David E. Stock

Computation of electrical conditions inside wire‐duct electrostatic precipitators using a combined finite‐element, finite‐difference technique

An accurate and efficient numerical scheme is presented for calculating electrical conditions inside wire‐duct electrostatic precipitators. A Galerkin finite‐element method with quadratic interpolation is employed in solving Poisson’s equation to yield the electric potential solution. A backward difference method is utilized to compute the space‐charge density from the continuity equation. The two methods are iteratively applied until convergence criteria for electric potential and current density are met. Computed potential and electric field values show good agreement with analytic solutions and experimental measurements. Comparisons between the present scheme and a finite‐difference scheme show that the finite‐element method offers distinct advantages in predicting the electrical characteristics of precipitators.

Particle Dispersion in Flowing Gases—1994 Freeman Scholar Lecture

Particle-laden gas flows are common in many man-made and natural environments. Their importance to industrial processes, agriculture, and human health has made them of great theoretical and practical interest over the past 50 years. Because particles are often carried by a turbulent gas stream, progress in understanding and predicting behavior of particle-laden flows has closely followed developments in understanding and prediction of turbulent flow. The motion of a particle in a gas flow is governed by gravity and the particle`s interaction with the turbulent fluid surrounding it. However, to determine the location and thus the local turbulence surrounding the particle, the trajectory of the particle must be known. It is this nonlinear coupling between the particle motion and the turbulence that makes predicting particle dispersion in gas flow difficult. During the past two decades, fundamental understanding of the dispersion of particles in simple turbulent gas flows has been reached, and the capability of predictive tools has increased exponentially as a result. This review is an attempt to summarize the current state of knowledge about gas-particle flows, and to highlight areas where more research is needed.

Stochastic trajectory models for turbulent diffusion: Monte Carlo process versus Markov chains

Abstract Turbulent diffusion of passive scalars and particles is often simulated with either a Monte Carlo process or a Markov chain. Knowledge of the velocity correlation generated by either of these stochastic trajectory models is essential to their application. The velocity correlation for Monte Carlo process and Markov chain was studied analytically and numerically. A general relationship was developed between the Lagrangian velocity correlation and the probability density function for the time steps in a Monte Carlo process. The velocity correlation was found to be independent of the fluid velocity probability density function, but to be related to the time-step probability density function. For a Monte Carlo process with a constant time step, the velocity correlation is a triangle function; and the integral time scale is equal to one-half of the time-step length. When the time step was chosen randomly with an exponential pdf distribution, the resulting velocity correlation was an exponential function. Other time-step probability density functions, such as a uniform distribution and a half-Gaussian distribution, were also tested. A Markov chain, which presumes one-step memory, has a piecewise linear velocity correlation function with a finite time step. For a Markov chain with a short time step, only an exponential velocity correlation function can be realized. Thus, a Monte Carlo process with random time steps is more versatile than a Markov chain. Direct numerical calculation of the velocity correlation verified the analytical results. A new model which combines the ideas of the Monte Carlo process and the Markov chain was developed. By examining the long-time mean square dispersion, we found an exact solution for the Lagrangian integral time scale of the new model in terms of the intercorrelation parameter and the mean and the variance of the time steps. Using this new model, we can generate any velocity correlation, including one with a negative tail. Two approximate solutions that give upper and lower bounds for the Lagrangian velocity correlation are proposed.

Chaotic dynamics of particle dispersion in fluids

An analysis of the Lagrangian motion for small particles denser than surrounding fluid in a two‐dimensional steady cellular flow is presented. The Stokes drag, fluid acceleration, and added mass effect are included in the particle equation of motion. Although the fluid motion is regular, the particle motion can be either chaotic or regular depending on the Stokes number and density ratio. The implications of chaotic motion to particle mixing and dispersion are discussed. Chaotic orbits lead to the dispersion of particle clouds which has many of the features of turbulent dispersion. The mixing process of particles is greatly enhanced since the chaotic advection has the property of ergodicity. However, a high dispersion rate was found to be correlated with low fractal dimension and low mixing efficiency. A similar correlation between dispersion and mixing was found for particles convected by a plane shear mixing layer.

The Numerical Simulation of Airflow and Dispersion in Three-Dimensional Atmospheric Recirculation Zones

Abstract A three-dimensional, nonhydrostatic numerical code using the two-equation turbulence closure was developed to model the atmospheric transport and diffusion of pollutants over buildings and a three-dimensional hill. The standard engineering two-equation, first-order turbulence closure was modified to account for surface layer effects and the reduced production of dissipation in the region above the surface layer found in an atmospheric boundary layer. The computations for the dispersion of a building rooftop release showed good agreement with wind tunnel measurements, except when very close to the ground. The transport and dispersion of a plume over a 300-m conical hill, Steptoe Butte, was also simulated. The computations are compared with near ground-level field measurements.

Flow visualization inside a wire-plate electrostatic precipitator

A flow visualization study was performed in a wire-plate precipitator with a plate-plate spacing of 20.32 cm and wire-wire spacing of 20.32 cm. Smoke was used as the flow tracer, where injection and illumination were accomplished by two different techniques. In one method smoke was released from a single heated probe and illuminated by electronic flash. The other method employed a uniform smoke flow made visible by a laser sheet. The latter technique proved to be superior, providing well-defined views of the flow in both streamwise and spanwise planes over a wide range of velocities (0.2-2 m/s) and current densities (0-0.5 mA/m). The illuminated flow patterns were recorded by still 35 mm photography and color video taping. Of particular interest was the interaction between the precipitator gas flow and the corona-generated electric wind for both polarities of discharge. Results showed that positive corona discharge produces a stable two-dimensional smoke flow with negligible turbulent dispersion for precipitator velocities greater than 0.7 m/s. Lower velocities allowed the electric wind to dominate producing unstable, recirculating flow with widespread turbulence. Negative discharges were inherently unsteady and three-dimensional at all operating conditions but displayed extreme instability and recirculation (similar to positive polarity) for precipitator velocities less than 0.7 m/s. >

Computational Fluid Dynamic Simulations of Plume Dispersion in Urban Oklahoma City

Abstract A 3D computational fluid dynamics study using Reynolds-averaged Navier–Stokes modeling was conducted and validated with field data from the Joint Urban 2003 dispersion study in Oklahoma City, Oklahoma. The modeled flow field indicated that the many short buildings in this domain had a relatively small effect on the flow field, whereas the few tall buildings considerably influenced the transport and diffusion of tracer gas through the domain. Modeled values were compared with observations along a vertical profile located about 500 m downwind of the source. The isothermal base case using the standard k–e closure model was within 50% of the concentration measurements, and a convective case with ground and building surfaces 10°C hotter than ambient temperatures improved the modeled profile to within 30% of observations. Varying wind direction and source location had a marked effect on modeled concentrations at the vertical profile site. Ground-level concentrations were 6 times the observed values whe...

Interpretation of Measured Tracer Concentration Fluctuations Using a Sinusoidal Meandering Plume Model

Abstract Simultaneous instantaneous concentration and wind velocity fluctuations were measured 100 to 752 m downwind of a point source release of SF6 tracer during two field studies conducted amid rolling wheat fields and at a flat desert site in eastern Washington. Data from stable, neutron, and unstable conditions are interpreted using a meandering plume model where the meander is defined to be sinusoidal and the instantaneous plume profile is Gaussian. A sensitivity analysis of the model shows that the characteristic concentration time scale is a direct function of the meander time scale and the receptor position relative to the meander centerline. For narrow instantaneous plumes relative to the meander amplitude, the predicted mean crosswind profiles of concentration, intermittency factor, concentration fluctuation intensity, and peak-to-mean ratios exhibit bimodal distributions. Conditional (nonzero) concentration fluctuation intensifies calculated from the model are scattered about 1.0;, the scatter...

Determination of plume capture by the building wake

Flow and dispersion about a cubical building were computed using a fourth-order accurate finite elements scheme. The time-averaged Navier-Stokes equations were closed with the standard k−ϵ turbulence model as well as with a k−ϵ turbulence model modified to allow production of turbulent kinetic energy to depend on the product of the strain rate and vorticity. The computed flow agreed with the wind tunnel measurements. Releases from a stack located at various positions within the recirculation zone behind the building were simulated. The effect of stack velocity on the concentration in the recirculation cavity was quantified by comparing the mass of pollutant in the recirculation cavity at very low stack exit velocities with the mass of pollutant in the recirculation cavity for higher stack exit velocities. The mass of pollutant in the recirculation zone decreased considerably at the higher stack velocities. The results of this work can be used to help develop and improve the modeling of pollutant transport in recirculation zones and wakes.

Quantification of chaotic dynamics for heavy particle dispersion in ABC flow

A six‐dimensional nonlinear dynamic system describing the Lagrangian motion of a heavy particle in the Arnold–Beltrami–Childress (ABC) flow was numerically studied. Lyapunov exponents and fractal dimension were used to quantify the chaotic motion. A single set of ABC flow parameters and a limited set of initial conditions were used. Given these restrictions, the following were found. (1) Attractor fractal dimension varies significantly with Stokes number, and, depending on inertia, periodic, quasiperiodic, and chaotic attractors may exist. (2) Particle drift reduces the fractal dimension when the drift is small. It can also cause irregular jumps when the drift parameter is close to one. (3) Quasiperiodic orbits on smooth two‐dimensional manifolds were shown to be the most common ultimate solutions of the system when either the inertia or the drift is relatively large. (4) Different initial conditions can lead to different attracting sets; however, most of them have the same dimension. (5) A direct measure...