Analytical model has been developed to predict possible unstable behavior in supercritical heat exchangers. From complete model, greatly simplified stability criterion is derived. As result of this criterion, stability of heat exchanger system can be predicted in advance

Friedly, J. C.

Krueger, P. G.

Manganaro, J. L.

English

NASA Technical Reports Server

September 1972	 B72-10598 
NASA TECH BRIEF 
Marshall Space Flight Center 
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Thermal Induced Flow Oscillations in Heat

Exchangers for Supercritical Fluids 
C C 
a	 .2 0 c 
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o	 0 
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I ,	 0 
Fluid - 
Flow
Position	 A	 B	 C 
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The problem: 
When a cryogenic fluid is heated close to its critical 
point as it passes through the heat exchanger, it produces 
severe flow oscillations. This instability phenomenon can 
be detrimental to the system operation. A concise 
investigation is needed to predict the conditions under 
which these events occur and how to minimize them. 
With this information, a designer can prevent potentially 
unstable heat-exchanger configurations. 
The solution: 
An analytical model has been developed to predict 
the possible unstable behavior in supercritical heat 
exchangers. It is found that the rate of the heat transfer 
plays an important role in the stability of the system. 
From the complete model, a greatly simplified stability 
criterion is derived. This criterion states that, for 
stability, a ratio of stabilizing to destabilizing pressure 
drops in the fluid must be greater than the fluid 
expansion factor. As a result of this criterion, the 
stability of a heat-exchanger system can be predicted in 
advance. 
How it's done: 
A simplified drawing of a fluid in motion is shown in 
the figure. The fluid flows through a tube from left to
right. Between positions A and B, there is a constriction 
before the test section is reached. In the test section 
between points C and D, the fluid is heated from an 
external source. Downstream from the test section is a 
plenum and another constriction. 
The dynamic state of the fluid in the test section can 
be completely defined by a series of equations which 
relate to continuity, fluid-energy momentum, wall ener-
gy, and wall boundary conditions. Adhering to the 
normal procedure for stability analysis, these equations 
are solved for small perturbations about the steady-state 
values of the variables. The test-section pressures will 
then be related to the pressure drops in the rest of the 
system. This will yield the system response to any 
external stimulus, such as the upstream pressure. A 
steady-state solution will then be unstable if the pertur-
bation variables increase exponentially as a result of any 
disturbance. 
After the pressure drops for the entire system are 
formulated in the steady and perturbed states, the total 
system response to an external pressure is derived. This 
is called the characteristic equation for the system and 
determines its stability. In addition, by the use of 
Nyquist plots, the characteristic curves can be analyzed 
to determine whether the system is unstable. 
(continued overleaf) 
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The use of the complete characteristic equation and 
the Nyquist diagram to predict the system stability is a 
cumbersome procedure. Although this procedure can be 
automated, it is still desirable to apply a much simpler 
criterion. By making some approximations to the 
characteristic equation, a simplified stability criterion 
equation can be formulated. It includes the effects of 
up-stream and down-stream orifices and the acceleration 
and friction pressure drops in the test section. It does 
not include the inertia or body-force pressure drops. 
This criterion and its equation are documented for 
general use. 
Notes: 
1. It is recommended that this criterion be used as a 
guide in designing stable supercritical heat exchangers. 
Since the available data do not seem to point out 
all the limitations of the criterion, more data are 
needed. Therefore, it is recommended that the con-
trolled laboratory experimentation be performed 
to further confirm or disprove the utility of the 
criterion.
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: B72-10598 
Patent status: 
NASA has decided not to apply for a patent. 
Source: J. C. Friedly, J. L. Manganaro, and

P. G. Krueger of

General Electric Company
under contract to

Marshall Space Flight Center
(MFS-2 1262)
O 
B72-10598	 Category 06, 09


Thermal induced flow oscillations in heat exchangers for supercritical fluids

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