Statistical structure of the fluctuating wall pressure and its in-plane gradients at high Reynolds number

2008 ◽  
Vol 609 ◽  
pp. 195-220 ◽  
Author(s):  
J. C. KLEWICKI ◽  
P. J. A. PRIYADARSHANA ◽  
M. M. METZGER
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
High Reynolds Number ◽  
Low Reynolds Number ◽  
Wall Pressure ◽  
Low Frequencies ◽  
Flux Intensity ◽  
Low Reynolds ◽  
High Reynolds ◽  
Surface Layer Thickness

The fluctuating wall pressure and its gradients in the plane of the surface were measured beneath the turbulent boundary layer that forms over the salt playa of Utah's west desert. Measurements were acquired under the condition of near-neutral thermal stability to best mimic the canonical zero-pressure-gradient boundary-layer flow. The Reynolds number (based on surface-layer thickness, δ, and the friction velocity, uτ) was estimated to be 1 × 106 ± 2 × 105. The equivalent sandgrain surface roughness was estimated to be in the range 15≤ks+≤85. Pressure measurements acquired simultaneously from an array of up to ten microphones were analysed. A compact array of four microphones was used to estimate the instantaneous streamwise and spanwise gradients of the surface pressure. Owing to the large length scales and low flow speeds, attaining accurate pressure statistics in the present flow required sensors capable of measuring unusually low frequencies. The effects of imperfect spatial and temporal resolution on the present measurements were also explored. Relative to pressure, pressure gradients exhibit an enhanced sensitivity to spatial resolution. Their accurate measurement does not, however, require fully capturing the low frequencies that are inherent and significant in the pressure itself. The present pressure spectra convincingly exhibit over three decades of approximately −1 slope. Comparisons with low-Reynolds-number data support previous predictions that the inner normalized wall pressure variance increases logarithmically with Reynolds number. The wall pressure autocorrelation exhibits its first zero-crossing at an advected length that is between one tenth and one fifth of the surface-layer thickness. Under any of the normalizations investigated, the present surface vorticity flux intensity values are difficult to reconcile with low-Reynolds-number data trends. Inner variables, however, do yield normalized flux intensity values that are of the same order of magnitude at low and high Reynolds number. Spectra reveal that even at high Reynolds number, the primary contributions to the pressure gradient intensities occur over a relatively narrow frequency range. This frequency range is shown to be consistent with the scale of the sublayer pocket motions. In accord with low-Reynolds-number data, the streamwise pressure gradient signals at high Reynolds number are also characterized by statistically significant pairings of opposing sign fluctuations.

Experiments on the instability waves in a supersonic jet and their acoustic radiation

1975 ◽  
Vol 69 (1) ◽  
pp. 73-95 ◽  
Author(s):  
Dennis K. Mclaughlin ◽  
Gerald L. Morrison ◽  
Timothy R. Troutt
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Large Scale ◽  
Acoustic Radiation ◽  
Low Reynolds Number ◽  
Supersonic Jet ◽  
Hot Wire ◽  
Theoretical Predictions ◽  
Low Reynolds ◽  
High Reynolds

An experimental investigation of the instability and the acoustic radiation of the low Reynolds number axisymmetric supersonic jet has been performed. Hot-wire measurements in the flow field and microphone measurements in the acoustic field were obtained from different size jets at Mach numbers of about 2. The Reynolds number ranged from 8000 to 107000, which contrasts with a Reynolds number of 1·3 × 106for similar jets exhausting into atmospheric pressure.Hot-wire measurements indicate that the instability process in the perfectly expanded jet consists of numerous discrete frequency modes around a Strouhal number of 0·18. The waves grow almost exponentially and propagate downstream at a supersonic velocity with respect to the surrounding air. Measurements of the wavelength and wave speed of theSt= 0·18 oscillation agree closely with Tam's theoretical predictions.Microphone measurements have shown that the wavelength, wave orientation and frequency of the acoustic radiation generated by the dominant instability agree with the Mach wave concept. The sound pressure levels measured in the low Reynolds number jet extrapolate to values approaching the noise levels measured by other experimenters in high Reynolds number jets. These measurements provide more evidence that the dominant noise generation mechanism in high Reynolds number jets is the large-scale instability.

scholarly journals Turbulence Measurements of High Shear Flow Fields in a Turbomachine Seal Configuration

1993 ◽  
Vol 115 (4) ◽  
pp. 670-677 ◽  
Author(s):  
G. L. Morrison ◽  
R. E. DeOtte ◽  
H. D. Thames
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Recirculation Zone ◽  
Low Reynolds Number ◽  
Suction Side ◽  
Pressure Side ◽  
Tangential Momentum ◽  
Low Reynolds ◽  
High Reynolds ◽  
Number Case

The mean velocity and Reynolds stress tensor throughout a whirling annular seal are presented. The data were collected with a three-dimensional laser Doppler velocimeter using phase averaging. Two axial flow conditions (Re = 12,000 and 24,000) were studied at one shaft speed (Ta = 6,600). The eccentricity and whirl ratios were 50 percent and 100 percent, respectively. There is a region of high axial momentum at the inlet on the pressure side of the clearance that migrates around the seal to the suction side at the exit. The normalized axial momentum in this region is higher in the low Reynolds number case due to an axial recirculation zone that occurs on the suction side of the rotor at the inlet. The recirculation zone does not occur in the high Reynolds number case. At both Reynolds numbers there is a recirculation zone on the rotor surface in the pressure side of the inlet. This recirculation zone extends from 20 to 200 deg past the rotor zenith in the tangential direction, and is one third of a clearance wide radially. The high Reynolds number circulation zone is 1.5 mean clearances long, while the low Reynolds number zone extends two mean clearances downstream. When compared to previous studies, it is apparent that the tangential momentum is no greater for a seal with whirl than for one without if other parameters are constant. Areas of high tangential momentum occur in the clearance where the axial momentum is low. Average exit plane tangential velocities in the low Reynolds number case are 1.5 times greater than those in the other flow case. These results are in general agreement with predictions made by other investigators.

Shear-induced mixing in geophysical flows: does the route to turbulence matter to its efficiency?

2013 ◽  
Vol 725 ◽  
pp. 216-261 ◽  
Author(s):  
A. Mashayek ◽  
W. R. Peltier
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Large Scale ◽  
Low Reynolds Number ◽  
Geophysical Flows ◽  
Mixing Efficiency ◽  
Stratified Turbulence ◽  
Diapycnal Mixing ◽  
Low Reynolds ◽  
High Reynolds

AbstractMotivated by the importance of diapycnal mixing parameterizations in large-scale ocean general circulation models, we provide a detailed analysis of high-Reynolds-number mixing in density stratified shear flows which constitute an archetypical example of the small-scale physical processes occurring in the oceanic interior that control turbulent diffusion. Our focus is upon the issue as to whether the route to fully developed turbulence in the stratified mixing layer is in any significant way determinant of diapycnal mixing efficiency as represented by an effective turbulent diffusivity. We characterize different routes to fully developed turbulence by the nature of the secondary instabilities through which a primary Kelvin–Helmholtz billow executes the transition to this state. We then demonstrate that different mechanisms of turbulence transition characterized in these different transition mechanisms lead to considerably different values for the efficiency of diapycnal mixing and also for the effective vertical flux of buoyancy. We show that the widely employed value of 0.15–0.2 for the efficiency of mixing in shear-induced stratified turbulence based upon both laboratory measurements and similarly low-Reynolds-number numerical simulations may be too low for the high-Reynolds-number regime characteristic of geophysical flows. Our results show that the mixing efficiency tends to a value of approximately $1/ 3$ for sufficiently large Reynolds number at an intermediate value of 0.12 for the Richardson number. This is in agreement with a theoretical predictions of Caulfield, Tang and Plasting (J. Fluid Mech., vol. 498, 2004, pp. 315–332) for the asymptotic value of mixing efficiency in stratified Couette flows. In the high-Reynolds-number regime, mixing efficiency is shown to vary over a considerable range during the course of a particular shear-induced mixing event. We explain this variation on the basis of a detailed examination of the underlying dynamics. Since values in the range 0.15–0.2 for mixing efficiency have been extensively employed to infer an effective diffusivity from ocean microstructure measurements and also in energy balance analyses of the requirements of the global ocean circulation, our findings have potentially important implications for large-scale ocean modelling. We also quantify the errors introduced by employing the Osborn (J. Phys. Oceanogr., vol. 10, 1980, pp. 83–89) formula along with an efficiency of 0.15 to infer values for effective diffusivity, and explain the logical underpinnings of this conclusion. One of the more important aspects of this work from the perspective of our theoretical understanding of stratified turbulence is the demonstration that the inverse cascade of energy, which is facilitated by the vortex-merging process that is typical of laboratory experiments and of the low-Reynolds-number simulations of shear flow evolution, is strongly suppressed by increase of the Reynolds number to values typical of geophysical flows. Based on this finding, the application of results based on low-Reynolds-number (numerical or laboratory) experiments to high-Reynolds-number geophysical shear flows needs to be reconsidered.

Well Resolved Wall Pressure Measurements in a High Reynolds Number Turbulent Boundary Layer

2004 ◽  
Author(s):  
Brendan F. Perkins
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Surface Pressure ◽  
High Reynolds Number ◽  
Wall Pressure ◽  
Pressure Measurements ◽  
Boundary Layer Turbulence ◽  
High Reynolds ◽  
Salt Playa

In order to better understand boundary layer turbulence at high Reynolds number, the fluctuating wall pressure was measured within the turbulent boundary layer that forms over the salt playa of Utah’s west desert. Pressure measurements simultaneously acquired from an array of nine microphones were analyzed and interpreted. The wall pressure intensity was computed and compared with low Reynolds number data. This analysis indicated that the variance in wall pressure increases logarithmically with Reynolds number. Computed autocorrelations provide evidence for a hierarchy of surface pressure producing scales. Space-time correlations are used to compute broadband convection velocities. The convection velocity data indicate an increasing value for larger sensor separations. To the author’s knowledge, the pressure measurements are the highest Reynolds number, well resolved measurements of fluctuating surface pressure to date.

The wall-pressure spectrum of high-Reynolds-number turbulent boundary-layer flows over rough surfaces

2015 ◽  
Vol 768 ◽  
pp. 261-293 ◽  
Author(s):  
Timothy Meyers ◽  
Jonathan B. Forest ◽  
William J. Devenport
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
High Reynolds Number ◽  
Wall Pressure ◽  
Boundary Layer Flows ◽  
High Frequency Region ◽  
Pressure Drag ◽  
Roughness Elements ◽  
High Reynolds

Experiments have been performed on a series of high-Reynolds-number flat-plate turbulent boundary layers formed over rough and smooth walls. The boundary layers were fully rough, yet the elements remained a very small fraction $({<}1.4\,\%)$ of the boundary-layer thickness, ensuring conditions free of transitional effects. The wall-pressure spectrum and its scaling were studied in detail. One of the major findings is that the rough-wall turbulent pressure spectrum at vehicle relevant conditions is comprised of three scaling regions. These include a newly discovered high-frequency region where the pressure spectrum has a viscous scaling controlled by the friction velocity, adjusted to exclude the pressure drag on the roughness elements.

scholarly journals Low-Reynolds-number turbulent boundary layers

1991 ◽  
Vol 230 ◽  
pp. 1-44 ◽  
Author(s):  
Lincoln P. Erm ◽  
Peter N. Joubert
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Low Reynolds Number ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Wall Region ◽  
Mean Flow ◽  
Low Reynolds ◽  
High Reynolds ◽  
Turbulent Wall

An investigation was undertaken to improve our understanding of low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. In practice, such flows generally occur in close proximity to a tripping device and, though it was known that the flows are affected by the actual low value of the Reynolds number, it was realized that they may also be affected by the type of tripping device used and variations in free-stream velocity for a given device. Consequently, the experimental programme was devised to investigate systematically the effects of each of these three factors independently. Three different types of device were chosen: a wire, distributed grit and cylindrical pins. Mean-flow, broadband-turbulence and spectral measurements were taken, mostly for values of Rθ varying between about 715 and about 2810. It was found that the mean-flow and broadband-turbulence data showed variations with Rθ, as expected. Spectra were plotted using scaling given by Perry, Henbest & Chong (1986) and were compared with their models which were developed for high-Reynolds-number flows. For the turbulent wall region, spectra showed reasonably good agreement with their model. For the fully turbulent region, spectra did show some appreciable deviations from their model, owing to low-Reynolds-number effects. Mean-flow profiles, broadband-turbulence profiles and spectra were found to be affected very little by the type of device used for Rθ ≈ 1020 and above, indicating an absence of dependence on flow history for this Rθ range. These types of measurements were also compared at both Rθ ≈ 1020 and Rθ ≈ 2175 to see if they were dependent on how Rθ was formed (i.e. the combination of velocity and momentum thickness used to determine Rθ). There were noticeable differences for Rθ ≈ 1020, but these differences were only convincing for the pins, and there was a general overall improvement in agreement for Rθ ≈ 2175.

scholarly journals Prediction of Heat Transfer For Turbulent Flow in Rotating Radial Duct

1995 ◽  
Vol 2 (1) ◽  
pp. 51-58
Author(s):  
P. Tekriwal
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Number ◽  
Turbulence Model ◽  
High Reynolds Number ◽  
Low Reynolds Number ◽  
Rotating Flows ◽  
Wall Function ◽  
Model Predictions ◽  
High Reynolds

The objective of the current modeling effort is to validate the numerical model and improve upon the prediction of heat transfer in rotating systems. Low-Reynolds number turbulence model (without the wall function) has been employed for three-dimensional heat transfer predictions for radially outward flow in a square cooling duct rotating about an axis perpendicular to its length. Computations are also made using the standard and extended high-Reynolds number kturbulence models (in conjunction with the wall function) for the same flow configuration. The results from all these models are compared with experimental data for flows at different rotation numbers and Reynolds number equal to 25,000. The results show that the low-Reynolds number model predictions are not as good as the high-Re model predictions with the wall function. The wall function formulation predicts the right trend of heat transfer profile and the agreement with the data is within 30% or so for flows at high rotation number. Since the Navier-Stokes equations are integrated all the way to wall in the case of low-Re model, the computation time is relatively high and the convergence is rather slow, thus rendering the low-Re model as an unattractive choice for rotating flows at high Reynolds number.The extended k-ε turbulence model is also employed to compute heat transfer for rotating flows with uneven wall temperatures and uniform wall heat flux conditions. The comparison with the experimental data available in literature shows that the predictions on both the leading wall and the trailing wall are satisfactory and within 5-25% agreement.

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