Abstract: A new numerical method for solving the twodimensional,
steady, incompressible, viscous flow equations on a
Curvilinear staggered grid is presented in this paper. The proposed
methodology is finite difference based, but essentially takes
advantage of the best features of two well-established numerical
formulations, the finite difference and finite volume methods. Some
weaknesses of the finite difference approach are removed by
exploiting the strengths of the finite volume method. In particular,
the issue of velocity-pressure coupling is dealt with in the proposed
finite difference formulation by developing a pressure correction
equation in a manner similar to the SIMPLE approach commonly
used in finite volume formulations. However, since this is purely a
finite difference formulation, numerical approximation of fluxes is
not required. Results obtained from the present method are based on
the first-order upwind scheme for the convective terms, but the
methodology can easily be modified to accommodate higher order
differencing schemes.
Abstract: A 3D simulation study for an incompressible
slip flow around a spherical aerosol particle was performed.
The full Navier-Stokes equations were solved and the velocity
jump at the gas-particle interface was treated numerically by
imposition of the slip boundary condition. Analytical solution
to the Stokesian slip flow past a spherical particle was used as
a benchmark for code verification, and excellent agreement
was achieved. The Simulation results showed that in addition
to the Knudsen number, the Reynolds number affects the slip
correction factor. Thus, the Cunningham-based slip corrections
must be augmented by the inclusion of the effect of
Reynolds number for application to Lagrangian tracking of
fine particles. A new expression for the slip correction factor
as a function of both Knudsen number and Reynolds number
was developed.
Abstract: This is the second part of the paper. It, aside from the
core subroutine test reported previously, focuses on the simulation of
turbulence governed by the full STF Navier-Stokes equations on a
large scale. Law of the wall is found plausible in this study as a model
of the boundary layer dynamics. Model validations proceed to
include velocity profiles of a stationary turbulent Couette flow, pure
sloshing flow simulations, and the identification of water-surface
inclination due to fluid accelerations. Errors resulting from the
irrotational and hydrostatic assumptions are explored when studying
a wind-driven water circulation with no shakings. Illustrative
examples show that this numerical strategy works for the simulation
of sloshing-shear mixed flow in a 3-D rigid rectangular base tank.
Abstract: In this paper, the differential quadrature method is applied to simulate natural convection in an inclined cubic cavity using velocity-vorticity formulation. The numerical capability of the present algorithm is demonstrated by application to natural convection in an inclined cubic cavity. The velocity Poisson equations, the vorticity transport equations and the energy equation are all solved as a coupled system of equations for the seven field variables consisting of three velocities, three vorticities and temperature. The coupled equations are simultaneously solved by imposing the vorticity definition at boundary without requiring the explicit specification of the vorticity boundary conditions. Test results obtained for an inclined cubic cavity with different angle of inclinations for Rayleigh number equal to 103, 104, 105 and 106 indicate that the present coupled solution algorithm could predict the benchmark results for temperature and flow fields. Thus, it is convinced that the present formulation is capable of solving coupled Navier-Stokes equations effectively and accurately.
Abstract: A parallel computational fluid dynamics code has been
developed for the study of aerodynamic heating problem in hypersonic
flows. The code employs the 3D Navier-Stokes equations as the basic
governing equations to simulate the laminar hypersonic flow. The cell
centered finite volume method based on structured grid is applied for
spatial discretization. The AUSMPW+ scheme is used for the inviscid
fluxes, and the MUSCL approach is used for higher order spatial
accuracy. The implicit LU-SGS scheme is applied for time integration
to accelerate the convergence of computations in steady flows. A
parallel programming method based on MPI is employed to shorten
the computing time. The validity of the code is demonstrated by
comparing the numerical calculation result with the experimental data
of a hypersonic flow field around a blunt body.
Abstract: In this study, the numerical solution of unsteady flow
between two concentric rotating spheres with suction and blowing at
their boundaries is presented. The spheres are rotating about a
common axis of rotation while their angular velocities are constant.
The Navier-Stokes equations are solved by employing the finite
difference method and implicit scheme. The resulting flow patterns
are presented for various values of the flow parameters including
rotational Reynolds number Re , and a blowing/suction Reynolds
number Rew . Viscous torques at the inner and the outer spheres are
calculated, too. It is seen that increasing the amount of suction and
blowing decrease the size of eddies generated in the annulus.
Abstract: A numerical study on the influence of electroosmotic flow on analyte preconcentration by isotachophoresis ( ITP) is made. We consider that the double layer induced electroosmotic flow ( EOF) counterbalance the electrophoretic velocity and a stationary ITP stacked zones results. We solve the Navier-Stokes equations coupled with the Nernst-Planck equations to determine the local convective velocity and the preconcentration dynamics of ions. Our numerical algorithm is based on a finite volume method along with a secondorder upwind scheme. The present numerical algorithm can capture the the sharp boundaries of step-changes ( plateau mode) or zones of steep gradients ( peak mode) accurately. The convection of ions due to EOF reduces the resolution of the ITP transition zones and produces a dispersion in analyte zones. The role of the electrokinetic parameters which induces dispersion is analyzed. A one-dimensional model for the area-averaged concentrations based on the Taylor-Aristype effective diffusivity is found to be in good agreement with the computed solutions.
Abstract: The purpose of this paper is to elucidate the flow unsteady behavior for moving plug in convergent-divergent variable thrust nozzle. Compressible axisymmetric Navier-Stokes equations are used to study this physical phenomenon. Different velocities are set for plug to investigate the effect of plug movement on flow unsteadiness. Variation of mass flow rate and thrust are compared under two conditions: First, the plug is placed at different positions and flow is simulated to reach the steady state (quasi steady simulation) and second, the plug is moved with assigned velocity and flow simulation is coupled with plug movement (unsteady simulation). If plug speed is high enough and its movement time scale is at the same order of the flow time scale, variation of the mass flow rate and thrust level versus plug position demonstrate a vital discrepancy under the quasi steady and unsteady conditions. This phenomenon should be considered especially from response time viewpoints in thrusters design.
Abstract: In the present study, the surface temperature history of the adaptor part in a two-stage supersonic launch vehicle is accurately predicted. The full Navier-Stokes equations are used to estimate the aerodynamic heat flux and the one-dimensional heat conduction in solid phase is used to compute the temperature history. The instantaneous surface temperature is used to improve the applied heat flux, to improve the accuracy of the results.
Abstract: The exact solutions of the equations describing the steady plane motion of an incompressible fluid of variable viscosity for an arbitrary state equation are determined in the (ξ,ψ) − or (η,ψ )- coordinates where ψ(x,y) is the stream function, ξ and η are the parts of the analytic function, ϖ =ξ( x,y )+iη( x,y ). Most of the solutions involve arbitrary function/ functions indicating
that the flow equations possess an infinite set of solutions.