Independent Study
Atmospheric Effects on Aircraft Gas Turbine Life
Humidity Section
Revised 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.
Atmospheric Composition
Symbol
Name
N2
Nitrogen
O2
Oxygen
Ar
Molecular Weight
Fractional Molecular
Weight
Volume Fraction
28.01
78.08
32
20.95
Argon
39.95
0.93
Ne
Neon
20.18
0.0018
He
Helium
H2
Hydrogen
Xe
21.870208
6.704
0.371535
4
0.0005
0.0003632
0.00002
2.02
0.00005
1.01E-06
Xenon
131.3
0.000009
CO2
Carbon dioxide
44.01
0.035
CH4
Methane
16.04
0.00017
N2O
Nitrous Oxide
44.01
0.00003
CO
Carbon Monoxide
28.01
0.0035
SO2
Sulfur Dioxide
64.06
0.000014
O3
Ozone
48
0.000012
NO2
Nitrogen Dioxide
46.01
0.000005
Totals
100.00
1.182E-05
0.0154035
2.727E-05
1.32E-05
0.0009804
8.968E-06
5.76E-06
2.301E-06
28.96
• Individual gasses may be analyzed using partial pressure (Dalton’s Law)
• Water Vapor may be 0-4% by Volume
Atmospheric Structure
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)
Standard Model of the Atmosphere
Aircraft generally operate within the troposphere and tropopause.
Conditions within these portions of the atmosphere can be modeled using:
Troposphere (T>216.65 K)
𝐾
𝑇 = 𝑇𝑠𝑙 − (6.5𝑘𝑚
)∙𝐻
288.15𝐾
𝑃 = 𝑃𝑎𝑑𝑗 ∙
𝑇
−5.255877
𝐾
The value 6.5 𝑘𝑚
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.
Where:
𝑇𝑠𝑙 is a sea level temperature (288.15K for standard conditions)
𝑃𝑎𝑑𝑗 is a constant so the P is equal to sea level pressure
at seal level (101.325kPa for standard
conditions).
(Refer to companion paper for development of these equations)
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
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
𝐻=
216.65𝐾
𝐾
𝑇𝑠𝑙 − 6.5𝑘𝑚
𝑃 = 𝑃𝑡𝑝 ∙
216.65𝐾
−0.1577∙ 𝐻−
𝐾
𝑇𝑠𝑙 − 6.5𝑘𝑚
𝑒
Where:
𝑃𝑡𝑝 is the pressure of the troposphere when the temperature is 216.65K
(22.632kPa for standard conditions)
Sample Altitude Model Result
2.5
100
2
Pressure (kPa)
120
80
1.5
60
1
40
0.5
20
0
0
-1
Divergence (kPa)
Atmospheric Pressure by Altitude Adjusted to Sea Level
Actual
0°C
15°C
Divergence
-0.5
1
3
5
7
9
11
13
15
Altitude (km)
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:
𝑅𝐻
𝑒
𝜌𝑣 𝑟
= =
≈
100% 𝑒𝑠 𝜌𝑠 𝑟𝑠
All 𝒔 subscripts indicate the saturation condition
𝑒 is partial pressure
𝜌𝑣 is absolute humidity
𝑟 is mixing ratio
𝑒 = 0.611𝑘𝑃𝑎 ∙ 𝑒𝑥𝑝
𝜌𝑣 =
0.611𝑘𝑃𝑎 ∙ 𝑇 − 273.16𝐾
𝑇 − 35.86𝐾
𝑒
𝑒
= 𝜀 ∙ 𝜌𝑑
ℜ𝑣 ∙ 𝑇 𝑃
ℜ𝑑
𝜀=
= 0.622
ℜ𝑣
𝜌𝑑 is the density of dry air
ℜ𝑑 is the gas constant of dry air: 0.287053 𝑘𝑃𝑎 ∙ 𝐾 −1 ∙ 𝑚3 ∙ 𝑘𝑔−1
ℜ𝑣 is the gas constant of water vapor: 0.4615 𝑘𝑃𝑎 ∙ 𝐾 −1 ∙ 𝑚3 ∙ 𝑘𝑔−1
𝜀∙𝑒
𝑟=
(Equations from Stull pages 98-99)
𝑃−𝑒
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:
𝑇𝑣 = 1 + 0.61 ∙ 𝑟 𝑇 (Stull p. 8)
Thus humid air acts like hotter air.
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)
Daily Variation:
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.
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 SolarTerrestrial 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.