Showing papers on "Incompressible flow published in 1970"

Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100

Abstract: Finite-difference solutions of the equations of motion for steady incompressible flow around a circular cylinder have been obtained for a range of Reynolds numbers from R = 5 to R = 100. The object is to extend the Reynolds number range for reliable data on the steady flow, particularly with regard to the growth of the wake. The wake length is found to increase approximately linearly with R over the whole range from the value, just below R = 7, at which it first appears. Calculated values of the drag coefficient, the angle of separation, and the pressure and vorticity distributions over the cylinder surface are presented. The development of these properties with Reynolds number is consistent, but it does not seem possible to predict with any certainty their tendency as R → ∞. The first attempt to obtain the present results was made by integrating the time-dependent equations, but the approach to steady flow was so slow at higher Reynolds numbers that the method was abandoned.

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.

On the re-connexion of magnetic field lines in conducting fluids

Abstract: Magnetic field lines reconnection in steady incompressible hydromagnetic two dimensional flow, formulating governing equations with cylindrical polar coordinates

Kelvin–Helmholtz instability of finite amplitude

Abstract: Non-linear Kelvin–Helmholtz instability, of two parallel horizontal streams of inviscid incompressible fluids under the action of gravity, is studied theoretically. The lower stream is denser and there is surface tension between the streams. Some progressing waves of finite amplitude are found as the development of a slightly unstable wave of infinitesimal amplitude. In particular, the non-linear elevation of the interface between the fluids is calculated. The finite amplitude of the waves does not equilibrate to a constant after a long time, but varies periodically with time. In practice, slight dissipation should lead to equilibration at an amplitude close to a value given by the present theory.

Numerical study of steady flow past spheroids

Abstract: Numerical methods have been used to investigate the steady incompressible flow past oblate and prolate spheroids for Reynolds numbers up to 100. The ratio of minor to major axis of the spheroids investigated were 0·9, 0·5 and 0·2, together with 1·0, which represents the limiting case of a sphere. The pressure distribution and the skin and form drag coefficients were numerically evaluated for the various Reynolds numbers. Streamlines, equi-vorticity lines and equivelocity lines are presented and show in detail the flow characteristics.

Lifting Surface Theory for the Problem of an Arbitrarily Yawed Sinusoidal Gust Incident on a Thin Aerofoil in Incompressible Flow

Abstract: The solution to the problem of the loading generated on a two-dimensional thin aerofoil by an incompressible flow whose normal velocity component is of the general form exp [i(λx+/μy — ωt)] is calculated. The method used extends the two-dimensional integral equation solution for the induced vorticity by means of a Chebyshev expansion of part of the kernel function. Thin aerofoil approximations are made throughout, but no collocation procedure, as such, is required.

Trailing-edge stall

Abstract: A study is made of the laminar flow in the neighbourhood of the trailing edge of an aerofoil at incidence. The aerofoil is replaced by a flat plate on the assumption that leading-edge stall has not taken place. It is shown that the critical order of magnitude of the angle of incidence α* for the occurrence of separation on one side of the plate is , where R is a representative Reynolds number, for incompressible flow, and α* = O(R−¼) for supersonic flow. The structure of the flow is determined by the incompressible boundary-layer equations but with unconventional boundary conditions. The complete solution of these fundamental equations requires a numerical investigation of considerable complexity which has not been undertaken. The only solutions available are asymptotic solutions valid at distances from the trailing edge that are large in terms of the scaled variable of order R−⅜, and a linearized solution for the boundary layer over the plate which gives the antisymmetric properties of the aerofoil at incidence. The value of α* for which separation occurs is the trailing-edge stall angle and an estimate is obtained from the asymptotic solutions. The linearized solution yields an estimate for the viscous correction to the circulation determined by the Kutta condition.

Numerical solutions of laminar separated flows

Abstract: Numerical techniques and solutions for compressible and incompressible laminar separated flows using time dependent finite difference equations

Turbulent boundary-layer studies at high Reynolds numbers at mach numbers between 0.2 and 2.8

Abstract: Measurements of the turbulent boundary layer on the sidewall of the RAE 8ft x 8ft wind tunnel are described. The measurements consisted of surface shearing stress, using a large strain-gauge balance, together with velocity and temperature profiles. Maximum Reynolds numbers, based on an effective streamwise run, range from about 200 million at M = 0.2 to 60 million at M = 2.8. The analysis of the results shows that accepted descriptions of turbulent boundary layers in incompressible flow, derived from the concept of a universal velocity defect law, are preserved for compressible flows if the boundary-layer parameters are expressed in kinematic form. This leads to a simple method of calculating skin friction and velocity profiles for constant pressure flows without heat transfer.

The hygrocyst--a stability phenomenon in continuum mechanics.

Abstract: CONSIDER a long sealed container partially filled with a liquid or completely filled with two immiscible liquids and oriented horizontally. If the container is rotated about a horizontal axis, a laminar secondary flow pattern develops that is characterized by large regular regions of segregated material. The onset of this new flow pattern appears to be the result of a natural instability in the normal flow, and is found to occur in containers of all geometries. The flow instability and the associated laminar secondary flow pattern discussed here are, to my knowledge, being reported and studied for the first time and do not appear anywhere in the published scientific literature. This might seem surprising at first in view of the apparent simplicity of the phenomenon, but when it is viewed in terms of its mathematics, with its difficult boundary conditions and unusual body force orientation, it becomes understandable why it would be unlikely that anyone could predict its existence from mathematical considerations alone. Further, it is rather difficult to demonstrate the instability by experiment with inelastic fluids.

On the motion of incompressible fluids

Abstract: We have shown [2] that given Vo, there exists a unique V satisfying (/::), defined on a time interval depending on Vo. In this report we will discuss the methods of [2]. Our approach to the problem is p .. llerned after the work of Arnold, [I J ; that is, we translate the problem into a Hamiltonian system on a certain lIon·lillrar infinite dimensional space. We show that this space has a natural Riemannian structure and we solve the problem by finding geodesics on this space.

Unsteady airfoil stall review and extension

Abstract: Unsteady airfoil stall in incompressible flow, including pitch rate induced accelerated flow effect on leading edge and trailing edge stall

Incompressible Laminar Flow in the Entrance Region of a Rectangular Duct

Abstract: Incompressible laminar flow in entrance region of rectangular duct allowing direct computation of eigenvalues

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.

A study of hypersonic corner flow interactions

Abstract: Hypersonic corner flow in He investigated by heat transfer, surface pressure, pitot surveys, oil and electron beam flow measurements

Oscillatory Flow Measurements with a Directionally Sensitive Laser Velocimeter

Abstract: The concept, design, and construction of a directionally sensitive laser velocimeter for unsteady flow measurements are presented. Oscillatory flow measurements are compared with theoretical predictions.

A phenomenological theory of streaming birefringence

Abstract: Streaming birefringence theory, discussing incompressible fluids, shear and Couette flows, fading memory, deformations

The aerodynamic noise of small-perturbation subsonic flows

Abstract: The method of matched asymptotic expansions is used to simplify calculations of noise produced by aerodynamic flows involving small perturbations of a stream of non-negligible subsonic Mach number. This technique is restricted to problems for which the dimensionless frequency e, defined as ωb/a0, is small, ω being the circular frequency, b the typical body dimension, and a0 the speed of sound. By combining Lorentz and Galilean transformations, the problem is transformed to a space in which the approximation appropriate to the inner region is found to be incompressible flow and that appropriate to the outer, classical acoustics. This approximation for the inner region is the unsteady counterpart of the Prandtl-Glauert transformation, but is not identical to use of that transformation in a straightforward quasi-steady manner. For wings in oscillatory motion, it is the same approximation as was given by Miles (1950).To illustrate the technique, two examples are treated, one involving a pulsating cylinder in a stream, the other the impinging of plane sound waves upon an elliptical wing in a stream.

Coaxial turbulent jets

Abstract: : The flow field generated by two coaxial jets was investigated experimentally with hot-wire anemometers. The area ratio between the external and internal nozzle was varied as well as the velocity issuing from each of the nozzles. The distribution of the mean velocities, turbulence intensities, and shear stresses were determined for the various cases. The development of the flow field and its approach to a self-preserving state is discussed. The Reynolds numbers based on the nozzle diameters varied from 0 to 100,000 and the velocities were low enough that the flow can be considered incompressible. (Author)

Effect of finite plate length on supersonic turbulent boundary layerwith large distributed surface injection

Abstract: The two-dimensional, supersonic, turbulent boundary layer on a finite length flat plate with large injection is analyzed using integral moment methods which include the interaction between the viscous and inviscid flows. Data obtained at Mm = 2.6 are presented and show agreement with the analysis. As injection is increased, the velocity profiles become inflected, the sonic line moves away from the wall and the flow becomes "subcritical." Under this condition, the effect of termination of injection can be felt upstream of the end of injection. In particular, as injection rates approaching the maximum value which can be entrained by a constant pressure mixing layer are approached, the analysis predicts that virtually the entire blowing region experiences a falling pressure due to the effect of finite length. It is postulated that this effect provides for a smooth transition from a boundary-layer flow to one where mixing is negligible, except in a thin layer near the streamline which divides the injected and freestream gas.

SYNOPTIC: Two-Dimensional Potential Flow Theory for Multiple Bodies in Small Amplitude Motion

Abstract: This paper describes a very general method for determining the unsteady, two-dimensional, incompressible flow about one or more bodies of arbitrary shape. Specifically the surface pressure, forces and moments are obtained for bodies oscillating with small amplitude about their steady equilibrium position and on bodies in small amplitude gust fields. The equilibrium configuration of the bodies may also be arbitrary. Calculated results for single bodies in and out of gust fields are compared to results obtained by existing methods. Calculations and comparisons are also presented for two interacting bodies.