Article records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 13:29:18 +0000Acceleration of Slender Bodies of Revolution through Sonic Velocity
https://resolver.caltech.edu/CaltechAUTHORS:20140807-142832610
Authors: {'items': [{'id': 'Cole-J-D', 'name': {'family': 'Cole', 'given': 'J. D.'}}]}
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://authors.library.caltech.edu/records/1t0zm-fa703Some Interior Problems of Hydromagnetics
https://resolver.caltech.edu/CaltechAUTHORS:20131121-140116896
Authors: {'items': [{'id': 'Cole-J-D', 'name': {'family': 'Cole', 'given': 'J. D.'}}, {'id': 'Huth-J-H', 'name': {'family': 'Huth', 'given': 'J. H.'}}]}
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://authors.library.caltech.edu/records/r0nat-91h53On cylindrical magnetohydrodynamic shock waves
https://resolver.caltech.edu/CaltechAUTHORS:GREpof61
Authors: {'items': [{'id': 'Greifinger-C', 'name': {'family': 'Greifinger', 'given': 'Carl'}}, {'id': 'Cole-J-D', 'name': {'family': 'Cole', 'given': 'Julian D.'}}]}
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://authors.library.caltech.edu/records/nwk91-2jv63Similarity solution for cylindrical magnetohydrodynamic blast waves
https://resolver.caltech.edu/CaltechAUTHORS:GREpof62
Authors: {'items': [{'id': 'Greifinger-C', 'name': {'family': 'Greifinger', 'given': 'Carl'}}, {'id': 'Cole-J-D', 'name': {'family': 'Cole', 'given': 'Julian D.'}}]}
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://authors.library.caltech.edu/records/m62p4-5nq11The Flow of a Viscous Compressible Fluid Through a Very Narrow Gap
https://resolver.caltech.edu/CaltechAUTHORS:20120925-154506131
Authors: {'items': [{'id': 'Cole-J-D', 'name': {'family': 'Cole', 'given': 'J. D.'}}, {'id': 'Keller-H-B', 'name': {'family': 'Keller', 'given': 'H. B.'}}, {'id': 'Saffman-P-G', 'name': {'family': 'Saffman', 'given': 'P. G.'}}]}
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://authors.library.caltech.edu/records/z9bcp-z4p64Wave drag due to lift for transonic airplanes
https://resolver.caltech.edu/CaltechAUTHORS:20200929-143506669
Authors: {'items': [{'id': 'Cole-J-D', 'name': {'family': 'Cole', 'given': 'Julian D.'}}, {'id': 'Malmuth-N-D', 'name': {'family': 'Malmuth', 'given': 'Norman D.'}}]}
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://authors.library.caltech.edu/records/1xsbr-56c93