Effect of Atmospheric 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 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

4 30°C

25°C 3

2 15°C 1

Saturation Pressure (kPa) Saturation Pressure 0 0 20 40 60 80 100 120

Total Pressure (kPa)

Steam table values for es: 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 pw = 7.5 t / (t+237.3) + 0.7858 with t in [°C] and pw in [hPa] Log10 pw = -7.90298 (373.16/T-1) + 5.02808 Log (373.16/T) 10 Buck (1981, 1996) - 1.3816 10-7 (1011.344 (1-T/373.16) -1) + 8.1328 10-3 (10-3.49149 (373.16/T-1) -1) + Log (1013.246) pw = 6.1121 e(18.678 - t / 234.5) t / (257.14 + t) 10 [1996] p = 6.1121 e17.502 t / (240.97 + t) with T in [K] and pw in [hPa] w [1981] with t in [°C] and pw in [hPa] Hyland and Wexler (1983) Sonntag (1994) 4 Log pw = -0.58002206 10 / T 1 + 0.13914993 10 Log pw = -6096.9385 / T - 0.48640239 10-1 T + 16.635794 + 0.41764768 10-4 T2 - 2.711193 10-2 * T - 0.14452093 10-7 T3 + 1.673952 10-5 * T2 + 0.65459673 101 Log(T) + 2.433502 * Log(T) with T in [K] and p in [hPa] with T in [K] and pw in [Pa] w → 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. ·25 ...... ' .. 1 0 kPa

-''I ...... 1. 2

I. t5 ~ ~5 0 .kPa ~ - , •. 20 .kP .. . , . , '" . , -- - i ., I.. 05

·"~"'It- _ _ I_~_"I. .. _ _ • I 10 kP:::I. -_. . ,-_• •-- ._., .. -r---...... , .. . N .. • _ _ .. . _- - L_· , · .. • ...... _L. t.- I.. 0 o

Effect of 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 ) -1

d 14 Relative -2 12 Humidity

10 95%

8 65%

6 50%

4 poration Rate (L m 2 Eva 0 0 25 50 75 100

Pressure (kPa)

→ Related to increased gas rates at reduced pressures Diffusion Coefficient (Dv) of Water Vapour at 25ºC

600

Fick's Law for : ) -1 s 500 JB = -C Dv [d(CB/C)/dy] -2

where Dv is the mass diffusivity

(mm or the “diffusion coefficient”

v 400

D 2.5 and Dv = (0.926/P)[T /(T+245)]

300 Coefficient n 200 Diffusio 100

0 020406080100120 Pressure (kPa) If evaporation rates increase at reduced pressures….. then wet-bulb (WB) depression should also increase. Psychrometric Equation using Wet Bulb Temperature

es’ = e + γ (Tdb –Twb ) 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 ’ is saturation vapour pressure at the wet bulb temperature ! s Thus this equation can’t be used the to solve directly for T . wb WATER-~1ARTIANATMOSPHERE SYSTEM

~) 50.0 kPo. p~SSUJt\ .OBO 1 BO i ... A. I'/:j If V k.."%, .osa HO : y.. l!:uL bJm u.id wnl:e .611 PD. ~ :'V If En lpy da : liq r 0.00 -C. k ,· .O~ / I " .' : il . I dry Martian tlOOsph.@r@ 0.00 "C. 1 U kPD. 160 . .054 .052 T Martian t1lmospb@~ composition : .O~) C'O:l 95.49 mol % .048 .049 ~ HO m l . ;;;'" .0oU .c L 60 mol <>. .042 13 mol > .04) g co are mol , .oaa ~ v . , " , .038 .f! To OOtalD lru_o:>e ntb.:il Pl' iJdd. entb.:11p} ' y : , .OM ~ de,,·jiluan Lo entbil'lp)' lilt I~UL.itiOD. .' I .032 2:- 'C .O~) .2' .OM .01l3 9 .024 ~ 'iii .022 E ::J .O~) .c .018 J! .01 8 ]'" .014 ...: .012: .010 .oos .008 .004 '. ". ". I '. ' " '", o 10 80 40

Dry tolb 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 25ºC Dry Bulb in Air and Martian Atmosphere)

25.0

70% RH

20.0 50% RH

30% RH C) º 15.0

Open Symbols -- 10.0 Air ( 78% N2 21% O2 ) Temperature ( (MW = 28.96)

5.0 Solid Symbols -- Martian Atmosphere (95% CO2 ) ( MW = 43.23) (from Shallcross 1997; 2005) 0.0 0 50 100 150 200 Pressure (kPa) Psychrometric Chart for Pressure using “Composite” Thermodynamic Properties

4.5 "::]-.N:-:.!?"""" 2!J ~;;g;~~~~2~ 27 ~

2~ • 24 23 35 +~~~ 22

~~~~~2 1

3

1~

~ m ~~~~ 11 .D GI 25 - 1!I!lIiIl!!I!!!I!!!I!II!i!!i1I!!llIlIiillilllillili~~~~~ 1l~e~ 0... ~ ..., 1~ 0) C:i: ;: '~~~~~~~l14~ 13 2 12

11 -.l '><""l '" 10 1.5 9 6 ~~~~~~~~~7

~~~~~~t~~~ 4

o ~ -10 -8 -6 -4 -~ 0 2 01 0; B 10 1~ 14 1~ 1·8 <0 22 2-" 2:0; 26 30 32 ~ 3& 3D ~O ~l dd "6 46 SO

~oC

H.-S. Ren. 2004. Construction of a generalized psychrometric chart for different pressures. J. Mech. Eng. Ed. 32(3):212-222. Composite Psychrometric Chart Nomograph

p, Pro· ,IP, l ~ kP~ baf

r~ I~ D.

Il

I~

IlP 01 I , OHo I ~

O~!

o L~

OJ , .

Q , 01-

O! 12 ~.1

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% C) 70% 20

Temperature (º 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 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, , 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 25 Dry Bulb Temp. = 25°C y = 0.826 Ln(x) + 16.64 R 2 = 0.722 70% RH 20

y = 1.593 Ln(x) + 10.23 R 2 = 0.976 15 ature (ºC) r 50% RH y = 3.002 Ln(x) + 1.349 R 2 = 0.993 10 Tempe

5 30% RH Filled symbols represent our Wet Bulb measurements; Open symbols are adiabatic saturation temperatures from Shallcross (1997, 2005) and Ren (2004) (red triangles).

0 020406080100120 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 ! Wet Bulb Temperature vs. Adiabatic Saturation Temperature

Wet Bulb Temperature: The temperature of a sensor covered with pure water that is evaporating freely into the ambient air stream. Typically taken with a “matched” dry bulb (DB) reading under constant aspiration (3-5 m s-1) and shielded from radiation. But WB readings can be affected by the aspiration rate, mass of the sensor, water temperature, properties of the wick, and water purity.

Adiabatic Saturation Temperature (also called Thermodynamic Wet Bulb Temperature): The thermodynamic state resulting from adiabatic saturation, where there is no heat or mass transfer involved, and is independent of the measurement technique. The Psychrometric Chart Averaged* Chart of Dynamic WB Temperature vs. Pressure

25.0 y = 0.897 Ln (x) + 16.88 ; R2 = 0.976

70% RH 20.0 y = 1.844 Ln (x) + 9.445 ; R2 = 0.980 C) º 15.0

y = 3.245 Ln (x) - 0.410 ; R2 = 0.992 50% RH

10.0 Temperature (

5.0 30% RH

0.0 0 50 100 150 200 250 Pressure (kPa)

Data for 12 and 20 kPa for CO2 (95%) atmosphere; 80, 140, and 200 kPa for air; 50 and 100 averaged for CO2 and air (Shallcross, 1997).