Nonlinear evolution and breakdown in unstable boundary layers

1980 ◽  
Vol 99 (2) ◽  
pp. 247-265 ◽  
Author(s):  
A. D. D. Craik
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Boundary Layers ◽  
Nonlinear Evolution ◽  
Secondary Instability ◽  
Nonlinear Instability ◽  
Weakly Nonlinear ◽  
Theory And Experiment

The nonlinear evolution and breakdown of laminar flow in the boundary layer on a flat plate is examined with the aim of making a closer comparison of theory and experiment than has been attempted previously. The importance of three-dimensionality is emphasized. It is concluded that many features of the nonlinear instability are consistent with existing linear and weakly nonlinear theories even as breakdown is approached. The development of the secondary instability, or ‘spike’, is also considered and suggestions for an improved theory of its growth are made.

Computation and Simulation of Wake-Generated Unsteady Pressure and Boundary Layers in Cascades: Part 1 — Description of the Approach and Validation

1994 ◽  
Author(s):  
S. Fan ◽  
B. Lakshminarayana
Keyword(s):  
Boundary Layer ◽  
Unsteady Flow ◽  
Flat Plate ◽  
Boundary Layers ◽  
Guide Vane ◽  
Numerical Procedure ◽  
Computational Domain ◽  
Unsteady Pressure ◽  
Blade Row ◽  
Euler Solver

The unsteady pressure and boundary layers on a turbomachinery blade row arising from periodic wakes due to upstream blade rows are investigated in this paper. A time accurate Euler solver has been developed using an explicit four-stage Runge-Kutta scheme. Two dimensional unsteady non-reflecting boundary conditions are used at the inlet and the outlet of the computational domain. The unsteady Euler solver captures the wake propagation and the resulting unsteady pressure field, which is then used as the input for a 2-D unsteady boundary layer procedure to predict the unsteady response of blade boundary layers. The boundary layer code includes an advanced k-ε model developed for unsteady turbulent boundary layers. The present computational procedure has been validated against analytic solutions and experimental measurements. The validation cases include unsteady inviscid flows in a flat plate cascade and a compressor exit guide vane (EGV) cascade, unsteady turbulent boundary layer on a flat plate subject to a traveling wave, unsteady transitional boundary layer due to wake passing and unsteady flow at the mid-span section of an axial compressor stator. The present numerical procedure is both efficient and accurate in predicting the unsteady flow physics resulting from wake/blade-row interaction, including wake induced unsteady transition of blade boundary layers.

Use of k−ε−γ Model to Predict Intermittency in Turbulent Boundary-Layers

2000 ◽  
Vol 122 (3) ◽  
pp. 542-546 ◽  
Author(s):  
Anupam Dewan ◽  
Jaywant H. Arakeri
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Rate Of Dissipation ◽  
Dissipation Equation ◽  
Averaged Model

The intermittency profile in the turbulent flat-plate zero pressure-gradient boundary-layer and a thick axisymmetric boundary-layer has been computed using the Reynolds-averaged k−ε−γ model, where k denotes turbulent kinetic energy, ε its rate of dissipation, and γ intermittency. The Reynolds-averaged model is simpler compared to the conditional model used in the literature. The dissipation equation of the Reynolds-averaged model is modified to account for the effect of entrainment. It has been shown that the model correctly predicts the observed intermittency of the flows. [S0098-2202(00)02403-2]

Eddy Heat Transfer by Secondary Görtler Instability

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
L. Momayez ◽  
G. Delacourt ◽  
P. Dupont ◽  
H. Peerhossaini
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flat Plate ◽  
Heat Transfer Enhancement ◽  
Secondary Instability ◽  
Surface Boundary ◽  
Transfer Enhancement ◽  
Surface Boundary Layer ◽  
Heat Transfer Intensification ◽  
Primary Instability

Experimental measurements of flow and heat transfer in a concave surface boundary layer in the presence of streamwise counter-rotating Görtler vortices show conclusively that local surface heat-transfer rates can exceed that of the turbulent flat-plate boundary layer even in the absence of turbulence. We have observed unexpected heat-transfer behavior in a laminar boundary layer on a concave wall even at low nominal velocity, a configuration not studied in the literature: The heat-transfer enhancement is extremely high, well above that corresponding to a turbulent boundary layer on a flat plate. To quantify the effect of freestream velocity on heat-transfer intensification, two criteria are defined for the growth of the Görtler instability: Pz for primary instability and Prms for the secondary instability. The evolution of these criteria along the concave surface boundary layer clearly shows that the secondary instability grows faster than the primary instability. Measurements show that beyond a certain distance the heat-transfer enhancement is basically correlated with Prms, so that the high heat-transfer intensification at low freestream velocities is due to the high growth rate of the secondary instability. The relative heat-transfer enhancement seems to be independent of the nominal velocity (global Reynolds number) and allows predicting the influence of the Görtler instabilities in a large variety of situations.

Heat Transfer in the Laminar Boundary Layer Over an Impulsively Started Flat Plate

1975 ◽  
Vol 97 (3) ◽  
pp. 482-484 ◽  
Author(s):  
C. B. Watkins
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Constant Temperature ◽  
Laminar Boundary Layer ◽  
Temperature Difference ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Prandtl Numbers

Numerical solutions are described for the unsteady thermal boundary layer in incompressible laminar flow over a semi-infinite flat plate set impulsively into motion, with the simultaneous imposition of a constant temperature difference between the plate and the fluid. Results are presented for several Prandtl numbers.

The production of subharmonic waves in the nonlinear evolution of wavepackets in boundary layers

1999 ◽  
Vol 399 ◽  
pp. 301-318 ◽  
Author(s):  
MARCELLO A. F. MEDEIROS ◽  
MICHAEL GASTER
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Nonlinear Interaction ◽  
Strong Influence ◽  
Nonlinear Evolution ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Tollmien Schlichting ◽  
Acoustic Excitations ◽  
Dimensional Wave

The nonlinear evolution of wavepackets in a laminar boundary layer has been studied experimentally. The packets were generated by acoustic excitations injected into the boundary layer through a small hole in the plate. Various packets with different phases relative to the envelope were studied. It was found that for all the packets the nonlinearity involved the appearance of oblique modes of frequency close to the subharmonic of the dominant two-dimensional wave. Moreover, the results confirmed that the phase had a strong influence on the strength of the nonlinear interaction. The experimental observations also indicated that although a subharmonic resonance appeared to be present in the process, it alone could not explain the nonlinear behaviour. The experiment demonstrated that the process must also involve a mechanism that generates oblique waves of frequency lower than the Tollmien–Schlichting band.

Mass transfer in laminar flow

1954 ◽  
Vol 221 (1144) ◽  
pp. 78-99 ◽  
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Natural Convection ◽  
Laminar Flow ◽  
Flat Plate ◽  
The Body ◽  
Liquid Fuels ◽  
Fluid Stream ◽  
Mean Values ◽  
Fluid Properties

Starting from the differential equation of mass transfer in laminar flow and the appropriate boundary condition, expressions are derived for the rate of mass transfer from ( a ) a flat plate in a longitudinal fluid stream, ( b ) a vertical flat plate by natural convection, ( c ) the forward stagnation point of a sphere in a fluid stream. Only outward mass transfer is considered; this corresponds to blowing outwards from the plate at a rate inversely proportional to the boundary-layer thickness. The Kármán-Pohlhausen-Kroujiline method is used. Where appropriate the Prandtl or Schmidt number has been taken as 0⋅71. The calculations are valid for all mass-transfer processes for which a single diffusion coefficient can be ascribed to the diffusing property, but are particularly relevant to the combustion of liquid fuels, for which the outward mass-transfer rates are so high that important deviations occur from boundary-layer profiles without mass transfer. Despite the great temperature variations present in boundary layers with combustion, mean values for the fluid properties are assumed. In the case of natural convection, it is assumed that the body forces on the fluid in the boundary layer are everywhere zero; this leads to a less serious over-estimate of the buoyancy than the usual assumptions which are valid only for small temperature differences.

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