Streamline integration as a method for structured grid generation in X-point geometry

We investigate structured grids aligned to the contours of a two-dimensional flux-function with an X-point (saddle point). Our theoretical analysis finds that orthogonal grids exist if and only if the Laplacian of the flux-function vanishes at the X-point. In general, this condition is sufficient for the existence of a structured aligned grid with an X-point. With the help of streamline integration we then propose a numerical grid construction algorithm. In a suitably chosen monitor metric the Laplacian of the flux-function vanishes at the X-point such that a grid construction is possible. We study the convergence of the solution to elliptic equations on the proposed grid. The diverging volume element and cell sizes at the X-point reduce the convergence rate. As a consequence, the proposed grid should be used with grid refinement around the X-point in practical applications. We show that grid refinement in the cells neighboring the X-point restores the expected convergence rate

Turbulence coefficients and stability studies for the coaxial flow or dissimiliar fluids

Analytical investigations of fluid dynamics problems of relevance to the gaseous core nuclear reactor program are presented. The vortex type flow which appears in the nuclear light bulb concept is analyzed along with the fluid flow in the fuel inlet region for the coaxial flow gaseous core nuclear reactor concept. The development of numerical methods for the solution of the Navier-Stokes equations for appropriate geometries is extended to the case of rotating flows and almost completes the gas core program requirements in this area. The investigations demonstrate that the conceptual design of the coaxial flow reactor needs further development

The finite element method in low speed aerodynamics

The finite element procedure is shown to be of significant impact in design of the 'computational wind tunnel' for low speed aerodynamics. The uniformity of the mathematical differential equation description, for viscous and/or inviscid, multi-dimensional subsonic flows about practical aerodynamic system configurations, is utilized to establish the general form of the finite element algorithm. Numerical results for inviscid flow analysis, as well as viscous boundary layer, parabolic, and full Navier Stokes flow descriptions verify the capabilities and overall versatility of the fundamental algorithm for aerodynamics. The proven mathematical basis, coupled with the distinct user-orientation features of the computer program embodiment, indicate near-term evolution of a highly useful analytical design tool to support computational configuration studies in low speed aerodynamics

Aerodynamic interaction between vortical wakes and lifting two-dimensional bodies

Unsteady rotor wake interactions with the empennage, tail boom, and other aerodynamic surfaces of a helicopter have a significant influence on its aerodynamic performance, the ride quality, and vibration. A numerical method for computing the aerodynamic interaction between an interacting vortex wake and the viscous flow about arbitrary two-dimensional bodies was developed to address this helicopter problem. The method solves for the flow field velocities on a body-fitted computational mesh using finite-difference techniques. The interacting vortex wake is represented by an array of discrete vortices which, in turn, are represented by a finite-core model. The evolution of the interacting vortex wake is calculated by Lagrangian techniques. The viscous flow field of the two-dimensional body is calculated on an Eulerian grid. The flow around circular and elliptic cylinders in the absence of an interacting vortex wake was calculated. These results compare very well with other numerical results and with results obtained from experiment and thereby demonstrate the accuracy of the viscous solution. The interaction of a rotor wake with the flow about a 4 to 1 elliptic cylinder at 45 degree incidence was calculated for a Reynolds number of 3000. The results demonstrate the significant variations in the lift and drag on the elliptic cylinder in the presence of the interacting rotor wake

Computational methods for internal flows with emphasis on turbomachinery

Current computational methods for analyzing flows in turbomachinery and other related internal propulsion components are presented. The methods are divided into two classes. The inviscid methods deal specifically with turbomachinery applications. Viscous methods, deal with generalized duct flows as well as flows in turbomachinery passages. Inviscid methods are categorized into the potential, stream function, and Euler aproaches. Viscous methods are treated in terms of parabolic, partially parabolic, and elliptic procedures. Various grids used in association with these procedures are also discussed

Viscid/inviscid interaction analysis of thrust augmenting ejectors

A method was developed for calculating the static performance of thrust augmenting ejectors by matching a viscous solution for the flow through the ejector to an inviscid solution for the flow outside the ejector. A two dimensional analysis utilizing a turbulence kinetic energy model is used to calculate the rate of entrainment by the jets. Vortex panel methods are then used with the requirement that the ejector shroud must be a streamline of the flow induced by the jets to determine the strength of circulation generated around the shroud. In effect, the ejector shroud is considered to be flying in the velocity field of the jets. The solution is converged by iterating between the rate of entrainment and the strength of the circulation. This approach offers the advantage of including external influences on the flow through the ejector. Comparisons with data are presented for an ejector having a single central nozzle and Coanda jet on the walls. The accuracy of the matched solution is found to be especially sensitive to the jet flap effect of the flow just downstream of the ejector exit

A subsonic transonic and supersonic nozzle flow by the inverse technique

Inverse solution of two dimensional gas dynamic flow fields of rotational or irrotational characte

A calculation procedure for viscous flow in turbomachines, volume 1

A method for analyzing the nonadiabatic viscous flow through turbomachine rotors is presented. The field analysis is based upon the numerical integration of the full incompressible stream function vorticity form of the Navier-Stokes equations, together with the energy equation, over the rotor blade-to-blade stream channels. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system that suits the most complicated blade geometries. A numerical scheme is used to carry out the necessary integration of the elliptic governing equations. The flow characteristics within the rotor of a radial inflow turbine are investigated over a wide range of operating conditions. The calculated results are compared to existing experimental data. The flow in a radial compressor is analyzed in order to study the behavior of viscous flow in diffusing cascades. The results are compared qualitatively to known experimental trends. The solution obtained provides insight into the flow phenomena in this type of turbomachine. It is concluded that the method of analysis is quite general and gives a good representation of the actual flow behavior within turbomachine passages

Derivation and evaluation of an approximate analysis for three-dimensional viscous subsonic flow with large secondary velocities

An approximate analysis is presented for calculating three-dimensional, low Mach number, laminar viscous flows in curved passages with large secondary flows and corner boundary layers. The analysis is based on the decomposition of the overall velocity field into inviscid and viscous components with the overall velocity being determined from superposition. An incompressible vorticity transport equation is used to estimate inviscid secondary flow velocities to be used as corrections to the potential flow velocity field. A parabolized streamwise momentum equation coupled to an adiabatic energy equation and global continuity equation is used to obtain an approximate viscous correction to the pressure and longitudinal velocity fields. A collateral flow assumption is invoked to estimate the viscous correction to the transverse velocity fields. The approximate analysis is solved numerically using an implicit ADI solution for the viscous pressure and velocity fields. An iterative ADI procedure is used to solve for the inviscid secondary vorticity and velocity fields. This method was applied to computing the flow within a turbine vane passage with inlet flow conditions of M = 0.1 and M = 0.25, Re = 1000 and adiabatic walls, and for a constant radius curved rectangular duct with R/D = 12 and 14 and with inlet flow conditions of M = 0.1, Re = 1000, and adiabatic walls