File Size2.10 MB
Tags   Flows     NACA     Technical Notes  
naca-tn-2641 A Vector Study of Linearized Supersonic Flow Applications to Nonplanar Problems.pdfDownload 

National Advisory Committee for Aeronautics, Technical Notes - A Vector Study of Linearized Supersonic Flow Applications to Nonplanar Problems

A vector study of the partial-differential equation of steady
linearized supersonic flow is presented. General expressions, which
relate the velocity potential in the stream to the conditions on the
disturbing surfaces, are derived. In connection with these general
expressions the concept of the finite part of an integral is discussed.

A discussion of problems dealing with planar bodies is given and
the conditions for the solution to be unique are investigated.

Problems concerning nonplanar systems are investigated, and methods
are derived for the solution of some simple nonplanar bodies. The sur-
face pressure distribution and the damping in roll are found for rolling
tails consisting of four, six, and eight rectangular fins for the Mach
number range where the region of interference between adjacent fins
does not affect the fin tips.

In the presentation of the theory of the flow of an idealized
incompressible fluid, vector methods can be used to reduce greatly the
mathematical manipulations involved. The study of steady linearized
supersonic flow may also be aided by the use of vector methods. Two
types of approaches, however, can be used. Perhaps the more obvious is
to make use of common vector methods as was done in reference 1. The
other vector method, which was introduced by Robinson in reference 2
and is used in this paper, appears to be more suited to the study of
the linearized partial-differential equation of steady supersonic flow.
This method allows a derivation of a hyperbolic scalar potential and a
hyperbolic vector potential along lines analogous to the derivation
sometimes used (reference 3, ch. VIII) in dealing with common scalar
and vector potentials.

The present paper presents a vector derivation of many general
results which have been found by various methods and are given in the
published literature on the linearized partial-differential equation
of supersonic flow and also presents some results which are not found
in the literature. The general results of Hadamard (reference h,
p. 207); Puckett (reference 5), and.Heaslet and Lomax (reference 6)
are found as special cases of a general expression for a scalar potenr
tial, and the results found by Robinson (reference 2) are obtained by
the use of a vector potential. The derivation of the scalar potential
doubtlessly'helps to clarify the concept of the finite part of an

Have A Comment On This Article? Post It Here.

Comments are moderated and will not be published until approved. Your email address will be kept confidential. Please review our Comment Policy before posting your comment.


Microsoft Excel Spreadsheets

FREE ANALYSIS SPREADSHEETS 3 Over the last 10 years we have developed hundreds of spreadsheet tools to help us with our structural analysis work. We have made these available through the Abbott Aerospace web site and the XL Viking project. We have now brought them into the technical library. They have been updated, improved and the collection has been expanded to cover more analysis methods than ever before.

The XL-Viking Add-In for Excel

XL-Viking 2 We created the XL-Viking Excel add-in to satisfy our own need to make Excel a better engineering tool. XL-Viking shows your Excel Formula in a way that makes sense and brings essential new functionality to Microsoft Excel by providing an additional user interface and easy to use functions.

The Indispensable Tool For Engineers, Mathematicians, Scientists, Accountants and Teaching Professionals!


Technical Papers & Reports

This is our collection of public domain references. All of the material we make available has been placed in the public domain by the authors/owners. If you believe this is not the case and any of the library material is not in the public domain please let us know. If you have any reference material that you would like to see included in the library we would love to hear from you.

Market Analysis and Market Information

Our newest addition to the library is an on-going series of articles on the aircraft and aerospace market. These are part quantitative and part qualitative and introduce a new aspect to the competencies within Abbott Aerospace.