On the modelling of heat exchangers and heat exchanger network dynamics using bond graphs

Figures & data

Figure 1. Generic bond graph model for heat transfer through a material separating hot and cold flows. Solid bonds represent hydraulic flow, while dashed bonds represent the flow of thermal energy. Flows are assumed to be incompressible.

Figure 2. Temperature profiles between hot and cold liquid through the wall with two liquid control volumes for a single wall control volume and for three wall control volumes.

Figure 3. Heat exchanger schematics for (a) a shell and tube heat exchanger with baffles, (b) an U-arranged plate heat exchanger.

Figure 4. Thermal bonds for a shell and tube heat exchanger with two pass tube flow, single pass shell flow and two baffles.

Figure 5. Bond graph representation of a U-arranged plate heat exchanger.

Figure 6. Bond graph representation of a pipe.

Figure 7. Heat exchanger bypass flow arrangement with parallel heat exchangers being controlled. Some examples of causality assignments are given in the subfigures, where all assignments results in algebraic loops.

Figure 8. Heat exchanger bypass with bulk modulus C-elements and parallel heat exchangers.

Table 1. Data set for measured STHE used for comparison of steady state model prediction.

Parameter	Value
Shell diameter	382[mm]
Tube outer diameter	12.7 [mm]
Tube inner diameter	10.7 [mm]
Centre tube to tube distance	16.5 [mm]
Pitch	Rectangular
Tube length	1500 [mm]
Number of baffles	7
Number of tube passes	2
Tubes per pass	206
Tube liquid	Sea water
Shell liquid	Lubrication oil
Lubrication oil inlet temperature	60.2 [C${ }^{\circ }$]
Sea water inlet temperature	6.2 [C${ }^{\circ }$]
Lubrication oil outlet temperature	47.5 [C${ }^{\circ }$]
Sea water outlet temperature	11.0 [C${ }^{\circ }$]
Lubrication oil flow rate	12.2 [kg/s]
Sea water flow rate	14.8 [kg/s]

Table 2. Comparison between simulation and measured data.

	Lubrication oil outlet	Sea water outlet
Measured values	11.0 [C${ }^{\circ }$]	47.5 [C${ }^{\circ }$]
Simulation results	11.4 [C${ }^{\circ }$]	47.5 [C${ }^{\circ }$]

Table 3. Design features difference between the four pass three baffle and two pass six baffle STHE design.

Design feature	2 pass 6 baffles	4 pass 3 baffles
Number of tubes	313	626
Shell diameter	0.353 [m]	0.50 [m]
Tube length	1.2 [m]	0.6 [m]

Figure 9. Comparison of two STHE layouts, 4 pass 3 baffles (4P3B) and 2 pass 6 baffles (2P6B), during start up.

Table 4. Comparison of simulation speeds for a 60 s scenario with different values of the bulk modulus. Simulation time in seconds on a standard laptop computer.

Bulk modulus [Pa]	Simulation speed (times faster)	Simulation time [s]
2.2e9	1	108.1
2.2e8	20	5.5
2.2e7	35	3.1
2.2e6	120	0.9
2.2e5	272	0.4

Figure 10. Simulation results for mass flow in hot flow heat exchanger one, the bypass temperature out and the cold flow temperature out. Comparison of the effect of different values of the bulk modulus on the simulation results. Flow 1 is the flow controlled by the bypass valve (hot), while Flow 2 is the uncontrolled flow in the heat exchangers (cold).

Figure 11. Simulation results for mass flow in hot flow heat exchanger one, the bypass temperature out and the cold flow temperature out. Difference between results when using a bulk modulus of 2.2e9 and modified bulk modulus values.