Computation of rarefied diatomic gas flows through a plane microchannel

A numerical method based on a model kinetic equation was developed for computing diatomic rarefied gas flows in two dimensions. Nitrogen flows through a plane microchannel were computed, and the gas flow rate was constructed as a function of the Knudsen number for various channel lengths.     

Eulerian Simulation of Gas‐Solid Particle Flow by BDIM

The numerical scheme based on the boundary domain integral method (BDIM) for the numerical simulation of twophase two‐component flows is presented. A program is being developed to model the hydrodynamics of fluidized bed systems by using the Eulerian approach in terms of velocity‐vorticity variables formulation. With the vorticity vector both phases motion computation scheme is partitioned into its kinematic and kinetic aspect. Influence of the drag coefficient on the two‐phase two‐component flow field is studied on the two‐phase gas‐solid particles vertical channel flow.     

Semiclassical lattice hydrodynamics of rarefied channel flows

The two-dimensional channel flows of gas of arbitrary statistics in the slip and transition regimes as characterized by the Knudsen number are studied using a newly developed semiclassical lattice Boltzmann method. The method is directly derived by projecting the Uehling-Uhlenbeck Boltzmann-BGK equations onto the tensor Hermite polynomials using moment expansion method. The intrinsic discrete nodes of the Gauss-Hermite quadrature provide the natural lattice velocities for the semiclassical lattice Boltzmann method. The mass flow rates and the velocity profiles are calculated for the three particle statistics over wide range of Knudsen numbers and the Knudsen minimum can be captured. The results indicate distinct characteristics of the effects of quantum statistics.     

Depth-averaged modeling of free surface flows in open channels with emerged and submerged vegetation

The resistance induced by vegetation on the flow in a watercourse should be considered in projects of watercourse management and river restoration. Depth-averaged numerical model is an efficient tool to study this problem. In this study, a depth-averaged model using the finite volume method on a staggered curvilinear grid and the SIMPLEC algorithm for numerical solution is developed for simulating the hydrodynamics of free surface flows in watercourses with vegetation. For the model formulation the vegetation resistance is treated as a momentum sink and represented by a Manning type equation, and turbulence is parameterized by the k–ε equations. An analytical equation is derived to represent the resistance induced by submerged vegetation by an equivalent Manning roughness coefficient. Numerical simulation is carried out for the flow in an open channel with a 180° bend, and the flow in a curved open channel partly covered by emerged vegetation, as well as the flow in a straight trapezoidal channel with submerged vegetation. The agreement between the computed results and the measured data is generally good, showing that the resistance due to emerged or submerged vegetation can be represented accurately by the Manning roughness equation. The computed results demonstrate that the depth-averaged modeling is a reasonable and efficient tool to study flows in watercourses with vegetations.     

Numerical study of unsteady rarefied diatomic gas flows in a plane microchannel

The numerical solution of a kinetic equation for a diatomic gas (nitrogen) is used to study two-dimensional unsteady gas flows in a plane microchannel caused by discontinuous in the initial distributions of macroscopic gas parameters. The plane discontinuity fronts are perpendicular to the walls of the channel. The arising flows are model ones for gas flows in a shock tube and a microchannel. The reflection of an incident shock wave from a flat end face is studied. It is found that the gas piles up at the cold wall, which slows down the shock wave detachment. The numerical results are in qualitative agreement with experimental data.     

On the numerical modelling of the transitional flow in rarefied gases

The aim of this work is to simulate rarefied gas flow in complex geometries, under flow conditions that range from the hydrodynamic, through the transitional, to the molecular regimes. Existing computational models apply to molecular or viscous flow, but the treatment of the transitional flow is still underdeveloped.To deal with the difficult transitional flow, two models with overlapping ranges of applicability are introduced. A direct simulation Monte Carlo (DSMC) type model, which can be used in the molecular and up to the lower transitional flow, has been designed. For the viscous to the upper transitional flow, a numerical model using a particle method is proposed. The objective is to obtain a smooth transition between the probabilistic simulation of particle histories and the deterministic approach of the solution of partial differential equations.The DSMC model has been successfully applied to molecular and lower transitional flow in a complex geometry with stationary and moving boundaries. The test results agree well with published data. The particle method was tested using simplified Navier-Stokes equations in a channel. Preliminary results in the low viscous range seem to indicate that the approach is viable.     

Iber: herramienta de simulación numérica del flujo en ríos

The recent requirements of Spanish regulations and directives, on their turn based on European directives, have led to the development of a new two dimensional open channel flow modelling tool. The tool, named Iber, combines a hydrodynamic module, a turbulence module and a sediment transport module, and is based in the finite volume method to solve the involved equations. The simulation code has been integrated in a pre-process and post-process interface based on GiD software, developed by CIMNE. The result is a flow and sediment modelling system for rivers and estuaries that uses advanced numerical schemes, robust and stable, which are especially suitable for discontinuous flows taking place in torrential and hydrologically irregular rivers.     

Method for solving the equations describing the interaction of a three-dimensional boundary layer with an outer inviscid flow

A new method is developed for solving the three-dimensional time-independent equations describing the interaction of a laminar boundary layer with an outer inviscid flow. The method also applies to the interaction of plane flows. By applying the method, the problem of the three-dimensional viscous supersonic gas flow over a roughness element (a hump and a cavity) is solved for the first time within the framework of the classical triple-deck theory. The asymptotic height of the roughness element corresponding to the nonseparated flow is determined, and separated flow patterns are constructed.     

Numerical simulation two phase flows of casting filling process using SOLA particle level set method

Mould filling process is a typical gas–liquid metal two phase flow phenomenon. Numerical simulation of the two phase flows of mould filling process can be used to properly predicate the back pressure effect, the gas entrapment defects, and better understand the complex motions of the gas phase and the liquid phase. In this paper, a novel sharp interface incompressible two phase numerical model for mould filling process is presented. A simple ghost fluid method like discretization method and a density evaluation method at face centers of finite difference staggered grid are proposed to overcome the difficulties when solving two phase Navier–Stokes equations with large-density ratio and large-viscosity ratio. A new mass conservation particle level set method is developed to capture the gas–liquid metal phase interface. The classical pressure-correction based SOLA algorithm is modified to solve the two phase Navier–Stokes equations. Two numerical tests including the Zalesak disk problem and the broken dam problem are used to demonstrate the accuracy of the present method. The numerical method is then adopted to simulate three mould filling examples including two high speed CCD camera imaging water filling experiments and an in situ X-ray imaging experiment of pure aluminum filling. The simulation results are in good agreement with the experiments.     

Kinetic model of the Boltzmann equation for a diatomic gas with rotational degrees of freedom

A system of model kinetic equations is proposed to describe flows of a diatomic rarefied gas (nitrogen). A conservative numerical method is developed for its solution. A shock wave structure in nitrogen is computed, and the results are compared with experimental data in a wide range of Mach numbers. The system of model kinetic equations is intended to compute complex-geometry three-dimensional flows of a diatomic gas with rotational degrees of freedom.     

Unidirectional flows of viscoelastic fluids and their gasdynamic counterparts

We have shown that unidirectional flows of viscoelastic fluids are mathematically equivalent to plane potential flows of a fictitious gas. The classification of type and some exact solutions of the equations describing fictitious gas flows are presented. The Prandtl-Mayer flow and its viscoelastic counterpart is discussed in more details in connection with the Sternberg-Koiter paradox.     

Numerical Solution of Newtonian and Non-Newtonian Flows

This paper deals with the numerical solution of Newtonian and non-Newtonian flows. The flows are supposed to be laminar, viscous, incompressible and steady. The model used for non-Newtonian fluids is some variant of power-law. Governing equations in this model are incompressible Navier-Stokes equations. For numerical solution one could use artificial compressibility method with three stage Runge-Kutta finite volume method in cell centered formulation for discretization of space derivatives. Following cases of flows are solwed: flow through a bypass connected to main channel in 2D and 3D and non-Newtonian flow through branching channels in 2D. These results are presented for 2D and 3D case. This problem could have an application in the area of biomedicine. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Supersonic flow past a flat lattice of cylindrical rods

Two-dimensional supersonic laminar ideal gas flows past a regular flat lattice of identical circular cylinders lying in a plane perpendicular to the free-stream velocity are numerically simulated. The flows are computed by applying a multiblock numerical technique with local boundary-fitted curvilinear grids that have finite regions overlapping the global rectangular grid covering the entire computational domain. Viscous boundary layers are resolved on the local grids by applying the Navier–Stokes equations, while the aerodynamic interference of shock wave structures occurring between the lattice elements is described by the Euler equations. In the overlapping grid regions, the functions are interpolated to the grid interfaces. The regimes of supersonic lattice flow are classified. The parameter ranges in which the steady flow around the lattice is not unique are detected, and the mechanisms of hysteresis phenomena are examined.     

Numerical Analysis of Spatial Hydrodynamic Stability of Shear Flows in Ducts of Constant Cross Section

A technique for analyzing the spatial stability of viscous incompressible shear flows in ducts of constant cross section, i.e., a technique for the numerical analysis of the stability of such flows with respect to small time-harmonic disturbances propagating downstream is described and justified. According to this technique, the linearized equations for the disturbance amplitudes are approximated in space in the plane of the duct cross section and are reduced to a system of first-order ordinary differential equations in the streamwise variable in a way independent of the approximation method. This system is further reduced to a lower dimension one satisfied only by physically significant solutions of the original system. Most of the computations are based on standard matrix algorithms. This technique makes it possible to efficiently compute various characteristics of spatial stability, including finding optimal disturbances that play a crucial role in the subcritical laminar–turbulent transition scenario. The performance of the technique is illustrated as applied to the Poiseuille flow in a duct of square cross section.     

Development of the Raleigh-Tailor instability in inhomogeneous magnetic gas-dynamic flows

Results of the numerical simulation of the development of the hydrodynamic Raleigh-Tailor instability, which occurs when a high-current discharge is moving in a rail accelerator and in MHD flows with a current layer, are presented. It is established that the development of the instability under the conditions of the flow of cold gas around the discharge region leads to the formation of an irregular vortex structure of the magnetic gas-dynamic flow in the channel.     

Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid

In this paper, Adomian’s decomposition method is used to solve non-linear differential equations which arise in fluid dynamics. We study basic flow problems of a third grade non-Newtonian fluid between two parallel plates separated by a finite distance. The technique of Adomian decomposition is successfully applied to study the problem of a non-Newtonian plane Couette flow, fully developed plane Poiseuille flow and plane Couette–Poiseuille flow. The results obtained show the reliability and efficiency of this analytical method. Numerical solutions are also obtained by solving non-linear ordinary differential equations using Chebyshev spectral method. We present a comparative study between the analytical solutions and numerical solutions. The analytical results are found to be in good agreement with numerical solutions which reveals the effectiveness and convenience of the Adomian decomposition method.     

Numerical simulation of the unsteady aerodynamic interaction of two plane airfoil cascades

A method for the calculation of unsteady aerodynamic interaction of two plane airfoil cascades that are in relative motion in a subsonic flow of ideal gas is developed. This interaction provides a two-dimensional approximation of the flow in a stage of an axial turbomachine. The method is based on the reduction of the problem to the calculation of the unsteady flow in a single interblade passage of each of the cascades. The calculation uses generalized space-time periodicity relations corresponding to the unsteady process of interest. The calculation is based on the direct numerical integration of the non-stationary gas dynamics equations with the use of the finite difference Godunov-Kolgan-Rodionov scheme of the second approximation order with respect to time and space. The calculation procedure includes the determination of the acoustic fields that are generated by the stage in the incident flow and in the flow behind it. The results of the calculations that illustrate the accuracy of the numerical solution and the capabilities of the method are presented.     

Investigation of the effect of seepage or evaporation from a free surface by the method of circular polygons

It is proposed to use a technique developed for polygons in polar nets to integrate equations of the Fuchs class that arise when solving a wide range of problems of plane steady seepage flow using the Polubarinova-Kochina method, based on the use of the analytical theory of linear differential equations. It is shown that, for a large class of pentagons in domains where the flows,which are very characteristic of seepage problems when there is infiltration or evaporation from the free surface, have a complex velocity, the solution of the problem of determining the unknown parameters which appear in the conformal mapping can be completed. In this case, the mapping is carried out in closed form in terms of elementary functions and it is simple and convenient for subsequent application. The results obtained are used to solve the problem of seepage from a channel, taking account of the capillarity of the ground when there is evaporation from the free surface. The results of numerical calculations are presented and a hydrodynamic analysis of the effect of the basic physical parameters of the model on the dimensions of the saturation zone is given.     

Regularized shallow water equations for numerical simulation of flows with a moving shoreline

A numerical algorithm for simulating free-surface flows based on regularized shallow water equations is adapted to flows involving moving dry-bed areas. Well-balanced versions of the algorithm are constructed. Test computations of flows with dry-bed areas in the cases of water runup onto a plane beach and a constant-slope beach are presented. An example of tsunami simulation is given.     

Modeling of flow separation of assist gas as applied to laser cutting of thick sheet metal

The present paper describes the results of mathematical modeling of supersonic flows of a viscous compressible gas, obtained by numerically solving three-dimensional full Navier–Stokes equations, and also the results of experiments with visualization of gas jet flows in channels geometrically similar to the laser cut. Separation of the gas flow from the cut front is predicted numerically and then validated by experiments on a model setup. The gas flow structure arising in a narrow channel behind a sonic (conical) or supersonic nozzle is described. Specific features of originating in the flow separation on a smooth surface in a narrow channel are examined, and mechanisms controlling the separation are proposed. Flow separation directly affects the changes in the shape and structure of striations and is the one of main reason for the worse quality of the laser cut surface. It is shown that the changes in the structures of striations over the thickness of the sheet being cut are closely related to aerodynamic features of jet flows of the assisting gas in the cut channel.