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compressible flow Flashcards

1
Q

what is compressible flow?

A

branch of fluid mechanics dealing with fluids whose density varies significantly in response to changes in pressure

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2
Q

when are compressibility effects considered important?

A

Mach number of the flow exceeds 0.3

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3
Q

why must high speed compressible flow be studied?

A

understand pressure, temperature, density and internal energy variations

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4
Q

define gas

A

a collection of molecules in random motion

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5
Q

define perfect gas

A

gas in which the intermolecular forces are negligible

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6
Q

can we assume gases are perfect in high-speed flow? if so, why?

A
  • yes
  • average distance between molecules is large enough
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7
Q

what is a calorically perfect gas?

A

gas in which the specific heats are constants

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8
Q

what does adiabatic mean?

A

no heat transfer

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9
Q

what does reversible mean?

A

no energy dissipation

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10
Q

what does isentropic mean?

A

adiabatic and reversible

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11
Q

is the flow in a boundary layer isentropic?

A
  • no
  • boundary layer has a velocity gradient due to viscosity, the viscosity causes additional losses
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12
Q

which condition validates an isentropic relation?

A

if there are no shockwaves in the region outside the boundary layer

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13
Q

why can a large proportion of flow be assumed to be isentropic?

A

the boundary layer adjacent to the surface is thin compared to the entire flow

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14
Q

define what is meant by stagnation conditions

A

conditions which exist at a point if fluid were brought to rest isentropically

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15
Q

true or false: higher the speed of sound, the higher the compressibility

A

false

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16
Q

define Mach number

A

measure of the relative magnitude of motion of the gas to random thermal motion of the molecules

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17
Q

list the effects of a stationary weak disturbance source

A
  • V = 0
  • wavefront produced by stationary disturbance source propagates radially at a speed of a
  • given long enough time, wavefronts produced by disturbance will reach entire flow field
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18
Q

list the effects of a subsonic weak disturbance source

A
  • V < a
  • wavefronts produced by the source always arrive before the source
  • the region upstream knows the source is coming before its arrival
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19
Q

list the effects of a sonic weak disturbance source

A
  • V = a
  • wavefronts produced by the disturbance source arrive at the same time with the source
  • the disturbance is unable to reach the region upstream of the source
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20
Q

list the effects of a supersonic weak disturbance source

A
  • V > a
  • wavefronts produced by a source lag behind the source and are confined within the Mach cone
  • the region upstream does not know the source is coming
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21
Q

define Mach wave

A

weak pressure wave travelling at the speed of sound

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22
Q

fill in the missing words: mach angle _ as mach number _

A

mach angle decreases as mach number increases

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23
Q

strength, shape/orientation, speed of propagation

list the features of shockwaves

A
  • strength: large change in pressure across it
  • shape/orientation: depending on shape of object and freestream Mach
  • speed of propagation: larger propagation velocity, the larger the pressure rise, the greater the propagation velocity
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24
Q

strength, shape/orientation, speed of propagation

list the features of Mach waves

A
  • strength: infinitely weak shock wave
  • shape/orientation: angle the Mach wave forms is the Mach angle
  • speed of propagation: speed of sound
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25
Q

describe the physical model of a shock wave

A
  • theoretically treated as having 0 thickness
  • due to viscosity, some KE dissipated into heat which causes wave drag
  • process is adiabatic and non-isentropic
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26
Q

describe the formation of a shockwave from the object’s point of view

A
  • when disturbances cannot work their way upstream, they crash and form a standing wave
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27
Q

describe the formation of a shockwave from the point of view of subsonic flow

A
  • presence of object can be felt upstream since disturbances produced by object arrive before object
  • flow capable of negotiating its way around the object
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28
Q

describe the formation of a shockwave from the point of view of supersonic flow

A
  • presence of object unknown to incoming flow since disturbances lag behind object
  • shock wave produced as flow crashes onto object and is slowed down abruptly
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29
Q

fill the missing words: a shockwave will become progressively _ further away from the object, eventually becoming a _ wave

A

a shockwave will become progressively weaker further away from the object, eventually becoming a weak Mach wave

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30
Q

what is the characteristic Mach number?

A
  • defined using a^(star) which is constant along the streamline
  • a^(star) is used to show that if at a certain point in the flow, the velocity reaches the local sonic speed
31
Q

is entropy constant along a normal shock? explain

A
  • entropy increases across normal shock
  • increase due to strong viscous dissipation within the shock
32
Q

is temperature constant across a normal shock?

A
  • yes
  • due to adiabatic assumption
33
Q

what happens to pressure over a normal shock?

A

total pressure decreases across a normal shock

34
Q

what happens to Mach number over a normal shock?

A

Mach number decreases, specifically, M2 < 1

35
Q

describe how a Pitot-static tube measures the velocity of subsonic compressible flow

A
  • no shock waves produced
  • flow brought to rest isentropically by tip of pitot tube
  • pressure felt is freestream total pressure p0,1
36
Q

describe how a Pitot-static tube measures the velocity of supersonic compressible flow

A

shockwave forms in front of probe, total and static pressure measured behind shock are different before it

37
Q

describe the area-velocity relationship for subsonic flows through a convergent-divergent nozzle

A
  • area decreases = velocity increases
  • area increases = velocity decreases
38
Q

describe the area-velocity relationship for supersonic flows through a convergent-divergent nozzle

A
  • density decreases more significantly as velocity increases such that area has to increase to ensure mass continuity
  • area decrease = velocity decreases
  • area increase = velocity increases
39
Q

what is meant by a supersonic nozzle, and describe the effects of subsonic and supersonic flow

A
  • a convergent-divergent nozzle where M = 1 at the throat resulting in an increase of Mach number continously from subsonic to supersonic
  • subsonic flow: velocity increase with decreasing area
  • supersonic flow: velocity increases with increasing area
40
Q

what is meant by a supersonic diffuser, and describe the effects of subsonic and supersonic flow

A
  • convergent-divergent nozzle where M = 1 at the throat, resulting in a decrease in Mach number continuously from supersonic to subsonic
  • subsonic flow: velocity decreases with increasing area
  • supersonic flow: velocity decreases with decreasing area
41
Q

what does the area-Mach number relation provide?

A

gives area ratio of local section to sonic throat, allows us to estimate Mach number in a given nozzle

42
Q

describe shock-free nozzle conditions

A
  • Mach number at any location in the nozzle is a function of A/A^star
  • two solutions exist - subsonic and supersonic
  • the area at the throat may not be equal to A^star as the velocity may not be sonic at the throat
  • there are 2 shock-free nozzle conditions
  • 1) subsonic everywhere except at the throat
  • 2) supersonic at the divergent nozzle
43
Q

describe scenario 1-3

A

subsonic flow throughout the nozzle

44
Q

describe scenario 6

A
  • isentropic expansion to supersonic flow
  • convergent = subsonic
  • throat = sonic
  • divergent = supersonic
45
Q

describe scenario 4

A
  • normal shock occurs in divergent nozzle, due to high exit pressure
  • isentropic flow acceleration from subsonic to supersonic just before shock
  • after shock, flow becomes subsonic and decelerates
46
Q

describe scenario 5

A
  • normal shock at nozzle exit
  • flow isentropic before exit
  • convergent = subsonic, throat = sonic, divergent = supersonic
47
Q

how to calculate mass flow rate of nozzle?

A

use throat flow conditions

48
Q

what is an oblique shockwave?

A

shockwave which makes an oblique angle 𝛽 with respect to the upstream flow

49
Q

what is the deflection angle?

A

after going through the oblique shock, the flow is deflected by an angle πœƒ so that it becomes parallel to the surface of the object

50
Q

what happens to the flow velocity after an oblique shock?

A

decomposed in component normal to shockwave (𝑒) and parallel to shockwave (𝑀)

51
Q

what are changes across an oblique shockwave caused by?

A

velocity component normal to the
wave

52
Q

for oblique shocks, what happens if πœƒ>πœƒπ‘šπ‘Žπ‘₯, if πœƒ<πœƒπ‘šπ‘Žπ‘₯, πœƒ=0?

A
  • πœƒ>πœƒπ‘šπ‘Žπ‘₯: no solution exists for a straight oblique shock, a curved detached shock is produced
  • πœƒ<πœƒπ‘šπ‘Žπ‘₯: two straight oblique shock solutions, 𝑀2 <1 for strong shock and 𝑀2 >1 for oblique
  • πœƒ=0: no flow deflection, 𝛽=90Β° is normal to shock or 𝛽=π‘€π‘Žπ‘β„Ž π‘Žπ‘›π‘”π‘™π‘’ is Mach wave
53
Q

For a given ΞΈ<ΞΈmax, how does Ξ² vary as M1 increases?

A

Ξ² reduces as M1 increases.

54
Q

For a given M1, how does Ξ² vary as ΞΈ increases?

A

Ξ² Increases as ΞΈ increases till ΞΈ > ΞΈmax when a detached shock forms.

55
Q

what is the condition for an oblique shockwave to form?

A

when a supersonic flow is β€œturning into itself” (a less
than 180o turn)

56
Q

what is a key difference between normal and oblique shockwaves?

A

in normal shock waves: 𝑀2 <1, in oblique waves: 𝑀2 >1

57
Q

how do properties change across an oblique shock?

A
  • Mach wave: decreases discontinuously
  • pressure: increases discontinuously
  • density: increases discontinuously
  • temperature: increases discontinuously
  • non-isentropic process, p0,2 < p0,1
58
Q

true or false: total pressure loss across an oblique shock is less than that across a normal shock at the same 𝑀1

A

true

59
Q

define wave angle 𝛽

A

angle between the
shock wave and the incoming flow
direction.

60
Q

in regular reflection of a shockwave from a solid surface, is the wave angle 𝛽1 = 𝛽2?

A
  • no, to ensure same deflection angle, the two wave angles cannot be equal due to differing Mach numbers
61
Q

what happens if the Mach number is not large enough to enable the required deflection angle?

A

to ensure the flow becomes parallel to the
wall a normal shock is formed on the
opposite wall instead and a curved shock
wave also branches from the normal shock

62
Q

when using the shock tables, to calculate stagnation pressures and temperatures, which Mach number should be used and why?

A
  • use freestream Mach number
  • because stagnation is based on bringing the free stream flow to rest isentropically
63
Q

what is the difference between a oblique and expansion wave?

A
  • oblique known as concave corner
  • expansion known as convex
64
Q

how do properties change over an expansion wave?

A
  • 𝑀 increases
  • 𝑝, 𝜌 and 𝑇 decrease continously
64
Q

are expansion waves isentropic?

A

yes

65
Q

what happens when supersonic flow passes through an expansion fan?

A

static pressure decreases

66
Q

when does the theoretical maximum deflection angle πœƒπ‘šπ‘Žπ‘₯ occur?

A

occurs when the flow
expands from 𝑀1 =1 to 𝑀2 β†’βˆž

67
Q

consider supersonic flow over a flat plate, which waves can we expect to see on the upper and bottom surfaces of the leading and trailing edges?

A
  • leading edge: bottom = oblique, top = expansion
  • trailing edge: bottom = expansion, top = oblique
68
Q

define back pressure

A

pressure in the surrounding downstream of the nozzle

69
Q

what happens if 𝑀𝑒 <1, 𝑝𝑒 =𝑝𝐡

A

no pressure jump is allowed in subsonic
flow

70
Q

what happens if 𝑀𝑒 >1, 𝑝𝑒 <𝑝𝐡

A

flow is β€œoverexpanded”, oblique shock
waves will occur at the exit

71
Q

what happens if 𝑀𝑒 >1, 𝑝𝑒 >𝑝𝐡

A

flow is β€œunder expanded”, expansion
waves will occur at the exit.

72
Q

what are shock diamonds and how do they occur?

A
  • pattern of evenly spaced rings sometimes visible in the exhaust of an engine
  • occurs when a flow exits a nozzle at supersonic speeds and at a pressure that is different than that of
    the ambient pressure

fluids (4 decks)

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