Numerical flow modelling in a locally refined grid

Abstract

SUMMARYAn algorithm is presented to model two-dimensional, non-isothermal, low Mach number flows with a local steep density gradient. The algorithm uses an adaptive, locally refined, non-staggered grid and has been developed, especially for modelling laminar flames. The governing equations, based on a stream-function-vorticity formulation, are presented and discretized using hybrid finite differences. A (isothermal) tcst problem is presented to compare the accuracy of the results of the solver presented in this paper, with the results of algorithms found in the literature. However, this test problem proves to be not well suited for the application of a locally refined grid, since it does not contain a local steep gradient. For this reason an additional test problem is constructed that clearly shows the advantages of the locally refined grid as compared to a uniform grid with respect to both the calculation time as well as the number of grid nodes needed. Furthermore, a laminar premixed flame is modelled with simple chemistry to show that the algorithm, presented in this paper, converges to a stabilized flame when an adaptive grid technique is used.

Numerical simulation of laminar reacting flows with complex chemistry

“…Local refinement for steady combustion has been discussed by a number of authors. See for example, Smooke et al [36], Coelho and Pereira [7], de Lange and de Goey [10], Mallens et al [22] Somers and de Goey [34] and Bennett and Smooke [4] and the references cited in these works.…”

Bunsen flame simulation by finite elements on adaptively refined, unstructured triangulations

“…Bunsen flames arise in several practical applications including household and industrial burners. Furthermore, they provide a relatively simple flow configuration on which to investigate fundamental aspects of laminar premixed combustion, including flame stabilization 4 Author to whom any correspondence should be addressed. mechanisms as well as chemically and hydrodynamically controlled extinction limits.…”

“…A first strategy consists in using local estimates of the gradient and curvature of the numerical solution. Applications to combustion include [1][2][3][4][5][6][7][8]. These error indicators are the only possibility if finite difference discretizations are employed.…”

Two-dimensional simulation of an oxy-acetylene torch diamond reactor with a detailed gas-phase and surface mechanism

“…[4][5][6] Recently, for methane-air flames, these approaches have started to come together Several groups have simulated premixed 2D methane-air flames with detailed chemistry. [7][8][9] Somers and de Goey 7 applied the so-called skeletal reaction mechanism for methane combustion, consisting of 25 reactions and 15 species.…”