Showing papers on "Fluid dynamics published in 1973"

Effects of Streamline Curvature on Turbulent Flow.

Abstract: : Streamline curvature in the plane of the mean shear produces large changes in the turbulence structure of shear layers, usually an order of magnitude more important than normal pressure gradients and other terms in the mean-motion equations for curved flows. The effects on momentum and heat transfer in boundary layers are noticeable on typical wing sections and are very important on highly-cambered turbomachine blades: turbulence may be nearly eliminated on highly-convex surfaces, while on highly-concave surfaces momentum transfer by quasi-steady longitudinal vortices dominates the ordinary turbulence processes. The greatly enhanced mixing rates of swirling jets and the characteristic non-turbulent cores of trailing vortices are also consequences of the effects of streamline curvature on the turbulence structure. A progress report, comprises a review of current knowledge, a discussion of methods of predicting curvature effects, and a presentation of principles for the guidance of future workers.

Pressure Drop Correlations for Fuel Element Spacers

Abstract: An accurate prediction of the hydraulic losses in multirod fuel bundles is necessary for reactor design calculations. Correlations of the pressure drop at the spacers are important for these calcul...

Similarity Methods in Engineering Dynamics: Theory and Practice of Scale Modeling

Abstract: Parts: I. General Concepts of Similarity and Modeling. 1. Concepts of Dimensions and Similarity. 2. Development of Model Laws from the Buckingham Pi Thoerem. 3. Development of Model Laws from Differential Equations. II. Scaling of Air Blast Waves and Gas Dynamics. 4. Scaling of Air Blast Waves. III. Response of Structures and Materials Under Transient Loads. 5. Simulating Rigid Body Motion. 6. "Replica" Modeling of Structural Response under Transient Loads. 7. Dissimilar Material Modeling and Seismic Response Modeling for Structural Dynamics. 8. Modeling Penetration Mechanics. IV. Fluid Dynamics and Fluid-Structure Interaction. 9. Modeling of Fluid Motions. 10. Modeling of Fluid and Structure Interaction. V. Special Topics. 11. Modeling in Soil Dynamics. 12. Thermal Modeling. VI. Critique of Modeling. 13. Limitations of Modeling, Instrumentation and Building of Models. 14. Distortions and Accuracy in Modeling. Problems. General references. Bibliography.

Free boundary problems in the theory of fluid flow through porous media: Existence and uniqueness theorems

Abstract: Elliptic free boundary problems in the theory of fluid flow through porous media are studied by a new method, which reduces the problems to variational inequalities: existence and uniqueness theorems are proved.

The free surface on a liquid between cylinders rotating at different speeds part II

Abstract: This paper is a further contribution to our work on the Weissenberg effect. One goal of our work is to show how the free-surface deformations on a viscoelastic fluid which is sheared between two concentric rotating cylinders can be used to determine rheological data about the fluid. In this paper we report the results of an experimental program in which free surface shapes have been measured on three viscoelastic fluids undergoing shearing in an apparatus consisting of a stationary outer cylinder and four interchangeable rotating inner cylinders. Experimentally-measured profiles are compared with profiles predicted from second-order theory, and found to be in excellent agreement for STP and TLA-227 in the range of applicability of the second-order theory, but there is some disagreement in the results for a 2% solution of polyacrylamide in 49% water −49% glycerin.

Solid state fluid flow sensor

Abstract: A fluid flow sensor fabricated by integrated circuit techniques is positioned within fluid flow passages for measuring the mass flow of fluid therethrough. The sensor comprises three solid state circuit devices wherein two are fabricated on a chip separate from the third device. The first device is responsive to forced convective heat transfer by the fluid flowing thereover for generating a first electrical signal. The third device is responsive to temperature of the fluid thereover for generating a second signal and the second device is responsive to both said first and second electrical signals for maintaining said first device at a predetermined temperature above said third device. A fuel metering system for internal combustion engines is described utilizing a fluid flow sensor for measuring the mass flow of both fuel and air into the throttle body. Circuit means responsive to said sensors operate to maintain a predetermined fuel-air ratio in said internal combustion means.

Compressible fluid flow

Abstract: This book is an introductory text on one dimensional and simple wave flows. The topics dealt with are one dimensional, adiabatic, frictionless flow, Fanno and Rayleigh flows, Prandtl-Meyer flow, normal and oblique shock waves and simple, unsteady wave propagation. For each topic, the basic equations are derived and manipulated to obtain various appropriate expressions, these expressions are then applied to a number of worked examples which are interwoven with the development of new material. A set of examples for the student to attempt is also included. The book is made self-contained by the inclusion of suitable flow tables. The material is well presented but little comment is made on its relationship to real flows and, consequently, the stgdent is unlikely to be left with any clear feeling for either the power or the limitations of these approximate methods. For example, shock-boundary layer interaction is given only the briefest mention despite the fact that numerous diagrams show shock waves produced at or reflecting from duct walls. The main attractions of the book lie in its relatively modest price and in the numerous and varied worked examples. Studying the examples should considerably improve the ability of an undergraduate student to solve examination questions. B. L. HUNT

A numerical simulation of the cavity filling process with PVC in injection molding

Abstract: : In this work a numerical simulation of the mold cavity filling process was attempted. The mold filled in this simulation is a disk which hot polymer melt enters through a tubular entrance located at the center of the top plate. The tube is 2.54 cm. long and has a radius of 0.24 cm. The plate separation and outer radius of the disk cavity may be varied. A constant pressure applied at the entrance of the tube causes the flow. The cavity walls are kept at various low temperatures. The reported results are for rigid PVC. Continuity, momentum, and energy transport equations for a constant density power law fluid are used to solve the flow problem. It is assumed that the outer radius of the disk is very much greater than the plate separation, that there is axisymmetry, that only one of the viscous terms in the momentum equation is significant, and that in the flow direction heat conduction is negligible compared with convection. Constant values for the thermal conductivity and heat capacity of the melt are used. The resulting differential equations are transformed into difference equations explicity, except for the energy equation. In this case a Six Point Crank- Nicholson implicit differencing technique was necessary to assure thermal stability of the solution. The difference equations were solved by using a Fourth Order Ruhge-Kutta integration formula for the velocity profiles and the Thomas method for the temperature profiles. Convergence to the differential solutions is guaranteed but since a lower limit was imposed on the time increment by the core storage limit of the computer facilities (27K) and long execution times, all results are semi-quantitative for the problem as stated. (Author, modified-PL)

Fluid flow around and through a screen

Abstract: A mathematical model is proposed for steady two-dimensional flow around a submerged screen. The general problem analysed is the flow in a parallel-sided channel partially spanned by a screen, and the fluid is considered to be inviscid except at the screen, where the flow has the required pressure drop. The model is constructed by first replacing the screen with a distribution of sources and then manipulating the stream function for this flow so that the mass and momentum balances across the screen are satisfied. Consequently the model predicts a flow field which is realistic except for the expected discontinuity in velocity between the wake and external flow. In general, the governing equations must be solved numerically, but for the important case of a plane screen oriented normal or roughly normal to the approaching flow, an approximate analytical solution is possible. The accuracy of the model was ascertained by conducting wind-tunnel tests on screens of various solidities and orientations, and comparing the measured downstream velocity distributions with those predicted by the numerical and analytical solutions of the model. Overall, the theoretical results agree well with the experimental data, showing that the model is valid for screens of low and high solidity, in fact, for pressure drop coefficients up to 10. Comparisons with the work of others show that the proposed model is also accurate for the special cases of a screen submerged in an infinite flow field and of a screen spanning the full width of the channel.

Studies of the Behavior of heavy Particles in a Turbulent Fluid Flow

Abstract: A statistical analysis has been made of individual particle transport in a homogeneous, turbulent fluid flow. Expressions for dispersion, correlation coefficients, and turbulent energy content have been obtained. In the course of the development two parameters were found to characterize particulate transport, one of which relates to inertial effects acting on the particle, while the other describes the effects of crossing trajectories. As in previous studies by others, crossing-trajectories effects are found to he of particular importance; inertial effects, however, even for heavy particles, are not insignificant. Comparison of theoretical predictions with experimental data shows good agreement.

Dynamic Behavior of Solid Particles Suspended by Polluted Flow in a Turbine Stage

Abstract: The equations that govern the three dimensional motion of solid particles suspended by a compressible gas flow through a rotating cascade of a turbomachine are formulated. These equations are solved for the case of flow through a turbine stage. The solution takes into account the loss in particle momentum due to their collision with the turbine blades or casing. The dynamic characteristics of the solid particles; namely, their absolute trajectories, paths relative to the turbine rotor, velocity distributions, and the combined stage velocity diagrams, are calculated. The effects of changing the particles mean diameter, material density, and initial particle and gas velocities at the stator inlet on the dynamic characteristics of the solid particles are investigated. The results obtained from this study indicate the locations on the turbine blades subjected to severe erosion damage. Nomenclature a = particle absolute acceleration B = frame fixed in blades /# = angle between particle relative velocity and tangent to surface C = absolute velocity C" = absolute velocity component in the x,0 plane Cpg , = specific heat of gas at constant pressure

Friction Factor and Reynolds Number in Porous Media Flow

Abstract: The concept of hydraulic radius of pore space is used to substantiate that the square root of the permeability is the important length parameter in defining the friction factor and Reynolds number in flow through porous media. Hydraulic radius was defined by applying the Kozeny-Carman theory of hydraulic radius of pore space. It was found that various porous media had different relationships between friction factor and Reynolds number. Experimental results showed a similarity to the Moody diagram used for pipe flow, with a ratio of particle mean diameter to the mean hydraulic radius of pore spaces as the third parameter.

An experimental investigation of a magnetically driven rotating liquid-metal flow

Abstract: Flow and turbulence in a 50-Hz rotating-field MHD system are investigated using the hot-film constant-temperature anemometer. Factors affecting anemometer disturbances and response time are discussed. From measurements of the magnetic field at points within the liquid, the distribution of MHD forces is estimated. The mean rotational velocity of the flow is of the expected order of magnitude but much less dependent on the axial coordinate than the corresponding MHD force. With the aid of a thermal transit-time anemometer, a weak secondary flow is detected. A note on scale-model studies of MHD systems envisaged in metallurgical applications of magnetohydrodynamics points out some basic difficulties in modeling large high-powered systems on a small scale. (auth)

Film thichness, entrainment, and pressure drop in upward annular and dispersed flow

Abstract: Correlations for prediction of film, thickness, entrainment, and pressure drop are required for modeling of annular and dispersed flow in tubular heat transfer and reactor systems. Existing correlations are rather poor predictors of film thickness and entrainment. The relatively large quantity of experimental data for upwardly flow at isothermal conditions provides the basis to develop these correlations. This note represents a design method that has been developed and used in a computer program to predict these variables from the input variables of the mass flow rates of the gas and liquid phases, tube diameter, and fluid physical properties. The discussion is developed in the following areas: (1) film thickness; (2) entrainment; (3) pressure drop; and (4) solution procedure. (22 refs.)

Hydrodynamic Modeling of Two-Dimensional Watershed Flow

Abstract: Unsteady surface flow over watersheds is modeled hydrodynamically by a system of quasilinear partial differential equations for two velocity components and a flow depth at any point on the watershed. Computer solution is made possible by a new difference scheme based on the combination of the Lax-Wendroff scheme with Burstein-Lapidus modifications. A numerical example is given for the solution of watershed flow resulting from a uniform rainfall intensity and finite duration and its result is tested experimentally in the University of Illinois Watershed Experimentation System Laboratory. Preliminary results indicate that the proposed two-dimensional hydrodynamic model is suitable for the study of the watershed flow under consideration.

Numerical marching techniques for fluid flows with heat transfer

Abstract: The finite difference formulation and method of solution is presented for a wide variety of fluid flow problems with associated heat transfer. Only a few direct results from these formulations are given as examples, since the book is intended primarily to serve a discussion of the techniques and as a starting point for further investigations; however, the formulations are sufficiently complete that a workable computer program may be written from them. In the appendixes a number of topics are discussed which are of interest with respect to the finite difference equations presented. These include a very rapid method for solving certain sets of linear algebraic equations, a discussion of numerical stability, the inherent error in flow rate for confined flow problems, and a method for obtaining high accuracy with a relatively small number of mesh points.

Hydraulic control system for load supporting hydraulic motors

Abstract: A load supporting hydraulic system having a pilot operated main control valve is provided with pilot controlled load check valve operative to permit free flow of fluid from said control valve toward the load supporting means of the system in response to pilot pressure and to block fluid flow from the load supporting means toward the control valve. The system includes vent valve means operative with the main control valve to permit the load check valve to be opened by fluid pressure in the load supporting means to allow fluid flow therefrom to the reservoir.

Self synchronous noise rejection circuit for fluid velocity meter

Abstract: A noise rejection circuit for use with electromagnetic fluid flow meters. An electromagnetic fluid flow meter with an electromagnet to induce a magnetic flux of periodically changing polarity. Sensors are positioned so as to receive the voltages induced therein by reason of flow of fluid cutting the flux lines. The low level signal of the sensors requires extremely efficient noise elimination circuits.

Reverse circulating sub for fluid flow systems

Abstract: A reverse circulating device which supplies flowing carrier fluids and returns flowing fluids through a fluid conduit or string to efficiently and speedily remove the carrier fluids by providing a return conduit of less cross sectional flow area than that of the conduit or string through which the fluid is supplied. Also, and more specifically, a reverse circulating device which is connected to an inhole fluid motor so that carrier fluid can be supplied between the casing or the wall of the hole and the conduit or string and returned in the restricted fluid conduit.

Jacket construction for fluid flow fittings

Abstract: To aid in maintaining at a desired temperature a fluid flowing through a fitting in a fluid conveying system, a jacket means is provided which has a hollow housing of heat-conductive material which substantially surrounds the body of the fitting and through which a temperature-controlling fluid is circulated in heat-transferring relation to the body of the fitting.

Prandtl's Boundary-Layer Theory from the Viewpoint of a Mathematician

Abstract: The fluid flow of a continuous medium is described by the Navier-Stokes differ­ ential equations. These equations are nonlinear and-in the subsonic range-of elliptic type. Only a few explicit solutions are known; it is also quite difficult to determine approximations. An existence theory has been known for a few years, although many important questions are still unanswered. An example of a very simple unsolved problem is: does there exist a solution of the Navier-Stokes equation for the two-dimensional steady (hence laminar) flow of an incom­ pressible medium around a simply connected finite body with smooth boundary? Because of these difficulties, Ludwig Prandtl (1904) simplified the Navier­ Stokes equations by omitting nonessential terms. He thus obtained his famous boundary-layer equations. Though these equations are also nonlinear they are parabolic and hence much "simpler" from the theoretical and also practical point of view than the Navier-Stokes differential equations. They can be regarded as asymptotic equations of the Navier-Stokes equations in the limit of vanishing viscosity. The Prandtl boundary-layer theory very early became an invaluable device for the practical treatment of a fluid flow. Blasius (1908) first successfully computed the flow over a flat plate as an explicit solution of the Prandtl equations (but not of the Navier-Stokes equations). Many other new results were obtained in the next decades with the aid of the Prandtl concept. Viscous fluid flows were treated for twoand three-dimensional, steady and unsteady flow of an incom­ pressible or compressible medium consisting of one or more components, with or without energy addition, under the influence of magnetic forces, etc, etc. It is true that the practical success of the boundary-layer theory was over­ whelming. Therefore most people overlooked the fact that the theoretical foundation of that theory was rather vague. During the first 50 years of boundary­ layer theory the fundamental mathematical questions could not be answered. It was not possible to establish a sound mathematical connection to the Navier­ Stokes differential equations. There was no evidence of the existence, uniqueness,