Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques

	This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization

	An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques



	
		Will provide you with the knowledge required to develop and understand modern flow simulation codes
	
		Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics
	
		Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

Computational Fluid Dynamics: Principles and Applications Ed. 3

Detached-eddy simulation (DES) was first proposed in 1997 and first used in 1999, so its full history can be surveyed. A DES community has formed, with adepts and critics, as well as new branches. The initial motivation of high–Reynolds number, massively separated flows remains, for which DES is convincingly more capable presently than either unsteady Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES). This review discusses compelling examples, noting the visual and quantitative success of DES. Its principal weakness is its response to ambiguous grids, in which the wall-parallel grid spacing is of the order of the boundary-layer thickness. In some situations, DES on a given grid is then less accurate than RANS on the same grid or DES on a coarser grid. Partial remedies have been found, yet dealing with thickening boundary layers and shallow separation bubbles is a central challenge. The nonmonotonic response of DES to grid refinement is disturbing to most observers, as is the absence of...

Detached-Eddy Simulation

Detached eddy simulation of massively separated flows

This paper presents a reformulated version of the author'sk-ω model of turbulence. Revisions include the addition of just one new closure coefficient and an adjustment to the dependence of eddy viscosity on turbulence properties. The result is a significantly improved model that applies to both boundary layers and free shear flows and that has very little sensitivity to finite freestream boundary conditions on turbulence properties. The improvements to the k-ω model facilitate a significant expansion of its range of applicability. The new model, like preceding versions, provides accurate solutions for mildly separated flows and simple geometries such as that of a backward-facing step. The model's improvement over earlier versions lies in its accuracy for even more complicated separated flows. This paper demonstrates the enhanced capability for supersonic flow into compression corners and a hypersonic shock-wave/ boundary-layer interaction. The excellent agreement is achieved without introducing any compressibility modifications to the turbulence model.

Formulation of the k-w Turbulence Model Revisited

Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

Detached-eddy simulation is applied to an axisymmetric base flow at supersonic conditions. Detached-eddy simulation is a hybrid approach to modeling turbulence that combines the best features of the Reynolds-averaged Navier-Stokes and large-eddy simulation approaches. In the Reynolds-averaged mode, the model is currently based on either the Spalart-Allmaras turbulence model or Menter’s shear stress transport model; in the largeeddy simulation mode, it is based on the Smagorinski subgrid scale model. The intended application of detached-eddy simulation is the treatment of massively separated, highReynolds number flows over complex configurations (entire aircraft, automobiles, etc.). Because of the intented future application of the methods to complex configurations, Cobalt, an unstructured grid Navier-Stokes solver, is used. The current work incorporates compressible shear layer corrections in both the Spalart-Allmaras and shear stress transport-based detached-eddy simulation models. The effect of these corrections on both detached-eddy simulation and Reynolds-averaged Navier-Stokes models is examined, and comparisons are made to the experiments of Herrin and Dutton. Solutions are obtained on several grids—both structured and unstructured—to test the sensitivity of the models and code to grid refinement and grid type. The results show that predictions of base flows using detached-eddy simulation compare very well with available experimental data, including turbulence quantities in the wake of the axisymmetric body. @DOI: 10.1115/1.1517572#

Detached-eddy simulation with compressibility corrections applied to a supersonic axisymmetric base flow

https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1003&context=aero_fac

Computational challenges in high angle of attack flow prediction

This paper presents a Spalart-Allmaras based Detached-Eddy Simulation (DES) of the Ahmed reference car model with 25° and 35° slant angles using unstructured grids and the solverCobalt. Comparisons are made to experimental laser doppler velocity measurements as well as total and surface pressure integrated drag. The Reynolds number based on body length was 2.78 ×106, making the boundary layers approaching the slant fully turbulent. The flow over the base slant in the experiments is attached at 25° and separated at 35°. This causes a large drop in the drag with the increased slant angle as the vortices on the side of the slant are weakened due to the separation. These cases stress turbulence models due to the need to accurately predict the boundary layer separation over the slant as well as predict the pressures in the massively separated base region accurately. The DES results are compared to the experiments as well as the Spalart-Allmaras RANS model. DES is seen to predict separation at 25◦ slant angle, in contrast to the experiments. Drag is relatively close to the experiments, but the distribution of drag is more on the rear than on the slant due to the separation. At the 35 ° slant angle, DES is in good agreement to the experimental drag, with the correct distribution, while RANS over-predicts the drag.

Detached-Eddy Simulation over a Reference Ahmed Car Model

Detached-eddy simulation of fighter aircraft at high alpha

Detached-eddy simulation (DES) is used to predict the massively separated flow around an F-15E at 65-deg angle of attack. The calculations are performed at flight conditions corresponding to a chord-based Reynolds number of 13.6 × 10 6 and Mach number of 0.3. Flowfield solutions are obtained using unstructured grids with the commercial solver Cobalt: the average mesh spacing from solid surfaces to the first cell center from the wall under one viscous unit. The influence of the mesh size is assessed using a series of three grids ranging from 2.85 × 10 6 cells to 10 × 10 6 cells. In addition, the influence of the time step is investigated using three simulations with varied time steps. DES predictions are assessed via comparison to Boeing's stability and control database as well as to solutions of the Reynolds-averaged Navies-Stokes (RANG) equations. These are steady, with the Spalart-Allmaras model. Both RANS and DES predictions of integrated forces exhibit a relatively weak dependence on the grid density for the range examined. In the DES the wake region is characterized by complex and chaotic three-dimensional structures with direct resolution of a reasonable range of length and timescales

James R. Forsythe

Papers

Detached-eddy simulation with compressibility corrections applied to a supersonic axisymmetric base flow

Computational challenges in high angle of attack flow prediction

Detached-Eddy Simulation over a Reference Ahmed Car Model

Detached-eddy simulation of fighter aircraft at high alpha

Detached-Eddy Simulation of the F-15E at High Alpha