Compressible Flow_9 April

1

Course CHT-221: Fluid Flow Operations

Flow of Compressible Fluid

Instructor: Engr. Muhammad Tanveer

Compressible & Incompressible Fluids:

• A Compressible Fluid is one in which the fluid density changes when it is subjected to high pressure

• All fluids are compressible to some extent, that is changes in pressure or temperature will result in changes in density.

• In many situations the changes in pressure and temperature are sufficiently small that the changes in density are negligible.  Incompressible Fluids.

Cont’d…

• The density ρ of a fluid  does not change as it moves in the flow field, i.e.,

• Compressible flow is the area of fluid mechanics that deals with fluids in which the fluid density varies significantly in response to a change in pressure.

Cont’d…

•  Gases (especially at higher velocities) and those cases dealing with liquids with large pressure changes, the significant variations in density can occur, and the flow should be analyzed as a compressible flow if accurate results are to be obtained

• Two of the most distinctive phenomena which occur in compressible are the possibility of choked flow and the presence of acoustic waves

Cont’d…

• Choked flow is a compressible flow effect. The parameter that becomes "choked" or "limited" is the velocity or the mass flow rate.

• Choked flow is a limiting condition which occurs when the mass flow rate will not increase with a further decrease in the downstream pressure environment while upstream pressure is fixed.

Continued….

• Acoustic Waves are a type of longitudinal waves that propagate by means of adiabatic compression and expansion. These waves travel with the speed of sound which depends on the medium they're passing through.

• Longitudinal Waves are waves that have the same direction of vibration as their direction of travel

Basic Parameter

• Reynolds Number(For incompressible flows)

• At ordinary densities and high Velocities basic parameter for compressible flows.

Mach Number• Basic factor which deals when there is

changing in velocities and densities of fluid occur (Compressible flow)

What is Compressibility

Definition:

Mach Number Mach number is a dimensionless quantity

representing the ratio of speed of an object moving through a fluid and the local speed of sound.

Where u= speed of fluid & a= Speed of sound in the fluid

It is a dynamic measure of fluid compressibility.

What is a Mach number?Definition of Mach number (M):

M ≡ Speed of the flow (u)

Speed of sound (c) in the fluid at the flow temperature

Incompressible flow assumption is not valid if Mach number > 0.3

RTc For an ideal gas,

specific heat ratio

specific gas constant (in J/kg.K)absolute temperature of the flow at the point concerned (in K)

For an ideal gas,

Unit of c = [(J/kg.K)(K)]0.5

= [m2/s2]0.5 = m/s

= [kg.(m/s2).m/kg]0.5

M = u u

RTc

=

Unit of u = m/s

= [J/kg]0.5 = (N.m/kg)0.5

Constant Area Duct

One-dimensional flow

Compressible Flow

steady flow

isothermal flow

ideal gas

Diameter (D) 4/2DA is a constant

speed (u)

xu varies only in x-direction

Density (ρ) is NOT a constant

Temperature (T) is a constant

Obeys the Ideal Gas equation

uAm Mass flow rate is a constant

Assumptions for Compressible Flow

Density change Vs Mach Number

Continued…..

Subsonic Flow

Sonic Flow

Supersonic Flow Which one situation is more interesting???

Significance of Mach Number

• Ma ≡

Speed of the fluid (u)

Speed of sound (c) in the fluid at the flow temperature

 commonly used to represent the speed of an object when it is traveling close to or above the speed of sound.

The Mach number is named after Austrian physicist and philosopher Ernst Mach.

Continued….

• Flow Regime Density Gradient Shock Waves

Incompressible Negligible None

Subsonic Small None

Transonic Significant First appear

Supersonic Significant Significant

Hypersonic Dominant Dominant

3.0Ma

8.03.0 Ma

2.18.0 Ma

0.32.1 Ma

Ma0.3

Continued….

•  A shock wave (also called shock front or simply "shock") is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium (solid, liquid, gas or plasma)

The Mach number is commonly used both with objects traveling at high speed in a fluid, and with high-speed fluid flows inside channels such as nozzles, diffusers or wind tunnels

Stagnation Properties:The stagnation properties at a point are defined as

those which are to be obtained if the local flow were imagined to cease to zero velocity isentropically.

An isentropic flow is a flow that is both adiabatic and reversible. That is, no heat is added to the flow, and no energy transformations occur due to friction or dissipative effects.

Note: An adiabatic process is a process that occurs without the transfer of heat or matter between a system and its surroundings.

Stagnation Properties• Enthalpy of any system is

which is the sum of internal energy u and flow energy P/

• For high-speed flows, enthalpy and kinetic energy are combined into stagnation enthalpy h0

Stagnation PropertiesSteady Adiabatic Flow• Steady adiabatic flow through

duct with no shaft work (Pump) and no change in elevation and potential energy

• Therefore, stagnation enthalpy remains constant during steady-flow process

Stagnation Properties

• If a fluid were brought to a complete rest (V2 = 0)

• Therefore, h0 represents the enthalpy of a fluid when it is brought to rest adiabatically.

• During a stagnation process, kinetic energy is converted to enthalpy.

• Properties at this point are called stagnation properties (which are identified by subscript 0)

Stagnation Properties• If the process is also reversible,

the stagnation state is called isentropic stagnation state.– Stagnation enthalpy is the

same for isentropic and actual stagnation states

– Actual stagnation pressure P0,act is lower than P0 due to increase in entropy s as a result of fluid friction.

– Stagnation processes are often approximated to be isentropic, and isentropic properties are referred to as stagnation properties.

• Isentropic expansion

• Adiabatic friction flow

• Isothermal friction flow

Processes of Compressible Flow

Isentropic Expansion:

In thermodynamics, entropy is a measure of the number of specific ways in which a thermodynamic system may be arranged, often taken to be a measure of disorder, or a measure of progressing towards thermodynamic equilibrium.Expansion which occurs without any change in entropy is called Isentropic Expansion.

 isentropic process is one in which for purposes of engineering analysis and calculation, one may assume that the process takes place from initiation to completion without an increase or decrease in the entropy of the system, i.e., the entropy of the system remains constant

• Isentropic flow in convergent-divergent nozzle

Continued…

• An adiabatic process is a process that occurs without the transfer of heat or matter between a system and its surroundings.

• Adiabatic friction flow

Adiabatic friction flow

Features of Adiabatic Friction FlowProcess is irreversibleConstant cross sectionEntropy increasesStagnation temperature is constant through out the

conduitTotal heat Q=0

Continued…

• An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0.

•

• Isothermal Friction Flow

Isothermal friction flow

Features of Isothermal Friction Flow• Process is non adiabatic• Constant cross section• Entropy increases• Temperature constant• Process is non-isentropic

Continued…

Applications of Compressible Flow

2. Mai 2023 /

32