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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

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Bondgraph modeling of thermo-fluid systems

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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

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”

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

Simulink model

T1 = 373K, T2 = 273K

hGW = 0.037 W/mK

hAl = 237 W/mK

Heat transfer

Glass Wool Aluminum

Tank emptying

• Incompressible, one-dimensional flow

• Model gives estimate of the time it takes to empty a tank

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”

-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

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

Air cylinder

• Models compressible flow

• Capacitive fields

• Resistive fields

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

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 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

• 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

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.