Showing papers on "Fluid dynamics published in 1970"

Interdendritic fluid flow and macrosegregation; influence of gravity

Abstract: An analysis is given of interdendritic flow behavior during solidification of castings and ingots, assuming resistance to flow is as in other types of porous media. Driving forces for the flow are solidification contractions and gravity acting on a fluid of variable density. Detailed flow calculations are given for horizontal, unidirectional, steady-state solidification, using aluminum-copper alloys as examples. Conditions are quantitatively described under which gravity induced convection becomes an important contributory cause of macrosegregation. A critical condition of flow is shown to produce local melting with resulting formation of “channel-type” segregates. Qualitative examples are given of application of the ideas presented to interpretation of macrosegregation in commercial ingots, with specific reference to centerline segregation and “channel-type” segregation, including “V” segregates, “A” segregates and “freckles”.

Magnetic-field re-connexion in a highly conducting incompressible fluid

Abstract: A theoretical model is proposed for the process of re-connexion of frozen-in magnetic-field lines at an X-type null point in the field. The model involves a diffusion region, immediately adjacent to the null point and an outer wave- dominated region. For the latter an exact solution to the magneto-hydrodynamic equations is obtained; for the former an approximate relationship is derived between the field-re-connexion rate, measured by the Alfven number of the incident flow, and the magnetic Reynolds number, based on the width of the diffusion region. The maximum field-re-connexion rate is determined entirely by conditions near the null point and may under suitable conditions become large. A condition for maximum conversion of magnetic energy is derived.

Initial Instability of Fine Bed Sand

Abstract: The initial entrainment characteristics of fine bed sand are objectively defined in terms of the measured distributions of critical instantaneous bed shear stress associated with the observed movement of individual surface grains. Critical flow conditions are then predicted by equating the lower extremes in these characteristic critical shear stress distributions to the upper extremes in the distribution of instantaneous bed shear stress produced by the particular type of background flow under consideration. The method is applied to the case of two-dimensional channel flow over a flat bed and yields sufficiently consistent results to suggest an extension to Shields' curve for small grain Reynolds numbers. The detailed experimental observations clearly illustrate the important role played by bed region turbulence in the interaction process between the fluid and the mobile bed grains constituting the deformable boundary.

Asymptotic matching of plasma and sheath in an active low pressure discharge

Abstract: The method of matched asymptotic expansions is applied to the fluid model of the low-pressure positive column. The expansion of the eigenvalue in the plasma balance equation is obtained to second order in plane and in cylindrical geometry, and uniformly valid expressions for charged particle densities and fluid velocity in two separate regions are indicated.The free-fall model is also examined and the scales of the transition layer and sheath layer found. Comparison is made with the results of direct numerical integration of the equations involved for both models.

The Fluid Dynamics of a Shrouded Disk System With a Radial Outflow of Coolant

Abstract: This paper describes an experimental study of an air-cooled gas turbine disk using the model of a disk rotating near a shrouded stator. Measurements of pressure distribution, frictional moment, and the cooling air flow necessary to prevent the ingress of hot gases over the turbine disk are described for a range of rotational speeds, mass flow rates, and different geometries. The pressure distribution is shown to be calculable by the superposition of the pressure drop due to the shroud and the unshrouded distribution. Moment coefficients are shown to increase with increasing mass flow rate and decreasing shroud clearance, but are little affected by the rotor/stator gap. Applying Reynolds analogy to the moment coefficients, it is estimated that heat transfer from the rotor will be controlled primarily by rate of radial cooling flow at low rotational Reynolds numbers, and will be governed primarily by Reynolds number at large rotational speeds.

Electrohydrodynamic stability: fluid cylinders in longitudinal electric fields.

Abstract: The stability of a fluid cylinder, stressed by an axial electric field, has heretofore been studied assuming that the cylinder and its surroundings behave as perfect dielectrics and viscous effects are ignored. With many fluids this is unrealistic since the existence of even a small conductivity implies that the deformed interface carries an electric charge. Upon deformation of the interface the charge interacts with the field to produce an electrical shearing stress. Thus, to avoid singular behavior viscous shear must be considered from the outset. The analysis is applicable to situations where the relaxation time for free charges is short compared with the time scale for fluid motion. It is found that electrical shearing forces can, under some conditions, completely stabilize the cylindrical interface to axisymmetric deformations. On the other hand, the conditions under which these same forces produce instability are delineated. In instances where both fluids have low viscosities a boundary layer effect produces additional damping and, in the presence of an axial electric field, electrical shearing stresses in this boundary layer may render an otherwise stable oscillation unstable.

Fluid applicator apparatus

Abstract: The present disclosure deals with fluid applicator apparatus wherein a substantially uniform fluid flow is produced through novel lateral-expansion nozzle design for such purposes as the intermittent application of fluid deposits upon moving sheets or articles.

Electrohydrodynamic instability in plane layers of fluid

Abstract: The instability of a plane layer of non-conducting fluid which is in hydrostatic equilibrium between two semi-infinite conducting fluids with surface charges is discussed for both inviscid and viscous fluid models. It is shown that for both the inviscid and viscous fluid cases, the criteria for instability are the same. Consideration is given to the relevance of the results in explaining the mechanism by which the presence of an electric field promotes more readily the coalescence of water droplets on a water surface by viewing the onset of disruption of the air film as the instability of the air film under the action of the electrostatic field produced by the surface charges on the water surfaces.

Apparatus for reducing flowing fluid pressure with low noise generation

Abstract: Fluid pressure reducing apparatus presenting low noise throttling plates. The low noise fluid pressure throttling apparatus provides an assembly of a plurality of such plates, and which may comprise a segment of or be interposed in a fluid flow containing conduit. The low noise throttling plates are passaged by multiple small section orifices producing a high frequency pressure wave whose noise is more readily attenuated by the conduit. The spacing of the plates in the pressure reducing assembly defines with the intervening flow containing means a volume which is dimensioned to produce resonant damping of the noise pressure wave generated in the primary orifices. The pressure drop through the reducing apparatus is divided into nearly equal ratio drops across each plate, further minimizing noise generation.

Mass flow meter

Abstract: THE INVENTION RELATES TO MASS FLOW MEASUREMENTS A CYLINDRICAL BODY HAVING A CURVED NOSE AT ONE END AND A FLAT BASE AT THE OTHER END IS CONNECTED TO A DISC OF SMALLER DIAMETER, WITH THE DISC BEING CENTERED COINCIDENT WITH THE LONGITUDINAL AXIS OF THE BODY AND BEING SPACED AXIALLY FROM THE BASE THEREOF THIS ASSEMBLY, WHEN ALIGNED AXIALLY AT MIDSTREAM OF A FLOWING FLUID WITH THE NOSE POINTED UPSTREAM, GENERATES A DOWNSTREAM WAKE IN WHICH THE FLUID TRACES AN OSCILLATORY FLOW PATTERN THE MASS FLOW OF THE FLUID IS DETERMINED FROM THE FREQUENCY AND AMPLITUDE OF THE OSCILLATIONS THE FREQUENCY VARIES DIRECTLY WITH THE VELOCITY OF THE FLUID FLOW WHEREAS THE AMPLITUDE VARIES WITH THE PRODUCT OF THE FLUID DENSITY AND THE SQUARE OF THE FLOW VELOCITY THE DEVICE PRODUCES SESIRABLE LOW PRESSURE LOSSES AND HAS A SIMPLE INTERNAL GEOMETRY

Fluid circulation apparatus including deaeration and negative pressure control

Abstract: A FLUID CIRCULATION SYSTEM INCLUDES A SUCTION PUMP AND VALVE CONTROLLED RECIRCULATING LOOP FOR ADJUSTABLY MAINTAINING FLUID PRESSURE WITHIN A SPECIFIED RANGE AT THE PUMP, WITH A DEAERATOR DISPOSED IN A FLUID SUPPLY LINE TO CONTINUOUSLY REMOVE AIR FROM THE FLUID AND TO PASS IT VIA A BLEED LINE TO THE PUMP. A FLUID FLOW RESTRICTOR IN THE RECIRCULATING LOOP MAINTAINS A PRESSURE DIFFERENTIAL BETWEEN THE PUMP AND THE FLUID SUPPLY SOURCE. TWO STAGES OF DEAERATION MAY BE PROVIDED AS WELL AS A RESTRICTOR IN THE BLEED LINE TO LIMIT PASSAGE OF FLUID THROUGH THE BLEED LINE.

Energy-dissipation theorem and detailed josephson equation for ideal incompressible fluids.

Abstract: The dissipation of energy in the flow of an ideal incompressible fluid is described by a theorem whose derivation relies upon the exact three-dimensional Magnus formula discussed in the previous paper. The theorem, which explicitly demonstrates the role of vortex motion in the process of energy dissipation, can be used to calculate the trajectories of vortices. Also derived is a detailed Josephson equation - an extension of Anderson's "new corollary in classical hydrodynamics" - which provides an exact non-time-average relation between chemical potentials and vortex motion.

Surface Irrigation Using Kinematic-Wave Method

Abstract: In the kinematic-wave method, one-dimensional unsteady mathematical model for flow in surface irrigation consists of the equation of continuity for the surface flow, the simplified equation of motion, a uniform-flow formula, for the surface flow, the simplified flow equation for the subsurface flow, the infiltration equation or an empirical formula, and appropriately prescribed initial and boundary conditions. By means of the kinematic-wave method that is only valid for supercritical flow, the model is solved to yield the general solution that depends on the solution form of the cumulative depth of the subsurface flow at the head ditch. A particular solution for a constant infiltration rate reduced from the general solution is shown to be compatible with that obtained from the modified Lewis-Milne equation. The solution has different expressions for laminar and turbulent flows.

Power regulation for fluid machines

Abstract: A SWASH PLATE FLUID PUMP OF MOTOR IS CONTROLLED FOR CONSTANT POWER THROUGH FLUID REGULATION CONTROL DEVICES OPERATING WITH FEEDBACK WHICH PROVIDES FOR HYPERBOLIC REGULATING CHARACTERISTICS AS BETWEEN FLUID FLOW AND OPERATING PRESSURE. THE REGULATOR INCLUDES A CONTROL PISTON AND A REGULATOR VALVE PISTON IN A CASING THE RELATIVE POSITION OF WHICH IS DETERMINED THROUGH FEEDBACK FROM THE CONTROL PISTON-SWASH PLATE LINKAGE.

Steady hydromagnetic boundary layer near a rotating, electrically conducting plate.

Abstract: Gilman and Benton's study of the steady fluid motions and magnetic fields induced by a differentially rotating, electrically insulating infinite flat plate in the presence of a uniform magnetic field is generalized by allowing the electrical conductivity of the plate to be an arbitrary function of distance from the fluid‐plate interface. It is found that the important measure of the conductivity of the plate is the ratio of plate conductance to conductance of a layer of fluid whose thickness is one Ekman depth. The form of the steady Ekman‐Hartmann layer is found to be completely independent of the conductivity of the plate. The steady perturbation magnetic field within the plate is found to be entirely azimuthal and its magnitude is directly proportional to the conductance ratio. For values of parameters approximating conditions within the earth, the perturbation field may not be small. This azimuthal field causes an axial electric current to be drawn into the plate from the fluid, effectively strenghtening the coupling between fluid and plate. If the conductance ratio is large, as it is within the earth, spin‐up is accomplished primarily by this current and the Ekman‐Hartmann layer no longer plays a dominant role in coupling the fluid with its boundary.

Laminar-flow heat transfer for in-line flow through unbaffled rod bundles.

Abstract: The findings of a theoretical study of heat transfer for laminar, in-line flow through unbaffled rod bundles are reported. The results of a numerical solution are given for equilateral triangular b...

A numerical solution of unsteady flow in a two-dimensional square cavity

Abstract: Two dimensional unsteady fluid flow in square cavity numerically analyzed from continuity and Navier-Stokes equations and recorded as computer-generated motion picture

Inception and Entrainment in Self-Aerated Flows

Abstract: Inception and entrainment of air in self-aerated open channel flows are studied. For inception to occur surface eddies should leave the free surface and the whole fluid should be turbulent. A criterion for the surface eddy to leave the free surface is formulated using the energy concept. A method to locate the zone of boundary layer emergence to the free surface which causes the whole fluid to be turbulent in the case of flow over free overfall spillways is developed. Using the concept of entrainment, the basic equations for aerated flow down prismatic channels are formulated. Using these equations, several flow characteristics of the uniform aerated flow are studied. The investigations help in computing uniform aerated flow characteristics knowing the non-aerated flow data.