Effect Of Favorable Pressure Gradient Research Articles

Semi-empirical wall pressure spectral modeling for zero and favorable pressure gradient flows.

Semi-empirical models are used to predict the power spectral density of wall pressure fluctuations in the turbulent boundary layer. Current advancements in power spectral density wall pressure fluctuation prediction have focused on expanding the range of experiments that can be predicted to include adverse pressure gradient flows; however, favorable pressure gradient flows have not received much attention. An experiment was performed to capture the effects of the favorable pressure gradient on the power spectral density. A model was then created to improve upon some of the limitations of existing models. The proposed model improves upon the prediction of the high-frequency roll-off location, incorporates improvements made by past models, and captures the effects of favorable pressure gradients.

Effects of favorable pressure gradient on turbulence structures and statistics of a flat-plate supersonic turbulent boundary layer

A Mach 2.9 flat-plate supersonic turbulent boundary layer subject to a moderate favorable pressure gradient (FPG) induced by external expansion waves is investigated through direct numerical simulation and compared with a zero pressure gradient (ZPG) boundary layer. It is found that under FPG, the logarithmic region in the van Driest transformed velocity profile is lifted above the log law, while the wake region deviates below its ZPG counterpart. The near-wall streaks are elongated in the streamwise direction with wider spanwise spacing, which leads to an attenuated meandering effect compared to the ZPG case. Although small-scale motions in the outer layer are evidently suppressed, they survive mostly in the inner layer. On the other hand, large-scale motions tend to correlate further with the lifted fluid from upstream due to bulk dilatation. However, their relative locations within the boundary layer remain unchanged. Different responses of turbulence structures in the inner and the outer layer to FPG show that this two-layer feature within the boundary layer is mainly associated with the bulk dilatation rather than the wall curvatures. The profiles of turbulent kinetic energy (TKE) and turbulent Mach number also show a two-layer behavior, where the reduction in turbulence in the outer layer is more prominent than in the inner. Positive convection occurs from the buffer to the outer layer according to the TKE budget analysis, which compensates the production and resists the decrease in the turbulence level.

Frequency-domain prediction of broadband trailing edge noise from a blunt flat plate

The aim of this study is to develop an efficient methodology for frequency-domain prediction of broadband trailing edge noise from a blunt flat plate where non-zero pressure gradient may exist in its boundary layer. This is achieved in two ways: (i) by developing new models for point pressure spectra within the boundary layer over a flat plate, and (ii) by deriving a simple formula to approximate the effect of convective velocity on the radiated noise spectrum. Firstly, two types of point pressure spectra-required as input data to predict the trailing edge noise in the frequency domain-are used. One is determined using the semi-analytic (S-A) models based on the boundary-layer theory combined with existing empirical models. It is shown that the prediction using these models show good agreements with the measurements where zero-pressure gradient assumption is valid. However, the prediction show poor agreement with that obtained from large eddy simulation results where negative (favorable) pressure gradient is observed with the boundary layer. Based on boundary layer characteristics predicted using the large eddy simulations, new model for point wall pressure spectra is proposed to account for the effect of favorable pressure gradient over the blunt flat plate on the wall pressure spectra. Sound spectra that were predicted using these models are compared with measurements to validate the proposed prediction scheme. The advantage of the semi-analytic model is that it can be applied to problems at Reynolds numbers for which the empirical model is not available. In addition, it is expected that the current models can be applied to the cases where favorable pressure gradient exists in the boundary layer over a blunt flat plate. Secondly, in order to quantitatively analyze contributions of the pressure field within the turbulent boundary layer on the flat plate to trailing edge noise, total pressure over the surface of airfoil is decomposed into its two constituents: incident pressure generated in the boundary layer without a trailing edge and the pressure formed by the scattering of the incident pressure at the trailing edge. The predictions made using each of the incident and scattered pressures reveal that the convective velocity of turbulence in the boundary layer dominantly affects the radiated sound pressure spectrum, both in terms of the gross behavior of the overall acoustic pressure spectrum through the scattered pressure and in terms of the narrow band small fluctuations of the spectrum through the incident pressure. The interaction term between the incident and the scattered is defined and the incident is shown to contribute to the radiated acoustic pressure through the interaction term. Based on this finding, a simple model to effectively compute the effects of convection velocities of the turbulence on the radiated sound pressure spectrum is proposed. It is shown that the proposed method can effectively and accurately predict the broadband trailing edge noise from the plate with considering both the incident and the scattered contributions.

Study of Underexpanded Sonic Jets by Numerical Simulation

This paper deals with the numerical simulation of sonic underexpanded axi-symmetric jets, issuing from a convergent nozzle, at different nozzle pressure ratios. The simulations have been carried out by solving the unsteady Reynolds Average Navier-Stokes (RANS) equations utilizing the realizable k-ε (epsilon) two equations turbulence model in the commercial software FLUENT (version 6.3.26). The flow is assumed to be axi-symmetric and turbulent. The computational domain included a convergent nozzle of length 50 mm and a rectangular domain of size 25 times the nozzle exit diameter (D) verses 4D, which have been modeled and meshed in GAMBIT (version 2.46). The grid consisted of 81020 cells, while gradient grid adaptions were performed later to pronounce the accuracy of the results and visualize the shock-cell structures. From the simulations, it is inferred that, for correctly expanded jets, the potential core extends upto 6D, where D is the exit diameter of the nozzle. For underexpanded jets, the shock-cell structures in the jet flow field were captured properly. A pattern of ‘shock-diamonds’ or shock-cells were observed in the flow at low NPR. The formation of shock-cell is found to change considerably and also its strength increases with increase in nozzle pressure ratio (NPR). From this study, it is clear that the effect of favorable pressure gradient in the underexpanded jet influences the jet characteristics significantly. At high NPRs, ‘Mach disc’ formation is observed in the flow field. The flow after the Mach disc becomes subsonic and regains energy from the surrounding fluid.

Oscillation Effects on Boundary-Layer Development Under the Influence of Favourable Pressure Gradients

An experimental study has been conducted to investigate the effects of oscillation at a range of Strouhal numbers (0.0006 to 0.0113) on the boundary-layer development of a flat plate under the influence of favorable pressure gradients. The Reynolds number was 10 6 based on the flat-plate chord length. An inverted airfoil placed in the turbulent region over the flat plate was used to create the effects of favorable pressure gradients. Hot-wire anemometry was used to measure the velocities in the streamwise direction. The flow separates near the rounded leading edge, causing the formation of the separation bubble. It is found that the time-averaged velocity and turbulence intensity profiles remain mostly unaffected by oscillation in the turbulent flow regions (II and III). The boundary-layer properties such as the boundary-layer displacement thickness, momentum thickness, andthe shape factor remain almost constant. However, in region I, in which the flow is in its transitional state, oscillation slows the reattachment process under the influence of favorable pressure gradients.

FLOW AND HEAT RRANSFER MEASUREMENT IN LAMINAR AND TURBULENT CONVEX SURFACE BOUNDARY LAYERS

Convex surface boundary layers have been experimentally investigated in a low speed wind tunnel, in the presence of pressure gradients (k) of -3.6x10 -6 ≤k≤+3.6x10 -6 for laminar and -0.6x10 -6 ≤k≤+0.6x10 -6 for turbulent flows. Flow and heat transfer measurements showed that stabilising effects of favourable pressure gradients caused thinner boundary layers, fuller velocity profiles and corresponding higher heat transfer rates

THE TURBULENT FLOW STRUCTURE IN STEPPED STEEP OPEN-CHANNEL

Stepped steep open-channels have watched with interests such as landscape effect and water quality purification function by aeration besides the energy dissipator. The authors have made some experiments to clarify the flow structure and considered mean flow characteristics by measuring flow depth fluctuations, mean flow velocity and pressure head on one step. In this study, we conducted an experimental examination on the turbulent flow characteristics obtained with hot-film anemometer to elucidate accelerating flow over one step. Experimental results showed that Reynolds normal stress and shear stress clearly decreased with downstream distance from step edge by the effects of favorable pressure gradient, and inverse cascade of energy happened.

Effect of favorable pressure gradient on transitional spot formation rate

The calculation of the transitional boundary layer requires estimates of the extent of the transition zone, which in turn depends on the rate at which turbulent spots are formed. This rate has been found to scale with local boundary layer thickness and viscosity, and the resulting nondimensional group (called crumble) is a function of the pressure gradient, among other parameters. Available experimental data are analyzed to show that the crumble increases slowly with increasing favorable pressure gradients, being about four times as large as in constant-pressure flow when the Thwaites pressure gradient parameter at the effective origin of the resulting turbulent boundary layer is 0.1 and when transition is driven by free-stream turbulence.

Non‐reacting and equilibrium chemically reacting turbulent boundary‐layer flows

AbstractTurbulent boundary‐layer flows of non‐reacting gases are predicted for both internal (nozzle) and external flows. Effects of favourable pressure gradients on two eddy viscosity models were studied in rocket and hypervelocity wind tunnel flows. Nozzle flows of equilibrium air with stagnation temperatures up to 10,000°K were computed. Predictions of equilibrium nitrogen flows through hypervelocity nozzles were compared with experimental data. A slender spherically blunted cone was studied at 70,000 ft altitude and 19,000 ft/sec in the earth's atmosphere. Comparisons with available experimental data showed good agreement. A computer program was developed and fully documented during this investigation for use by interested individuals.