Mach ’ s Measure of Flying P M V Subbarao Professor Mechanical Engineering Department Lecture - 8 A Thoughtful Measure of Speed of Fast Flyers….

Jet engine Performance Parameters

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 ( )

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 Mach number of a flight Speed of Propagation of A Disturbance in an Ideal Gas or Sonic Speed.

Stagnation Properties (Ideal Gas)

In general for an adiabatic Flow Field the Stagnation Temperature is defined by the relationship Stagnation Temperature is constant throughout an adiabatic flow field. T 0 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 …

The Columbia Disaster !!!!

Mach’s Analysis of the Problem Loss Of Signal at 61.2 km altitude T ∞ ~ 243 K ~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

Propulsive Power or Thrust Power: Thrust Specific Fuel Consumption TSFC

Performance of a Ideal Turbojet Engine : effect of Mach Number Specific Thrust TSFC r 0p,comp = 10  0,cc =4.5 M ac S TSFC

Parametric Cycle Analysis of Ideal Turbo Jet Engine Selection of Optimal Design Cruising Conditions….

Effect of Flight Mach Number on Compactness M ac Specific Thrust kN.s/kg  0,cc =4.5 r 0p =1 r 0p =2 r 0p =3 r 0p =5 r 0p =10 r 0p =20 r 0p =30

Effect of Flight Mach Number on Fuel Air Ratio M ac r 0p  0,cc =4.5

Effect of Flight Mach Number on Fuel Economy TSFC kg/ kN.hr M ac r 0p =1 r 0p =3r 0p =5r 0p =10r 0p =20 r 0p =30 r 0p =2  0,cc =4.5

Effect of Flight Mach Number on Fuel Air Ratio M ac r 0p  0,cc =4.5

Effect of Flight Mach Number on Propulsion Efficiency M ac  0,cc =4.5

Effect of Flight Mach Number on Thermal Efficiency M ac r 0p  0,cc =4.5

Effect of Flight Mach Number on Overall Efficiency M ac OO r 0p  0,cc =4.5