Continuum Mechanics Analysis of Supersonic Flow

1. Continuum Mechanics Analysis of Supersonic Flow Submitted by Rajendra B Dubagunta Siva Prasad Rao Batchu Visweswara Mudiam Sandeep Kancharla Narayana Kalpana Thota

2. OVERVIEW • Introduction • Supersonic Flow • Continuum Mechanics Applied to Supersonic Flow • Vorticity Surfaces and Bernoulli Function • P,ρ relationship for inviscid flow • Conclusions • Example

3. INTRODUCTION • What is a wave? • a wave can be described as a disturbance that travels through a medium, transporting energy from one location to another location. • Types of wave propagation based on speed • Subsonic • Transonic • Supersonic

4. INTRODUCTION contd. • Subsonic • Mach number less than unity. • Generally ranges form 0<M<1 • Transonic • For this type of flow the Mach number ‘M’ is approximately unity • Transonic flow. • Compressibility effects like the flow choking becomes very important.

5. INTRODUCTION contd. • Supersonic • Mach number for this kind of flow is greater than unity. • Mach number for this flow ranges from 1<M<3.

6. SUPERSONIC FLOW • Mach number greater than unity • Reynolds number is greater than unity • For supersonic flow we can regard the fluid as ideal. • This behavior is exemplified by the supersonic flow associated with shock waves. • A disturbance starting for any point in a supersonic flow is propagated only downstream within a cone whose opening angles decreases. Where as in subsonic flow it propagates in upstream.

7. CONTINUUM MECHANICS APPLIED TO SUPERSONIC FLOW • Reynolds number in supersonic flows is much larger than unity. • When the Reynolds number is large viscous forces are small compared to inertial forces, and can be ignored, except in highly localized regions of the flow. For supersonic flow we can regard the fluid as ideal. This behavior is exemplified by the supersonic flow associated with shock waves. The thickness of the shock front is , and elsewhere the fluid can be treated as inviscid.

8. VORTICITY STREAM SURFACES FOR INVISCID FLOW VORTICITY STREAM SURFACES FOR INVISCID FLOW

9. P,ρ RELATIONSHIP FOR INVISCID FLOW P,ρ RELATIONSHIP FOR INVISCID FLOW

10. Example A column of fluid is contained with in a vertical circular cylinder as shown below. The cylinder and the fluid rotate as a rigid body about the axis of the cylinder with a constant angular velocity. What are the vorticity-stream surfaces? Show that the Bernoulli function varies across the vorticity-stream surfaces. Also prove that the isobaric stream surfaces are paraboloids of revolution. Assume the fluid has a constant density.

12. SOLUTION SOLUTION

13. CONCLUSIONS In this project we studied different kinds of flows like the Sub-Sonic, Sonic, Supersonic flows and the Supersonic flow is discussed with Continuum Mechanics behavior of the flow. In this project we discussed the Vorticity-Stream functions and the P, relationship of the flow using Continuum Mechanics.

14. HOME WORK Find the speed of propagation of a plane of small disturbances in the direction normal to the plane in an infinite, compressible, in viscid fluid initially at rest with a unique p, -relationship in the absence of body forces.

15. THANK YOU

16. QUESTIONS