Direct Numerical Simulation

The statistics of isotropic homogeneous decaying at moderately large Reynolds number are studied in detail using a Fourier-space band-filtering method on flow fields obtained by direct numerical simulation. Two distinct aspects of the non-Gaussianity of the turbulent field are ...

Turbulent flow over a sinusoidal solid wavy surface was investigated by a direct numerical simulation using a spectral element technique. The train of waves has an amplitude to wavelength ratio of 0.05. For the flow conditions (Re=hU b/2ν= 3460) considered, adverse pressure gradients were large enough to cause flow separation. Numerical results compare favorably with those of Hudson's (1993) measurements. Instantaneous flow fields show a large variation of the flow pattern in the spanwise direction in the separated bubble at a given time. A surprising result is the discovery of occasional velocity bursts which originate in the separated region and extend over large distances away from the wavy wall. Turbulence in this region is very different from that near a flat wall in that it is associated with a shear layer which is formed by flow separation.

This book contains a collection of the main contributions from the first five workshops held by Ercoftac Special Interest Group on Synthetic Turbulence Models (SIG42. It is intended as an illustration of the sig’s activities and of the latest developments in the field.

This volume investigates the use of Kinematic Simulation (KS) and other synthetic turbulence models for the particular application to environmental flows.
This volume offers the best syntheses on the research status in KS, which is widely used in various domains, including Lagrangian aspects in turbulence mixing/stirring, particle dispersion/clustering, and last but not least, aeroacoustics. Flow realizations with complete spatial, and sometime spatio-temporal, dependency, are generated via superposition of random modes (mostly spatial, and sometime spatial and temporal, Fourier modes), with prescribed constraints such as: strict incompressibility (divergence-free velocity field at each point), high Reynolds energy spectrum. Recent improvements consisted in incorporating linear dynamics, for instance in rotating and/or stably-stratified flows, with possible easy generalization to MHD flows, and perhaps to plasmas. KS for channel flows have also been validated. However, the absence of "sweeping effects" in present conventional KS versions is identified as a major drawback in very different applications: inertial particle clustering as well as in aeroacoustics. Nevertheless, this issue was addressed in some reference papers, and merits to be revisited in the light of new studies in progress.

Content Level » Research

Keywords » atmospheric flows - fractal fluids - isotropic turbulence - lagrangian dispersion - multiphase flows - super fluids - synthetic turbulence models

Direct numerical simulations (DNS) are carried out to investigate fully developed turbulent heat transfer in a pipe at low Kármán number (Reτ = 171) and different Prandtl numbers (Pr = 0.026, 0.1, 0.2, 0.4, 0.71 and 1.0) using spectral element method. The isoflux boundary condition is applied on the pipe walls and temperature is considered as a passive scalar by neglecting buoyancy effect and viscous dissipation. The grid resolution used in the present computation in terms of wall units are [Δz+, Δr+, RΔθ+] = [14.3, 0.5-3.6, 8.4]. Important turbulent quantities such as the mean temperature, rms of temperature fluctuations, and both streamwise and radial turbulent heat fluxes are calculated to analyse the effect of Prandtl number. Comparison with other available DNS data shows a good agreement, validating the current numerical model. Similar to velocity boundary layer structure, inner scaling of the lower and higher orderturbulent thermal statistics follows the traditional theory

We present some remarks about the CFL condition for explicit time discretization methods of Adams–Bashforth and Runge–Kutta type and show that for convection-dominated problems stability conditions of the type Δt≤CΔx^α are found for high order space discretizations, where the exponent α depends on the order of the time scheme. For example, for second order Adams–Bashforth and Runge–Kutta schemes we find α=4/3.

This guide recommends methods for the estimation of pressure drop for the steady state flow of single phase Newtonian liquids and compressible fluids (gases and vapors) in pipe systems. It covers most of the geometries likely to be encountered in normal design cases.

"Quantitative methods are increasingly important in the earth sciences but there are few good books specifically written to help earth scientists develop the mathematical tools that they need. This book helps to fill the gap by providing a concise introduction to mathematical modelling with an emphasis on examples taken from the earth sciences. One of the major strengths of the book is that it is possible to get a good overview of a whole topic during an initial read of the relevant chapter without getting too bogged down in detail. Where additional detail is provided it is invariably worth further study. Another strength of the book is the large number of worked examples embedded in the text almost every other double-page spread seems to have one. With very few exceptions, these examples are of great help in providing both focus and clarity to what may sometimes seem a little obscure. The style of the book is informal - I wish that it had been available when I was an undergraduate to help counterbalance the theorem-and-proof approach that I was subjected to... In short, the book provides excellent value for money and is a well-crafted introduction to mathematical modelling for earth scientists. Armed with insights obtained from this book, the reader will be well placed for further study of selected topics at the next level of detail. "
--Geoscientist, January 2009


Mathematical modelling and computer simulations are an essential part of the analytical toolset used by earth scientists. Computer simulations based on mathematical models are routinely used to study geophysical, environmental and geological processes in many areas of work and research from geophysics to petroleum engineering and from hydrology to environmental fluid dynamics. Dr Yang has carefully selected topics which will be of most value to students and has recognised the need to be careful in his examples whilst being comprehensive enough to include important topics and popular algorithms. The book is designed to be theorem-free and yet to balance formality and practicality. Using worked examples and tackling each problem in a step-by-step manner the text is especially suitable for non-mathematicians approaching this aspect of earth sciences for the first time, The coverage and level, for instance in the calculus of variation and pattern formation, that even mathematicians will find the examples interesting. Topics covered include: vector and matrix analysis ordinary differential equations partial differential equations calculus of variations integral equations probability geostatistics numerical integration optimisation finite difference methods finite volume methods finite element methods reaction-diffusion system elasticity fracture mechanics poroelasticity, and flows in porous media. Mathematical Modelling for Earth Sciences introduces a wide range of mathematical modelling and numerical techniques, and is written for undergraduates and graduate students.

This document is one of a series on fluid flow produced by GBH Enterprises.

If a rapid change is made to the flowrate of a liquid in a piping system, for example by the operation of a valve, a transient pressure change will be propagated through the system. This transient pressure may be significantly greater than either the initial pressure or the final steady state pressure which the system reaches. This may cause damage to the piping system; either by exceeding the design pressure of the piping system with consequent risk of rupture, or by producing out of balance forces which are greater than can be sustained by the pipe supports. The phenomenon known as 'water hammer' is a special case of 'pressure surge'.

The losses in European Union distribution transformers are estimated at about 33 TW · h/year, whereas reactive power and harmonic losses add a further 5 TW · h/year. The reduction of distribution transformer no-load loss is particularly important as the ratio of no-load to load losses is nearly three. In this paper, the no load operation of wound-core transformers under sinusoidal and distorted supply-voltage conditions is investigated. For that purpose, a 2-D nonlinear transient finite-element analysis taking into account hysteresis has been developed. The hysteresis model is based on a modified Jiles–Atherton representation, and the proposed analysis is compared to experimental data.

We use a direct numerical simulation database of turbulent boundary layers, to identify hairpin packets and their wall signature. We investigate the variation of time scales and length scales associated with coherent structures and the role of hairpin packets on the generation of skin friction, wall-pressure loading and heat transfer. Martin, M.P., JFM, vol. 570, pp. 347- 364, 2006 Martin, M.P., AIAA Paper 2004-2337 Beekman & Martin, APS DFD08 statistical tools, Brown & Thomas, Phys. Fluids, vol. 20, pp243-251, 1977 scientifically-rooted packet-pattern recognition, Ringuette, Wu & Martin, JFM, vol. 594, pp. 59-69, 2008 and validated visualization algorithms O'Farrell, C. Senior Thesis, Princeton University 2008

This paper describes MicroHH 1.0, a new and open-source (www.microhh.org) computational fluid dynamics code for the simulation of turbulent flows in the atmosphere. It is primarily made for direct numerical simulation but also supports large-eddy simulation (LES). The paper covers the description of the governing equations, their numerical implementation, and the parameterizations included in the code. Furthermore, the paper presents the validation of the dynamical core in the form of convergence and conservation tests, and comparison of simulations of channel flows and slope flows against well-established test cases. The full numerical model, including the associated parameteriza-tions for LES, has been tested for a set of cases under stable and unstable conditions, under the Boussinesq and anelas-tic approximations, and with dry and moist convection under stationary and time-varying boundary conditions. The paper presents performance tests showing good scaling from 256 to 32 768 processes. The graphical processing unit (GPU)-enabled version of the code can reach a speedup of more than an order of magnitude for simulations that fit in the memory of a single GPU.

A diffuse interface model is used to model a two-phase flow. It is incorporated into an incompressible Navier-Stokes solver based on a multi-directional finite difference method with third-order upwinding. In order to test the reliability of the code, 2D simulations are performed of a jet into a still fluid. The evolution of the jet is captured with the instability manifesting itself as waves along the surface of the fluids. A simple comparison between the wavelength obtained here and that given by the Kelvin-Helmholtz instability theory shows excellent agreement with the discrepancy been less than 5%. These instabilities grow, and finally break-up into separate chunks, filaments and droplets. This behavior is in qualitative agreement with those reported in the literature. The present results show the accuracy of the present method with consideration of compressibility effects left for future investigation.

Turbulent drag reduction by polymer additives in a channel is investigated using direct numerical simulation. The dilute polymer solution is expressed with an Oldroyd-B model that shows a linear elastic behaviour. Simulations are carried out by changing the ...

A strategy for adaptive control and energetic optimization of aerobic fermentors was implemented, with both air flow and agitation speed as manipulated variables. This strategy is separable in its components: control, optimization, estimation. We optimized parameter’s estimation (from the usual KLa correlation) using sinusoidal excitation of air flow and agitation speed. We have implemented parameter’s estimation trough recursive least squares algorithm with forgetting factor. We carried separate essays on control, optimization and estimation algorithms. We carried our essays using an original computational simulation environment, with noise and delay generating facilities for data sampling and filtering.

Our results show the convergence and robustness of the estimation algorithm used, improved with use of both forgetting factor and KLa dead-band facilities. Control algorithm used in our work compares favorably with PID using the integrated area criteria for deviation between oxygen molarity and critical molarity (set point). Optimization algorithm clearly reduces energetic consumption, respecting critical molarity. Integration of control, optimization and adaptive algorithms was implemented, but future work is needed for stability. Methods were defined and implemented for stability improvement. We have implemented data acquisition and computer manipulation of air flow and agitation speed for actual fermentors.

"This paper describes a Chebyshev collocation method for solving the eigenvalue problem that governs the linear stability of fluid film flow down an inclined plane in presence or absence of surfactant at arbitrary Reynolds numbers. The method is based on the expansion of the eigenfunctions in terms of Chebyshev polynomials, point collocation, and the subsequent solution of the resulting generalized eigenvalue problem with the QZ-algorithm. This method is developed to solve Orr-Sommerfeld equation. The results in the absence of surfactant are compared with those presented by Yih. Finally the effect of inertia and Marangoni mode which appears when insoluble surfactant is present is investigated. The effect of instability modes, the Yih mode which is associated with perturbation on fluid film surface and Marangoni mode which is associated with variation of surfactant surface concentration, are studied for flow instability at arbitrary Reynolds numbers. The agreement between the obtained results at limited conditions and also results from other researchers shows the effectiveness of Collocation Method and suggested profiles.
Key words: Collocation, linear stability; Orr-Sommerfeld; Marangoni; Surfactant; Perturbation analysis"