Wall Boundary Layer Research Articles

1108 せん断乱流中の速度及び圧力スペクトルとその普遍性(2)(OS11-2 広範囲レイノルズ数におけるせん断流,OS11広範囲レイノルズ数におけるせん断流)

The local isotropy hypothesis presented by Kolmogorov seems to work well as a good approximation depending on the nature of large-scale anisotropy. We discuss how the large-scale anisotropy penetrates the small scales by investigating the anisotropic spectrum measured in the rough wall boundary layers and also the pressure spectra.

Two‐Dimensional Rotating Stall Analysis in a Wide Vaneless Diffuser

We report a numerical study on the vaneless diffuser core flow instability in centrifugal compressors. The analysis is performed for the purpose of better understanding of the rotating stall flow mechanism in radial vaneless diffusers. Since the analysis is restricted to the two-dimensional core flow, the effect of the wall boundary layers is neglected. A commercial code with the standard incompressible viscous flow solver is applied to model the vaneless diffuser core flow in the plane parallel to the diffuser walls. At the diffuser inlet, rotating jet-wake velocity pattern is prescribed and at the diffuser outlet constant static pressure is assumed. Under these circumstances, two-dimensional rotating flow instability similar to rotating stall is found to exist. Performed parameter analysis reveals that this instability is strongly influenced by the diffuser geometry and the inlet and outlet flow conditions.

RANS-Based Very Large Eddy Simulation of Thermal and Magnetic Convection at Extreme Conditions

Abstract For thermal and magnetic convection at very high Rayleigh and Hartman numbers, which are inaccessible to the conventional large eddy simulation, we propose a time-dependent Reynolds-average-Navier-Stokes (T-RANS) approach in which the large-scale deterministic motion is fully resolved by time and space solution, whereas the unresolved stochastic motion is modeled by a “subscale” model for which an one-point RANS closure is used. The resolved and modeled contributions to the turbulence moments are of the same order of magnitude and in the near-wall regions the modeled heat transport becomes dominant, emphasizing the role of the subscale model. This T-RANS approach, with an algebraic stress/flux subscale model, verified earlier in comparison with direct numerical simulation and experiments in classic Rayleigh-Bénard convection, is now expanded to simulate Rayleigh-Bénard (RB) convection at very high Ra numbers—at present up to O(1016)—and to magnetic convection in strong uniform magnetic fields. The simulations reproduce the convective cell structure and its reorganization caused by an increase in Ra number and effects of the magnetic field. The T-RANS simulations of classic RB indicate expected thinning of both the thermal and hydraulic wall boundary layer with an increase in the Ra number and an increase in the exponent of the Nu∝Ran correlation in accord with recent experimental findings and Kraichnan asymptotic theory.

Re-entrant corner flows of UCM fluids: the initial formation of lip vortices

We discuss here a third type of boundary-layer structure that arises in steady planar flows at re-entrant corners for the upper convected Maxwell fluid. This structure extends the class of similarity solutions that are associated with the inviscid flow equations and hold in an outer core region local to the corner. In previous work ( Renardy 1995 J. Non-Newtonian Fluid Mech. 58 , 83–39 ; Evans 2005 Proc. R. Soc. A 461 , 117–142 ), single and double layer structures were used to the match outer core similarity solutions to wall boundary layers in which viscometric behaviour is obtained. Here a second double layer structure is discussed, which completes the range of validity for the core similarity solutions. This structure is fundamentally different to the single layer structure in that it only admits reverse flow solutions at the upstream wall, a situation of practical relevance to describe the initial formation of lip vortices in contraction flows.

Flux-gradient profiles for momentum and heat over an urban surface

In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height zh is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5zh < z < 4zh. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed \(\phi_M =(dU/dz)kz^\prime/u_{\ast}\) followed a conventional semi-empirical function for a flat surface at a level (z/zh = 2.9), whereas, in the vicinity of the canopy height \({\phi_M}^{-1}\) was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature \((\phi_H=(d\theta/dz){kz^\prime/T_{\ast}})\) is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5zh < z < 4zh was rather similar to that for flat surfaces than that for vegetated canopies.

Flow past a circular cylinder in the vicinity of a plane wall

Results have been reported here for flow past a stationary cylinder in the vicinity of a solid wall. Navier–Stokes equations are solved here in stream-function/vorticity formulation using an improved overset grid method while using a very high spectral accuracy compact scheme to represent the convection process. To study the effect of changing the gap ( G) between the cylinder (of diameter D) and the wall, lift and drag coefficients are obtained for (a) an intermediate gap ratio of G / D = 0.5 and (b) a larger gap ratio of G / D = 1.5 . Computed results are compared with flow visualization results of Price et al. for Re = 1200 only. This problem can be viewed as one of vortex-induced instability problem where the instability arises due to mutual interaction of the vorticity field associated with the plane wall boundary layer and the vortices that are created on the cylinder surface that are shed subsequently. Such an instability mechanism was introduced in Sengupta et al. (2003a) and the flow behaviour in the present case is explained via vorticity dynamics and the developed by-pass instability theory of Sengupta et al.

Outer layer similarity in fully rough turbulent boundary layers

Turbulent boundary layer measurements were made on a flat plate covered with uniform spheres and also on the same surface with the addition of a finer-scale grit roughness. The measurements were carried out in a closed return water tunnel, over a momentum thickness Reynolds number (Re θ ) range of 3,000–15,000, using a two-component, laser Doppler velocimeter (LDV). The results show that the mean profiles for all the surfaces collapse well in velocity defect form. Using the maximum peak to trough height (Rt) as the roughness length scale (k), the roughness functions (ΔU+) for both surfaces collapse, indicating that roughness texture has no effect on ΔU+. The Reynolds stresses for the two rough surfaces also show good agreement throughout the entire boundary layer and collapse with smooth wall results outside of the roughness sublayer. Quadrant analysis and the velocity triple products show changes in the rough wall boundary layers that are confined to y<8ks, where ks is the equivalent sand roughness height. The present results provide support for Townsend’s wall similarity hypothesis for uniform three-dimensional roughness. However, departures from wall similarity may be observed for rough surfaces where 5ks is large compared to the thickness of the inner layer.

Penetration of a Transverse Supersonic Jet into a Subsonic Compressible Crossflow

Particle image velocimetry data have been acquired in the far field of the interaction generated by an overexpanded axisymmetric supersonic jet exhausting transversely from a flat plate into a subsonic compressible crossflow. Mean velocity fields were found in the streamwise plane along the flowfield centerline for different values of the crossflow Mach number M∞ and the jet-to-freestream dynamic pressure ratio J. The magnitude of the streamwise velocity deficit and the vertical velocity component both decay with downstream distance and were observed to be greater for larger J while M∞ remained constant. Jet trajectories derived independently using the maxima of each of these two velocity components are not identical, but show increasing jet penetration for larger J. Similarity in the normalized velocity field was found for constant J at two different transonic M∞ ,b utat two lower M∞ the jet appeared to interact with the wall boundary layer and data did not collapse. The magnitude and width of the peak in the vertical velocity component both increase with J, suggesting that the strength and size of the counter-rotating vortex pair increase and, thus, may have a stronger influence on aerodynamic surfaces despite further jet penetration from the wall.

Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls

The Reynolds number similarity hypothesis of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, UK, 1976)] states that the turbulence beyond a few roughness heights from the wall is independent of the surface condition. The underlying assumption is that the boundary layer thickness δ is large compared to the roughness height k. This hypothesis was tested experimentally on two types of three-dimensional rough surfaces. Boundary layer measurements were made on flat plates covered with sand grain and woven mesh roughness in a closed return water tunnel at a momentum thickness Reynolds number Reθ of ∼14000. The boundary layers on the rough walls were in the fully rough flow regime (ks+⩾100) with the ratio of the boundary layer thickness to the equivalent sand roughness height δ∕ks greater than 40. The results show that the mean velocity profiles for rough and smooth walls collapse well in velocity defect form in the overlap and outer regions of the boundary layer. The Reynolds stresses for the two rough surfaces agree well throughout most of the boundary layer and collapse with smooth wall results outside of 3ks. Higher moment turbulence statistics and quadrant analysis also indicate the differences in the rough wall boundary layers are confined to y&amp;lt;5ks. The present results provide support for Townsend’s Reynolds number similarity hypothesis for uniform three-dimensional roughness in flows where δ∕ks⩾40.

Re–entrant corner flows of the upper convected Maxwell fluid

Steady planar flow of the upper convected Maxwell (UCM) fluid is described for re–entrant corners with angles 180°/α, where ½ ⩽α&lt; 1. Local to the corner we consider a class of similarity solutions associated with the inviscid flow equations which arise from the dominance of the upper convective stress derivative in the constitutive equations. These solutions, first noted by Hinch, hold in an outer (core–flow) region and give stress singularities ofO(r−2(1−α)) (withrthe radial distance from the corner) and a stream function behaviour ofO(rnα). Herenis a parameter defining distinct solutions within this similarity class. We match such solutions to wall boundary layers, in which viscometric behaviour is retrieved. We discuss two types of boundary–layer structure. The first is a single–layer structure, previously noted by Renardy. This single layer occurs forn= 3 −αand has the viscoelastic balance of the constitutive equations holding uniformly within it. Here we complete previous analysis by considering the downstream case. The second type of boundary layer considered is a double–layer structure, which we discuss for the range 1 &lt;n&lt; 3 −α. Now the elastic balance of the constitutive equations holds within its main region, with a thinner region closer to the wall in which the relaxation terms are recovered. This structure extends the range of the core similarity solutions and has not been previously noted.

Mechanism of Momentum Exchange in the Vicinity of a Roughness Element for the Boundary Layer Developing over the Rough Wall Arranged with Two-Dimensional Square Ribs (Flow Visualization of Eddy Formed in a Cavity)

Flow visualization has been performed in the vicinity of a roughness element for the rough wall boundary layers developing over the roughness with pitch ratio p of 2 and 4 at a low Reynolds-number. The momentum thickness Reynolds numbers at streamwise distance x=865mm for p=2 and 4 were 300 and 500, respectively. For p=2, typical flow patterns are classified into 4 patterns which are consistent with those of Townes et al., otherwise 3 patterns were recognized for p=4. The frequency fm, the sum of the frequency of each flow pattern, which is closely associated with the momentum exchange normalized with the cavity width b and the friction velocity uτ for p=4 takes larger value compared with that of p=2. This quantitative result can be related that the pressure drag acting on a roughness element for p=4 s larger than that of p=2.

Flow influence on a mode of flow choking in the airfoil cascade of the thin plates

Flow of viscous compressible gas is considered in the airfoil cascade of the thin plates with great negative angle of attack. Influence of wall boundary layer upon a mode of flow choking in the airfoil cascade is estimated in the article.

404 粗面乱流境界層の対数速度分布と変動速度確率密度関数型について(G05-8 乱流,G05 流体工学)

The logarithmic velocity region is studied in zero-pressura-gradient turbulent boundary layers on the rough wall. We have already proposed the definition of log-law region in the case of smooth wall with using the probability density of velocity fluctuation. In this report this idea is expanded into the rough wall boundary layers, and extracted log-law region is discussed from the point of PDF profiles, and also its Reynolds number dependence is studied based on the experimental data.

Effect of Initial Temperature Profile on Recovery Factor Computations

Effect of Initial Temperature Profile on Recovery Factor Computations

Active Flow Control Using Steady Blowing for a Low-Pressure Turbine Cascade

The paper presents mid-span measurements for a turbine cascade with active flow control. Steady blowing through an inclined plane wall jet has been used to control the separation characteristics of a high-lift low-pressure turbine airfoil at low Reynolds numbers. Measurements were made at design incidence for blowing ratios from approximately 0.25 to 2.0 (ratio of jet-to-local freestream velocity), for Reynolds numbers of 25,000 and 50,000 (based on axial chord and inlet velocity), and for freestream turbulence intensities of 0.4% and 4%. Detailed flow field measurements were made downstream of the cascade using a three-hole pressure probe, static pressure distributions were measured on the airfoil suction surface, and hot-wire measurements were made to characterize the interaction between the wall jet and boundary layer. The primary focus of the study is on the low-Reynolds number and low-freestream turbulence intensity cases, where the baseline airfoil stalls and high profile losses result. For low freestream turbulence (0.4%), the examined method of flow control was effective at preventing stall and reducing the profile losses. At a Reynolds number of 25,000, a blowing ratio greater than 1.0 was required to suppress stall. At a Reynolds number of 50,000, a closed separation bubble formed at a very low blowing ratio (0.25) resulting in a significant reduction in the profile loss. For high freestream turbulence intensity (4%), where the baseline airfoil has a closed separation bubble and low profile losses, blowing ratios below 1.0 resulted in a larger separation bubble and higher losses. The mechanism by which the wall jet affects the separation characteristics of the airfoil is examined through hot-wire traverse measurements in the vicinity of the slot.

Microbubble drag reduction in rough walled turbulent boundary layers with comparison against polymer drag reduction

Experiments were conducted in the 12-inch diameter tunnel at the Applied Research Laboratory, Pennsylvania State University using the tunnel wall boundary layer to determine the influence of surface roughness on microbubble drag reduction. To accomplish this, carbon dioxide was injected through a slot at rates of 0.001 m3/s to 0.011 m3/s, and the resulting skin friction drag measured on a 317.5-mm long by 152.4-mm span balance. In addition to the hydrodynamically smooth balance plate, additional plates were covered with roughly 75, 150, and 300 micron grit. Over the speed range tested of 7.6, 10.7, and 13.7 m/s, the roughness ranged from smooth to fully rough. Not only was microbubble drag reduction achieved over the rough surfaces, but the % drag reduction at a given gas flow rate was larger for larger roughness. Scaling of the data is discussed. Comparison against results of a polymer drag reduction experiment, using the same facility, is made. Finally, a measure of the expected persistence of the phenomenon is given.

Shear flow past a square cylinder near a wall

A numerical study on the wake behind a square cylinder placed parallel to a wall has been made. The cylinder is considered to be within the boundary layer of the wall, so that the outside flow is taken to be due to uniform shear. Flow has been investigated in the laminar Reynolds number (based on the cylinder height) range. The interaction of wall boundary layer on the vortex shedding at Reynolds number up to 1400.0 has been investigated for cylinder to wall gap height 0.5 and 0.25 times the cylinder height. The gap flow between the cylinder and wall during a period of vortex shedding has been obtained. The governing unsteady Navier–Stokes equations are discretised through the finite volume method on staggered grid system. An algorithm SIMPLE has been used to compute the discretised equations iteratively. Our results show that at the gap height 0.5 times the cylinder height the vortex shedding occurs at a Strouhal number greater than for an isolated cylinder. Vortex shedding suppression occurs and wake becomes steady up to a certain value of Reynolds number at gap height 0.25 time the cylinder height. At higher Reynolds number the formation of a single row of negative vortices behind the cylinder when it is in close proximity to wall is noteworthy. Due to the shear, the drag experienced by the cylinder is found to decrease with the reduction of gap height.

Transient mixed convection flow instabilities in a vertical pipe

The present paper investigates a numerical study of flow instabilities in transient mixed convection in a vertical pipe. At the entrance of the pipe, the flow is suddenly submitted to a temperature step. The convection heat transfer on the outer surface of the pipe is taken into account. The governing equations are solved using a finite difference explicit scheme. The numerical results show that the time development of streamlines and isotherms is strongly dependent on the inlet temperature steps. For positive temperature steps, the unsteady vortex is significant in the vicinity of the wall and the reversal flow appears below the wave instability. In the case of negative temperature steps and especially for the low Reynolds number, the reversal flow appears on top of the wave instability. During the transient, the apparition of the vortical structures along the wall leads to the wall boundary layer instability. This phenomenon is due to the transient mixed convection flows. The temperature step effects on the heat transfer of the flow are presented in our paper.

On Disturbance Propagation in Internal-Flow Boundary Layers

The unsteady interaction of plane-channel wall boundary layers with a supersonic inviscid flow is investigated. The flow regimes in which disturbances introduced by the boundary layer developing on one wall influence the boundary layer on the other wall are considered. The regime of relatively large pressure disturbance amplitudes generated near the nozzle outlet or by deforming the channel walls is studied. In these conditions, the interaction process is described by a system of Burgers equations with retarded arguments. Numerical solutions of this system are obtained for symmetric and antisymmetric perturbations of the channel walls.

Numerical simulation of magnetic control of heat transfer in thermal convection

We report on numerical study of effects of orientation and distribution of an external magnetic field on the reorganization of convective structures and heat transfer in thermal convection in electrically conductive fluids. The simulations were performed using a transient RANS (T-RANS) approach in which the large-scale deterministic structures are numerically resolved in time and space and the unresolved contribution is modelled using an algebraic stress–flux three-equation subscale model. For low Prandtl ( Pr) fluids the subscale model was extended to include Pr-dependent molecular dissipation of heat flux. The method was first validated in natural convection in a side-heated cubical enclosure subjected to magnetic fields of different orientation, strength and penetration depth, showing good agreement with the previous benchmark studies. Subsequently, a series of simulations was performed of turbulent Rayleigh–Bénard convection subjected to different magnetic fields over a range of Rayleigh ( Ra) and Hartmann ( Ha) numbers. The computed Nusselt number showed good agreement with the available experimental results. Numerical visualization of instantaneous flow patterns showed dramatic differences in the convective structures and local heat transfer for different orientation of the magnetic field with respect to the gravitation vector. A gradual, step-like increase in the magnetic strength revealed an interesting outcome of the “competition” between the buoyancy and the Lorentz forces, leading first to chaotic transition and eventually to laminarization. For specific ranges of Ha, it was found that a local magnetic field confined to the wall boundary layer along the thermally active walls provides almost equal effects as the homogeneous field over the whole flow, indicating an interesting possibility for controlling thermal convection and associated heat transfer.