A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points. All essential turbulence scales are resolved on the computational grid and no subgrid model is used. A large number of turbulence statistics are computed and compared with the existing experimental data at comparable Reynolds numbers. Agreements as well as discrepancies are discussed in detail. Particular attention is given to the behavior of turbulence correlations near the wall. A number of statistical correlations which are complementary to the existing experimental data are reported for the first time.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112087000892

Turbulence statistics in fully developed channel flow at low reynolds number

A new subgrid scale model is proposed for Large Eddy Simulations in complex geometries. This model which is based on the square of the velocity gradient tensor accounts for the effects of both the strain and the rotation rate of the smallest resolved turbulent fluctuations. Moreover it recovers the proper y
3 near-wall scaling for the eddy viscosity without requiring dynamic procedure. It is also shown from a periodic turbulent pipe flow computation that the model can handle transition.

/pdf/subgrid-scale-stress-modelling-based-on-the-square-of-the-e05h19jine.pdf

Subgrid-scale stress modelling based on the square of the velocity gradient tensor

The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.

A dynamic subgrid‐scale model for compressible turbulence and scalar transport

▪ Abstract We review the direct numerical simulation (DNS) of turbulent flows. We stress that DNS is a research tool, and not a brute-force solution to the Navier-Stokes equations for engineering problems. The wide range of scales in turbulent flows requires that care be taken in their numerical solution. We discuss related numerical issues such as boundary conditions and spatial and temporal discretization. Significant insight into turbulence physics has been gained from DNS of certain idealized flows that cannot be easily attained in the laboratory. We discuss some examples. Further, we illustrate the complementary nature of experiments and computations in turbulence research. Examples are provided where DNS data has been used to evaluate measurement accuracy. Finally, we consider how DNS has impacted turbulence modeling and provided further insight into the structure of turbulent boundary layers.

/pdf/direct-numerical-simulation-a-tool-in-turbulence-research-2a650vh1lf.pdf

DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research

Fully developed turbulent channel flow was simulated numerically at Reynolds number 13800, based on centerline velocity and channel halt width. The large-scale flow field was obtained by directly integrating the filtered, three dimensional, time dependent, Navier-Stokes equations. The small-scale field motions were simulated through an eddy viscosity model. The calculations were carried out on the ILLIAC IV computer with up to 516,096 grid points. The computed flow field was used to study the statistical properties of the flow as well as its time dependent features. The agreement of the computed mean velocity profile, turbulence statistics, and detailed flow structures with experimental data is good. The resolvable portion of the statistical correlations appearing in the Reynolds stress equations are calculated. Particular attention is given to the examination of the flow structure in the vicinity of the wall.

/pdf/numerical-investigation-of-turbulent-channel-flow-4kp9lt0z26.pdf

Numerical investigation of turbulent channel flow

Space-time correlation measurements in the roughly isotropic turbulence behind a regular grid spanning a uniform airstream give the simplest Eulerian time correlation if we choose for the upstream probe signal a time delay which just ‘cancels’ the mean flow displacement. The correlation coefficient of turbulent velocities passed through matched narrow-band niters shows a strong dependence on nominal filter frequency (∼ wave-number at these small turbulence levels). With plausible scaling of the time separations, a scaling dependent on both wave-number and time, it is possible to effect a good collapse of the correlation functions corresponding to wave-numbers from 0·5 cm−1, the location of the peak in the three-dimensional spectrum, to 10 cm−1, about half the Kolmogorov wave-number. The spectrally local time-scaling factor is a ‘parallel’ combination of the times characterizing (i) gross strain distortion by larger eddies, (ii) wrinkling distortion by smaller eddies, (iii) convection by larger eddies and (iv) gross rotation by larger eddies.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112071001599

Simple Eulerian time correlation of full-and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence

A numerical technique for simulating the behavior of an acoustic wave propagating through a turbulent medium is introduced. The technique involves two elements: the generation of 3‐D, random, hypothetical, isotropic velocity fields in terms of a collection of discrete Fourier velocity modes; and the integration of the ray‐trace equations to describe the trajectories of points tagging an acoustic wave front. The propagation times for these points to travel fixed distances through each of an ensemble of random velocity fields are recorded, and the variance of travel time (or acoustic phase) over the ensemble is calculated. In numerical ray‐trace experiments through fields having average perturbation indices ≊0.01, acoustic travel‐time variances are obtained that have a higher‐order dependence on travel distance R than the classical Chernov prediction—a linear increase with R. The Chernov result is obtained, however, when the rays are confined to axial trajectories. Additional numerical experiments integrating the stochastic Helmholtz equation and its parabolic approximation yield time‐variance estimates consistent with the ray‐trace results. Predictions from these simulations are then applied to the laboratory experiments of Blanc‐Benon and found to be in qualitative agreement. Finally, a set of 2‐D travel‐time experiments are presented to identify differences between source–receiver eigenray propagation and preassigned initial direction ray propagation.

Simulation of the propagation of an acoustic wave through a turbulent velocity field: A study of phase variance

The present investigation is oriented towards a better understanding of the turbulent structure in the core region of fully developed and completely wall-bounded flows. In view of the already existing results concerning the bursting process in boundary layers (which are semi-bounded flows), an amplitude analysis of the Reynolds shear stress fluctuation u1 u2, sorted into four quadrants of the u1, u2 plane, was carried out in a turbulent pipe flow. For the wall side of the core region, in which the correlation coefficient u1u2/u’1 u’2 does not change appreciably with the distance from the wall, the structure of the Reynolds stress is found to be similar to that obtained in boundary layers: bursts, i.e. ejections of low speed fluid, make the dominant contribution to the Reynolds stress; the regions of violent Reynolds stress are small fractions of the overall flow; and the mean time interval between bursts is found to be almost constant across the flow. For the core region, the large cross-stream evolution of the correlation coefficient u1 u2/u’1 u’2 is associated with a new structure of the Reynolds stress induced by the completely wall-bounded nature of the flow. Very large amplitudes of u1u2 are still observed, but two distinct burst-like patterns are now identified and related to ejections originating from the two opposite halves of the flow. In addition to this interaction, a focusing effect caused by the circular section of the pipe is observed. As a result of these two effects, the mean time interval between the bursts decreases significantly in the core region and reaches a minimum on the pipe axis. Investigation of specific space-time velocity correlations reveals the possible existence of rotating structures similar to those observed at the outer edge of turbulent boundary layers. These coherent motions are found to have a scale noticeably larger than that of the bursts.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112076002048

Geneviève Comte-Bellot

Papers

Simple Eulerian time correlation of full-and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence

Simulation of the propagation of an acoustic wave through a turbulent velocity field: A study of phase variance

Intermittency of coherent structures in the core region of fully developed turbulent pipe flow

Filtered azimuthal correlations in the acoustic far field of a subsonic jet

Velocity, vorticity, and mach number