Role of buoyancy and the Boussinesq approximation in horizontal boundary layers (Buoyancy effect on shear stress and heat transfer in horizontal boundary layer, considering Boussinesq approximation)

1972 ◽  
Vol 6 (1) ◽  
pp. 34-39 ◽  
Author(s):  
L. G. REDEKOPP ◽  
A. F. CHARWAT
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Stress ◽  
Boundary Layers ◽  
Boussinesq Approximation ◽  
Buoyancy Effect ◽  
Horizontal Boundary

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Laminar boundary layers behind detonation waves

1983 ◽  
Vol 387 (1793) ◽  
pp. 331-349 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Flow Analysis ◽  
Time Dependent ◽  
Detonation Waves ◽  
Planar Geometry ◽  
Laminar Boundary Layers ◽  
Spherical Detonation ◽  
Layer Flow

New solutions are presented for non-stationary boundary layers induced by planar, cylindrical and spherical Chapman-Jouguet (C-J) detonation waves. The numerical results show that the Prandtl number ( Pr ) has a very significant influence on the boundary-layer-flow structure. A comparison with available time-dependent heat-transfer measurements in a planar geometry in a 2H 2 + O 2 mixture shows much better agreement with the present analysis than has been obtained previously by others. This lends confidence to the new results on boundary layers induced by cylindrical and spherical detonation waves. Only the spherical-flow analysis is given here in detail for brevity.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2—Fluctuation Quantities

1996 ◽  
Vol 118 (4) ◽  
pp. 728-736 ◽  
Author(s):  
S. P. Mislevy ◽  
T. Wang
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Transition Region ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Turbulent Shear ◽  
Wall Region ◽  
Pressure Gradients ◽  
Baseline Case ◽  
Near Wall

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. Boundary layer measurements were conducted for two constant-K cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The fluctuation quantities, u′, ν′, t′, the Reynolds shear stress (uν), and the Reynolds heat fluxes (νt and ut) were measured. In general, u′/U∞, ν′/U∞, and νt have higher values across the boundary layer for the adverse pressure-gradient cases than they do for the baseline case (K = 0). The development of ν′ for the adverse pressure gradients was more actively involved than that of the baseline. In the early transition region, the Reynolds shear stress distribution for the K2 case showed a near-wall region of high-turbulent shear generated at Y+ = 7. At stations farther downstream, this near-wall shear reduced in magnitude, while a second region of high-turbulent shear developed at Y+ = 70. For the baseline case, however, the maximum turbulent shear in the transition region was generated at Y+ = 70, and no near-wall high-shear region was seen. Stronger adverse pressure gradients appear to produce more uniform and higher t′ in the near-wall region (Y+ < 20) in both transitional and turbulent boundary layers. The instantaneous velocity signals did not show any clear turbulent/nonturbulent demarcations in the transition region. Increasingly stronger adverse pressure gradients seemed to produce large non turbulent unsteadiness (or instability waves) at a similar magnitude as the turbulent fluctuations such that the production of turbulent spots was obscured. The turbulent spots could not be identified visually or through conventional conditional-sampling schemes. In addition, the streamwise evolution of eddy viscosity, turbulent thermal diffusivity, and Prt, are also presented.

scholarly journals Measurement of Unsteady Flow and Heat Transfer in a Linear Turbine Cascade

1992 ◽  
Author(s):  
X. Liu ◽  
W. Rodi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Unsteady Flow ◽  
Boundary Layers ◽  
Suction Side ◽  
Turbine Cascade ◽  
Transfer Coefficients ◽  
Flow And Heat Transfer ◽  
Background Turbulence ◽  
Hot Film

A detailed experimental study has been conducted on the wake-induced unsteady flow and heat transfer in a linear turbine cascade. The unsteady wakes with passing frequencies in the range zero to 240 Hz were generated by moving cylinders on a squirrel cage device. The velocity fields in the blade-to-blade flow and in the boundary layers were measured with hot-wire anemometers, the surface pressures with a pressure transducer and the heat transfer coefficients with a glue-on hot film. The results were obtained in ensemble-averaged form so that periodic unsteady processes can be studied. Of particular interest was the transition of the boundary layer. The boundary layer remained laminar on the pressure side in all cases and in the case without wakes also on the suction side. On the latter, the wakes generated by the moving cylinders caused transition, and the beginning of transition moves forward as the cylinder-passing frequency increases. Unlike in the flat-plate study of Liu and Rodi (1991a) the instantaneous boundary layer state does not respond to the passing wakes and therefore does not vary with time. The heat transfer increases under increasing cylinder-passing frequency even in the regions with laminar boundary layers due to the increased background turbulence.

Free-convection effects in the boundary layer along a vertically stretching flat surface

1992 ◽  
Vol 70 (12) ◽  
pp. 1253-1260 ◽  
Author(s):  
John E. Daskalakis
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Convection ◽  
Skin Friction ◽  
Flat Surface ◽  
Relaxation Method ◽  
Boussinesq Approximation ◽  
Axial Coordinate ◽  
Prandtl Numbers ◽  
Energy Equations

We assess the effects of free convection on the boundary layer formed along a flat surface stretching vertically in a quiescent fluid. The flow is laminar and incompressible, the buoyancy forces conform to the Boussinesq approximation and the surface temperature is variable. The two-point boundary value problem of the coupled momentum and energy equations is solved using a simple and accurate relaxation method that provides the general nonsimilar solution to the flow. The effect of free-convection currents on velocity and temperature profiles, skin friction, and heat transfer is studied by varying the flow Grashof and Prandtl numbers. Zero shear stress and heat-transfer rate are predicted at some axial coordinate on a surface with decreasing wall temperature. Also the skin friction is markedly modified by the buoyancy while the heat transfer at the surface is correspondingly only moderately influenced.

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.

scholarly journals NUMERICAL MODELING OF A TURBULENT BOTTOM BOUNDARY LAYER UNDER SOLITARY WAVES ON A SMOOTH SURFACE

2018 ◽  
pp. 26
Author(s):  
Ahmad Sana ◽  
Hitoshi Tanaka
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Solitary Waves ◽  
Bottom Boundary Layer ◽  
Stream Velocity ◽  
Bottom Boundary ◽  
Sediment Movement ◽  
Bottom Boundary Layers ◽  
Turbulent Models

A number of studies on bottom boundary layers under sinusoidal and cnoidal waves were carried out in the past owing to the role of bottom shear stress on coastal sediment movement. In recent years, the bottom boundary layers under long waves have attracted considerable attention due to the occurrence of huge tsunamis and corresponding sediment movement. In the present study two-equation turbulent models proposed by Menter(1994) have been applied to a bottom boundary layer under solitary waves. A comparison has been made for cross-stream velocity profile and other turbulence properties in x-direction.

scholarly journals Prediction of Heat Transfer From Laminar Boundary Layers, With Emphasis on Large Free-Stream Velocity Gradients and Highly Cooled Walls

1966 ◽  
Vol 88 (3) ◽  
pp. 249-256 ◽  
Author(s):  
L. H. Back ◽  
A. B. Witte
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Gradient ◽  
Free Stream ◽  
Variable Density ◽  
Similarity Solutions ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Gradient Parameter

Laminar boundary-layer heat transfer and shear-stress predictions from existing similarity solutions are extended in an approximate way to perfect gas flows with a large free-stream velocity gradient parameter β and variable density-viscosity product ρμ across the boundary layer resulting from a highly cooled wall. The dimensionless enthalpy gradient at the wall gw′, to which the heat flux is related, is found not to vary appreciably with β. Thus the application of similarity solutions on a local basis to predict heat transfer from accelerated flows to an arbitrary surface may be a reasonable approximation involving a minimum amount of calculation time. Unlike gw′, the dimensionless velocity gradient at the wall fw″, to which the shear stress is related, is strongly dependent on β.

Mechanical Augmentation of Convective Heat Transfer in Air

1975 ◽  
Vol 97 (4) ◽  
pp. 516-520 ◽  
Author(s):  
J. K. Hagge ◽  
G. H. Junkhan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Convective Heat Transfer ◽  
Boundary Layers ◽  
Convective Heat ◽  
Convection Heat Transfer ◽  
Renewal Theory ◽  
Surface Renewal ◽  
Mechanical Removal ◽  
Blade Element

An experimental investigation was conducted into augmentation of forced convection heat transfer in air by mechanical removal of the boundary layer. A rotating blade element passing in close proximity to a flat plate convective surface was found to increase the rate of convective heat transfer by up to eleven times in certain situations. The blade element effectively scrapes away the boundary layer, thus reducing the resistance to heat flow. Parameters investigated include scraping frequency, scraper clearance, and type of boundary layer. Increased coefficients were found for higher scraping frequencies. Significant augmentation was obtained with clearance as large as 0.15 in. (0.0038 m) between the moving blade element and the convective surface. The technique appears most useful for laminar and transitional boundary layers, although some improvement was obtained for the turbulent boundary layers investigated. The simple surface renewal theory developed for scraped surface augmentation in liquids was found to approximately predict the coefficients obtained. A new relation is proposed which gives a better prediction and includes the effect of scraper clearance.

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