Boundary Layer Reattachment Research Articles

Experimental Investigation on the Mechanism of Flow-Type Changes in Supersonic Cavity Flows.

Compressible flows over cavities with a series value of length-to-depth ratio (L⁄D) were investigated experimentally, with the objective being to elucidate the mechanism of the transition of types of cavity flows as their L⁄D increases or decreases. For open-type cavity flows, the freedom of backflow inside the cavity is found to be crucial in smoothing out adverse pressure gradient. The spreading of the shear layer and its gradual approach toward the cavity floor as L⁄D increases tend to suppress the freedom of backflow, causing the cavity flow to change from the open-type to the transitional-type. For closed-type cavity flows, the finite thickness of the upstream boundary layer leads to the presence of three kinds of characteristic lengths that correspond to the recirculation region, the deflection of the main flow and the recovery or the abrupt rise of the pressure, respectively. The compression fans at the foot of the impingement and the exit shock waves will approach each other well in advance of the possible merge of the vertices of the conventionally defined separation and recompression wakes. As the L⁄D of a closed cavity decreases, the reattached boundary layer on the mid-portion of the cavity floor will have less developing distance, thus it will be more susceptible to adverse pressure gradient and prone to separation. For the present two-dimensional cavity models, the critical values of L⁄D were found to be about 10 and 14 for the transition of cavity flows from the open- to the transitional-type and from the transitional- to the closed-type, respectively. The sum of the pressure lengths at the front and rear wakes agrees remarkably well with the second critical L⁄D.

Analysis of DNS and LES of Flow in a Low Pressure Turbine Cascade with Incoming Wakes and Comparison with Experiments

The flow around a low-pressure turbine rotor blade with incoming periodic wakes is computed by means of DNS and LES. The latter adopts a dynamic sub-grid-scale model. The computed results are compared with time-averaged and instantaneous measured quantities. The simulation sreveal the presence of elongated flow structures, stemming from the incoming wake vorticity, which interact with the pressure side boundary layer. As the wake approaches the upstream half of the suction side, its vortical structures are stretched and align with the main flow, resulting in an impingement at virtually zero angle of attack. Periodically, in the absence of impinging wakes, the laminar suction side boundary layer separates in the adverse pressure gradient region. Flow in the laminar separation bubble is found to undergo transition via a Kelvin–Helmholtz instability. Subsequent impingement of the wake inhibits separation and thus promotes boundary layer reattachment. LES provides a fair reproduction of the DNS results both in terms of instantaneous, phase-averaged, and time-averaged flow fields with a considerable reduction in computational effort.

Effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics of a sphere

Experiments were conducted in water and wind tunnels on spheres in the Reynolds number range 6 × 103 to 6.5 × 105 to study the effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics. In the subcritical range of Re (<2 × 105), ventilation caused a marginal downstream shift in the location of laminar boundary layer separation; there was only a small change in the vortex shedding frequency. In the supercritical range (Re > 4 × 105), ventilation caused a downstream shift in the mean locations of boundary layer separation and reattachment; these lines showed significant axisymmetry in the presence of venting. No distinct vortex shedding frequency was found. Instead, a dramatic reduction occurred in the wake unsteadiness at all frequencies. The reduction of wake unsteadiness is consistent with the reduction in total drag already reported. Based on the present results and those reported earlier, the effects of natural ventilation on the flow past a sphere can be categorized in two broad regimes, viz., weak and strong interaction regimes. In the weak interaction regime (subcritical Re), the broad features of the basic sphere are largely unaltered despite the large addition of mass in the near wake. Strong interaction is promoted by the closer proximity of the inner and outer shear layers at supercritical Re. This results in a modified and steady near-wake flow, characterized by reduced unsteadiness and small drag.

Measurements in Separated and Transitional Boundary Layers Under Low-Pressure Turbine Airfoil Conditions

Detailed velocity measurements were made along a flat plate subject to the same dimensionless pressure gradient as the suction side of a modern low-pressure turbine airfoil. Reynolds numbers based on wetted plate length and nominal exit velocity were varied from 50,000 to 300,000, covering cruise to takeoff conditions. Low and high inlet free-stream turbulence intensities (0.2 and 7 percent) were set using passive grids. The location of boundary-layer separation does not depend strongly on the free-stream turbulence level or Reynolds number, as long as the boundary layer remains nonturbulent prior to separation. Strong acceleration prevents transition on the upstream part of the plate in all cases. Both free-stream turbulence and Reynolds number have strong effects on transition in the adverse pressure gradient region. Under low free-stream turbulence conditions, transition is induced by instability waves in the shear layer of the separation bubble. Reattachment generally occurs at the transition start. At Re=50,000 the separation bubble does not close before the trailing edge of the modeled airfoil. At higher Re, transition moves upstream, and the boundary layer reattaches. With high free-stream turbulence levels, transition appears to occur in a bypass mode, similar to that in attached boundary layers. Transition moves upstream, resulting in shorter separation regions. At Re above 200,000, transition begins before separation. Mean velocity, turbulence, and intermittency profiles are presented.

Particle erosion—a new concept of flow visualization and boundary layer investigations of rotating machines at high Reynolds numbers

Erosive wear due to solid particles is an undesirable phenomenon. It causes structural failure directly or in combination with fatigue or corrosion. This generally is more serious in rotating machinery of all types mainly the blades of hydro, steam and gas turbines. However, there are positive aspects of this unwanted phenomenon, which in this paper, are utilized for investigation of boundary layer growth, separation and reattachment of separated flow. In the present investigation, flow visualization of two-dimensional objects viz., circular, aerofoil and hydrofoil based on above concept has been described.

A Complementary Experimental and Numerical Study of the Flow and Heat Transfer in Offset Strip-Fin Heat Exchangers

A detailed analysis of experimental and numerical results for flow and heat transfer in similar offset strip-fin geometries is presented. Surface-average heat transfer and pressure drop, local Nusselt numbers and skin friction coefficients on the fin surface, instantaneous flow structures, and local time-averaged velocity profiles are contrasted for a range of Reynolds numbers using both prior and new experimental and numerical results. This contrast verifies that a two-dimensional unsteady numerical simulation captures the important features of the flow and heat transfer for a range of conditions. However, flow three-dimensionality appears to become important for Reynolds numbers greater than about 1300, and thermal boundary conditions are important for Reynolds numbers below 1000. The results indicate that boundary layer development, flow separation and reattachment, wake formation, and vortex shedding are all important in this complex geometry.

Turbulence measurements around a mild separation bubble and downstream of reattachment

This paper describes the behaviour of a turbulent boundary layer on a smooth, axisymmetric body exposed to an adverse pressure gradient of sufficient strength to cause a short region of mean reverse flow ('separation’). The pressure distribution is tailored such that the boundary layer reattaches and then develops in a nominally zero pressure gradient. Hot-wire and pulsed-wire measurements are presented over the separated region and downstream of reattachment. The response of the turbulence quantities to separation and to reattachment is discussed, with emphasis on the relaxation behaviour after reattachment. Over the separation bubble, the response is characteristic of that seen by other workers: the Reynolds stresses in the inner region are reduced and stress peaks develop away from the wall. At reattachment, the skewness of the fluctuating wall shear stress vanishes, as it is known to do at separation. After reattachment, the outer-layer stresses decay towards levels typical of unperturbed boundary layers. But the inner-layer relaxation is unusual. As the viscous wall stress increases downstream of reattachment, the recovery does not start at the wall and travel outward via the formation of an ‘internal’ layer, the process observed in many other relaxing flows. In fact, the inner layer responds markedly more slowly than the outer layer, even though response times are shortest near the wall. It is concluded that the large-scale, outer structures in the turbulent boundary layer survive the separation process and interfere with the regeneration of Reynolds stresses in the inner region after reattachment. This behaviour continues for at least six bubble lengths (20 boundary-layer thicknesses) after reattachment and is believed to have profound implications for our understanding of the interaction between inner and outer layers in turbulent boundary layers.

A nonlinearity-coupled receptivity process generating a Tollmien-Schlichting wave behind a backward-facing step

A nonlinear process generating a Tollmien-Schlichting wave in a boundary-layer flow over a backward-facing step is examined by analyzing the numerical solution of the incompressible Navier-Stokes equations. The flow under consideration has two types of instabilities: the Kelvin-Helmholtz instability of the separated shear layer and the viscous instability of the downstream reattached boundary layer. When the instability of the separated shear layer is excited at the two mutually close frequencies ω 1 and ω 2, the difference, ω 2 − ω 1 component, is generated and developed through the nonlinear interaction between the two primary waves of frequency ω 1 and ω 2 in the separated region. The low-frequency ω 2 − ω 1 component soon changes in structure near the reattachment location and evolves into the viscosity-conditioned Tollmien-Schlichting wave in the downstream reattached boundary layer.

Turbulence Characteristics of Supersonic Turbulent Boundary Layer Reattaching downstream of Backward-Facing Step.

The aim of this paper is to clarify the turbulence characteristics of the supersonic boundary layer which is reattaching downstream of a backward-facing step. The boundary layer flow was analyzed by a two-dimensional laser Doppler velocimeter and flow visualizations. The results showed that there was a higher level of momentum exchange between the reattaching boundary layer flow and the main supersonic stream than that of over a flat plate case. Numerical simulation was conducted in this flow field, and the results were compared with the experimental ones. It was clarified that the present CFD code exhibits good performance of simulation for the mean characteristics of flow field, and it was suggested that the improvement of the compressible turbulence model was needed.

Investigation of a turbulent cylindrical wall jet impinging normally on a flat plate. 1st Report. Fundamental properties of each jet flow.

This paper presents the results of an experimental investigation of a turbulent cylindrical wall jet impinging normally on a flat plate. This type of jet flow may have properties including boundary layer separation and reattachment on the wall. Before dealing with this jet flow, this report describes the fundamental properties of three types of jet flow : a circular free jet from a circular nozzle, a cylindrical wall jet from an annular nozzle, and the impinging jet of a circular free jet with the flat plate normally. The changes of the maximum jet velocity, the jet half-width, the turbulence at the velocity maxima, and the static pressure for each jet flow are examined, and the results are compared with those obtained for the jet flow by the other investigators.

Bulk flow parameters in turbulent wall boundary layers near separation

Experiments were conducted in a turbulent boundary layer near separation along a flat plate. The pressure gradient in flow direction was varied such that three significant boundary layer configurations could be maintained. The flow in the test section thus had simultaneously a region of favourable pressure gradient, a region of strong adverse pressure gradient with boundary layer separation and a region of reattached boundary layer. Specially designed fine probes facilitated the measurements of skin friction and velocity distribution very close to the wall. Bulk flow parameters such as skin friction coefficient C f, Reynold's number Reδ2 and shape factors H and G, which are significant characteristics of wall boundary layers were evaluated. The dependence of these parameters on the Reynolds number and along the test section was explored and the values were compared with other empirical and analytical formulae known in the literature.

Combined Heat Transfer and Fluid Dynamic Measurements Downstream of a Backward-Facing Step

Combined heat transfer and fluid dynamic measurements in a separated and reattaching boundary layer, with emphasis on the near-wall region, are presented. A constant heat-flux surface behind a single-sided sudden expansion is used to obtain Stanton number profiles as a function of Reynolds number and boundary-layer thickness at separation. Fluctuating skin-friction and temperature profiles demonstrate the importance of the near-wall region in controlling the heat transfer rate. The fluctuating skin friction controls the heat transfer rate near reattachment, while the conventional Reynolds analogy applies in the redeveloping boundary layer beginning two or three step heights downstream of reattachment.

Laminar boundary-layer reattachment in supersonic flow. Part 2. Numerical solution

A possible model of the flow in the neighbourhood of a point of reattachment of a supersonic laminar boundary layer consists of a three-tiered ‘triple-deck’ structure in which the basic problem reduces to that of solving the incompressible boundary-layer equations in the lower deck, a region of lateral and streamwise extent , where R is a representative Reynolds number of the flow (Daniels 1979). The present paper describes a scheme for the numerical solution of this problem which provides evidence in support of the proposed model and quantitative values for the O(R−¼) correction to the base pressure in the flow upstream and the O(R−⅝) correction to the position of reattachment relative to the point of intersection of the incoming shear layer and the wall. An important feature of the scheme is that it copes successfully with a flow which contains substantial reverse velocities.

Laminar boundary-layer reattachment in supersonic flow

A rational theory is developed to describe the reattachment of a laminar shear layer in supersonic flow. In the neighbourhood of reattachment the flow develops a threetiered or ‘triple-deck’ structure analogous to that which occurs at a point of separation (Stewartson &amp; Williams 1969) and, as in the separation problem, the local flow pattern may be found independently of the flow in the surrounding regions. The fundamental problem of the reattachment triple deck reduces to the solution of the incompressible boundary-layer equations in the lower deck, which is of streamwise and lateral dimensions O(R−⅜) and O(R−⅝), where R [Gt ] 1 is a representative Reynolds number for the flow. Pressure variations in this region are O(R−¼). Asymptotic solutions in terms of x, the scaled streamwise lower-deck variable, are derived to confirm the transition from a reverse flow profile at x = 0+, through reattachment, to a forward flow as x → ∞, the attainment of the required asymptotic form downstream (as x → ∞) being shown to depend crucially upon the correct choice of the finite part of the pressure in the lower deck at x = 0+. The lower-deck solution is singular at x = 0+ and assumes a complicated multi-structured form which is shown to match upstream with the solution in a largely inviscid region of dimension O(R−½) where the pressure is O(1) and the major part of the flow reversal takes place. Solutions are presented for reattachment at a wall and for symmetric reattachment behind a wedge or bluff body. In the former case the results also explain the apparent ignorance of upstream conditions in the expansive triple-deck solution formulated by Stewartson (1970) in the context of supersonic flow around a convex corner.

Boundary-layer displacement and leading edge bluntness effects on attached and separated laminar boundary layers in a compression corner. I - Theoretical study

This paper describes a theoretical analysis of highly cooled attached and separated regions of shock wave-laminar boundary-layer interaction in the presence of strong streamwise pressure gradients generated by boundary-layer displacement effects at the leading edge. This method is an extension of an earlier analysis by Holden1'12 to conditions where the inviscid flow cannot be described by simple isentropic flow relationships, and where the boundarylayer upstream of the main interaction is subjected to a strong pressure gradient. The analysis is compared with measurements described in Part II of the study. For strong leading edge displacement effects (%z, > 1), the analysis predicts that highly cooled boundary layers in hypersonic flow will be supercritical; a supercritical-subcritical jump is therefore required to join the solution to the subcritical viscous layer at separation. An examination of the experimental measurements indicates that the supercritical-subcritical jump does not reflect a sudden and basic change in the flow mechanics of separation, but is an approximation necessary because the conventional boundary-layer equations cannot adequately describe the viscous interaction process leading to separation. For some high Mach number, low Reynolds number conditions, we were unable to obtain a unique solution, without recourse to experimental data, by locating a critical point in the throat region of the flow. As in the separated region, there is serious question whether the conventional boundary-layer equations can be used to adequately describe the mechanism of boundary-layer reattachment in these flows.

A study of the turbulent separated-flow region occurring at a compression corner in supersonic flow

The turbulent separated-flow region occurring at a compression corner under certain circumstances at supersonic speed has been examined in the light of recent improvements to base pressure theory (McDonald 1964). This base pressure theory is further extended from what could be termed a single-layer model of the re-attaching boundary layer to a two-layer model, thus enabling the inviscid shock configuration which occurs at the corner to be determined. Application of this analysis to some experimental results indicates a substantial measure of agreement.While this analysis has been framed for estimating the scale of the corner interaction, the extension can of course be applied to increase the range of initial boundary-layer thicknesses to which McDonald's analysis is applicable. An example of such an application is shown to be in good agreement with experiment.

Boundary-Layer Transition by Roughness Element

Measurements were made on the boundary layer along a flat plate in a two-dimensional low turbulence wind tunnel. A fine rod was attached to the plate as a two-dimensional roughness element, and the resulting transition from laminar to turbulent flow was investigated by hot-wire equipment. The transition was found to differ in marked contrast according as the height of roughness element k is small or large as compared with the thickness of boundary layer δ k at the element. When k /δ k is small, the boundary-layer flow separates at the element, but reattaches to the plate at some distance producing scarcely any disturbance. Transition occurs in the reattached boundary layer. A sinusoidal velocity fluctuation, characteristic of the laminar-boundary-layer oscillation, is observed at a distance downstream from the roughness element. When k /δ k is large, transition occurs in the separated layer before it reattaches to the plate. Within the separated layer, a sinusoidal fluctuation is observed having the frequ...