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ABSTRACT
In this paper, several micromixing models are applied to the prediction of turbulent nonreacting flows. All micromixing models predict the mean mixture fraction and root mean squared (RMS) mixture fraction well. For higher mixture fraction moments, there is a tendency to overpredict the skewness and kurtosis field. The exception to this is a modification to the Langevin model which produces predictions more consistent with the measured fields. Where intermittency effects do not dominate the flow, the modified Curl model and the limited Langevin model can accurately predict the measured probability density function. Of the micromixing models tested for nonhomogeneous flows, the modified Curl model represents an appropriate balance between predictive capabilities, ease of implementation, and short run times for simulating nonreacting flows.
Nomenclature
| A, B | = | constants in the binomial Langevin model |
| C1, C2 | = | turbulence model parameters |
| Cφ, κ | = | constants in the micromixing models |
| Cμ | = | turbulence model parameter |
| cL, cU | = | flammability limits |
| 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 |
| 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 |
| Reλ | = | Taylor Reynolds number |
| S | = | skewness |
| tstand, MC | = | run time of the standard Monte Carlo method |
| tcons, MC | = | run time of the consistent Monte Carlo method |
| 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 |
| 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 |
| t | = | turbulence property |
| 0 | = | source conditions |
| Over bar | = | |
| _ | = | Reynolds average |
| ~ | = | Favre average |
Nomenclature
| A, B | = | constants in the binomial Langevin model |
| C1, C2 | = | turbulence model parameters |
| Cφ, κ | = | constants in the micromixing models |
| Cμ | = | turbulence model parameter |
| cL, cU | = | flammability limits |
| 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 |
| 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 |
| Reλ | = | Taylor Reynolds number |
| S | = | skewness |
| tstand, MC | = | run time of the standard Monte Carlo method |
| tcons, MC | = | run time of the consistent Monte Carlo method |
| 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 |
| 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 |
| t | = | turbulence property |
| 0 | = | source conditions |
| Over bar | = | |
| _ | = | Reynolds average |
| ~ | = | Favre average |