1/2005 Computational Fluid Dynamics

Contents:

• E.Tuliszka-Sznitko, A.Zielinski and J.Polus, Numerical Investigation of Instability of an Annular Rotating Cavity - abstract | full text
• Z. Kosma, Method of Lines for the Incompressible Navier-Stokes Equations in the Stream-Function Formulation - abstract | full text
• Z. Kosma, Calculation of Viscous Incompressible Flow Around an Aerofoil Using a Modified Velocity Correction Method - abstract | full text
• K.Namiesnik and P.Doerffer, Numerical Simulation of Shock Wave Patterns in Supersonic Divergent Symmetric Nozzles - abstract | full text
• D.Kardas and S.Golec, Flow Charateristics of a Low NO_x Emission Burner - abstract | full text
• J.Kozicki and J.Tejchman, Simulations of Flow Patterns in Silos with a Cellular Automaton: Part 1 - abstract | full text
• J.Kozicki and J.Tejchman, Simulations of Flow Patterns in Silos with a Cellular Automaton: Part 2 - abstract | full text
• P.Doerffer, O.Szulc and F.Magagnato, Unsteady Shock Wave: Turbulent Boundary Layer Interaction in the Laval Nozzle - abstract | full text
• L.Zashkowa and N.Penkova, Modelling and Simulation of Fluid Flow and Heat Processes in a Regenerator with Ceramic Chimney Block Checker Work - abstract | full text
• L.Zashkowa and N.Penkova, Thermal and Fluid Flow Fields in a Regenerator with Ceramic Chimney Block Checker Work - abstract | full text

Abstracts:

• E.Tuliszka-Sznitko, A.Zielinski and J.Polus, Numerical Investigation of Instability of an Annular Rotating Cavity

  A direct two-dimensional numerical simulation has been performed to study the transition flow in an annual rotating cavity. The spectral collocation method based on the Chebyshev polynomial is used to solve the incompressible Navier-Stokes equation. The time scheme is semi-implicit and second-order accurate; it corresponds to a combination of the second-order backward differentiation formula for the viscous diffusion term and the Adams-Bashforth scheme for the non-linear terms. The method uses a projection scheme to maintain the incompressibility constrain. The numerical computations, performed for an annular cavity of the aspect ratio L=2 and 5 and for the curvature parameters R_m=(R₁+R₀)/(R₁-R₀)=5, exhibit instability structures in the form of circular rolls. These structures are in good agreement with the other investigations, both experimental and theoretical.

• Z. Kosma, Method of Lines for the Incompressible Navier-Stokes Equations in the Stream-Function Formulation

  The aim of this paper is to simulate the laminar motion of viscous incompressible fluid and the transition between the laminar and the turbulent state in simply connected domains. The developed numerical algorithms are based on the solution of an initial-boundary value problem for the full incompressible Navier-Stokes equations, written in the form of a fourth-order equation for the stream function. The spatial derivatives and the boundary conditions are discretized on uniform grids by means of sixth-order compact schemes together with fourth-order finite-difference formulas, while the continuity of the time variable is preserved. The resulting system of ordinary differential equations has been integrated using the backward-differentiation predictor-corrector method. The efficiency of the numerical algorithms is demonstrated by solving two problems of viscous liquid plane flows in a square driven cavity and a backward-facing step. Calculations for the cavity flow configuration have been obtained for Reynolds numbers ranging from Re=100 to Re=30000 on uniform 50×50 and 100×100 grids. Calculations for the backward-facing step have been made for Re≤3000 with channel lengths, L, within the range 10-30, on 30L×30 uniform grids. The computed stream-function contours and velocity fields have been compared with numerical results reported in the literature.

• Z. Kosma, Calculation of Viscous Incompressible Flow Around an Aerofoil Using a Modified Velocity Correction Method

  The two-dimensional unsteady motion of viscous incompressible fluid around an aerofoil at a large angle of attack has been computed. A modified velocity correction method splitting the velocity field has been designed to solve this problem. First, a tentative velocity field is determined from the equations of momentum conservation for explicit gradients of computational pressure. Then, the Neumann problem for the Poisson equation is solved to estimate the computational pressure, and velocity components are corrected. Test calculations have been made for the case of flow around the NACA 0012 aerofoil with an incidence of 34°. The domain outside the aerofoil was transformed into a canonical one using conformal mapping. Computations were made on 100×100 and 100×200 grids for Reynolds numbers of Re=400, 600 and 1000. Comparison with numerical and experimental data reported in the literature has shown that the method is suitable for simulating 2D external viscous flows.

• K.Namiesnik and P.Doerffer, Numerical Simulation of Shock Wave Patterns in Supersonic Divergent Symmetric Nozzles

  This paper presents the results of numerical simulations of supersonic flows with shock waves in a divergent symmetric nozzle of an opening angle ranging from 2° to 6°. At certain Mach number values the shock pattern becomes asymmetric. This asymmetry is analysed here for different values of velocity upstream of the shock wave and for different nozzle divergence angles. Only the divergent part of the nozzle is considered. Supersonic conditions at the nozzle inlet were prescribed with a chosen Mach number value Ma>1. The inlet velocity profile included a turbulent boundary layer profile on side walls. The steady flow simulation was applied for nozzle opening angles, α, of 1.877°, 2.5° and 3°, whereas the unsteady approach was necessary for a nozzle of the divergence angle α=6.54° to obtain a converged solution. The asymmetry of the shock structure is visible in the unevenness of the heights of both λ-feet. It happens at the same Mach number, at the same boundary layer and with the same geometrical constraints. This is in contradiction with our current understanding of the parameters affecting λ-foot size. The paper provides an explanation of this problem.

• D.Kardas and S.Golec, Flow Charateristics of a Low NO_x Emission Burner

  Recent technological changes in the Polish power industry have created opportunities for reducing NO_x and CO emissions, but - at the same time - created another operation problem: sulphur corossion of boilers' rear water-wall. This has been the motivation for performing a detailed study of the air flow and pulverized coal transport in low-NO_x burners. A measuring stand was built inside a real medium power OP-230 boiler equipped with a low-NO_x burner to measure the velocity field at the burner's outlet and to prepare experimental characteristics of the burner. To extend the description, a numerical model of the burner was constructed and numerical calculations were executed by means of the Fluent program. Numerically calculated velocity profiles were compared with the results of measurements. Further investigations of the low NO_x burner included the flow of the air-pulverized coal mixture. The measured concentration of the coal dust was compared with numerically predicted distribution of particles. Both the measurements and the calculations have shown a highly non-uniform concentration of particles at the burner outlet. The obtained results have been helpful in formulating recommendations to improve burner geometry.

• J.Kozicki and J.Tejchman, Simulations of Flow Patterns in Silos with a Cellular Automaton: Part 1

  A simplified cellular automaton was used to calculate the kinematics of non-cohesive granular materials during confined flow in silos. In this model, granular flow was assumed to be an upward propagation of holes through a lattice composed of cells representing single particles. Calculations were carried out with different silo shapes and inserts, transition probabilities, migration rules, outflow schemes, grid types, wall roughness and cell numbers. To visualize the calculation process, horizontal layers of various shades were introduced. The simulation results were compared with laboratory tests in model silos.

• J.Kozicki and J.Tejchman, Simulations of Flow Patterns in Silos with a Cellular Automaton: Part 2

  An improved cellular automaton has been used to calculate the kinematics of non-cohesive granular materials during confined flow in mass and funnel flow model silos. In this model, based on a gas model of hydrodynamics, collisions and dissipation of particles were taken into account during granular flow. The model allowed for investigations of dilatant zones in granular material during silo flow.

• P.Doerffer, O.Szulc and F.Magagnato, Unsteady Shock Wave: Turbulent Boundary Layer Interaction in the Laval Nozzle

  The flow in transonic diffusers and supersonic air intakes often becomes unsteady due to shock wave-boundary layer interaction. Oscillations may be induced by natural separation unsteadiness or forced by boundary conditions. Significant improvements of CFD tools, increased computer resources and the development of experimental methods have again drawn the attention of researchers to this topic. Forced oscillations of a transonic turbulent flow in an asymmetric two-dimensional Laval nozzle have been considered to investigate the problem. A viscous, perfect gas flow was numerically simulated using SPARC, a Reynolds-averaged compressible Navier-Stokes solver, employing a two-equation, eddy viscosity, turbulence closure in the URANS approach. For time-dependent and stationary flow simulations, Mach numbers upstream of the shock between 1.2 and 1.4 were considered. Comparison of computed and experimental data for steady states generally gave acceptable agreement. In the case of forced oscillations, a harmonic pressure variation was prescribed at the exit plane resulting in shock wave motion. Excitation frequencies between 0Hz and 1024Hz were investigated at a constant pressure amplitude. The main result of the work is the relation between the amplitude of shock wave motion and the excitation frequency in the investigated range. Increasing excitation frequency resulted in decreasing amplitude of the shock movement. At high frequencies, a natural mode of shock oscillation (of small amplitude) was observed, which was insensitive to forced excitement.

• L.Zashkowa and N.Penkova, Modelling and Simulation of Fluid Flow and Heat Processes in a Regenerator with Ceramic Chimney Block Checker Work

  Selected results of mathematical modelling and computer simulation of fluid flow and heat transfer processes in a glass furnace regenerator are reported. The conjugate heat transfer problem is solved in 3D using the ANSYS 8.0/FLOTRAN programme. The regenerator's geometry, finite element mesh, thermal loads and boundary conditions are presented. The momentum, continuity and energy equations are solved.

• L.Zashkowa and N.Penkova, Thermal and Fluid Flow Fields in a Regenerator with Ceramic Chimney Block Checker Work

  Selected results of mathematical modelling and computer simulation of transient conjugate heat transfer in a vertical contraflow glass furnace regenerator are reported. The problem is solved three-dimensionally (3D) using the ANSYS 8.0/FLOTRAN program. The main regenerator fluid flow and thermal fields about a cyclic equilibrium of the regenerator are visualized. Heat and fluid flow parameters for the regenerator's cyclic equilibrium are presented by T_m=T_m(H',t); T_m,f=T_m,f(H',t); h_m=h_m(H',t); V=V(H',t); k=k(H',t) and ε=ε(H',t) graphics. Remarks about transient heat transfer in this kind of regenerators are made based on the obtained numerical values and relationships.