Three-Dimensional Boundary Layers Over an Infinite Swept Bump and Free Wing

1995 ◽  
Vol 117 (4) ◽  
pp. 605-611 ◽  
Author(s):  
Xiaohua Wu ◽  
Kyle D. Squires
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Spanwise Direction ◽  
Step Method ◽  
Fractional Step Method ◽  
Dimensional Boundary ◽  
Single Transition ◽  
Separating Flows

Three-dimensional laminar boundary layers past an infinite swept bump and free wing were investigated numerically using the fractional step method. The objective of the work was to study the effect of surface curvature induced changes in pressure gradient and changes in the freestream flow on boundary layer skewness and growth. Simulation results demonstrate that for flows over the bump the first transition from adverse to favorable pressure gradient occurs at the front concave/convex inflexion and the second transition from favorable to adverse pressure gradient occurs at the summit. For flows past a free wing, the only transition from favorable to adverse pressure gradient occurs in front of the summit and the subsequent adverse pressure gradient is larger than the corresponding value for the bump. For both the bump and wing, the increase of initial skewing angle from 0 to 30 deg causes a 10 percent reduction in the length of the wake; the wake behind the wing is about 12 percent longer in streamwise extent than the corresponding wake behind the bump. Integral parameters in the flows over the bump display a wavy trend due to the two transitions of the pressure gradient. On the other hand, the single transition from favorable to adverse pressure gradient brings about a monotonic increase of the integral parameters for flows past the wing. Near separation and reattachment, surface-streamlines are skewed strongly in the spanwise direction. Conditions of flow detachment for the bump and wing are in good agreement with correlations for laminar separating flows with power-law velocity profiles as well as correlations for wall-curvature-induced turbulent separating flows.

scholarly journals A numerical study of strained three-dimensional wall-bounded turbulence

2000 ◽  
Vol 416 ◽  
pp. 75-116 ◽  
Author(s):  
G. N. COLEMAN ◽  
J. KIM ◽  
P. R. SPALART
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Numerical Study ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Model Testing ◽  
Turbulent Shear ◽  
Shear Stresses ◽  
Dimensional Boundary ◽  
The Mean

Channel flow, initially fully developed and two-dimensional, is subjected to mean strains that emulate the effect of rapid changes of streamwise and spanwise pressure gradients in three-dimensional boundary layers, ducts, or diffusers. As in previous studies of homogeneous turbulence, this is done by deforming the domain of a direct numerical simulation (DNS); here however the domain is periodic in only two directions and contains parallel walls. The velocity difference between the inner and outer layers is controlled by accelerating the channel walls in their own plane, as in earlier studies of three-dimensional channel flows. By simultaneously moving the walls and straining the domain we duplicate both the inner and outer regions of the spatially developing case. The results are used to address basic physics and modelling issues. Flows subject to impulsive mean three-dimensionality with and without the mean deceleration of an adverse pressure gradient (APG) are considered: strains imitating swept-wing and pure skewing (sideways turning) three-dimensional boundary layers are imposed. The APG influences the structure of the turbulence, measured for example by the ratio of shear stress to kinetic energy, much more than does the pure skewing. For both deformations, the evolution of the Reynolds stress is profoundly affected by changes to the velocity–pressure-gradient correlation Πij. This term – which represents the finite time required for the mean strain to modify the shape and orientation of the turbulent motions – is primarily responsible for the difference (lag) in direction between the mean shear and the turbulent shear stresses, a well-known feature of perturbed three-dimensional boundary layers. Files containing the DNS database and model-testing software are available from the authors for distribution, as tools for future closure-model testing.

The Law of the Wake and Plane of Symmetry Flows in Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Vol 88 (1) ◽  
pp. 101-108 ◽  
Author(s):  
F. J. Pierce
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Flows ◽  
Three Dimensional Model ◽  
Law Of The Wall ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
The Law

Coles’ model incorporating the law of the wall and the law of the wake, proposed for two and three-dimensional turbulent boundary-layer flows, is examined for the special case of plane of symmetry flows in collateral and skewed three-dimensional boundary layers. Contrary to other published results, it is shown that the model is appropriate for adverse pressure gradient plane of symmetry flows in collateral environments away from separation. Additional, it appears that the departure from Coles’ law of the wake for recently reported three-dimensional flows is of the same basic form as that observed for plane of symmetry flows in transient development or two-dimensional flow with imminent separation. Since the Coles’ model, as most velocity profile models, is proposed only in an asymptotic sense for a well-developed flow, the fact that most of the three-dimensional flows heretofore reported are in transient or undeveloped states, suggests that the three-dimensional model be examined in well-developed three-dimensional boundary-layer flows before the question of the model’s validity can be properly answered.

Adjoint-based optimization of steady suction for disturbance control in incompressible flows

2002 ◽  
Vol 467 ◽  
pp. 129-161 ◽  
Author(s):  
JAN O. PRALITS ◽  
A. HANIFI ◽  
D. S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Optimization Procedure ◽  
Adverse Pressure Gradient ◽  
Flow Mode ◽  
Mean Flow ◽  
Parabolized Stability Equations ◽  
Dimensional Boundary

The optimal distribution of steady suction needed to control the growth of single or multiple disturbances in quasi-three-dimensional incompressible boundary layers on a flat plate is investigated. The evolution of disturbances is analysed in the framework of the parabolized stability equations (PSE). A gradient-based optimization procedure is used and the gradients are evaluated using the adjoint of the parabolized stability equations (APSE) and the adjoint of the boundary layer equations (ABLE). The accuracy of the gradient is increased by introducing a stabilization procedure for the PSE. Results show that a suction peak appears in the upstream part of the suction region for optimal control of Tollmien–Schlichting (T–S) waves, steady streamwise streaks in a two-dimensional boundary layer and oblique waves in a quasi-three-dimensional boundary layer subject to an adverse pressure gradient. The mean flow modifications due to suction are shown to have a stabilizing effect similar to that of a favourable pressure gradient. It is also shown that the optimal suction distribution for the disturbance of interest reduces the growth rate of other perturbations. Results for control of a steady cross-flow mode in a three-dimensional boundary layer subject to a favourable pressure gradient show that not even large amounts of suction can completely stabilize the disturbance.

On turbulent spots in a laminar boundary layer subjected to a self-similar adverse pressure gradient

1995 ◽  
Vol 296 ◽  
pp. 185-209 ◽  
Author(s):  
Avi Seifert ◽  
Israel J. Wygnanski
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Laminar Boundary Layer ◽  
Three Dimensional ◽  
Adverse Pressure Gradient ◽  
Spreading Rate ◽  
Major Influence ◽  
Spanwise Direction ◽  
Rate Of Spread ◽  
Self Similar

The characteristics of a turbulent spot propagating in a laminar boundary layer subjected to a self-similar adverse pressure gradient (defined by a Falkner–Skan parameter β = -0.1) were investigated experimentally. It was observed that some small differences in the normalized shape of the undisturbed velocity profile caused by the pressure gradient had a major influence on the spreading rate of the spot at comparable Reδ*. The rate of spread of the spot in the spanwise direction was affected most dramatically by the pressure gradient where the average angle at which the tips of the spots moved outward relative to the plane of symmetry was 21°. It was noted that the strength and duration of the disturbance initiating the spots had an effect on their spanwise rate of spread. For example, a strong impulsive disturbance and a disturbance caused by a stationary three-dimensional roughness generated spots which spread at a much smaller rate. The interaction of the spot with the wave packet existing beyond its tip was enhanced by the adverse pressure gradient because the Reynolds number of the surrounding boundary layer was everywhere supercritical. Thus, the maximum linear amplification rate in this case is approximately four times larger than in Blasius flow. Some features of the breakdown and their relationship to the shape and the perturbation velocities in the spot are discussed. The normalized length of the calmed region relative to the length of the spot is enhanced by the adverse pressure gradient and by an increase in the intensity of the disturbance.

Measurements in adverse-pressure-gradient turbulent boundary layers with a step change in surface roughness

1975 ◽  
Vol 70 (3) ◽  
pp. 573-593 ◽  
Author(s):  
W. H. Schofield
Keyword(s):  
Surface Roughness ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Step Change ◽  
Internal Layer ◽  
Mean Velocity ◽  
Law Of The Wall

The response of turbulent boundary layers to sudden changes in surface roughness under adverse-pressure-gradient conditions has been studied experimentally. The roughness used was in the ‘d’ type array of Perry, Schofield & Joubert (1969). Two cases of a rough-to-smooth change in surface roughness were considered in the same arbitrary adverse pressure gradient. The two cases differed in the distance of the surface discontinuity from the leading edge and gave two sets of flow conditions for the establishment and growth of the internal layer which develops downstream from a change in surface roughness. These conditions were in turn different from those in the zero-pressure-gradient experiments of Antonia & Luxton. The results suggest that the growth of the new internal layer depends solely on the new conditions at the wall and scales with the local roughness length of that wall. Mean velocity profiles in the region after the step change in roughness were accurately described by Coles’ law of the wall-law of the wake combination, which contrasts with the zero-pressure-gradient results of Antonia & Luxton. The skin-friction coefficient after the step change in roughness did not overshoot the equilibrium distribution but made a slow adjustment downstream of the step. Comparisons of mean profiles indicate that similar defect profile shapes are produced in layers with arbitrary adverse pressure gradients at positions where the values of Clauser's equilibrium parameter β (= δ*τ−10dp/dx) are similar, provided that the pressure-gradient history and local values of the pressure gradient are also similar.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

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