Effect of Atmospheric Pressure on Wet Bulb Depression Raymond M. Wheeler, Michael A. Stasiak, Jamie Lawson, Cara Ann P. Wehkamp, and Michael A. Dixon NASA Biological Sciences Office Kennedy Space Center, Florida, USA Department of Environmental Biology University of Guelph Guelph, Ontario, Canada
Reduced Pressures for Space Missions? • Reduced gas leakage and hence reduced resupply costs • Reduced structural mass • Increased potential for finding transparent materials for space “greenhouses” • Rapid egress for EVAs (spacewalks) without prolonged prebreathing and acclimation ------------------- • How do environmental sensors perform at reduced pressures?
Effect of Pressure on Saturation Vapour Pressure (Rygalov et al., 2004, NASA Ken Space Center , FL ) 5 Saturation Pressure (kPa) 30°C 4 25°C 3 2 15°C 1 0 0 20 40 60 80 100 120 Total Pressure (kPa) Steam table values for e s : 30ºC = 4.24 kPa; 25ºC = 3.17 kPa; 15ºC = 1.70 kPa (Kennan, Keyes, et al., 1978)
Different Equations for Calculating Saturation Water Vapour Pressures Magnus Teten (Murray, 1967) Goff-Gratch (1946) / and Smithsonian Tables (1984) Log10 p w = 7.5 t / ( t +237.3) + 0.7858 with t in [°C] and p w in [hPa] Log 10 p w = -7.90298 (373.16/ T -1) + 5.02808 Log 10 (373.16/ T ) Buck (1981, 1996) - 1.3816 10 -7 (10 11.344 (1- T /373.16) -1) + 8.1328 10 -3 (10 -3.49149 (373.16/ T -1) -1) p w = 6.1121 e(18.678 - t / 234.5) t / (257.14 + t ) + Log 10 (1013.246) [1996] p w = 6.1121 e17.502 t / (240.97 + t ) with T in [K] and p w in [hPa] [1981] with t in [°C] and p w in [hPa] Hyland and Wexler (1983) Sonntag (1994) Log p w = -0.58002206 10 4 / T Log p w = -6096.9385 / T + 0.13914993 10 1 - 0.48640239 10 -1 T + 16.635794 + 0.41764768 10 -4 T 2 - 2.711193 10-2 * T - 0.14452093 10 -7 T 3 + 1.673952 10-5 * T 2 + 0.65459673 10 1 Log( T ) + 2.433502 * Log( T ) with T in [K] and p w in [hPa] with T in [K] and p w in [Pa]
→ All of these equations are related to saturation pressure of pure water vapour, but water vapour in air does not behave as a completely ideal gas and a corrections are required. Buck (1981) Equation : 17.502 T e’ s =( f ) 6.1121 exp 240.97 + T Where f = the “enhancement factor” for calculating vapor pressure of moist air instead of pure water vapor. Buck (1981) J. Appl. Meteorol. 20:1527-1532.
"' ~ ~ ·" _ ~ _ "I I ~ ~ ...... • • ................ I. ·25 ........ ' .. 1 0 kPa -''I ...... .. ..... 1. 2 I. t5 50 . kPa - , • . .. 20 . kP . , . , . , '" -- - i ., I. . 05 .. -r---. .. . 10 kP:::I . I t- _ _ . .. _ _ • I -_ .. ,- _ •• -- ._ ., _ .. . _- - L _· , · .. • .... . .. _L . t.- . ... ., .. . N .. • _ I.. 0 o Effect of temperature and pressure on enhancement factor for correcting moist air properties to that of pure water vapor. From: D.C. Shallcross. 2005. Intl. J. Heat and Mass Transfer 48:1785-1796.
Effects of Pressure on Evaporation Rates (Rygalov et al., 2004) 16 Evaporation Rate (L m -2 d -1 ) 14 Relative Humidity 12 95% 10 65% 8 50% 6 4 2 0 0 25 50 75 100 Pressure (kPa) → Related to increased gas diffusion rates at reduced pressures
Diffusion Coefficient ( D v ) of Water Vapour at 25ºC 600 Fick's Law for Molecular Diffusion: Diffusion Coefficient D v (mm -2 s -1 ) 500 J B = -C D v [d(C B /C)/dy] where D v is the mass diffusivity or the “diffusion coefficient” 400 and D v = (0.926/P)[T 2.5 /(T+245)] 300 200 100 0 0 20 40 60 80 100 120 Pressure (kPa)
If evaporation rates increase at reduced pressures….. then wet-bulb (WB) depression should also increase.
Psychrometric Equation using Wet Bulb Temperature e s ’ = e + γ (T db – T wb ) γ = the psychrometric constant where γ = p A with p = pressure and A ≈ 6.53 x 10 -4 K -1 for average size thermometers and aspiration rate of 4 m s -1 But e s ’ is saturation vapour pressure at the wet bulb temperature ! Thus this equation can’t be used the to solve directly for Twb .
~) .O~) . D ti O L.i U ~ :'V .O~ .O ~ ) ~ @~ b ~ .O ~ ) WATER t\ - UJ ~S ~ p 1 ARTIAN ATMOSPHERE SYSTEM 50.0 kPo. A. I'/:j ... . OBO If i V k.."%, 1 BO .osa : y.. If ,· HO En l!: uL lp y da bJm : liq u.id wnl:e r 0.00 -C . .6 11 k PD. I il . / I " .' : dry Martian t lOO s ph . 0.00 "C. 1 U k PD. @r@ .054 1 60 . .052 T Martian t1lmosp co mpo sition : C'O:l 9 5.4 9 mol % .048 .049 '" HO m l . .0oU ;;; .c L 60 mol <>. .042 g 3 mol > 1 .04) co are mol , , .oaa v . " .038 . f! , y , To OOtal D o:> e ntb. : il Pl ' iJd d . e ntb. : 11 p}' lru_ .OM ~ : de ,,·jiluan L o entbil'lp)' lilt I ~ .' I .032 2:- 'C .2' . 01l3 9 .OM .024 ~ .022 'iii E ::J .c .018 J! '" .01 8 ] .014 . ..: .012: .010 .oos .008 .004 ". ". '. '. I ' " '", o 10 80 40 Dry to lb tempera:lUre (" C) Psychometric chart for water vapor in Martian atmosphere brought to 50 kPa pressure. From: D.C. Shallcross. 2005. Intl. J. Heat and Mass Transfer 48:1785-1796.
Themodynamic Wet Bulb Temperature vs. Pressure (at 25 º C Dry Bulb in Air and Martian Atmosphere) 25.0 70% RH 20.0 50% RH Temperature ( º C) 30% RH 15.0 Open Symbols -- 10.0 Air ( 78% N 2 21% O 2 ) (MW = 28.96) 5.0 Solid Symbols -- Martian Atmosphere (95% CO 2 ) ( MW = 43.23) (from Shallcross 1997; 2005) 0.0 0 50 100 150 200 Pressure (kPa)
o C 1~ 1~ 1 ~ ~ l e 1 ~2 ~ 2 +~ ~ ~ ~ 2 ~ ~;g;~2~ 1 1 ~ ~l ~ O ~ 1~ ~ - ~ '~l ~ 4 ~t~ ~7 ~ 14 ~ Psychrometric Chart for Pressure using “Composite” Thermodynamic Properties 4.5 "::]-.N:-:.!?"""" 2!J 27 24 • 23 35 3 ~ m !I!lIiIl!!I!!!I!!!I!II!i!!i1I!!llIlIiillilllillili .D 1 25 - GI ..., 0... 0) C:i: ;: 13 2 12 11 -.l '><""l '" 10 1.5 9 6 o -10 -8 0 2 01 B 10 14 1·8 22 2-" 26 30 32 3& 3D dd "6 46 SO -6 -4 0; <0 2:0; H.-S. Ren. 2004. Construction of a generalized psychrometric chart for different pressures. J. Mech. Eng. Ed. 32(3):212-222.
kP ~ r~ ~ . 1 L~ O~! I~ I~ ~ Composite Psychrometric Chart Nomograph ,IP, p, Pro · baf l D. Il IlP 01 I , I ~ OHo o OJ , . Q , 01- O! 12 011 ! H.-S. Ren. 2004. Construction of a generalized psychrometric chart for different pressures. J. Mech. Eng. Ed. 32(3):212-222.
Thermodynamic Wet Bulb Temperature vs. Pressure (at Dry Bulb of 25ºC) Relative Humidity 25 90% Temperature (ºC) 70% 20 50% 15 30% Data estimated from "Composite“ Psychrometric Charts Ren (2004) 10 40 50 60 70 80 90 100 110 Pressure (kPa)
Our objective was to directly measure wet bulb depression at different pressures and compare our results published psychrometric models for pressure effects.
Experimental Approach •Measure wet bulb temperatures five different pressures and three different relative humidities: –Pressures: 10, 20, 50, 80, and 100 kPa –Relative Humidities: 30, 50, and 70% Each combination allowed to equilibrate for at least 90 minutes, then a 30-min segment of data was averaged for WB, DB, Dew Point, Chamber Air Temperature, Chamber RH, and Water Temperature
Hypobaric Test Chamber University of Guelph, CESF
Environmental Monitoring and Control: • Wet Bulb / Dry Bulb – Enercorp Model HT-WD-A Psychrometer •Two matched platinum RTD temperature probes •Constant aspiration -- 3 m s -1 • Humidity Control – Honeywell Model HIH-3602-A Capacitance Sensors (2) • Temperature Control –Argus TN 21 Thermisters (2) • Dew Point Measurements – General Eastern Model 1100DP (1) • Humidity Calibration / Comparison (at 100 kPa) –Vaisala HMP42 Handheld RH/Temp Probe • Pressure Monitoring / Control – MKS ‘Barotron’ Capacitance Manometer • Water temperature for the psychrometer reservoir
Wet / Dry Psychrometer Enercorp Inst. Ltd. (Model HT-WD-A) Signal Transmitter Exhaust Air Inlet Fan Tube with Cotton Wick Water Reservoir RTD Temp Probe
Wet Bulb Measurements versus Atmospheric Pressure 25 Dry Bulb Temp. = 25 ° C y = 0.826 Ln(x) + 16.64 2 = 0.722 R 70% RH 20 y = 1.593 Ln(x) + 10.23 Temperature (ºC) 2 = 0.976 R 15 50% RH y = 3.002 Ln(x) + 1.349 2 = 0.993 R 10 30% RH 5 Filled symbols represent our Wet Bulb measurements; Open symbols are adiabatic saturation temperatures from Shallcross (1997, 2005) and Ren (2004) (red triangles). 0 0 20 40 60 80 100 120 Pressure (kPa)
Conclusions • Our measurements of wet bulb depression at different pressures matched the modeled adiabatic saturation temps reasonably well. • At a dry bulb temp of 25 ° C, the normal wet bulb temp for 30% RH and 100 kPa is ~15 ° C, but this dropped to ~8 ° C at 10 kPa. • The results suggest that psychrometers need direct calibration at the target pressures or that pressure corrected charts are required. • For a given vapour pressure deficit, any moist surfaces, including transpiring plant leaves, will be cooler at lower pressures due to the increased evaporation rates.
Thanks to the CESRF Team at University of Guelph Mike Stasiak Jamie Lawson
Questions ? Welcome to Florida !
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