Stagnation temperature

Stagnation temperature is the temperature at a stagnation point in a fluid flow. At a stagnation point the speed of the fluid is zero and all of the kinetic energy has been converted to internal energy and is added to the local static enthalpy. In incompressible fluid flow, and in isentropic compressible flow, the stagnation temperature is equal to the "total temperature" at all points on the streamline leading to the stagnation point. [Van Wylen and Sonntag, "Fundamentals of Classical Thermodynamics", section 14.1] See gas dynamics.

Stagnation temperature can be derived from the First Law of Thermodynamics. Applying the Steady Flow Energy Equation [Van Wylen and Sonntag, "Fundamentals of Classical Thermodynamics", equation 5.50] and ignoring the work, heat and gravitational potential energy terms, we have:

$H\; =\; h\; +\; frac\{V^2\}\{2\},$

where:

$H\; =,$ stagnation (or total) enthalpy at a stagnation point

$h\; =,$ static enthalpy at any other point on the stagnation streamline

$V\; =,$ velocity at that other point on the streamline

Substituting for enthalpy by assuming a constant specific heat capacity at constant pressure ($h\; =\; C\_p\; T$) we have:

$T\; =\; t\; +\; frac\{V^2\}\{2C\_p\},$

where:

$C\_p\; =,$ specific heat at constant pressure

$T\; =,$ stagnation (or total) temperature at a stagnation point

$t\; =,$ temperature (also known as static temperature) at any other point on the stagnation streamline

$V\; =\; ,$ velocity at that other point on the streamline

Strictly speaking, enthalpy is a function of both temperature and density.However, invoking the common assumption of a perfect gas, enthalpy canbe converted directly into temperature as given above, which enables oneto define a stagnation temperature in terms of the more fundamental property,stagnation enthalpy.

Stagnation properties (e.g. stagnation temperature, stagnation pressure) are useful in jet engine performance calculations. In engine operations, stagnation temperature is often called total air temperature. A bimetallic thermocouple is often used to measure stagnation temperature, but allowances for thermal radiation must be made.

ee also

• Stagnation point
• Stagnation pressure
• Total air temperature

References

*Van Wylen, G.J., and Sonntag, R.E. (1965), "Fundamentals of Classical Thermodynamics", John Wiley & Sons, Inc., New York