Effect Of Boundary Layer Growth Research Articles

Slow-growth approximation for near-wall patch representation of wall-bounded turbulence

Wall-bounded turbulent shear flows are known to exhibit universal small-scale dynamics that are modulated by large-scale flow structures. Strong pressure gradients complicate this characterization, however. They can cause significant variation of the mean flow in the streamwise direction. For such situations, we perform asymptotic analysis of the Navier–Stokes equations to inform a model for the effect of mean flow growth on near-wall turbulence in a small domain localized to the boundary. The asymptotics are valid whenever the viscous length scale is small relative to the length scale over which the mean flow varies. To ensure the correct momentum environment, a dynamic procedure is introduced that accounts for the additional sources of mean momentum flux through the upper domain boundary arising from the asymptotic terms. Comparisons of the model's low-order, single-point statistics with those from direct numerical simulation and well-resolved large eddy simulation of adverse-pressure-gradient turbulent boundary layers indicate the asymptotic model successfully accounts for the effect of boundary layer growth on the small-scale near-wall turbulence.

The effect of upstream duct boundary layer growth and compressor blade lean angle variation on an axial compressor performance

The compressor of a gas turbine engine is extremely vulnerable on upstream duct-induced flow non-uniformities whether the duct is an engine intake or an interconnecting duct. This is justified by its position being literally an extension of the duct flow path, coupled to the fact that it operates under adverse pressure gradients. In particular, this study focuses on performance deviations between installed and uninstalled compressors. Test results acquired from a test bed installation will differ from those recorded when the compressor operates as an integral part of an engine. The upstream duct, whether an engine intake or an inter-stage duct, will affect the flow-field pattern ingested into the compressor. The case study presented here aims mostly at qualifying the effect of boundary layer growth along the upstream duct wall on compressor performance. Additionally, the compressor performance response on blade lean angle variation is also addressed, with the aim of acquiring an understanding as to how compressor blade lean angle changes interact with intake-induced flow non-uniformities. Such studies are usually conducted as part of the preliminary design phase. Consequently, experimental performance investigation is excluded at this stage of development, and therefore, computer-aided simulation techniques are used if not the only option for compressor performance prediction. Given the fact that many such design parameters need to be assessed under the time pressure exerted by the tight compressor development programme, the compressor flow simulation technique needs to provide reliable results while consuming the least possible computational time. Such a low computational time compressor flow simulation method, among others, is the two-dimensional streamline curvature (SLC) method, being also applied within the frame of reference of the current study. The paper is introduced by a brief discussion on SLC method. Then, a reference is made to the radial equilibrium equation, which is the mathematical basis of SOCRATES, a turbomachinery flow simulation tool that was used in this study. Subsequently, the influence of the upstream duct on the compressor inlet radial flow distribution is being addressed, with the aim of adjusting the compressor blade inlet lean angle, in order to minimize compressor performance deterioration. The paper concludes with a discussion of the results.

TURBIDITY CURRENT IN RECTANGULAR SETTLING TANK

The paper deals with turbidity current in settling tank. The flow field is assumed to be twodimensional, steady, isothermal and turbulent. Special attention is paid on the effect of boundary layer growth along the tank bottom on density affected flow.To predict velocity profile and sediment concentration distribution, a mathematical model is presented using k-ε turbulence model. Laboratory experiments are excuted and numerical solutions of the model predict well the results of the experiments. It is demonstrated that the growth of bottom boundary layer promotes vertical mixing of suspended solids and at the same time bottom shear depresses turbidity currents and that the flow patterns are similar to that of ideal tank, near the inlet zone, since the boundary layer thickness is small.

The linear stability of boundary-layer flow over compliant walls: effects of boundary-layer growth

The linear stability of boundary-layer flow over compliant or flexible surfaces has been studied by Carpenter & Garrad (1985), Yeo (1988) and others on the assumption of local flow parallelism. This assumption is valid at large Reynolds numbers. Non-parallel effects due to growth of the boundary layer gain in significance and importance as one gets to lower Reynolds number. This is especially so for a compliant surface, which can sustain a variety of wall-related instabilities in addition to the Tollmien—Schlichting instabilities (TSI) that are found over rigid surfaces. The present paper investigates the influence of boundary-layer non-parallelism on the TSI and wall-related travelling-wave flutter (TWF) on compliant layers. Corrections to the growth rate of locally parallel theory for boundary-layer non-parallelism are obtained through a multiple-scale analysis. The results indicate that flow non-parallelism has an overall destabilizing influence on the TSI and TWF. Flow non-parallelism is also found to have a very strong destabilizing effect on the branch of TWF that stretches to low Reynolds number. The results obtained have important implications for the design and use of compliant layers at low Reynolds numbers.

On the Görtler instability in hypersonic flows: Sutherland law fluids and real gas effects

The Görtler vortex instability mechanism in a hypersonic boundary layer on a curved wall is investigated in this paper. Our aim is to clarify the precise roles of the effects of boundary layer growth, wall cooling and gas dissociation in the determination of stability properties. We first assume that the fluid is an ideal gas with viscosity given by Sutherland’s law. It is shown that when the free-stream Mach number M is large, the boundary layer divides into two sublayers: a wall layer of O ( M 3/2 ) thickness (in terms of the boundary layer variable) over which the basic state temperature is O ( M 2 ), and a temperature adjustment layer of O (1) thickness over which the basic state temperature decreases monotonically to its free-stream value. Görtler vortices which have wavelength comparable with the boundary layer thickness (i.e. have local wavenumber of order M -3/2 ) are referred to as wall modes. We show that their downstream evolution is governed by a set of parabolic partial differential equations and that they have the usual features of Görtler vortices in incompressible boundary layers. As the local wavenumber increases, the neutral Görtler number decreases and the centre of vortex activity moves towards the temperature adjustment layer. Görtler vortices with wavenumber of order one or larger must necessarily be trapped in the temperature adjustment layer, and it is this mode which is the most dangerous. For this mode, we find that the leading-order term in the Görtler number expansion is independent of the wavenumber and is due to the curvature of the basic state. This term is also the asymptotic limit of the neutral Görtler numbers of the wall mode. To determine the higher-order correction terms in the Görtler number expansion, we have to distinguish between two wall curvature cases. When the wall curvature is proportional to (2 x ) -3/2 , where x is the streamwise variable, the Mach number M can be scaled out of the problem and the boundary layer growth takes place over an O (1) lengthscale. The evolution properties of Görtler vortices are then similar to those in incompressible flows. In the more general case when the wall curvature is not proportional to (2 x ) -3/2 , the effect of the curvature of the basic state persists in the downstream development of Görtler vortices; non-parallel effects are important over a larger range of wavenumbers, and they become of second order only when the local wavenumber is of order higher than O ( M 1/4 ). In the latter case the Görtler number expansion has the first two terms independent of non-parallel effects; the first term being due to the curvature of the basic state and the second term due to viscous effects. The second term becomes comparable with the first term when the wavenumber reaches the order M 3/8 , in which case another correction term can also be found independently of non-parallel effects. Next we investigate real gas effects by assuming that the fluid is an ideal dissociating gas. We find that both gas dissociation and wall cooling are destabilizing for the mode trapped in the temperature adjustment layer, but for the wall mode trapped near the wall the effect of gas dissociation can be either destabilizing or stabilizing.

Analytical and Experimental Investigation of Flow Through a Turbine Vane Cascade .

Present day military aero-gas turbines demand higher stage loadings for turbines so as to meet the growing for higher thrust/power with fuel consumption. This calls for improved methods of blade element profiles. Details of a computer code developed for the design of blade elements for the prescribed distribution of surface velocity (Mach number) based on Stanitz's inverse methods are presented in this paper. Effects of boundary layer growth on the blade surface has also been incorporated in this code. Turbine vane was designed making use of this program and a four-bladed cascade was fabricated. It was tested in a blow down wind tunnel for different blowing pressures and stagger angles. Mach number distribution was determined from measured static pressure on the suction and pressure surfaces of the blade. Based on stream filament technique a computer code was developed to predict the characteristics of flow thorough a blade cascade. Results of this study show reasonable agreement between experimentally obtained Mach number distribution and the initially prescribed as well as analytically predicted Mach number distributions.

Waves produced from a harmonic point source in a supersonic boundary-layer flow

The disturbance wave pattern produced from a harmonic point source in a compressible flat-plate boundary layer is computed using linear stability theory and the direct numerical integration approach. Receptivity coefficients are computed for a wide band of least-stable spanwise modes generated at the source, which are followed in the streamwise direction in order to study the wave-interference pattern. The effect of boundary-layer growth on the development of linear waves is determined by using the method of multiple scales. Results are presented for Mach numbers of 0, 2 and 7. It is found that disturbances spread in wedge-shaped regions behind the source and the wedge angle decreases with Mach number. The lateral spreading angle for the instability waves turns out to be quite close to the angle found experimentally for lateral contamination of turbulence. It is found that, owing to wave cancellation, the computed maximum disturbance amplitude is significantly lower than that obtained by following the most-amplified single normal mode.

ON THE EFFECT OF CROSSFLOW ON NONLINEAR GÖRTLER VORTICES IN CURVED CHANNEL FLOWS

It is known that the two-dimensional flow through a curved channel of narrow width is unstable to nonlinear vortices for sufficiently high Taylor-Gortler numbers and that the instability arises because of centrifugal effects. In many practical applications the basic flow of interest is three-dimensional and here we look for nonlinear, small-wavelength vortices in a three-dimensional and here we look for nonlinear, small-wavelength vortices in a three-dimensional flow through a curved channel and show that the crossflow needed to dramatically change the results for the case of a two-dimensional basic flow is extremely tiny. We derive the governing equation for constant-sized, streamwise-independent nonlinear vortices and by using a combination of asymptotics, numerical methods and phase-plane techniques we describe the solutions of this equation. Significantly, these solutions suggest that above a certain critical value for the crossflow the vortices cannot persist and that for lesser crossflows two different structures for the vortices are possible. The relevance of the results found here to the important case of external boundary-layer flows (where the effect of boundary-layer growth plays a crucial role) is indicated and suggestions for extensions of this work are made.

On the effects of boundary-layer growth on flow stability

The stability of small travelling-wave disturbances in the flow over a flat plate is discussed. An iterative method is used to generate an asymptotic series solution in inverse powers of the Reynolds number Rx = Ux/v to the power one half. The neutral-stability boundaries given by the first two terms of this series are obtained and compared with experimental data. It is shown that the parallel flow approximation leads to a valid solution at very large Reynolds numbers.

Effect of boundary-layer growth on stability of incompressible flat plate boundary layer with pressure gradient

The stability of an incompressible flat plate boundary layer with pressure gradient (Hartree pressure gradient parameter β = 1.0, 0.6, 0.4, 0.2, 0, −0.1, −0.14, and −0.1988) is computed from the linearized complete small disturbance equations. The analysis is nevertheless a quasiparallel treatment because although boundary layer growth is accounted for, the disturbance wave function is correct only in a strictly parallel flow. It is found that the nonparallel flow effect has a negligible influence on the critical Reynolds number Rδ*−c for 0.4 ≤ β ≤ 1.0, but leads to a decrease in Rδ*−c in the range −0.1988 ≤ β ≤ 0.4. The V terms lead to an increase in Rδ*−c in the range 0.4 ≤ β ≤ 1.0, and to a decrease in the range −0.1988 ≤ β ≤ 0.4. The stream tube stretching term led to a decrease in Rδ*−c in the range 0.4 ≤ β ≤ 1.0, and to an increase in the range 0.4 ≥ β ≥ −0.1988. The effect of the V terms and the stream tube stretching term ∂2U/∂x∂y appear to dominate all other boundary layer growth terms; near Rδ*−c for β = −0.1988 however, the stream tube stretching term and ∂2V/∂x2 appear to be of the same order of magnitude.

Rate constant of OH + OH = H2O + O from 1500 to 2000 K

It was shown several years ago that concentration profiles of the OH radical in the shock-initiated combustion of lean ([H2]/[O2] = 0.1) hydrogen-oxygen-argon mixtures at low pressures (≃ 30 kPa) and high temperatures (1200–2000 K) exhibit transient maxima prior to attainment of partial equilibrium. At that time, the maxima could not be accounted for quantitatively in terms of the accepted mechanism of the H2–O2 reaction. The profiles have been reanalyzed utilizing more sophisticated computational techniques and increased knowledge of the reaction mechanism. The occurrence of maxima at temperatures above 1500 K was found to depend upon the ratio of the rate constants of the elementary reactions O+H2→OH+H and OH+OH→H2O+O. Using the rate constant expression 1.6×1014 exp(−56.6 kJ/R T) cm3 mol−1 s−1 for the former reaction, the rate constant expression for the latter was found to be 5.5×1013 exp(−29 kJ/R T) cm3 mol−1 s−1. This latter expression does not extrapolate linearly on an Arrhenius plot to the available room temperature data. The effect of boundary layer growth on the data analysis is discussed.

Effect of boundary-layer growth on tailored interface operation of ashock tunnel.

Effect of boundary-layer growth on tailored interface operation of ashock tunnel.

Effect of Boundary-Layer Growth in a Shock Tube on Shock Reflection from a Closed End

The pressure behind a shock wave propagating in a constant-area duct increases slightly with time as a result of the growing boundary layer. This rise is considerably magnified by the shock reflection from the closed end of the duct. Analysis of the local interaction of the reflected shock with the boundary layer yields information on the shock configuration, but the combined effects of the waves produced by the growing boundary layer along the entire shock tube must be considered to obtain the state of the gas behind the reflected shock. The theory of the flow field behind the incident shock is modified to allow for effects in addition to boundary-layer growth which cause deviations from an ideal shock-tube flow. Experimental observations of the pressure rise behind the reflected shock, obtained for shock pressure ratios up to about 4.5 are in satisfactory agreement with the computed results, and estimates for stronger shock waves are presented.

Nonsteady Supercritical Discharge Through an Orifice

Previous studies of shock reflection from open-ended duct configurations indicate that a steady discharge is not instantaneously formed and that the effects of this lag may occasionally be important. A theory is available which satisfactorily describes the lag effects in subcritical flow, but its validity for supercritical flow has not previously been verified. Shock-tube experiments are therefore carried out to study the lag effects in supercritical flow from a sharp-edged orifice. The incident shock wave either modifies an initial supercritical discharge, or establishes such a discharge with the gas initially being at rest. Schlieren photographs show a violent transition of the flow downstream of the orifice that lasts several milliseconds. Pressure records taken inside the duct indicate a small, but distinct, pressure rise that also lasts for several milliseconds following the passage of the reflected shock wave. It is shown that this apparent agreement of the transition times is accidental. A method is described to evaluate the effect of boundary-layer growth on the pressure behind the reflected shock wave, and the results indicate that the entire observed pressure rise is accounted for by this effect. Consequently, flow adjustment in the orifice may be considered as instantaneous for all practical purposes.

The Performance of Axial-Flow Compressors As Affected by Single-Stage Characteristics

A series of calculations were carried out to obtain the performance of a six-, an eight-, and a 13-stage compressor, each designed for the same tip speed, to handle the same mass flow, and to develop a pressure ratio of 3.2. The simplified analysis was based on experimental cascade and single-stage studies. The effects of boundary-layer growth and distortion of the velocity profiles, which occur at the rear of multistage axial-flow compressors, were neglected.