A diffusion kinetic model for epitaxial growth of gallium arsenide layers from the gas phase

1985 ◽  
Vol 50 (8) ◽  
pp. 1774-1783 ◽  
Author(s):  
Emerich Erdös ◽  
Petr Voňka ◽  
Josef Stejskal ◽  
Přemysl Klíma
Keyword(s):  
Boundary Layer ◽  
Gallium Arsenide ◽  
Gas Phase ◽  
Diffusion Rate ◽  
Heterogeneous Reaction ◽  
Leading Edge ◽  
Quantitative Model ◽  
Diffusion Kinetic ◽  
The Mean ◽  
Substrate Size

The growth model of gallium arsenide epitaxial layers has been further extended in two ways. First of all, the location of the substrate in experiments in the reactor has been taken into account, and a general relationship has been derived for dependence of the mean effective thickness of the boundary layer on the distance of the substrate from the leading edge and on the substrate size. Secondly, the effect of rate of the chemical heterogeneous reaction has been investigated in addition to the diffusion rate on the resulting growth velocity of epitaxial gallium arsenide layers. A quantitative model comprising the rates of the both partial processes has been formulated. The theoretical relationships obtained in this way have been confronted with experimental results.

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 Boundary-layer receptivity for a parabolic leading edge. Part 2. The small-Strouhal-number limit

1997 ◽  
Vol 353 ◽  
pp. 205-220 ◽  
Author(s):  
P. W. HAMMERTON ◽  
E. J. KERSCHEN
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Acoustic Waves ◽  
Asymptotic Theory ◽  
Free Stream ◽  
Leading Edge ◽  
Numerical Results ◽  
Two Dimensional ◽  
Mean Flow ◽  
The Mean

In Hammerton & Kerschen (1996), the effect of the nose radius of a body on boundary-layer receptivity was analysed for the case of a symmetric mean flow past a two-dimensional body with a parabolic leading edge. A low-Mach-number two-dimensional flow was considered. The radius of curvature of the leading edge, rn, enters the theory through a Strouhal number, S=ωrn/U, where ω is the frequency of the unsteady free-stream disturbance and U is the mean flow speed. Numerical results revealed that the variation of receptivity for small S was very different for free-stream acoustic waves propagating parallel to the mean flow and those free-stream waves propagating at an angle to the mean flow. In this paper the small-S asymptotic theory is presented. For free-stream acoustic waves propagating parallel to the symmetric mean flow, the receptivity is found to vary linearly with S, giving a small increase in the amplitude of the receptivity coefficient for small S compared to the flat-plate value. In contrast, for oblique free-stream acoustic waves, the receptivity varies with S1/2, leading to a sharp decrease in the amplitude of the receptivity coefficient relative to the flat-plate value. Comparison of the asymptotic theory with numerical results obtained in the earlier paper confirms the asymptotic results but reveals that the numerical results diverge from the asymptotic result for unexpectedly small values of S.

Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature

2001 ◽  
Vol 439 ◽  
pp. 305-333 ◽  
Author(s):  
ZHIYIN YANG ◽  
PETER R. VOKE
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Two Dimensional ◽  
Layer Transition ◽  
Transition Mechanism ◽  
The Mean ◽  
Dimensional Instability

Transition arising from a separated region of flow is quite common and plays an important role in engineering. It is difficult to predict using conventional models and the transition mechanism is still not fully understood. We report the results of a numerical simulation to study the physics of separated boundary-layer transition induced by a change of curvature of the surface. The geometry is a flat plate with a semicircular leading edge. The Reynolds number based on the uniform inlet velocity and the leading-edge diameter is 3450. The simulated mean and turbulence quantities compare well with the available experimental data.The numerical data have been comprehensively analysed to elucidate the entire transition process leading to breakdown to turbulence. It is evident from the simulation that the primary two-dimensional instability originates from the free shear in the bubble as the free shear layer is inviscidly unstable via the Kelvin–Helmholtz mechanism. These initial two-dimensional instability waves grow downstream with a amplification rate usually larger than that of Tollmien–Schlichting waves. Three-dimensional motions start to develop slowly under any small spanwise disturbance via a secondary instability mechanism associated with distortion of two-dimensional spanwise vortices and the formation of a spanwise peak–valley wave structure. Further downstream the distorted spanwise two-dimensional vortices roll up, leading to streamwise vorticity formation. Significant growth of three-dimensional motions occurs at about half the mean bubble length with hairpin vortices appearing at this stage, leading eventually to full breakdown to turbulence around the mean reattachment point. Vortex shedding from the separated shear layer is also observed and the ‘instantaneous reattachment’ position moves over a distance up to 50% of the mean reattachment length. Following reattachment, a turbulent boundary layer is established very quickly, but it is different from an equilibrium boundary layer.

Behavior of Separation Bubble and Reattached Boundary Layer Around a Circular Leading Edge

1994 ◽  
Author(s):  
B. K. Hazarika ◽  
C. Hirsch
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Separation Bubble ◽  
Low Frequency ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Low Frequency Oscillations ◽  
Lower Reynolds Number ◽  
The Mean

The flow around a circular leading edge airfoil is investigated in an incompressible, low turbulence freestream. Hot-wire measurements are performed through the separation bubble, the reattachment and the recovery region till development of the fully turbulent boundary layer. The results of the experiments in the range of Reynolds numbers 1.7×103 to 11.8×103 are analysed and presented in this paper. A separation bubble is present near the leading edge at all Reynolds numbers. At the lowest Reynolds number investigated, the transition is preceded by strong low frequency oscillations. The correlation given by Mayle for prediction of transition of short separation bubbles is successful at the lower Reynolds number cases. The length of the separation bubble reduces considerably with increasing Reynolds number in the range investigated. The turbulence in the reattached flow persists even when the Reynolds number based on momentum thickness of the reattached boundary layer is small. The recovery length of the reattached layer is relatively short and the mean velocity profile follows logarithmic law within a short distance downstream of the reattachment point and the friction coefficient conforms to Prandtl-Schlichting skin-friction formula for a smooth flat plate at zero incidence.

On the stability of attachment-line boundary layers. Part 2. The effect of leading-edge curvature

1997 ◽  
Vol 333 ◽  
pp. 125-137 ◽  
Author(s):  
RAY-SING LIN ◽  
MUJEEB R. MALIK
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Leading Edge ◽  
Mean Flow ◽  
Eigenvalue Approach ◽  
Curvature Effects ◽  
The Mean ◽  
The Stability ◽  
Attachment Line

The stability of the incompressible attachment-line boundary layer has been studied by Hall, Malik & Poll (1984) and more recently by Lin & Malik (1996). These studies, however, ignored the effect of leading-edge curvature. In this paper, we investigate this effect. The second-order boundary-layer theory is used to account for the curvature effects on the mean flow and then a two-dimensional eigenvalue approach is applied to solve the linear stability equations which fully account for the effects of non-parallelism and leading-edge curvature. The results show that the leading-edge curvature has a stabilizing influence on the attachment-line boundary layer and that the inclusion of curvature in both the mean-flow and stability equations contributes to this stabilizing effect. The effect of curvature can be characterized by the Reynolds number Ra (based on the leading-edge radius). For Ra = 104, the critical Reynolds number R (based on the attachment-line boundary-layer length scale, see §2.2) for the onset of instability is about 637; however, when Ra increases to about 106 the critical Reynolds number approaches the value obtained earlier without curvature effect.

scholarly journals Effect of Incidence Angle on Entropy Generation in the Boundary Layers on the Blade Suction Surface in a Compressor Cascade

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1049 ◽  
Author(s):  
Shi ◽  
Ma
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Separation Bubble ◽  
Incidence Angle ◽  
Leading Edge ◽  
Generation Process ◽  
Mean Flow ◽  
Compressor Cascade ◽  
The Mean

The entropy generation that occurs within boundary layers over a C4 blade at a Reynolds number of 24,000 and incidence angles (i) of 0°,2.5°,5°,7.5°, and 10° are investigated experimentally using a particle image velocimetry (PIV) technique. To clarify the entropy generation process, the distribution of the entropy generation rates (EGR) and the unsteady flow structures within the PIV snapshots are analyzed. The results identify that for a higher incidence angle, the separation and transition occur further upstream, and the entropy generation in the boundary layer increases. When the separation takes place at the aft portion of the blade, the integral EGR decrease near the leading edge, remain minimal values in the middle portion of the blade, and increase sharply in the vicinity of the mean transition. More than 35% of the entropy generation is generated at the region downstream of the mean transition. When the separation occurs at the fore portion of the blade, the contributions of mean-flow viscous dissipation decrease to less than 20%. The entropy generation with elevated value can be detected over the entire blade. The entire integral entropy generation in the boundary layer increases sharply when the laminar separation bubble moves upstream to the leading edge.

The mean velocity profile in three-dimensional turbulent oundary layers

1963 ◽  
Vol 15 (3) ◽  
pp. 368-384 ◽  
Author(s):  
H. G. Hornung ◽  
P. N. Joubert
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Three Dimensional ◽  
Leading Edge ◽  
Viscous Sublayer ◽  
Scale Model ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

The mean velocity distribution in a low-speed three-dimensional turbulent boundary-layer flow was investigated experimentally. The experiments were performed on a large-scale model which consisted of a flat plate on which secondary flow was generated by the pressure field introduced by a circular cylinder standing on the plate. The Reynolds number based on distance from the leading edge of the plate was about 6 x 106.It was found that the wall-wake model of Coles does not apply for flow of this kind and the model breaks down in the case of conically divergent flow with rising pressure, for example, in the results of Kehl (1943). The triangular model for the yawed turbulent boundary layer proposed by Johnston (1960) was confirmed with good correlation. However, the value ofyuτ/vwhich occurs at the vertex of the triangle was found to range up to 150 whereas Johnston gives the highest value as about 16 and hence assumes that the peak lies within the viscous sublayer. Much of his analysis is based on this assumption.The dimensionless velocity-defect profile was found to lie in a fairly narrow band when plotted againsty/δ for a wide variation of other parameters including the pressure gradient. The law of the wall was found to apply in the same form as for two-dimensional flow but for a more limited range ofy.

Absolute and Convective Instabilities of a Separated Boundary Layer Near the Leading Edge of an Aerofoil

2017 ◽  
Author(s):  
S. Sarkar ◽  
K. S. Jadhav
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Constant Thickness ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
Convective Instabilities ◽  
Image Velocimetry ◽  
Through Flow ◽  
The Mean ◽  
The Stability

Present work describes the stability analysis of a separated boundary layer over a constant thickness aerofoil subjected to an impulse at the boundary for varying angles of attack (α1) and tail flap deflections (β1), where, the Reynolds number (Rec) based on chord is 1.6 × 105 and the inlet free-stream turbulence (fst) being 1.2%. The features of the boundary layer are investigated through flow field measurement by a planar particle image velocimetry (PIV) and hotwire anemometer. The response to the impulse can grow either in space and time. The Orr-Sommerfield (O-S) equation has been solved, where the mean velocity field is obtained from the experiment. Criteria following Huerre and Monkewitz [1] are used here to decide the type of instability. It has been observed that the separated boundary layer near the leading edge is absolutely unstable for low angles of attack, whereas, it is convectively unstable for higher angles of attack, when the Kelvin-Helmholtz instability is bypassed. Further, it shows a convective instability for flap angles of ±30 deg.

Wind Effects on a Stretched Membrane Heliostat

1993 ◽  
Vol 115 (3) ◽  
pp. 138-142 ◽  
Author(s):  
B. Bienkiewicz
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Leading Edge ◽  
Wind Effects ◽  
Operational Conditions ◽  
The Mean

Wind effects on stretched membrane heliostat were investigated in a boundary layer wind tunnel. The membrane response was measured at stow and representative operational conditions. It was found that both at the stow and operational conditions the mean response was much higher than the rms response. At stow conditions the largest response occurred near the leading edge of the membrane, while the rms response was the largest at the membrane centerpoint. For the operational conditions, the largest mean and rms responses were found at the membrane centerpoint. The membrane response was significantly reduced by the membrane focusing induced through the internal underpressure.

The permeability of heterocysts to the gases nitrogen and oxygen

1985 ◽  
Vol 226 (1244) ◽  
pp. 345-366 ◽  
Keyword(s):  
Gas Phase ◽  
Permeability Coefficient ◽  
Doubling Time ◽  
Diffusion Rate ◽  
Pressure Rise ◽  
Gas Diffusion ◽  
Fixation Rate ◽  
Gas Vacuoles ◽  
The Mean ◽  
Anaerobic Environment

Heterocysts of the cyanobacterium Anabaena flos-aquae retina gas vacuoles for several days after differentiation. It is demonstrated that the rate of gas diffusion into a heterocyst that is near an overlying gas phase can be determined approximately from observations on the rate of gas pressure rise required to collapse 50% of its gas vacuoles. The mean permeability coefficient ( α ) of heterocysts O 2 and N 2 was found to be 0.3 s -1 . From this it was calculated that the average permeability ( k ) of the heterocyst surface layer is about 0.4 μm s -1 (within a factor of 2). This is probably within the range that could be provided by a few layers of the 26-C glycolipids in the heterocyst envelope. It is likely, but not proven, that the main route for gas diffusion is through the envelope rather than through the terminal pores of the heterocyst. From measurements of cell nitrogen content (2.7 pg). doubling time (3 days) and heterocyst: vegetative cell ratio (1:24) it was calculated that the average heterocyst fixed 5.9 x 10 -18 mol N 2 s -1 ; this must equal the diffusion rate of N 2 inside the average heterocyst that was 22% below the outside air-saturated concentration. the maximum N 2 fixation rate allowed by the estimated permeability coefficeint would be 2.7 x 10 -17 mol s -1 per heterocyst, slightly greater than the maximum calcualted N 2 fixation rate. The observed permeability coefficient is low enough for the oxygen concentration in the heterocyst to be maintained close to zero by the probable rate of respiration, providing an anaerobic environment for nitrogenase. The rate of O 2 diffusion will limit the N 2 -fixation rate in the dark by limiting the rate at which ATP is supplied by oxidative phosphorylation.

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