Stagnation temperature
Encyclopedia
In thermodynamics
and fluid mechanics
, 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
(adiabatically) 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.
See gas dynamics
.
. Applying the Steady Flow Energy Equation
and ignoring the work, heat and gravitational potential energy terms, we have:
where:
stagnation (or total) enthalpy at a stagnation point
static enthalpy at any other point on the stagnation streamline
velocity at that other point on the streamline
Substituting for enthalpy by assuming a constant specific heat capacity at constant pressure (
) we have:
or
where:
specific heat
at constant pressure
stagnation (or total) temperature at a stagnation point
temperature (also known as static temperature) at any other point on the stagnation streamline
velocity at that other point on the streamline
Mach number at that other point on the streamline
Ratio of Specific Heats
(
), 1.4 for air
Strictly speaking, enthalpy is a function of both temperature and density. However, invoking the common assumption of a calorically perfect gas, enthalpy can
be converted directly into temperature as given above, which enables one to 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.
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
and fluid mechanics
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
, stagnation temperature is the temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
at a stagnation point
Stagnation point
In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object...
in a fluid flow. At a stagnation point the speed of the fluid is zero and all of the kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
has been converted to internal energy
Internal energy
In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal...
(adiabatically) and is added to the local static enthalpy
Enthalpy
Enthalpy is a measure of the total energy of a thermodynamic system. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for it by displacing its environment and establishing its volume and pressure.Enthalpy is a...
. In incompressible fluid flow
Incompressible flow
In fluid mechanics or more generally continuum mechanics, incompressible flow refers to flow in which the material density is constant within an infinitesimal volume that moves with the velocity of the fluid...
, and in isentropic compressible flow
Compressible flow
Compressible flow is the area of fluid mechanics that deals with fluids in which the fluid density varies significantly in response to a change in pressure. Compressibility effects are typically considered significant if the Mach number of the flow exceeds 0.3, or if the fluid undergoes very large...
, the stagnation temperature is equal to the total temperature at all points on the streamline leading to the stagnation point.
See gas dynamics
Gas dynamics
Gas dynamics is a branch of fluid dynamics concerned with studying the motion of gases and its consequent effects. Gas dynamics combines the principles of fluid mechanics and thermodynamics...
.
Adiabatic
Stagnation temperature can be derived from the First Law of ThermodynamicsFirst law of thermodynamics
The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...
. Applying the Steady Flow Energy Equation
and ignoring the work, heat and gravitational potential energy terms, we have:
where:
stagnation (or total) enthalpy at a stagnation point static enthalpy at any other point on the stagnation streamline velocity at that other point on the streamlineSubstituting for enthalpy by assuming a constant specific heat capacity at constant pressure (
) we have:or
where:
specific heatHeat capacity ratio
The heat capacity ratio or adiabatic index or ratio of specific heats, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume . It is sometimes also known as the isentropic expansion factor and is denoted by \gamma or \kappa . The latter symbol kappa is...
at constant pressure
stagnation (or total) temperature at a stagnation point temperature (also known as static temperature) at any other point on the stagnation streamline velocity at that other point on the streamline Mach number at that other point on the streamline Ratio of Specific HeatsHeat capacity ratio
The heat capacity ratio or adiabatic index or ratio of specific heats, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume . It is sometimes also known as the isentropic expansion factor and is denoted by \gamma or \kappa . The latter symbol kappa is...
(
), 1.4 for airFlow with Heat Addition
- q = Heat per unit mass added into the system
Strictly speaking, enthalpy is a function of both temperature and density. However, invoking the common assumption of a calorically perfect gas, enthalpy can
be converted directly into temperature as given above, which enables one to 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
Jet engine
A jet engine is a reaction engine that discharges a fast moving jet to generate thrust by jet propulsion and in accordance with Newton's laws of motion. This broad definition of jet engines includes turbojets, turbofans, rockets, ramjets, pulse jets...
performance calculations. In engine operations, stagnation temperature is often called total air temperature
Total air temperature
Total air temperature is a term used generally in aviation. In other applications it is called stagnation temperature. Total air temperature is measured by a specially designed temperature probe mounted on the surface of the aircraft. The probe is designed to bring the air to rest relative to the...
. A bimetallic thermocouple is often used to measure stagnation temperature, but allowances for thermal radiation must be made.