Our Math


A Novel and Accurate Numerical Method for Fluid-Particle Flow

CPFD Software, LLC was founded by Dr. Ken Williams and Dr. Dale Snider, two veterans of the very earliest work on CFD which began inside the USDOE National Laboratories; they have both been closely involved in CFD technology for over thirty-five years.

The origins of the underlying numerical algorithm in Barracuda date back to the late 1990s for a problem General Motors was having with metal casting operations using sand core technology. GM wanted a technology to model the flow of the sand particles from a magazine, through blow tubes into a metal die to form a sand core, into which the liquid metal is poured. But there was no software capable of modeling gas-particle flows.

Because of the complexity and inaccuracy of closure models for a fluid description of particle flow, a fresh approach to modeling fluid-particle flow was pursued. The particle phase description is based on the Multiphase Particle-in-Cell (MP-PIC) method. The MP-PIC description of the particle phase is based on a particle probability distribution function. Rather than directly integrating (moments) the distribution function, the acceleration of particles is calculated using parameters from integration of the distribution function and spatial gradients derived on a grid. This unique approach has proved to be an accurate description of the particle phase. The general CPFD method includes solution of the fluid momentum with strong coupling to the particle phase, conservation of mass of all phases, conservation energy all phases with strong coupling between phases, homogeneous and heterogeneous chemistry, plus other physics to describe the fluid and gas phases.

The development of the CPFD software is an interconnected approach between the particle and fluid phases allowing seamless predictions of dilute particle flow to close-pack. In general, the phases are coupled together in their solutions, and in key numerical approximation to physics, such as the fluid momentum solution, the phases are tightly coupled. By using the MP-PIC description of the particle phase, the spectrum of particle sizes can be modeled, and the uniqueness of particle parameters such as the chemistry on a mix of different particles is naturally accommodated.

The development of the umbrella CPFD numerical scheme continues. New and exciting MP-PIC methods of describing particle flow such as particle collisions are being developed. New developments in calculating chemistry of multi-material particles is advancing the ability to predict complex commercial systems. Numerical methods are being improved for faster solutions. Development has always been aimed at the best method for solution, and this is true for parallel-process development. Rather than fit parallelization to the code architecture, the code architecture was completely changed to be parallel friendly, which will give the best speed gains.

Since the founding of CPFD in 2006, Dr. Snider and the code development team have worked relentlessly to refine the numerics and advance the speed, accuracy and applicability of the Barracuda product. As such, it offers the high-fidelity, speed and reliability required to make critical fluidized reactor design and operational decisions in a practical time frame.