Library

Notes: Abstract The appearance of a pronounced velocity-field nonuniformity beyond the granular bed has been established experimentally for the case in which a stream compresses the bed. This effect is absent in the opposite case, when the bed is made friable by a stream.

Notes: Abstract A calculation is made of coefficients (which are linear and nonlinear in the number of photons) appearing in the equations that determine the evolution of the mean and the variance of the number of bremsstrahlung photons emitted in Born scattering of electrons by Coulomb potentials. The effect of electron injection conditions upon the consequences of the saturation produced by increasing the magnetic field is discussed.

Notes: Abstract The evolution of the bremsstrahlung density matrix is considered for scattering of a nonrelativistic electron beam by randomly distributed potentials. A system of equations for the first two moments of the density matrix is considered in the weak nonlinearity approximation, and solutions are given for coherent initial photon statistics.

Notes: Abstract The distribution function of amplitude a and phase ϕ of an arbitrary quantum magnetic field is investigated on the basis of the combined use of two representations, related with a Fourier transform. The square of the wave function in one of these representations determines the distribution function α cos ϕ and in the other, α sin ϕ. As an application, the structure of the bremsstrahlung of a wave packet of electrons is considered. It is shown that the nature of the radiation density matrix depends significantly on the spatial nonuniformity of the electron packet in the region of the scattering centers. A comparison is carried out with the quasiclassical theory of radiation.

Notes: Abstract An equation for concentration pulsations is derived, and an approximation is given for the unknown correlations in the equation. An approximation is proposed for the probability distribution of the passive-impurity concentration, taking account of intermittency and allowing the effect of pulsations on the jet-flow parameters to be taken into account. Using the semiempirical (e−ɛ) model of turbulence and equations for concentration pulsations in the boundary-layer approximation, the characteristics of isothermal submerged axisymmetric jets and of axisymmetric submerged diffusion flames of propane and hydrogen in air are calculated. It is established that with increase in Froude number the intensity of the concentration pulsations decreases both for isothermal jets and for diffusion flames. The concentration pulsations have a significant effect on the characteristics of the turbulent diffusion flame in its initial region. In the absence of buoyancy forces, concentration fluctuations have little effect on the characteristics in the main region of the flame. A burning jet has a longer range than a jet that is not burning. Combustion has little effect on the intensity of velocity and concentration pulsations. The approaches that are widely used at present for the theoretical investigation of the turbulent mixing of jet-type flows use, as closure relations, a two-parameter model of turbulence consisting of semiempirical differential equations [1, 2]. As a rule, one of the equations in the turbulence model is an equation for the turbulent energy, $$e \equiv {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\left\langle {u_\alpha ^\prime u_\alpha ^\prime } \right\rangle $$ (u′α is the pulsational component of the velocity; α = 1, 2, 3; 〈 〉 are the averaging brackets), and the other is either an equation for the integral scale L of the turbulence [3], or an equation for different combinations of these parameters—the turbulent viscosity $$\varepsilon \sim \sqrt {eL} $$ [4], the the dissipation rate ɛ ∼ e2/ɛ [5], etc. The need to use such an approach is associated primarily with the possibility of calculating mean parameters and turbulence characteristics of complex non-self-similar flows depending on the previous development of the flow. In addition, by this means of closure it is possible, using a semiempirical equation for the concentration pulsations σ $$\sigma \equiv \sqrt {\left\langle {\left( {c - \left\langle c \right\rangle } \right)^2 } \right\rangle } $$ [6, 7] (c is the mass concentration) to calculate the meansquare value of the concentration pulsations and also to determine the intermittency coefficient γ and the distribution function of the probability density P(c). A knowledge of these values is particularly important in investigating turbulent mixing in the presence of diffusion combustion. It is known [8] that pulsations of the gasdynamic parameters must be taken into account in describing turbulent combustion, since the calculation of diffusion-combustion characteristics in the “quasilaminar” formulation does not allow a number of qualitative features of the process to be taken into account. Despite the many works on turbulent-flow calculations now available, there has been little investigation of a whole series of aspects of this type of flow. For example, there has not been sufficient study of the effect of the buoyancy forces arising because of the density difference between jets of different gases on the level of the concentration pulsations. Very little data is available on the effect of combustion on the turbulent flow characteristics. The present work takes up these questions. A semiempirical equation is proposed for the concentration pulsations. This equation, which is related to the (e−ɛ) model of turbulence developed in [4], is tested in calculations of isothermal jets and also diffusional combustion flames. Particular attention is paid to the behavior of the concentration pulsations.