Momentum Exchange Coefficients Research Articles

Exchange coefficients and mathematical modelsof jet-diffusion flames

Complete mathematical models for the calculation of the flow and temperature fields of turbulent flames and their combustion chambers are still not available. They could be obtained from calculations of heat exchange, for instance, by nonluminiscent radiation, and a description of the turbulent flow field. The principle lack, at this time, is a method for computing turbulent exchange of momentum,mass, and heat. In the present paper, exchange coefficients for momentum, matter, and heat have been obtained by calculations and by measurements. Attempts have also been made to derive unmixedness values from turbulence-measurements data, since unmixedness, as well as exchange of matter, determines the reaction rate. Transport coefficients for momentum are derived both from time mean values of velocity and from the fluctuating velocity and turbulent microscale. Results of these calculations are in good agreement, the order of magnitude of the turbulent exchange coefficient for momentum was 10–30×10 −3 m 2 /sec. The coefficients increase in enclosed jets with the onset of the recirculation zone. They depend on nozzle diameter and flow velocity. In order to derive unmixedness from turbulence data, a relation between the rates of mixingand combustion is given that is based on the assumption that the combustion rate increases with turbulence intensity and decreases with turbulence scale. An empirical formula is given for the local unmixedness on the flame axis which covers the unmixedness data derived from mean concentrations, excepted in the first part of the jet where very special conditions exist which this formula cannot be expected to cover.

Some problems of gas-solid surface interaction

Gas-surface interaction occurs in a variety of physical processes and attracts the attention of various specialists. We consider these phenomena in the aspect of rarefied gas dynamics where the surface interaction problem is one of the most interesting and complex at present. The main attention is paid to neutral monatomic gas interaction with a simple clean surface at energies 10 −2−10 2 eV. Quantum mechanical methods, high-temperature effects and electromagnetic phenomena are not considered here. Section 1 contains a general statement of the problem and a brief review of the physical and computational data results. Fundamental notions characterizing interaction on different levels of description and permitting the order of the phenomena of interest in a natural way are introduced in a new fashion. Each of the following sections is devoted to the central problem of a certain scale level: molecular (II), Boltzmannian (III) and that of random roughness (IV). The study is aimed at obtaining theoretical and analytical results rather than a lot of numerical data. Atomic lattice scattering is considered within the framework of the two-particle-collision theory. Hard sphere scattering is studied in detail and then attraction and softness corrections are introduced. The scattering function model account begins with a critical review and is completed by an algorithm of successive modelling incidence and re-emission velocity dependencies leading to useful formulas for the momentum and energy exchange coefficients. The roughness problem is stated for an arbitrary reflection law in the small area. A complete solution is obtained in the case of a homogeneous isotropic differentiable random surface. Asymptotic expansions are obtained for a slightly rough Gaussian surface.

Predictions of the Momentum Exchange Coefficient for Flow over Heterogeneous Terrain

Predictions of the eddy viscosity K are presented for neutrally stable flow in the surface layer after a change in surface roughness. These predictions indicate that the standard techniques for estimating eddy diffusivities or exchange coefficients may lead to substantial errors for flow over heterogeneous terrain.

Flow in the wake of bluff-body flame stabilizers

Experimental results for the flow around bluff bodies situated in a nozzle are reported in two parts: o (a) The influence of initial flow-boundary conditions on the characteristics of the mean flow field are given. The spatial distributions of reverse mass-flow rate and of the normalized wake boundary (σ/σ o =0) are presented as functions of bluff body blockage ratios in the range 0 to 0.54 and of forebody geometry. (b) The turbulence characteristics of the flow in the immediate wake of a “disc-in-nozzle” arrangement are given; for example, the spatial distributions of turbulent shear stress, turbulence intensities, and turbulence kinetic energy. These were determined using a new method of interpreting anemometer responses, developed for use in highly turbulent flows. When correlated with the mean flow characteristics, the turbulence measurements show that simple models of turbulence are inadequate for the evaluation of momentum exchange coefficients in highly turbulent flows. The correlation between the spatial distributions of mean stream function and local kinetic energy of turbulence, both calculated from measurement data, shows good agreement with that predicted for a similar flow system using the Prandtl-Kolmogorov model of turbulence.

Turbulent Transport Near the Ground in Stable Conditions

Abstract The variation of the nondimensional transfer coefficients, k* and K*, and the Monin-Obukhov function ϕ in strong stability, are examined. The exchange coefficients for heat, water vapor and momentum are shown to be approximately equal even at large Ri. The relationships suggest that the decay of turbulent motion in the lower atmosphere begins at Ri=0.1, and completely ceases at Ri>0.3. In these nonturbulent conditions the profiles of wind and water vapor show very little variation with height, but the temperature profile reflects the increasing importance of infrared radiation.

Temperaturverteilungen in der turbulenten grenzschicht an der ebenen platte

The influence of the turbulent Prandtl number (ratio of the exchange coefficients for momentum and heat) on the temperature distributions in the turbulent boundary layer on a flat plate in incompressible flow is investigated theoretically. Two special cases are treated, viz. the case of “equilibrium wall temperature” and the case of “heat transfer at constant wall temperature”. The laws of the wall and the temperature distributions in the outer part of the boundary layer are given for arbitrary distributions of the turbulent Prandtl number. The heat-transfer coefficients and the recovery factors are calculated. The results are discussed.

Similarity theory and temperature structure in the lower atmosphere

AbstractAn equation based on similarity theory is used to explain the properties of various temperature statistics. Extensive observations indicate that wind and temperature profiles are nearly similar, and the ratio of the exchange coefficients for heat and momentum is of order one.

On the Vertical Velocity Field in a Steady Symmetric Hurricane

It is shown how a system of equations (motion, mass continuity and the first law of thermodynamics) can be integrated for a steady symmetric vortex with a prescribed tangential motion. The method of characteristics is used to obtain a solution for the vertical-velocity field. For the normally observed characteristic lines in a hurricane no vertical velocity is possible for a frictionless atmosphere, and therefore numerical experiments are carried out with different magnitudes of the momentum exchange coefficients. It is also shown that as long as the ratio of the lateral and the vertical exchange coefficients is kept fixed, one calculation of the vertical velocity field enables an examination of a wide range of variation of the individual coefficients. A consistent structure of an Atlantic hurricane is constructed from the National Hurricane Research Project data. DOI: 10.1111/j.2153-3490.1961.tb00076.x

On the Vertical Velocity Field in a Steady Symmetric Hurricane

It is shown how a system of equations (motion, mass continuity and the first law of thermodynamics) can be integrated for a steady symmetric vortex with a prescribed tangential motion. The method of characteristics is used to obtain a solution for the vertical-velocity field. For the normally observed characteristic lines in a hurricane no vertical velocity is possible for a frictionless atmosphere, and therefore numerical experiments are carried out with different magnitudes of the momentum exchange coefficients. It is also shown that as long as the ratio of the lateral and the vertical exchange coefficients is kept fixed, one calculation of the vertical velocity field enables an examination of a wide range of variation of the individual coefficients. A consistent structure of an Atlantic hurricane is constructed from the National Hurricane Research Project data.