STUDY OF COMPRESSIBLE SHOCK FOR A TWO DIMENSIONAL MODEL OF A DELAVAL NOZZLE

1. STUDY OF COMPRESSIBLE SHOCK FOR A TWO DIMENSIONAL MODEL OF A DELAVAL NOZZLE

2. What is Computational Fluid Dynamics? • CFD is a method for solving complex fluid flow and heat transfer problems • STEP 1:-CFD divides a flow area into a large number of cells or control volumes, collectively referred to as the “mesh” or “grid”. • STEP 2:-In each of the cells ,the Navier Stokes Equations ,i.e. the partial differential equations that describe fluid flow are rewritten algebraically, to relate such variables as pressure, velocity and temperature in neighboring cells. • STEP 3:-The equations are then solved numerically yielding a picture of the flow corresponding to the level of resolution of the mesh.

3. Overview of the Problem • Description of the problem. • Governing Equations and their dicretised finite volume form • Shock in a Delaval nozzle and its importance. • Developing the two dimensional model according to the geometric equations. • Applying Boundary conditions and initial conditions. • Modification of the model in order to visualize the shock • Analysis of the results from the contours and plots for both viscid and inviscid cases. • Conclusions

4. Description of the problem The Equations that describe the nozzle geometry are

5. Governing Equations for Inviscid Form of NS Equations Governing Equations for the K-Epsilon form of the compressible NS Equations

6. FINITE VOLUME DISCRETISATION OF THE GENERAL CONSERVATION FORM • The conservation principles are applied to a fixed region in space known As a control volume. • Cell centered Finite Volume scheme. • We assume that all properties in the center are averaged over each cell • We calculate the values of the conserved variables averaged across the volumes. j+1 c d j-1 i,j b a i+1 i-1

9. What is SHOCK? • A surface or sheet of discontinuity (i.e., of abrupt changes in conditions) set up in a supersonic field or flow, through which the fluid undergoes a finite decrease in velocity accompanied by a marked increase in pressure, density, temperature, and entropy. • In other words ,Shock is a thin section of a control volume where there are abrupt changes in fluid properties. • Formed due to the compressibility effects of fluids. • Normal shock occurs in a plane perpendicular to the flow.

10. What happens when there is a shock? • Fluid velocity increases in converging part lowering pressure until max velocity reaches at throat (Mach=1). • Diverging section continues to accelerate fluid to supersonic speed with continued drop in pressure until we hit region of normal shock in nozzle. • At normal shock region pressure and temperature increase across the wave and velocity drops.

12. PRE-PROCESSING 1)Building the model and applying the mesh(HYPERMESH) 2)Where to apply the boundary conditions(GAMBIT) SOLVING Calculating and producing the results Using FLUENT POST PROCESSING Organization and interpretation Of the data and images Using FLUENT

13. CONDITIONS FOR THE VISCOUS MODEL SOLVER-SEGREGATED MODEL- K-epsilon Operating Pressure- 101325 Pascal Inlet Conditions- Mass Flow Inlet Mass flow rate-1.3 kg/sec Total temperature-300 K Turbulence Specification method-Intensity and Hydraulic Diameter Outlet conditions - Pressure Outlet Outlet Pressure-88000 Backflow total Temperature-300K

14. CONDITIONS FOR THE INVISCID MODEL SOLVER-COUPLED MODEL- INVISCID Operating Pressure- 101325 Pascal Inlet Conditions- Mass Flow Inlet Mass flow rate-1 kg/sec Total temperature-300 K Turbulence Specification method-Intensity and Hydraulic Diameter Outlet conditions - Pressure Outlet Outlet Pressure-88000 Backflow total Temperature-300K

15. CONTOURS FOR THE ACTUAL GEOMETRIC MODEL Mach number contours Pressure contours

16. MODIFIED MODEL OF DELAVAL NOZZLE DIVERGING REGION CONVERGING REGION THROAT GRID HAS BEEN STRETCHED IN THE X DIRECTION BY FIVE TIMES TOTAL LENGTH OF MODEL IN X DIRECTION IS 5 mm TOTAL LENGTH OF MODEL IN Y DIRECTION IS 5 mm

17. VELOCITY CONTOURS FOR THE VISCOUS CASE Regions of shock

18. MACH NUMBER CONTOURS FOR THE VISCOUS CASE Shock Mach Number

19. TEMPERATURE CONTOURS FOR THE VISCOUS CASE Temperature increases

20. PRESSURE CONTOURS FOR THE VISCOUS CASE Effect of Back Pressure

21. VELOCITY CONTOURS FOR THE INVISCID CASE-COUPLED SOLVER Sharp change in velocity

22. MACH NUMBER CONTOURS FOR THE INVISCID CASE-COUPLED SOLVER Sharp change in mach number

23. TEMPERATURE CONTOURS FOR THE INVISCID CASE-COUPLED SOLVER

24. PRESSURE CONTOURS FOR THE INVISCID CASE-COUPLED SOLVER

25. COMPARISON OF MACH NUMBER FOR VISCOUS AND INVISCID CASES VISCOUS INVISCID

26. COMPARISON OF VELOCITY FOR VISCOUS AND INVISCID CASES VISCOUS INVISCID

27. COMPARISON OF PRESSURE FOR VISCOUS AND INVISICID CASES VISCOUS INVISCID

28. COMPARISON OF TEMPERATURE FOR VISCOUS AND INVISCID CASES VISCOUS INVISCID

29. CONCLUSIONS Purpose of Shock Analysis? • Finding fluid properties before and after a shockwave. • Understanding of normal shock is vital for effects of high speed nozzle flow. • Allows us to find the best fluids to use in an application. • Setting the back pressure( Pressure applied at the nozzle discharge region)