The propagation of a reaction front through a packed bed is analyzed theoretically. The chemical reaction rate is represented by Arrhenius temperature kinetics with external transfer limitation and general power law dependency on both gaseous and solid reactant concentrations. Analogous to so-called "Activation Energy Asymptotics" developed for premixed laminar flames, the largeness of the activation energy of the chemical reaction is exploited to derive asymptotic solutions from the three governing differential equations pertaining to transport of heat, of solid reactant, and of gaseous reactant, making use of the method of matched asymptotic expansions. Two regions are distinguished, i.e., an outer region or preheat zone and an inner region or reaction zone. In the preheat zone, the reaction terms can be neglected as compared to the convective and diffusive terms. In the reaction zone, the diffusion of heat is dominating over the convective heat transport mechanism and balances the heat of reaction. In accordance with the magnitudes taken for the Lewis numbers, for solid and gaseous reactants convective transports are dominating and submitting diffusive transports in the reaction zone, respectively. Solutions in closed form are presented for governing variables including reaction front velocity whereby previously published results appear as special cases. The solutions provide direct insight into underlying physical processes and enable the effects of important parameters to be quantified analytically. © 2001 by The Combustion Institute

A derivation of the Langevin and diffusion equations describing the statistics of fluid particle displacement and passive admixture in turbulent flow is presented. Use is made of perturbation expansions. The small parameter is the inverse of the Kolmogorov constant C 0 , which arises from Lagrangian similarity theory. The value of C 0 in high Reynolds number turbulence is 5-6. To achieve sufficient accuracy, formulations are not limited to terms of leading order in C 0 −1 including terms next to leading order in C 0 −1 as well. Results of turbulence theory and statistical mechanics are invoked to arrive at the descriptions of the Langevin and diffusion equations, which are unique up to truncated terms of O͑C 0 −2 ͒ in displacement statistics. Errors due to truncation are indicated to amount to a few percent. The coefficients of the presented Langevin and diffusion equations are specified by fixed-point averages of the Eulerian velocity field. The equations apply to general turbulent flow in which fixed-point Eulerian velocity statistics are non-Gaussian to a degree of O͑C 0 −1 ͒. The equations provide the means to calculate and analyze turbulent dispersion of passive or almost passive admixture such as fumes, smoke, and aerosols in areas ranging from atmospheric fluid motion to flows in engineering devices.

We derive a comprehensive statistical model for dispersion of passive or almost passive admixture particles such as fine particulate matter, aerosols, smoke, and fumes in turbulent flow. The model rests on the Markov limit for particle velocity. It is in accordance with the asymptotic structure of turbulence at large Reynolds number as described by Kolmogorov. The model consists of Langevin and diffusion equations in which the damping and diffusivity are expressed by expansions in powers of the reciprocal Kolmogorov constant C_{0}. We derive solutions of O(C_{0}^{0}) and O(C_{0}^{-1}). We truncate at O(C_{0}^{-2}) which is shown to result in an error of a few percentages in predicted dispersion statistics for representative cases of turbulent flow. We reveal analogies and remarkable differences between the solutions of classical statistical mechanics and those of statistical turbulence.

Using the theory of functions of a complex variable, in particular the method of conformal mapping, the irrotational and solenoidal flow in two-dimensional radialflow pump and turbine impellers fitted with equiangular blades is analysed. Exact solutions are given for the fluid velocity along straight radial pump and turbine impeller blades, while for logarithmic spiral pump impeller blades solutions are given which hold asymptotically as (r1/r2)n→0, in whichr1is impeller inner radius,r2is impeller outer radius andnis the number of blades. Both solutions are given in terms of a Fourier series, with the Fourier coefficients being given by the (Gauss) hypergeometric function and the beta function respectively. The solutions are used to derive analytical expressions for a number of parameters which are important for practical design of radial turbomachinery, and which reflect the two-dimensional nature of the flow field. Parameters include rotational slip of the flow leaving radial impellers, conditions to avoid reverse flow between impeller blades, and conditions for shockless flow at impeller entry, with the number of blades and blade curvature as variables. Furthermore, analytical extensions to classical one-dimensional Eulerian-based expressions for developed head of pumps and delivered work of turbines are given.

Asymptotic analysis is presented of the energy balance equations derived from statistically averaged Navier-Stokes equations pertinent to wall-induced turbulence. Attention is focused on the inertial sublayer, the region outside the viscous sublayer, and the buffer layer where the log-law for mean flow holds. Production and dissipation of turbulence are shown to be equal with a relative error of O͑x 2 / L͒, where x 2 is the distance from the wall and L is the external length ͑pipe radius, channel half-height, boundary layer thickness͒. Diffusion of pressure and kinetic energy together are only of relative magnitude O͑x 2 / L͒. Pressure gradient terms are shown to redistribute longitudinal turbulence production in equal portions dissipated in the three orthogonal directions.