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At least 325 records · Page 18

A mixing-length model for the prediction of convex curvature effects on turbulent boundary layers

A mixing-length model is developed for the prediction of turbulent boundary layers with convex streamwise curvature. For large layer thickness ratio, delta/R greater than 0.05, the model scales mixing length on the wall radius of curvature, R. For small delta/R, ordinary flat wall modeling is used for the mixing-length profile with curvature corrections, following the recommendations of Eide and Johnston (1976). Effects of streamwise change of curvature are considered; a strong lag from equilibrium is required when R increases downstream. Fifteen separate data sets were compared, including both hydrodynamic and heat transfer results. Six of these computations are presented and compared to experiment.

Adams, E. W.↗

Estimation of the turbulent boundary layer pressure wavenumber-frequency spectrum using a fixed probe pair

The turbulent boundary layer (TBL) pressure fluctuations represent a dominant source of aircraft interior noise during cruise. The wavenumber-frequency characteristics of the TBL pressure field become important when determining its coupling with the aircraft structure and the resulting sound radiation into the interior of the aircraft. A technique is presented to estimate the TBL pressure wavenumber-frequency spectrum using a fixed probe pair consisting of two microphones. Flight test data from the McDonnel Douglas Ultra High Bypass Demonstrator aircraft were used to estimate the TBL pressure wavenumber-frequency spectra. These data were compared with selected wall pressure prediction models based on the existing wind tunnel data. The estimated in-flight spectral levels for the Demonstrator aircraft were in good agreement with the TBL wall pressure prediction models in the medium wavenumber range. The estimated TBL wavenumber spectral levels were found to be on the higher side in the low wavenumber region when compared with the predicted levels.

Mathur, Gopal P.↗

Lateral straining of turbulent boundary layers. I - Streamline divergence

The effect of prolonged streamline divergence on developing turbulent boundary layers is investigated using an experimental approximation of the source flow over a flat plate to achieve a simple divergence. Results are presented of hot-wire measurements for the planes of symmetry of two layers which had the same (low) Reynolds number and were developed in the presence of the same amount of simple divergence with a maximum divergence parameter of about 0.075 but with different (by a factor of 2) pressure-gradient parameters. It was found that there were two overlapping stages of development. In the initial stage, which covered a distance of about 20 initial boundary-layer thicknesses from the start of divergence, the coupled effects of both the pressure gradient and divergence were present. In the second region, which lasts nearly to the end of the diverging section, the pressure-gradient effects were negligible.

Saddoughi, Seyed G.↗

The measurement of shear stress and total heat flux in a nonadiabatic turbulent hypersonic boundary layer

Turbulent shear stress and direct turbulent total heat-flux measurements have been made across a nonadiabatic, zero pressure gradient, hypersonic boundary layer by using specially designed hot-wire probes free of strain-gauging and wire oscillation. Heat-flux measurements were in reasonably good agreement with values obtained by integrating the energy equation using measured profiles of velocity and temperature. The shear-stress values deduced from the measurements, by assuming zero correlation of velocity and pressure fluctuations, were lower than the values obtained by integrating the momentum equation. Statistical properties of the cross-correlations are similar to corresponding incompressible measurements at approximately the same momentum-thickness Reynolds number.

Mikulla, V.↗

A theoretical and flight test study of pressure fluctuations under a turbulent boundary layer. Part 2: Flight test study

The study of pressure fluctuations under a turbulent boundary layer was undertaken with the objective of extending previous work to lower frequencies. Wind tunnel and flight test measurements are invalid at low frequencies because of extraneous acoustic noises and free stream turbulence. A glider was instrumented and used as a test bed to carry microphones into a smooth flow free of acoustic noise. Hodgson had previously measured the spectrum of boundary layer noise on a glider wing. These tests showed a drop off at low frequencies that could not be reproduced in any other facility. The measurements were made on the forward fuselage of a glider where the boundary layer could develop naturally and have some length in a zero pressure gradient before the measurements were made. Two different sets of measurements were made.

Panton, R. L.↗

Large-scale motions in a supersonic turbulent boundary layer on a curved surface

This paper presents measurements in a Mach 3 turbulent boundary layer which was subjected to a short region of concave surface curvature. Mean velocity and time-averaged turbulence measurements are presented to indicate the severity of the distortion, although the focus of this study is on how the large-scale organized motions are affected by the distortion. A 12 deg increase in the inclination angle of organized motions is observed, and correlation measurements indicate an increase in the streamwise length scale. VITA conditional sampling is used to identify strong positive streamwise mass-flux gradients as the large-scale structure responsible for the measured structure angle and to determine the ensemble-averaged flowfield associated with the mass-flux gradient structures.

Donovan, J. F.↗

On the Contribution of Turbulent Boundary Layers to the Noise Inside a Fuselage

The following report deals in preliminary fashion with the transmission through a fuselage of random noise generated on the fuselage skin by a turbulent boundary layer. The concept of attenuation is abandoned and instead the problem is formulated as a sequence of two linear couplings: the turbulent boundary layer fluctuations excite the fuselage skin in lateral vibrations and the skin vibrations induce sound inside the fuselage. The techniques used are those required to determine the response of linear systems to random forcing functions of several variables. A certain degree of idealization has been resorted to. Thus the boundary layer is assumed locally homogeneous, the fuselage skin is assumed flat, unlined and free from axial loads and the 'cabin' air is bounded only by the vibrating plate so that only outgoing waves are considered. Some of the details of the statistical description have been simplified in order to reveal the basic features of the problem. The results, strictly applicable only to the limiting case of thin boundary layers, show that the sound pressure intensity is proportional to the square of the free stream density, the square of cabin air density and inversely proportional to the first power of the damping constant and to the second power of the plate density. The dependence on free stream velocity and boundary layer thickness cannot be given in general without a detailed knowledge of the characteristics of the pressure fluctuations in the boundary layer (in particular the frequency spectrum). For a flat spectrum the noise intensity depends on the fifth power of the velocity and the first power of the boundary layer thickness. This suggests that boundary layer removal is probably not an economical means for decreasing cabin noise. In general, the analysis presented here only reduces the determination of cabin noise intensity to the measurement of the effect of any one of our variables (free stream velocity, boundary layer thickness, plate thickness or the characteristic velocity of propagation in the plate). The plate generates noise by vibrating in resonance over a wide range of frequencies and increasing the damping constant is consequently an effective method of decreasing noise generation. One of the main features of the results is that the relevant quantities upon which noise intensity depends are non-dimensional numbers in which boundary layer and plate properties enter as ratios. This is taken as an indication that in testing models of structures for boundary layer noise it is not sufficient to duplicate in the model the structural characteristics of the fuselage. One must match properly the characteristics of the exicitng pressure fluctuations to that of the structure.

Corcos, G. M.↗

Transducer Resolution Effect on Pressure Fluctuations Beneath Hypersonic Turbulent Boundary Layers

The size of a pressure transducer is known to affect the accuracy of measurements of wall-pressure fluctuations beneath a turbulent boundary layer because of spatial averaging over the sensing area of the transducer. In this paper, the effect of finite transducer size is investigated by applying spatial averaging or wavenumber filters to a database of hypersonic wall pressure generated from a direct numerical simulation (DNS) that simulates the turbulent portion of the boundary layer over a sharp 7° half-angle cone at nominally Mach 8. Here, a good comparison between the DNS and the experiment in the Sandia Hypersonic Wind Tunnel at Mach 8 is achieved after spatial averaging is applied to the DNS data over an area similar to the sensing area of the transducer. The study shows that a finite sensor size similar to that of the PCB132 transducer can cause significant attenuation in the root-mean-square and power spectral density (PSD) of wall-pressure fluctuations, and the attenuation effect is identical between cone and flat plate configurations at the same friction Reynolds number. The Corcos theory is found to successfully compensate for the attenuated high-frequency components of the wall-pressure PSD.

42 ENGINEERING↗

An experimental study of the properties of surface pressure fluctuations for separating turbulent boundary layers

Noise generated by helicopter and turbomachine rotors is a nuisance that designers would like to predict and to minimize within other design constraints. A key element for the noise calculation procedure is knowledge relating the flowfield structure to the surface pressure fluctuation structure. Surface pressure fluctuation data for zero-pressure-gradient and accelerating turbulent boundary layers were obtained. The zero-pressure-gradient turbulent boundary layers were examined with freestream velocities of 72 and 105 fps. Mean and fluctuation velocity profiles and streamwise velocity spectra and wavespeeds were obtained for momentum thickness Reynolds numbers up to 18000 for the zero-pressure-gradient case and up to 4000 for the favorable-pressure-gradient case. The wall shearing stress was estimated from a Clauser plot of the near wall data. It is clear that turbulent pressure fluctuations are produced by turbulent velocity fluctuations. Detailed simultaneous measurements of all of these fluctuations are needed to determine in more detail the structural relationships between velocity and pressure fields. Although some measurements were made for unseparated flows, none were made for separated flows.

Simpson, Roger L.↗

Calculation of skin-friction coefficients for low Reynolds number turbulent boundary layer flows

An analysis is presented of the reliability of various generally accepted empirical expressions for the prediction of the skin-friction coefficient C/sub f/ of turbulent boundary layers at low Reynolds numbers in zero-pressure-gradient flows on a smooth flat plate. The skin-friction coefficients predicted from these expressions were compared to the skin-friction coefficients of experimental profiles that were determined from a graphical method formulated from the law of the wall. These expressions are found to predict values that are consistently different than those obtained from the graphical method over the range 600 Re/sub theta 2000. A curve-fitted empirical relationship was developed from the present data and yields a better estimated value of C/sub f/ in this range. The data, covering the range 200 Re/sub theta 7000, provide insight into the nature of transitional flows. They show that fully developed turbulent boundary layers occur at Reynolds numbers Re/sub theta/ down to 425. Below this level there appears to be a well-ordered evolutionary process from the laminar to the turbulent profiles. These profiles clearly display the development of the turbulent core region and the shrinking of the laminar sublayer with increasing values of Re/sub theta/.

Barr, P. K.↗

Accuracy and convergence of a finite element algorithm for turbulent boundary layer flow

The Galerkin-Weighted Residuals formulation is employed to derive an implicit finite element solution algorithm for the nonlinear parabolic partial differential equation system governing turbulent boundary layer flow. Solution accuracy and convergence with discretization refinement are quantized in several error norms using linear and quadratic basis functions. Richardson extrapolation is used to isolate integration truncation error in all norms, and Newton iteration is employed for all equation solutions performed in double-precision. The mathematical theory supporting accuracy and convergence concepts for linear elliptic equations appears extensible to the nonlinear equations characteristic of turbulent boundary layer flow.

Soliman, M. O.↗

Effect of Pressure Gradients on Plate Response and Radiation in a Supersonic Turbulent Boundary Layer

Using the model developed by the author for zero-pressure gradient turbulent boundary layers, results are obtained for adverse and favorable pressure gradients. It is shown that when a flexible plate is located in an adverse pressure gradient area, it vibrates more than if it were in a favorable pressure gradient one. Therefore the noise generated by the plate in an adverse pressure gradient is much greater than that due to the plate in a favorable pressure gradient. The effects of Reynolds number and boundary layer thickness are also analyzed and found to have the same effect in both adverse and favorable pressure gradient cases. Increasing the Reynolds number is found to increase the loading on the plate and therefore acoustic radiation. An increase in boundary layer thickness is found to decrease the level of the high frequencies and therefore the response and radiation at these frequencies. The results are in good qualitative agreement with experimental measurements.

Frendi, Abdelkader↗

Measurements and a model for convective velocities in the turbulent boundary layer

A physical model is presented which describes convective velocities within a flat plate turbulent boundary layer. A production zone concept is used as a basis for the physical model. The production zone concept employs the idea that packets of turbulent fluid are generated near the viscous sublayer. These packets are found to be discernible from the mean motion and may move either outward from the production zone or inward depending on their circulation relative to the fluid surrounding the packet. The packets are predicted to travel with a convective velocity different from the local mean velocity throughout most of the boundary layer. The model also predicts that the convective velocities will be functions of wave number outside the production zone.

Cliff, W. C.↗

Correlation and prediction of thermophoretic and inertial effects on particle deposition from non-isothermal turbulent boundary layers

The problem of small particle deposition which can cause hot stage corrosion and/or fouling in combustion turbines operating on fuels containing ash or inorganic salts is investigated. Two boundary layer transport phenomena are shown to assume importance in these cases: particle thermophoresis (migration down a temperature gradient) and particle inertia. Thermophoretic and eddy transport across turbulent boundary layers without and with particle inertia effects are quantitatively analyzed. The effects of streamwise blade curvature on particle transport across turbulent boundary layers are determined. It is shown that these phenomena destroy the analogy between mass and heat transfer or mass and momentum transfer. Also studied are the effects on particle deposition of distributed or localized wall blowing, surface roughness, and mainstream turbulence.

Rosner, D. E.↗

A review of turbulent-boundary-layer heat transfer research at Stanford, 1958-1983

For the past 25 years, there has existed in the Thermosciences Laboratory of the Mechanical Engineering Department of Stanford University a research program, primarily experimental, concerned with heat transfer through turbulent boundary layers. In the early phases of the program, the topics considered were the simple zero-pressure-gradient turbulent boundary layer with constant and with varying surface temperature, and the accelerated boundary layer. Later equilibrium boundary layers were considered along with factors affecting the boundary layer, taking into account transpired flows, flows with axial pressure gradients, transpiration, acceleration, deceleration, roughness, full-coverage film cooling, surface curvature, free convection, and mixed convection. A description is provided of the apparatus and techniques used, giving attention to the smooth plate rig, the rough plate rig, the full-coverage film cooling rig, the curvature rig, the concave wall rig, the mixed convection tunnel, and aspects of data reduction and uncertainty analysis.

Moffat, R. J.↗

Extraction of the large eddy structure of a turbulent boundary layer

Much attention is currently being focused on turbulence modeling by separation of large-scale and small-scale turbulence. One major difficulty with this method is the problem of separating and defining the large-scale structure. In this paper, a method is presented which does this separation by analyzing time-averaged, two-point double velocity correlation measurements. The basis of the method is a maximization of the inner product of a candidate velocity field with the measured turbulent velocity field. An eigenvalue problem results, whose solution provides a set of orthogonal eigenfunctions associated with specific modes of turbulent motion. The large-scale eddy, containing most of the turbulent energy, is associated with the first (largest) mode. The turbulent velocity field is then represented as a sum of the eigenfunctions. A short description of the equations is given, the methods of solution are discussed, and some results for a two-dimensional fully developed turbulent boundary layer are presented.

Lemmerman, L. A.↗