As a launch vehicle ascends, air
contained within compartments and bays must be vented
overboard to a decreasing atmospheric pressure. At
front-facing openings, the increasing vehicle speed
means hotter air entering the compartments at those
points.
Sometimes the design concern is
to provide adequate (but not excessive) pressure
equalization paths, and sometimes the concern is
to keep avionics from getting too hot or too cold
(for example, below the dew point). Such thermal
design concerns can be complicated by expansion cooling
and compression heating of air, which can include
a strong dependency on adjacent compartments. For
example, compression heating of a compartment can
be exaggerated when the air entering that compartment
is itself being warmed by compression of an upstream
compartment.
Other times the goal is simply to
calculate the pressures in the bays particularly
if there are multiple holes around the vehicle that
air can escape or enter. If the vehicle is
at a high Mach number, the external pressure can
vary significantly from front to back and top to
bottom. This
can cause the differential pressure across the external
to be quite large which is a particular concern if
there are doors, hatches, or other moveable components
that have to seal.
Another purpose in such analyses could be to satisfy
a general ventilation requirement (for example, 10
air changes per minute in each compartment) so that
any gas (such as leaking fuel vapor) will be exhausted
quickly.
Similar problems face scientific
balloons, aircraft bays and cabins, instrument pods,
and other flight vehicles.
An intentionally generic example
problem of bay venting and refilling has been developed
to illustrate key modeling concepts.
Problem Statement
A vehicle ascends from sea level
to 40,000 feet and then returns, simultaneously accelerating
from Mach=0.1 to 1.4 and decelerating again to Mach=0.1
as it lands. The entire flight takes 6 minutes (tf
= 0.1 hours). While normally such flight scenarios
would be represented by tables (including nonzero
yaw and pitch), for simplicity the pitch and yaw
are assumed to always be zero, and the altitude and
velocity (as Mach number) profiles are assumed to
be sinusoidal:
A = 40000.*sin(p*t/tf)
(altitude in feet)
M = 0.1 + 1.3*sin(p*t/tf) (vehicle
velocity as Mach number, as plotted below)
Four bays are arranged as follows
(the openings are flush and sharp-edged, whereas
in the drawing they are exaggerated in order to make
them more visible):
The areas for each of the gaps or
openings between compartments in the initial design
are as follows:
Inlet to Bay 1: 1.7 in2
Bay 1 to
2: 0.6 in2
Bay 2 to 3: 0.2 in2
Bay 3 exhaust: 0.1
in2
Bay 2 to 4: 0.1 in2
Bay 4 exhaust: 0.02 in2
The bays are assumed to be insulated.
In Bay #2, electronics are present that dissipate
a constant 100W. (Thermal models of avionics and
structure are easy to include, but have been neglected
for simplicity.)
Structurally,
the internal compartments must never exceed 5 psid
above atmospheric (freestream, static) pressure,
and must never drop below 1 psid vacuum pressure.
Also, equipment contained within Bay #3 should never
be subjected to an air temperature warmer than 40°C
(104°F).
The current design does not quite
meet these requirements for the proposed flight scenario.
Therefore, the size of the openings must be adjusted
accordingly, as will be described below.
Mathematical Model
The compartments themselves are
represented as FLUINT control volumes, or “tanks.” The
openings between each bay, including those to the
outside, are represented as ORIFICE connectors, relying
upon the default methods for restriction losses and
choking.
The temperature and pressure outside
of the vehicle (e.g., the static pressure to which
Bays #3 and #4 vent) is calculated using the 1976
US Standard Atmosphere as a function of altitude.
This is available via the STDATMOS routine, and is
called from within the FLOGIC 0 user logic block.
The upstream state is assumed to be stagnation, which
is calculated from the static conditions using perfect
gas relationships as a function of Mach number (see
registers below). Plots of the altitude, inlet stagnation
state, and freestream static state are presented
below.
Note that this treatment (pure stagnation
state at the inlet, and pure static state at the
sides of the vehicle) is highly simplified for this
example problem. For example, this treatment assumes
that flow is nearly always exhausting (vs. entering)
through the Bay #3 and Bay #4 vents, since ingested
air would be at a higher temperature than static.
Usually external skin boundary conditions are supplied
by an aerodynamic program that may or may not include
boundary layer effects.
A SinAPS® diagram of the compartments
and orifices is shown below.
The user-defined variables, or registers,
employed in the development of this model are shown
below:
Results
Near the top of the flight,
the pressure difference between the compartments
and the environment reaches almost 6 psid … in
excess of the design requirement of 5 psid. (The
vacuum pressure requirement does not present a problem.)
At the end of the flight, the air temperature in
Bay #3 has exceeded the allowable limit by more than
10°F: it reaches 114.5°F as the bays re-compress
and flow rates slow.
The SINDA/FLUINT Solver (an
optimization and tasking module) was set up to find
new sizes for the intercompartmental openings, inlet,
and exhausts (6 variables in total) that will meet
the design requirements (3 constraints) for the flight
profile while minimizing the inlet size (the opening
at the leading edge to Bay #1).
After evaluating
about 80 candidate designs, a design (set of hole
sizes) meeting the requirements was found. The areas
for each of the gaps or openings between compartments
in the final design are as follows:
Inlet to Bay
1: 0.32 in2 (minimized) (was 1.7)
Bay 1 to 2: 4.47
in2 (was 0.6)
Bay 2 to 3: 3.38 in2 (was 0.2)
Bay
3 exhaust: 0.45 in2 (was 0.1)
Bay 2 to 4: 0.69 in2
(was 0.1)
Bay 4 exhaust: 0.01 in2 (essentially closed)
(was 0.02)
Comparisons of the initial and final
design are presented next.
While the design optimizer is not
following a strategy per se, it is useful to think
in such terms. The chart at the left (below) shows
that the bay pressures in the initial design are
closer to that of the inlet (stagnation pressure
at front of the vehicle) than that of the outlet
(static pressure at the side). The strategy for reducing
the pressure differential is to restrict the inlet
more, and to open up the Bay 3 exhaust such that
the bay pressures all drop at the highest vehicle
speeds. This of course means more expansion cooling
and more compressive heating since the bay pressures
all change more in the final design than they did
in the initial design.
 
This “strategy” (of
increased compression and expansion by tracking static
pressures more closely than before) means that more
air flows through the compartments, as evidenced
in the plots below. This has the synergistic benefit
of increasing flow through the system, which helps
reduce Bay 3 final temperatures as explained below.
 
The temperature responses,
and the difference between the initial and final
design in particular, are more complex than a simple “increase
in flow rate strategy” would explain.
 
While an increase in
overall flow means that the bay temperature approach
the inlet temperature more in the final design than
in the initial design, note that the temperature
of Bay #4 becomes much colder than in the original
design because its exhaust has been restricted to
the minimum: expansion and compression effects become
more pronounced in that bay.
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