Compressible flow is that branch of fluid mechanics which deals with flow of fluids having significant changes in fluid density. Gases display such a behavior since liquids are in-compressible. Mach number (the ratio of the speed of the fluid flow to the speed of sound) decides about the compressible and in-compressible flow. When Mach number is greater than 0.3, it is a compressible flow since as Mach number (M) increases, the density changes become significant. This flow is found in high-speed aircraft, space-exploration vehicles, jet engines, gas pipelines, modern aircraft, missiles, and spacecraft. Compressible fluid flow study is complex. To date its analysis is empirical in nature and hence it is based on experimental data and practical experience.
Salient features of a compressible flow
Ludwig Prandtl found the following features linked with the compressible flow.
- Boundary layer
- Supersonic shock waves
- wind tunnels have supersonic flow
- Design of nozzles with supersonic flow.
Methods to Study Gas Dynamics
1. Model experiments in a wind tunnel
2. Shock tubes using optical techniques
Computational Fluid Dynamics
Computational fluid dynamics
It analysis the compressible flow. It uses supercomputers to analyze a variety of geometries and flow characteristics in a compressible flow. Both internal and external compressible flows can be evaluated. Computational fluid dynamics is an inexpensive alternative to experimental studies.
Assumptions Used in Compressible Flow
- Fluid flow as a continuous substance. There are no voids or impurities in it.
- There is no-slip condition. In most cases, the velocity of solid surface is zero. Because of no slip condition, flow becomes viscous and a boundary layer is developed.
- In an in-compressible fluid flow, pressure and velocity are two unknown parameters. These are solved by using two equations, the continuity and linear momentum conservation equations. In compressible flow, pressure, velocity, density and temperature are four unknown variables. This requires the use of two more equations i.e. the conservation of energy equation and the equation of state.
- Compressible fluid dynamics uses both Lagrangian and Eulerian frame of references because of its complex nature. The Lagrangian approach follows a particular particle or a group of particles of fixed identity. The Eulerian reference frame uses a fixed control volume that fluid can flow through.