Gas dynamics
The gas dynamics is a field of fluid mechanics and fluid mechanics and sets itself flows with compressible ( variable density ) apart.
It includes both external currents, eg on airplanes or reentry vehicle ( space shuttle, landing capsules of spaceships ), and internal flows through nozzles and diffusers, which are observed in, for example, in missiles and aircraft engines.
Mathematical description of one-dimensional isentropic gas flow
Principles and assumptions
It is assumed for the mathematical description that the gas, no heat is supplied or removed, and no friction losses occur. The entropy is thus constant. And it is the Isentropenbeziehung:
The energy conservation law can be formulated as follows, and states that the sum of kinetic energy and enthalpy is constant along the current thread.
It is the continuity equation, which expresses that no mass is lost. The mass flow along the current thread is constant.
Can be described by the equation of state of an ideal gas, the properties of the gas.
Thus, four equations are available to the four variables ( velocity u, pressure p, temperature T, density ρ ) clearly described. With a mathematical conversion can be the variable state variables of the flow as dimensionless relations express. This pressure, temperature and density on the rest relative sizes (index t). The rest variables describe the state that is activated when the flow would lossless delayed until standstill. With a flow that starts from a large pressure vessels, containers are pressure, temperature and density of the rest variables ( loss of freedom provided ).
The speed can not be related to the idle state ( division by zero), but are presented as Mach number Ma and Lavalzahl M *. For this, the speed of sound c is taken.
Dimensionless relations
The above dimensionless quantities are similarity metrics and can be converted as follows into one another.