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ABSTRACT
A nonreacting methane turbulent jet flame is simulated using a composition Probability Density Function (PDF) transport model combined with a parabolic flow model closed using a k–ε turbulence model. The model is validated using the measurements of Birch et al. The turbulent concentration field of a methane jet, J. Fluid Mech., vol. 88, pp. 431–449, 1978. For the most part, the agreement between the model predictions and measured PDFs, mean mixture fraction, Root Mean Squared (RMS) mixture fraction, and higher moments is very good, except where jet intermittency effects are important.
Although the validation of the model is encouraging, the requirement for large sample sizes limits how the model implemented with the standard Monte Carlo method can be taken forward. To address this issue, the Monte Carlo method is modified such that the number of particles in a control volume is adapted based on a criterion developed from the central limit theorem. The adaptive Monte Carlo method requires approximately 20% of the runtime of the standard Monte Carlo method.
Nomenclature
| C1,C2 | = | turbulence model parameters |
| CD | = | constant in the micromixing model |
| Cµ | = | turbulence model parameter |
| d | = | source diameter |
| fi | = | particles representing the PDF |
| = | mean mixture fraction | |
| = | variance of mixture fraction | |
| g | = | gravitational acceleration |
| K | = | kurtosis |
| k | = | turbulence kinetic energy |
| lt | = | turbulent length scale |
| NA | = | number of particle advection processes |
| ND,E, ND,W | = | number of particle diffusion processes |
| NM | = | number of particle mixing processes |
| Nr | = | number of control volumes in the radial direction |
| Nref | = | maximum number of particles per control volume |
| Nsam | = | number of particles per control volume |
| P | = | probability density function |
| Pk | = | production of turbulence kinetic energy |
| r | = | radial coordinate |
| r0 | = | source radius |
| Re | = | Reynolds number |
| S | = | skewness |
| U0 | = | source velocity |
| U | = | axial velocity component |
| V | = | radial velocity component |
| z | = | axial coordinate |
| Δr | = | mesh spacing in the radial direction |
| Δt* | = | pseudo time step |
| Δz | = | space step in the z-coordinate direction |
| ϵ | = | dissipation rate of turbulence kinetic energy |
| κ | = | Von Karman constant |
| µ,σ | = | mean and standard deviation of a Gaussian distribution |
| µeff | = | effective dynamic viscosity |
| ρ | = | density |
| σk | = | turbulent Prandtl number for turbulence kinetic energy |
| σϵ | = | turbulent Prandtl number for dissipation rate of turbulence kinetic energy |
| σP | = | turbulent Prandtl number for the PDF transport equation |
| ω | = | turbulent frequency |
| Subscript | = | |
| amb | = | ambient value |
| E,W | = | neighbors of P in the radial dimension |
| P | = | current control volume |
| t | = | turbulence property |
| 0 | = | source conditions |
| Over bar | = | |
| _ | = | Reynolds average |
| ∼ | = | Favre average |
Nomenclature
| C1,C2 | = | turbulence model parameters |
| CD | = | constant in the micromixing model |
| Cµ | = | turbulence model parameter |
| d | = | source diameter |
| fi | = | particles representing the PDF |
| = | mean mixture fraction | |
| = | variance of mixture fraction | |
| g | = | gravitational acceleration |
| K | = | kurtosis |
| k | = | turbulence kinetic energy |
| lt | = | turbulent length scale |
| NA | = | number of particle advection processes |
| ND,E, ND,W | = | number of particle diffusion processes |
| NM | = | number of particle mixing processes |
| Nr | = | number of control volumes in the radial direction |
| Nref | = | maximum number of particles per control volume |
| Nsam | = | number of particles per control volume |
| P | = | probability density function |
| Pk | = | production of turbulence kinetic energy |
| r | = | radial coordinate |
| r0 | = | source radius |
| Re | = | Reynolds number |
| S | = | skewness |
| U0 | = | source velocity |
| U | = | axial velocity component |
| V | = | radial velocity component |
| z | = | axial coordinate |
| Δr | = | mesh spacing in the radial direction |
| Δt* | = | pseudo time step |
| Δz | = | space step in the z-coordinate direction |
| ϵ | = | dissipation rate of turbulence kinetic energy |
| κ | = | Von Karman constant |
| µ,σ | = | mean and standard deviation of a Gaussian distribution |
| µeff | = | effective dynamic viscosity |
| ρ | = | density |
| σk | = | turbulent Prandtl number for turbulence kinetic energy |
| σϵ | = | turbulent Prandtl number for dissipation rate of turbulence kinetic energy |
| σP | = | turbulent Prandtl number for the PDF transport equation |
| ω | = | turbulent frequency |
| Subscript | = | |
| amb | = | ambient value |
| E,W | = | neighbors of P in the radial dimension |
| P | = | current control volume |
| t | = | turbulence property |
| 0 | = | source conditions |
| Over bar | = | |
| _ | = | Reynolds average |
| ∼ | = | Favre average |