CaltechAUTHORS: Combined
https://feeds.library.caltech.edu/people/Cole-J-D/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 26 Jun 2024 12:54:27 -0700Acceleration of Slender Bodies of Revolution through Sonic Velocity
https://resolver.caltech.edu/CaltechAUTHORS:20140807-142832610
Year: 1955
DOI: 10.1063/1.1721986
The linearized theory of slender bodies in arbitrary motion at zero angle of attack has been worked out. The results have been applied to a smooth body accelerating uniformly through sonic velocity. The results theory can be used to estimate the nonlinear or transonic effects.
For an accelerating body, the parameter (bl/c^2)^½ is important where 2b = acceleration, 2l = length of body, c = sound speed at infinity. For sufficiently high (bl/c^2)^½, transonic effects can be neglected. Using linearized theory to estimate the ratio of nonlinear terms in the differential equation gives
λ= (nonlinear terms/significant linear terms) = 3/4 (γ+1) δ^2/(bl/c^2)^(1/2) {log2/δ^2 (c^2/bl)^(1/2) − 9/4}
, where δ = thickness ratio of body. The result above is evaluated at the maximum thickness of a symmetric parabolic arc body at the instant it passes through sonic velocity. For λ<1 transonic effects can be neglected while for λ>1 they begin to dominate. For practical applications the result shows that there is a possibility of a sufficiently long and slender missile accelerating fast enough to avoid transonic effects (e.g., 50 feet long, 5 percent thick, 3g acceleration). For conventional aircraft, transonic effects will dominate. An interesting side result is that when the acceleration is sufficiently large so that transonic effects do not matter the drag coefficient near sonic speed is independent of the acceleration (C_D≐3δ^2 for parabolic arc body).https://resolver.caltech.edu/CaltechAUTHORS:20140807-142832610Some Interior Problems of Hydromagnetics
https://resolver.caltech.edu/CaltechAUTHORS:20131121-140116896
Year: 1959
DOI: 10.1063/1.1705963
The static boundary problems of line currents and dipoles immersed in a perfectly conducting static fluid are considered first. The perturbing effect of moving fluid on the magnetostatic boundary about an isolated line current is then investigated. In this case, the initial circular boundary is distorted into an ellipse with major axis transverse to the direction of flow.https://resolver.caltech.edu/CaltechAUTHORS:20131121-140116896On cylindrical magnetohydrodynamic shock waves
https://resolver.caltech.edu/CaltechAUTHORS:GREpof61
Year: 1961
DOI: 10.1063/1.1706358
If an axial rod is surrounded by an ionized gas, an expanding cylindrical shock wave can be produced by passing through the gas a current which returns along the rod. The azimuthal magnetic field of the current acts like a piston, pushing the plasma away from the rod and leaving behind a cylindrical vacuum region. The case considered is that where a uniform magnetic field parallel to the axis is initially present in the gas; in this case a transverse magnetohydrodynamic shock wave results from the current discharge. The flow is analyzed under the assumptions that the plasma is a nonviscous, nonheat-conducting, ideal gas of infinite electrical conductivity, and that the discharge current increases linearly with time. The analysis is made first on the basis of the "snowplow" theory of Rosenbluth, and then from a similarity solution of the full magnetohydrodynamic equations. The results of the two solutions are compared for the case = 7/5. It is found that the speed predicted by the snowplow theory is in very good agreement with the speed of the contact front obtained from the solution of the full equations over the entire range of shock strength, but that the snowplow speed is a good approximation to the shock speed only in the limit of strong shocks. The effect on the flow of varying the axial field is discussed.https://resolver.caltech.edu/CaltechAUTHORS:GREpof61Similarity solution for cylindrical magnetohydrodynamic blast waves
https://resolver.caltech.edu/CaltechAUTHORS:GREpof62
Year: 1962
DOI: 10.1063/1.1706571
A similarity solution is obtained for the flow behind a very strong (in the hydrodynamic sense) cylindrical magnetohydrodynamic shock wave produced by the sudden release of energy along a line of infinite extent in a plasma. The plasma is assumed to be an ideal gas with infinite electrical conductivity, and to be permeated by the azimuthal magnetic field of a line current. It is shown that it is of critical importance to take into account the ambient magnetic pressure, no matter how small. It is found that, to preserve similarity, the external circuit is required to maintain a constant axial current; this result also appears in the related problem, treated by Greenspan, where the ambient plasma is nonconducting. This boundary condition is shown to have some interesting consequences, especially with regard to the energy content of the system. The dependence of the shock speed on the explosive energy is determined as a function of the ambient magnetic field both for the present case and for Greenspan's case, and interesting differences are noted. Other differences between the two cases are also discussed.https://resolver.caltech.edu/CaltechAUTHORS:GREpof62The Flow of a Viscous Compressible Fluid Through a Very Narrow Gap
https://resolver.caltech.edu/CaltechAUTHORS:20120925-154506131
Year: 1967
DOI: 10.1137/0115051
The effect of compressibility on the pressure distribution
in the narrow gap between a rotating cylinder and a plane in a viscous fluid was studied by Taylor and Saffman [1] during an investigation of the centripetal pump effect discovered by Reiner [2].https://resolver.caltech.edu/CaltechAUTHORS:20120925-154506131Wave drag due to lift for transonic airplanes
https://resolver.caltech.edu/CaltechAUTHORS:20200929-143506669
Year: 2005
DOI: 10.1098/rspa.2004.1376
Lift–dominated pointed aircraft configurations are considered in the transonic range. To make the approximations more transparent, two–dimensionally cambered untwisted lifting wings of zero thickness with aspect ratio of order one are treated. An inner expansion, which starts as Jones's theory, is matched to a nonlinear outer transonic theory as in Cheng and Barnwell's earlier work. To clarify issues, minimize ad hoc assumptions existing in earlier studies, as well as provide a systematic expansion scheme, a deductive rather than inductive approach is used with the aid of intermediate limits and matching not documented for this problem in previous literature. High–order intermediate–limit overlap–domain representations of inner and outer expansions are derived and used to determine unknown gauge functions, coordinate scaling and other elements of the expansions. The special role of switchback terms is also described. Non–uniformities of the inner approximation associated with leading–edge singularities similar to that in incompressible thin airfoil theory are qualitatively discussed in connection with separation bubbles in a full Navier–Stokes context and interaction of boundary–layer separation and transition. Non–uniformities at the trailing edge are also discussed as well as the important role of the Kutta condition. A new expression for the dominant approximation of the wave drag due to lift is derived. The main result is that although wave drag due to lift integral has the same form as that due to thickness, the source strength of the equivalent body depends on streamwise derivatives of the lift up to a streamwise station rather than the streamwise derivative of cross–sectional area. Some examples of numerical calculations and optimization studies for different configurations are given that provide new insight on how to carry the lift with planform shaping (as one option), so that wave drag can be minimized.https://resolver.caltech.edu/CaltechAUTHORS:20200929-143506669Magnetohydrodynamic Simple Waves
https://resolver.caltech.edu/CaltechAUTHORS:20141017-142702707
Year: 2014
The simple wave solutions, which in ordinary gas dynamics
correspond lo expansion flows or Prandtl-Meyer flows are generalized here to ideal magnetohydrodynamic flows. The one-dimensional unsteady (x, t) case is considered. Due to magnetic effects more than one component
of field and velocity must be considered, To carry out the simple wave formalism the equations of motion (continuity, momentum, induction) are written in terms of flow velocities (u_1, u_2), Alfvén velocities
(b_1, b_2) and sound speed (a), These velocities are then functions only of the phase ξ = x_1 - U(ξ)t; each phase line can be thought of as an infinitesimal wave propagating with a speed c = U - u_1 related to the
flow. By elimination of (u_1, u_2) the system of five first-order ordinary differential equations can be reduced to three (homogeneous) equations. The vanishing of the determinant of coefficients provides a famous
relation for wave speed c and reduces the problem to integration of two first-order equations, The further introduction of dimensionless variables, ratios of wave speeds, reduces the problem to integration
of a single first-order equation, By studying the trajectories of this differential equation an overall view of all possible solutions is obtained;
numerical integration is also carried out in the case of slow waves. As applications of this theory various physical problems are studied, the receding piston and waves produced by a current sheet.https://resolver.caltech.edu/CaltechAUTHORS:20141017-142702707Expansion Procedures and Similarity Laws for Transonic Flow Part I. Slender Bodies at Zero Incidence
https://resolver.caltech.edu/CaltechAUTHORS:20141114-102933695
Year: 2014
DOI: 10.7907/shy1-ra36
The purpose of this report is to provide a detailed and comprehensive account of a transonic approximation as applied to flows past wings and bodies. It is mainly concerned with the derivation of approximate
equations, boundary conditions, etc., rather than with the more difficult problem of the solution of transonic flow problems. Thus the report contains for the most part a re-examination of the basic ideas, as presented for example, in Ref. 1. The essential new point of view
introduced here is to regard the approximate transonic equations as part of a systematic expansion procedure. Thus, it becomes possible, in principle, to compute the higher terms of this approximation or at least
to estimate errors.
In the next section the form of the expansion and the reasons for it are explained. In the succeeding sections the equations of motion, shock relations, and boundary conditions for the flow problem are presented
and then the expansion procedure is applied systematically.
The resulting system of equations for the first, second, and
higher approximations i s presented in Section 5. The main results of interest for practical applications concern similarity laws and the pressure coefficient on the surface of slender bodies and these appear in Section 6. The remaining section treats bodies of non-circular
cross-section.https://resolver.caltech.edu/CaltechAUTHORS:20141114-102933695Magnetohydrodynamic Waves
https://resolver.caltech.edu/CaltechAUTHORS:20141114-103522370
Year: 2014
DOI: 10.7907/23q5-kx32
The aim of this paper is to study some special magnetohydrodynamic waves and their connection with the methods of their production, that is, the boundary conditions. Possible wave motions of a fluid
form the underlying structure of the mathematical description; hence a knowledge of their behavior leads to a deeper understanding of fluid dynamical problems. Furthermore there is some evidence that these
waves can be produced in the laboratory and may occur in nature. These waves occur in a model fluid which is an ordinary gas dynamic fluid endowed with a scalar electrical conductivity σ. In practice there is a fairly direct application to slightly ionized gases and to conducting
liquids. However the general method of approach also applies to fully ionized plasmas described by continuum equations.https://resolver.caltech.edu/CaltechAUTHORS:20141114-103522370Acceleration of Slender Bodies of Revolution through Sonic Velocity
https://resolver.caltech.edu/CaltechAUTHORS:20141114-100228549
Year: 2014
DOI: 10.7907/6tw0-7q49
[see PDF for abstract]https://resolver.caltech.edu/CaltechAUTHORS:20141114-100228549Transonic Limits of Linearized Theory
https://resolver.caltech.edu/CaltechAUTHORS:20141114-104653926
Year: 2014
DOI: 10.7907/xmcf-qs18
The transonic regime, extending from Mach numbers at which shock waves first appear with the associated drag rise to Mach numbers at which the head shock wave is firmly attached to the nose of the body, is well known. Not so well known, perhaps, is the reason for the failure of linearized theory to describe the flow in this regime, in particular, to permit an accurate calculation of the pressure.https://resolver.caltech.edu/CaltechAUTHORS:20141114-104653926Problems in the Theory of Viscous Compressible Fluids
https://resolver.caltech.edu/CaltechAUTHORS:20151207-111508765
Year: 2015
The present study was suggested by several problems and difficulties that had appeared in previous experimental and theoretical investigations of viscosity effects in compressible fluids. The outstanding problem was the extension of the classical (Prandtl) boundary-layer theory to high-speed flow, especially supersonic flow. In the boundary-layer theory the equations of motion are simplified by assuming that viscous effects are confined to a narrow region close by the wall through which changes are rapid compared to those in the direction of the wall. Then the resulting non-linear equations are studied with the aim of obtaining the flow field in this narrow region or boundary layer. The pressure is usually obtained from the potential or no-viscous flow about the body. Several authors have studied a boundary-layer theory which has the same basic assumptions but which allows for compressibility and heat conduction. However, in supersonic flow several phenomena are known which show that the basic assumptions of boundary-layer theory do not apply, at least in certain regions.https://resolver.caltech.edu/CaltechAUTHORS:20151207-111508765