ALBERT

Description: The plane and axisymmetric hypersonic flow past blunted bodies is investigated as an inverse problem (shock shape given). The fluid may behave as a real gas in local thermodynamic equilibrium. Viscosity and heat conduction are neglected. An analytical solution uniformly valid in the whole flow field (from the stagnation region up to large distances from the body nose) is given. The solution is based on two main assumptions: (i) the density ratio ε across the shock is very small, (ii) the pressure at a pointPof the disturbed flow field isnotvery small compared with the pressure immediately behind the shock in the intersection point of the shock surface with its normal throughP.TermsO(ε) are neglected in comparison with 1, but it is not necessary for the shock layer to be thin. The change of velocity along streamlines is taken into account. In order to calculate the flow quantities one has to evaluate only two integrals (equations (49) and (53) together with the boundary values (5) and (10)). The application of the solution is illustrated and the accuracy is tested in some examples.

Description: The two-phase flow in settling vessels with walls that are inclined to the vertical is investigated. By neglecting inertial effects and the viscosity of the suspension it is shown that the particle concentration remains constant on kinematic-wave fronts. The wave fronts are horizontal and propagate in a quasi-one-dimensional manner, but are imbedded in a two-dimensional or three-dimensional basic flow which, in turn, depends on the waves via the boundary conditions. Concentration discontinuities (interfaces) are described by kinematic-shock theory. The kinematic shocks are shown to be horizontal, with the possible exception of discontinuities that separate the suspension from the sediment. At downward-facing inclined walls conservation of mass enforces the existence of a boundary-layer flow with relatively large velocity. As G/R2→∞ and G/R4→0, where G and R are respectively a sedimentation Grashof number and a sedimentation Reynolds number, the entrainment of suspended particles into the boundary-layer flow of clear liquid is negligibly small. This provides an appropriate boundary condition for the basic flow of the suspension. Thus, in the double limit considered, a kinematic theory suffices to determine the convective flow of the suspension due to the presence of inclined walls. As an example batch sedimentation in vessels with inclined plane or conical walls is investigated. The settling process is terminated after a time that can be considerably smaller than the time required in a vertical vessel under the same conditions. Depending on the initial particle concentration, there are centred kinematic waves that are linked to a continuous increase of the particle concentration in the suspension. In an appendix, the flow in the boundary layer at a downward facing, inclined wall is investigated. With G/R2→∞ and G/R→0 the boundary layer consists of an inviseid particle-free main part, a viscous sublayer at the wall, and a free shear sublayer at the liquid/particle interface. © 1982, Cambridge University Press. All rights reserved.

Description: The order of magnitude of the flow velocity due to the entrainment into an axisymmetric, laminar or turbulent jet and an axisymmetric laminar plume, respectively, indicates that viscosity and non-slip of the fluid at solid walls are essential effects even for large Reynolds numbers of the jet or plume. An exact similarity solution of the Navier-Stokes equations is determined such that both the non-slip condition at circular—conical walls (including a plane wall) and the entrainment condition at the jet (or plume) axis are satisfied. A uniformly valid solution for large Reynolds numbers, describing the flow in the laminar jet region as well as in the outer region, is also given. Comparisons show that neither potential flow theory (Taylor 1958) nor viscous flow theories that disregard the non-slip condition (Squire 1952; Morgan 1956) provide correct results if the flow is bounded by solid walls. © 1981, Cambridge University Press. All rights reserved.

Description: SUMMARYA rapid method for measuring gas production during incubation of feedingstuffs with rumen liquor in vitro is described. Gas production in 24 h from 200 mg feed dry matter was well correlated with digestibility of organic matter, determined in vivo with sheep. Multiple regression analysis, when it included data from proximate analysis, resulted in an equation (R = 0·98) for prediction of metabolizable energy content, based on 30 experiments with rations varying in protein and crude fibre content, and 59 other experiments with concentrates. Energy content was in the range of 7·7–13·2 MJ ME/kg D.M. (± S.D. = 11·17 ± 1·08). The residual standard deviation of the equation was 0·25 MJ. Gas production was measured in calibrated syringes. The only chemical determinations needed are dry matter, protein and fat. Differences in activity between batches of rumen liquor are corrected by reference to gas production with standard feedingstuffs (hay meal and maize starch).