AN UNPROTECTED human organism is not adaptable to the

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1 JOURNAL OF AIRCRAFT Vol. 47, No. 2, Marh April 2010 Airraft Deompression with Installed Cokpit Seurity Door Nihad E. Daidzi and Matthew P. Simones Minnesota State University, Mankato, Minnesota DOI: / A zero-dimensional model of okpit and abin deompression with okpit seurity door is presented. The hinged panels in the seurity door were modeled to aount for the pressure-equalization dynamis in the ase of okpit deompression. A omprehensive isentropi and isothermal theoretial analysis is presented with many losed-form and asymptoti solutions. New analytial estimates for the total deompression time and the pressure half-time were derived. The simulations for typial orporate and large-transport-ategory airplanes with different abin geometries, disharge oeffiients, rupture ross-setional areas, pressure altitudes, and abin altitudes have been obtained. The ase in whih the okpit depressurizes first and its effet on the abin deompression and on the seurity door integrity has been extensively studied. The reently required okpit doors may be hazardous for flight rew in the ase okpit depressurizes first and other venting and blowout panels malfuntion or are too slow to respond. The resulting pressure differential between the okpit and the abin an reate instantaneous fores in exess of 80 kn on the okpit seurity door. In addition, this puts the rew in danger due to explosive deompression on the time sale of 100 ms and inreases the possibility of the seurity door being blown out of the frame. Nomenlature F = fore, N or lb (1 lb 4:45 N) g = gravitational aeleration, m 2 =s or ft 2 =s h = altitude, m or ft (1 m 3:28 ft) m = mass of air, kg or lb _m = mass flow rate, kg=s or lb=s p = pressure, Pa or psi (1 psi 6894:7 Pa) ~p = pressure ratio (p =p a ) R = gas onstant, J=kg K (287 J=kg K for dry-air mixture) T = temperature (absolute), K = pressure deay half-time, s = angle of the swing panel, rad = isentropi (adiabati) oeffiient of expansion (1.4 for dry-air mixture) = air density, kg=m 3 = time onstant, s = deompression (total) time, s = subritial (subsoni) deompression time, s = pressure-ratio funtion = oeffiient 0 = oeffiient = superritial (hoked flow) deompression time, s Subsripts ACM = air yle mahine (air pak) a = atmospheri (environmental) = hamber b = abin = okpit ontrol = ontrolled leak (outflow valve) i = inlet/in Reeived 1 November 2008; aepted for publiation 23 November Copyright 2009 by the Amerian Institute of Aeronautis and Astronautis, In. All rights reserved. Copies of this paper may be made for personal or internal use, on ondition that the opier pay the $10.00 per-opy fee to the Copyright Clearane Center, In., 222 Rosewood Drive, Danvers, MA 01923; inlude the ode /10 and $10.00 in orrespondene with the CCC. Assoiate Professor of Aviation, Adjunt Assoiate Professor of Mehanial Engineering, Airline Transport Pilot, Federal Aviation Administration Certified Flight Instrutor for Airplanes and Gliders, Aviation Department, Armstrong Hall 324E; Nihad.Daidzi@mnsu.edu. Member AIAA (Corresponding Author). Graduate Student, Mehanial Engineering. 205 Trafton Siene Center. Student Member AIAA. 490 leak = unontrolled leak o = outlet/out I. Introdution AN UNPROTECTED human organism is not adaptable to the hazardous fators of very-high-altitude environment. Extended exposure to low atmospheri pressure and temperature ould be fatal for unproteted human. The risk of death or irreversible serious illnesses/injuries inreases exponentially with the derease of atmospheri pressure. Therefore, the flight rew and the passengers must use protetive systems to maintain near-sea-level (SL) loal pressure and temperature. Passive protetive systems suh as pressurized abins are an exellent hoie, as they make human ativity not muh different from that at low altitudes. Existing modern ivilian jet airplanes are flying at high altitudes, some of them exeeding 45,000 ft. Frenh British supersoni passenger jet Conorde regularly ruised at altitudes of 55,000 59,000 ft, where the environmental pressures and temperatures are extremely low. Physiologially, these Conorde altitudes an be regarded as spae-equivalent zones. Aording to the International Civil Aviation Organization, the Federal Aviation Administration (FAA), and the Joint Aviation Authority, flights above 51,000 ft would require pressurized suits. The urrent aviation regulations also say that at no time ould airplane abin altitude (CA) exeed 40,000 ft, and it ould not surpass 25,000 ft for more than 2 min. For example, at 40,000 ft (12,200 m), the International Standard Atmosphere (ISA) pressure is only about 18.8 kpa (2.73 psi), and the air temperatures are about 56:5 C (217 K). The boiling temperature of water at this atmospheri pressure is about 59 C (332 K). Above 63,000 ft or 19,200 m (Armstrong line), the ISA environmental pressure drops below 6.3 kpa (0.91 psi) and the boiling temperature of water reahes the normal human body temperature (about 37 C). Any prolonged exposure to suh an environment ould lead to ebullism, anoxia, and ultimate death, after several minutes. These are indeed very hostile onditions for human life. A good overview of the effets of hypoxia, dysbarism, embolism, anoxia, ebullism, and other high-altitude aeromedial fators of the human organism an be found in a number of papers dealing with aviation and spae mediine [1 11]. A thin, yet very strong, struture of the airplane pressure vessel provides a safety ooon that protets pilots and passengers from the lethal environmental effets. However, aidents aused by slow, rapid, or explosive deompression have oasionally led to the loss of airplanes and/or human lives. Espeially today, in the age of a renewed push toward the spae tourism and suborbital passenger

2 DAIDZIC AND SIMONES 491 ommerial flights and more frequent low-earth-orbit and deepspae manned flights, the problem of hamber deompressions deservedly regained our attention. In suborbital and orbital flights, the additional risks, suh as the shower of the ultrafast mirometeorites, an our [12,13]. Suh mirometeorites an punh large holes in the airraft/spaeraft struture, ausing rapid deompressions. Considering the inreased frequeny and duration of the future suborbital and orbital tourism and sheduled ommerial flights, the deompression problems and assoiated hazards have to be addressed again. In addition, the installation of the new reinfored flight-dek seurity door that seals the okpit from the abin during the flight introdued some, perhaps unexpeted, risks. A simplified altitude profile of a typial high-altitude ommerial airraft flight is shown in Fig. 1. Title 14 of the Code of Federal Regulations (CFRs), ommonly known as Federal Aviation Regulations, restrits maximum CA to 8000 ft (CFR Se [14]). At 10,000 ft the CA okpit warning is issued, and at a CA of 14,000 ft, the passenger oxygen mask will deploy. Typially, in ommerial operations, the abin rates of limb are set to no more than 500 fpm, and rates of desent are not more than 300 fpm to prevent any passenger disomfort. In most airplanes, the modern pressurization/environmental system is ompletely automated, requiring minimum input from the rew. In the early jet age, the rapid-deompression aidents and the subsequent loss of human lives were relatively frequent [15 17]. Several British-made Comet ivilian jets (historially, the first passenger jets in ommerial servie) were lost due to the strutural failures and rapid/explosive deompressions. In the early 1950s, the problem of material fatigue was not well understood. Aordingly, serious onsideration has been given to the topi of abin deompression during the same period, partly also due to the development of human spae programs in the United States and the former U.S.S.R. and the growth of the high-altitude passenger jet traffi. Oasionally, inorret maintenane of the airframe [15,16], instruments, equipment, inappropriate operations [18], and engine blade separation [17,19] led to in-flight failures and aidents that sometimes resulted in a high human toll [16,17]. The reent FAA-mandated installation of reinfored okpit (flight-dek) seurity (safety) doors (Title 14 CFR Se [20], Se [21], and Se [22]), intended to prevent unauthorized intrusion into the okpit during flight, presents a new, perhaps unforeseen, danger. In the ase of rapid okpit deompression, an extreme fore an be exerted on the seurity door. Suh a senario an our due to hail damage of the okpit windshield, bird strike, engine blade separation, rak propagation, meteorite strikes at very high altitudes, et. In the ase of a pressure differential of 41 kpa (6 psi) between the okpit and the abin, with a door surfae area of 2m 2 (21:5 ft 2 ), about 82 kn (18,500 lb) of fore an be instantaneously exerted on the door and its frame. The pressure differential and the fore on the sealed okpit door might be too muh for the frame struture to handle if the okpit depressurizes first. Passive and ative internal venting (dado panels) may malfuntion, get logged by flying debris, or simply not reat fast enough to relive the pressure differential on the seurity door. Fig. 1 Simplified altitude flight profile and airplane and abin b pressure hanges for a typial ommerial flight (not to sale). A loose, heavy, armored door an be muh more dangerous than no door at all (or light door), as it ould seriously injure or kill the flight rew, jam and/or destroy flight ontrols, damage and destroy flight instruments, and reate mayhem in the okpit. Suh a senario is inredibly dangerous, as it may prevent emergeny desent. The rise of pressure differential and the fore aross the okpit seurity door may well be muh quiker than the designed venting system is apable of handling. Passive and ative venting between various pressurized hambers, swing panels, and blowout panels in the seurity door are supposed to minimize these risks [23 25]. But it is not lear that the existing airplanes in servie, now retrofitted with the intrusion-proof flightdek doors, have enough fast bypass-venting apaity to timely redue the peak fores on the door. This paper is also a ontribution toward better understanding of the omplex airraft deompression phenomena and interation with the seurity door pressureequalization panels. A searh of the National Transportation Safety Board (NTSB) data on deompression aidents and inidents yielded only eight deompression events in the past four years in the United States. Out of these, only one was a fatal aident. This definitely speaks well for the safety of the pressurized abin in flight, but it is not the whole piture by any means. Aording to 49 CFR Part 830 [26], the NTSB needs to be notified only under ertain irumstanes. There is no diret requirement to notify the NTSB when an airraft has experiened deompression. However, aording to other statistis, the deompression inidents are muh more frequent and many are never reported [17,27]. Another soure of information onerning events of deompression omes from a voluntary reporting program in the United States alled the Aviation Safety Reporting System (ASRS). This is a site set up by NASA and the FAA that enourages those involved with aviation to report events, suh as aidental oversights, whose ourrene would enourage future poliy development, human fators researh, eduation, and training. The results of a study of the events in the ASRS and Australian Transportation Safety Board databases are listed in [27]. The authors found that 32% of the reported auses were due to the pressurization ontroller. The next most ommon ause was the pressurization soure. The remaining 21% were reported as strutural failures. The authors of the report also suggest that atually rapid deompressions per annum our worldwide, but many stay unreported as long as there is no damage, serious inapaitation, or injuries involved. One of the most infamous aidents involving strutural failures of airframes and abin deompression ourred in 1988 on an Aloha Airline s Boeing (N73711) near Maui, Hawaii [16]. Aording to the NTSB report, Flight 243 was at flight level (FL) 240 when a setion of the upper fuselage separated from the airraft near the front passenger setion. Approximately 18 ft were torn off. Although the flight did make a suessful landing in Maui, one flight attendant was swept overboard from the fore of the explosive deompression and many passengers were injured from flying debris. In-flight deompression inidents and aidents are thus relatively ommon even today [18,19,28 30]. Haber and Clamann (H-C) [31] delivered a report in 1953 that was onsidered a general theory of airraft abin deompressions. Their model was zero-dimensional, assuming uniform pressure, temperature, and density in the hamber. In addition to developing theoretial polytropi models of deompression, the authors also performed measurements using small hambers. Their experiments resulted in an average polytropi exponent of n 1:16 averaged over 75 deompression experiments. H-C also provided analytial expression for the deompression time (DT), whih inludes ritial and subritial outflow, but whih also requires a separate diagram to be used in alulating their pressure-ratio funtion. Still today, H-C theory is onsidered a standard in airraft deompression analysis. The first published paper on abin deompression omes from Demetriades [32]. The author examines isentropi deompression of a pressurized abin in vauum (spaeraft). Demetriades estimated relationships between the initial and final pressures as a funtion of DT. No repressurization was onsidered and the outflow did not

3 492 DAIDZIC AND SIMONES inlude disharge oeffiient orretion. The idea in his paper was to examine deompression dynamis and develop ountermeasures that would seure early human spae flights. Mavriplis [33] published an extensive lumped-parameter study of the deompression of pressurized abins for both atmospheri vehiles (airplanes) and spaeraft. Many losed-form solutions for isothermal, polytropi, and isentropi deompressions were derived. Mavriplis also studied the effet of repressurization for airraft and spaeraft. In the ase of three ommuniating ompartments, the Runge Kutta fourth-order numerial simulation was used to solve the omplex interonneted-hambers deompression dynamis. Mavriplis, just as with previous authors, did not onsider the dynamis of the valves and panels that separate those ompartments. However, we found the Mavriplis work to be the most useful for our own investigations. Langley [23] studied ompartmentalization of airraft using the marine ship experiene and suggested using it in airplane design. By sealing off different ompartments, deompression an be prevented from propagating throughout the whole airplane. That would, however, imply that some passengers ould be sarified in a sealed-off ompartment, whih would not be an aeptable solution today. Jakovlenko [34] alulated the exess pressure in human lungs and the dangers of dysbarism in ase of spae abin deompression. The main feature of his mathematial model was simultaneous omputation of the air outflowing from human lungs and lung expansion due to abin deompression, resulting in good agreement of experimental results and theoretial preditions. Shroll and Tibbals [35] have presented a zerodimensional model and assoiated omputer program with a graphial user interfae that simulates rapid airraft abin deompression. Their model is based on a simple isentropi outflow and abin air state hange to obtain depressurization dynamis. They used disharge oeffiient of 0.7 orresponding to rupture with sharp edges. The main objetive of their work was to estimate the amount of emergeny oxygen supply aounting for emergeny desent toward safe breathable altitudes. However, no airraft emergeny desent performane, multiple ompartments, venting system dynamis, and seurity door were inluded. The only paper dealing with the problems of okpit seurity door that we ould find was by Bréard et al. [36]. The authors used ommerial 3-D omputational fluid dynamis (CFD) ode to alulate the external veloity and pressure distribution around the okpit of a ruising airplane and the internal flight-dek pressure distribution aused by side-window failure. The CFD ode solves the Navier Stokes equations with turbulene quantities. Bréard et al. simulated window panel breakup in whih a okpit depressurizes very quikly, and then they alulated the fore on the blowout panels, pressure differential, and the dynamis of abin deompression. However, little insight has been given about their model limitations and apabilities. Reently, Pratt [25] onsidered the dynamis of passive and ative venting blowout panels and hinged doors between different pressurized airplane ompartments in ase of rapid deompression. Mass and the moment of inertia of the panels were onsidered, but otherwise the model seems to be too simplisti. From the results it is very diffiult to estimate the reliability of Pratt s model. Some inonsistenies, errors, and inauraies were noted in his work. No okpit seurity door and hinged panels were modeled in Pratt s work. II. Mathematial Model A. General Formulation A simple zero-dimensional (lumped-parameter) mathematial model with spatially uniform air pressure, temperature, and density temporal hange in the airplane s pressurized vessel is presented. In general, the thermodynami hanges in the air are irreversible and polytropi [31,33,37], as they inlude heat transfer and water phase hange, but in the ase of explosive deompression (less than 500 ms) or rapid deompression (less than 10 s), a reversible adiabati hange an be assumed with reasonable auray. The ase of slow deompression (more than 2 min) an be approximated by isothermal expansion, in whih the air ooling due to expansion will be ompensated by the airraft s environmental system; in between (say, s), the polytropi proess must be used. This requires an additional energy, and possibly entropy, equation in a differential (or integral) form to be solved simultaneously. In this study we did not separately model the pressurized argo and avionis ompartments. The passive and ative venting systems enabling ommuniation with the abin are assumed to be instantaneous. Other assumptions and limitations adopted in the present model are as follows: 1) The effet of relative humidity (RH) and latent heat of ondensation and sublimation is negleted. The airplane environmental air is usually very dry. 2) The abin and the okpit volume do not hange with the air pressure. In reality, there is a very small volume hange aused by pressurization, but it will be negleted here. 3) The atmosphere is regarded as an infinite volume of air and the atmospheri pressure does not hange with the outflow of the abin or okpit air. 4) Airplane maintains altitude and the atmospheri pressure is onstant. In reality, this means that no emergeny desent maneuver is initiated. 5) Air is regarded as an ideal (perfet) gas. 6) The air properties are uniform throughout the volume. No spatial dependene is modeled. The model has lumped parameters. 7) The diabati mass flow rate through the rupture is aounted for by using the experimental disharge oeffiient. 8) There is no okpit air RAM pressure reovery if the side window breaks. 9) The loal outside pressure variations along the fuselage aused by variable loal veloities are aounted for by using an equivalent average flight level (altitude). 10) The dynamis of passive and ative venting through the pressurized argo departments or other passages and hambers were negleted in this study. It is assumed that the argo air is immediately available for abin deompressions. We are modeling proesses in the okpit and abin-argo ompartments separately. In this study, the only possible ommuniation between the okpit and abin is through the hinged flap/panel in the okpit seurity door, with the purpose of relieving the exessive pressure differential when flight-dek deompression ours first. This ommuniation is one way only, i.e., the pressure annot be equalized through the door panels if the abin depressurizes first. In general, deompression an our in the passenger abin, rew okpit, or both in the same time. Furthermore, we assume the deompression to our during level ruise flight. The airplane emergeny desent was not modeled here. It normally would take a minimum of 6 10 s for pilots to initiate the emergeny desent: donning the oxygen masks, establishing oxygen flow and ommuniation, heking bleed air and air paks, and perhaps reonfiguring the airplane before the desent is started. In addition, the atmosphere is quite flat (dp=dh is small) at ruising jet altitudes, and no signifiant hange in atmospheri pressure ours for an altitude hange of several thousand feet. Normally, it would take a well-trained and oordinated rew over 1 min to desend below 25,000 ft from the most ommon ruising altitudes (33,000 39,000 ft). In Fig. 2, the simplified shemati drawing of the okpit-abin pressure vessel is shown. It is assumed in this study that abin(s) an ommuniate with argo ompartment(s) instantaneously and without any resistane, making argo air available in deompression. ISA onditions will be used when alulating environmental air variables. The airplane s environmental pressurization and aironditioning system (air paks) are ontinuously providing relatively dry (RH of 30 35%) onditioned air to the abin and okpit [24,38,39]. Beause of the installed seurity doors, whih are losed and loked during the flight, these two air reservoirs do not ommuniate. Conditioned air is ontinually supplied to the abin and okpit ( _m i ) by separate air paks, to maintain pressure and offset ever-present unontrolled vessel leakage. Outflow valve(s) operate to maintain the abin pressure in a speified range [24]. The safety relief valve will open if neessary to redue the exess pressure differential, thus proteting the strutural integrity of the pressure vessel. The

4 DAIDZIC AND SIMONES 493 Fig. 2 Simplified shemati of the airplane pressurization. Passenger abin and argo ompartment ommuniate without any delay. No other passive or ative venting dynamis between these hambers were modeled (not to sale). airplane s pneumati bleed-air pressurization and environmental ontrol systems (ECSs) for large transport-ategory airplanes, for example, are desribed in [24] and, partiularly for the Boeing ER, in [38,39]. In a level ruising flight at onstant airspeed, the inflow of the aironditioned air from the air paks is assumed to be onstant. The mixture of fresh and filtered reirulated air will offset air lost due to unontrolled leakage, and the exess air will leave the pressure vessel through the outflow valve as ontrolled disharge. Normally, air is exhanged many times per hour in an airplane abin. Hunt et al. [38,39] examined abin environment, air quality, and pressurization for a Boeing ER, a popular twin-engine wide-body ommerial jet transport. The integral mass balane for the pressurized hamber, when the outflow valve is not fully losed, an be written as dm _m ACM _m leak _m ontrol 0 _m ACM onst (1) We also assumed the inflow of air-onditioned pressurized air _m ACM to be steady for the onstant engine fan (N 1 ) speed. When the outflow valve is fully losed, _m ontrol 0. Aordingly, the outflow valve(s) annot ompensate for any additional unontrolled leaks, _m ACM _m leak 0, where _m ACM onst. The maximum pressure differential is a strutural limit that restrits the airplane s maximum ertified flight altitude, so that CA does not exeed 8000 ft ( psi or 75.2 kpa ISA). For example, a Boeing ER has maximum pressure differential of 8.6 psi, restriting the airplane s maximum ertified altitude to 2.32 psi (43,100 ft), although the B767 s aerodynami eiling is higher. Reently, there has been a renewed interest to lower the maximum CA to 6000 ft, whih would require higher pressure differentials or flying at lower altitudes. It is very unlikely that airplanes will fly at lower altitudes, so the airplane manufaturers will have to build even stronger pressure vessels, perhaps by using advaned lightweight omposite materials (e.g., new Boeing 787 or Airbus 350). Conditions inside the abin are defined as p b, T b, and b. Similarly, for the okpit, we have p, T, and. Outside (atmospheri) onditions are defined as p a, T a, and a. Atmosphere is regarded as a perfet infinite sink. When rupture ours in the fuselage struture, the pressure differential will ause outflow of pressurized hamber air until the internal pressure stabilizes with respet to the existing inflow of the onditioned air and the outflow aused by the lower loal atmospheri pressure. The temporal hange of the hamber (abin or okpit) air pressure an be estimated from an integral mass balane equation. We use the subsript to denote any pressurized airplane hamber, and in our ase, it an be either abin or okpit-argo ombination: dm _m i _m o (2) where _m o is unontrolled outflow through the rupture in the pressure vessel and _m i is the repressurization inflow of air, whih is in exess of the air required _m ACM to offset the regular unontrolled leaks in the struture. In this way, we an simulate repressurization senarios in whih extra air is pumped into the abin for the purpose of reduing the rate of pressure drop and inrease of the CA. However, repressurization (reompression) is tehnially diffiult to ahieve and has been onsidered for many years. In existing ommerial airplane designs, it is not possible to ahieve signifiant repressurization, and so _m i will always be zero in our simulations. However, we will arry on derivations with repressurization in mind, as that will provide generality to our approah and an be helpful for future studies on reompression rates required in various deompression situations. In the ase of deompression, the outflow valve would lose quikly, unsuessfully trying to maintain the hamber pressure. Therefore, we are primarily interested in the ases in whih the outflow valve(s) are already fully losed. If the outflow valve(s) were able to ompensate for the additional leaks by losing some more, that would have been a trivial ase, not requiring our analysis. Sine the hamber volume does not hange, and by using the ideal-gas law, the total hange of abin air density is 1 dp RT p RT 2 dt 1 _m V i _m o ) dp nrt _m V i _m o (3) where n is the unknown polytropi oeffiient of expansion. Obviously, to solve for the three unknowns of hamber air pressure p, absolute temperature T, and air density, one needs three simultaneous equations; differential and/or algebrai. The above derived mass balane provides one equation, and the ideal-gas law with partiular relationships between thermodynami variables (equation of state) provides the seond equation. However, we do need a third equation, and the energy equation is the best andidate for that. The unontrolled outflow from the pressurized hamber to outside environment will our either under soni (hoked or ritial/ superritial) or subsoni (subritial) flow onditions in the throat of therupture [32,33,37,40 43]. For soni onditions to our, a ertain ritial ratio between the hamber and the environmental air pressure must exist. If the hamber air pressure is roughly twie, or more, the environmental air pressure (p 1:893p a ) and the mass flow rate through the rupture will be at theoretial maximum, with the loal Mah number in the rupture throat equal to one. Otherwise, the flow will be subritial. Aordingly, our mathematial model will be separated into two parts, one modeling hoked flow and the other modeling subsoni flow: p p! hoked or soni flow M 1 _m o fp p <p! subsoni flow M<1; _m o fp ;p a When the Mah number reahes 1 in the narrowest part of the opening (throat) of the simple rupture, the mass flow rate is at the theoretial maximum. Then the outflow depends on the upstream (hamber) pressure only, but not at all on the downstream pressure [32,33,37]: _m o;max C D A p p RT RT A p eff p p RT A 0 p eff p (4) RT Here, C D :<1is the disharge oeffiient and A is the ross-setional area of the rupture (opening, rak, hole, ompromise, punture). The disharge oeffiient is the ratio between the atual diabati (or possibly fast adiabati) irreversible outflow and the theoretially maximum possible or isentropi outflow [37]. The produt of the rupture ross-setional area and the disharge oeffiient is atually the effetive ross-setional outflow area. For a dry-air mixture, we have p = v 1:4, R 287 J=kg K, and p 0: :6847

5 494 DAIDZIC AND SIMONES when the hamber air versus atmospheri pressure ratio (PR) dereases to a ritial ratio: p a 2 1 p 0:5283 ) p 1:893 p 1 a (5) The outflow transitions smoothly from hoked to subsoni (subritial) and the mass flow rate now depends on the outside (atmospheri) pressure as well [32,33,37,40 43]: s 2 _m o C D A u 1 pa 2 pa 1 p p p 2 1=2 1 1=2 1 p a ~p 1 ~p 1 1=2 (6) 1 RT where ~p p =p a, is the dimensionless hamber-to-environment pressure ratio, with the ross-setional averaged outflow veloity s u 1 RT 1 ~p 2 1=2RT 1= ~p 1 1=2 (7) Although the air pressure hange in the hamber an be isothermal, isentropi, or, in general, polytropi, the disharge proess through the rupture is modeled as isentropi. This is a reasonable assumption, as the outflow is very rapid and the punture nozzle is relatively short. However, to aount for the frition, jet ontration, and diabati outflow, a disharge oeffiient C D is used [31,37,40 43]. The easiest way to estimate the disharge oeffiient is to measure it, but this is of no pratial use, as the exat geometry of the rupture is unpreditable in most ases and an vary dramatially. Using the ompliated, expensive, and time-onsuming CFD odes just to model the disharge oeffiient takes us away from the fundamental problem and does not inrease the auray signifiantly. The best way to deal with this unertainty in disharge oeffiient is to perform sensitivity analysis by varying the value of C D. In Fig. 3, the dynamis are shown of the hamber s deompression into atmosphere or vauum, with and without repressurization. If the atmospheri pressure has nonzero value, then the transition to subritial flow will our at a hamber pressure roughly equal to 1.9 times the atmospheri pressure. In addition, the minimum pressure to whih the hamber pressure an derease is the atmospheri pressure p a. In the ase of pratial vauum (spaeraft), the pressure will derease to zero and the reompression from reserve air will keep the hamber pressure higher than vauum. B. Isothermal Model of Chamber Deompression The simplest possible form of the energy balane equation is to assume that the uniform hamber temperature stays onstant Fig. 3 Deompression proesses into vauum or finite atmosphere with and without repressurization (reompression) (not to sale). (T onst.) during deompression, resulting in isothermal hange, where n 1 in Eq. (3): dp RTo _m i _m o T T o (8) The onstant hamber temperature approximation during slow deompression results in _m o _m o;max K p K C p D p A R T Aeff 0 (9) p onst o R T o It follows that the parameter K is diretly proportional to the effetive rupture area and inversely proportional to the square root of the initial (onstant) air hamber temperature. Sine the repressurization or reompression inflow is assumed to be onstant, the differential equation is linear with onstant oeffiients and an be easily solved analytially: dp RTo _m i RTo K p A B p ) dp B p A (10) As long as the outflow is hoked, the hamber does not know or are about the outside environmental pressure. Deompression into vauum (negleting nonontinuum effets) will ontinue until equilibrium zero pressure is ahieved, in whih ase Eq. (10) is valid and has the solution onsisting of a partiular and a homogeneous part: p tp 1 1e Bt p o e Bt p 1 A 1 B B (11) The reiproal value of onstant B is atually the time-onstant of the outflow proess and RTo B K A RTo _m i _m V i p 0 R T o Aeff (12) The proess of pressure hange in Eq. (11) is a rather interesting one. We have two exponential funtions, one dereasing monotonially with time from the initial hamber pressure to zero as desribed by the homogeneous solution and the other rising from zero and asymptotially approahing the final hamber pressure desribed by the partiular solution and depending on the extra inflow of repressurization air. This analysis is stritly valid for isothermal spaeraft or suborbital airraft deompression in pratial vauum. The effet of repressurization is not only to maintain higher pressure than environmental, but also to redue the rate of pressure drop, whih is important for human physiologial response and enables more time for ountermeasures. The pressure drop now beomes dp t p o B e Bt A e Bt (13) from whih it is obvious how repressurization redues deompression rate. At the initial instant, the total pressure hange rate is dp 0 p o B A 0 (14) The speed of pressure derease in exess of 650 psi=s (4:48 MPa=s) may ause serious lung hemorrhage [33]. Although not a partiular problem in an airplane abin, unless total abin destrution ours almost instantaneously, it ould be a problem in a okpit. Obviously, the hoked outflow annot ontinue for the entire time unless the outflow is in vauum, and then only in an approximation. Demetriades [32] did not make this distintion in his study of depressurization of spaeraft abins, but, in all honesty, it would not make a big differene, sine pressures at whih ontinuum vanishes

6 DAIDZIC AND SIMONES 495 are muh below the minimum pressure required for human survival. The final hamber pressure reahed in vauum is thus lim p tp 1 p 1 A t!1 B _m i K _m i 0 p R T o The larger this ratio, the slower the hamber will deompress and the higher the final pressure will be. This method is used in spaeraft deompression prevention. In the ase when repressurization is negligible, the ritial outflow into vauum will only ontain the homogeneous solution of the differential equation (11). However, when disharged into atmosphere, the hoked outflow will ontinue only as long as the PR is higher than ritial: p p o e B 1:893 p a The elapsed time for whih the hoked hamber isothermal expansion exists an be now estimated from ln0:5283 ~p o V ln 0:5283 ~p o p (15) 0 RT o where ~p o p o =p a onst is the initial hamber-to-environment pressure ratio. This is the same result obtained previously in [33]. In the ase of hamber air temperature of 296 K, this redues to a simple expression when ~p o 1:893: 1 V ln0:5283 ~p o 1 V B 1 (16) If the reompression air is pumped into the hamber, the superritial (hoked) DT is alulated from Eq. (10): Z 1:893pa p o dp A B p ) V Z 0 ln A B p o A 1:893 p a B (17) Even small reompression an signifiantly redue the pressure drop rate and lower the final CA. In retrospet, isothermal approximation is inaurate for rapid deompression, as it would be impossible to maintain onstant air temperature in rapid expansions. A nonlinear ordinary differential equation (ODE) for the isothermal hange with subsoni outflow in the rupture throat and with onstant repressurization rate an be written as RTo _m p a V i A eff 2 1=2 R T o 1=2 1 ~p 1 ~p 1 1=2 (18) 1 In the ase of the initially onstant hamber air temperature of 296 K and no repressurization, this redues to 771 ~p ~p 7 1=2 (19) The following indefinite integral represents the isothermal subsoni PR funtion and an be represented in terms of elementary funtions: Z ~p t ~p 1 ~p ~p 7 1=2 7 5 ~p ~p Z ~p 1 q ~p 1 2 ~p ~p 7 1 1=2 (20) The total subritial isothermal deompression takes plae between pressure ratios ~p o of to 1. The DT for entire isothermal subritial (subsoni) expansion without repressurization is now Z 0 t1: V V 4: (21) In the ase when isothermal deompression starts in the subritial range (entirely only subsoni outflow) with the same air temperature of 296 K, the DT beomes 1: t ~p o V 1 ~p o < 1:893 t 10 (22) The total isothermal DT is a sum of the superritial and subritial deompression times. For air at 296 K and no reompression, we obtain V 4: :08 ln 0:5283 ~p o ~p o 1:893 (23) The theoretial model of isothermal deompression derived here serves us suffiiently well in analyzing slow-deompression senarios on the order of several minutes. C. Isentropi Model of Chamber Deompression The previous model assumed the isothermal hamber s hange, whih is a good approximation during slow deompressions (greater than 2 3 min). The model will now be expanded to inlude hanges in both pressure and temperature during the isentropi (explosive or rapid) deompression. Suh an isentropi (adiabati and reversible or onstant entropy) model in whih heat transfer and irreversible effets have been negleted is more representative of rapid/explosive deompressions. Using the first law of thermodynamis [37] for an isentropi proess and employing the pressure density temperature relationship in the form of an ideal-gas law, one obtains familiar isentropi relationships: 1 1 T p ) T tt 0 p t (24) T 0 p 0 This expression an be substituted into the mass balane equation (3) to obtain the expression in terms of the pressure rate: 1 dp RT p R T RT 2 dp 1 _m p p V i _m o (25) Noting that the hamber pressure and temperature are now both funtions of time, this equation an be redued further using Eq. (4) for hoked (superritial) outflow, n : dp t RT _mi _m V i _m o R T t Aeff p 0 p R T tp t (26) However, temperature an be removed from Eq. (25) by using the isentropi relationships, resulting in dp t _mi R& p 1= Aeff p 0 R & 1=2 p 31=2 (27) where & T=p is a onstant depending on the initial hamber onditions. There are no obstales in numerially solving this equation. However, some approximate solutions an be dedued from Eq. (27). In the ase of polytropi hange, one need only to replae the oeffiient of adiabati (isentropi) expansion with the polytropi oeffiient n. The problem is that the polytropi oeffiient is not known a priori and will depend on the rate of heat transfer and other irreversible effets. In the ase of isothermal hange without repressurization, n 1, Eq. (26) redues to Eq. (10). p 0

7 496 DAIDZIC AND SIMONES Let us now analyze the nonlinear ODE in Eq. (27) more losely. The first term on the right-hand side (RHS) is a term dependent on the repressurization (reompression) air and an be set to zero for all pratial purposes in today s airplanes. The seond term on the RHS is thus normally muh larger than the first, resulting in dp t Aeff p 0 R & 1=2 p 31=2 (28) This ODE an be separated and integrated analytially to yield p tp 0 1 Aeff p 2=1 RT 0 t (29) This is the same solution obtained originally by Demetriades [32], whih was derived here independently using a slightly different approah. Partiularly for air at the initial abin temperature of 296 K (23 C), 1 p p Aeff t (30) This expression is similar to the expression obtained in [32] for the depressurization of sealed spaeraft abins. The duration of the hoked (superritial) deompression is thus V 0:025 0:5283 ~p o 1=7 1 ~p o 1:893 (31) The previous analysis represented theoretial model of the hoked (superritial) outflow. On the other hand, for the subritial (subsoni) outflow, we have dp RT _mi t s Aeff 2 RT t 1 p p a p 2 a 1 (32) p p Together with the hamber s isentropi temperature hange relationships, this yields a omplete mathematial model of subritial deompression. After tedious redutions and rearrangements with the assumption of zero reompression, one obtains Aeff 2 1 1=2 p R T o ~p o1 2 ~p ~p 1 1=2 (33) Separating the variables and integrating, Z ~p 1 ~p ~p 1 1=2 Aeff 2 1 1=2 p RT o Z ~p o1 2 0 (34) For air as a working fluid, the integral on the left-hand side represents isentropi PR funtion and an be obtained in losedform via elementary funtions: Z ~p Z ~p s ~p 1 ~p 3 71 ~p 2 7 1=2 1 ~p 2 7 ~p =2 7 q 7 4 ~p1 ~p ~p q 2 8 ln ~p1 7 ~p (35) In partiular, the integral between limits of subritial outflow (1.893 to 1) yields a value of about Using hamber air at 296 K, the total time elapsed during subritial isentropi deompression is 3: V ~p o 1:893 s 1:8933: (36) Interestingly, isothermal and isentropi PR funtions do not differ muh, with maximum differene being less than 3.4% at the very end of the interval, where PR 1:893. Mavriplis [33] used the average value of these two funtions in his alulations. By omparing Eqs. (21) and (36), we onlude that isentropi expansion is about 25% shorter than isothermal. In the ase when deompression starts in the subritial range (entirely only subsoni flow), and with the same air properties as above, the DT beomes 9: s ~p o ~p o1=7 V 1 ~p o < 1:893 s 10 (37) The total (super- and subritial) DT for hamber air s isentropi expansion [Eqs. (31) and (36)] is thus V 0:0228 ~p o 1=7 0:0215 ~p o 1:893 (38) In the ase of isentropi expansion, the time required for the abin pressure to halve (DHT), provided the outflow remains hoked, is 1=2 0:0449 p T 0 p p0 2 (39) The DHT value annot be simply doubled to arrive at the atual total DT, sine outflow will neessarily slow down as the onditions in the throat of an opening transition to subritial. For the initial hamber temperature of 296 K, the isentropi DHT without repressurization beomes partiularly simple: V 1=2 0:0026 ~p o 3:786 (40) The hamber temperature at this DHT is a fixed ratio of the initial abin temperature and for 296 K, one an write with suffiient auray, T ;1=2 T 0 p t p T 0 p 1 2:32 T 0 1=2 2 0:82 T 0 (41) This temperature and pressure half-time parameters provide simple, yet reliable, haraterization of the rapid-deompression proess and no separate diagram, suh as in the H-C model [31], or other inputs or variables are required. D. Model of the Cokpit Seurity Doors Hinged Panel Dynamis A mathematial model of abin-to-okpit flow through the hinged (swinging) panels in the intrusion-proof sealed okpit seurity door is presented. We assume two stainless-steel hinged panels with dimensions of m and 1 m thikness. No partiular ommerial model of the okpit seurity door is modeled. The analysis presented here an also be applied to other venting passages between different pressurized airplane hambers (dado panels). The hinged panels may be proteted by sreens on the abin side. The panels are prestressed with a torsion spring at 300 Nm to withstand the fore of 2 kn (450 lb) in the enter of the panel. When the threshold pressure differential of about 22.2 kpa (3.22 psi) is reahed between the abin and the okpit, the panels start swinging to open. The outflow area will be the funtion of the pressure differential and the panel opening angle. The FAA regulation Title 14 CFR Part Se [20] for large transport-ategory airplanes requires the okpit seurity door to withstand the impat of 300 J (Nm) at its weakest point. That would

8 DAIDZIC AND SIMONES 497 orrespond to a 150 kg (330 lb) person running into the seurity door at 2m=s (6:6 ft=s) or an almost 67 kg (148 lb) person hitting the door at 3m=s (9:9 ft=s). The shemati of the okpit seurity door and the hinged panels is shown in Fig. 4. The onservation of the angular momentum for the individual hinged panel yields I d2 X M (42) 2 i The moments (torques) ating on the single hinged panel are X M A p os pt b 2 os 0 k W p i sin b d (43) 2 where the detent torque an be alulated from the pressure (fore) required to starting opening the panels: 0 p A p b 2 p ab2 2 F b (44) 2 The momentum on the panel is proportional to the pressure differential. The resultant fore ats in the enter of pressure. The moment of inertia of a retangular panel (a 0:3 mand b 0:3 m) and thikness ( 0:01 m) is I W p b 2 3 g m p b 2 3 The mass of the stainless-steel hinged panel ( p 7450 kg=m 3 )is m p a b p A p p, where A p a b is the surfae area of the door. The differential equation for the hinge angle is, aordingly, I d2 2 pta p b 2 os2 0 k m p g sin b d 2 IC: t 0 0 _ t 0; 1 ptp b tp t (45) The open area for ommuniation between the abin and the okpit for two panels will be the funtion of the hinge angle: A open 2 a b sin a 2 sin os (46) The disharge oeffiient will also be a funtion of the hinge angle. We propose the following relationship, whih also inludes the resistane of sreens in front of the panels: Fig. 4 Shemati of okpit seurity door with two hinged swinging panels. D D0 0:5 sin where D0 0:3. The panels an only open in the diretion of the okpit. The panels annot rotate toward the abin past the stops in the panel frame. This is also to prevent okpit depressurization if the abin depressurizes first. Cokpit pressure an vent through dado panels to prevent exessive fore on the okpit door. The spring that resists the opening of the hinged panels is assumed to be linear within its working range. However, it would present no problem to inlude hard- or soft-spring effets. The prestressed stati resistane must be overome first before the hinged panels start to open. The hinged panels are flushed losed due to the prestressed torsion spring, 0 k, with Nm, and k 175 Nm=rad. The impliation of this is that the pressure differene needs to reah about 22.2 kpa (3.22 psi) before the panels start opening. The temporal fore on the door an be alulated at any time as F d tpta D 2 a b sin A D H L (47) This fore an reah extreme values and stay high for extended periods, whih ould possibly disloate the door from the frame and blow it into the okpit with the atastrophi onsequenes. The strongly nonlinear seond-order ODE for panel hinge angle is now I d2 d 2 k m p g sin b 2 pta p b 2 os 2 0 d t t 0; 1 (48) The pressure differential provides a normal fore that is dependent on the hinge angle. Both hinged panels will start opening after the pressure differene of 22.2 kpa has been reahed between the abin and the okpit. The panels may swing past 90, whih would be aused by rotation inertia. Osillations in hinged panel rotations are ertainly to be expeted, and the amount of damping in the hinge mehanism ontrols the deay of osillation amplitudes. Although osillating, the panels will be losing on average, due to prestressed spring torque, weight, and the dereasing pressure differential between the abin and the okpit. One the pressure differential drops below 22.2 kpa (3.22 psi), the panels will stay losed. Thus, the abin will end up at a somewhat higher pressure (lower CA) than the okpit, whih would provide additional benefit. In reality, passive and ative vents would inrease abin pressure altitude further, albeit with some delay. The outflow through the two door panels will be hoked or subritial, depending on the pressure ratio between the uniform abin and okpit pressures. III. Methods and Materials A. Airraft Configurations We used two different airplane types in deompression simulations. The first is The Boeing Company s ommerial twinengine heavy jet B ER (extended range) and is urrently still the most popular and most ommon airplane on long-range routes. Boeing ER has a net okpit volume of 8m 3 (282 ft 3 ) and the net available abin and argo (aft and forward) air volume of about 980 m 3 (34; 582 ft 3 ). The maximum pressure differential for the pressure vessel is 8.6 psi (59.31 kpa). The seond airraft for whih deompression events were simulated is a new Raytheon business jet: Hawker The Hawker s okpit volume is 150 ft 3 (4:25 m 3 ) and the abin has a net volume of 762 ft 3 (21:58 m 3 ). The Hawker 4000 has maximum strutural pressure differential of 9.8 psi (67.58 kpa) and an maintain SL abin altitude up to 25,240 ft (7,695 m). The limitation of maximum strutural pressure differential was stritly observed in simulations for eah airplane model. The uniform atmospheri pressure at the effetive FL 390 is kpa (2.85 psi), and the abin pressure of kpa (11.45 psi or about 6500 ft CA) was used for B767. This orresponds to the

9 498 DAIDZIC AND SIMONES B ER s maximum strutural pressure differential. The Hawker 4000 pressure vessel an sustain larger maximum pressure differential, and the abin pressure used in simulations was psi (87.23 kpa or about 4000 ft CA), resulting in lower CA than B767 with the fully losed outflow valve(s). The uniform abin and okpit temperature was 23 C (296 K) for both airplane models. The effet of the loal atmospheri pressure and air veloity distribution has been replaed by the equivalent ISA altitude and loal stati environmental pressure. The ISA model was used to desribe the environmental hanges with altitude [44]. B. Numerial Simulation The in-house-developed simulation program based on the MATLAB platform was used. Numerial integration of the set of oupled nonlinear first-order ODEs was performed using the MATLAB ODE solver ode23s. This solver has an adaptive step-size feature obtained through solving the ODE using the seond- and the third-order Runge Kutta methods. This methodology is appliable to stiff systems, in whih multiple time onstants oexist [40 43,45 47]. The initial time step used was ms for slower deompressions, down to 0:1 10 ms for faster deompressions. The iterations were monitored to stop the integration proess when the relative differene between temporal neighboring points was small. The frition oeffiient in the panel door was set to 0.1 and the disharge oeffiient was set to 0.8 for the window frames and all other geometries. Three rupture sizes were simulated: 1, 0.1, and 0:01 m 2 (e.g., m square opening). For Hawker 4000, we did not use the okpit rupture sizes of 1m 2, as that would probably result in a atastrophi strutural failure, onsidering the airplane overall size. Eah panel door weighs about 6.7 kg, and we assumed that the same okpit door was installed in both airplane types. C. Deompression Model Verifiations Let us ompare DTs derived here with those derived by Haber and Clamann [31] and Fliegner (as reported in [3]). Fliegner s equation for DT with volume in ubi meters and surfae area in meters squared is 0:005 V H-C s total DT equation yields V p o P p a a 1 p o P ~p o p V ~p o 1 1 a P 1 1 1~p o (49) (50) where P 1 is a omplex funtion depending on the relative PR and obtained from the H-C diagram [31]. It needs to be said here that the longer the deompression, the more polytropi the expansion proess beomes, as the heat transfer and other irreversible proesses annot be negleted. The omparison between our isentropi and isothermal theoretial models and those of H-C and Fliegner for various volume-to-area V=Aratios is shown in Fig. 5. The Fliegner model [Eq. (49)] atually yields DTs longer than for isothermal deompression, whih is physially impossible in spontaneous expansion unless extra heat is added to the system. Fliegner s model ould be used pratially only as an approximation of the isothermal deompression. As expeted, the H-C data, whih has beome a standard in deompression analysis, is loated between our isothermal and isentropi results. This is not surprising, as the H-C model is based on some ensembleaveraged typial deompression. H-C s polytropi expansion is slightly loser to isothermal than to isentropi deompression. The H-C model is slightly less aurate for very rapid airraft deompressions. An important aspet of our mathematial model and omputer simulations is verifiation and omparison with experimental data and/or other models. Inredibly, not muh has been published on the Fig. 5 Comparison of different theoretial models of hamber deompression for the initial PR of 4.0 (80=20 kpa) and variable V=A ratio. H-C spris80 20=80 0:75. phenomenon of airraft deompression, and no diret experiments of atual airraft deompression exist to the best of our knowledge. However, some limited referenes exist on the deompression (and pressurization) of pressurized vessels, pipes, et. In several researh projets, Daidzi [40 43] obtained many experimental results and reated mathematial model with omputer simulation ode of pressurization dynamis in preignition flow transients in a liquid oxygen (LOX) dome of Messershmitt-Bölkow-Blohmn s HM-7B third-stage roket engine for roket launher Ariane IV. The isentropi model was able to predit pressure ramps of up to 2 3 MPa=s extremely well. This pressure ramps were used to simulate the starting yle of turbopumps supplying LOX for ignition. Experiments and modeling of LOX injetor elements also demonstrated the auray of the isentropi ompression models. Chan [48] presented numerial and experimental data on depressurization of pressurized vessels. We made several omparisons with Chan s experimental data. In Fig. 6, we ompared Chan s data for onstant V=A 1171:1 m. The air in Chan s high- PR experiments was at RH of 80% and about 20 K warmer than air in our simulations. Obviously, ondensation and warmer air will slow down the depressurization proess, explaining the differene of several hundred milliseonds or 6.25% at the higher PR with C D 1:0 in our model. However, when we used C D 0:9, the fit was almost perfet. It appears that by adjusting the C D in our isentropi model, we an simulate all additional effets, suh as diabati onditions, polytropi hange, et. In Fig. 7, we show the time history of the pressure hange as a funtion of time using our isentropi model with C D 0:9 and Chan s [48] experimental pressure measurements. The fit is almost perfet. Beause of latent heat of ondensation of the very humid air in Chan s experiment, the temperature drop shows a large disrepany of K ompared with our isentropi simulations. Fig. 6 Comparison of isentropi model DT with Chan s [48] experiment for two distint PRs of 2.59 and 4.08, RH 80% air, and V=A 1171.