. Lavagnoli
Keyword(s):  
Boundary Layer ◽  
Flow Control ◽  
Boundary Layers ◽  
Thermal Boundary Layer ◽  
Free Stream ◽  
Test Model ◽  
Additional Time ◽  
Time Required ◽  
Momentum Boundary Layer

The behavioural characteristics of thermal boundary layer inception dictate the efficiency of heat exchangers and the operational limits of fluid machinery. The specific time required by the thermal boundary layer to be established is vital to optimize flow control strategies, as well as the thermal management of systems exposed to ephemeral phenomena, typically on the millisecond scale. This paper presents the time characterization of the momentum and thermal boundary layer development in transient turbulent compressible air flows. We present a new framework to perform such estimations based on detailed unsteady Reynolds averaged Navier–Stokes simulations that may be extended to higher fidelity simulations. First of all, the aerodynamic boundary layer initiation is described using adiabatic simulations. Additional numerical calculations were then performed by setting the isothermal wall condition to evaluate the additional time required by the thermal boundary layer to establish after the aerodynamic boundary layer reaches its steady state. Finally, full conjugate simulations were executed to compute the warm up effect of the solid during the blowdown of a hot fluid over a colder metallic test model. The transient performance of the turbulent thermal and momentum boundary layers is quantified through numerical simulations of air blowdown over a flat plate for different mainstream flow conditions. The effects of Reynolds number, free stream velocity, transient duration, test article length and free stream temperature were independently assessed, to then define a mathematical expression of the momentum boundary layer settlement. This paper presents a novel numerical correlation of the additional time required by the thermal boundary layer to be stablished after the settlement of the momentum boundary layer. The time scales of the aerodynamic and thermal boundary layers are presented as a function of relevant non-dimensional numbers, as well as the description of the response of the near wall flow to sudden free stream changes. The characterization of the boundary layer mechanisms discussed in this paper contribute to the establishment of an evidence-based foundation for advances in the field of flow control.

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