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Sylvain Quoilin Chapter 5 : Models model as a polynomial function of the inputs. A 2nd order polynomial with cross terms is used. Such a polynomial with one output and two inputs would be written : output=C0 A⋅input1B⋅input2C⋅input1⋅input2D⋅input12E⋅input22 C0, A, B, C, D and E being identified. Figure 47 shows a fairly good agreement between the predicted and measured values. However, the linear regression has to be used very cautiously : a deeper analysis shows that this solution is not acceptable, since it diverges as soon as one parameter is modified from its initial value to another very close value. This solution is thus rejected. ● Identified correlation : in order to express the output as a function of the inputs in a better way than with the linear regression, all the values are transformed into nondimensional numbers and the following relation is investigated : Figure 47: Predicted vs measured evaporator exhaust temperature T M ̇C2T C3T C4T C5 p C6 f ,ex,ev,pred=C1⋅ a ⋅ a,su,hx3 ⋅ a,su,hx12 ⋅ f ,su,hx1 ⋅ ref M ̇ T T T ref ref ref C1, C2, C3, C4, C5 and C6 are identified to minimize the error between the model and the measurements. Their identified values are : C1 = 1.027 ; C2 = 0.1545 ; C3 = 0.8302 ; C4 = 0.07308 ; C5 = 2.201 ; C6 = 0.02383 Figure 48 shows the agreement between the predicted and measured values if this correlation is used. The agreement is not as good as with the linear regression, but no divergence of the predicted 92 T ref p f ,ex,hx3 ref Tref=298K Where M ̇ref=0.1kg/s rate and pressure and are chosen arbitrarily. All the temperatures are expressed in Kelvin. pref=105Pa are the reference temperature, flowPDF Image | Modeling of a Low Temperature Rankine Cycle for Small Scale Cogen
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