Gas Motion in a Local Supersonic Region and Conditions of Potential-Flow Breakdown

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For a certain Mach number of the oncoming flow, the local velocity first reaches the value of the local velocity of sound (M = 1) at some point on the surface of the body located within the flow. This Mach number is designated the critical Mach number M(sub cr). By increasing the flow velocity, a supersonic local region is formed bounded by the body contour and the line of transition from subsonic to supersonic velocity. As is shown by observations with the Toepler apparatus, at a certain flow Mach number M > M(sub cr) a shock wave is formed near ... continued below

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Nikolskii, A. A. & Taganov, G. I. May 1, 1949.

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  • Main Title: Gas Motion in a Local Supersonic Region and Conditions of Potential-Flow Breakdown
  • Series Title: NACA Technical Memorandums

Description

For a certain Mach number of the oncoming flow, the local velocity first reaches the value of the local velocity of sound (M = 1) at some point on the surface of the body located within the flow. This Mach number is designated the critical Mach number M(sub cr). By increasing the flow velocity, a supersonic local region is formed bounded by the body contour and the line of transition from subsonic to supersonic velocity. As is shown by observations with the Toepler apparatus, at a certain flow Mach number M > M(sub cr) a shock wave is formed near the body that closes the local supersonic region from behind. The formation of the shock wave is associated with the appearance of an additional resistance defined as the wave drag. In this paper, certain features are described of the flow in the local supersonic region, which is bounded by the contour of the body and the transition line, and conditions are sought for which the potential flow with the local supersonic region becomes impossible and a shock wave occurs. In the first part of the paper, the general properties of the potential flow in the local supersonic region, bounded by the contour of the profile and the transition line, are established. It is found that at the transition line, if it is not a line of discontinuity, the law of monotonic variation of the angle of inclination of the velocity vector holds (monotonic law). An approximation is given for the change in velocity at the contour of the body. The flow about a contour having a straight part is studied. In the second part of the paper, an approximation is given of the magnitudes of the accelerations at the interior points of the supersonic region. With the aid of these approximations, it is shown that for profiles convex to the flow the breakdown of the potential flow,associated with an increase of the Mach number of the oncoming flow, cannot be due to the formation of an envelope of the characteristics within the supersonic region. On the basis of the monotonic law, the transitional Mach number M is found, beyond which the potential flow with local supersonic region becomes impossible.

Source

  • Prikladnaya Matematika i Mekhanika; Volume 10; No. 4; 481-502

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  • URL: http://hdl.handle.net/2060/20050028439 External Link
  • Report No.: NACA-TM-1213
  • Center for AeroSpace Information Number: 20050028439
  • Archival Resource Key: ark:/67531/metadc64516

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National Advisory Committee for Aeronautics Collection

The National Advisory Committee for Aeronautics (NACA) was a U.S. federal agency founded on March 3, 1915 to undertake, promote, and institutionalize aeronautical research. On October 1, 1958 the agency was dissolved, and its assets and personnel transferred to the newly created National Aeronautics and Space Administration (NASA).

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This selection of materials from the Technical Report Archive and Image Library (TRAIL) includes hard-to-find reports published by various government agencies. The technical publications contain reports, images, and technical descriptions of research performed for U.S. government agencies. Topics range from mining, desalination, and radiation to broader physics, biology, and chemistry studies. Some reports include maps, foldouts, blueprints, and other oversize materials.

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Creation Date

  • May 1, 1949

Added to The UNT Digital Library

  • Nov. 17, 2011, 5:13 p.m.

Description Last Updated

  • Feb. 6, 2017, 6:04 p.m.

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Nikolskii, A. A. & Taganov, G. I. Gas Motion in a Local Supersonic Region and Conditions of Potential-Flow Breakdown, report, May 1, 1949; (digital.library.unt.edu/ark:/67531/metadc64516/: accessed December 14, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.