ten Jhm Jan Thije Boonkkamp

A flamelet description of premixed laminar flames and the relation with flame stretch

A laminar flamelet description is derived for premixed laminar flames. The full set of 3D instationary combustion equations is decomposed in three parts: (1) a flow and mixing system without chemical reactions, described by the momentum, enthalpy, and element conservation equations, (2) the G-equation for the flame motion, and (3) a flamelet system describing the inner flame structure and the local mass burning rate. Local fields for the flame curvature and the flame stretch couple the flamelet system with the flow and flame motion. To derive an efficient model, the flamelet equations are analyzed in depth, using the Integral Analysis, first introduced by Chung and Law [1]. It appears that the flamelet response is governed by algebraic equations describing the influence of flame stretch on the local mass burning rate, the enthalpy variation, and element composition. Known expressions for the mass burning rate, found by Joulin, Clavin, and Williams are recovered in some special cases. Furthermore, the validity of the expressions has been shown for weak and strong stretch by comparing the results with numerical results of lean stretched premixed methane/air flames, computed with skeletal chemistry. Finally, the theory is illustrated for the tip of a 2D stationary Bunsen flame.

An analytical solution for mechanical etching of glass by powder blasting

Masked erosion of glass by powder blasting is studied and a nonlinear partial differential equation of first order describing the displacement of the glass surface is proposed. This equation is solved by means of the characteristic-strip equations. If so-called transition regions are introduced near the edges of the mask, an analytical solution can be obtained which is in reasonable agreement with measurements.

An efficient, second order method for the approximation of the Basset history force

The hydrodynamic force exerted by a fluid on small isolated rigid spherical particles are usually well described by the Maxey-Riley (MR) equation. The most time-consuming contribution in the MR equation is the Basset history force which is a well-known problem for many-particle simulations in turbulence. In this paper a novel numerical approach is proposed for the computation of the Basset history force based on the use of exponential functions to approximate the tail of the Basset force kernel. Typically, this approach not only decreases the cpu time and memory requirements for the Basset force computation by more than an order of magnitude, but also increases the accuracy by an order of magnitude. The method has a temporal accuracy of O ( Δ t 2 ) which is a substantial improvement compared to methods available in the literature. Furthermore, the method is partially implicit in order to increase stability of the computation. Traditional methods for the calculation of the Basset history force can influence statistical properties of the particles in isotropic turbulence, which is due to the error made by approximating the Basset force and the limited number of particles that can be tracked with classical methods. The new method turns out to provide more reliable statistical data.

A Mass-Based Definition of Flame Stretch for Flames with Finite Thickness

The flame stretch concept is extended for the case of 3D instationary flames with finite flame front thickness. It is shown that additional contributions to the stretch rate appear apart from the terms which are usually used in flame studies. These extra terms are associated with variations in the mass density along the flame iso-contours and with variations in flame front thickness in time and space. It is finally shown that the following definition for the stretch rate is applicable: K = \/m (dm/dt), denoting the fractional change of mass in an infinitesimally small flame volume.

The Finite Volume-Complete Flux Scheme for Advection-Diffusion-Reaction Equations

We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional advection-diffusion-reaction equation, which is derived from the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying suitable quadrature rules to the integral representation gives the complete flux scheme. Extensions of the complete flux scheme to two-dimensional and time-dependent problems are derived, containing the cross flux term or the time derivative in the inhomogeneous flux, respectively. The resulting finite volume-complete flux scheme is validated for several test problems.

An Evaluation of Different Contributions to Flame Stretch for Stationary Premixed Flames

The concept of flame stretch is extended to study stationary premixed flames with a finite thickness. It is shown that the analysis results in additional contributions to the stretch rate due to changes in the flame thickness and due to density variations along the flame. Extended expressions are derived that describe the effect of stretch on variations in scalar quantities, such as the enthalpy. These expressions are used to determine local variations in the flame temperature, and it is shown that known results are recovered when a number of approximations are introduced. The extended stretch formalism might be useful to analyze and quantify the different flame stretch contributions and their effects in numerical flame studies. Finally, the different contributions to the total stretch rate and the effects thereof on the flame stabilization are numerically computed for the flame tip of a two-dimensional Bunsen flame as illustration.

Axisymmetric multiphase lattice Boltzmann method

A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [Phys. Rev. E 47, 1815 (1993)] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equations is demonstrated analytically by means of a Chapmann-Enskog expansion and numerically through several test cases. In particular, the model is benchmarked for its accuracy in reproducing the dynamics of the oscillations of an axially symmetric droplet and on the capillary breakup of a viscous liquid thread. Very good quantitative agreement between the numerical solutions and the analytical results is observed.

Mass conservative finite volume discretization of the continuity equations in multi-component mixtures

The Stefan-Maxwell equations for multi-component diffusion result in a system of coupled continuity equations for all species in the mixture. We use a generalization of the exponential scheme to discretize this system of continuity equations with the finite volume method. The system of continuity equations in this work is obtained from a non-singular formulation of the Stefan-Maxwell equations, where the mass constraint is not applied explicitly. Instead, all mass fractions are treated as independent unknowns and the constraint is a result of the continuity equations, the boundary conditions, the diffusion algorithm and the discretization scheme. We prove that with the generalized exponential scheme, the mass constraint can be satisfied exactly, although it is not explicitly applied. A test model from the literature is used to verify the correct behavior of the scheme.

The complete flux scheme : error analysis and application to plasma simulation

The complete flux scheme (CFS) [J. ten Thije Boonkkamp, M. Anthonissen, The finite volume-complete flux scheme for advection–diffusion–reaction equations, J. Sci. Comput. 46 (1) (2011) 47–70. http://dx.doi.org/10.1007/s10915-010-9388-8] is an extension of the widely used exponential difference scheme for advection–diffusion–reaction equations. In this paper, we provide a rigorous proof that the convergence order of this scheme is 2 for all grid Peclet numbers, whereas that of the exponential difference scheme reduces to 1 for high grid Peclet numbers in the presence of source terms. The performance of both schemes is compared in two case studies: a test problem and a physical model of a parallel-plate glow discharge. The results indicate that the usage of the CFS allows a considerable reduction of the number of grid points that is required to obtain the same accuracy. The MATLAB/Octave source code that has been used in these studies has been made available.

A least-squares method for optimal transport using the Monge-Ampère equation

In this article we introduce a novel numerical method to solve the problem of optimal transport and the related elliptic Monge--Ampere equation. It is one of the few numerical algorithms capable of solving this problem efficiently with the proper transport boundary condition. The computation time scales well with the grid size and has the additional advantage that the target domain may be nonconvex. We present the method and several numerical experiments.