Algebraic Grid Generation Technique Research Articles

Natural convection in a cavity with a sloping upper surface filled with an anisotropic porous material

Steady natural convection in a viscous incompressible fluid flowing in a vertical permeable non-rectangular cavity is considered. The permeability of the porous medium and the thermal diffusivity of the fluid are assumed to be anisotropic in nature. Using the Boussinesq approximation and the Darcy law to model the porous medium, the governing equations—recast in terms of a stream function—are solved numerically. An algebraic grid generation technique is employed to transform the non-rectangular domain to a square domain. The influence of a number of parameters, arising due to geometrical and physical aspects, is discussed in relation to the flow and heat transfer.

Numerical solution of solidification in a square prism using an algebraic grid generation technique

The solidification of an infinitely long square prism was analyzed numerically. A front fixing technique along with an algebraic grid generation scheme was used, where the finite difference form of the energy equation is solved for the temperature distribution in the solid phase and the solid–liquid interface energy balance is integrated for the new position of the moving solidification front. Results are given for the moving solidification boundary with a circular phase change interface. An algebraic grid generation scheme was developed for two-dimensional domains, which generates grid points separated by equal distances in the physical domain. The current scheme also allows the implementation of a finer grid structure at desired locations in the domain. The method is based on fitting a constant arc length mesh in the two computational directions in the physical domain. The resulting simultaneous, nonlinear algebraic equations for the grid locations are solved using the Newton-Raphson method for a system of equations. The approach is used in a two-dimensional solidification problem, in which the liquid phase is initially at the melting temperature, solved by using a front-fixing approach. The difference of the current study lies in the fact that front fixing is applied to problems, where the solid–liquid interface is curved such that the position of the interface, when expressed in terms of one of the coordinates is a double valued function. This requires a coordinate transformation in both coordinate directions to transform the complex physical solidification domain to a Cartesian, square computational domain. Due to the motion of the solid–liquid interface in time, the computational grid structure is regenerated at every time step.

Natural convection in a non-rectangular porous enclosure

This paper describes a numerical solution procedure to study heat transfer process by two dimensional natural convection phenomena in a non-rectangular enclosure of arbitrary geometry. Momentum transfer in the system is described by an elliptic partial differential equation, which governs the behaviour of the stream function. An algebraic grid generation technique is used to transform the governing equations into a body fitted rectangular co-ordinate system that allows coincidence of all boundary lines with the co-ordinate lines. Numerical solutions of the resulting equations in the computational domain are obtained using an alternating directional implicit method by adding false transient terms. Results from the numerical experiments in the case of a non-rectangular enclosure are obtained that show the magnitude and directions of convection currents and contours of the temperature. The effect of increase in the inclination of the upper boundary is to increase the average Nusselt number.

Grid sensitivity and aerodynamic optimization of generic airfoils

An algorithm is developed to obtain the grid sensitivity with respect to design parameters for aerodynamic optimization. The procedure is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B- Splines) for defining the airfoil geometry. An interactive algebraic grid generation technique is employed to generate C-type grids around airfoils. The grid sensitivity of the domain with respect to geometric design parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations such as a wing or fuselage. The aerodynamic sensitivity coefficients are obtained by direct differentiation of the compressible two-dimensional thin-layer Navier-Stokes equations. An optimization package has been introduced into the algorithm in order to optimize the airfoil surface. Results demonstrate a substantially improved design due to maximized lift/drag ratio of the airfoil.

STUDY OF TURBULENT HEAT TRANSFER IN RECIPROCATING ENGINE USING AN ALGEBRAIC GRID GENERATION TECHNIQUE

The process of turbulent heat transfer in reciprocating engines was studied. The theoretical analysis was performed under the assumption that it was an axisymmetric two-dimensional transient process. The effect of the shapes of cylinder head on the turbulent wall heat flux was investigated. A series of valid solutions was obtained employing an algebraic grid generation technique. Hence the metrics of the coordinate transformation can be determined by direct analytic differentiation; it was found that the turbulent wall heat flux was dependent on the shape of the cylinder head. The existing experimental results of wall heat flux at three different radial locations on the cylinder head surface were compared. Simulated results were found to be nearly identical to the corresponding experimental results. It appears that the present computational algorithm gives a successful simulation for the transient turbulent wall heat flux in reciprocating engines.

Investigation of three-dimensional separation at wing/body junctions in supersonic flows

The problem of three-dimensional separation at a wing/body junction has been investigated numerically using a three-dimensional Navier-Stokes code which employs the MacCormack's time split, finite volume technique. An algebraic grid generation technique is used for generating the grid at a wing/body junction. Specific computational results on velocity and pressure distribution in the separated flow region are compared with the experimental results. A parametric study of flow parameters, such as Mach and Reynolds numbers, have been carried out to understand their effect in interaction flowfield. The parametric study indicates dependency of the number of vortices at the junction on Mach number and Reynolds number.

A GRID GENERATION TECHNIQUE FOR NUMERICAL MODELLING HEAT and MOISTURE MOVEMENT IN PEAKED BULKS of GRAIN

ABSTRACTThis paper describes a numerical solution procedure to study heat and moisture transfer processes by two‐dimensional natural convection phenomena in grain stores with arbitrary geometries. This enables grain storage technologists to investigate the design and performance of grain stores in which the grain surface is peaked, as in bunker storage, for example. Momentum transfer is described by an elliptic partial differential equation, which governs the behavior of the stream function. Using an algebraic grid generation technique, the governing equations are transformed into a body‐fitted rectangular coordinate system that allows coincidence of all boundary lines with a coordinate line. Numerical solutions of the resulting equations are obtained using an alternating direction implicit method. Results from numerical experiments on a peaked bulk of stored grain retained between two vertical walls are obtained that show the magnitude and directions of convection currents and contours of temperature, moisture, dry matter loss and chemical pesticide concentrations.

GRID GENERATION AND ITS APPLICATION TO SEPARATED FLOWS

A method for the computation of recirculating flows on a nonorthogonal boundary-fitted coordinate system is presented. The algebraic grid generation technique is used to generate grids in a flow field of arbitrary shape. Computations are performed by using the set of governing equations transformed for use on a generalized curvilinear coordinate system. Turbulent flow computations were made by using the k-epsilon model for most of the flow cases. Three pressure correction algorithms - SIMPLE, SIMPLEC, and PISO - were incorporated for use on a nonorthogonal grid. Comparisons were made on the basis of numerical stability and accuracy. The present method was found to be efficient for computations of recirculating flows.

Study on the Flow Fields of Irregular-Shaped Domains by an Algebraic Grid-Generation Technique

A finite-difference solution algorithm is developed to solve the Navier-Stokes equations in a nonorthogonal curvilinear coordinate system. The governing equations are written in the strong-conservative-law form. A rectangular computational domain is yielded by Morettis transformation. The matrix of the transformation can be determined by direct analytic differentiation. The discretized conservation equations are derived on a control volume basis and solved by the extended SIMPLE calculation procedure. Numerical results obtained by employing the present methodology wil be compared with results from analytical solutions. The relative merits of three numerical representations for approximating the convection terms in the momentum equations are compared

Numerical study of turbulent in-cylinder flow during motoring utilizing a general curvilinear coordinate system

A finite-volume numerical calculation method is presented to predict the flow field at unsteady, turbulent levels in a motoring reciprocating engine. An algebraic grid generation technique is used to map the complex fluid domain, on which the cylinder head is a deformed boundary, onto a rectangle for every time step. Hence the metric of the coordinate transformation can be determined by direct analytic differentiation. The model gives a good account of the axial, radial, and swirl velocity components and engine turbulence by means of a two-equation model of turbulence and wall functions. Effects of the shapes of both cylinder head and grid distribution on in-cylinder air motion are investigated.

STUDY OF AIR MOTION IN RECIPROCATING ENGINE USING AN ALGEBRAIC GRID GENERATION TECHNIQUE

An algorithm for a multidimensional numerical solution is developed that predicts axisym-metric two-dimensional in-cylinder flows on the boundaries of curved wall cylinder heads. Three types of cylinder heads are considered: “deep hemisphere,” “flat hemisphere,” and “flat plate.” The time-dependent strong conservative law forms of the governing equations are written in axisymmetric nonorthogonal curvilinear coordinates. A fully staggered grid system is used for all variables, so that no explicit description of the pressure boundary conditions is necessary. An algebraic grid generation technique is used to map the complex fluid domain onto a rectangle for every time step. Hence the metric of the coordinate transformation can be determined by direct analytic differentiation. The discretized conservation equations are derived from a control volume approach and are solved by using a modification of the simple calculation procedure. The effects of the shapes of cylinder head on the velocity distribution are in...

An algebraic grid generation technique for time‐varying two‐dimensional spatial domains

AbstractAn efficient and versatile algebraic grid generation technique is presented for generating grid points in irregularly shaped and time‐varying spatial domains. The method presented is based on the ‘two‐boundary technique’ of Smith. The usefulness and the feasibility of the grid generation technique were demonstrated by (1) generating grid points inside one of the combustion chambers of a motored two‐dimensional rotary engine and (2) obtaining numerical solutions for the flow field inside one of those combustion chambers.