Eddy Viscosity Distributions in Compressible Turbulent Boundary Layers with Injection

1971 ◽  
Vol 22 (2) ◽  
pp. 169-182 ◽  
Author(s):  
L. C. Squire
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Mixing Length ◽  
Carbon Dioxide Injection ◽  
Displacement Thickness ◽  
Porous Surfaces ◽  
Injection Ratio

SummaryShear stress, eddy viscosity and mixing length distributions have been obtained from measured boundary-layer developments over porous surfaces with air and carbon dioxide injection at Mach numbers up to M=3·6. It is found that, if the eddy viscosity is non-dimensionalised by dividing by the product of the free-stream velocity and the kinematic displacement thickness then this non-dimensional ratio is almost independent of injection ratio, but decreases slightly with Mach number.

An Aspect of Heat Transfer in Accelerating Turbulent Boundary Layers

1969 ◽  
Vol 91 (2) ◽  
pp. 229-234 ◽  
Author(s):  
B. E. Launder ◽  
F. C. Lockwood
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Thermal Boundary Layer ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Stanton Number ◽  
Stream Velocity ◽  
Velocity Boundary Layer ◽  
Positive Exponent

Theoretical consideration indicates that, in an accelerated turbulent flow, the thermal boundary layer may penetrate significantly beyond the edge of the velocity boundary layer. This effect may contribute in part to the marked decrease in Stanton number which has been reported in accelerated turbulent boundary layers. This paper presents theoretical solutions to turbulent velocity and thermal boundary layers in flow between converging planes where the wall temperature varies as the free-stream velocity raised to a positive exponent. The solutions clearly illustrate that, as the wall-temperature variation is made less rapid, the thermal boundary layer penetrates progressively further beyond the velocity boundary layer, causing the Stanton number to decrease.

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.

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.

The Removal of the Boundary Layer of a Supersonic Flow by Means of a Slot

1963 ◽  
Vol 30 (2) ◽  
pp. 275-278
Author(s):  
M. Cloutier
Keyword(s):  
Boundary Layer ◽  
Mass Flow ◽  
Static Pressure ◽  
Free Stream ◽  
Subsequent Development ◽  
Displacement Thickness ◽  
Free Stream Mach Number ◽  
Slot Opening ◽  
Flow Through ◽  
Transverse Slot

The influence of slot opening and of suction pressure upon the mass flow through the slot and the subsequent development of the boundary layer has been studied for the case of a single transverse slot opening into a boundary layer with a displacement thickness of 0.168 in. at a free-stream Mach number of 2.92. The results show that as much as 85 percent of the mass flow in the boundary layer between the wall and the position of the slot lip enters the slot, and that this result is independent of the slot reservoir pressure, providing the latter is less than approximately twice the tunnel static pressure.

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.

Effects of Partial Slip on Chemically Reactive Solute Distribution in MHD Boundary Layer Stagnation Point Flow Past a Stretching Permeable Sheet

2015 ◽  
Vol 13 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Swati Mukhopadhyay
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Stream Velocity ◽  
Slip Parameter ◽  
Mhd Boundary Layer

Abstract This paper presents the magnetohydrodynamic (MHD) boundary layer stagnation point flow with diffusion of chemically reactive species undergoing first-order chemical reaction over a permeable stretching sheet in presence of partial slip. With the help of similarity transformations, the partial differential equations corresponding to momentum and the concentration equations are transformed into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity and the stretching velocity. Velocity decreases with the increasing magnetic parameter when the free-stream velocity is less than the stretching velocity but the opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. With increasing velocity slip parameter, velocity increases when the free-stream velocity is greater than the stretching velocity. But the concentration decreases in this case. Concentration decreases with increasing mass slip parameter.

Hydraulic jumps in a channel

2009 ◽  
Vol 618 ◽  
pp. 71-87 ◽  
Author(s):  
DANIEL BONN ◽  
ANDERS ANDERSEN ◽  
TOMAS BOHR
Keyword(s):  
Boundary Layer ◽  
Flow Rate ◽  
Eddy Viscosity ◽  
Fluid Layer ◽  
Momentum Conservation ◽  
Opening Angle ◽  
Normal Velocity ◽  
Hydraulic Jumps ◽  
Mixing Length ◽  
Critical Height

We present a study of hydraulic jumps with flow predominantly in one direction, created either by confining the flow to a narrow channel with parallel walls or by providing an inflow in the form of a narrow sheet. In the channel flow, we find a linear height profile upstream of the jump as expected for a supercritical one-dimensional boundary layer flow, but we find that the surface slope is up to an order of magnitude larger than expected and independent of flow rate. We explain this as an effect of turbulent fluctuations creating an enhanced eddy viscosity, and we model the results in terms of Prandtl's mixing-length theory with a mixing length that is proportional to the height of the fluid layer. Using averaged boundary-layer equations, taking into account the friction with the channel walls and the eddy viscosity, the flow both upstream and downstream of the jump can be understood. For the downstream subcritical flow, we assume that the critical height is attained close to the channel outlet. We use mass and momentum conservation to determine the position of the jump and obtain an estimate which is in rough agreement with our experiment. We show that the averaging method with a varying velocity profile allows for computation of the flow-structure through the jump and predicts a separation vortex behind the jump, something which is not clearly seen experimentally, probably owing to turbulence. In the sheet flow, we find that the jump has the shape of a rhombus with sharply defined oblique shocks. The experiment shows that the variation of the opening angle of the rhombus with flow rate is determined by the condition that the normal velocity at the jump is constant.

Influence of Free-Stream Turbulence on Turbulent Boundary Layer Heat Transfer and Mean Profile Development, Part I—Experimental Data

1983 ◽  
Vol 105 (1) ◽  
pp. 33-40 ◽  
Author(s):  
M. F. Blair
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layer Flow ◽  
Free Stream ◽  
Full Range ◽  
Stream Velocity ◽  
Free Stream Turbulence ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

An experimental research program was conducted to determine the influence of free-stream turbulence on zero pressure gradient, fully turbulent boundary layer flow. Connective heat transfer coefficients and boundary layer mean velocity and temperature profile data were obtained for a constant free-stream velocity of 30 m/s and free-stream turbulence intensities ranging from approximately 1/4 to 7 percent. Free-stream multicomponent turbulence intensity, longitudinal integral scale, and spectral distributions were obtained for the full range of turbulence levels. The test results with 1/4 percent free-stream turbulence indicate that these data were in excellent agreement with classic two-dimensional, low free-stream turbulence, turbulent boundary layer correlations. For fully turbulent boundary layer flow, both the skin friction and heat transfer were found to be substantially increased (up to ∼ 20 percent) for the higher levels of free-stream turbulence. Detailed results of the experimental study are presented in the present paper (Part I). A comprehensive analysis is provided in a companion paper (Part II).

scholarly journals NUMERICAL INVESTIGATION OF THE WAKE AFFECTED UNSTEADINESS ON FLAT PLATE BOUNDARY LAYER

2013 ◽  
Vol 43 (1) ◽  
pp. 15-22
Author(s):  
Sanchita Amin ◽  
Dipak Kanti Das
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Plate Boundary ◽  
Elliptic Cylinder ◽  
Stream Velocity ◽  
Element Formulation ◽  
Weighted Residual Method ◽  
Focal Distance ◽  
Coupled Equations

The present numerical simulation has been conducted with the aim to observe the unsteady boundarylayer characteristics on a flat plate induced by a von Karman vortex street wake. This flow situation is anidealization of that occurring on turbomachinery blades where unsteady wakes are generated by the precedingrow of blades. In this research, the boundary layer is developed under zero pressure gradients while the vortexstreet is generated by an elliptic cylinder positioned in the free stream. The minor-major axes ratio of theelliptic cylinder is taken as 0.6 with an angle of attack 00. The investigation has been performed for differentcylinder-to-plate relative position and a Reynolds number of 500 based on the focal distance of the ellipticcylinder and free stream velocity. The time dependent, two dimensional flow is simulated numerically. Theconsequent mathematical model is governed by the coupled equations of mass, and momentum and solved byemploying Galerkin weighted residual method of finite element formulation. The development of the flow fieldup to certain time period is considered. Instantaneous streamlines of the disturbed flow field, instantaneousvelocity field, boundary layer integral parameters, and skin friction on different streamwise locations on theplate are presented in this paper. The result shows that the wake vortices strongly affect the boundary layerover the flat plate.DOI: http://dx.doi.org/10.3329/jme.v43i1.15771

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