Review on Space-Time Correlations in Turbulent Fluids

1965 ◽  
Vol 32 (2) ◽  
pp. 241-257 ◽  
Author(s):  
A. J. Favre
Keyword(s):  
Turbulent Flows ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Space Time ◽  
Main Flow ◽  
Wall Pressure ◽  
Time Correlations ◽  
The Mean ◽  
Supersonic Wake ◽  
Turbulent Fluids

Turbulent flows, even when stationary on the average, are time-dependent. The study of such flows must take into account their statistical properties, not only spatial but temporal as well. A review is given of the main results of space-time measurements pertaining to: (a) In incompressible flows, double and triple velocity correlations, double correlations of wall pressure and of wall pressure and velocity of the main flow; (b) in compressible flows, double correlations of pressure at the wall and outside supersonic boundary layers, and autocorrelations of velocity in a supersonic wake. The space-time correlations give evidence to the heredity and (a) the convection velocities of the vorticity and entropy modes, as compared to the mean material convection velocity, and (b) the propagation of the acoustical mode.

New space-averaging procedure for inhomogeneous flow fields using balance equation formulations

2006 ◽  
Vol 220 (9) ◽  
pp. 1363-1374
Author(s):  
S Wattananusorn
Keyword(s):  
Compressible Flows ◽  
Incompressible Flows ◽  
Flow Fields ◽  
Coupling Factor ◽  
Balance Equations ◽  
Mean Velocity ◽  
New Space ◽  
Inhomogeneous Flow ◽  
The Mean ◽  
Dependent Flow

This paper features the possibility of averaging space-dependent flow fields using a coupling factor that links the equations of momentum and energy. The scheme is applied to the mean velocity, which is derived straightforwardly through the continuity equation. It creates a small imbalance, which can be eliminated later completely. Smaller discrepancies in the integration of systems of balance equations for inhomogeneous flow are the consequence. The procedure is verified on various flow patterns, and comparisons are made with other conventional methods and with some available experimental data. Despite investigating only numerical examples of incompressible flows here, the technique, in principle, is capable of dealing with compressible flows as well. Furthermore, the proposed method discards some variables required in other techniques while still providing useful and acceptable results for practical problems.

Further space-time correlations of velocity in a turbulent boundary layer

1958 ◽  
Vol 3 (4) ◽  
pp. 344-356 ◽  
Author(s):  
A. J. Favre ◽  
J. J. Gaviglio ◽  
R. J. Dumas
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Flow Direction ◽  
Space Time ◽  
Mean Flow ◽  
Taylor’S Hypothesis ◽  
Time Correlations ◽  
The Mean ◽  
Hot Wires

This paper describes the results of further experimental investigation of the turbulent boundary layer with zero pressure gradient. Measurements of autocorrelation and of space-time double correlation have been made respectively with single hot-wires and with two hot-wires with the separation vector in any direction. Space-time correlations reach a maximum for some optimum delay. In the case of two points set on a line orthogonal to the plate, the optimum delay Ti is not zero. In the general case it is equal to the corresponding delay Ti, increased by compensating delay for translation with the mean flow. Taylor's hypothesis may be applied to the boundary layer at distances from the wall greater than 3% of the layer thickness. Space-time isocorrelation surfaces obtained with optimum delay have a large aspect ratio in the mean flow direction, even if they are relative to a point close to the wall (0·03δ); the correlations along the mean flow then retain high values on account of the large scale of the turbulence.

scholarly journals Analysis and correlation of fluid motions in natural thermal convection in a cylindrical vessel

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 859-865
Author(s):  
Wei Wang ◽  
Xin-Lei Guan ◽  
Li-Jun Wang ◽  
Chu-Wen Guo
Keyword(s):  
Temperature Gradient ◽  
Thermal Convection ◽  
Vertical Direction ◽  
Space Time ◽  
Cylindrical Vessel ◽  
Mean Velocity ◽  
Time Correlations ◽  
Characteristic Points ◽  
Order Of Magnitude ◽  
The Mean

A natural thermal convection system is set up in a cylindrical vessel with aspect ratio of 2 having a temperature gradient in the vertical direction, and the fluid motions due to convection are investigated. The 2-D velocity field along the plane passing through the diameter of the vessel is obtained using particle image velocimetry. The results indicate that the convection is in the transition stage and the mean velocity fields show two pairs of counter-rotating circulations. The mean motions are predominant in the vertical direction under the influence of the temperature gradient, while the fluctuations in the x- and y-directions have the same order of magnitude. Probability density functions of fluctuation velocities at seven characteristic points show different behaviors. The space-time correlations in the regions where the circulations interact exhibit the iso-correlation-lines predicted by the elliptical approximation hypothesis. The space-time correlations of the streamwise and vertical fluctuations show distinct movements which imply the existence of anisotropy around the interaction region.

Turbulence correlations in a compressible wake

1976 ◽  
Vol 74 (2) ◽  
pp. 251-267 ◽  
Author(s):  
A. Demetriades
Keyword(s):  
Single Point ◽  
Axisymmetric Body ◽  
Mean Flow ◽  
Space Correlation ◽  
Taylor’S Hypothesis ◽  
Time Correlations ◽  
Theory Comparison ◽  
The Mean ◽  
Convection Speed ◽  
Supersonic Wake

Space-time correlations have been measured in the turbulent supersonic wake behind a slender axisymmetric body. The data were obtained with two independently-positioned hot-wire anemometers, and interpreted with the aid of an extension of compressible anemometry theory. Comparison with earlier single-point Eulerian spectra showed a breakdown of Taylor's hypothesis near the wake edge, and thus also the expected differences in the scale lengths. The eddy convection speed appears equal to that of the mean flow, and the eddy shape is inclined to the wake axis, although it becomes nearly parallel to it at the wake edge. As a consequence, radial and longitudinal space correlation functions appear nearly equal. An upstream-downstream asymmetry was noted in the latter.

The wall pressure signature of transonic shock/boundary layer interaction

2011 ◽  
Vol 671 ◽  
pp. 288-312 ◽  
Author(s):  
MATTEO BERNARDINI ◽  
SERGIO PIROZZOLI ◽  
FRANCESCO GRASSO
Keyword(s):  
Boundary Layer ◽  
Dynamic Pressure ◽  
Pressure Fluctuations ◽  
Low Frequency ◽  
Space Time ◽  
Wall Pressure ◽  
Spanwise Direction ◽  
Frequency Spectra ◽  
Wall Pressure Fluctuations ◽  
Time Correlations

The structure of wall pressure fluctuations beneath a turbulent boundary layer interacting with a normal shock wave at Mach number M∞ = 1.3 is studied exploiting a direct numerical simulation database. Upstream of the interaction, in the zero-pressure-gradient region, pressure statistics compare well with canonical low-speed boundary layers in terms of fluctuation intensities, space–time correlations, convection velocities and frequency spectra. Across the interaction zone, the root-mean-square wall pressure fluctuations attain very large values (in excess of 162 dB), with a maximum increase of about 7 dB from the upstream level. The two-point wall pressure correlations become more elongated in the spanwise direction, indicating an increase of the pressure-integral length scales, and the convection velocities (determined from space–time correlations) are reduced. The interaction qualitatively modifies the shape of the frequency spectra, causing enhancement of the low-frequency Fourier modes and inhibition of the higher ones. In the recovery region past the interaction, the pressure spectra collapse very accurately when scaled with either the free-stream dynamic pressure or the maximum Reynolds shear stress, and exhibit distinct power-law regions with exponent −7/3 at intermediate frequencies and −5 at high frequencies. An analysis of the pressure sources in the Lighthill's equation for the instantaneous pressure has been performed to understand their contributions to the wall pressure signature. Upstream of the interaction the sources are mainly located in the proximity of the wall, whereas past the shock, important contributions to low-frequency pressure fluctuations are associated with long-lived eddies developing far from the wall.

Direct Numerical Simulation Of Turbulent Flows

1996 ◽  
Author(s):  
Anthony Leonard
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flows ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Isotropic Turbulence ◽  
Turbulent Channel Flow ◽  
Spectral Element ◽  
Von Neumann ◽  
Eddy Simulation ◽  
Parallel Supercomputers

The numerical simulation of turbulent flows has a short history. About 45 years ago von Neumann (1949) and Emmons (1949) proposed an attack on the turbulence problem by numerical simulation. But one could point to a beginning 20 years later when Deardorff (1970) reported on a large-eddy simulation of turbulent channel flow on a 24x20x14 mesh and a direct simulation of homogeneous, isotropic turbulence was accomplished on a 323 mesh by Orszag and Patterson (1972). Perhaps the arrival of the CDC 6600 triggered these initial efforts. Since that time, a number of developments have occurred along several fronts. Of course, faster computers with more memory continue to become available and now, in 1994, 2563 simulations of homogeneous turbulence are relatively common with occasional 5123 simulations being achieved on parallel supercomputers (Chen et al., 1993) (Jimenez et al., 1993). In addition, new algorithms have been developed which extend or improve capabilities in turbulence simulation. For example, spectral methods for the simulation of arbitrary homogeneous flows and the efficient simulation of wall-bounded flows have been available for some time for incompressible flows and have recently been extended to compressible flows. In addition fast, viscous vortex methods and spectral element methods are now becoming available, suitable for incompressible flow with complex geometries. As a result of all these developments, the number of turbulence simulations has been increasing rapidly in the past few years and will continue to do so. While limitations exist (Reynolds, 1990; Hussaini et al., 1990), the potential of the method will lead to the simulation of a wide variety of turbulent flows. In this chapter, we present examples of these new developments and discuss prospects for future developments.

scholarly journals Wavelet-Based Adaptive Eddy-Resolving Methods for Modeling and Simulation of Complex Wall-Bounded Compressible Turbulent Flows

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 331
Author(s):  
Xuan Ge ◽  
Giuliano De De Stefano ◽  
M. Yousuff Hussaini ◽  
Oleg V. Vasilyev
Keyword(s):  
Modeling And Simulation ◽  
Turbulent Flows ◽  
Compressible Flows ◽  
High Efficiency ◽  
Incompressible Flows ◽  
Adaptive Methods ◽  
Companion Paper ◽  
High Fidelity ◽  
Detached Eddy Simulation ◽  
Predictive Tool

This article represents the second part of a review by De Stefano and Vasilyev (2021) on wavelet-based adaptive methods for modeling and simulation of turbulent flows. Unlike the hierarchical adaptive eddy-capturing approach, described in the first part and devoted to high-fidelity modeling of incompressible flows , this companion paper focuses on the adaptive eddy-resolving framework for compressible flows in complex geometries, which also includes model-form adaptation from low to high fidelity models. A hierarchy of wavelet-based eddy-resolving methods of different fidelity has been developed for different speed regimes, various boundary conditions, and Reynolds numbers. Solutions of various fidelity are achieved using a range of modeling approaches from unsteady Reynolds-averaged Navier–Stokes simulation to delayed detached eddy simulation, wall-modeled and wall-resolved large eddy simulations. These novel methodologies open the door to construct a hierarchical approach for simulation of compressible flows covering the whole range of possibilities, from only resolving the average or dominant frequency, to capturing the intermittency of turbulence eddies, and to directly simulating the full turbulence spectrum. The generalized hierarchical wavelet-based adaptive eddy-resolving approach, once fully integrated into a single inherently interconnected simulation, results in being a very competitive and predictive tool for complicated flows in industrial design and analysis with high efficiency and accuracy.

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