1. Bondgraph modeling of thermo-fluid systems ME270 Fall 2007 Stephen Moore Professor Granda

2. Introduction Study of thermofluid bondgraphs Series of three thermofluid bondgraph example models –Heat transfer- Conduction –Incompressible flow –Compressible flow To gain knowledge of bondgraph modeling of thermofluid systems

3. Heat transfer Resistance is thermal T- temperature - heat flow - entropy flow Pseudo bonds –T * ≠ Power Note: Refer to Figure 12.1, “System Dynamics” T1T2 R T1 T2

4. Heat transfer Related equations H- heat conduction coefficient R is a function of the average to maintain linearity

5. Heat transfer Results –Differential equations in Matlab are developed from momentum and displacement- I and C elements –Simulink used to display results

6. Heat transfer Simulink model T1 = 373K, T2 = 273K h GW = 0.037 W/mK h Al = 237 W/mK Glass Wool Aluminum

7. Tank emptying Incompressible, one-dimensional flow Model gives estimate of the time it takes to empty a tank

8. Tank emptying ATAT ρ p1 p2 A2 pl=0 h l A T >>A2 0 Rb C Q I Sp Q 11 p1 Note: Refer to Figure 12.9, “System Dynamics”

9. Tank emptying - Volumetric flow rate out of the tank -Rate of pressure momentum in the pipe R b - Bernoulli resistance of pipe –Indicates a loss of kinetic energy as the fluid leaves the system –Difficult to accurately determine without experimental data C - capacitance of the tank I – inertia of the flow

10. Tank emptying System parameters –Water at ambient conditions (μ, λ, ρ) –Tank diameter- 10 m –Tank depth- 10 m –Outlet pipe diameter- 0.5 m –Length- 1 m Resistance- 5625 N*s/m^5 Resistance was determined by P 3 /Q 3 (R~ P 3 /Q 3 ) Capacitance-.008 m^4*s^2/kg Inertia- 4000 kg/m*s

11. Tank emptying

14. Air cylinder Models compressible flow Capacitive fields Resistive fields

15. Air cylinder F(t)xdot P1,T1,m1,V1 P2,T2m2,V2 mp,Ap Ar P1 C C R 0 1 0 0 0 0 0 Sf Se:F T1 P2 T2 P2 TF: Ap (Ap-Ar):TF P1 I:mp Note: Refer to Figure 12.17, “System Dynamics”

16. Air cylinder The single R element with 4 bonds requires 16 values Two C elements 4 bonds each require 18 values The values are approximate values

17. Air cylinder The working fluid: –Air at 25 o C and 100 KPa –Cp - 1005 N-m/Kg K –Cv - 718 N-m/Kg K –Volume - 0.012272 m 3 –Mass – 0.014253 Kg –Lower chamber is empty –Upper chamber is full Geometry: –Cylindrical chamber –0.25 m diameter –0.25 m height –Mass cylinder is 3.4 kg Applied force –25 N upward

18. Air cylinder Results –Volume in upper and lower chambers Expect upper chamber to decrease volume and lower chamber to increase volume with time

19. Air cylinder Results –Pressures in upper and lower chambers Expect pressure in the upper chamber to increase while the lower chamber decreases

20. Air cylinder Results –Mass flow in the chambers Expect mass flow out of the upper chamber and into the lower chamber

21. Air cylinder The model worked, however, the results obtained are incorrect The values of the R-field and C-field are based on rough approximations More work is required to adequately model the air cylinder

22. Conclusion Thermofluid bondgraphs are significantly different than typical bondgraphs Care must be taken to ensure the correct parameters are chosen for C, I and R elements, especially for R-fields, C-fields and I-fields Expect most thermofluid bondgraphs to represent non-linear systems CampG and Matlab obtains the differential equations easily.