Radiative Heat Transfer in a Particle Laden Flow

This work is a subtask of a larger research program, called Predictive Simulations of Particle-laden Turbulence in a Radiation Environment. The larger research program involves investigating the effect of radiation on particle motion in a turbulent flow, a physical process that is not well-understood. This research may result in opportunities for efficiency gains in solar energy systems and other applications. In conventional solar-receivers, the solar radiation is absorbed by a surface and heat is then transfered to an operating fluid. In particle-based receivers, a dispersed particle phase is used to transfer heat throughout the fluid volume. Particle-based receivers allow for higher heat transfer rates and increased efficiency relative to conventional solar-receivers. The Center focuses on developing simulation tools that can be used on the next-generation of supercomputers, called Exascale systems. These are computers which can perform 1018 floating-point operations per second. A dedicated experimental campaign is on-going alongside the computational work. Learn more about the larger research program at the Stanford PSAAP II website .

The NGPDL is responsible for the high-fidelity radiation modeling portion of the research program. The Monte Carlo Ray Tracing (MCRT) approach is adopted as it is the only method of solving the Radiative Transfer Equation (RTE) that can produce exact solutions for any set of optical properties and domain configuration. Development of a new MCRT code is underway, based on previous work involving the analysis of rocket thruster plumes [1][2].

A diagram of the experiment is shown in Figure 1 (left). Radiation from a bank of lamps is directed towards the test section, in which a turbulent, particle laden flow passes. Figure 1 (right) shows the computational domain used in the first MCRT simulations, including a description of the boundary conditions. These MCRT simulations are carried out on a very coarse mesh, with cell side length of 4mm.

Figure 1: Diagram of the PSAAP II experiment (left) and computational domain used in MCRT simulations (right).

The results of the first MCRT simulations performed on a snap-shot of particle-laden turbulence are shown in Figures 2 and 3. The particle field is produced by a coupled DNS-Lagrangian particle tracking simulation. Figure 2 (left) shows contours of particle density on an X-Z plane extracted through the center of the computational domain. Areas of preferential concentration are clearly seen in this image, especially near the walls of the channel. Figure 2 (right) shows contours of particle temperature on the same extraction plane. The particles are heated as they move through the channel and their temperature increases. The highest temperatures are found near the walls of the channel, where the particle density, and therefore percentage of absorbed radiation, is the highest.

Figure 2: Contours of solid particle density (left) and solid particle temperature (right) from the DNS-Lagrangian particle tracking simulations.

Figure 3 (left) shows the incident radiation on the same extraction plane, normalized by the lamp intensity. Fluctuations in the incident radiation contours are due to both the statistical scatter that is inherent in the MCRT method, and the inhomogeneities in the particle density field. The incident radiation is highest at the Z=0m boundary, as this is where the lamp boundary condition is located. Figure 3 (right) shows the associated net heat flux to particles at each spatial location. The net heat flux is highest near the lamp boundary as expected, and decreases with increasing axial location as the particle temperature increases.

Figure 3: Contours of incident radiation (left) and net particle heat flux (right) from the MCRT simulations.


Erin Farbar and Nomita Vazirani


This work is funded by the Department of Energy through the Stanford PSAAP II Center.


  1. Burt, J. M. and Boyd, I. D., "High Altitude Plume Simulations for a Solid Propellant Rocket," AIAA Journal, Vol. 45, No. 12, 2007, pp. 2872-2884.
  2. Burt, J. M. and Boyd, I. D., "Monte Carlo Simulation of a Rarefied Multiphase Plume Flow", AIAA Paper 2005-0964, January 2005.