2. First step in Understanding the Nature of Fluid Flow…. P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Analysis of Simplest Flow using Mach’s View

3. 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)

4. Propagation of Steady disturbance in A Inviscid Fluid c-u p,  c P+dp,  d 

5. Speed of sound in ideal and perfect gases The speed of sound can be obtained easily for the equation of state for an ideal gas because of a simple mathematical expression. The pressure for an ideal gas can be expressed as a simple function of density and a function molecular structure or ratio of specific heats,  namely Mach’s measure of speed =

6. Finite Disturbance in a simplest flow A control volume for this analysis is shown, and the gas flows from left to right. The control volume is having a very narrow width. No chemical reactions. There is no friction or heat loss across this CV. NO work transfer is possible as this is so narrow. The increase of the entropy is fundamental to any thing that happens in this world.

7. Propagation of Finite Disturbance in 1D inviscid Adiabatic Ideal Gas Flow

8. Solution of Simultaneous Equations If the conditions upstream are known, then there are four unknown conditions downstream. A system of four unknowns and four equations is solvable. There exist two solutions because of the quadratic nature of the equations. Both of these two possible solutions may or may not feasible. Thermodynamics dictates the feasibility of these solutions. Changes in pressure, temperature, volume cannot detect the possible solution. The only tool that helps in identifying the possible solution is change in entropy. For the adiabatic process, the entropy must increase or remain constant.

9. The relation between Upstream & Downstream Mach Numbers Conservation of mass: Mach number is a true measure of speed !!! Replace velocity by Mach number.

10. Conservation of momentum:

11. Introduce Mach number in place of speed

12. & Combined study of Conservation of Mass and Momentum

13. Conservation of energy Energy equation in terms velocity of sound for a perfect gas Replace velocity by Mach number

14. Combined Mass & Momentum Equation : Combined Mass, Momentum and Energy Conservation : The Unified Equation for the Vorticity Generator Simplified Energy Equation :

15. Reversible flow : No vorticity generation between x & y, Discovery of Entropy Generator

16. With a vorticity (entropy) generator between x & y, This equation relates the downstream Mach number to the upstream Mach Number. It can be used to derive pressure ratio, the temperature ratio, and density ratio. The Normal Shock !!!! The Culprit !!!

17. Nature of Normal Shock The flow across the shock is adiabatic and the stagnation temperature is constant across a shock. The effect of increase in entropy across a shock will result in a decrease of stagnation pressure. This feasible only if

18. Obtain a pressure temperature relation across shock. & Change in entropy for an ideal gas

19. M Infeasible Shock is possible only in supersonic flows

20. 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 General Adiabatic Flow

21. The difference between Stagnation and Static temperatures is a measure of the Kinetic Energy of the flow Field. Largely responsible for the high Level of heating that occurs on high speed aircraft or reentering space Vehicles … “stagnation” (total) pressure : Constant throughout Isentropic flow field. The Art of Reentry

22. What was Stagnation Temperature At Columbia Breakup Loss Of Signal at: 61.2 km altitude ~18.0 Mach Number T ∞ ~ 243  K

23. How Nature Makes the Impossible Events into Possible ?!?!?!

24. Human Inventions : Protection of Space Vehicle Loss Of Signal at: 61.2 km altitude ~18.0 Mach Number T ∞ ~ 243  K