On the Theory of the Laval Nozzle

One of 1,437 reports in the series: NACA Technical Memorandums available on this site.

PDF Version Also Available for Download.

Description

In the present paper, the motion of a gas in a plane-parallel Laval nozzle in the neighborhood of the transition from subsonic to supersonic velocities is studied. In a recently published paper, F. I. Frankl, applying the holograph method of Chaplygin, undertook a detailed investigation of the character of the flow near the line of transition from subsonic to supersonic velocities. From the results of Tricomi's investigation on the theory of differential equations of the mixed elliptic-hyperbolic type, Frankl introduced as one of the independent variables in place of the modulus of the velocity, a certain specially chosen function of ... continued below

Creation Information

Falkovich, S. V. April 1, 1949.

Context

This report is part of the collection entitled: National Advisory Committee for Aeronautics Collection and one other and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 76 times . More information about this report can be viewed below.

Who

People and organizations associated with either the creation of this report or its content.

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this report. Follow the links below to find similar items on the Digital Library.

Titles

Description

In the present paper, the motion of a gas in a plane-parallel Laval nozzle in the neighborhood of the transition from subsonic to supersonic velocities is studied. In a recently published paper, F. I. Frankl, applying the holograph method of Chaplygin, undertook a detailed investigation of the character of the flow near the line of transition from subsonic to supersonic velocities. From the results of Tricomi's investigation on the theory of differential equations of the mixed elliptic-hyperbolic type, Frankl introduced as one of the independent variables in place of the modulus of the velocity, a certain specially chosen function of this modulus. He thereby succeeded in explaining the character of the flow at the point of intersection of the transition line and the axis of symmetry (center of the nozzle) and in studying the behavior of the stream function in the neighborhood of this point by separating out the principal term having, together with its derivatives, the maximum value as compared with the corresponding corrections. This principal term is represented in Frankl's paper in the form of a linear combination of two hypergeometric functions. In order to find this linear combination, it is necessary to solve a number of boundary problems, which results in a complex analysis. In the investigation of the flow with which this paper is concerned, a second method is applied. This method is based on the transformation of the equations of motion to a form that may be called canonical for the system of differential equations of the mixed elliptic-hyperbolic type to which the system of equations of the motion of an ideal compressible fluid refers. By studying the behavior of the integrals of this system in the neighborhood of the parabolic line, the principal term of the solution is easily separated out in the form of a polynomial of the third degree. As a result, the computation of the transitional part of the nozzle is considerably simplified.

Source

  • Prikladnaya Matematika I Mekhanika; Volume 10; No. 4; 503-512

Language

Item Type

Identifier

Unique identifying numbers for this report in the Digital Library or other systems.

  • URL: http://hdl.handle.net/2060/20050028438 External Link
  • Report No.: NACA-TM-1212
  • Center for AeroSpace Information Number: 20050028438
  • Archival Resource Key: ark:/67531/metadc64513

Collections

This report is part of the following collections of related materials.

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).

Technical Report Archive and Image Library

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.

What responsibilities do I have when using this report?

When

Dates and time periods associated with this report.

Creation Date

  • April 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.

Usage Statistics

When was this report last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 76

Interact With This Report

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

Citations, Rights, Re-Use

Falkovich, S. V. On the Theory of the Laval Nozzle, report, April 1, 1949; (digital.library.unt.edu/ark:/67531/metadc64513/: accessed December 10, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.