A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

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

Dynamics and stability of lean-premixed swirl-stabilized combustion

Most numerical integration techniques consist of approximating the integrand by a polynomial in a region or regions and then integrating the polynomial exactly. Often a complicated integrand can be factored into a non-negative ''weight'' function and another function better approximated by a polynomial, thus $\int_{a}^{b} g(t)dt = \int_{a}^{b} \omega (t)f(t)dt \approx \sum_{i=1}^{N} w_i f(t_i)$. Hopefully, the quadrature rule ${\{w_j, t_j\}}_{j=1}^{N}$ corresponding to the weight function $\omega$(t) is available in tabulated form, but more likely it is not. We present here two algorithms for generating the Gaussian quadrature rule defined by the weight function when: a) the three term recurrence relation is known for the orthogonal polynomials generated by $\omega$(t), and b) the moments of the weight function are known or can be calculated.

Calculation of Gauss quadrature rules.

The cost of including full kinetics in realistic computations remains extremely high. This has led many researchers to develop reduction techniques for the chemistry. These methods are generally valid only in a very limited range of equivalence ratio, pressure, or temperature and require extensive human time to develop the reduced schemes. Recently, an automatic method based on intrinsic low-dimensional manifolds (ILDM) has been proposed. Because of ILDM, the reduction of detailed reaction schemes is much simuplified, leading to the fast generation of look-up tables containing the information corresponding to the reduced chemical schemes. Nevertheless, the ILDM method is not well suited to describe the low-temperature domain, since the dimension and therefore the complexity of the databases increase tremendously in this zone. In this work, we propose a new version of the ILDM method, called flame prolongation of ILDM (FPI), which enables us to solve the problem at low temperatures. We used laminar premixed free flames to extend the manifolds generated with ILDM, thus leading to smooth and accurate evolutions of the species along all the flame front. In order to demonstrate the interest of FPI, we computed the response of a premixed flame to straining using the double-premixed counterflow flame configuration. We show that using FPI, the correct evolution is obtained for all species from almost unstrained flames up to flames near extinction. The computational times are tremendously reduced with FPI in comparison with full chemistry.

Liminar premixed hydrogen/air counterflow flame simulations using flame prolongation of ILDM with differential diffusion

Accurate Boundary Conditions for Multicomponent Reactive Flows

Dynamics of flame/vortex interactions

Optimal blade shape of a modified Savonius turbine using an obstacle shielding the returning blade

Many models are now available to describe chemistry at a low CPU cost, but only a few of them can be used to describe correctly premixed, partially premixed and diffusion combustion. One of them is the FPI model that uses two coordinates: the mixture fraction Z and the progress variable c. In this paper, we introduce a new evolution of the FPI method that can now handle heat losses. After a short review of kinetic models used in turbulent combustion, the main features of the new three-dimensional FPI method, in which we introduce a third coordinate for enthalpy h, are presented. First, a one-dimensional radiative premixed flame validation case is presented for a large range of radiative heat losses. Second, we present the results of simulations of two laminar burners. Both the fully and the partially premixed burner simulations give a good estimation of all the flame features such as the flame stabilization (driven by heat losses), the flame structure and the profile of major and minor species.

Dominique Thévenin

Papers

Liminar premixed hydrogen/air counterflow flame simulations using flame prolongation of ILDM with differential diffusion

Accurate Boundary Conditions for Multicomponent Reactive Flows

Dynamics of flame/vortex interactions

Optimal blade shape of a modified Savonius turbine using an obstacle shielding the returning blade

Modelling non-adiabatic partially premixed flames using flame-prolongation of ILDM