ME Subjects – Concepts Simplified

COMPRESSIBLE FLOW-2

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.

1. Boundary layer
2. Supersonic shock waves
3.  wind tunnels have supersonic flow
4. 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

1. Fluid flow as a continuous substance. There are no voids or impurities in it.
2. 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.
3. 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.
4. 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.

COMPRESSIBLE FLOW

NORMAL SHOCK IN A COMPRESSIBLE FLUID FLOW

When the flow passes from a supersonic to subsonic in a SMALL distance, the velocity decreases suddenly and pressure rises sharply. This sudden pressure rise is a normal to the pipe surface and is called the NORMAL SHOCK. It happens only in a compressible flow (gas flow). The vice versa is not applicable i.e. there is no shock wave from subsonic to super- sonic flow. These shock waves are perpendicular to the flow. Shock waves are highly localized IR-REVERSIBILITIES in a compressible fluid (gas flow) flow. These are highly undesirable and should be avoided as far as possible.

Shock wave occurs when flow is changing from super-sonic to subsonic in a compressible flow (air/gas flow) over a very small (molecular) distance. There is a sudden increase in pressure, density, temperature and entropy when a shock is formed.
A shock wave is a moving disturbance. When a disturbance moves faster than the speed of sound in a fluid, it is a shock wave. A shock wave carries energy, and can propagate through a medium. It is characterized by an ABRUPT AND INSTANTANEOUS CHANGE in temperature, pressure, density, entropy, velocity and Mach number of the medium (fluid). It is normal to the flow direction and is thus called a normal shock.
A sound wave, similar to a shock wave, is heard as the familiar “thud” when a supersonic aircraft moves in the air. A shock wave is similar to a sound wave created by an object traveling through the air faster than the speed of sound. In smooth flight, the shock wave starts at the nose of the aircraft and ends at the tail. There is a rise in pressure at the front nose of the aircraft and pressure decreases steadily and becomes a negative pressure at the tail of the aircraft. Suddenly there is a return to normal pressure after the object passes. This is called Normal-wave.

Normal Shock, Fanno Line and Rayleigh Line in a Compressible Flow (Gas FLOW)

FANNO LINE
Fanno flow is the locus of points with the same mass flux (G=constant) and the same stagnation enthalpy (h⁰=constant). Stagnation means at zero velocity. Fanno lines are thus lines of CONSTANT STAGNATION TEMPERATURE, and hence of CONSTANT STAGNATION ENTHALPY:
Fanno flow is for one dimensional adiabatic flow (dq=0) in a duct of constant area with FRICTION.

RAYLEIGH LINE

Rayleigh line is a locus of points with same impulse pressure and same mass flux. It represents states of constant mass flux (flow per unit area) when heat is transferred to or from a gas (dq ≠0). It is a non- adiabatic flow line.

FANNO LINE AND RAYLEIGH LINE

Fanno lines and Rayleigh lines are often considered together. These lines are represented on enthalpy entropy chart. The intersection of Fanno line and Rayleigh line represents the end points in a normal shock for the same mass flux ‘G’. Each point on the Fanno line has a different Mach number.
Each point on the Rayleigh line has a different Mach number.
Even the sonic points ( M=1) are different on these lines. But these lines do intersect at two points. One of these intersecting point lies on supersonic region while other lies on subsonic region. Thus line joining these points represents the normal shock wave. FLOW WITH A CONSTANT AREA DUCT CAN SWITCH BETWEEN THE FANNO AND RAYLEIGH LINE.