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.

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.

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.

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.

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.

Effects of Weak Free Stream Nonuniformity on Boundary Layer Transition

2005 ◽  
Vol 128 (2) ◽  
pp. 247-257 ◽  
Author(s):  
Jonathan H. Watmuff
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Free Stream ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Bypass Transition ◽  
Mean Flow ◽  
Low Speed ◽  
Free Stream Turbulence ◽  
Thickness Variations

Experiments are described in which well-defined weak Free Stream Nonuniformity (FSN) is introduced by placing fine wires upstream of the leading edge of a flat plate. Large amplitude spanwise thickness variations form in the boundary layer as a result of the interaction between the steady laminar wakes from the wires and the leading edge. The centerline of a region of elevated layer thickness is aligned with the centerline of the wake in the freestream and the response is shown to be remarkably sensitive to the spanwise length-scale of the wakes. The region of elevated thickness is equivalent to a long narrow low speed streak in the layer. Elevated Free Stream Turbulence (FST) levels are known to produce randomly forming arrays of long narrow low speed streaks in laminar boundary layers. Therefore the characteristics of the streaks resulting from the FSN are studied in detail in an effort to gain some insight into bypass transition that occurs at elevated FST levels. The shape factors of the profiles in the vicinity of the streak appear to be unaltered from the Blasius value, even though the magnitude of the local thickness variations are as large as 60% of that of the undisturbed layer. Regions of elevated background unsteadiness appear on either side of the streak and it is shown that they are most likely the result of small amplitude spanwise modulation of the layer thickness. The background unsteadiness shares many of the characteristics of Klebanoff modes observed at elevated FST levels. However, the layer remains laminar to the end of the test section (Rx≈1.4×106) and there is no evidence of bursting or other phenomena associated with breakdown to turbulence. A vibrating ribbon apparatus is used to examine interactions between the streak and Tollmien-Schlichting (TS) waves. The deformation of the mean flow introduced by the streak is responsible for substantial phase and amplitude distortion of the waves and the breakdown of the distorted waves is more complex and it occurs at a lower Reynolds number than the breakdown of the K-type secondary instability that is observed when the FSN is not present.

scholarly journals Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat plate

1988 ◽  
Vol 186 ◽  
pp. 223-241 ◽  
Author(s):  
B. Y. Wang ◽  
I. I. Glass
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Leading Edge ◽  
Expansion Method ◽  
Boundary Layer Flows ◽  
Two Phase ◽  
Displacement Thickness ◽  
Slip Region ◽  
Two Phases

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions: the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a series-expansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

Effect of Leading Edge Geometry on Boundary Layer Transition-An Experimental Approach

2014 ◽  
Vol 590 ◽  
pp. 53-57 ◽  
Author(s):  
Dinesh Bhatia ◽  
Guang Jun Yang ◽  
Jing Sun ◽  
Jian Wang
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Boundary Layer Thickness ◽  
Experimental Approach ◽  
Flow Characteristics ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Layer Transition ◽  
Edge Geometry ◽  
Displacement Thickness

Boundary layers are affected by a number of different factors. Transition of the boundary layer is very sensitive to changes in geometry, velocity and turbulence levels. An understanding of the flow characteristics over a flat plate subjected to changes in geometry, velocity and turbulence is essential to try and understand boundary layer transition. Experiments were conducted in Low Turbulence wind tunnel (LTWT) at Northwestern Polytechnical University (NWPU), China to understand the effects due to changes in geometric profiles on boundary layer transition. The leading edge of the flat plate was changed and several different configurations ranging from Aspect Ratio (AR) 1 to 12 were used. Turbulence level was kept constant at 0.02% and the velocity was kept at default value of 30 m/s. The results indicated that as the AR increases, boundary layer thickness reduces at the same location along the plate. The displacement thickness shows that the fluctuations increase with an increase with AR which denotes the effect of leading edge on turbulence spot’s production. For AR≥4, an increase in AR led to an elongation of the transition zone and a delay in transition onset. Nomenclature

scholarly journals Development of an Aerostructural Analysis Tool for a Low-Sweep Parametric Wing

2021 ◽  
Author(s):  
Julian Bardin
Keyword(s):  
Boundary Layer ◽  
Direct Method ◽  
Three Dimensional ◽  
Beam Theory ◽  
Leading Edge ◽  
Analysis Tool ◽  
Two Dimensional ◽  
Viscous Boundary Layer ◽  
Drag Forces ◽  
Displacement Thickness

An aerostructural analysis program was developed to predict the aerodynamic performance of a non-rigid, low-sweep wing. The wing planform was geometrically defined to have a rectangular section, and a trapezoidal section. The cross-section was further set to an airfoil shape which was consistent across the entire wingspan. Furthermore, to enable the inclusion of this multidisciplinary analysis module into an optimization scheme, the wing geometry was defined by a series of parameters: root chord, taper ratio, leading-edge sweep, semi-span length, and the kink location. Aerodynamic analysis was implemented through the quasi-three-dimensional approach, including a three-dimensional inviscid solution and a sectional two-dimensional viscous solution. The inviscid analysis was provided through the implementation of the vortex ring lifting surface method, which modelled the wing about its mean camber surface. The viscous aerodynamic solution was implemented through a sectional slicing of the wing. For each section, the effective angle of attack was determined and provided as an input to a two-dimensional airfoil solver. This airfoil solution was comprised of two subcomponents: a linear-strength vortex method inviscid solution, and a direct-method viscous boundary layer computation. The converged airfoil solution was developed by adjusting the effective airfoil geometry to account for the boundary layer displacement thickness, which in itself required the inviscid tangential speeds to compute. The structural solution was implemented through classical beam theory, with a torsion and bending calculator included. The torque and bending moment distribution along the wing were computed from the lift distribution, neglecting the effects of drag, and used to compute the twist and deflection of the wing. Interdisciplinary coupling was achieved through an iterative scheme. With the developed implementation, the inviscid lift loads were used to compute the deformation of the wing. This deformation was used to update the wing mesh, and the inviscid analysis was run again. This iteration was continued until the lift variation between computations was below 0.1%. Once the solution was converged upon by the inviscid and structural solutions, the viscous calculator was run to develop the parasitic drag forces. Once computation had completed, the aerodynamic lift and drag forces were output to mark the completion of execution.

Sign in / Sign up

Export Citation Format

Share Document