The role of coherent structures in the production and dissipation of turbulence in a boundary layer is characterized, summarizing the results of recent investigations. Coherent motion is defined as a three-dimensional region of flow where at least one fundamental variable exhibits significant correlation with itself or with another variable over a space or time range significantly larger than the smallest local scales of the flow. Sections are then devoted to flow-visualization experiments, statistical analyses, numerical simulation techniques, the history of coherent-structure studies, vortices and vortical structures, conceptual models, and predictive models. Diagrams and graphs are provided.

Coherent Motions in the Turbulent Boundary Layer

This paper describes the principles of a novel 3D PIV system based on the illumination, recording and reconstruction of tracer particles within a 3D measurement volume The technique makes use of several simultaneous views of the illuminated particles and their 3D reconstruction as a light intensity distribution by means of optical tomography The technique is therefore referred to as tomographic particle image velocimetry (tomographic-PIV) The reconstruction is performed with the MART algorithm, yielding a 3D array of light intensity discretized over voxels The reconstructed tomogram pair is then analyzed by means of 3D cross-correlation with an iterative multigrid volume deformation technique, returning the three-component velocity vector distribution over the measurement volume The principles and details of the tomographic algorithm are discussed and a parametric study is carried out by means of a computer-simulated tomographic-PIV procedure The study focuses on the accuracy of the light intensity field reconstruction process The simulation also identifies the most important parameters governing the experimental method and the tomographic algorithm parameters, showing their effect on the reconstruction accuracy A computer simulated experiment of a 3D particle motion field describing a vortex ring demonstrates the capability and potential of the proposed system with four cameras The capability of the technique in real experimental conditions is assessed with the measurement of the turbulent flow in the near wake of a circular cylinder at Reynolds 2,700

Tomographic particle image velocimetry

The present paper addresses some topical issues in modelling compressible turbulent shear flows. The work is based on direct numerical simulation (DNS) of two supersonic fully developed channel flows between very cold isothermal walls. Detailed decomposition and analysis of terms appearing in the mean momentum and energy equations are presented. The simulation results are used to provide insights into differences between conventional Reynolds and Favre averaging of the mean-flow and turbulent quantities. Study of the turbulence energy budget for the two cases shows that compressibility effects due to turbulent density and pressure fluctuations are insignificant. In particular, the dilatational dissipation and the mean product of the pressure and dilatation fluctuations are very small, contrary to the results of simulations for sheared homogeneous compressible turbulence and to recent proposals for models for general compressible turbulent flows. This provides a possible explanation of why the Van Driest density-weighted transformation (which ignores any true turbulent compressibility effects) is so successful in correlating compressible boundary-layer data. Finally, it is found that the DNS data do not support the strong Reynolds analogy. A more general representation of the analogy is analysed and shown to match the DNS data very well.

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Compressible turbulent channel flows: DNS results and modelling

In this paper a concept of dilatation dissipation ed for high Reynolds number compressible turbulence is introduced. The concept is predicated on the existence of shocklike structures embedded within energetic turbulent eddies. A parametric expression for ed is found that contains calculable parameters of a turbulent field: turbulence energy and length scale, rms (turbulent) Mach number, and the kurtosis of the fluctuating velocity. The dilatation dissipation is incorporated in a second‐order closure model for compressible mixing layers and model predictions of mean and turbulence quantities are presented and, where possible, compared with experiments. It is shown that the model is capable of predicting the reduction of layer growth rates as a function of the convective Mach number Mc in accordance with Papamoschou–Roshko experiments; the computations are also shown to compare well with available measurements of Reynolds stresses at Mc=0.5–0.86. Finally, the physical implications of the new model and resu...

Dilatation dissipation: The concept and application in modeling compressible mixing layers

Compressibility Effects on Turbulence

When a vehicle travels at Mach numbers greater than one, a significant temperature gradient develops across the boundary layer due to the high levels of viscous dissipation near the wall. In fact, the static-temperature variation can be very large even in an adiabatic flow, resulting in a low­ density, high-viscosity region near the wall. In turn, this leads to a skewed mass-flux profile, a thicker boundary layer, and a region in which viscous effects are somewhat more important than at an equivalent Reynolds number in subsonic flow. Intuitively, one would expect to see significant dynamical differences between subsonic and supersonic boundary layers. However, many of these differences can be explained by simply accounting for the fluid-property variations that accompany the temperature

The Physics of Supersonic Turbulent Boundary Layers

Multiple distinct peaks of comparable strength in unsteady pressure autospectra often characterize compressible flow-induced cavity oscillations. It is unclear whether these different large-amplitude tones (i.e., Rossiter modes) coexist or are the result of a mode-switching phenomenon. The cause of additional peaks in the spectrum, particularly at low frequency, is also unknown. This article describes the analyses of unsteady pressure data in a cavity using time-frequency methods, namely the short-time Fourier transform (STFT) and the continuous Morlet wavelet transform, and higher-order spectral techniques. The STFT and wavelet analyses clearly show that the dominant mode switches between the primary Rossiter modes. This is verified by instantaneous schlieren images acquired simultaneously with the unsteady pressures. Furthermore, the Rossiter modes experience some degree of low-frequency amplitude modulation. An estimate of the modulation frequency, obtained from the wavelet analysis, matches the low-fr...

Mode-switching and nonlinear effects in compressible flow over a cavity

Experimental results are presented that reveal key features of the large-scale organized structures in a supersonic, turbulent boundary layer. Measurements were obtained in a Mach 3 zero-pressure-gradient boundary layer using a crossed-wire probe and arrays of normal hot wires with vertical, spanwise, and streamwise separations ranging from 0.1 to 0.6δ. Space–time correlation results indicate the existence of large-scale structures of a size comparable to δ, with a spanwise extent only slightly less than the vertical scale. The convection velocity of the large-scale motions is nearly constant across 80% of the boundary layer and is equal to approximately 0.9U∞.It is shown that positive events detected with the VITA conditional sampling technique correspond to steep gradients in the streamwise mass flux which extend across most of the boundary layer. These sharp gradients appear to be the upstream interfaces of large-scale turbulent ‘bulges’, similar to those seen in incompressible boundary layers. In a reference frame moving with the convection speed of the sharp gradients, low-momentum fluid is observed rotating on a large-scale, while high-momentum fluid forms a saddle point on the upstream edge of the large-scale motion. These motions are associated with elevated levels of the shear product, emphasizing their role in the dynamics of the boundary layer.

On the structure of high-Reynolds-number supersonic turbulent boundary layers

Experimental results are presented that show the existence of organized structures in a compressible, turbulent boundary layer. Results were obtained using arrays of hot wires and wall pressure transducers in a Mach-3 zero-pressure-gradient boundary layer. The VITA method of conditional sampling was used to deduce average pressure events at the wall and mass flux events throughout the boundary layer; these results show qualitative similarity to those found in incompressible flows. By conditioning upon the middle hot wire from a three-wire probe, evidence is found suggesting that structures exist of a height comparable with the boundary-layer thickness. Furthermore, two-point conditional sampling was used to show that an average pressure event could be extracted by conditioning upon mass-flux events. From this procedure we found that the structures maintain their shape as they travel downstream and also that their spanwise extent is very limited.The inferred angle from correlations between two hot wires, and between a hot wire and a wall-pressure transducer, indicate that the average structure is inclined at approximately 45° for a large part of the boundary layer. This result agrees well with structures observed in schlieren photographs of supersonic boundary layers. Measurements of the instantaneous angle show a wide distribution of structure angles, and the general behaviour of the large-scale structures is consistent with the hairpin loop model of wall turbulence.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112087002258

Organized structures in a compressible, turbulent boundary layer.

A comparison of the turbulence structure of subsonic and supersonic boundary layers reveals that, despite broad similarities, significant differences exist. The length scales derived from space‐time correlations indicate that the spanwise scales are almost identical but that the streamwise scales in the supersonic flow are about half the size of those in subsonic flow. The large‐scale structures in the subsonic boundary layer appear to move slightly slower, and lean more toward the wall than those observed in supersonic flows, and their shear stress content is distributed differently among the four quadrants. These observations should have a strong impact on deriving turbulence models for high Reynolds number supersonic flows.

Eric F. Spina

Papers

The Physics of Supersonic Turbulent Boundary Layers

Mode-switching and nonlinear effects in compressible flow over a cavity

On the structure of high-Reynolds-number supersonic turbulent boundary layers

Organized structures in a compressible, turbulent boundary layer.

A comparison of the turbulence structure of subsonic and supersonic boundary layers