Potential Flow Assumption Research Articles

Experiments on apparent mass torque coefficients of two-dimensional centrifugal impellers. 1st report Measurements of torque coefficients.

Apparent mass torque coefficients for fluctuations of the flow rate and angular velocity are determined experimentally for two-dimensional centrifugal impellers. Nearly sinusoidal fluctuations of the flow rate and angular velocity are given by using crank mechanisms, and the resulting torque on the impeller is measured. The torque is divided into components in-phase and out-of-phase with the displacements. The in-phase component is attributed to the apparent mass effect and is represented by the apparent mass torque coefficients. Drag torque coefficients are defined and used to represent the out-of-phase components. The apparent mass coefficients are compared with theoretical values obtained under the assumption of a two-dimensional potential flow. The experimental values are 5 to 20 per cent larger than the theoretical ones, and no appreciable effects of the frequency and the amplitude are observed within the range varied in the experiments.

An unsteady momentum integral calculation for the turbulent spot

Velocity and wall shear stress measurements were made along the centerline of turbulent spots generated in a laminar boundary layer on a flat plate. A momentum integral calculation method based on two-dimensional boundary layer theory and the assumption of potential flow above the spot was developed by transforming the unsteady momentum equation into nondimensional similarity coordinates. The centerline wall shear stress, calculated using ensemble-averaged data for the velocity field, shows fairly good agreement with the measured values.

Hydrodynamic Interaction of Flexible Structures

In order to investigate the nature of hydrodynamic interaction on multiple, flexible structures subjected to earthquake ground motion, a numerical analysis for determining the hydrodynamic forces and the corresponding structural responses on three‐dimensional offshore structures is presented. With the assumption of potential flow, the finite element method is developed to solve the boundary value problem in the fluid domain. If the structures have uniform cross sections in the vertical direction, the problem can be reduced to a two‐dimensional one. Moreover, the principle of symmetry and antisymmetry can also be applied to the problem to reduce the fluid domain such that the computation becomes much more efficient. A computer program is developed to analyze the structural behavior according to the aforementioned approach. From the results of the examples presented, we arrive at the conclusion that hydrodynamic interaction is relevant if the structures are in close proximity. This phenomenon depends on the...

A note on the critical flow to initiate closure of pivoting disc mitral valve prostheses

Newton's second law of motion for rotating bodies and potential flow theory is used to mathematically model the closing process of a pivoting disc prosthetic heart valve in mitral position. The model predicts closure to be dependent upon disc curvature, eccentricity, mass, diameter, density, opening angle and fluid properties. Experiments using two commercially available prostheses are shown to give good correlation with the theory for large opening angles. Divergence between theory and experiment occur at small opening angles because of the limitation of the potential flow assumption.

Numerical solution of free-boundary problems in fluid mechanics. Part 3. Bubble deformation in an axisymmetric straining flow

We consider the deformation of a bubble in a uniaxial extensional flow for Reynolds numbers in the range 0.1 [les ] R [les ] 100. The computations show that the bubble bursts at a relatively early stage of deformation for R [ges ] O(10), never reaching the highly elongated shapes observed and predicted at lower Reynolds numbers. We also compute the deformation of the bubble under the assumption of potential flow, and conclude that the potential-flow solution provides a good approximation to the real flow in this case for R [ges ] O(100).

A Method for Predicting Annular Diffuser Performance with Swirling Inlet Flow

A method for predicting the performance of annular diffusere with swirled flow at inlet is presented. The method is based on the assumptions of one-dimensional potential flow using a frictional coefficient parameter to account for friction losses. Theoretical predictions are in good agreement with available experimental data for a variety of annular diffuser geometries. In addition a computer program has been developed, allowing the present analytical technique to be readily applied to the design of any annular diffuser with swirled flow at inlet.

On particle trajectory and capture efficiency around many wires

The particle trajectory and the capture efficiency are calculated for a two-layer high gradient magnetic filter (HGMF) with following structure : Infinitely long and many ferromagnetic wires are placed within two capturing planes which are perpendicular to the magnetic field and to the slurry velocity. All the wires in each capturing plane are parallel with each other with an equal separation to the neighbouring wires, but the wire axes in the back plane shift a finite distance with respect to those in the front plane in the direction perpendicular to the slurry velocity. Under the assumptions of potential flow and large magnetic field, it is found that the capture radius is essentially the same as that for a single wire except the effect of geometrical masking of the back wires by the front ones, though the trajectories of the particles captured by the back wires or escaped are substantially influenced by the front wires.

The motion of small paramagnetic particles in a high gradient magnetic separator

The force balance equation describing the motion of a small paramagnetic particle near a cylindrical ferromagnetic collector is presented in general form. The capture cross-section for a particle approaching a bare wire is found to be a function of the coefficient of magnetic force and the magnetization of the cylinder. Calculations show that the assumption of potential flow versus creeping flow is a critical one which can change the capture cross-section by as much as a factor of three.

An analytical investigation of the impingement of jets on curved deflectors.

Numerical solutions are obtained for the cases of straight circular jets impinging on axisymmetric curved surfaces and plane jets impinging symmetrically on two-dimensional curved surfaces. These geometries are representative of some types of thrust reversers for transport aircraft. The solutions are based on the assumptions of incompressible and potential flow. The velocity field, pressure distribution at the deflector surface and reverser effectiveness are predicted for deflector turning angles of 15 to 75 deg, deflector width to jet diameter ratios of 1.5 to 2.0, and ratios of deflector clearance to jet diameter of 1.0 to 3.0. Reverser effectiveness is found to be a maximum for a ratio of deflector clearance to jet diameter of about 2.0. The effect of back pressuring due to the presence of the deflector is predicted. Experimental verification of the theoretical predictions is obtained. A compressible solution obtained for a limited number of cases indicates that the incompressible solution is satisfactory for jet exit Mach numbers less than 0.8.

The capture of airborne particles by water drops and simulated snow crystals

AbstractCollection efficiencies of falling water drops ranging from 1/10 to 1 mm in radius for spores of Lycoperdon (mean radius r = 2.25 μ), spores of black rust (r = 2.6 μ), and grains of Paper Mulberry pollen (r = 6.4 μ) have been determined. The experimental results are in fair agreement with calculations based on the assumption of potential flow around the larger drops. With both kinds of small spore the collection efficiencies reach maximum values for drops of about 400 μ radius and fall sharply for smaller drops. In this latter regime, where the potential flow solution is inappropriate and the viscous flow solution gives zero values, a sharp fall in collection efficiency is to be expected. Aggregates of two or three spores are collected slightly more efficiently than single spores, but the results show very similar trends in all cases.Some preliminary results have been obtained on the collection of pollen grains by circular, hexagonal and star‐shaped paper discs that simulate snow crystals. The collection efficiencies, as deduced from the numbers of particles caught on their leading faces, are usually < 0.05, but the appearance of similar numbers of particles on the trailing faces suggests that particle capture in the wake of the disc is important at these Reynolds numbers of about 100.

A Linear Perturbation Method for Stability and Flutter Calculations on Hypersonic Bodies

The equations governing linear perturbations in three space variables and time of steady supersonic potential flow past bodies of revolution are derived. The equations are referred to a characteristic coordinate system, and a general numerical process of solution is described. The assumption of potential flow simplifies the theory considerably and is justified in most flutter calculations and in estimating the contribution to stability derivatives from the rear part of a body. However, there is no obstacle in principle to generalizing the technique to apply to nonisentropic flow fields. As an example, to represent the contribution of a typical hypersonic afterbody, the static stability derivatives associated with the exterior surface of a converging conical duct are calculated. Dynamic stability derivatives can be found by a simple extension of this calculation.

Three-Dimensional Investigation of Flow in Centrifugal Impeller with Straight-Radial Blades

The flow through the passage of rotating impellers with single and double shrouds (full shrouds) has been studied experimentally by means of a test rig, so designed that it is possible to measure directly the relative velocity, flow direction, total and static pressure on several points in the passage while the impeller is rotating. On the other hand, the theoretical analysis was made under the assumption of two-dimensional potential flow, and the calculated results are compared with the measured results in terms of relative velocity under the given operating conditions. The velocity distribution and the flow direction obtained in the experiments indicate that secondary flows in the boundary layer tend to shift the low-energy air toward the negative surface (Suction surface) of the blade in the passage. In case of single shrouded impeller, there is observed a counter effect along the casing surface apparently caused by the leakage through the clearance space between the blade and the casing. This results in a voltex flow in the passage. It can be concluded that the secondary flows consequently dominate the flow condition, and make it so complicated that it is impossible for us to conjecture it by means of theory.

An Approximate Method of Determining the Slip Factor of the Radial Outward-Flow Impellers

The flow through radial impellers is, in general, of such a complex nature that an exact solution is not obtainable, even if it is assumed that the flow to be inviscid, incompressible and irrotational so that the methods of potential theory may be employed. For a particular outward-flow impeller whose blades are of logarithmic spiral shape and of constant height, an accurate velocity distribution along the blades has been computed, under the assumption of the two-dimensional potential flow, by making use of the author's rigorous method (1)† of solving the problem. In the same case, an approximate velocity distribution is obtained following the procedures of a new method, described in detail in this paper, and it agrees fairly well with the aforementioned accurate one. Deducing out of this fact that the two results agree fairly well for the special case, it is assumed that the usefulness of the new approximate method of obtaining the velocity distribution may be extended to any radial outward-flow impeller in which the blades are of any shape and of varying heights. From thus determined approximate velocity distribution, the pressure distribution along the blades, then the torque exerted by the impeller on the fluid, and further the slip factor of the radial impeller, can be derived. The application of this approximate method for two centrifugal pump impellers and test data are presented, and the agreement of the results of the approximate method and the experiment is satisfactory.

One Method of calculating the Wind Tunnel Interference in the Cascade Test

This paper deals with the theoretical calculation of the wind tunnel interference in the cascade test on the assumption of two-dimensional potential flow. Using the theory of the wind tunnel wall interference upon the turning angle, as mentioned in the other paper, we can calculate the induced velocities and velocity gradients on each airfoil in the cascade by the tunnel walls. Hence we can introduce the induced ones into the theory of cascade composed of airfoils with arbitrary shape and obtain the theory of the wind tunnel interference with the airfoil characteristics in the cascade test. A numerical example is shown in the case of cascade composed of N. A. C. A. 6409.

On the Wind Tunnel Interference and the Wall Boundary Layer Effects in the Airfoil Cascade

This paper deals with the theoretical calculation of the wind tunnel interference in the cascade test on the assumption of two-dimensional potential flow and then with the influence of the wall boundary layer upon the tuning angle of flow in the cascade. Part I contains the theory of the wind tunnel wall interference upon the turning angle, and Part II the method of calculating the wall boundary layer effects upon the turning angle.