Mean Reaction Rate Research Articles

Die Struktur turbulenter Freistrahl‐Diffusionsflammen

AbstractThe structure of turbulent jet diffusion flames. This review considers recent developments in the description of kinetic effects in turbulent jet diffusion flames without swirl. The model of laminar flamelets is introduced, which allows description of effects far from chemical equilibrium – for instance local quenching phenomena. A similar solution is given for the equations governing round jet flames. Finally, relations for the mean chemical reaction rate and the formation rate of NO are derived. The article concludes by mentioning recent investigations on flame stability.

Turbulent mean reaction rates in the limit of large activation energies

Closed-form expressions for the turbulent mean reaction rate and its covariance with the temperature are derived for premixed and non-premixed combustion. The limit of large activation energies is exploited for a chemical reaction rate that, by virtue of coupling functions, depends on the mixture fraction and a non-equilibrium progress variable only. The probability density function (p.d.f.) formulation with an assumed shape of the p.d.f. is used; a beta-function distribution is assumed for the progress variable. The mean reaction rate is expressed in terms of the mean and the variance of the temperature and, for non-premixed combustion, of the mixture fraction. The reaction kinetics are represented by the non-dimensional activation energy and the laminar flame velocity. For non-premixed systems the possibility of local extinction by flame stretch is considered.

17-Hydroxyprogesterone metabolism in the monkey fetal adrenal: C 17–20Lyase and 21-hydroxylase activities

C 17–20Lyase and 21-hydroxylase activities were measured during late gestation In the rhesus monkey ( Macaca mulatta ) fetal adrenal. Activities were assessed in 10,000 × g supernatants with 17-hydroxyprogesterone and NADPH as substrates. Although conversion of [ 14C]17-hydroxyprogesterone to [ 14C]androstenedione was noted, activity was often nonlinear and far less than the rate of hydroxylation which together prevented an accurate estimation of lyase rate, K m and V max. 21-Hydroxylase activity was characterized; the mean reaction rate was 1.6 × 10 −3 μmoles NADPH oxidized/min. × mg −1 protein with an apparent K m of 3.6 × 10 −7 M and a V max of 2.2 × 10 −3 μmoles/min. × mg −1 protein. These values were similar to data obtained In adrenals from adult monkeys. A relatively high level of hydroxylase activity in the fetal gland might lead to an Inadequate supply of precursors for the synthesis of dehydroepiandrosterone sulfate (DHEAS) in the adrenal if it also contained 3β-hydroxysteroid dehydrogenase (3β-hsdh). However, the fact that the fetal adrenal reportedly is deficient in 3β-hsdh may serve to protect both DHEAS and corticoid synthesis.

Joint probability density function in turbulent combustion

Knowledge of the probability density function (p.d.f.) of fluctuations in gasdynamic and chemical parameters is of prime interest if one is concerned with mean reaction rates in turbulent combustion systems. In the general case, the parameters to be taken into account are the pressure, the temperature and the concentration or mass fraction of prominent chemical species; for the simple case of a global single reaction, and if the influence of pressure fluctuations is negligible, three variables must be retained. In the first part, the usefulness and the properties of the multidimensional p.d.f. are discussed, following previous contributions. In the second part, after a discussion of some examples of p.d.f. measured in non-reacting flows, a theoretical study of the p.d.f. in reactive flows is presented. We first find, by the method of Dopazo and O'Brien, an equation for the 3-D probability density function (in the sense of Favre) and discuss its closure; we show whether this p.d.f. could be two or one-dimensional and where its boundaries are located in the phase space. Secondly, we describe a numerical method to solve the equation thus obtained; the solutions are obtained and discussed for the cases of 1-D or 2-D p.d.f., applicable to turbulent combustion in stirred combustors.

On the scales of the fluctuations in turbulent combustion

Turbulent combustion can be calculated by integrating conservation equations for mean values and some significant turbulent quantities, provided that certain terms have been suitably “modelled.” Mean reaction rates have been modelled previously by a method that uses approximated shapes of the one point probability density function (p.d.f.) of temperature or/and concentration. In the present paper, the closure of the turbulent diffusion flux and the molecular destruction of the fluctuations of a reactive species (or temperature) are studied by considering the shapes of the joint p.d.f. for species and transverse velocity, or of the two-point p.d.f. for species concentration. In the simple case of a perfectly premixed flame, closure assumptions are proposed that allow a numerical study of the influence of reaction on the turbulent diffusion coefficient (related to an integral scale of the fluctuations) and on a Taylor microscale.

Time History of Velocity Waves in a Reacting Fluid

Abstract The interaction between two arbitrary shear waves in an infinite homogeneous reacting fluid is studied. The reaction is taken as first order in reactant and fifth order in temperature. Each variable—velocity, temperature, density, pressure and composition—is written as a Fourier series and the initial derivatives of each coefficient through the third are calculated from the initial data and the conservation equations. The initial development of each variable is calculated by a Taylor series. Many different wave configurations are studied. It is found that the mean reaction rate can be increased, that the mean square velocity and mean square vorticity can increase very rapidly and that this increase occurs preferentially in the high wavenumber components. Extrapolating these results to continuous spectrum turbulence in a homogeneous reacting fluid, the reaction rate should increase, the turbulence intensity should increase and the spectrum of the turbulence should be shifted toward higher wavenumbers.

Intensification of Turbulence by Chemical Heat Release

Volumetric chemical energy release is studied as a mechanism for enhancing the isotropic turbulent motion of a compressible fluid medium. Both the vortical and dilatational components are examined to determine the influence of irreversible heat addition from exothermic reactions. To a first-order approximation, the density fluctuations caused by eddy production and destruction are shown to be insensitive to the behavior of internal degrees of freedom in the gas (including chemistry). Based on this finding, the pressure fluctuations are determined from a linearized analysis of the combined chemical and gasdynamic response to density fluctuations. The results for amplitudes and phase relationship between pressure and density fluctuations are used to obtain an estimate of the power delivered. The leading contribution to the work integral is of second order in fluctuation amplitudes. A generalized rate model for a highly dissociated gas relaxing toward equilibrium is retained through-out the analysis. Limiting cases are examined by the use of the resulting general expression. The power delivered is proportional (in all cases) to the product of the mean reaction rate and the fourth power of turbulence Mach number (fluctuation velocity divided by local frozen acoustic velocity). For eddy lifetimes shorter than chemical relaxation times, it is shown that the power delivered is essentially independent of frequency.

Nuclear Reactions in the Stars. I. Proton-Proton Chain

The rates are calculated for the main reactions making up the "proton-proton chain," whose net effect is the conversion of four hydrogen atoms into one helium atom. These calculations are carried out for temperatures and densities corresponding to central conditions in main sequence stars.The mean reaction rate for the beta-decay conversion of two protons into one deuteron is calculated accurately, using the latest data on the two-nucleon system and on beta-decay. It is shown that, under normal stellar conditions, the reaction chain is completed by the radiative capture of a proton by a deuteron and by the collision between two of the resultant ${\mathrm{He}}^{3}$ nuclei to form one ${\mathrm{He}}^{4}$ nucleus and two protons. Values are given for the rate of energy production and for the concentrations of deuterium and ${\mathrm{He}}^{3}$ at various temperatures.