1. Phase Change Analysis Chapter 9

2. Training Manual Inventory #001445 March 15, 2001 9-2 Chapter Overview Phase Change –Terminology –Theory –Material Properties –Transient Solution Guidelines Example Problem - Casting of a Flywheel –Using enthalpy material data –General postprocessing –Time history postprocessing

3. Training Manual Inventory #001445 March 15, 2001 9-3 Phase - A distinct molecular structure of a substance, homogeneous throughout. –There are three principal phases: Phase Change - A change of energy to a system (either added or taken away) may cause the substance to change phase. –Common phase change processes are called freezing, melting, vaporization, or condensation. Terminology Gas LiquidSolid

4. Training Manual Inventory #001445 March 15, 2001 9-4 ANSYS Applicability Important finite element applications involving phase change which can be approached with ANSYS are: –The freezing (or solidification) of a liquid –The melting of a solid Liquid-vapor phase change problems require fluid flow solutions in addition to heat transfer analysis. Some computational fluid dynamics programs may handle liquid-vapor flow and phase change. A phase change analysis MUST be solved as a thermal transient analysis. This chapter will focus on solidification of metals as a typical phase change analysis example.

5. Training Manual Inventory #001445 March 15, 2001 9-5 Latent Heat When a substance changes phase, the temperature remains constant. For example, solid ice at 0  C is ready to melt. –Heat is added to the ice and it becomes liquid water. –When the ice has just become completely liquid, it is still 0  C. Where did the heat energy go, if there was no temperature change? –The heat energy is absorbed in changes in the molecular structure of the substance. –The energy required for the substance to change phase is called latent heat of fusion.

6. Training Manual Inventory #001445 March 15, 2001 9-6 Enthalpy A phase change analysis must account for the latent heat of fusion of the material. The enthalpy material property (ENTH) is used to account for the latent heat. Enthalpy is derived from density and specific heat material properties and is the preferred property input for the materials experiencing phase change. Density and specific heat should be defined for the other materials in the model. One should define either specific heat and density for a material, or enthalpy; not both. The enthalpy property varies with temperature. Therefore, the thermal analysis is non-linear.

7. Training Manual Inventory #001445 March 15, 2001 9-7 Enthalpy (continued) For a phase change analysis, the enthalpy data must be defined as a material property. Typical (thermodynamic) enthalpy data has units of energy, that is kJ or BTU. Specific enthalpy is given in units of energy/mass, that is kJ/kg or BTU/lbm. ANSYS enthalpy material property data must be specified in units of energy/volume, that is kJ/m 3 or BTU/ft 3. If energy/volume enthalpy data is not available for a particular material, it can be computed using the density, specific heat, and the latent heat of the substance.

8. Training Manual Inventory #001445 March 15, 2001 9-8 Phase Change In a phase change analysis, a small temperature range exists in which both the solid and liquid phases exist together. The temperature at which the substance is completely liquid (the liquidus temperature) is Tl. The temperature at which the substance is completely solid (the solidus temperature) is Ts. Between those two temperatures the latent heat effect is included in the finite element formulation.

9. Training Manual Inventory #001445 March 15, 2001 9-9 Delta H, latent heat TlTl TsTs H “Mushy zone” Ts = Solid temperature Tl = Liquid temperature Note: In this diagram, Tl -Ts is small. For a pure material, Tl -Ts would be zero. Ts = Solid temperature Tl = Liquid temperature Note: In this diagram, Tl -Ts is small. For a pure material, Tl -Ts would be zero. A change of phase is indicated by a rapid variation in enthalpy with respect to temperature. T Relationship of Latent Heat to Enthalpy

10. Training Manual Inventory #001445 March 15, 2001 9-10 Not impacted by phase change Phase change is accounted for here Governing Equations When phase change effects are present in a system, the governing thermal equations are effected as follows:

11. Training Manual Inventory #001445 March 15, 2001 9-11 Solving a Phase Change Analysis When solving a phase change analysis, use: –Transient analysis with time integration activated. –A small value for the initial time step and minimum time step sizes. –Automatic time stepping. –Lower-order elements (PLANE55 or SOLID70). –If higher order elements are chosen, activate the diagonalized specific heat matrix option.

12. Training Manual Inventory #001445 March 15, 2001 9-12 Solving a Phase Change Analysis (continued) When solving a phase change analysis, stability and convergence may be improved by using: 1.Backward Euler time integration (backward difference). Set the transient integration parameter (theta) to 1.0. This is the default setting with Solution Control on. 2.The Line Search tool, since phase change is a highly non-linear problem.

13. Training Manual Inventory #001445 March 15, 2001 9-13 Postprocessing The results of a phase change analysis may include: –Temperature vs. time (time-history plots). –The time required for the phase to completely change (melting or freezing time). –Prediction of the melting/freezing front within the substance at any time interval (from a temperature contour plot). These results are useful in evaluating the design parameters of processes involving phase change (e.g. mold material or wall thickness for a casting process).

14. Training Manual Inventory #001445 March 15, 2001 9-14 An ANSYS input file for this example is provided in Appendix B Example - Flywheel Casting Analysis To demonstrate the concepts and techniques presented thus far, we will study the solidification of a flywheel casting: Problem Description: –Perform a phase change analysis for the casting of an aluminum flywheel. The flywheel is produced by filling a sand mold with molten aluminum. Analysis Goals: –To characterize the solidification of the flywheel.

15. Training Manual Inventory #001445 March 15, 2001 9-15 Flywheel Casting Example-Guidelines The part is centered in a cylinder-shaped sand mold 25 cm in radius and 20 cm high. The aluminum is introduced into the mold at 750  C. The mold is initially at 25  C. The top face and side of the mold exchange heat with the environment by free convection. The environment temperature is 30 °C and the film coefficient is 7.5 W/m 2 -  C on the side of the mold and 5.75 W/m 2 -  C on the top. Axisymmetric behavior is assumed for sand mold and aluminum casting. Thermal material properties are assumed constant for the sand, but vary with temperature for the aluminum. Example - Flywheel Casting Analysis

16. Training Manual Inventory #001445 March 15, 2001 9-16 Flywheel Geometry: Example - Flywheel Casting Analysis

17. Training Manual Inventory #001445 March 15, 2001 9-17 Sand Mold Geometry: Example - Flywheel Casting Analysis

18. Training Manual Inventory #001445 March 15, 2001 9-18 Example - Flywheel Casting Analysis Geometry - Flywheel Model

19. Training Manual Inventory #001445 March 15, 2001 9-19 Example - Flywheel Casting Analysis Geometry - Sand Mold Model:

20. Training Manual Inventory #001445 March 15, 2001 9-20 Example - Flywheel Casting Analysis Two Dimensional, Axisymmetric Model of Flywheel and Sand Mold

21. Training Manual Inventory #001445 March 15, 2001 9-21 Example - Flywheel Casting Analysis Properties of the Sand mold (constant): Thermal conductivity:0.346 W/m-°C Density:1520 kg/m3 Specific Heat:816 J/kg-°C Thermal Conductivity of the Aluminum:

22. Training Manual Inventory #001445 March 15, 2001 9-22 Example - Flywheel Casting Analysis Material Data Plot:KXX vs. Temperature for Material 2

23. Training Manual Inventory #001445 March 15, 2001 9-23 The enthalpy data for aluminum is not given directly, however we do have the following data which can be used to calculate enthalpy: To define the enthalpy material property: –Choose T s = 695  C and T l = 697  C ( giving a 2 degree transition zone between liquid and solid phases.) Example - Flywheel Casting Analysis

24. Training Manual Inventory #001445 March 15, 2001 9-24 –Below the solid temperature: –At the solid temperature: Example - Flywheel Casting Analysis

25. Training Manual Inventory #001445 March 15, 2001 9-25 Example - Flywheel Casting Analysis –For the phase change transition region:

26. Training Manual Inventory #001445 March 15, 2001 9-26 Between the solid and liquid temperatures: At the liquid temperature: Above the liquid temperature: Example - Flywheel Casting Analysis

27. Training Manual Inventory #001445 March 15, 2001 9-27 T1T1 H HsHs HlHl CsCs ClCl C* HsHs TsTs TlTl T2T2 T T Latent Heat (area under the curve) Example - Flywheel Casting Analysis

28. Training Manual Inventory #001445 March 15, 2001 9-28 Example - Flywheel Casting Analysis Using these relations to construct the enthalpy data, the result is:

29. Training Manual Inventory #001445 March 15, 2001 9-29 Example - Flywheel Casting Analysis Plot of Enthalpy for Material 2 (Aluminum):

30. Training Manual Inventory #001445 March 15, 2001 9-30 Example - Flywheel Casting Analysis This model uses one element type: PLANE55, axisymmetric. Two materials: Aluminum (with phase change) and sand (with constant properties). A steady-state load step is used to establish the initial temperatures: –sand mold at 25 °C –aluminum at 750 °C (This could have also been done using the IC command) The side and top surface convections are included on the mold exterior. No surface boundary conditions are specified on the bottom or centerline (adiabatic).

31. Training Manual Inventory #001445 March 15, 2001 9-31 Example - Flywheel Casting Analysis The transient load step starts by deleting the initial temperature specifications. Time integration is activated. Backward Euler time integration is used. The line search convergence enhancement tool is activated. A final time of 2400 seconds (40 minutes) is defined. The initial time step is set at 0.01 seconds. The minimum and maximum time steps are set at 0.0001 and 100 seconds, respectively. Automatic time stepping is activated.

32. Training Manual Inventory #001445 March 15, 2001 9-32 Example - Flywheel Casting Analysis The time history postprocessor is used to evaluate the time step size.

33. Training Manual Inventory #001445 March 15, 2001 9-33 Example - Flywheel Casting Analysis A time history postprocessor plot of the temperature at several points (T1, T2, T3 and T4) in the aluminum shows:

34. Training Manual Inventory #001445 March 15, 2001 9-34 Example - Flywheel Casting Analysis The temperature at several points in the sand mold can be displayed in the time history postprocessor:

35. Training Manual Inventory #001445 March 15, 2001 9-35 Example - Flywheel Casting Analysis The General Postprocessor can be used to visualize the progress of the “freezing front” in the material. To do so: –Set two contour values, one at the solid temperature (695 °C), and one above the highest temperature (900 °C). –On a contour plot of nodal temperature, the solidified material will be colored blue. The red color represents the liquid or material in the phase change transition.

36. Training Manual Inventory #001445 March 15, 2001 9-36 Example - Flywheel Casting Analysis At time = 639 seconds, the “freezing front” display shows that only the material in the thinnest sections and extremities has solidified:

37. Training Manual Inventory #001445 March 15, 2001 9-37 Example - Flywheel Casting Analysis At time = 839 seconds, the “freezing front” display shows that most of the material has solidified:

38. Training Manual Inventory #001445 March 15, 2001 9-38 Example - Flywheel Casting Analysis At time = 939 seconds, the “freezing front” display shows nearly all material has solidified. As one might predict, the material near the center solidifies last: