1. A Universal Model of Droplet Vaporization Applicable to Supercritical Condition November 19, 1999 Zhou Ji Advisor: Dr.Jiada Mo

2. Sections: 1 Introduction1 Introduction 2 Model Establishment2 Model Establishment 3 Implementation & Tests3 Implementation & Tests 4 Conclusions4 Conclusions

3. Introduction The phenomenon of droplet vaporization and combustion has many different applications. Behavior of liquid fuel in combustor is the one that motivates most researches including this work. There are two aspects of this problem: Droplet vaporization & supercritical phenomenon.

4. Droplet Vaporization Basic physical process No convection, no combustion

5. Basic physical process with combustionwith combustion

6. Basic physical process with convectionwith convection

7. Basic physical process higher rate of blowinghigher rate of blowing

8. Droplet Vaporization Classic Model: d 2- law To predict: evaporation rate K flame temperature T f flame front standoff ratio r f /r s

9. Simplifying Assumptions of d 2- law Constant temperature of droplet Simultaneous gasification and combustion Constant transport properties Gas-phase quasi-steadiness No supercritical condition

10. Supercritical Phenomenon Equation of state p=p(v,T) p-v diagram

11. Equation of state p=p(v,T) p-T diagram

12. Equation of state p=p(v,T) p-v-T diagram

13. Conceived image of blurred droplet

14. Supercritical Phenomenon It is an open question in physics. universality long range correlation

15. Model Establishment Conservation Equations Transport relations Equations of State Other properties (coefficients)

16. Continuity equation: Momentum equation: u =1, 2, 3 Species equation: i, i=1, 2, …, k-1 Energy equation: h Conservation EquationsConservation Equations

17. General form of the relation between fluxes and driven force. Driven force: gradient of chemical potential and temperature Fluxes of mass and heat Transport RelationsTransport Relations

18. Thermal Equation of State: p=p(v,T, X 1 ) Caloric Equation of State: h=h(v,T, X 1 ) Equation of statesEquation of states

19. Some can be derived from thermal or caloric EOS, like coefficient D, heat capacity; others need to be modeled individually. Diffusivity, Thermal-to-Mutual Diffusion Ratio (transport matrix); Viscosity; conductivity; expansion rate; Mixing rule of critical properties. Other coefficientsOther coefficients

20. Reorganized model For spherically symmetric case with two species

21. Reorganized model (continued) where

22. Implementation and Tests Two species: droplet O 2, environment H 2 Discontinuity at the initial instant In some cases, the spherical region occupied by O 2 is actually in gas phase or supercritical condition at the specific temperature and pressure.

23. Equation of State p=p(T, v, X 1 ) Peng-Robinson Equation of State Hydrogen plus Evaporation Part.

24. Species concentration Initial temperature 200K

25. Density

26. Temperature

27. Velocity

28. Simulated Images Species concentrationSpecies concentration TemperatureTemperature

29. Density Initially two phases

30. Temperature

31. Species concentration Initially two phases

32. Conclusions A universal model is established.A universal model is established. Numerical test indicates that such a model can be implemented.Numerical test indicates that such a model can be implemented. Temperature change shows different pattern for liquid droplet and gas sphere.Temperature change shows different pattern for liquid droplet and gas sphere. Equations of state and formulations of other coefficients are critical in the model.Equations of state and formulations of other coefficients are critical in the model.

33. Thank you for your attention. Any questions or comments?