Numerical simulation of single gas bubbles under shear flow conditions

Disperse gas bubbles play an important role in many industrial applications. Knowing the rising velocity, the interfacial area, or the critical size for break-up or coalescence in different systems can be crucial for the process design. Usually the flow experienced by bubbles is not uniform but sheared. Under shear-flow conditions bubbles develop a lift force perpendicular to the flow direction. In the present work direct numerical simulations are applied to examine the dependency of the lift force on the shear rate for bubbles in pure liquids. A level-set based volume-tracking method is implemented into the CFD-code OpenFOAM, to follow the free interface of the gas bubble. Results show good agreement with available experimental results from single bubbles in a rotating chamber. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Exponential difference scheme for numerical simulation of viscous gas flow

Translated from Matematicheskie Modeli i Optimizatsiya Vychislitel'nykh Algoritmov, pp. 43–49, 1994.     

Non-isothermal,compressible gas flow for the simulation of an enhanced gas recovery application

In this work, we present a framework for numerical modeling of CO₂ injection into porous media for enhanced gas recovery (EGR) from depleted reservoirs. Physically, we have to deal with non-isothermal, compressible gas flows resulting in a system of coupled non-linear PDEs. We describe the mathematical framework for the underlying balance equations as well as the equations of state for mixing gases. We use an object-oriented finite element method implemented in C++. The numerical model has been tested against an analytical solution for a simplified problem and then applied to CO₂ injection into a real reservoir. Numerical modeling allows to investigate physical phenomena and to predict reservoir pressures as well as temperatures depending on injection scenarios and is therefore a useful tool for applied numerical analysis.     

Lattice Boltzmann model for the perfect gas flows with near-vacuum region

It is known that the standard lattice Boltzmann method has near-vacuum limit, i. e., when the density is near zero, this method is invalid. In this letter, we propose a simple lattice Boltzmann model for one-dimensional flows. It possesses the ability of simulating near-vacuum area by setting a limitation of the relaxation factor. Thus, the model overcomes the disadvantage of non-physical pressure and the density. The numerical examples show these results are satisfactory.     

Sufficient conditions for time optimal heating of rigid bodies by internal heat sources

We derive sufficient conditions for the time optimality of the control of heating of rigid bodies by internal heat sources under constraints on phase coordinates. We numerically solve the optimal-control problem in the case of heating of an unbounded plats with constraints on temperature and thermoelastic stresses.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 56–60, 1987.     

Heat transfer at high energy devices with prescribed cooling flow

We study the heat transfer from a high‐energy electric device into a surrounding cooling flow. We analyse several simplifications of the model to allow an easier numerical treatment. First, the flow variables velocity and pressure are assumed to be independent from the temperature which allows a reduction to Prandtl's boundary layer model and leads to a coupled nonlinear transmission problem for the temperature distribution. Second, a further simplification using a Kirchhoff transform leads to a coupled Laplace equation with nonlinear boundary conditions. We analyse existence and uniqueness of both the continuous and discrete systems. Finally, we provide some numerical results for a simple two‐dimensional model problem. Copyright © 2006 John Wiley & Sons, Ltd.     

On conditions of flutter onset for elongated plate in supersonic gas flow

The scheme developed in [1] of the investigation of Poincaré–Andronov-Hopf bifurcation on the base of the Lyapounov-Schmidt method is applied to two boundary value problems for nonlinear ordinary differential equation describing the oscillations of an elongated plate in supersonic gas flow. Necessary conditions for the existence of periodic solutions are obtained. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient high-order compact exponential time differencing method for space-fractional reaction-diffusion systems with nonhomogeneous boundary conditions

Numerical Algorithms - This paper introduces an efficient unconditionally stable fourth-order method for solving nonlinear space-fractional reaction-diffusion systems with nonhomogeneous Dirichlet...     

Software package for 3D viscous gas flow simulation on multiprocessor computer systems

A parallel software package designed for the numerical simulation of three-dimensional viscous gas flows is presented. The numerical algorithm is based on kinetically consistent difference schemes used on locally refined grids. The software package has been tested in various super-and subsonic flow problems. It provides an opportunity for the direct simulation of turbulent flows. The efficiency of parallelization is analyzed depending on the problem size and the number of processors.     

A kinetic model for polytropic gases with internal energy

We consider a mixture of N ideal, polytropic gases. Each species is described by a distribution function f_i(t, x, v, I) ≥ 0, 1 ≤ i ≤ N, defined on , and its evolution is governed by a Boltzmann-type equation. In order to recover the energy law of polytropic gases, the authors of [4] proposed a kinetic model in the framework of a weighted L¹ space. Another approach has been developed in [3] in the context of polyatomic gases. Following this previous lead, our model provides a L² framework in both variables v and I, to eventually perform a mathematical study of the diffusion asymptotics, as it was done in [2] for a model without energy exchange. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

A three-dimensional (3D) predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa-tions with a free surface. The 3D irreg...     

Energy-economy simulation with the Argonne energy model for Portugal

This paper discusses energy-economy interactions in energy-poor newly industrializing countries (NICs), describes the structure and operation of the Argonne Energy Models (AEMs), and reports the results of an energy-economy simulation based upon the Argonne Energy Model for Portugal (AEM-P).The problem facing the energy-poor NICs is to achieve sufficient economic growth to pay for energy imports and energy sector development, with something left over. In addressing this issue, the energy-economy modeler finds that no existing analytic methodology is completely adequate. The AEMs contribute to the refinement of methodology by deriving least-cost energy-sector configurations in terms of energy flows and prices for specific energy transformation technologies.The energy-economy simulation for Portugal indicates that higher energy costs due to further industrialization could be offset substantially by application of energy conservation technologies, by adoption of fuel switching strategies, and by promotion of domestic energy production. Under varying economic scenarios, and with high world oil price assumptions, between 1977 and 1997 the energy sector would account for about 30 percent of GDP. As a proportion of total energy supply, imported oil would decrease from around 90 to 50 percent, imported coal would increase from under 1 to over 25 percent, and the contribution from domestic uranium and biomass would expand from about 9 to 14 percent.     

Semi-infinite programming method for optimal power flow with transient stability and variable clearing time of faults

This paper presents a new nonlinear programming problem arising in the control of power systems, called optimal power flow with transient stability constraint and variable clearing time of faults and abbreviated as OTS-VT. The OTS-VT model is converted into a implicit generalized semi-infinite programming (GSIP) problem. According to the special box structure of the reformulated GSIP, a solution method based on bi-level optimization is proposed. The research in this paper has two contributions. Firstly, it generalizes the OTS study to general optimal power flow with transient stability problems. From the viewpoint of practical applications, the proposed research can improve the decision-making ability in power system operations. Secondly, the reformulation of OTS-VT also provides a new background and a type of GSIP in the research of mathematical problems. Numerical results for two chosen power systems show that the methodology presented in this paper is effective and promising.     

Sufficient conditions for optimal control problems with time delay

Various first-order and second-order sufficient conditions of optimality for nonlinear optimal control problems with delayed argument are formulated. The functions involved are not required to be convex. Second-order sufficient conditions are shown to be related to the existence of solutions of a Riccati-type matrix differential inequality. Their relation with the second variation is discussed.The authors are indebted to an anonymous referee for valuable suggestions that lead to various improvements in the paper.     

An explicit staggered-grid method for numerical simulation of large-scale natural gas pipeline networks

We present an explicit second order staggered finite difference (FD) discretization scheme for forward simulation of natural gas transport in pipeline networks. By construction, this discretization approach guarantees that the conservation of mass condition is satisfied exactly. The mathematical model is formulated in terms of density, pressure, and mass flux variables, and as a result permits the use of a general equation of state to define the relation between the gas density and pressure for a given temperature. In a single pipe, the model represents the dynamics of the density by propagation of a non-linear wave according to a variable wave speed. We derive compatibility conditions for linking domain boundary values to enable efficient, explicit simulation of gas flows propagating through a network with pressure changes created by gas compressors. We compare our staggered grid method with an explicit operator splitting method and a lumped element scheme, and perform numerical experiments to validate the convergence order of the new discretization approach. In addition, we perform several computations to investigate the influence of non-ideal equation of state models and temperature effects on pipeline simulations with boundary conditions on various time and space scales.     

Boundary element method based algorithm for simulation of fluid flow in 3D

A boundary element method based numerical scheme that solves the velocity-vorticity formulation of Navier-Stokes equation is presented. The developed method is validated and used to simulate laminar viscous flow coupled with heat transfer in 3D. Benchmark test cases were use to determine the validity of the method. Flow around a hotstrip is presented as a test case. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient method for computing rarefied gas flow in a long finite plane channel

The linearized kinetic S-model is used to study the nonisothermal steady rarefied gas flow driven by differences in pressure and temperature in a plane channel between long finite parallel plates joining two tanks of infinite volume. An efficient composite (asymptotic) method is developed: a one-dimensional asymptotic solution corresponding to an infinitely long channel is constructed in the middle part of the computational domain, while a solution of the two-dimensional kinetic equation matched with the middle-part asymptotic solution is constructed near the ends of the channel. The latter solution is found numerically by a high-order accurate conservative method. The basic quantity to be computed is the gas flow rate through the channel. Characteristic flow features are also investigated. The resulting solutions are compared with previously known results.