Advanced Materials & Sustainable Manufacturing 2024 , 1, 10003
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In the ideal state, the mass balance and energy balance are Equations (1) – (3): M is = M oc
(1) (2)
M ow = M iw
Q is + Q iw = Q ow + Q oc (3) Among them, secondary steam, cold water, hot water and condensate heat calculation Equations (4) – (7), C is the specific heat capacity of water: Q is = M is × (28.054 × ln( P is ) + 2583.6) (4) Q ow = M ow × T ow × C (5) Q iw = M iw × T iw × C (6) Q oc = M oc × T oc × C (7) After constructing the mechanistic equations, the first assumption is made for a specific case and the two methods are compared with different numbers of known parameters for the solution. The number of known parameters is assumed to be 5, 4, 3, 2, and 1. Each parameter has different combinations and the number of known parameters is decremented in the order of Table 3 until the number of known parameters is one. The idea of the solution is to output the results directly if the known parameters can be calculated exactly by the mechanism equation. If the missing parameters do not give the full result, the solution continues in other ways. When substituting the unknown parameters into the mechanism equation, if the error and error sum of each equation is relatively small, the parameters can be considered as acceptable calculated values at this time.
Figure 3. Surface condenser module. Table 3. Input and output variables.
Input Variables Mass of cold water, Temperature of cold water Heat of cold water Mass of secondary steam Temperature of secondary steam
Output Variables Mass of warm water Temperature of warm water Heat of warm water Mass of condensated water Temperature of condensated water
M iw (kg) T iw ( ℃ ) Q iw (kJ) M is (kg) P is (kpa) Q is (kJ)
M ow (kg) T ow ( ℃ ) Q ow (kJ) M oc (kg) T oc ( ℃ ) Q oc (kJ)
Heat secondary steam Heat condensated water As the relative error has the advantage of reflecting the magnitude and direction of the error and can more accurately reflect the level of confidence in the measurement, it is set in terms of relative error when setting the objective function over the error. The objective function is as follows: Equation (8).
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(8)
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