We consider the propagation of a non-Boussinesq gravity current in an axisymmetric configuration (full cylinder or wedge). The current of density ρc is released from rest from a lock of radius r0 and height h0 into an ambient fluid of density ρa in a container of height H. When the Reynolds number is large, the resulting flow is governed by the parameters ρc/ρa and H* = H/h0. We show that the one-layer shallow-water model, carefully combined with a Benjamin-type front condition, provides a versatile formulation for the thickness and speed of the current, without any adjustable constants. The results cover in a continuous manner the range of light ρc/ρa ≪ 1, Boussinesq ρc/ρa ≈ 1, and heavy ρc/ρa ≫ 1 currents in a fairly wide range of depth ratio, H*. We obtain finite-difference solutions for the propagation and show that a self-similar behaviour develops for large times. This reveals the main features, in particular: (a) The heavy current propagates faster and its front is thinner than that for the light counterpart; (b) For large time, t, both the heavy and light currents spread like t1/2, but the thickness profiles display significant differences; (c) The energy-constrained propagation with the thickness of half-ambient-depth (when H* is close to 1) is a very limited occurrence, in contrast to the rectangular geometry counterpart in which this effect plays a major role. The predictions of the simple model are supported by some axisymmetric Navier–Stokes finite-difference simulations.

In this paper, a direct boundary element method (DBEM) is formulated numerically for the problems of the unbounded potential flows past supercavitating bodies of revolution (cones and also disks which are special case of cones with tip vertex angle of 180 degree) at zero degree angle of attack. In the analysis of potential flows past supercavitating cones and disks, a cavity closure model must be employed in order to make the mathematical formulation close and the solution unique. In the present study, we employ Riabouchinsky closure model. Since the location of the cavity surface is unknown at prior, an iterative scheme is used. Where, for the first stage, an arbitrary cavity surface is assumed. The flow field is then solved and by an iterative process, the location of the cavity surface is corrected. Upon convergence, the exact boundary conditions are satisfied on the body-cavity boundary. For this work, powerful software, based on CFD code, is developed in CAE center of IUST. The predictions of the software are compared with those generated by analytical solution and with the experimental data. The predictions of software for supercavitating cones and disks are seen to be excellent. Using the obtained data from software, we investigate the mathematical behavior of axisymmetric supercavitating flow parameters including drag coefficients of supercavitating cones and disks, cavitation number and maximum cavity width for a wide range of cone and disk diameters, cone tip angles and cavity lengths. The main objective of this study is to propose appropriate mathematical functions describing the behavior of these parameters. As a result, among all available functions such as linear, polynomial, logarithmic, power and exponential, only power functions can describe the behavior of mentioned parameters, very well.

Hydrodynamic instabilities play an important role in the target compression for inertial confinement fusion (ICF). We present the analytical solution of a perturbed isentropic implosion. We compare the analytical solution to the results obtained with perturbation and bi-dimensional Lagrangian hydrodynamic codes. We also compare results from bi-dimensional code and perturbation code on an ICF like test case.