Gas dynamics
The gas dynamics is a field of fluid mechanics and fluid mechanics and deals with compressible (density varying) flows apart.
It includes both
- external currents, e.g. B. bodies on aircraft or reentry ( space shuttle , landing capsules of spaceships ), as well
- internal flows through nozzles and diffusers
Mathematical description of the one-dimensional, isentropic gas flow
Laws and Assumptions
If the assumptions of the streamline theory are fulfilled, a flow can be described as one-dimensional. Due to the relatively low density of gases, the effect of gravity can usually be neglected. It is also assumed for the mathematical description that no heat is added to or removed from the gas and that no friction losses occur. The entropy is therefore constant. And the isentropic relationship applies:
The law of conservation of energy can be formulated as follows and states that the sum of kinetic energy and enthalpy is constant along the current filament .
- is constant
The continuity equation applies , which expresses that no mass is lost. The mass flow along the stream filament is constant.
- is constant
The properties of the gas can be described by the equation of state of the ideal gas .
This means that four equations are available to uniquely describe the four variables (speed u , pressure p , temperature T , density ρ ). With a mathematical transformation, the variable state variables of the flow can be expressed as dimensionless relationships. Pressure, temperature and density are related to the rest parameters (index t). The quiescent variables describe the state that occurs if the flow were decelerated to a standstill without loss. In the case of a flow that starts from a large pressure vessel, the vessel pressure, temperature and density are the rest parameters (assuming there is no loss).
The speed cannot be related to the state of rest (division by zero), but can be represented as Mach number Ma and Laval number M * . The speed of sound c is used for this purpose.
Dimensionless relationships
The specified dimensionless values are similarity indicators and can be converted into one another as follows.
Square of the mach number | Square of the Laval number | Temperature ratio | Pressure ratio | Density ratio | |
Formula symbols used
Temperature (always as absolute temperature in Kelvin) | |
Resting temperature | |
Pressure (always as absolute pressure compared to vacuum) | |
Resting pressure | |
density | |
specific heat capacity | |
specific gas constant | |
Isentropic exponent | |
Flow velocity | |
Speed of sound | |
Mass flow | |
cross-sectional area flowed through | |
Mach number | |
Laval number |
See also
literature
- Werner Albring : Applied Fluid Mechanics , Akademie Verlag Berlin, 1990, ISBN 3-05-500206-7 .