Compressible Inviscid Flow 6 - Introduction to Compressible Flows

Question 1

When is the incompressible assumption valid?

Answer 1

For most liquid flows and low speed gas flows
M<0.3

Question 2

When is flow assumed to be compressible?

Answer 2

Variable density flow (no longer assume constant density)
Usually high speed gas flows (compressibility for air is more than 4 orders higher than that for water)
Bernoulli equation is not valid for compressible flow

Question 3

Difference between compressibility of fluids and flows

Answer 3

Fluids are always compressible to different degrees
Flows are only compressible if there are significant variations of density in the flow field

Question 4

How can density variations be visualised?

Answer 4

Schlieren photography
Can visualise shock waves, shear layers, oblique shocks and density variations
CFD
Green - free air/atmospheric density
Yellow - higher density than free air
Blue - lower density than free air

Question 5

How does temperature vary for compressible flow?

Answer 5

Increases across the shocks
Reduces through expansion

Question 6

Thermodynamics concepts

Answer 6

For a perfect/ideal gas, intermolecular forces are neglected
Use ideal gas equation of state and specific enthalpy

Question 7

What is the gas constant and ratio of specific heat capacities of air at standard conditions?

Answer 7

R = 287 J/kgK
gamma = 1.4

Question 8

First law of thermodynamics

Answer 8

The heat added and work done in a system causes a change of energy in it (i.e. energy conservation)

Question 9

Why is the energy equation required for inviscid compressible flows?

Answer 9

Density is an additional variable (i.e. now treated as a state variable), so this additional equation is required to solve it
Compressible flow is a thermodynamic process, whereas incompressible flow is a mechanical process

Question 10

Types of gasdynamic processes

Answer 10

Adiabatic
Reversible
Isentropic

Question 11

Define adiabatic process

Answer 11

One in which no heat is added to or taken from the system

Question 12

Define reversible process

Answer 12

A process can be reversed by returning all the heat or work lost/gained during the process
Viscous (fluid friction) effect is a source of irreversibility
No dissipative phenomena occur (i.e. the effects of viscosity, thermal conductivity and mass diffusion are absent)

Question 13

Define isentropic process

Answer 13

Constant entropy
Process must be adiabatic and reversible (frictionless) for this to happen

Question 14

Second law of thermodynamics

Answer 14

The physical process of an ice cube melting with the addition of heat is irreversible - it will proceed in a direction such that the entropy of the system always increases
Ice cube (crystal structure, minimum entropy, maximum order) -> water (no structure, maximum entropy, minimum order)

Question 15

What is entropy defined by?

Answer 15

A reversible heat addition

Question 16

How will a process proceed?

Answer 16

In a direction such that the entropy of the system always increases, or, at best, stays the same

Question 17

How does a supersonic wind tunnel work?

Answer 17

Air flow is accelerated through the convergent-divergent nozzle to a supersonic speed in the test section and then decelerated through the diffuser to subsonic speed to exit
If there are no viscous effects, no shock waves and no heat transfer with the tunnel wall, the flow can be considered as inviscid and isentropic