Bondgraph modeling of thermo-fluid systems

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

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. Simulink model T1 = 373K, T2 = 273K hGW = 0.037 W/mK hAl = 237 W/mK Heat transfer Glass Wool Aluminum

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

8. AT AT>>A2 h ρ pl=0 p2 p1 A2 l I Rb C 0 1 1 Sp Q Q p1 Tank emptying Note: Refer to Figure 12.9, “System Dynamics”

9. -Volumetric flow rate out of the tank -Rate of pressure momentum in the pipe Rb- 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 Tank emptying

10. 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 P3/Q3 (R~ P3/Q3) Capacitance- .008 m^4*s^2/kg Inertia- 4000 kg/m*s Tank emptying

11. Tank emptying

12. Tank emptying

13. Tank emptying

14. Air cylinder • Models compressible flow • Capacitive fields • Resistive fields

15. xdot F(t) Sf P2 Ar P2 C 0 0 P2,T2 m2,V2 T2 0 (Ap-Ar):TF Se:F mp,Ap 1 I:mp P1,T1,m1,V1 R TF: Ap Sf 0 P1 0 C T1 0 Air cylinder Note: Refer to Figure 12.17, “System Dynamics” P1

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

17. The working fluid: Air at 25oC and 100 KPa Cp - 1005 N-m/Kg K Cv - 718 N-m/Kg K Volume - 0.012272 m3 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 Air cylinder

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

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.