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

Numerical simulations of fully developed turbulent channel flow at three Reynolds numbers up to Reτ=590 are reported. It is noted that the higher Reynolds number simulations exhibit fewer low Reynolds number effects than previous simulations at Reτ=180. A comprehensive set of statistics gathered from the simulations is available on the web at http://www.tam.uiuc.edu/Faculty/Moser/channel.

Direct numerical simulation of turbulent channel flow up to Reτ=590

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

The structure of energy-containing turbulence in the outer region of a zero-pressure-
 gradient boundary layer has been studied using particle image velocimetry (PIV) to measure the instantaneous velocity fields in a streamwise-wall-normal plane. Experiments performed at three Reynolds numbers in the range 930 0) that occur on a locus inclined at 30–60° to the wall.In the outer layer, hairpin vortices occur in streamwise-aligned packets that propagate with small velocity dispersion. Packets that begin in or slightly above the buffer layer are very similar to the packets created by the autogeneration mechanism (Zhou, Adrian & Balachandar 1996). Individual packets grow upwards in the streamwise direction at a mean angle of approximately 12°, and the hairpins in packets are typically spaced several hundred viscous lengthscales apart in the streamwise direction. Within the interior of the envelope the spatial coherence between the velocity fields induced by the individual vortices leads to strongly retarded streamwise momentum, explaining the zones of uniform momentum observed by Meinhart & Adrian (1995). The packets are an important type of organized structure in the wall layer in which relatively small structural units in the form of three-dimensional vortical structures are arranged coherently, i.e. with correlated spatial relationships, to form much longer structures. The formation of packets explains the occurrence of multiple VITA events in turbulent ‘bursts’, and the creation of Townsend's (1958) large-scale inactive motions. These packets share many features of the hairpin models proposed by Smith (1984) and co-workers for the near-wall layer, and by Bandyopadhyay (1980), but they are shown to occur in a hierarchy of scales across most of the boundary layer.In the logarithmic layer, the coherent vortex packets that originate close to the wall frequently occur within larger, faster moving zones of uniform momentum, which may extend up to the middle of the boundary layer. These larger zones are the induced interior flow of older packets of coherent hairpin vortices that originate upstream and over-run the younger, more recently generated packets. The occurence of small hairpin packets in the environment of larger hairpin packets is a prominent feature of the logarithmic layer. With increasing Reynolds number, the number of hairpins in a packet increases.

Vortex organization in the outer region of the turbulent boundary layer

▪ 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

Measurements of turbulence properties of solutions of polymers have been made over a large range of drag-reduction, in a fully-developed channel flow. At flows close to maximum drag-reduction the Reynolds stresses were approximately zero over the whole cross section of the channel. Added mean polymer stresses were observed in the viscous wall region for small drag-reduction and over the whole cross-section for large drag-reduction. Even though the Reynolds stresses are zero, the velocity profile is not parabolic because of the presence of these mean stresses. We interpret the results by arguing that the interaction of turbulence with the polymers introduces mean and fluctuating polymer stresses which can create turbulence. The observation that the turbulence modification depends on the manner by which the polymers are introduced into the flow supports the notion that the polymers need to form aggregates in order to be effective.

Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing

New measurements are presented for film height and pressure drop for vertical gas-liquid annular flows. Improved methods for predicting the film height and interfacial friction factor are developed for situations in which the liquid film flow rate is known.

Interfacial drag and film height for vertical annular flow

A method to predict the height of the wall layer and the interfacial drag in annular flow under conditions that the flow rate of the entrained liquid is known is developed from measurements on air-water flow in circular tubes. Flow conditions are found to be characterized by a generalized Martinelli flow parameter.

The interfacial drag and the height of the wall layer in annular flows

Prediction of the initiation of slugs with linear stability theory

Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Re h = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.

Thomas J. Hanratty

Papers

Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing

Interfacial drag and film height for vertical annular flow

The interfacial drag and the height of the wall layer in annular flows

Prediction of the initiation of slugs with linear stability theory

Large-scale modes of turbulent channel flow: transport and structure