7 introduction to compressible flow

7/29/2019 7 Introduction to Compressible Flow

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HCMC University of Technology

17/11/200957:020 Fluid Mechanics 1

Introduction to Compressible Flow

Incompressible Flow over a Cylinder

Shock Wave Induced Condensationaround a F18


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17/11/200957:020 Fluid Mechanics

Content1. Review of Thermodynamics

2. Propagation of Sound Waves

3. Reference State: Local Isentropic Stagnation Properties

4. Critical Conditions


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Review of Thermodynamics

Density changes mean that the thermodynamic state of the fluid willchange (T, p, u, h, s)

Ideal gas equation of state:

Internal energy of a simple substance u = u(v, T). For ideal gas:

cv specific heat at constant volume

Enthalpy energy of a any substance h = u + p/. For ideal gas:

cp specific heat at constant pressure


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Relations of specific heats

Entropy: extremely useful property in analyzing compressible flows.Entropy is defined by the equation

For an adiabatic process, Q/m = 0:


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Useful Relationship among properties (p,v,T,s,u) Gibbs Equation:

For constant specific heats

For an ideal gas, isentropic process


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T-S diagram


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Example 11.1: Flows steadily through a short section of constant area ductthat is cooled by liquid nitrogen

FIND: (a) Duct area (b) h (c) u (d) s


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Propagation of Sound Waves

Speed of Sound Determination

Continuity Equation

Momentum Equation

For ideal gas:


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Speed of Sound in Steel, Water, Seawater, Air at SL on standard day


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Types of Flow The Mach Cone


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Types of Flow The Mach Cone

V = c: observer who is ahead of the source will nothear the pulses before the source reaches her. Sound

wave of unlimited amplitude (sound barrier)

V > c: zone of action, zone of silence


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Reference state: Local Isentropic Stagnation Properties

Local Isentropic Stagnation Point

A reference condition is obtained when the fluid is brought torest (V = 0) Isentropic Process

For a steady, incompressible, frictionless flow

(Bernoulli Equation)


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Continuity Equation


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Momentum Equation

Relation among properties during the deceleration process:


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For an ideal gas:


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Example 11.4: Local Isentropic Stagnation Conditions in Channel Flow

FIND: (a) p01 (b) T01 (c) p2 (d) T2 (e) State points 1 and 2 on Ts diagram;

indicate the stagnation processes


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Example 11.4: Local Isentropic Stagnation Conditions in Channel Flow


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Example 11.5: Mach number limit for Incompressible Flow

M0.3 : error < 2%

M0.4 : error < 4%

M0.45: error < 5%


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Critical Conditions

Reference value for velocity = critical speed (the speed V attained when aflow is either accelerated or decelerated isentropically until we reach M = 1)

7 introduction to compressible flow

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