What is compressible flow?

Short Answer:

Compressible flow is a type of fluid flow in which the density of the fluid changes significantly as it moves from one point to another. This happens mainly when the fluid velocity approaches or exceeds the speed of sound, or when there are large pressure and temperature variations.

In compressible flow, the effects of density change must be considered in calculations. Such flow is common in gases, especially in applications like jet engines, nozzles, turbines, and high-speed aerodynamics, whereas liquids are usually treated as incompressible since their density change is very small.

Detailed Explanation:

Compressible Flow

Compressible flow refers to the movement of fluids (mainly gases) in which the density of the fluid varies due to changes in pressure and temperature during motion. In contrast to incompressible flow, where the fluid density is assumed constant, compressible flow analysis must take into account the relationship between pressure, temperature, and density through the gas laws.

In mechanical and aerospace engineering, compressible flow becomes important when fluid velocities are high enough that density variations significantly affect the performance and behavior of the flow.

Nature of Compressible Flow

For most gases, compressibility effects become significant when the Mach number (M) — the ratio of flow velocity () to the local speed of sound () — exceeds about 0.3.

Where:

  •  = Mach number
  •  = velocity of the fluid (m/s)
  •  = local speed of sound in the medium (m/s)

If , the density change is negligible, and the flow can be treated as incompressible. However, if , compressibility effects become significant, and the variation in density must be considered in flow calculations.

Important Characteristics of Compressible Flow

  1. Density Variation:
    • The most important characteristic is the continuous change in density as the fluid moves through different pressure and temperature zones.
  2. Pressure-Temperature Relationship:
    • Pressure, temperature, and density are interrelated by the ideal gas law,

where  = pressure,  = density,  = gas constant, and  = temperature.

  1. Velocity Near Sound Speed:
    • Compressibility effects become prominent when the velocity of the fluid is close to or greater than the speed of sound.
  2. Shock Waves and Expansion Fans:
    • At high velocities (supersonic flow), sudden changes in pressure and density can form shock waves or expansion fans.
  3. Energy Changes:
    • Since compression and expansion processes affect internal energy, thermodynamic effects like heat transfer and work done must be included in the analysis.

Classification Based on Mach Number

Compressible flow is classified according to the Mach number (M) as follows:

  1. Subsonic Flow (M < 1):
    • The flow velocity is less than the speed of sound.
    • Density variation is small but may still be considered in gases.
  2. Transonic Flow (M ≈ 1):
    • Flow velocity is around the speed of sound.
    • Both subsonic and supersonic regions coexist, and shock waves start to appear.
  3. Supersonic Flow (1 < M < 5):
    • The velocity is greater than the speed of sound.
    • Shock waves, expansion waves, and significant changes in density and pressure occur.
  4. Hypersonic Flow (M > 5):
    • Extremely high velocity flow, often associated with spacecraft reentry and missile applications.
    • Temperature becomes very high, leading to gas dissociation and ionization.

Governing Equations for Compressible Flow

Compressible flow is governed by a set of fundamental equations derived from conservation laws:

  1. Continuity Equation (Mass Conservation):

This shows that the mass flow rate remains constant along the flow direction.

  1. Momentum Equation:

This expresses the balance between applied forces and momentum change.

  1. Energy Equation:

Here,  is the specific enthalpy, and this equation expresses conservation of total energy in adiabatic flow.

  1. Equation of State:

It relates pressure, temperature, and density for perfect gases.

These equations together describe the behavior of compressible flow under various conditions.

Examples of Compressible Flow

  1. Flow through Nozzles and Diffusers:
    • In nozzles, gases accelerate to high velocities, often reaching supersonic speeds, leading to strong density variations.
  2. Flow in Jet Engines and Rockets:
    • The working fluid undergoes compression, combustion, and expansion, all involving compressible flow principles.
  3. Supersonic Aircraft:
    • Airflow over wings and fuselage involves shock waves, making compressible flow analysis essential.
  4. Flow through Pipes at High Pressure Ratios:
    • When gas flows through long pipes or valves at high speed, the density changes due to pressure variations.
  5. Turbomachinery (Compressors and Turbines):
    • Air or steam experiences compression and expansion, making density variations significant.

Effects of Compressibility

  1. Change in Flow Area Requirement:
    • For compressible flow, an increase in velocity requires a decrease in density, which affects the required cross-sectional area.
  2. Temperature and Pressure Variations:
    • Rapid compression or expansion leads to heating or cooling of the gas.
  3. Shock Formation:
    • Sudden pressure changes create shock waves that alter flow direction and cause energy losses.
  4. Energy Transfer:
    • Both kinetic and thermal energy are exchanged in compressible flows, requiring thermodynamic considerations.

Importance in Engineering Applications

  • Aerospace Engineering: Analysis of aircraft, rockets, and reentry vehicles.
  • Mechanical Systems: Design of compressors, turbines, and nozzles.
  • High-Speed Flow Devices: Venturi meters, gas pipelines, and supersonic tunnels.
  • Power Plants: Steam flow in turbines and expansion systems.

Understanding compressible flow ensures the safe, efficient, and reliable design of systems operating under high velocity and pressure conditions.

Conclusion

Compressible flow is the study of fluid motion in which density varies significantly with pressure and temperature, typically occurring in gases moving at high velocities. Unlike incompressible flow, it requires thermodynamic analysis using relations between pressure, temperature, and density. Compressible flow plays a crucial role in high-speed aerodynamics, jet propulsion, and energy systems. By understanding compressibility effects, engineers can design efficient systems involving nozzles, diffusers, turbines, and supersonic devices with accurate performance and safety.