John Schwarzkopf

Carrier Phase Turbulence in Fluid-Particle Flows (Plenary)

Turbulence in the carrier phase of fluid-particle flows plays an important role in mixing and shear stress. The availability of a reliable model for turbulence is essential to the development of computational models that can be applied with confidence to engineering systems. The general approach is to add a term to the Navier-Stokes equations that represents the force on the fluid due to due to particle drag and to carry out the procedures used for single phase flows to derive equations for carrier-phase turbulence. The problem with this approach is presented. A flow configuration representing a basic test case, which can be used to judge the viability of any model, is introduced. A recently developed turbulence model using volume averaging and based on the turbulence energy-dissipation description of turbulence is presented. This model is applied to the basic test case and to experiments for particles dropping in a quiescent fluid and gas-particle vertical channel flow. The predictions show good agreement with experimental data.Copyright

A k-ε Model for Particle-Laden Turbulent Flows

A dissipation transport equation for the carrier phase of particle-laden turbulent flows was recently developed. This equation shows a new production of dissipation term due to the presence of particles that is related to the velocity difference between the particle and the surrounding fluid. In the development, it was assumed that each coefficient was the sum of the coefficient for single phase flow and a coefficient quantifying the contribution of the particulate phase. The coefficient for the new production term (due to the presence of particles) was found from homogeneous turbulence generation by particles and the coefficient for the dissipation of dissipation term was analyzed using DNS. A numerical model was developed and applied to particles falling in a channel of downward turbulent air flow. Boundary conditions were also developed to ensure that the production of turbulent kinetic energy due to mean velocity gradients and particle surfaces balanced with the turbulent dissipation near the wall. The turbulent kinetic energy is compared with experimental data. The results show attenuation of turbulent kinetic energy with increased particle loading; however the model does under predict the turbulent kinetic energy near the center of the channel. To understand the effect of this additional production of dissipation term (due to particles), the coefficients associated with the production of dissipation due to mean velocity gradients and particle surfaces are varied to assess the effects of the dispersed phase on the carrier phase turbulent kinetic energy across the channel. The results show that this additional term plays a significant role in predicting the turbulent kinetic energy and a reason for under predicting the turbulent kinetic energy near the center of the channel is discussed. It is concluded that the dissipation coefficients play a critical role in predicting the turbulent kinetic energy in particle-laden turbulent flows.© 2009 ASME

Volume Average Turbulence Dissipation Equation for Multiphase Flow

A dissipation transport equation for the carrier phase turbulence in particle-laden flow is derived from fundamental principles. The equation is obtained by volume averaging the same equation used for single phase flows. This process yields three additional terms that reflect the effect of the particles; these terms are evaluated assuming Stokes flow around the particles. Two of the terms reduce to zero and only one term remains which is identified as the production of dissipation due to the particles. The dissipation equation for the standard k-e model is reformulated to include the additional term. The equation is then applied to the case of particles falling in an initially quiescent fluid and experimental data are used to evaluate the empirical coefficients. The ratio of the coefficient for the production of dissipation (due to the presence of particles) to the coefficient for the dissipation of dissipation is found to correlate well with the relative Reynolds number.Copyright

Modeling of Multiphase Flow Boiling in Meso-Channels

Modeling two-phase heat transfer coefficients and corresponding surface temperatures can be difficult. In macro flows, the Chen and Bennett model showed good agreement with experimental data from various researchers. This model was derived from the original Chen model and is primarily based on physical properties with some empiricism. The purpose of this paper is to present a method of modifying a macro-boiling model to predict surface temperatures and heat transfer coefficients associated with meso-channel flow boiling and augmented boiling associated with spray cooling in mesochannels. In order to validate the model, experimental data was gathered. The spray module consisted of 17 sloped channels each having an inlet and exit hydraulic diameter of 1.55 mm and 1.17 mm respectively and a plan length of 33 mm. The heat flux was in the range of 11 – 61kW/m2 and the mass flux was 80 kg/m2 -s. The quality of fluid (PF5050) ranged from 0 – 75%. The fluid inlet temperature was 29°C and the saturation temperature was 34°C. The modified model shows good agreement with the experimental data with deviations on the order of 10%.Copyright