scholarly journals Sonic Eddy Model of the Turbulent Boundary Layer

Fluids ◽  
2022 ◽  
Vol 7 (1) ◽  
pp. 37
Author(s):  
Paul Dintilhac ◽  
Robert Breidenthal
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Entrainment Rate ◽  
Square Root ◽  
Reynolds Stresses ◽  
Free Shear Layer ◽  
Velocity Fluctuations ◽  
Acoustic Signaling

The effects of Mach number on the skin friction and velocity fluctuations of the turbulent boundary layer are considered through a sonic eddy model. Originally proposed for free shear flows, the model assumes that the eddies responsible for momentum transfer have a rotation Mach number of unity, with the entrainment rate limited by acoustic signaling. Under this assumption, the model predicts that the skin friction coefficient should go as the inverse Mach number in a regime where the Mach number is larger than unity but smaller than the square root of the Reynolds number. The velocity fluctuations normalized by the friction velocity should be the inverse square root of the Mach number in the same regime. Turbulent transport is controlled by acoustic signaling. The density field adjusts itself such that the Reynolds stresses correspond to the momentum transport. In contrast, the conventional van Driest–Morkovin view is that the Mach number effects are due to density variations directly. A new experiment or simulation is proposed to test this model using different gases in an incompressible boundary layer, following the example of Brown and Roshko in the free shear layer.

The Effect of Biofilms on Turbulent Boundary Layers

1999 ◽  
Vol 121 (1) ◽  
pp. 44-51 ◽  
Author(s):  
M. P. Schultz ◽  
G. W. Swain
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Layer Structure ◽  
Reynolds Shear Stress ◽  
Skin Friction Coefficient ◽  
Laser Doppler Velocimeter ◽  
Reynolds Stresses ◽  
The Mean

Materials exposed in the marine environment, including those protected by antifouling paints, may rapidly become colonized by microfouling. This may affect frictional resistance and turbulent boundary layer structure. This study compares the mean and turbulent boundary layer velocity characteristics of surfaces covered with a marine biofilm with those of a smooth surface. Measurements were made in a nominally zero pressure gradient, boundary layer flow with a two-component laser Doppler velocimeter at momentum thickness Reynolds numbers of 5600 to 19,000 in a recirculating water tunnel. Profiles of the mean and turbulence velocity components, including the Reynolds shear stress, were measured. An average increase in the skin friction coefficient of 33 to 187 percent was measured on the fouled specimens. The skin friction coefficient was found to be dependent on both biofilm thickness and morphology. The biofilms tested showed varying effect on the Reynolds stresses when those quantities were normalized with the friction velocity.

The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 1. The turbulent boundary layer

1998 ◽  
Vol 359 ◽  
pp. 329-356 ◽  
Author(s):  
H. H. FERNHOLZ ◽  
D. WARNACK
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Reynolds Stresses ◽  
The Mean

The effects of a favourable pressure gradient (K[les ]4×10−6) and of the Reynolds number (862[les ]Reδ2[les ]5800) on the mean and fluctuating quantities of four turbulent boundary layers were studied experimentally and are presented in this paper and a companion paper (Part 2). The measurements consist of extensive hot-wire and skin-friction data. The former comprise mean and fluctuating velocities, their correlations and spectra, the latter wall-shear stress measurements obtained by four different techniques which allow testing of calibrations in both laminar-like and turbulent flows for the first time. The measurements provide complete data sets, obtained in an axisymmetric test section, which can serve as test cases as specified by the 1981 Stanford conference.Two different types of accelerated boundary layers were investigated and are described: in this paper (Part 1) the fully turbulent, accelerated boundary layer (sometimes denoted laminarescent) with approximately local equilibrium between the production and dissipation of the turbulent energy and with relaxation to a zero pressure gradient flow (cases 1 and 3); and in Part 2 the strongly accelerated boundary layer with ‘inactive’ turbulence, laminar-like mean flow behaviour (relaminarized), and reversion to the turbulent state (cases 2 and 4). In all four cases the standard logarithmic law fails but there is no single parametric criterion which denotes the beginning or the end of this breakdown. However, it can be demonstrated that the departure of the mean-velocity profile is accompanied by characteristic changes of turbulent quantities, such as the maxima of the Reynolds stresses or the fluctuating value of the skin friction.The boundary layers described here are maintained in the laminarescent state just up to the beginning of relaminarization and then relaxed to the turbulent state in a zero pressure gradient. The relaxation of the turbulence structure occurs much faster than in an adverse pressure gradient. In the accelerating boundary layer absolute values of the Reynolds stresses remain more or less constant in the outer region of the boundary layer in accordance with the results of Blackwelder & Kovasznay (1972), and rise both in the vincinity of the wall in conjunction with the rising wall shear stress and in the centre region of the boundary layer with the increase of production.

Axial Flutter Effects on the Axisymmetric Turbulent Boundary Layer Along Long Thin Circular Cylinders

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Stephen A. Jordan
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Reynolds Numbers ◽  
Wall Pressure ◽  
Analytical Models ◽  
Circular Cylinders ◽  
Reynolds Stresses ◽  
Turbulent Statistics ◽  
Oscillatory Instabilities

Experimental observations of towed sonar arrays as characterized by long thin circular cylinders indicate transverse motions that are clearly identified by low-amplitudes, low-wavelengths, and low-frequencies. Although the cylinder length (L) to radius (a) is commonly large [L/a = O(103)] with high Reynolds numbers [O(104)], the corresponding length scale involving the average skin friction [CfL/a = O(10)] remains within the many experimental determinations of short to moderate length cylinders that experience oscillatory instabilities. Prior to the present investigation, any detrimental effects of these oscillatory instabilities on the thin cylinder flow physics that serve construction of the respective semi-empirical and semi-analytical models remained chiefly unknown. Herein, we began examining those turbulent statistics via fine-scale numerical simulations to critique the pragmatic adequacy of the representative design models. We were concerned in particular about the streamwise effects on the turbulent boundary layer (TBL), skin friction and wall pressure evolutions as well as the radial distributions of the leading normal and shear Reynolds stresses. Fortunately, no major deviations (within 10%) were discovered in the TBL statistics over a characteristic range of Reynolds numbers and TBL thicknesses as compared to the axisymmetric state. However, acute spikes (both subharmonics and harmonics) were detected in the wall pressure autospectra similar to that suspected in the towed cylinder experiments, which were conducted in large tow tanks and lake-type basins. These spikes are of paramount importance and should be explored further because they may lead to signal-to-noise ratios above acceptable limits.

The measurement of skin friction in a turbulent boundary layer at a Mach number of 2.5, including the effect of a shock-wave

1952 ◽  
Vol 215 (1120) ◽  
pp. 84-99 ◽  
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Reynolds Number ◽  
Friction Coefficient ◽  
Mach Number ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Static Pressure ◽  
Pressure Rise ◽  
Skin Friction Coefficient

The skin friction of the wall of a wind tunnel has been measured at a Mach number of 2.5 using the surface-tube technique. The Reynolds number (with the distance from the throat as the representative length) was of the order of 2 to 3 millions and the boundary layer was turbulent. The skin friction coefficient was much less than for a very small Mach number (the incompressible case) and the amount of the decrease agreed with calculation. The effect of a shock-wave of strength 2 was also investigated—the strength of a shock-wave is defined as the pressure rise through it divided by the static pressure in front of it. The shock-wave only affected the boundary layer for a few thicknesses upstream of its point of impingement even though it was strong enough to cause local separation. The results show: ( а ) That the surface, or Stanton, tube is a reliable means of measuring skin friction in spite of the large values (over a million with the second as the unit of time) of the velocity gradient at the wall, and that the skin friction coefficient does decrease with Mach number in the manner predicted by calculation. ( b ) That disturbances due to a shock-wave impinging on a turbulent boundary layer are only propagated upstream a few multiples of the boundary layer thicknesses even when the shock-wave is strong enough to cause local separation.

The accelerated fully rough turbulent boundary layer

1977 ◽  
Vol 82 (3) ◽  
pp. 507-528 ◽  
Author(s):  
Hugh W. Coleman ◽  
Robert J. Moffat ◽  
William M. Kays
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Skin Friction ◽  
Shape Factor ◽  
Reynolds Shear Stress ◽  
Smooth Wall ◽  
Mean Velocity

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

Turbulent Boundary Layer Subjected to a Sudden Change in Surface Roughness and Temperature

1999 ◽  
Author(s):  
João Henrique D. Guimarães ◽  
Sergio J. F. dos Santos ◽  
Jian Su ◽  
Atila P. Silva Freire
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Sudden Change ◽  
Stanton Number ◽  
Temperature Profiles ◽  
Internal Layers ◽  
Mean Velocity ◽  
Wall Boundary Conditions

Abstract In present work, the dynamic and thermal behaviour of flows that develop over surfaces that simultaneously present a sudden change in surface roughness and temperature are discussed. In particular, the work is concerned with the physical validation of a newly proposed formulation for the near wall temperature profile. The theory uses the concept of the displacement in origin, together with some asymptotic arguments, to propose a new expression for the logarithmic region of the turbulent boundary layer. The new expressions are, therefore, of universal applicability, being independent of the type of rough surface considered. The present formulation may be used to give wall boundary conditions for two-equation differential models. The theoretical results are validated with experimental data obtained for flows that develop over flat surfaces with sudden changes in surface roughness and in temperature conditions. Measurements of mean velocity and of mean temperature are presented. A reduction of the data provides an estimate of the skin-friction coefficient, the Stanton number, the displacement in origin for both the velocity and the temperature profiles, and the thickness of the internal layers for the velocity and temperature profiles. The skin-friction co-efficient was calculated based on the chart method of Perry and Joubert (J.F.M., 17, 193–211, 1963) and on a balance of the integral momentum equation. The same chart method was used for the evaluation of the Stanton number and the displacement in origin.

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