Atmospheres and Decompression

Transcription

1 Atmospheres and Decompression Emergency and explosive decompression Denitrogenation and decompression sickness Tissue models Physics of bubble formation Atmosphere constituent analysis David L. Akin - All rights reserved

2 Effective Performance Time at Altitude Altitude, m Altitude, ft Effective Performance Time , minutes , minutes , minutes , minutes , minutes 10,700 35, minute 12,200 40, seconds 13,100 43, seconds 15,200 50, seconds 2

3 Cabin Depressurization Rates Fliegner s Equation t =0.22 V P B A B t=time of decompression (seconds) A=cross-sectional area of opening (square inches) V=cabin volume (cubic feet) P=initial cabin pressure (psia) B=external ambient pressure (psia) Decent approximation for aircraft cabins 3

4 Cabin Depressurization Rates Haber-Clamann Model t c = V AC t = t c 1.68 ln P B tc=time constant for cabin (sec) V=cabin volume (cubic feet) A=area of opening (square feet) C=speed of sound (1100 ft/sec) t=time of depressurization (sec) P=initial cabin pressure (psia) B=external ambient pressure (psia) 4

5 Cabin Depressurization Rates Violette s Equation t = V 220A cosh 1 P B t=time of depressurization (sec) V=cabin volume (cubic meters) A=area of opening (square meters) P=initial cabin pressure B=external ambient pressure 5

6 S/C Depressurization (Sonic Orifice) External environment at zero pressure Any hole is a sonic orifice Mass flow rate ṁ = dm dt = v flowa orifice Switch to pressure (ideal gas, isentropic) r dm dt = AP o RT o v flow = p RT

7 Sonic Orifice Analysis (2) J For air, =1.4; R = 287 kg K dm dt = AP o p To Solve for time to reach final pressure P f adiabatic: t = 0.43 p To V A " Po P f isothermal: t = p To V A ln # Po P f

8 S/C Depressurization (Bernoulli) Bernoulli s Law P v2 + gh = constant g=0 Interior and exterior to spacecraft P o v2 o = P e v2 e Inside v o ~0, outside P e =0 P o = 1 2 v2 e 8

9 Bernoulli Analysis (2) s 2P o v e = s dm dt = Av 2P o e = A = Ap 2 P o = m/v dm p m = A r 2Po V dt

10 Cabin Leak Pressure Loss 16" 14" 10 m 3 cabin volume 1 cm 2 leak area Cabin&Pressure&(psi)& 12" 10" 8" 6" 4" 2" 0" 0" 50" 100" 150" 200" 250" 300" 350" Depressuriza1on&Time&(sec)& Bernoulli" Sonic"Nozzle" 10

11 Lung Overpressure Following Decompression From Nicogossian and Gazenko, Space Biology and Medicine - Volume II: Life Support and Habitability, AIAA

12 Violette s Explosive Decompression Limits 12

13 Caissons 13 Pressurized chambers for digging tunnels and bridge foundations Late 1800 s - caisson workers exhibited severe symptoms joint pain arched back blindness death

14 Brooklyn Bridge Designed by John Roebling, who died from tetanus contracted while surveying it Continued by son Washington Roebling, who came down with Caisson Disease in 1872 Competed by wife Emily Warren Roebling 110 instances of caisson disease from 600 workers 14

15 Decompression Sickness (DCS) Dr. Alphonse Jaminet noted similarity between caisson disease and air embolisms Suggested procedural modifications Slow compression and decompression Limiting work to 4 hours, no more than 4 atm Restricting to young, healthy workers J.B.S. Haldane linked to dissolved gases in blood and published first decompression tables 15

16 Supersaturation of Blood Gases Early observation that factor of two (50% drop in pressure) tended to be safe Definition of tissue ratio R as ratio between saturated pressure of gas compared to ambient pressure R = P N2 P ambient =0.79 (nominal Earth value) 50% drop in pressure corresponds to R=1.58 (R values of ~1.6 considered to be safe ) 16

17 Tissue Models of Dissolved Gases Issue is dissolved inert gases (not involved in metabolic processes, like N2 or He) Diffusion rate is driven by the gradient of the partial pressure for the dissolved gas dp tissue (t) dt = k [P alveoli (t) P tissue (t)] where k=time constant for specific tissue (min -1 ) P refers to partial pressure of dissolved gas 17

18 Solution of Dissolved Gas Diff. Eq. Assume ambient pressure is piecewise constant (response to step input of ambient pressure) Result is the Haldane equation: P tissue (t) =P tissue (0) + [P alveoli (0) P tissue (0)] 1 e kt Need to consider value of P alveoli P alveoli =(P ambient P H2O P CO2 + P O2 ) Q P alveoli = P ambient P H2O + 1 RQ RQ P CO2 Q where Q=fraction of dissolved gas in atmosphere ΔP O2 =change in ppo2 due to metabolism 18

19 Linearly Varying Pressure Solution Assume R is the (constant) rate of change of pressure - solution of dissolved gases PDE is P t (t) =P alv0 + R t This is known as the Schreiner equation For R=0 this simplifies to Haldane equation Produces better time-varying solutions than Haldane equation Easily implements in computer models 1 k P alv0 P t0 R k e kt 19

20 Tissue Saturation following Descent 20

21 Tissue Saturation after Ascent 21

22 Effect of Multiple Tissue Times 22

23 Haldane Tissue Models Rate coefficient frequently given as time to evolve half of dissolved gases: T 1/2 = ln (2) k k = ln (2) T 1/2 Example: for 5-min tissue, k= min -1 Haldane suggested five tissue compartments : 5, 10, 20, 40, and 75 minutes Basis of U. S. Navy tables used through 1960 s Three tissue model (5 and 10 min dropped) 1950 s: Six tissue model (5, 10, 20, 40, 75, 120) 23

24 Workman Tissue Models Dr./Capt. Robert D. Workman of Navy Experimental Diving Unit in 1960 s Added 160, 200, 240 min tissue groups Recognized that each type of tissue has a differing amount of overpressure it can tolerate, and this changes with depth Defined the overpressure limits as M values 24

25 Workman M Values Discovered linear relationship between partial pressure where DCS occurs and depth M=partial pressure limit (for each tissue compartment) M 0 =tissue limit at sea level (zero depth) ΔM=change of limit with depth (constant) d=depth of dive M = M 0 + Md Can use to calculate decompression stop depth d min = P t M 0 M 25

26 PADUA (Univ of Penn.) Tissue Model Tissue T 1/2 (minutes) M 0 (bar)

27 Bühlmann Tissue Models Laboratory of Hyperbaric Physiology at University Hospital, Zurich, Switzerland Developed techniques for mixed-gas diving, including switching gas mixtures during decompression Showed role of ambient pressure on decompression (diving at altitude) Independently developed M-values, based on absolute pressure rather than SL depth Zurich 12 and 16-tissue models widely used 27

28 Bühlmann M-Value Models Modifies Workman model by not assuming sea level pressure at water s surface M = P amb b P amb =pressure of breathing gas + a b=ratio of change in ambient pressure to change in tissue pressure limit (dimensionless) a=limiting tissue limit at zero absolute pressure ZH-L16 model values for a and b a =2T 1 3 1/2 < bar > b =1.005 T 1 2 1/2 28

29 Physics of Bubbles Pressure inside a bubble is balanced by exterior pressure and surface tension P internal = P ambient + P surface = P ambient + 2 r where γ=surface tension in J/m 2 or N/m (=0.073 for water at 273 K) Dissolve gas partial pressure P g =P amb in equilibrium Gas pressure in bubble P int >P amb due to γ All bubbles will eventually diffuse and collapse 29

30 Critical Bubble Size Minimum bubble size is defined by point at which interior pressure P int = gas pressure P g r min = P g r<r min - interior gas diffuses into solution and bubble collapses r>r min - bubble will grow r=r min - unstable equilibrium 2 p ambient 30

31 Bubble Formation and Growth In equilibrium, external pressure balanced by internal gas pressure and surface tension Surface tension forces inversely proportional to radius 31

32 Clinical Discussion of DCS Tissue models are predictive, not definitive Every individual is different Overweight people more susceptible to DCS Tables and models are predictive limits - there will be outliers who develop DCS while adhering to tables Doppler velocimetry reveals prevalence of bubbles in bloodstream without presence of DCS symptoms - asymptomatic DCS 32

33 Implications of DCS in Space Flight Drop from sea level pressure to ~4 psi, 100% O2 pressure Equivalent to ascent from fully saturated 120 ft dive Launch in early space flight Extravehicular activity from shuttle or ISS R = P N2 = 14.7(0.78) P amb 4 =2.87 To have safe (R=1.4) EVA from shuttle requires suit pressure of 8.2 psi 33

34 Current Denitrogenation Approaches Depress to 10.2 psi for hours prior to EVA Full cabin depress in shuttle Campout in air lock module of ISS Exercise while breathing 100% O2 In-suit decompression on 100% O2 (3.5-4 hours) 34

35 Historical Data on Cabin Atmospheres from Scheuring et. al., Risk Assessment of Physiological Effects of Atmospheric Composition and Pressure in Constellation Vehicles 16th Annual Humans in Space, Beijing, China, May

36 Spacecraft Atmosphere Design Space from Scheuring et. al., Risk Assessment of Physiological Effects of Atmospheric Composition and Pressure in Constellation Vehicles 16th Annual Humans in Space, Beijing, China, May

37 Effect of Pressure and %O 2 on Flammability from Hirsch, Williams, and Beeson, Pressure Effects on Oxygen Concentration Flammability Thresholds of Materials for Aerospace Applications J. Testing and Evaluation, Oct

38 Atmosphere Design Space with Constraints from Scheuring et. al., Risk Assessment of Physiological Effects of Atmospheric Composition and Pressure in Constellation Vehicles 16th Annual Humans in Space, Beijing, China, May

39 EVA Denitrogenation psi Cabin Tissue&Nitrogen&Pressure&(psi)& 14.0# 12.0# 10.0# 8.0# 6.0# 4.0# 2.0# 0.0# Cabin Atmosphere 14.7 psi 21% O2 R Value = 1.4 Suit Pressure 4.3 psi 100% O2 0# 200# 400# 600# 800# 1000# 1200# Time&(min)& 5*min#.ssue# 80*min#.ssue# 240*min#.ssue# 39 Decompression/Neurovestibular Physiology

40 EVA Denitrogenation psi Cabin Tissue&Nitrogen&Pressure&(psi)& 6.0# 5.0# 4.0# 3.0# 2.0# 1.0# 0.0# R Value = 1.4 Suit Pressure 4.3 psi 100% O2 Cabin Atmosphere 8.3 psi 32% O2 0# 200# 400# 600# 800# 1000# 1200# Time&(min)& 5+min#/ssue# 80+min#/ssue# 240+min#/ssue# 40 Decompression/Neurovestibular Physiology

41 Constellation Spacecraft Atmospheres from Scheuring et. al., Risk Assessment of Physiological Effects of Atmospheric Composition and Pressure in Constellation Vehicles 16th Annual Humans in Space, Beijing, China, May