Showing papers on "Flow (mathematics) published in 1972"

Calculation of potential flow about arbitrary three-dimensional lifting bodies

Abstract: : The report presents a complete discussion of a method for calculating potential flow about arbitrary lifting three-dimensional bodies without the approximations inherent in lifting-surface theories. The basic formulation of three-dimensional lifting flow is pursued at some length and some difficulties are pointed out. All aspects of the flow calculation method are discussed, and alternate procedures for various aspects of the calculation are compared and evaluated. Particular emphasis is placed on the handling of the bound vorticity and the application of the Kutta condition, and it is concluded that the approach used in the method of this report has certain advantages over alternate schemes used by other existing methods. A considerable number of calculated results for various configurations are presented to illustrate the power and scope of the method.

Computational efficiency achieved by time splitting of finite difference operators.

Abstract: A technique is presented for computing multidimensional time-dependent flow fields that avoids much of the inefficiency typically found in finite difference calculations. The technique initially divides the flow field into regions, each containing a mesh of general quadrilateral cells chosen to provide spatial resolution of the local features of the flow. A finite difference operator of second order accuracy, consisting of a sequence of one-dimensional operators (each operating at near maximum Courant-Friedrich-Lewy number) is then constructed for each region. Numerical results illustrating the technique for inviscid flows about simple bodies that generate shock waves, embedded shock waves, and expansion fans are presented and compared with exact theory.

Identification of parameters in unsteady open channel flows

Abstract: This paper introduces the influence coefficient algorithm, a simple, easily implemented, and rapidly convergent computational procedure for the solution of the parameter identification problem in unsteady open channel flow from field observations on stage hydrograph and velocity distribution at one or more points along the channel. (Identification is a mathematical process whereby the parameters embedded in a differential equation defining a system are determined from observations of system input and output.) The parameters specifically chosen for identification are the two ‘friction slope’ characteristics: the channel roughness coefficient and the exponent of the hydraulic radius in the empirical friction slope relation, a number usually assumed to be 4/3. These parameters are not physically measurable and have to be determined from the solutions of the mathematical model using concurrent input and output measurements. This new procedure is related to both quasilinearization and gradient methods. Additionally, an effective formulation of the algorithm is shown to depend on certain stability and convergence features related to the finite difference solutions of the governing flow equations but often ignored or glossed over.

Low-flow investigations

Abstract: ____________~___________-____----------------------------..---------

Turbulence Model for Boundary Layers near Walls

Abstract: A turbulence model is proposed for the prediction of boundary‐layer flows near walls. Two differential equations are solved: one for the kinetic energy of turbulence, and one for its length scale. The local effective viscosity in the flow is taken as proportional to the product of the length and the square root of the energy. The constants appearing in the equations are determined by reference to experimental data. Four cases of self‐similar flow are predicted with the model and found to compare favorably with the relevant experimental data. Satisfactory predictions for more general flows are also reported.

Viscous Flow Past a Random Array of Spheres

Abstract: The steady, slow motion of a viscous fluid past a random, uniform array of identical nonoverlapping finite spheres is studied. The expected force F acting on any given sphere is obtained by averaging over the ensemble of possible positions of all other spheres. It is shown that, if the Stokes equations hold in the fluid, then for small particle volume concentration c, F has an expansion of the form F=[ 1 + (3 / 2) c1/2 + (135/64)c logc ] F0 + cD · F0 + 0 (c3/2logc), where F0 is the Stokes force on a single isolated sphere in the same flow and D is a tensor which is given in terms of the two‐sphere distribution function for the array and the Stokes solution for two spheres oriented arbitrarily in an unbounded flow. A physical model for the solution is presented and compared with the model of Brinkman.

Stationary toroidal equilibria at finite beta.

Abstract: We investigate the effects of plasma flow on axisymmetric, self-consistent equilibria in toroidal geometry. The investigation is of considerable interest in relation to hot plasmas confined in toroidal systems with longitudinal current. On the basis of the one-fluid MHD plasma model, we use a concise formulation to elucidate important features of the equilibrium. In contrast to previous flow calculations which were treated almost exclusively in the low-beta approximation, we retain, together with flow, all beta effects.As in the treatment of the full flow problem at low beta, we find conditions for equilibrium. The form of our description allows a quite general discussion of its nature and existence for finite beta. This shows that there is a close relationship between the solvability conditions for equations arising from integrals of the system, and the nature of the characteristics of the partial differential equation describing the radial force balance. In the case of large aspect-ratio, these considerations lead to a generalized Bennett relation and to an expression for plasma displacement exhibiting beta and flow effects.

Equilibrium Analysis of Power Systems

Abstract: The flow function of a power system is the vector of node powers expressed in terms of the node angles The Jacobian is the matrix of partial derivatives of the flow vector with respect to the angle vector The ratio of the determinant of the Jacobian to the value which it has when the node angles are set to zero is a dimensionless stability margin which lies between one and zero (steady-state in- stability) and is easily computed from a load flow The margin of torque is the least change in power flows that will cause instability Maximizing the torque margin or maximizing the stability margin with a load constraint yields the optimum dispatching change to maximize security

The unsteady laminar boundary layer on a semi-infinite flat plate due to small fluctuations in the magnitude of the free-stream velocity

Abstract: Asymptotic and numerical solutions of the unsteady boundary-layer equations are obtained for a main stream velocity given by equation (1.1). Far downstream the flow develops into a double boundary layer. The inside layer is a Stokes shear-wave motion, which oscillates with zero mean flow, while the outer layer is a modified Blasius motion, which convects the mean flow downstream. The numerical results indicate that most flow quantities approach their asymptotic values far downstream through damped oscillations. This behaviour is attributed to exponentially small oscillatory eigenfunctions, which account for different initial conditions upstream.

On the Question of Uniqueness of Stable Load-Flow Solutions

Abstract: Practical experience with load-flow solutions has indicated that stable solutions are probably unique, given sufficient data about a network to determine a solution from the standpoint of dimensionality, i.e., having as many equations as variables for the remaining unknowns. A counterexample is given here for which two stable solutions exist, and an approach towards the analysis of uniqueness is presented that adds some insight into the nature of load-flow solutions in general.

Numerical solution of the Navier-Stokes equations for symmetric laminar incompressible flow past a parabola

Abstract: Symmetric laminar incompressible flow past a parabolic cylinder is considered for all Reynolds numbers. In the limit as the Reynolds number based on nose radius of curvature goes to zero, the solution for flow past a semi-infinite flat plate is obtained. All solutions are found by using an implicit alternating direction method to solve the time-dependent Navier-Stokes equations. The solutions found are compared with various other exact and approximate solutions. Results are presented for skin friction, surface pressure, friction drag and pressure drag. The numerical method developed is of particular interest since it combines the alternating direction method with the implicit method for solving the boundary-layer equations. This leads to fast convergence and may be of use in other problems.

State Calculation of Power Systems from Line Flow Measurements, Part II

Abstract: Extending the theoretical foundations established in Part I(1), this paper further describes this efficient method of computing the real-time load flow solution for a power system network. An efficient numerical solution technique particularly applicable to this problem is outlined. Relative weighting of the measurements is analyzed in terms of the measurement accuracies. A method is given for dynamic determination of the frequency of the state estimate calculations. The effects of real-time changes in the network are discussed.

Flow Between Eccentric Rotating Cylinders

Abstract: The flow between eccentric rotating cylinders is studied using a modified bipolar coordinate system. The Sommerfeld pressure distribution and associated flow in a journal bearing are derived from the Navier-Stokes equations by a straightforward and systematic expansion in the clearance ratio (assumed small). First order corrections for curvature and inertial effects are given. There is no restriction on the eccentricity. (Author)

Gas Flow Pattern and Mass Transfer Analysis in a Horizontal Flow Reactor for Chemical Vapor Deposition

Abstract: To study mass transfer characteristics in a vapor deposition reactor, gas flow patterns in a horizontal tube were investigated. Combined free and forced convection spiral flow and pure forced convection laminar flow were observed depending on experimental conditions of various flow rates and pressures. Further, local deposition rates under two flow behaviors were numerically obtained by solving a three‐dimensional mass conservation equation. It was estimated on the basis of calculated results that forced convection laminar flow in a rectangular reactor produced better uniformity on the deposition rate distribution across the width than did combined convection spiral flow.

Non-local effects in the stability of flow between eccentric rotating cylinders

Abstract: The linear stability of the flow between two long eccentric rotating circular cylinders is considered The problem, which is of interest in lubrication technology, is an extension of the classical Taylor problem for concentric cylinders The basic flow has components in the radial and azimuthal directions and depends on both of these co-ordinates As a consequence the linearized stability equations are partial differential equations rather than ordinary differential equations Thus standard methods of stability theory are not immediately useful By letting the clearance ratio and eccentricity tend to zero in a given way a global solution to the stability problem is obtained

The use of moving meshes in gas-dynamical computations☆

Abstract: A finite-difference method for nonstationary onedimensional problems of gas dynamics was described in [ll, then later extended in [2] to two-dimensional problems, where the example of computing the flow past a sphere with an outgoing shock wave was considered. The method, developed by the present authors, has also been used elsewhere, notably in [3], for computing rotationally symmetric flows with high Mach numbers, involving bell-shaped bodies with varying degrees of bluntness.

A note on the operating characteristics of‘ balanced’ and ‘ unbalanced’ production flow lines

Abstract: Computer simulation is used to investigate the idle time and maximum queue occurring at stations on flow lines with ‘balanced’ independently normally distributed station service times. The effect of ‘inbalance’ in station service time mean and variability, on idle time, maximum queues and output is also investigated.

Pulsed field-gradient spin echo N.M.R. studies of flow in fluids

Abstract: An analysis is presented of the effects of various flow patterns on spin echo shapes and amplitudes in the presence of both static and pulsed gradients in the applied magnetic field. Two approaches are used, one based on the Bloch equations, the other on a molecular average picture. In the case of flow patterns with velocity gradients the effects of self-diffusion across these on the N.M.R. experiments is pointed out and shown to be negligible in most cases of interest. Extension of a multipulse sequence for the study of flow to include pulsed field gradients is outlined. Experiments are described which largely confirm the theoretical predictions (except in the case of echo shapes) for plug flow and laminar flow in a circular pipe. The problem of loss of labelled nuclei from the receiver coil during the experiment is treated in detail for the case of laminar flow. The method is applied to a brief study of the flow properties of agar gel as a function of agar concentration. It is shown by using both phase ...

Flow graph reducibility

Abstract: The structure of programs can often be described by a technique called “interval analysis” on their flow graphs. Here, we characterize the set of flow graphs that can be analyzed in this way in terms of two very simple transformation on graphs. We then give a necessary and sufficient condition for analyzability and apply it to “goto-less programs,” showing that they all meet the criterion.

Two-dimensional free-surface gravity flow past blunt bodies

Abstract: Most of the wave resistance of blunt bow displacement ships is caused by the bow-breaking wave. A theoretical study of the phenomenon for the two-dimensional steady flow past a blunt body of semi-infinite length is presented. The exact equations of free-surface gravity flow are solved approximately by two perturbation expansions. The small Froude number solution, representing the flow beneath an unbroken free surface before the body, is carried out to second order. The breaking of the free surface is assumed to be related to a local Taylor instability, and the application of the stability criterion determines the value of the critical Froude number which characterizes breaking. The high Froude number solution is based on the model of a jet detaching from the bow and not returning to the flow field. The outer expansion of the equations yields the linearized gravity flow equations, which are solved by the Wiener-Hopf technique. The inner expansion gives a nonlinear gravity-free flow in the vicinity of the bow a t zero order. The matching of the inner and outer expansions provides the jet thickness as well as the associated drag.

A class of exact, time-dependent, free-surface flows

Abstract: Attention is drawn to a class of inviscid irrotational flows which satisfy the conditions at a time-dependent free surface exactly. The flows are related to the ellipsoids of Dirichlet (1860).Depending on a parameter P, the cross-section may take the form of a variable ellipse (P 0) or a pair of parallel lines (P = 0). The elliptical case was investigated both theoretically and experimentally by Taylor (1960). The hyperbolic case (P > 0) is remarkable in that the flow develops a singularity when the angle between the asymptotes approaches a right-angle. It is suggested that this solution represents a possible instability near the crest of a standing gravity wave of large amplitude.In the intermediate case (P = 0) the solution describes an open-channel flow in which the fluid filaments are stretched uniformly in a horizontal direction. The latter flow is demonstrated experimentally.