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

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

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

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

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

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

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

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”

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

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 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 kg/m*s

Tank emptying

Air cylinder Models compressible flow Capacitive fields Resistive fields

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

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

Air cylinder The working fluid: –Air at 25 o C and 100 KPa –Cp N-m/Kg K –Cv N-m/Kg K –Volume m 3 –Mass – 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 Results –Volume in upper and lower chambers Expect upper chamber to decrease volume and lower chamber to increase volume with time

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

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

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

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.