The objective of this work is to provide a detailed study on the convergence behavior of the Simplified Bernoulli Trials (SBT) collision scheme in the direct simulation Monte Carlo (DSMC) method. One-dimensional Fourier heat conduction problem of argon gas at the early slip regime is considered. The problem consists of rarefied gas confined between two infinite parallel plates with different temperature magnitudes. The investigations compare the SBT solution for the Sonine-polynomial coefficients with theoretical predictions of the Chapman-Enskog theory. Also, the convergence behavior of the wall heat flux and the DSMC-calculated bulk thermal conductivity (KDSMC) are studied. The numerical performance of the DSMC method is affected by the number of computational particles (simulators) per cell, time step, and cell size. The dependence of the SBT collision scheme on discretization errors has been examined and compared with the no time counter (NTC) collision algorithm. Our results show that SBT captures analytical solutions of the Sonine polynomials using a few particles per cell. Unlike the NTC scheme, the SBT algorithm is not so sensitive to the number of simulators per cell, and the effective parameter in the convergence is the cell size to time step ratio, Δx/Δt, which should be adjusted properly for any specific test case. With setting a constant Δx/Δt, the SBT algorithm accurately predicts the wall heat flux solution by decreasing the average number of particles per cell to one particle or even less.
Here, a symmetrized and simplified Bernoulli trials (SSBT) scheme based on the probabilistic approach is introduced to provide less-restricted conditions in choosing selected pairs. Unlike the simplified Bernoulli trials (SBT) method, the SSBT scheme picks the second particle of a selected pair from a whole list of particles with equal probability; it prevents repetitive collisions by introducing a procedure to avoid duplicate colliding pairs. The efficiency of this newly introduced algorithm is investigated in benchmark problems such as a collision frequency test case, Fourier heat transfer, dissociation of simple gas, and hypersonic cylinder flow. Compared with SBT, no time counter (NTC), and nearest neighbor (NN) collision algorithms, the results show that the SSBT method predicts the solutions quite accurately. In the collision frequency test case and Fourier test case, we show that the SSBT scheme could work with few particles per cell (one or even less) if an appropriate space and time discretization is employed. The symmetrized algorithm of the SSBT scheme improves the quality of the selection process, which leads to a smaller sample size in the highly non-equilibrium problem of hypersonic cylinder flow to achieve the same convergence limit at that of the SBT and NN schemes. In addition, the SSBT scheme has inherently a lower separation of free paths in the stagnation point of the cylinder test case compared to the SBT scheme for the same grid test case. These features make SSBT a new, robust model that could be presented as an alternative to state-of-the-art models.
This is an experimental and numerical study on the effect of air swirl vane angle on combustion characteristics of liquid fuel burners. The swirl vane angle varied in a range from 0°to 75°and the values of the dependent variables were determined. The flame temperature was measured by an S-type thermocouple and a Testo 350 XL gas analyzer was used to determine the NO and CO pollutant concentrations. Also, sprint CFD code along with suitable models was used in analytical modeling. The results indicate that there is an optimum angle for the swirl vane (approximately 45°for the case study). At the optimum angle, the average temperature of the flame increases as much as 12.5% and 28.5% in comparison with small and large angles, respectively. Therefore, combustion efficiency reaches its maximum level and CO emission is at an extremely low level. The results also demonstrate that large swirl angles decreases NO emission. C⃝ 2016 Wiley Periodicals, Inc. Heat Trans Asian Res, 46 (7): 750-760, 2017; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj).
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