Applied Scientific Research

To assist the industrial engine design process, 3-D computational fluid dynamics simulations are widely used, bringing a comprehension of the underlying physics unattainable from experiments. However, the multiphase flow description involving a liquid fuel jet injected into the chamber is still in its early stages of development. There is a pressing need for a spray model that is time efficient and accurately describes the cloud of fuel and droplet dynamics downstream of the injector. Eulerian descriptions of the spray are well adapted to this highly unsteady configuration. The challenge is then to capture accurately both the evaporating spray polydispersity and its two-way mass, momentum and energy interactions with the surrounding gas phase in this framework. The Eulerian Multi-Size Moment (EMSM) model, a high-order (in size) moment model has proved to be well adapted for the treatment of polydispersity. Moreover, it requires less computational effort relative to competing methods, with a single section for the size phase space. Academic test cases have demonstrated its great potential for industrial applications using one-way coupling. Recent modeling and numerical development efforts have resulted in an extension to two-way coupling with an unconditionally stable and accurate numerical scheme, while preserving the size moment space. All these developments have been successfully verified through injection simulations in the context of laminar flow. In the present contribution, in preparation for comparisons with experimental data, an extension to two-way coupling to account for the droplet-gas turbulence interactions is developed and validated for academic cases using physical data for realistic internal combustion engine conditions.

Residual Reynolds number effects in the established data for the velocity profile in turbulent boundary layers (and in pipe or channel flows) are found to be remarkably large. We combine two eddy-viscosity models (with overlapping validity in the inertial sublayer) and show (both analytically and numerically) that this enhancement (which involves a viscous correlation length) arises from inner-outer sublayer interaction.

It is assumed that the materials considered consist of a large number of small elements so that on a macroscopic scale the behaviour approaches that of homogeneous continuous media. Assuming that the small elements follow prescribed strains it is possible to find an expression for the specific energy from which the average elastic constants can be derived.

Unsteady laminar free convection flow past a vertical infinite flat plate subjected to suction is considered. Exact solutions of momentum and energy equations are obtained in two cases: (1) When the plate temperature is proportional to some power of time and (2) when the heat flux at the plate is proportional to some power of time. It is assumed that the suction velocity varies as (time)−1/2. Expressions for the temperature and velocity profiles are obtained in closed forms in both the cases. Effect of suction on velocity, temperature, skin friction and rate of head transfer is studied for Prandtl numbers 0.02, 0.1, 0.72, 1 and 10.

Turbulence decay in a strongly stratified medium is simulated by a direct pseudo-spectral code solving the three-dimensional equations of motion under the Boussinesq approximation. The results are compared to non-stratified simulations results. We focus on the production of mean shear energy observed in the stratified case. We then simulate the decay of stratified turbulence when affected by an initial horizontal mean flow and show that this mean flow is the major component remaining at large t. Next, we give some analytical elements on wave-shear interaction by using a simple refraction calculation with WKB hypothesis. This calculation is illustrated by simulating the interaction between one monochromatic internal wave and a vertical shear profile. We conclude that the existence of singularities in the mean shear production term in the presence of internal gravity waves may be one of the possible mechanisms involved within stratified turbulent shear flows.

The problem of electromagnetic radiation and scattering from perfectly conducting bodies of revolution of arbitrary shape is considered. The mathematical formulation is an integro-differential equation, obtained from the potential integrals plus boundary conditions at the body. A solution is effected by the method of moments, and the results are expressed in terms of generalized network parameters. The expansion functions chosen for the solution are harmonic in ø (azimuth angle) and subsectional in t (contour length variable). Because of rotational symmetry, the solution becomes a Fourier series in ø, each term of which is uncoupled to every other term. Illustrative computations are given for radiation from apertures and plane wave scattering from bodies of revolution. The impedance elements, currents, radiation patterns, and scattering patterns for a conducting sphere are computed both from the general solution and from the classical eigenfunction solution. The agreement obtained serves to check the general solution. Similar computations for a cone-sphere illustrate the application of the general solution to problems not solvable by classical methods.

Adaptive wall-functions are developed for the near-wall elliptic-blending eddy-viscosity model (Billard and Laurence, Int. J. Heat Fluid Flow 33(1), 45–58, 2012). The aim of the new methodology is to make the predictions of this turbulence model less dependent on the spatial resolution in the viscous, buffer and logarithmic layer of the near-wall flow. It can be used in meshes for which localized areas with fine resolution are embedded into the coarsely meshed full domain. This allows reducing the computational cost by focusing the grid points density in critical non-equilibrium flow regions. It is based on Kalitzin et al. (J. Comput. Phys. 204(1), 265–291, 2005) but unlike the latter the dimensionless quantities provided by the wall-functions are converted into physical values by means of a turbulence rather than a mean-flow velocity scale. To justify this choice, the wall-function correction of wall shear-stress and heat-flux is presented as a Nusselt number linearization. Two wall-treatments are proposed for use in unstructured mesh finite-volume schemes: 1/ the wall-function values are applied as boundary conditions or 2/ the wall-function profiles are applied over a cluster of cells in the wall vicinity. The latter also addresses the issue of inner cell-size jumps as often produced by automatic mesh generators. The method is validated on channel flows for several types of meshes and Reynolds numbers. Heat-transfer application on a ribbed wall duct test-case is presented. The grid consists in a very coarsely meshed region upstream of a localized focus zone with classical down-to-the-wall resolution, and the heat-transfer and velocity profile are still accurately predicted.

The concept of superposability of hydromagnetic flows has been discussed by Kapur1). In the present paper, we have used the results of that paper to discuss: (i) superposability of wave motions, (ii) hydrostatic equilibrium of magnetic stars, (iii) effects of viscosity in axially symmetric hydromagnetic flows, (iv) axially symmetric force-free fields, (v) general force-free fields.