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Compressible flows
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- 2. INCOMPRESSIBLE FLOWS • Flowin which the material density is constant within a fluid parcel an infinitesimal volume that moves with the flow velocity. • Also known as Isochoric flow. • Purely incompressible flows are never exist. • Fluid flows which has less density changes can be assumed as incompressible flows. 2
- 3. COMPRESSIBLE FLOWS • Thedensity of fluid does not remain constant during the process of flow. • Density of the fluid changes from point to point in compressible flow. • All real fluids are compressible fluid flows. 3
- 4. COMPRESSIBLE FLOWS • Ex:-The flight of projectiles and aero planes moving at high altitude with high velocity -Flow of gases through nozzles and orifices -Flow of gases in compressors 4
- 5. COMPRESSIBILITY • The amountby which a substance can be compressed known as the compressibility of a fluid. • Denoted with symbol (τ) • Fractional changing volume of the fluid element per change in pressure. 5
- 6. COMPRESSIBILITY • 𝝉 =− 𝟏 𝝊 × 𝒅𝝊 𝒅𝒑 • 𝜐 is the specific volume of the fluid. • If compressibility measures under constant temperature (no heat transfer), it is known as isentropic compressibility. 6
- 7. COMPRESSIBILITY • Since 𝜐= 1 𝜌 • 𝒅𝝆 = 𝝉𝝆𝒅𝒑 • When velocity increases, compressibility of the flow will increase. • High velocity flows are more compressible. 7
- 8. CONSERVATION LAWS • Thereare 3 principles which governs the compressible flow • Mass conservation • Momentum conservation • Energy conservation 8
- 9. Mass Conservation • Netmass flowing out of the system = Net mass decreased in the system 9 Momentum Conservation • Rate of change of momentum = Momentum transfer through the surfaces – Forces (surface and body)
- 10. Energy Conservation • Rateof change of energy = Net heat flux + work done by body and surface forces • Surface forces – Shear stress, pressure, surface tension • Body forces – Gravity, centrifugal or electromagnetic 10
- 11. RELATIONSHIP BETWEEN SPEEDOF SOUND & COMPRESSIBILITY • Speed of sound can be written as, • a = 𝛾𝑅𝑇 • From the previous equation • 𝜏 = − 1 𝜐 × 𝑑𝜐 𝑑𝑝 • From above equations • 𝒂 = 𝟏 𝝆𝝉 11
- 12. RELATIONSHIP BETWEEN SPEEDOF SOUND & COMPRESSIBILITY • Speed of sound is low, when compressibility of the medium is high. • Speed of sound is high, when compressibility of the medium is low. • At low Mach numbers, compressibility of the flow is less. • At high Mach numbers, compressibility of the flow is high. 12
- 13. RELATIONSHIP BETWEEN SPEEDOF SOUND & COMPRESSIBILITY • When flow velocity is less than 0.3 Mach, that flow can be considered as a incompressible flow. • When flow velocity is higher than 0.3 Mach, flow can be considered as a compressible flow. • Flow properties will vary according to its Mach number. 13
- 14. RELATIONSHIP BETWEEN SPEEDOF SOUND & COMPRESSIBILITY Mach Number Regime 0<M<0.3 Incompressible subsonic 0.3<M<0.8 Compressible subsonic 0.8<M<1.2 Transonic 1.2<M<5 Supersonic 14
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Editor's Notes
- #8 When velocity increases, pressure changes will increase, due to that density changes will increase