In
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
and
fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them.
It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and bio ...
, stagnation temperature is the
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
at a
stagnation point
In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero.Clancy, L.J. (1975), ''Aerodynamics'', Pitman Publishing Limited, London. A plentiful, albeit surprising, example of such points seem ...
in a fluid flow. At a stagnation point the speed of the fluid is zero and all of the
kinetic energy
In physics, the kinetic energy of an object is the energy that 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 accele ...
has been converted to
internal energy
The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
and is added to the local
static enthalpy. In both
compressible
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a f ...
and
incompressible fluid flow
In fluid mechanics or more generally continuum mechanics, incompressible flow ( isochoric flow) refers to a flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves with the flow velocity. An ...
, the stagnation temperature is equal to the ''total temperature'' at all points on the streamline leading to the stagnation point. See
gas dynamics
Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the r ...
.
Derivation
Adiabatic
Stagnation temperature can be derived from the
First Law of Thermodynamics
The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amoun ...
. Applying the Steady Flow Energy Equation
and ignoring the work, heat and gravitational potential energy terms, we have:
:
where:
:
mass-specific stagnation (or total) enthalpy at a stagnation point
:
mass-specific static enthalpy at the point of interest along the stagnation streamline
:
velocity at the point of interest along the stagnation streamline
Substituting for enthalpy by assuming a constant specific heat capacity at constant pressure (
) we have:
:
or
:
where:
:
specific heat capacity
In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
at constant pressure
:
stagnation (or total) temperature at a stagnation point
:
temperature (or static temperature) at the point of interest along the stagnation streamline
:
velocity at the point of interest along the stagnation streamline
:
Mach number at the point of interest along the stagnation streamline
:
Ratio of Specific Heats
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volu ...
(
), ~1.4 for air at ~300 K
Flow 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
A jet engine is a type of reaction engine discharging a fast-moving jet of heated gas (usually air) that generates thrust by jet propulsion. While this broad definition can include rocket, Pump-jet, water jet, and hybrid propulsion, the term ...
performance calculations. In engine operations, stagnation temperature is often called
total air temperature
In aviation, stagnation temperature is known as total air temperature and is measured by a temperature probe mounted on the surface of the aircraft. The probe is designed to bring the air to rest relative to the aircraft. As the air is brought to ...
. A bimetallic thermocouple is often used to measure stagnation temperature, but allowances for thermal radiation must be made.
Solar thermal collectors
Performance testing of
solar thermal collector
A solar thermal collector collects heat by absorbing sunlight. The term "solar collector" commonly refers to a device for solar hot water heating, but may refer to large power generating installations such as solar parabolic troughs and sola ...
s utilizes the term ''stagnation temperature'' to indicate the maximum achievable collector temperature with a stagnant fluid (no motion), an ambient temperature of 30C, and incident solar radiation of 1000W/m
2. The aforementioned figures are 'worst case scenario values' that allow collector designers to plan for potential overheat scenarios in the event of collector system malfunctions.
See also
*
Stagnation point
In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is zero.Clancy, L.J. (1975), ''Aerodynamics'', Pitman Publishing Limited, London. A plentiful, albeit surprising, example of such points seem ...
*
Stagnation pressure
In fluid dynamics, stagnation pressure is the static pressure at a stagnation point in a fluid flow.Clancy, L.J., ''Aerodynamics'', Section 3.5 At a stagnation point the fluid velocity is zero. In an incompressible flow, stagnation pressure is equ ...
*
Total air temperature
In aviation, stagnation temperature is known as total air temperature and is measured by a temperature probe mounted on the surface of the aircraft. The probe is designed to bring the air to rest relative to the aircraft. As the air is brought to ...
References
{{Reflist
Bibliography
*Van Wylen, G.J., and Sonntag, R.E. (1965), ''Fundamentals of Classical Thermodynamics'', John Wiley & Sons, Inc., New York
Fluid dynamics