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F Numerical issues in dynamic heat exchanger models. Results and Discussion For the purpose of the comparison, the stressed system is simulated on a time period of 70 seconds with each method. Table 30 summarizes the simulation results and compares them with a reference case. This reference case is the stressed system described above, but with an internal volume of 1 liter instead of 3 liters. This volume difference is sufficient to avoid the simulation failure. The mass and energy unbalances are computed with the following equations: errorener=∫cpsf⋅M ̇ sf⋅(Tsf ,su,hx−Tsf ,ex ,hx)dt t − ∫ ( M ̇ e x ⋅ h e x − M ̇ s u ⋅ h s u ) d t t N −Vi⋅∑(ρi ,final⋅ui,final−ρi ,init⋅ui,init) Eqs 115 and 116 are absolute errors. The errors provided in Table 30 are relative errors, i.e. they have been divided by the total mass/energy transfer. i=1 errormass=∫(M ̇ ex−M ̇ su)−∑Vi(ρi ,final−ρi ,init) (115) (116) N t i=1 Simulation Time Number of non-linear equations Error on the mass balance Error on the energy balance Constant flow rate 19.8 s 20 3.3 ‰ Maximum derivative 33.2 s 20 3.0 ‰ Filtering 41.1 s 40 0.87 ‰ High number of cells 419 s 100 3.8 ‰ 3 ‰ Reference case 64.5 s 20 0.8 ‰ 1.1 ‰ Table 30: Simulation results with the different strategies 20 ‰ 3.5 ‰ 16 ‰ Figure 105 shows the predicted exhaust enthalpy with each strategy. The enthalpy profile is best predicted with the "high number of cells strategy", followed by the "filtered density" strategy and by the "maximum derivative strategy". The enthalpy is always under-predicted by the "constant flow rate" strategy, which should therefore be avoided. The following conclusions can be drawn: XXIIPDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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