Mean Flow Validation for Numerical Study of Leading Edge Boundary Layer Receptivity

1990 ◽  
Vol 43 (5S) ◽  
pp. S181-S184 ◽  
Author(s):  
Thomas B. Gatski
Keyword(s):  
Boundary Layer ◽  
Numerical Study ◽  
Leading Edge ◽  
The Body ◽  
Forced Flow ◽  
Stokes Wave ◽  
Parabolic Cylinder ◽  
Mean Flow ◽  
Displacement Thickness ◽  
Tollmien Schlichting

Numerical calculations are presented for the incompressible flow over a parabolic cylinder. Cylinder radii, smaller than the Tollmien-Schlichting wavelength of the boundary-layer flow, and smaller than those examined in previous studies, are considered. The calculation includes the flow upstream of the body, as well as the leading-edge region itself, and extends downstream into the region where the Blasius boundary-layer solution holds. A steady mean flow solution is computed and the results for the scaled surface vorticity and the displacement thickness are compared to previous studies. The unsteady problem is then formulated as a perturbation solution starting with and evolving from the mean flow. Comparisons are made with the Stokes wave solutions at various periods and locations within the boundary-layer. In the initial phase of this study reported here, these mean flow results are used to analyze some of the features observed in previous forced flow numerical studies.

Effects of Weak Free Stream Nonuniformity on Boundary Layer Transition (Keynote Paper)

2003 ◽  
Author(s):  
Jonathan H. Watmuff
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Mean Flow ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
Tollmien Schlichting ◽  
Distorted Waves ◽  
Thickness Variations

Experiments are described in which well-defined FSN (Free Stream Nonuniformity) distributions are introduced by placing fine wires upstream of the leading edge of a flat plate. Large amplitude spanwise thickness variations are present in the downstream boundary layer resulting from the interaction of the laminar wakes with the leading edge. Regions of elevated background unsteadiness appear on either side of the peak layer thickness, which share many of the characteristics of Klebanoff modes, observed at elevated Free Stream Turbulence (FST) levels. However, for the low background disturbance level of the free stream, the layer remains laminar to the end of the test section (Rx ≈ l.4×106) and there is no evidence of bursting or other phenomena associated with breakdown to turbulence. A vibrating ribbon apparatus is used to demonstrate that the deformation of the mean flow is responsible for substantial phase and amplitude distortion of Tollmien-Schlichting (TS) waves. Pseudo-flow visualization of hot-wire data shows that the breakdown of the distorted waves is more complex and occurs at a lower Reynolds number than the breakdown of the K-type secondary instability observed when the FSN is not present.

The role of displacement thickness fluctuations in hydroacoustics, and the jet-drive mechanism of the flug organ pipe

1981 ◽  
Vol 374 (1759) ◽  
pp. 543-568 ◽  
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Acoustic Energy ◽  
Theoretical Treatment ◽  
Energy Transfer Mechanism ◽  
Steady Flows ◽  
Mean Flow ◽  
Flow Energy ◽  
Displacement Thickness ◽  
Organ Pipe

This paper re-examines a proposal due to Liepmann in which the hydro­acoustic effects of a turbulent boundary layer are represented in terms of the displacement thickness fluctuations. The influence of the curvature of the surface that supports the boundary layer is discussed, and in particular the asymptotic condition is obtained under which Liepmann’s formalism is applicable in the vicinity of leading and trailing edges. This is important for the theoretical treatment of the interaction of nominally steady flows with wall cavities, slots in aerofoils, splitter plates, etc. Displacement thickness fluctuations in the form of Tollmien-Schlichting waves gene­ rated at a leading edge by a disturbance, such as an incident sound wave, are shown to result in a conversion of mean flow energy into sound. At a trailing edge, however, acoustic-mean flow interaction results in the absorption of acoustic energy. A consequence of the leading-edge effect is that it provides an energy transfer mechanism which is capable of main­taining edge tone and cavity oscillations, and this is illustrated by applica­tion of the theory to the flue organ pipe. In this case encouraging support for the asymptotic analysis is provided by a comparison with recently published experimental data.

scholarly journals Boundary-layer receptivity for a parabolic leading edge

1996 ◽  
Vol 310 ◽  
pp. 243-267 ◽  
Author(s):  
P. W. Hammerton ◽  
E. J. Kerschen
Keyword(s):  
Boundary Layer ◽  
Acoustic Waves ◽  
Free Stream ◽  
Asymptotic Methods ◽  
Leading Edge ◽  
Flow Speed ◽  
The Body ◽  
Large Reynolds Number ◽  
Mean Flow ◽  
Nose Radius

The effect of the nose radius of a body on boundary-layer receptivity is analysed for the case of a symmetric mean flow past a body with a parabolic leading edge. Asymptotic methods based on large Reynolds number are used, supplemented by numerical results. The Mach number is assumed small, and acoustic free-stream disturbances are considered. The case of free-stream acoustic waves, propagating obliquely to the symmetric mean flow is considered. The body nose radius, rn, enters the theory through a Strouhal number, S = ωrn/U, where ω is the frequency of the acoustic wave and U is the mean flow speed. The finite nose radius dramatically reduces the receptivity level compared to that for a flat plate, the amplitude of the instability waves in the boundary layer being decreased by an order of magnitude when S = 0.3. Oblique acoustic waves produce much higher receptivity levels than acoustic waves propagating parallel to the body chord.

A numerical investigation of the wake of an axisymmetric body with appendages

2016 ◽  
Vol 792 ◽  
pp. 470-498 ◽  
Author(s):  
A. Posa ◽  
E. Balaras
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Axisymmetric Body ◽  
The Body ◽  
Stream Velocity ◽  
Mean Flow ◽  
Self Similarity ◽  
Second Order Statistics ◽  
Flow Features ◽  
Yaw Angle

We report wall-resolved large-eddy simulations of an axisymmetric body of revolution with appendages. The geometry is that of the DARPA SUBOFF body at 0 yaw angle and a Reynolds number equal to $\mathit{Re}_{L}=1.2\times 10^{6}$ (based on the free-stream velocity and the length of the body). The computational grid, composed of approximately 3 billion nodes, is designed to capture all essential flow features, including the turbulent boundary layers on the surface of the body. Our results are in good agreement with measurements available in the literature. It is shown that the wake of the body is affected mainly by the shear layer from the trailing edge of the fins and the turbulent boundary layer growing along the stern, while the influence of the wake of the sail is minimal. In agreement with the reference experiments, a bimodal behaviour for the turbulent stresses is observed in the wake. This is due to the displacement of the maximum of turbulent kinetic energy away from the wall along the surface of the stern, where the boundary layer is subjected to strong adverse pressure gradients. The junction flows, produced by the interaction of the boundary layer with the leading edge of the fins, enhance this bimodal pattern, feeding additional turbulence in the boundary layer and the downstream wake. The evolution of the wake towards self-similarity is also investigated up to nine diameters downstream of the tail. We found the mean flow approaches this condition, while its development is delayed by the wake of the appendages, especially by the flow coming from the tip of the fins. However, the width of the wake and its maximum momentum deficit follow the expected power-law behaviour on the side away from the sail. The second-order statistics, on the other hand, are still far from self-similarity, which is consistent with experimental observations in the literature.

scholarly journals On strongly nonlinear vortex/wave interactions in boundary-layer transition

1991 ◽  
Vol 227 ◽  
pp. 641-666 ◽  
Author(s):  
P. Hall ◽  
F. T. Smith
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Transition ◽  
Transition To Turbulence ◽  
Flow Profile ◽  
Nonlinear Interactions ◽  
Mean Flow ◽  
Strongly Nonlinear ◽  
Special Cases ◽  
Displacement Thickness ◽  
Tollmien Schlichting

The interactions between longitudinal vortices and accompanying waves considered here are strongly nonlinear, in the sense that the mean-flow profile throughout the boundary layer is completely altered from its original undisturbed state. Nonlinear interactions between vortex flow and Tollmien-Schlichting waves are addressed first, and some analytical and computational properties are described. These include the possibility in the spatial-development case of a finite-distance break-up, inducing a singularity in the displacement thickness. Second, vortex/Rayleigh-wave nonlinear interactions are considered for the compressible boundary layer, along with certain special cases of interest and some possible solution properties. Both types, vortex/Tollmien-Schlichting and vortex/Rayleigh, are short-scale/long-scale interactions and they have potential applications to many flows at high Reynolds numbers. Their strongly nonlinear nature is believed to make them very relevant to fully fledged transition to turbulence.

Experimental and Theoretical Investigation of the Supersonic Boundary Layer Stability on the Swept Wing

2008 ◽  
Vol 3 (3) ◽  
pp. 34-38
Author(s):  
Sergey A. Gaponov ◽  
Yuri G. Yermolaev ◽  
Aleksandr D. Kosinov ◽  
Nikolay V. Semionov ◽  
Boris V. Smorodsky
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Supersonic Boundary Layer ◽  
Mean Flow ◽  
Swept Wing ◽  
Wing Model ◽  
Dimensional Boundary ◽  
The Stability ◽  
Good Agreement

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

Viscous boundary layers in reversing flow

1976 ◽  
Vol 74 (1) ◽  
pp. 59-79 ◽  
Author(s):  
T. J. Pedley
Keyword(s):  
Boundary Layer ◽  
Shear Rate ◽  
Leading Edge ◽  
Wall Shear Rate ◽  
Viscous Boundary Layer ◽  
Large Molecules ◽  
Displacement Thickness ◽  
The Mean ◽  
Wall Shear ◽  
Viscous Boundary

The viscous boundary layer on a finite flat plate in a stream which reverses its direction once (at t = 0) is analysed using an improved version of the approximate method described earlier (Pedley 1975). Long before reversal (t < −t1), the flow at a point on the plate will be quasi-steady; long after reversal (t > t2), the flow will again be quasi-steady, but with the leading edge at the other end of the plate. In between (−t1 < t < t2) the flow is governed approximately by the diffusion equation, and we choose a simple solution of that equation which ensures that the displacement thickness of the boundary layer remains constant at t = −t1. The results of the theory, in the form of the wall shear rate at a point as a function of time, are given both for a uniformly decelerating stream, and for a sinusoidally oscillating stream which reverses its direction twice every cycle. The theory is further modified to cover streams which do not reverse, but for which the quasi-steady solution breaks down because the velocity becomes very small. The analysis is also applied to predict the wall shear rate at the entrance to a straight pipe when the core velocity varies with time as in a dog's aorta. The results show positive and negative peak values of shear very much larger than the mean. They suggest that, if wall shear is implicated in the generation of atherosclerosis because it alters the permeability of the wall to large molecules, then an appropriate index of wall shear at a point is more likely to be the r.m.s. value than the mean.

scholarly journals Numerical Study of Bleed Slot Flow Characteristics Using Magneto-Aerodynamics

2021 ◽  
Author(s):  
Szym on Buhajczuk
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
High Speed ◽  
Numerical Study ◽  
Flow Characteristics ◽  
Past Research ◽  
Charge Generation ◽  
High Speed Engine ◽  
Displacement Thickness ◽  
Sonic Flow

A numerical study into magneto-aerodynamic bleed control systems has been undertaken with the intent of improving the shock swallowing ability of high speed engine intakes. Past research has shown that bleed slots effectively remove sufficient mass flow of air from the system to permit shocks to be swallowed. A magnetic field's influence on a charged boundary layer creates a possibility of sealing a bleed slot when not needed. 2D bleed slots were modeled using structured grids for use with the FLUENT CFD solver. User defined functions were written to simulate charge generation and magnetic field forces. Solutions revealed that bleed slot angles, free stream Mach numbers, pressure ratios, boundary layer displacement thickness, field strength and field position all affect how the system performs. Results have shown that a properly positioned magnetic field can reduce sonic flow coefficients up to 88%, thus justifying further research and investment in wind tunnel experiments.

A Turbulent Boundary Layer Flow Over an Open Shallow Cavity

2016 ◽  
Author(s):  
Khaled J. Hammad
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Vector Fields ◽  
Turbulence Models ◽  
Leading Edge ◽  
Field Measurements ◽  
Recirculation Region ◽  
Mean Flow ◽  
Trailing Edge ◽  
Cavity Depth

Particle Image Velocimetry (PIV) was used to study the flow structure and turbulence, upstream, over, and downstream a shallow open cavity. Three sets of PIV measurements, corresponding to a turbulent incoming boundary layer and a cavity length-to-depth ratio of four, are reported. The cavity depth based Reynolds numbers were 21,000; 42,000; and 54,000. The selected flow configuration and well characterized inflow conditions allow for straightforward assessment of turbulence models and numerical schemes. All mean flow field measurements display a large flow recirculation region, spanning most of the cavity and a smaller, counter-rotating, secondary vortex, immediately downstream of the cavity leading edge. The Galilean decomposed instantaneous velocity vector fields, clearly demonstrate two distinct modes of interaction between the free shear and the cavity trailing edge. The first corresponds to a cascade of vortical structures emanating from the tip of the leading edge of the cavity that grow in size as they travel downstream and directly interact with the trailing edge, i.e., impinging vortices. The second represents vortices that travel above the trailing edge of the cavity, i.e., non-impinging vortices. In the case of impinging vortices, a strong, large scale region of recirculation forms inside the cavity and carries the flow disturbances, arising from the impingement of vortices on the trailing edge of the cavity, upstream in a manner that interacts with and influences the flow as it separates from the cavity leading edge.

Potential and Viscous Parts of the Thrust Deduction and Wake Fraction for an Ellipsoid of Revolution

1960 ◽  
Vol 4 (03) ◽  
pp. 1-16
Author(s):  
Stavros Tsakonas ◽  
Winnifred R. Jacobs
Keyword(s):  
Boundary Layer ◽  
Potential Flow ◽  
Functional Dependence ◽  
Longitudinal Axis ◽  
Layer Growth ◽  
The Body ◽  
Displacement Thickness ◽  
Layer Effect ◽  
Ellipsoid Of Revolution ◽  
Equivalent Sources

Expressions are developed for wake fraction and thrust deduction due to the potential flow and to the boundary-layer effects for a fully-submerged prolate ellipsoid of revolution. The functional dependence of wake fraction and thrust deduction on axial-propeller clearance, body slenderness, after body geometry, and Reynolds number (scale effect) are exhibited for both potential and viscous-flow cases. Closed-form expressions are derived for the potential-flow case by representing the body by a line source-sink distribution and the propeller action by a sink disk. The boundary-layer effect is determined by Lighthill's method of equivalent sources distributed on the surface having strength proportional to the displacement thickness and its derivative. The wake is replaced by a cylinder of diameter equal to twice the displacement thickness at the stern. Although in practice the propeller is usually fully submerged in the wake of the hull, in this case the substitute cylinder has been shown by computation to be no wider than the hub diameter and thus the propeller is operating in a potential field. This consideration is fundamental to the construction of a possible mathematical model having the surface sources mentioned and an equivalent sink on the longitudinal axis whose position is determined on the basis of the velocity distribution in the wake. Computational work is carried out for a modification of the airship Akron. Four different methods, with various degrees of accuracy, are used for the evaluation of the boundary-layer growth in order to ascertain the degree of sensitivity of the thrust deduction and wake fraction to the boundary-layer development.

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