Mach’s Measure of Flying

P M V Subbarao

Professor

Mechanical Engineering Department

Lecture - 8

A Thoughtful Measure of Speed of Fast Flyers….

22)1(

12

acjet

acacjetpropulsion VVf

VVVf

..

121 22

VHf

VVf acjet

thermal

Jet engine Performance Parameters

ac

compp

cccc

cc

comppp V

TT

fTcf

fTSFC

,0

,00,0

,0

,0

1

1121

ac

compp

cccc

cc

comppp V

T

T

fTcfS

,0

,00,0

,0

,0

1

1121

Mach’s Measure of Speed

• Prof. Mach initiated the art of understanding the basic characteristics of high speed flow.

• He proposed that one of the most important variables affecting aerodynamic behavior is the speed of the air flow over a body (V) relative to the speed of sound (c).

• Mach was the first physicist to recognize that dependency.

• He was also the first to note the sudden and discontinuous changes in the behavior of an airflow when the ratio V/c goes from being less than 1 to greater than 1.

Ernst Mach (1838-1916)

A Dramatic Change in Concept of Sound….

Introductory Remarks

• The fact that the engineering student knows about the sound is great but it is not enough for today's sophisticated industry.

• A cat is pursuing a mouse and the mouse escape and hide in the hole.

• Suddenly, the mouse hear a barking dog and a cat yelling.

• The mouse go out to investigate, and cat is catching the mouse.

• The mouse ask the cat I thought I hear a dog.

• The cat reply, yes you right.

• My teacher was right, one language is not enough today.

Speed of Travel of A Disturbance

• The people had recognized for several hundred years that sound is a variation of pressure.

• The ears sense the variations by frequency and magnitude which are transferred to the brain which translates to voice.

• The New Language:

• The Disturbance in medium !!!

• What is the speed of the small disturbance travel in a quiet medium?

• This velocity is referred to as the speed of sound.

• Let us generate and analyze a disturbance.

A New Thermodynamic Property

RTd

dpc

Velocity Sonic

owMachine/fl Flying ofVelocity NumberMach

c

VM

Mach number of a flight

RT

V

c

VM acac

ac

Speed of Propagation of A Disturbance in an Ideal Gas or Sonic Speed.

Stagnation Properties (Ideal Gas)

0

2

2Tc

c

VTc p

pp

0

2

2h

Vh

0

2

2T

c

VT

p

0

2

21 T

R

VT

0

2

2

11 T

RT

VT

02

2

2

11 T

c

VT

20

2

11 M

T

T

20

2

11 acM

T

T

In general for an adiabatic Flow Field the Stagnation Temperature is defined by the relationship

T0

T1

1 2

M 2

Stagnation Temperature is constant throughout an adiabatic flow field.

• T0 is also sometimes referred to at Total Temperature

• T is sometimes referred to as Static Temperature

• Stagnation temperature is a measure of the total Kinetic Energy of the flow Field.

• Largely responsible for the high Level of heating that occurs on high speed aircraft or reentering space Vehicles …

T0

T1

1 2

M 2

The Columbia Disaster !!!!

Mach’s Analysis of the Problem

Loss Of Signal at 61.2 km altitude

T∞ ~ 243 K

T0

T1

1 2

M 2

~18.0 Mach Number

Ideal gas Variable Properties Real gas

Travel Cycle of Modern Spacecrafts

Rentering Space Craft

What was the Surface Temperature At Columbia Breakup?

The Cause

• Approximately 82 seconds after launch from Kennedy Space Center's LC-39-A, a suitcase-size piece of thermal insulation foam broke off the External Tank (ET), striking Columbia's left wing Reinforced Carbon-Carbon (RCC) panels.

• At the time of the foam strike, the orbiter was at an altitude of about 66,000 feet (20 km; 13 mi), traveling at Mach 2.46 (1,870 miles per hour or 840 m/s).

• As demonstrated by ground experiments conducted by the Columbia Accident Investigation Board, this likely created a 6-to-10-inch (15 to 25 cm) diameter hole, allowing hot gases to enter the wing when Columbia later reentered the atmosphere.

Back to Jet Analysis

Specific Thrust S acjet VVfS 1

ac

compp

ccccturbpp V

T

TTcfS

,0

,00,0,021

accompp

ccacccturbpp MRTMTcfS

,0

,02,0,0 2

1121

accompp

ccacccturbp MMfcS

,0

,02,0,0 2

11

1

21

accompp

ccacccturbp MRTMT

RfS

,0

,02,0,0 2

11

121

Propulsive Power or Thrust Power:

acjetacacTp VVfmVVFP 1

Thrust Specific Fuel Consumption TSFC

acjetacjet

fuel

T

fuel

VVf

f

VVfm

m

F

mTSFC

11

accompp

ccacccturbp MMfc

fTSFC

,0

,02,0,0 2

11

12

1

22)1(

12

acjet

acacjetpropulsion VVf

VVVf

compp

ccacccturbpjet McV

,0

,02,0,0 2

11

1

2

Performance of a Ideal Turbojet Engine : effect of Mach Number

Spe

cifi

c T

hrus

t

TS

FC

r0p,comp = 100,cc=4.5

Mac

S

TSFC

Parametric Cycle Analysis of Ideal Turbo Jet Engine

Selection of Optimal Design Cruising Conditions….

Effect of Flight Mach Number on Compactness

Mac

Spe

cifi

c T

hrus

t kN

.s/k

g

0,cc=4.5

r0p=1

r0p=2

r0p=3

r0p=5

r0p=10

r0p=20r0p=30

Effect of Flight Mach Number on Fuel Air Ratio

Mac

f

r0p

1

235

10

20

30

0,cc=4.5

Effect of Flight Mach Number on Fuel EconomyT

SF

C k

g/ k

N.h

r

Mac

r0p=1

r0p=3

r0p=5

r0p=10r0p=20

r0p=30

r0p=2

0,cc=4.5

Effect of Flight Mach Number on Fuel Air Ratio

Mac

f

r0p

1

235

10

20

30

0,cc=4.5

Effect of Flight Mach Number on Propulsion Efficiency

Mac

propulsion

0,cc=4.5

Effect of Flight Mach Number on Thermal Efficiency

Mac

Thermal

r0p

0,cc=4.5

Effect of Flight Mach Number on Overall Efficiency

Mac

O

r0p

0,cc=4.5