Turbulent flow computation

Launder, B. D., and D. B. Spalding. 1974. The numerical computation of turbulent flows. Comput. Meth. Appl. Mech. Eng. 3 269-289. 

Any turbulent flow computed by LES exhibits significant sensitivity to these parameters, leading to instantaneous solutions which can be totally different. Laminar flows are almost insensitive to these parameters. 

The objective of this survey is to provide a brief but reasonably complete account of the state of the art of turbulent-flow computations, and to reflect the excitement of current debate on equation models in this field. The review has been written for readers with a basic background in turbulent transport, such as is given in a contemporary graduate course on this subject. 

Ferziger JH, Leshe DC (1979) Large Eddy Simulation A Predictive Approach to Turbulent Flow Computation. American Institute of Aeronautics and Astronautics, Inc., paper A79-45272... 

Launder BE, Spalding DB (1974) The Numerical Computation of Turbulent Flows. Computer Methods in Applied Mechanics and Engineering, No. 3,... 

Shih, T.H. Uou, W.W. Shabbir, A Yang, Z G et al. 1995. A new k-e eddy viscosity model for high Reynolds number turbulent flows. Comput Fluid, 24 3) 227-238. 

Leschziner, M., Drikakis, D. Turbulence modelling and turbulent-flow computation in aeronautics. Aeronautical Journal 106(1061), 349-383 (2002)... 

Film Theory. Many theories have been put forth to explain and correlate experimentally measured mass transfer coefficients. The classical model has been the film theory (13,26) that proposes to approximate the real situation at the interface by hypothetical "effective" gas and Hquid films. The fluid is assumed to be essentially stagnant within these effective films making a sharp change to totally turbulent flow where the film is in contact with the bulk of the fluid. As a result, mass is transferred through the effective films only by steady-state molecular diffusion and it is possible to compute the concentration profile through the films by integrating Fick s law ... 

Computer simulation of the reactor kinetic hydrodynamic and transport characteristics reduces dependence on phenomenological representations and idealized models and provides visual representations of reactor performance. Modem quantitative representations of laminar and turbulent flows are combined with finite difference algorithms and other advanced mathematical methods to solve coupled nonlinear differential equations. The speed and reduced cost of computation, and the increased cost of laboratory experimentation, make the former increasingly usehil. 

In turbulent flow, axial mixing is usually described in terms of turbulent diffusion or dispersion coefficients, from which cumulative residence time distribution functions can be computed. Davies (Turbulence Phenomena, Academic, New York, 1972, p. 93), gives Di = l.OlvRe for the longitudinal dispersion coefficient. Levenspiel (Chemical Reaction Engineering, 2d ed., Wiley, New York, 1972, pp. 253-278) discusses the relations among various residence time distribution functions, and the relation between dispersion coefficient and residence time distribution. 

In Gaussian plume computations the change in wind velocity with height is a function both of the terrain and of the time of day. We model the air flow as turbulent flow, with turbulence represented by eddy motion. The effect of eddy motion is important in diluting concentrations of pollutants. If a parcel of air is displaced from one level to another, it can carry momentum and thermal energy with it. It also carries whatever has been placed in it from pollution sources. Eddies exist in different sizes in the atmosphere, and these turbulent eddies are most effective in dispersing the plume. 

Nullaswamy, M., Turbulence models and their applications to the predictions of internal flows, Computers and Eluids, 15, 151, 1987. 

Launder, B. E. On the computation of convective hear transfer in complex turbulent flow. Trans. ASME J. Heat Transfer, vol. 110, pp. 1112-1128, 1988. 

In these model equations it is assumed that turbulence is isotropic, i.e. it has no favoured direction. The k-e model frequently offers a good compromise between computational economy and accuracy of the solution. It has been used successfully to model stirred tanks under turbulent conditions (Ranade, 1997). Manninen and Syrjanen (1998) modelled turbulent flow in stirred tanks and tested and compared different turbulence models. They found that the standard k-e model predicted the experimentally measured flow pattern best. 

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

The availability of large and fast computers, in combination with numerical techniques to compute transient, turbulent flow, has made it possible to simulate the process of turbulent, premixed combustion in a gas explosion in more detail. Hjertager (1982) was the first to develop a code for the computation of transient, compressible, turbulent, reactive flow. Its basic concept can be described as follows A gas explosion is a reactive fluid which expands under the influence of energy addition. Energy is supplied by combustion, which is modeled as a one-step conversion process of reactants into combustion products. The conversion (combustion)... 

The discharge pressure for the large reactor, (Pout)2 may be set arbitrarily. Normal practice is to use the same discharge pressure as for the small reactor, but this is not an absolute requirement. The length of the large reactor, L2, is chosen to satisfy the inventory constraint of Equation (3.32), and the inlet pressure of the large reactor becomes a dependent variable. The computation procedure actually calculates it first. Substitute Equation (3.23) for p (for turbulent flow) into Equation (3.32) to give... 

The ability to resolve the dissipation structures allows a more detailed understanding of the interactions between turbulent flows and flame chemistry. This information on spectra, length scales, and the structure of small-scale turbulence in flames is also relevant to computational combustion models. For example, information on the locally measured values of the Batchelor scale and the dissipation-layer thickness can be used to design grids for large-eddy simulation (LES) or evaluate the relative resolution of LES resulfs. There is also the potential to use high-resolution dissipation measurements to evaluate subgrid-scale models for LES. 

This section presents a variety of reacting flows computed with the LES methodology. The cases presented in this study were chosen, because each features a different aspect of turbulent combustion and also addresses a specific technical difficulty. 

Kishan B. Mathur and Norman Epstein, Dynamics of Spouted Beds W. C. Reynolds, Recent Advances in the Computation of Turbulent Flows R. E. Peck and D. T. Wasan, Drying of Solid Particles and Sheets... 

Kishan B. Mathur and Norman Epstein Recent Advances in the Computation of Turbulent Flows W.G. Reynolds... 

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