One important aspect in these analyses is the derivation of physical mechanism of converted entropic perturbations, which is also directly related to mixing of fluids. In development of frictional fluid motion, entropy gradients of moving fluid particles perpetually increase. This growth is due to fluid particles which have been heated by frictional flow effects and are constantly lagging behind colder fluid

Peter, A. C.

English

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April 1974	 B73-10482 
•	 NASA TECH BRIEF Marshall Space Flight Center 
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Analyses of Unsteady Entropic-Flow Processes 
A report has been published which discusses the 
analyses of unsteady entropic-flow processes. One im-
portant aspect in these analyses is the derivation of the 
physical mechanism of converted entropic perturbations, 
which is also directly related to the mixing of fluids. In 
the development of frictional fluid motion, entropy 
gradients of the moving fluid particles perpetually 
increase. This entropy growth is due to fluid particles 
which have been heated by frictional flow effects and 
are constantly lagging behind the colder fluid. In par-
ticular, there is a continuous conversion process of the 
available mechanical energy into unavailable heat energy, 
which results in a constant steepening of the thermal 
gradients. 
Mathematically, this steepening of the thermal gradi-
ents is implicit in the nonlinear character of the govern-
ing equations and their solutions. Physically, such 
steepening processes cannot sustain themselves in-
definitely. Eventually, a sudden collapse of the con-
vected disturbance must occur with a resultant mixing 
of the warmer and colder fluids. 
The actual implementation of these analyses is accom-
plished by the introduction of the entropy as the 
relevant thermodynamic variable. In effect, it is postu-
lated that all the remaining thermodynamic variables 
may be regarded as functions of entropy only. The 
postulate also indicates that the analysis is restricted to 
simple, progressive wave motion, so that the Jacobian 
of the transformation of these variables vanishes identi-
cally in the flow region under consideration. In other
words, a given set of physical characteristics is mapped 
into a single characteristic in the thermodynamic 
velocity-entropy plane of the same family. 
It is shown that the collapse of the thermal gradients 
is inversely proportional to the initial shape of the 
entropy function, which indicates that large entropy 
gradients shorten the life-distance of the entropic 
perturbations. A sudden collapse of the entropic dis-
turbance induces mixing and an effective redistribution 
of entropy gradients. The resultant distribution of the 
thermal fluid properties causes a successive thermal 
gradient collapse. Therefore, the complete shear layer of 
fluid is subject to a mixing process. 
Notes: 
1. This information may be of interest to researchers 
in the field of unsteady gas dynamics and aero-
dynamic sound generation. 
2. Requests for further information may be directed to: 
Technology Utilization Officer 
Marshall Space Flight Center 
Code A&PS-TU 
Marshall Space Flight Center, Alabama 35812 
Reference: B73-10482
Source: A. C. Peter of
Rockwell International Corp.
under contract to

Marshall Space Flight Center

(MFS-24475) 
Category 03 
This document was prepared under the sponsorship of the National
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Aeronautics and Space Administration. Neither the United States
	 information contained in this document, or warrants that such use Government nor any person acting on behalf of the United States
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Analyses of unsteady entropic-flow processes

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