The Hybrid Method for the PDF Equations of Turbulent Reactive Flows: Consistency Conditions and Correction Algorithms

Muradoğlu, Metin; Pope, Stephen B.; Caughey, David A.

doi:10.1006/jcph.2001.6861

Cited by 141 publications

(111 citation statements)

References 17 publications

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“…In the hybrid approach, the mean conservation equations for mass, momentum, and energy are directly derived from the modeled joint PDF transport equation, and are coupled with the mean equation of state. The mean conservation equations are then solved by a FV method to obtain the mean density, mean velocity, and mean equivalent sensible internal energy fields, and the pressure field is subsequently obtained from the mean equation of state [6]. For the particle part, the transport equation for the modeled joint PDF of fluctuating velocity, turbulent frequency, and compositions is derived from the modeled joint velocityturbulent frequency-compositions PDF transport equation and is solved by a particle-based Monte Carlo method.…”

Section: Model Equationsmentioning

confidence: 99%

“…Significant progress has been recently made in this direction by the development of the consistent hybrid finite volume (FV)/particle-based Monte Carlo method [5,6]. The hybrid method combines the best features of the FV and particle-based Monte Carlo methods to efficiently solve the PDF model equations.…”

Section: Introductionmentioning

confidence: 99%

“…The hybrid method combines the best features of the FV and particle-based Monte Carlo methods to efficiently solve the PDF model equations. The method is completely consistent at the level of governing equations and the full consistency at the numerical solution level is enforced by using efficient correction algorithms [6]. It has been shown that the consistent hybrid method is computationally more efficient than the best available alternative solution technique by a factor of an order of magnitude or more [2,6].…”

Section: Introductionmentioning

confidence: 99%

“…The method is completely consistent at the level of governing equations and the full consistency at the numerical solution level is enforced by using efficient correction algorithms [6]. It has been shown that the consistent hybrid method is computationally more efficient than the best available alternative solution technique by a factor of an order of magnitude or more [2,6]. The numerical efficiency of the hybrid algorithm is further improved by the recent development of a local time stepping algorithm that has been shown to accelerate the global convergence of the hybrid method as much as by a factor of 10 depending on grid stretching [7].…”

Section: Introductionmentioning

confidence: 99%

“…Combined with the local time stepping algorithm, the consistent hybrid method thus makes the PDF methodology a feasible design tool for the practical applications in engineering or elsewhere. The complete descriptions of the consistent hybrid method and the local time stepping algorithm can be found in the references [5,6] and [7], respectively.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

PDF modeling of a bluff-body stabilized turbulent flame

Muradoğlu

Liu

Pope

2003

Combustion and Flame

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The velocity-turbulent frequency-compositions PDF method combined with the consistent hybrid finite volume (FV)/particle solution algorithm is applied to a bluff-body stabilized turbulent flame. The statistical stationarity is shown and the performance of the PDF method is assessed by comparing the mean fields with the available experimental data. The effects of the model constants C 1 in the turbulence frequency model and C in the mixing model on the numerical solutions are examined and it is found that all the mean fields are very sensitive to the changes in C 1 while only the mixture fraction variance seems to be very sensitive to the changes in C but not the other mean fields. The spatial and bias errors are also examined and it is shown that the hybrid method is second order accurate in space and the bias error is vanishingly small in all the mean fields. The grid size and the number of particles per cell are determined for a 5% error tolerance. The chemistry is described by the simplest possible flamelet/PDF model. Hence the main focus of the paper is on the accurate calculations of the mean flow, turbulence and mixing, which lays the foundation for future work in which the chemistry is described in greater detail.

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Section: Model Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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PDF modeling of a bluff-body stabilized turbulent flame

Muradoğlu

Liu

Pope

2003

Combustion and Flame

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Employment of an efficient particle tracking algorithm based on barycentric coordinates in hybrid finite‐volume/probability‐density‐function Monte Carlo methods

Barezban,

Darbandi

2024

Numerical Methods in Fluids

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One main concern of this work is to develop an efficient particle‐tracking‐managing algorithm in the framework of a hybrid pressure‐based finite‐volume/probability‐density‐function (FV/PDF) Monte‐Carlo (MC) solution algorithm to extend the application of FV/PDF MC methods to absolutely incompressible flows and speedup the convergence rate of solving the fluctuating velocity‐turbulent frequency joint PDF equation in turbulent flow simulations. Contrary to the density‐based algorithms, the pressure‐based algorithms have stable convergence rates even in zero‐Mach number flows. As another contribution, literature shows that the past developed methods mostly used mesh searching techniques to attribute particles to cells at the beginning of each tracking time‐step. Also, they had to calculate the linear basis functions at every time‐step to estimate the particle mean fields and interpolate the data. These calculations would be computationally very expensive, time‐consuming, and inefficient in computational domains with arbitrary‐shaped 3D meshes. As known, the barycentric tracking is a continuous particle tracking method, which provides more efficiency in case of handling 3D domains with general mesh shapes. The barycentric tracking eliminates any mesh searching technique and readily provides the convenient linear basis functions. So, this work benefits from these advantages and tracks the particles based on their barycentric coordinates. It leads to less computational work and a better efficiency for the present method. A bluff‐body turbulent flow case is examined to validate the present FV/PDF MC method. From the accuracy perspective, it is shown that the results of the present algorithm are in great agreement with experimental data and available numerical solutions. The present study shows that the number of particle time‐steps required to reach the statistically steady‐state condition is at least one‐sixth less than the previously developed algorithms. This also approves a faster convergence rate for the present hybrid pressure‐based algorithm.

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Simulations of Premixed Swirling Flames Using a Hybrid Finite-Volume/Transported PDF Approach

Lipp

Maas

High Performance Computing on Vector Systems 2007

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The Hybrid Method for the PDF Equations of Turbulent Reactive Flows: Consistency Conditions and Correction Algorithms

Cited by 141 publications

References 17 publications

PDF modeling of a bluff-body stabilized turbulent flame

PDF modeling of a bluff-body stabilized turbulent flame

Employment of an efficient particle tracking algorithm based on barycentric coordinates in hybrid finite‐volume/probability‐density‐function Monte Carlo methods

Simulations of Premixed Swirling Flames Using a Hybrid Finite-Volume/Transported PDF Approach

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