Chemical Engineering January 2015 - 48

Feature Report
Engineering Practice
Temperature Effects for
High-velocity Gas Flow
Guidelines are presented
to better understand the
temperature profiles of
high-velocity gases
Aubry Shackelford
Inglenook Engineering, Inc.
I
n high-velocity gas flows, such as
those that may occur within the
discharge piping of a pressurerelief
or depressurization valve,
the temperature experienced at the
wall of the pipe through which the
gas is flowing can be much higher
than the flowing stream's " static "
temperature. In fact, the wall temperature
approaches the stagnation
temperature, which is the temperature
that would be obtained if the
fluid were brought adiabatically and
reversibly (isentropically) to rest.
Experimental work in aeronautical
engineering has established this
effective adiabatic wall temperature,
and correlations have been
proposed to determine the " recovery
factor " as a function of the Prandtl
number (Pr) of the fluid. It has been
found that the adiabatic wall temperature
is about 90% of the difference
between the stagnation and
static temperatures for a turbulent
gas having a Prandtl number of 0.7,
which is typical for many gases.
When performing heat-transfer calculations
between the pipe and the
gas, or when specifying temperatures
for piping material selection,
this recovery factor is important,
and should be accounted for.
Recent investigations into the
potential for fluid temperatures to
exist below the embrittlement temNomeNclature
Variables
Cp
H
M
P
Pr
r
Re
T
U
a
aw
w
y
¤
»
*
Specific
heat capacity at constant pressure
Specific enthalpy
Mach number
Pressure
Prandtl number
Recovery factor
Reynolds number
Temperature
Mean velocity
Subscripts and superscripts
Under adiabatic constraint
At the pipe wall under the adiabatic constraint
At the pipe wall
Coordinate system in the direction normal to the pipe wall (radial)
At stagnation conditions
At flowing conditions (static) outside of the boundary layer
Reference condition for estimatiing fluid properties within the temperature
gradient
perature of relief-valve discharge
piping have shown that low-flowing
temperatures can exist for a wide variety
of systems, including: flashing
liquids or two-phase flow; autorefrigeration
and Joule-Thompson cooling
in response to pressure drops; and
high-velocity gas flow [1].
There is evidence that some systems
exhibiting these behaviors
have resulted in metal embrittlement
and failure. However, there
is an apparent lack of evidence
supporting embrittlement failures
involving high-velocity gas flow,
and there is some suspicion that
the flowing temperatures experienced
in high-velocity gas flow may
not be realistic, as evidenced by a
common refrain - " if the gas was
getting this cold, I would be seeing
ice on the pipes. " Some attempt to
reconcile this anecdotal evidence
with the " intuition " that the pipe
(or vessel) wall temperature can
approach the bulk fluid temperature
given a long enough pipe and
a low enough convective loss to ambient
from the pipe is needed. This
article provides guidance in determining
the wall temperature for
high-velocity gas systems.
Boundary layers
Before attempting reconciliation of
the various notions related to wall
temperatures, it is useful to recall
Prandtl's theory of the boundary
layer, which envisions a small layer
of fluid close to the pipe wall in
which the viscous forces are significant
due to the velocity gradient.
However, outside of this layer, the
core fluid flow approaches that of
an inviscid fluid. The velocity gradient
is established by the known
boundary condition of zero velocity
at the wall, as real fluids will " stick "
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Chemical Engineering January 2015

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