Bondgraph modeling of thermo fluid systems
This presentation is the property of its rightful owner.
Sponsored Links
1 / 22

Bondgraph modeling of thermo-fluid systems PowerPoint PPT Presentation


  • 57 Views
  • Uploaded on
  • Presentation posted in: General

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

Download Presentation

Bondgraph modeling of thermo-fluid systems

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Bondgraph modeling of thermo fluid systems

Bondgraph modeling of thermo-fluid systems

ME270 Fall 2007

Stephen Moore

Professor Granda


Introduction

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

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 transfer1

Heat transfer

  • Related equations

  • H- heat conduction coefficient

  • R is a function of the average to maintain linearity


Heat transfer2

Heat transfer

  • Results

    • Differential equations in Matlab are developed from momentum and displacement- I and C elements

    • Simulink used to display results


Heat transfer3

Simulink model

T1 = 373K, T2 = 273K

hGW = 0.037 W/mK

hAl = 237 W/mK

Heat transfer

Glass Wool Aluminum


Tank emptying

Tank emptying

  • Incompressible, one-dimensional flow

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


Tank emptying1

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”


Tank emptying2

-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


Tank emptying3

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


Tank emptying4

Tank emptying


Tank emptying5

Tank emptying


Tank emptying6

Tank emptying


Air cylinder

Air cylinder

  • Models compressible flow

  • Capacitive fields

  • Resistive fields


Air cylinder1

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


Air cylinder2

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


Air cylinder3

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


Air cylinder4

Air cylinder

  • Results

    • Volume in upper and lower chambers

      • Expect upper chamber to decrease volume and lower chamber to increase volume with time


Air cylinder5

Air cylinder

  • Results

    • Pressures in upper and lower chambers

      • Expect pressure in the upper chamber to increase while the lower chamber decreases


Air cylinder6

Results

Mass flow in the chambers

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

Air cylinder


Air cylinder7

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

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.


  • Login