Surface-mounted Obstacle Research Articles

Theoretical analysis of turbulent flow and heat transfer around a surface-mounted obstacle.

To estimate the distribution of turbulent eddy viscosity in the flow related to complicated geometries, a simple model was developed based on the mixing-length hypothesis. This model was applied to two cases of turbulent separated flows around a surface-mounted obstacle of circular cross section. The first case is film flow on the outer wall of a vertical tube, and the second is flow between parallel plates. Calculations were performed by using the Galerkin finite-element method. In view of heat transfer augmentation, the structure of the separating and reattaching flow around a surface-mounted obstacle was investigated in detail, together with the corresponding temperature field.It was shown that the reattachment distance depends on the Reynolds number; the isotherm contours are strongly distorted and pushed down toward the wall due to the back flow in the recirculating zone; the maximum Nusselt number occurs on the upstream side of the reattachment point; and the augmentation effect due to the obstacle is remarkable only in a limited turbulent range of relatively low Reynolds number.

Steady and unsteady 3-D interactive boundary layers

The paper describes theoretical and computational research on 3-D steady and unsteady flows at medium-to-high Reynolds numbers (Re), aimed at increasing understanding of 3-D separation and boundary-layer transition. Concerning steady 3-D flows first, an interactive-boundary-layer (IBL) formulation for 3-D laminar flow of an incompressible fluid over a surface-mounted obstacle is addressed computationally and compared with other methods at various Re. The computational approach is designed deliberately to capture the extra ellipticity present due to the three-dimensionality, making use of skewed shears in linear quasi-planar sweeps of the boundary layer and local updating in the 3-D interaction law. Results including separation are presented for a range of Re and obstacle heights, together with grid-effect studies, and comparisons are made, first with triple-deck predictions for high Re and, second, with an alternative IBL approach presented in a companion work. The latter and the current work together yield a broad agreement on predictions for the 3-D flow, stretching from the triple-deck through the IBL to thin-layer Navier-Stokes predictions, over a wide range of Re. Second, the computational approach is extended to unsteady 3-D flows, for the triple-deck limit including linear and nonlinear Tollmien-Schlichting waves. Results for small and non-small disturbances and comparisons are presented, showing fairly encouraging agreement between theory, computations and experiments.

Numerical simulation of turbulent flow over surface-mounted obstacles with sharp edges and corners

Results from numerical simulations of turbulent flow around a surface-mounted cube and over a surface-mounted square rib are presented. The first problem is treated by solving the Reynolds equations together with the standard k − ϵ turbulence model, for 0° and 45° orientation of the flow obstacle, in uniform and boundary layer incident flow. The second problem is solved by applying the concept of large-eddy simulation. In both calculation concepts, sufficient spatial resolution is essential to get satisfying agreement with experimental data in the critical flow regimes, e.g. above the top face of the flow obstacles. The computations based on large-eddy simulation are very expensive but can provide excellent agreement of the numerical results with the experimental data for the second-order statistics.

Application of body-fitted coordinates and the κ-ε turbulence model for wind field computation in a complex urban terrain

Body-fitted coordinates are used for the computation of viscous and turbulent flow past surface-mounted obstacles. Successful cases of neutral flow and stratified flow past a 3D hill are reported. With the two-equation model of turbulence added, the turbulent flow past two rows of buildings is computed. This paper shows the practicality of such an approach.

Numerical simulation of turbulent flow over surface-mounted obstacles with sharp edges and corners

Results from numerical simulations of turbulent flow around a surface-mounted cube and over a surface-mounted square rib are presented. The first problem is treated by solving the Reynolds equations together with the standard k−ϵ turbulence model, for 0° and 45° orientation of the flow obstacle, in uniform and boundary layer incident flow. The second problem is solved by applying the concept of large-eddy simulation. In both calculation concepts, sufficient spatial resolution is essential to get satisfying agreement with experimental data in the critical flow regimes, e.g. above the top face of the flow obstacles. The computations based on large-eddy simulation are very expensive but can provide excellent agreement of the numerical results with the experimental data for the second-order statistics.

Application of body-fitted coordinates and the k-ϵ turbulence model for wind field computation in a complex urban terrain

Body-fitted coordinates are used for the computation of viscous and turbulent flow past surface-mounted obstacles. Successful cases of neutral flow and stratified flow past a 3D hill are reported. With the two-equation model of turbulence added, the turbulent flow past two rows of buildings is computed. This paper shows the practicality of such an approach.

Trailing vortices in the wakes of surface-mounted obstacles

The generation of trailing vortices in the wakes of surface-mounted obstacles at moderate Reynolds numbers is examined by channel-flow experiments and numerical simulation. A skew-mounted obstacle generates a single concentrated trailing vortex, together with weak streamwise vorticity of opposite sense extending to considerable distances on either side and zero gross circulation across the whole stream. Cross-stream-symmetrical obstacles (having a streamwise plane of symmetry normal to the plane surface) generate one or more nested vortex pairs, usually of alternate sense, of which one pair is normally dominant. The sense of rotation of the dominant vortex pair depends on both the shape of the obstacle and its depth relative to that of the boundary layer. Obstacles that divide the stream laterally produce dominant vortex pairs with a central downwash, whereas those lifting the flow predominantly over their crests produce dominant vortex pairs with a central upwash. It is argued that the vorticity of the dominant trailing vortices is generated largely as a component of cross-stream vorticity at the boundary, shed as a shear layer from the body, and turned inertially by the flow to form trailing vortices. It should also be emphasized that the dominant trailing vortex or vortex pair is generally embedded in a weak distribution of trailing vorticity of opposite signs, but with net circulation comparable with that of the dominant core.

The Flow Over Two-Dimensional Surface-Mounted Obstacles at Low Reynolds Numbers

The flow over a fence and a block mounted in a fully developed channel flow is experimentally investigated as a function of the Reynolds number, blockage ratio and length-to-height ratio using a laser-Doppler-anemometer. The information obtained includes the location and size of the primary and secondary recirculation zones, and profiles of the mean streamwise velocity component. The experiments were carried out in a channel for a Reynolds number in the range 150 < ReH < 4500. Comparisons are drawn between the obstacle flow and the backward-facing step flow.

On short-scale inviscid instabilities in flow past surface-mounted obstacles and other non-parallel motions

SummaryA theoretical investigation of short-scale inviscid instability in boundary-layer flow past an obstacle on a surface is described, with the application to trip-wire transition and wall roughness effects in mind. An analytical model and computational results show that the occurrence of an inflexion point in a local velocity profile is necessary but not sufficient for the instability to arise.

On the development of large-sized short-scaled disturbances in boundary layers

For high Reynolds numbers the planar nonlinear stability properties of boundary layers, as governed first by the triple-deck interaction, are discussed theoretically. When a disturbance of relatively high frequency is introduced or as the distance downstream increases in the Blasius case the characteristic length scale shortens. An account is given of the possible progress of such a disturbance, from an initially small Tollmien-Schlichting state, through a weakly nonlinear first stage that does not interrupt the amplitude growth, and thence into a fully nonlinear second stage where the Benjamin-Ono equation comes into force. Still higher frequencies point to the full Euler equations holding, although significant non-parallel flow effects then emerge. In the Euler stage, however, and in the previous second stage, bursts of vorticity from the viscous sublayer closest to the solid surface are almost certain to occur. The relations with other basic flow problems, and with turbulence-modelling, are noted, as well as the need to consider three-dimensional motion. Finally, an Appendix deals with certain issues of practical importance arising with respect to non-parallel flow effects, for example in breakaway separations or flow over surface-mounted obstacles, and points out that the slope of the local displacement in the basic flow is then a dominant controlling feature of the short-scale instabilities.

Unsteady gravity current flows over obstacles: Some observations and analysis related to the phase II trials

The Phase II trials at Thorney Island were designed to provide a few full-scale results of the interaction of heavy gas clouds with surface-mounted obstacles. In this paper, we interpret some preliminary observations from the Phase II trials by reviewing and developing the theory of two-layer fluid flows over obstacles and comparing these results with visual observations of the field trials. The results are preliminary, and largely qualitative, because the concentration and other quantitative measurements are not yet available.

Closure to “Discussions of ‘The Flow Past a Surface-Mounted Obstacle’” (1984, ASME J. Fluids Eng., 106, pp. 111–112)

Closure to “Discussions of ‘The Flow Past a Surface-Mounted Obstacle’” (1984, ASME J. Fluids Eng., 106, pp. 111–112)

On wakes and the net forces produced by surface-mounted obstacles in neutrally stratified atmospheric boundary layers

Wakes well downstream of obstacles in the neutrally stratified atmospheric boundary layer are studied using numerical models with eddy viscosity and mixing-length closure hypotheses. Variations of eddy viscosity with height near the ground are shown to exert a strong influence on the rates of wake decay. In the planetary boundary layer, it is shown that a significant proportion of the initial momentum flux deficit in the wake can be balanced by changes in the Coriolis force.

The Flow Past a Surface-Mounted Obstacle

The length of the recirculating region past a two dimensional obstacle was investigated experimentally with a single hot wire. The width (W) of the obstacle could be changed in multiple values of obstacle height (H). The results show that upstream of the obstacle the length of the main recirculating region remains unchanged with obstacle width and equal to 0.85H; however the downstream length of the recirculating region is a strong function of the width and changes almost linearly from 11 obstacle heights for W/H=1.0 to 3 for W/H greater than four.

A numerical study of rapidly rotating flow over surface-mounted obstacles

Three-dimensional numerical integrations of the Navier-Stokes equations have been made for parameters corresponding to some previous laboratory studies of transverse flow past obstacles in a rotating fluid. In the laboratory experiments the character of the flow was found to depend upon the parameter [Sscr ]L = L/DR, where R is the Rossby number U0/ΩL, L is the horizontal scale of the obstacle, D the depth of the fluid, U0 the flow speed and ω the angular rate of rotation. For [Sscr ]L [Gt ] 1 the flows appeared twodimensional and our results confirm the applicability of this assumption in previous asymptotic theories. For [Sscr ]L ∼ 1 a leaning disturbance is produced which can look columnar in character (‘leaning Taylor column’) and our results enable a detailed examination of this structure. To clarify the importance of nonlinear effects in the leaning Taylor column we compare them with the predictions of a linear inertial wave theory. This theory is valid only for small obstacle slopes but provided it includes the effects of viscosity it gives good predictions of the amplitude of the disturbances. The main difference between the viscous linear theory and the Navier-Stokes solution is a flow asymmetry of nonlinear origin. The role of viscosity is important but passive in the sense that it does not alter the flow structure near the obstacle but progressively dissipates the disturbance with increasing distance from the obstacle. This viscous confinement of the disturbance makes the lee wave flow structure look columnar and is important in allowing some laboratory flows to seem unbounded. The results also confirm the conjecture of Mason (1975, 1977) that the large drag forces occurring in these flows are due to inertial wave radiation.

On the Split of the Compressible Stewartson Layer due to a Surface-Mounted Obstacle

The obstacle effects are clarified on the thermally driven compressible flow in a rapidly rotating annulus by using our finite difference method based on the DuFort-Frankel/upwind schemes. It is found that the circulation within the Stewartson layer separates partially or completely into two circulations whether the obstacle (mounted on the outer sidewall) height is smaller than the upstream width or not.

On the net forces produced by surface-mounted obstacles

On the net forces produced by surface-mounted obstacles

On the net forces produced by surface-mounted obstacles

Numerical calculations of the forces involved in Ekman layer flow past three-dimensional topography are presented. The forces are obtained from finite-difference solutions of the Navier-Stokes equations. The results confirm expectations from earlier two-dimensional work that many flows produce no significant change in total momentum transfer between the fluid and the surface. Only flows generating some form of trailing vortex system appear capable of changing the total force on the lower boundary. The effects of Ekman boundary layer instabilities, and their interaction with topography, are also discussed.

Relaxing wakes behind surface-mounted obstacles in rough wall boundary layers

Detailed measurements in the wakes behind two-dimensional square section blocks (height h) mounted in thick rough wall boundary layers (height δ) are presented for cases in which h/δ [Lt ] 1. The data provides some insight into the relaxing flow downstream of reattachment, confirming the conclusion of Bradshaw & Wong (1972) that reattaching flows are surprisingly complicated and involve considerable distortion of the separated shear layer. In particular, the measurements show that eddy length scales are considerably reduced and, since the flow eventually relaxes to a boundary layer similar to that upstream, turbulence models based on eddy viscosity concepts cannot, in principle, be expected to be satisfactory. Using the present data this is demonstrated by a more detailed comparison with the theoretical predictions of Counihan, Hunt & Jackson (1974) than has been previously possible. It is shown that, whilst their theory does not predict the behaviour of the turbulent stresses, it does give reasonable agreement with the mean velocity perturbations at least in the near wake −10 < x/h < 30. Except in the near wall region, where the roughness provides the dominant length scale, it is argued that the rate at which the perturbation flow decays is governed largely by the amount by which the separated shear layer is distorted prior to reattachment, which in turn is determined by, say, a turbulence Reynolds number of the body, (hU/v0)h, or, in other words, by the characteristics of the upstream flow at, say, the body height.

Three-dimensional numerical integrations of the Navier-Stokes equations for flow over surface-mounted obstacles

Numerical integrations of the Navier-Stokes equations for flow past a smooth, three-dimensional, surface-mounted obstacle are presented. The variation of the flow with Reynolds number, and with geometric ratios such as the maximum slope of the obstacle, are investigated. The separated flow is investigated using visualizations of the surface-stress patterns, and also particle trajectories through the flow.