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 OfficeKennedy Space Center, Florida, USA

Department of Environmental BiologyUniversity 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)

0

1

2

3

4

5

Satu

ratio

n Pr

essu

re (k

Pa)

0 20 40 60 80 100 120

15°C

25°C

30°C

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

Goff-Gratch (1946) / and Smithsonian Tables (1984)

Log10 pw = -7.90298 (373.16/T-1)+ 5.02808 Log10(373.16/T) - 1.3816 10-7 (1011.344 (1-T/373.16) -1)

+ 8.1328 10-3 (10-3.49149 (373.16/T-1) -1) + Log10(1013.246)

with T in [K] and pw in [hPa]

Hyland and Wexler (1983)

Log pw = -0.58002206 104 / T+ 0.13914993 101

- 0.48640239 10-1 T+ 0.41764768 10-4 T2

- 0.14452093 10-7 T3

+ 0.65459673 101 Log(T) with T in [K] and pw in [Pa]

Magnus Teten (Murray, 1967)

Log10 pw = 7.5 t / (t+237.3) + 0.7858with t in [°C] and pw in [hPa]

Buck (1981, 1996)

pw = 6.1121 e(18.678 - t / 234.5) t / (257.14 + t) [1996] pw = 6.1121 e17.502 t / (240.97 + t)[1981] with t in [°C] and pw in [hPa]

Sonntag (1994)

Log pw = -6096.9385 / T+ 16.635794 - 2.711193 10-2 * T+ 1.673952 10-5 * T2

+ 2.433502 * Log(T) with T in [K] and pw in [hPa]

→ 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.

17.502 Te’s =( f ) 6.1121 exp

240.97 + T

Buck (1981) Equation:

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.

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.

...... •

•

I. ·25

1. 2

................ ........

' .. 1 0 kPa -''I ....... . .....

I. t5 ~ ~ 50 .kPa

~ - ,

•. .. 20 .kP . , . ,

'" I. . 05

. , -- - i .,

·" ~ "' I t- _ _ I _ ~ _ "I . .. _ _ • I 10 kP:::I. -_ .. ,-_ •• --._., . ... ., .. . N .. • _ _ .. . _- - L_· , · .. • .... . .. _L. t.-

.. - r---. .. .

I.. 0 o

Effects of Pressure on Evaporation Rates(Rygalov et al., 2004)

0

2

4

6

8

10

12

14

16

0 25 50 75 100

Pressure (kPa)

Evap

orat

ion

Rat

e

(L m

-2d-1

)

95%

65%

50%

RelativeHumidity

→ Related to increased gas diffusion rates at reduced pressures

Diffusion Coefficient (Dv) of Water Vapour at 25ºC

0

100

200

300

400

500

600

0 20 40 60 80 100 120

Pressure (kPa)

Diff

usio

n C

oeffi

cien

t Dv

(mm

-2s-1

) Fick's Law for Molecular Diffusion:

JB = -C Dv [d(CB/C)/dy]

where Dv is the mass diffusivityor the “diffusion coefficient”

and Dv = (0.926/P)[T2.5 /(T+245)]

If evaporation rates increase at reduced pressures…..

then wet-bulb (WB) depression should also increase.

Psychrometric Equationusing Wet Bulb Temperature

es’ = e + γ (Tdb – Twb )γ = the psychrometric constant

where γ = p Awith p = pressure and A ≈ 6.53 x 10-4 K-1 for average size

thermometers and aspiration rate of 4 m s-1

But es’ is saturation vapour pressure at the wet bulb temperature !

Thus this equation can’t be used the to solve directly for Twb

.

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.

WATER-~1ARTIAN ATMOSPHERE SYSTEM

50.0 kPo. p~SSUJt\

En l!:uLlpy dabJm : liq u.id wnl:er 0.00 -C. .6 11 kPD. dry Martian tlOOsph.@r@ 0.00 "C. 1 U kPD.

Martian t1lmospb@~ composition :

C'O:l 95.49 mol %

~ HO m l .

L 60 mol

13 mol >

co are mol ,

To OOtalD lru_o:> entb.:il Pl' iJdd. entb.:11 p}'

de,,·jiluan Lo entbil'lp) ' lilt I~U L.itiOD .

o

I

10

160

80

Dry tolb tempera:lUre ("C)

HO

'. '. ' "

~)

1 BO A. I'/:j If i V ... ~ :'V I f ,·

/ I " .' : il .

k.."%, .OBO

.osa : y.. I

.O~

.054 . T

.052

.O~)

.048

.049 '" .0oU ;;; .c

v . , y ,

.' : ,

I

<>. .042 g .04)

.oaa ~ " .038 .f!

.OM ~

.032 2:-

.O~) 'C

.2' .OM

.01l3 9

.024 ~

.022 'iii E

.O~) ::J .c

.018 J!

'" .018 ] .014 . ..: .012:

.010

.oos

.008

". ". .004

'",

40

Themodynamic Wet Bulb Temperature vs. Pressure(at 25ºC Dry Bulb in Air and Martian Atmosphere)

0.0

5.0

10.0

15.0

20.0

25.0

0 50 100 150 200

Pressure (kPa)

Tem

pera

ture

(ºC

)

Open Symbols --Air ( 78% N2 21% O2 )

(MW = 28.96)

(from Shallcross 1997; 2005)

Solid Symbols --Martian Atmosphere (95% CO2 )

( MW = 43.23)

70% RH

50% RH

30% RH

Psychrometric Chart for Pressure using “Composite” Thermodynamic Properties

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

~

m .D GI 0... ..., C:i: ;:

4.5

•

35

3

25 -

2

1.5

"::]-.N:-:.!?"""" 2!J

~;;g;~~~~2~ 27

~

2~

24

23

+~~~22

~~~~~21

1!I!lIiIl!!I!!!I!!!I!II!i!!i1I!!llIlIiillilllillili 1~ 1~

~~~~ 11

~~~~~le ~ ~

1~ 0)

'~~~~~~~l 14 ~

-.l '><""l '"

13

12

11

10

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

Composite Psychrometric Chart Nomograph

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

p, ~

I~

Il

I~

IlP 01 I ,

OHo

O~!

o L~

, . Q ,

01-

O! 12

011

Pro · kP~

r~

D.

I ~

~ .1

!

, IP, baf l

OJ

Thermodynamic Wet Bulb Temperature vs. Pressure(at Dry Bulb of 25ºC)

10

15

20

25

40 50 60 70 80 90 100 110

Pressure (kPa)

Tem

pera

ture

(ºC

)

Data estimated from "Composite“Psychrometric Charts Ren (2004)

Relative Humidity

90%

70%

50%

30%

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 90minutes, then a 30-min segment of data was averagedfor 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 PsychrometerEnercorp Inst. Ltd. (Model HT-WD-A)

Air Inlet

WaterReservoir

Exhaust Fan

SignalTransmitter

RTD TempProbe

Tubewith

CottonWick

Wet Bulb Measurements versus Atmospheric Pressure

y = 3.002 Ln(x) + 1.349R 2 = 0.993

y = 1.593 Ln(x) + 10.23R 2 = 0.976

y = 0.826 Ln(x) + 16.64R 2 = 0.722

0

5

10

15

20

25

0 20 40 60 80 100 120

Pressure (kPa)

Tem

pera

ture

(ºC

)

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

30% RH

50% RH

70% RH

Dry Bulb Temp. = 25°C

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

CESRFTeam at Universityof 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.

ThePsychrometric

Chart

Averaged* Chart of Dynamic WB Temperature vs. Pressure

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

y = 1.844 Ln (x) + 9.445 ; R2 = 0.980

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

0.0

5.0

10.0

15.0

20.0

25.0

0 50 100 150 200 250

Pressure (kPa)

Tem

pera

ture

(ºC

)

30% RH

50% RH

70% RH

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).