Total enthalpy

The total enthalpy , also called total enthalpy , stagnation enthalpy or enthalpy of rest , is a thermodynamic state variable that is required in fluid mechanics to describe compressible flowing media , especially for calculations for heat engines such as steam turbines and rocket engines . ${\displaystyle H_{\text{total}}}$

The total enthalpy is a measure of how much “working capacity” a medium, for example steam , still has at a certain point in a steam turbine, regardless of whether this energy is thermal energy , pressure (these two make up the enthalpy) or kinetic energy is available.

definition

The total enthalpy is defined as the sum of the enthalpy and the kinetic energy of a flowing particle: ${\displaystyle H}$ ${\displaystyle {\frac {1}{2}}\cdot m\cdot u^{2}}$

${\displaystyle H_{\text{total}}=H+m\cdot {\frac {u^{2}}{2}}}$

in which

• ${\displaystyle m}$ the crowd
• ${\displaystyle u}$ is the speed of the particle.

Since the mass is retained in a flow, the specific total enthalpy , i.e. the total enthalpy per unit of mass, is often used: ${\displaystyle h_{\text{total}}}$

${\displaystyle h_{\text{total}}={\frac {H_{\text{total}}}{m}}=h+{\frac {u^{2}}{2}}}$

meaning

Enthalpy can be converted into kinetic energy of the flowing medium (in this case there is expansion and usually a decrease in temperature), and conversely, kinetic energy can be converted into enthalpy ( dynamic pressure , i.e. compression , usually associated with an increase in temperature). The total enthalpy is a measure of how much “working capacity” a medium, for example steam , still has at a certain point in a steam turbine, regardless of whether this energy is thermal energy , pressure (these two make up the enthalpy) or kinetic Energy is present.

The stagnation or total temperature can be derived from the total enthalpy : ${\displaystyle T_{\mathrm {t} }}$

${\displaystyle {\begin{aligned}T_{\mathrm {t} }&=T+{\frac {h_{\text{total}}-h}{c_{\mathrm {p} }}}\\&=T+{\frac {u^{2}}{2\cdot c_{\mathrm {p} }}}\end{aligned}}}$

where the specific heat is at constant pressure (it was assumed here that between and does not depend on the temperature). ${\displaystyle c_{\mathrm {p} }}$ ${\displaystyle c_{\mathrm {p} }}$ ${\displaystyle T}$ ${\displaystyle T_{\mathrm {t} }}$

If the flowing medium is slowed down to speed (for example by an obstacle), its enthalpy increases to total enthalpy: ${\displaystyle u=0}$

${\displaystyle h_{\text{total}}=h}$

and its temperature from to the total temperature: ${\displaystyle T}$

${\displaystyle T_{\mathrm {t} }=T}$,

In rocket and aircraft construction, the stagnation temperature is important for the thermal load on surfaces in supersonic flows .

The total enthalpy (and thus for ideal gases also ) remains in currents constant as long as no mechanical work is done even heat between the flowing medium and the environment flows: (see below first law.) this also applies to the shock waves of a supersonic flow. ${\displaystyle T_{\mathrm {t} }}$

Supplements through further energy terms

Further energy terms can be added ( e.g. for chemical reactions , phase changes, movement in fields ).

So in may gravitational field the potential energy are taken into account:

${\displaystyle h_{\text{total}}=h+{\frac {u^{2}}{2}}+g\cdot z}$

With

• the acceleration of gravity ${\displaystyle g}$
• the height . ${\displaystyle z}$

For example, the first law of thermodynamics (for an open system ) can be written as follows:

${\displaystyle {\begin{aligned}w_{12}+q_{12}&=\Delta h_{\text{total}}\\&=\Delta h+{\frac {1}{2}}({u_{2}}^{2}-{u_{1}}^{2})+g\cdot (z_{2}-z_{1})\end{aligned}}}$

Here are

• ${\displaystyle w}$the specific work (per mass element)
• ${\displaystyle q}$the specific heat .