Hydrodynamic numerical modeling

At first it was assumed that there was something unique about the explosive source that was resulting in these remarkable observations. The reactive compressible hydrodynamic numerical models available were unable to reproduce the experimental observations or suggest any possible physical mechanisms unique to explosives. 

We assume stationarity and radiative equilibrium for the energy balance because the radiative timescales are short in respect to the hydrodynamic timescales soon after the initial increase in luminosity. Spherical symmetry is assumed. According to detailed numerical models (Falk and Arnett, 1977 Muller, personal communication, 1987 Nompto, 1987 Nomoto et aL, 1987) and also analytical solutions for strong shock waves in spherical expanding enveloped (Sedov, 1959) density profiles are taken which are given by the self-similar expansion of an initial structure i.e. 

H.G. RAMMING and Z. KOWALIK NUMERICAL MODELLING MARINE HYDRODYNAMICS... 

Multidisciplinary analytical and numerical models require development. These models should involve considerations of equilibrium and irreversible thermodynamics and kinetics of carbonate mineral-organic matter-water interactions within a sound hydrodynamic and basin evolution framework. 

In contrast to diagnostic modeling, which is aimed at the construction of reliable current fields from the specified density fields, the principal goal of the so-called prognostic modeling lies in the understanding of the mechanisms of formation of the circulation in seas and oceans and their possible reproduction in numerical models. Only if thickness problem is resolved, one can speak about the hydrodynamic current forecasting. 

The effects of gas and coal/char feeds and reactor geometries upon these internal processes and, hence, upon the performance of the reactor, can be simulated with this numerical model. The model incorporates representations of particle-particle and particle-gas interactions which account for finite rate heterogeneous and homogeneous chemistry as well as the hydrodynamical processes associated with particle collisions and drag between the particles and the gas flow. The important influences of multicomponent gas phase properties as well as solid particle properties, such as shape and size, are included in the representations. 

Traditionally, the use of analytical models in environmental tracer studies has been far more widespread than numerical models. There are a number of reasons for this. Analytical models are easier to use and manipulate than numerical ones they require less hydrodynamic information and/or field data and the time required to build a transport model is much less than for a numerical model. Multiple examples of such models can be found in the literature for various tracers H, He, C, and C1 (e.g., Castro et al., 2000 Nolte et al., 1991 Schlosser et al., 1989 Solomon et al., 1996 Stute et al., 1992b Torgersen and Ivey, 1985). Generally, these models are either applied to a single aquifer in porous or fractured media or to one particular area within the aquifer such as recharge or discharge areas. 

Killion and Garimella conducted comprehensive critical reviews of analytical and numerical models [44] and experimental investigations [45] of absorption heat and mass transfer. Killion and Garimella [44] found that most of the literature on absorption heat and mass transfer work has focused on the particularly simplified case of absorption in laminar vertical films of LiBr/HjO. Fewer researchers have considered the important situations of wavy films, turbulent films, and films on horizontal tubes. They pointed out that attention must be paid to droplets and waves on horizontal tubes, and to the potential interaction of the heat and mass transfer process on the film hydrodynamics, surface wetting, and heat transfer in the vapor phase. In their review of experimental... 

Hydrodynamic conditions in a basin may in part result from tectonic forces. Ge and Garven (1989) applied a numerical model of coupled tectonic- and gravity-induced flow to evaluate the relative importance of tectonic influence on groundwater pressure and flow in an otherwise gravity-induced flow system in a hypothetical foreland basin. Forbes et al. (1992) included an evaluation of lateral compression in their numerical reconstruction of the present-day pressure distribution in the Venture Field, Eastern Canada. 

It is thus particularly important to accurately simulate the hydrodynamics of the fluorine cell so as to predict its operation correctly. KF-2HF molten salt at 95 °C is very corrosive and extremely delicate to handle. It was thus decided to build a hydraulic model using water and nitrogen bubbles, which is easier to study and presents fewer hazards, the final objective being to validate the EA numerical model used previously for the fluorine cell. 

We begin by positing a thermohydrodynamical equation for the lubricating layer, based on Penny et al. The primary hydrodynamic modelling assumption is the existence of a lubricating melt layer of thickness, / , below the skate blade. We create a time-dependent numerical model by solving the lubrication equation using finite-differences. 

It is possible to incorporate a good deal of advective information into numerical models. In fact, the water quality diffusion model can be coupled with a hydrodynamic model which predicts flow depth and velocity as a function of space and time. These predicted depths and velocities can then be used in the numerical model of the diffusion equation. An alternative is to use measured depth and velocity values as input. Earlier sections have pointed out the value of retaining as much advective detail as possible. 

Numerous models also exist for the contribution of hydrodynamic or frictional drag in straight cylindrical pores. These are well reviewed in Ref. 2. If a solute adsorbs onto the pore surface and spends some portion of its time immobile, its net rate of transport will be reduced. Additionally, in some cases adsorption of the solute can significantly diminish the size of the pore and may even block the pore, preventing passage of another solute [49]. However, less is known about how to model the hydrodynamic drag in the convex, multiply connected pores provided by colloidal assemblies. 

The results of these experimental measurements of the liner trajectory were compared with a numerical model for the implosion obtained from a 1-D, Lagrangian, hydrodynamic code containing a detailed treatment of the equation-of-state of the liner material. Figure 17 shows such a comparison for a 1.4 MJ shot. The point labeled as "abrupt current change" marks the discontinuity in the slope of the current trace caused by the sudden ending of the IL contribution to the voltage when the liner hits the axis. The... 

A number of experimental measurement techniques are discussed, with a focus on noninvasive optical techniques such as particle image velocimetry and digital image analysis, as well as a number of academic numerical modeling tools such as discrete particle model and two-fluid model. Not only hydrodynamic aspects, such as the emergence of defluidized zones and solids circulation profile inversion, but also the effect on the bubble size distributions are discussed for wall-mounted membranes and horizontally immersed membranes. 

This chapter deals with the recent research efforts on the benefits and pitfalls of FBMRs. Recent studies on the topic, using an experimental or numerical approach, wiU be covered. In Section 2, we cover several techniques to investigate the hydrodynamics of membrane FBRs, including several experimental techniques and numerical models, followed by a number of recent results that have been obtained with these techniques. 

---