A two-phase, two-component bubbly flow model.

This thesis is focused attention on one-dimensional models for fast transient flows in a kinematic non-equilibrium. Besides the thermodynamic non-equilibrium, there is another type of non-equilibrium: the kinematic non-equilibrium, or drift between the phases. Such flow models include bubbly gas/liquid flows which are characterized by strong coupling between the phases, due to the rapid interphase transfers of mass, momentum and energy. As a consequence the assumptions that the phase pressures and the phase temperatures are equal at any cross-section appear consistent with experimental observations. The set of equations includes a momentum equation which has the form of a relaxation law of the drift velocity. This equation is based on a simplified version of the so-called Voinov - Berne equation for the momentum of the gas in a bubbly flow. The ability of the model to predict steady state critical flows is tested first. This is done by means of an analysis of the sensitivity to variations of the main parameters, and also by comparing the results with two sets of original experimental data on air-water critical flows. Finally, the model is tested in transient conditions, modelling the water hammer phenomena.(FSA 3)--UCL, 200

Assessment of some high-order finite difference schemes on the scalar conservation law with periodical conditions

Supersonic/hypersonic flows with strong shocks need special treatment in Computational Fluid Dynamics (CFD) in order to accurately capture the discontinuity location and his magnitude. To avoid numerical instabilities in the presence of discontinuities, the numerical schemes must generate low dissipation and low dispersion error. Consequently, the algorithms used to calculate the time and space-derivatives, should exhibit a low amplitude and phase error. This paper focuses on the comparison of the numerical results obtained by simulations with some high resolution numerical schemes applied on linear and non-linear one-dimensional conservation low. The analytical solutions are provided for all benchmark tests considering smooth periodical conditions. All the schemes converge to the proper weak solution for linear flux and smooth initial conditions. However, when the flux is non-linear, the discontinuities may develop from smooth initial conditions and the shock must be correctly captured. All the schemes accurately identify the shock position, with the price of the numerical oscillation in the vicinity of the sudden variation. We believe that the identification of this pure numerical behavior, without physical relevance, in 1D case is extremely useful to avoid problems related to the stability and convergence of the solution in the general 3D case

Assessment of three WENO type schemes for nonlinear conservative flux functions

This paper focuses on a new comparison of the behavior of three Weighted Essentially Non-Oscillatory (WENO) type numerical schemes for three different nonlinear fluxes, in the case of scalar conservation law. The analytical solution is provided for various boundary conditions. For the time integration we adopt the 4-6 stage Low-Dispersion Low-Dissipation Runge-Kutta method (LDDRK 4-6). The schemes were tested on piecewise constant function for non-periodical conditions. The assessment was performed because the specialized literature mainly presents cases favorable illustrating only to a particular method while our purpose is to objectively present the performance and capacity of each method to simulate simple cases like scalar conservation law problems. All the schemes accurately identify the position of the shock and converge to the proper weak solution for the non-linear fluxes and different initial conditions. The paper is a continuation of the efficiency and accuracy analysis of high order numerical schemes previously published by the authors [1,2]

A Reduced Order Model based on Large Eddy Simulation of Turbulent Combustion in the Hybrid Rocket Engine

A combined method of large eddy simulations for non-premixed combustion in a turbulent boundary layer coupled with proper orthogonal decomposition of instantaneous velocity, pressure and temperature fields is developed in order to obtain a reduced order model. First, we investigate a channel turbulent reacting flow using Large Eddy Simulations (LES) technique. Polypropylene/O2 has been considered as fuel/oxidant pair. The turbulence-combustion interaction is based on a combination of finite rate/eddy dissipation model applied to a reduced chemical mechanism with four reactions. The LES numerical results are analyzed with respect to RANS simulations and with other reference data. The second part of the paper refers to the derivation of a Reduced Order Model (ROM) based on proper orthogonal decomposition (POD) technique for the unsteady flow field. In order to achieve that, the eigenmodes of the flow are computed from several snapshots of the instantaneous fields uniformly spaced and the most energetic ones are used to set up the Reduced Order Model. Constant regression rate of the fuel grain is considered. The flow and thermal fields obtained with ROMs are compared with the ones obtained from the full simulation and an analysis on the number of modes required to achieve the desired accuracy is presented

Assessment of Stochastic Numerical Schemes for Stochastic Differential Equations with “White Noise” Using Itô’s Integral

Stochastic Differential Equations (SDEs) model physical phenomena dominated by stochastic processes. They represent a method for studying the dynamic evolution of a physical phenomenon, like ordinary or partial differential equations, but with an additional term called “noise” that represents a perturbing factor that cannot be attached to a classical mathematical model. In this paper, we study weak and strong convergence for six numerical schemes applied to a multiplicative noise, an additive, and a system of SDEs. The Efficient Runge–Kutta (ERK) technique, however, comes out as the top performer, displaying the best convergence features in all circumstances, including in the difficult setting of multiplicative noise. This result highlights the importance of researching cutting-edge numerical techniques built especially for stochastic systems and we consider to be of good help to the MATLAB function code for the ERK method