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

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.

Download Full-text

An Investigation of Turbulent Boundary Layer on a Flat Plate With a Small Step Change in Surface Roughness

Aeronautical Quarterly ◽

10.1017/s0001925900008921 ◽

1980 ◽

Vol 31 (4) ◽

pp. 221-237

Author(s):

P.A. Aswatha Narayana

Keyword(s):

Boundary Layer ◽

Surface Roughness ◽

Turbulent Boundary Layer ◽

Flat Plate ◽

Sudden Change ◽

Outer Region ◽

Adverse Pressure Gradient ◽

Step Change ◽

Small Step ◽

Mean Velocity

SummaryThe response of turbulent boundary layer to sudden change in surface roughness have been studied experimentally. Mean velocity measurements have been made in the boundary layer on a flat plate, downstream of a small step change in surface roughness under 3 different pressure gradients. The surface upstream of the step consisted of ‘k* type ‘large roughness’ wall (or ‘small roughness’ wall) and downstream of the step consisted of smooth surface (or ‘small roughness’ wall). Velocity profiles after the step change have been analysed on the basis of the two layer model. The inner region responds very quickly to the new boundary condition while the outer region takes more time to attain equilibrium or a state of local self-preservation. The skin-friction coefficient initially increased after the step change and gradually reached towards a constant value except for a particular roughness combination under adverse pressure gradient wherein the change in the roughness function is gradual over the transition.

Download Full-text

The accelerated fully rough turbulent boundary layer

Journal of Fluid Mechanics ◽

10.1017/s0022112077000810 ◽

1977 ◽

Vol 82 (3) ◽

pp. 507-528 ◽

Cited By ~ 31

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.

Download Full-text

Measurements in a Turbulent Boundary Layer Over a d-Type Surface Roughness

Journal of Applied Mechanics ◽

10.1115/1.3423647 ◽

1975 ◽

Vol 42 (3) ◽

pp. 591-597 ◽

Cited By ~ 25

Author(s):

D. H. Wood ◽

R. A. Antonia

Keyword(s):

Boundary Layer ◽

Surface Roughness ◽

Turbulent Boundary Layer ◽

Turbulent Energy ◽

Shear Stresses ◽

Normal Velocity ◽

Mean Velocity ◽

Outer Flow ◽

Intensity Measurements ◽

Normal And Shear Stresses

Mean velocity and turbulence intensity measurements have been made in a fully developed turbulent boundary layer over a d-type surface roughness. This roughness is characterised by regular two-dimensional elements of square cross section placed one element width apart, with the cavity flow between elements being essentially isolated from the outer flow. The measurements show that this boundary layer closely satisfies the requirement of exact self-preservation. Distribution across the layer of Reynolds normal and shear stresses are closely similar to those found over a smooth surface except for the region immediately above the grooves. This similarity extends to distributions of third and fourth-order moments of longitudinal and normal velocity fluctuations and also to the distribution of turbulent energy dissipation. The present results are compared with those obtained for a k-type or sand grained roughness.

Download Full-text

New perspectives on the impulsive roughness-perturbation of a turbulent boundary layer

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.75 ◽

2011 ◽

Vol 677 ◽

pp. 179-203 ◽

Cited By ~ 31

Author(s):

I. JACOBI ◽

B. J. McKEON

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Flow Field ◽

Spectral Energy ◽

Internal Layers ◽

Hot Wire ◽

Mean Velocity ◽

Composite Maps ◽

Downstream Flow ◽

Near Wall

The zero-pressure-gradient turbulent boundary layer over a flat plate was perturbed by a short strip of two-dimensional roughness elements, and the downstream response of the flow field was interrogated by hot-wire anemometry and particle image velocimetry. Two internal layers, marking the two transitions between rough and smooth boundary conditions, are shown to represent the edges of a ‘stress bore’ in the flow field. New scalings, based on the mean velocity gradient and the third moment of the streamwise fluctuating velocity component, are used to identify this ‘stress bore’ as the region of influence of the roughness impulse. Spectral composite maps reveal the redistribution of spectral energy by the impulsive perturbation – in particular, the region of the near-wall peak was reached by use of a single hot wire in order to identify the significant changes to the near-wall cycle. In addition, analysis of the distribution of vortex cores shows a distinct structural change in the flow associated with the perturbation. A short spatially impulsive patch of roughness is shown to provide a vehicle for modifying a large portion of the downstream flow field in a controlled and persistent way.

Download Full-text

Boundary Layer Transition Under High Free-Stream Turbulence and Strong Acceleration Conditions: Part 1—Mean Flow Results

Journal of Heat Transfer ◽

10.1115/1.2824114 ◽

1997 ◽

Vol 119 (3) ◽

pp. 420-426 ◽

Cited By ~ 8

Author(s):

R. J. Volino ◽

T. W. Simon

Keyword(s):

Boundary Layer ◽

Skin Friction ◽

Free Stream ◽

Boundary Layer Transition ◽

Temperature Profiles ◽

Mean Flow ◽

Transfer Coefficients ◽

Mean Velocity ◽

Layer Transition ◽

Free Stream Turbulence

Measurements from heated boundary layers along a concave-curved test wall subject to high (initially 8 percent) free-stream turbulence intensity and strong (K = (ν/U∞2) dU∞/dx) as high as 9 × 10−6) acceleration are presented and discussed. Conditions for the experiments were chosen to roughly simulate those present on the downstream half of the pressure side of a gas turbine airfoil. Mean velocity and temperature profiles as well as skin friction and heat transfer coefficients are presented. The transition zone is of extended length in spite of the high free-stream turbulence level. Transitional values of skin friction coefficients and Stanton numbers drop below flat-plate, low-free-stream-turbulence, turbulent flow correlations, but remain well above laminar flow values. The mean velocity and temperature profiles exhibit clear changes in shape as the flow passes through transition. To the authors’ knowledge, this is the first detailed documentation of a high-free-stream-turbulence boundary layer flow in such a strong acceleration field.

Download Full-text

The Effects of Surface Roughness on the Mean Velocity Profile in a Turbulent Boundary Layer

Journal of Fluids Engineering ◽

10.1115/1.1493810 ◽

2002 ◽

Vol 124 (3) ◽

pp. 664-670 ◽

Cited By ~ 24

Author(s):

Donald J. Bergstrom ◽

Nathan A. Kotey ◽

Mark F. Tachie

Keyword(s):

Boundary Layer ◽

Surface Roughness ◽

Turbulent Boundary Layer ◽

Velocity Profile ◽

Friction Velocity ◽

Outer Region ◽

Stream Velocity ◽

Mean Velocity ◽

Outer Flow ◽

The Mean

Experimental measurements of the mean velocity profile in a canonical turbulent boundary layer are obtained for four different surface roughness conditions, as well as a smooth wall, at moderate Reynolds numbers in a wind tunnel. The mean streamwise velocity component is fitted to a correlation which allows both the strength of the wake, Π, and friction velocity, Uτ, to vary. The results show that the type of surface roughness affects the mean defect profile in the outer region of the turbulent boundary layer, as well as determining the value of the skin friction. The defect profiles normalized by the friction velocity were approximately independent of Reynolds number, while those normalized using the free stream velocity were not. The fact that the outer flow is significantly affected by the specific roughness characteristics at the wall implies that rough wall boundary layers are more complex than the wall similarity hypothesis would allow.

Download Full-text

Heat Transfer in the Turbulent Boundary Layer With a Step Change in Surface Roughness

Volume 4: Heat Transfer; Electric Power; Industrial and Cogeneration ◽

10.1115/91-gt-266 ◽

1991 ◽

Cited By ~ 5

Author(s):

Robert P. Taylor ◽

J. Keith Taylor ◽

M. H. Hosni ◽

Hugh W. Coleman

Keyword(s):

Heat Transfer ◽

Boundary Layer ◽

Surface Roughness ◽

Smooth Surface ◽

Plate Boundary ◽

Step Change ◽

Stanton Number ◽

Test Surface ◽

Temperature Profiles ◽

Boundary Layer Flows

Measurements of Stanton numbers, velocity profiles, temperature profiles, and turbulence intensity profiles are reported for turbulent flat plate boundary layer flows with a step change in surface roughness. The first 0.9 m length of the test surface is roughened with 1.27 mm diameter hemispheres spaced 2 base diameters apart in a staggered array. The remaining 1.5 m length is smooth. The experiments show that the step change from a rough to a smooth surface has a dramatic effect on the convective heat transfer. In many cases, the Stanton number drops below the smooth-wall correlation immediately downstream of the change in roughness. The Stanton number measurements are compared with predictions using the discrete element method with excellent results.

Download Full-text

An Investigation of two Turbulent Flows over Smooth and Rough Surfaces

Journal of Mechanical Engineering Science ◽

10.1243/jmes_jour_1974_016_014_02 ◽

1974 ◽

Vol 16 (2) ◽

pp. 71-78 ◽

Cited By ~ 1

Author(s):

W. K. Allan ◽

V. Sharma

Keyword(s):

Experimental Data ◽

Boundary Layer ◽

Surface Roughness ◽

Turbulent Boundary Layer ◽

Turbulent Flows ◽

Smooth Surface ◽

Two Dimensional ◽

Mean Velocity ◽

Turbulent Boundary Layer Flow ◽

Layer Flow

Experimental data for two-dimensional, low-speed, turbulent boundary layer flow has been used to verify the description of mean-velocity distributions proposed by Allan and to re-evaluate the entrainment function. The independence of pressure gradient and surface roughness as regards their effects on velocity profiles has been demonstrated. Boundary layer predictions agree with experimental data for a smooth surface, but further investigation is required for flow over a rough surface.

Download Full-text