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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

- 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

- Resistance is thermal
- T- temperature
- - heat flow
- - entropy flow
- Pseudo bonds
- T * ≠ Power

Note: Refer to Figure 12.1, “System Dynamics”

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

- 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

Glass Wool Aluminum

- 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

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

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

- 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

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

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

- Results
- Volume in upper and lower chambers
- Expect upper chamber to decrease volume and lower chamber to increase volume with time

- Volume in upper and lower chambers

- Results
- Pressures in upper and lower chambers
- Expect pressure in the upper chamber to increase while the lower chamber decreases

- Pressures in upper and lower chambers

Results

Mass flow in the chambers

Expect mass flow out of the upper chamber and into the lower chamber

- 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

- 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.