Radiation is the dominant mode of heat transfer in the boiler, with the largest section of the boiler dedicated to capturing the radiant energy generated by the coal and gas reactions. Because the boiler efficiency is ultimately decided based on this transfer of energy, it is paramount that the calculation be accurate and efficient. For this reason, we propose the use Reverse Monte-Carlo Ray Tracing (RMCRT) to solve the radiative transport equation.

### Radiation Physics

Radiative heat transfer greatly affects the gas and particle phases, including all the associated combustion chemistry. Particle-particle, particle-gas, gas-gas, and particle/gas-wall radiative transport are all important and must be captured in the simulation.

The accurate radiation model will capture the complexity of this multiphase system including

- Non-homogenous emitting, scattering, and absorbing media
- Non-homogenous emitting, absorbing, reflecting walls

Perhaps the biggest challenge facing the simulation of the radiation physics lies in the global coupling of radiation. This creates an "all-to-all" challenge for the computer simulation.

### All-to-All

The all-to-all problem remains the largest computational challenge facing radiation. That is, each computational cell at every point in the domain potentially requires information from every other computational cell. In order to alleviate the data requirements, we incorporate a multi-level, asynchronous adaptive focus mesh.

The figures below illustrate the concept. The most-left figure shows the standard CFD mesh on which the fluid/particle equations are solved. The middle figure shows a single level, asynchronous mesh at a coarser level for the radiation physics. The right-most figure shows the multi-level, adaptive-focus mesh.

### RMCRT Virtual Radiometer

Virtual radiometer objects emulate experimental sensors, and are essential for the VUQ analysis.

Concept |
Verification |

### RMCRT and DOM

The discrete ordinates model (DOM) has been the mainstay for the Arches LES code. DOM has proven to be reliable and reasonably accurate for many industrial applications. It has, however, been the most expensive operation for the simulation, occupying nearly %70 of the computational expense.

RMCRT offers the ability to provide the same level of accuracy at a lower cost by employing modern computer architectures and hybrid parallelism.

In addition, RMCRT also incorporates complex physics that would be otherwise difficult to implement in DOM such as scattering and reflection.

RMCRT predicts noisy and erratic derivatives due to the stochastic nature of the method. Work to reduce the noise from RMCRT is ongoing.

**Capability comparison of DOM and RMCRT for radiation calculations.**

## Capability |
## DOM |
## RMCRT |

code implementation of scattering | difficult and not done | simple and done |

code implementation of reflections | moderate | simple and done |

implementation of virtual radiometer | extremely difficult | possible and done |

angular discretization | ray effects | easy |

spectral | expensive | easier |

computational cost | cheap | varies |

accuracy | lower | higher |

parallelism | linear solver | requires ingenuity |

**Scaling test of the fully coupled RMCRT algorithm in Arches using the multi-level adaptive data scheme.**

Red markers: RMCRT using 10 rays per cell, 2 levels of adaptive- focus mesh, refinement ratio of 2, and 1283 cells on the fine level. Timing data were averaged over 50 timesteps. White: Ideal scaling |

### Parallelism in Massive-Scale Problems

- The use of the BSF geometry is being used as a baseline for enhancing CPU-scaling efficiency.
- Scaling for CPUs and GPUs is under investigation.
- Elegant multi-grid methods for reducing radiation costs are under development.

Radiative heat transfer greatly affects the gas and particle phases, including all the associated combustion chemistry. Particle-particle, particle-gas, gas-gas, and particle/gas-wall radiative transport are all important and must be captured in the simulation.

The accurate radiation model will capture the complexity of this multiphase system including

Perhaps the biggest challenge facing the simulation of the radiation physics lies in the global coupling of radiation. This creates an “all-to-all” challenge for the computer simulation.