E1C08 09/14/2010
14:54:2 Page 363
One shield with an emissivity of 1 provides for an improvement over the case of no shields, but a
better choice of the surface characteristics of the shield material can result in much better
performance. If the shield has an emissivity of 0.1, the shield temperature rises to 756
C and
the probe temperature to 771
C.
COMMENT Shielding provides improved temperature measurements by reducing radiative
heat transfer. Another area for improvement in this temperature measurement could be the elevation
of the wall temperature through insulation. This discussion of radiation shielding serves to
demonstrate the usefulness of shielding as a means of improving temperature measurements in
radiative environments. As with conduction errors, the development should be used to guide the
design and installation of temperature sensors rather than to correct measured temperatures. Further
information on radiation errors may be found in Benedict (5).
Recovery Errors in Temperature Measurement
The kinetic energy of a gas moving at high velocity can be converted to sensible energy by reversibly
and adiabatically bringing the flow to rest at a point. The temperature resulting from this process is
called the stagnation or total temperature T t . On the other hand, the static temperature of the gas, T 1 , is
the temperature that would be measured by an instrument moving at the local fluid velocity. From a
molecular point of view, the static temperature measures the magnitude of the random kinetic energy of
the molecules that comprise the gas, while the stagnation temperature includes both the directed and
random components of kinetic energy. Generally, the engineer would be content with knowledge of
either temperature, but in high-speed gas flows the sensor indicates neither temperature.
For negligible changes in potential energy, and in the absence of heat transfer or work, the
energy equation for a flow may be written in terms of enthalpy and kinetic energy as
h 1 þ
U
2
2
¼ h 2
ð8:33Þ
where state 2 refers to the stagnation condition, and state 1 to a condition where the gas is flowing
with the velocity U. Assuming ideal gas behavior, the enthalpy difference h 2 À h 1 may be expressed
as c p T 2 À T 1
ð
Þ , or in terms of static and stagnation temperatures
U
2
2c P
¼ T t À T 1
ð8:34Þ
The term U
2
=2c p is called the dynamic temperature.
What implication does this have for the measurement of temperature in a flowing gas stream?
The physical nature of gases at normal pressures and temperatures is such that the velocity of the gas
on a solid surface is zero, because of the effects of viscosity. Thus, when a temperature probe is
placed in a moving fluid, the fluid is brought to rest on the surface of the probe. Deceleration of the
flow by the probe converts some portion of the directed kinetic energy of the flow to thermal energy,
and elevates the temperature of the probe above the static temperature of the gas. The fraction of the
kinetic energy recovered as thermal energy is called the recovery factor, r, defined as
r
T p À T 1
U
2
=2c p
ð8:35Þ
8.7 Physical Errors in Temperature Measurement 363
14:54:2 Page 363
One shield with an emissivity of 1 provides for an improvement over the case of no shields, but a
better choice of the surface characteristics of the shield material can result in much better
performance. If the shield has an emissivity of 0.1, the shield temperature rises to 756
C and
the probe temperature to 771
C.
COMMENT Shielding provides improved temperature measurements by reducing radiative
heat transfer. Another area for improvement in this temperature measurement could be the elevation
of the wall temperature through insulation. This discussion of radiation shielding serves to
demonstrate the usefulness of shielding as a means of improving temperature measurements in
radiative environments. As with conduction errors, the development should be used to guide the
design and installation of temperature sensors rather than to correct measured temperatures. Further
information on radiation errors may be found in Benedict (5).
Recovery Errors in Temperature Measurement
The kinetic energy of a gas moving at high velocity can be converted to sensible energy by reversibly
and adiabatically bringing the flow to rest at a point. The temperature resulting from this process is
called the stagnation or total temperature T t . On the other hand, the static temperature of the gas, T 1 , is
the temperature that would be measured by an instrument moving at the local fluid velocity. From a
molecular point of view, the static temperature measures the magnitude of the random kinetic energy of
the molecules that comprise the gas, while the stagnation temperature includes both the directed and
random components of kinetic energy. Generally, the engineer would be content with knowledge of
either temperature, but in high-speed gas flows the sensor indicates neither temperature.
For negligible changes in potential energy, and in the absence of heat transfer or work, the
energy equation for a flow may be written in terms of enthalpy and kinetic energy as
h 1 þ
U
2
2
¼ h 2
ð8:33Þ
where state 2 refers to the stagnation condition, and state 1 to a condition where the gas is flowing
with the velocity U. Assuming ideal gas behavior, the enthalpy difference h 2 À h 1 may be expressed
as c p T 2 À T 1
ð
Þ , or in terms of static and stagnation temperatures
U
2
2c P
¼ T t À T 1
ð8:34Þ
The term U
2
=2c p is called the dynamic temperature.
What implication does this have for the measurement of temperature in a flowing gas stream?
The physical nature of gases at normal pressures and temperatures is such that the velocity of the gas
on a solid surface is zero, because of the effects of viscosity. Thus, when a temperature probe is
placed in a moving fluid, the fluid is brought to rest on the surface of the probe. Deceleration of the
flow by the probe converts some portion of the directed kinetic energy of the flow to thermal energy,
and elevates the temperature of the probe above the static temperature of the gas. The fraction of the
kinetic energy recovered as thermal energy is called the recovery factor, r, defined as
r
T p À T 1
U
2
=2c p
ð8:35Þ
8.7 Physical Errors in Temperature Measurement 363