What are we dealing with: (gas – air) high speed flow – Mach Number Perfect gas law applied – expression for pressure field Need some thermodynamic concepts, eg, enthalpy, entropy, etc | Compressible Flow Intro_L8_1 BACKGROUND INFO What are we dealing with: (gas – air) high speed flow – Mach Number > Perfect gas law applied – expression for pressure field Need some thermodynamic concepts, eg, enthalpy, entropy, etc Pressure always expressed as absolute pressure likewise Temperature will be in absolute unit, eg Kelvin Flow Classification: Subsonic: Ma 1 Hypersonic: Ma > 5 Density becomes a flow variable and Temperature is a variable too Application: turbomachinery – turbine, compressor, airfoil, missile Mach Number: Ma = fluid velocity / sonic velocity Sonic velocity , c,speed of sound in fluid medium Compressible Flow Intro_L8_2 What do we need from THERMODYNAMICS ? For a reversible process, Perfect Gas Law pV = mRT Mass of gas MR = J kg-1K-1 Mol wt of gas Another relation: p = rRT Few properties : P, T, u (internal energy), h (enthalpy), s (entropy) Few processes : adiabatic, isoentropic, reversible Adiabatic process: system insulated from surrounding – no heat exchange Isoentropic process: constant entropy, no change in entropy Reversible process: ideal process (most efficient); return to original state How does all these correlate? For an irreversible process, Adiabatic Ds = 0 Ds > 0 Note: the terms, u, h & s comes from 1st & 2nd law of thermodynamics Compressible Flow Intro_L8_3 Few more terms & relations (thermo) cp specific heat at constant pressure cv specific heat at constant volume ratio of sp heats, k = cp / cv kair cp = cv + R h = u + p / r Speed of Sound (sonic velocity) sound is a measure of pressure disturbance defined as propagation of infinitesimal pressure disturbance In fluid medium process is assumed isoentropic (reversible) In gas, sonic velocity, Ideal gas, Static pressure (or stream pressure), p Stagnation pressure (p0)- pressure when gas brought to rest isoentropically Compressible Flow Intro_L8_4 Note: more on stagnation pressure few slides later Sonic velocity in liquid or solid . | Compressible Flow Intro_L8_1 BACKGROUND INFO What are we dealing with: (gas – air) high speed flow – Mach Number > Perfect gas law applied – expression for pressure field Need some thermodynamic concepts, eg, enthalpy, entropy, etc Pressure always expressed as absolute pressure likewise Temperature will be in absolute unit, eg Kelvin Flow Classification: Subsonic: Ma 1 Hypersonic: Ma > 5 Density becomes a flow variable and Temperature is a variable too Application: turbomachinery – turbine, compressor, airfoil, missile Mach Number: Ma = fluid velocity / sonic velocity Sonic velocity , c,speed of sound in fluid medium Compressible Flow Intro_L8_2 What do we need from THERMODYNAMICS ? For a reversible process, Perfect Gas Law pV = mRT Mass of gas MR = J kg-1K-1 Mol wt of gas Another relation: p = rRT Few properties : P, T, u (internal energy), h (enthalpy), s (entropy) Few processes : adiabatic, isoentropic, reversible Adiabatic process: system insulated
