Independent StudyAtmospheric Effects on Aircraft Gas Turbine Life

Humidity SectionRevised May 23, 2011

Kevin Roberg

Contents:• Introduction• Atmospheric Composition• Atmospheric Structure• Standard Model of the Atmosphere• Sample Altitude Model Result• Measures of Humidity• Humidity Relationships• Virtual Temperature• Water Vapor Distribution• References

It is said in New England “Don’t like the weather? Wait a minute, it will change.” This is in fact true in the majority of locations on earth. It is also true that change can be found in any direction, including up.

This study examines the effect of atmospheric conditions on the life of aircraft gas turbines. It is impractical, if not impossible, to model the instantaneous structure of the atmosphere during every flight in the life of an engine. Fortunately, it is possible to describe an average atmosphere which, over the course of many flights and a long period of time, closely resembles the environment experienced in operation.

The relationships developed in this study describe average conditions. They will rarely, if ever, correctly describe instantaneous conditions exactly. Where there structure of the atmosphere can consistently differ from the average, such as a ground level inversion present each morning or evening, these effects are described.

Symbol Name Molecular Weight Volume FractionFractional Molecular Weight

N2 Nitrogen 28.01 78.0821.870208

O2 Oxygen 32 20.95 6.704Ar Argon 39.95 0.93 0.371535

Ne Neon 20.18 0.00180.0003632

He Helium 4 0.0005 0.00002H2 Hydrogen 2.02 0.00005 1.01E-06

Xe Xenon 131.3 0.0000091.182E-05

CO2 Carbon dioxide 44.01 0.0350.0154035

CH4 Methane 16.04 0.00017 2.727E-05

N2O Nitrous Oxide 44.01 0.000031.32E-05

CO Carbon Monoxide 28.01 0.00350.0009804

SO2 Sulfur Dioxide 64.06 0.0000148.968E-06

O3 Ozone 48 0.0000125.76E-06

NO2 Nitrogen Dioxide 46.01 0.0000052.301E-06

Totals 100.00 28.96

Atmospheric Composition

• Individual gasses may be analyzed using partial pressure (Dalton’s Law)• Water Vapor may be 0-4% by Volume

The earth’s atmosphere is divided into distinct layers delineated by temperature extremes. Beginning at the ground where temperatures are warmest, with energy being derived from absorption of visible light. Temperature decreases with distance from the ground until the stratosphere is reached. Temperature increases through the stratopause until the level where most ultraviolet light is absorbed, the stratopause. After passing the stratopause temperature again declines through the mesosphere, until entering the troposphere where most other radiation is absorbed.

The troposphere is the portion of the atmosphere nearest the ground in which nearly all clouds and weather occur. The temperature of the troposphere decreases linearly with altitude. The top portion of the troposphere is the tropopause. Within the tropopause temperature is constant. The transition from troposphere nominally occurs at a height of 11 km. The tropopause continues to a height of 20 km. Since aircraft activity using gas turbines is generally confined to altitudes well below 20 km only the tropopause and troposphere will be considered in this study.

(Refer to page 13 of Stull for additional detail)

Atmospheric Structure

Aircraft generally operate within the troposphere and tropopause. Conditions within these portions of the atmosphere can be modeled using:

Troposphere (T>216.65 K)

Where:

is a constant so the P is equal to sea level pressure at seal level (101.325kPa for standard conditions).

Standard Model of the Atmosphere

𝑇=𝑇 𝑠𝑙−(6.5 𝐾𝑘𝑚 ) ∙𝐻

𝑃=𝑃𝑎𝑑𝑗 ∙ ( 288.15𝐾𝑇 )−5.255877

is a sea level temperature (288.15K for standard conditions)

(Refer to companion paper for development of these equations)

The value is the temperature lapse rate, which on average is constant regardless of location and season (Dutton). As discussed on the previous slide, it may be far from constant at any given time due to inversions or other weather phenomena.

These equations are applicable for most day and night conditions but at night, in cases where the surface is cooler than that atmosphere, such as winter or marine conditions temperature may increase with altitude briefly before resuming the normal stratospheric pattern. Such a situation is termed an inversion. (Dutton)

Standard Model of the Atmosphere

𝐻=216.65𝐾

𝑇 𝑠𝑙−(6.5 𝐾𝑘𝑚 )

Temperature is constant within the tropopause. The tropopause begins when the troposphere reaches the tropopause temperature.

Tropopause (T=216.65 K)

Height (H) at which the tropopause begins

Where:

𝑃=𝑃𝑡𝑝 ∙𝑒

−0.1577 ∙(𝐻− 216.65𝐾

𝑇 𝑠𝑙−(6.5 𝐾𝑘𝑚 ))

is the pressure of the troposphere when the temperature is 216.65K (22.632kPa for standard conditions)

Sample Altitude Model Result

-1 1 3 5 7 9 11 13 150

20

40

60

80

100

120

-0.5

0

0.5

1

1.5

2

2.5

Atmospheric Pressure by Altitude Adjusted to Sea Level Actual

0°C15°CDivergence

Altitude (km)

Pres

sure

(kPa

)

Dive

rgen

ce (k

Pa)

Note that the divergence between temperatures increases until reaching the 0 degree C tropopause. At this point a small artifact of the model is evident, and pressures begin to converge.

Measures of Humidity

Relative Humidity: The amount of water in the atmosphere compared with the saturation level.

• 0% is not water vapor• 100% is maximum water vapor for current temperature.

Dew Point: The temperature at which the current amount of water in the atmosphere will reach saturation.

• Can be measured by chilling a mirror until dew forms

Partial Pressure: The portion of atmospheric pressure contributed by water vapor

Absolute Humidity: The mass of water vapor in a given volume (density).

Mixing Ratio: The ratio of the mass of water to the mass of air in the atmosphere.• Useful quantity for ideal gas law calculations

Humidity Relationships:

𝑅𝐻100%

= 𝑒𝑒𝑠

=𝜌 𝑣

𝜌𝑠≈ 𝑟𝑟 𝑠

𝑒=0.611𝑘𝑃𝑎∙𝑒𝑥𝑝 [0.611𝑘𝑃𝑎 ∙ (𝑇 −273.16 𝐾 )𝑇 −35.86𝐾 ]

𝜌𝑣=𝑒

ℜ 𝑣 ∙𝑇=𝑒𝑃 𝜀 ∙𝜌𝑑

𝑟=𝜀 ∙𝑒𝑃−𝑒

𝜀=ℜ𝑑

ℜ 𝑣=0.622

is partial pressure is absolute humidity

is mixing ratio

(Equations from Stull pages 98-99)

is the gas constant of dry air:

is the gas constant of water vapor:

All subscripts indicate the saturation condition

is the density of dry air

Virtual Temperature:

Water vapor (mol. weight 18) is less dense than dry air (mol. weight 28.96). Meteorologists account for the reduction in overall molecular weight by including a virtual temperature in ideal gas calculations:

Thus humid air acts like hotter air.

(Stull p. 8)

Water Vapor Distribution:

• In the actual atmosphere the water vapor distribution with increasing altitude cannot be predicted using an equation.

• By averaging over a period of time relative humidity can be assumed to be constant up to the tropopause.

• At the tropopause water content is negligible.

Instantaneous (Chiang, et al) Averaged (Tomasi, et al)

In a still atmosphere with no precipitation the amount of water, measured either by absolute humidity or mixing ratio, will remain stable throughout daily temperature variations. If local temperature drops below the dew point, dew will form. In cases when inversions occur due to a relatively cool surface, low lying fog may form though moisture remains in vapor form at higher elevations.

Daily Variation:

References:

Chiang, C.-W., & Subrata Kumar Das, J.-B. N.-x.-l. (2009, August). Simultaneous measurement of humidity and temperature in the lower troposphere over Chung-Li, Taiwan. Journal of Atmospheric and Solar-Terrestrial Physics, 71(12), 1389-1396.

Dutton, J. A. (1986). The Ceaseless Wind. Mineola, New York, United States of America: Dover Publications

Stull, R. B. (2000). Meteorology for Scientists and Engineers (2nd ed.). Belmont, CA, USA: Brooks/Cole.

Tomasi et al, C. (2004). Mean vertical profiles of temperature and absolute humidity from a 12-year radiosounding data set at Terra Nova Bay (Antarctica). Atmosperic Research(71), 139-161.