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SINDA예제[항공/기체역학] 발사체 환기 시스템 해석

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2020-11-24
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발사체 환기 시스템 해석

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 (t f = 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/t f ) (altitude in feet)

M = 0.1 + 1.3*sin( p *t/t f ) (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 in 2

Bay 1 to 2: 0.6 in 2

Bay 2 to 3: 0.2 in 2

Bay 3 exhaust: 0.1 in 2

Bay 2 to 4: 0.1 in 2

Bay 4 exhaust: 0.02 in 2

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 in 2 (minimized) (was 1.7)

Bay 1 to 2: 4.47 in 2 (was 0.6)

Bay 2 to 3: 3.38 in 2 (was 0.2)

Bay 3 exhaust: 0.45 in 2 (was 0.1)

Bay 2 to 4: 0.69 in 2 (was 0.1)

Bay 4 exhaust: 0.01 in 2 (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.