Question 9.2: Inverse problem with two anomalies. Heating and DHW installa......
Inverse problem with two anomalies. Heating and DHW installation We refer again to the installation previously described in Example E.9.1. Two anomalies are now incorporated into the system: one of them is in the RS radiator sys-tem consisting of a 10% decrease in its efficiency, and the other is in the HX heat exchanger, where there is now a 35% decrease in its heat transfer coefficient.
In the same way, as in the previous example, calculations of the exergy of the flows for the operating conditions (real state with faults), free conditions and for the refer-ence state are made. The accumulated values for the heating season are represented in Table E.9.6. However, only the values are shown for the free condition (which will be the reference used) and the real condition with anomalies; since the purpose of this example is to exclusively work the MF and DF theory related to failures.
The results of the analysis of malfunctions and dysfunctions are presented in Table E.9.7. The first column represents the component, with its corresponding num-ber. The second column corresponds to the malfunction, and then the expanded matrix of dysfunctions appears, in which the dysfunctions associated with the consumption of external resources D F_{i0} and those due to other components D F_{i j} are shown. The last column corresponds to the total product variation of the installation.
In view of these results we can make the following comments:
- The components with the highest values of malfunctions are those that contain the anomalies (HX and RS, M F_{6}=206\,M J and M F_{10}=1093\,M J, respectively). However, these values correspond to intrinsic and induced malfunctions, and so no immediate conclusions can be drawn.
- Precisely, due to the propagation of induced effects, other components also have malfunc-tions ([{M}F_{1}=-121{{4}}\,{M}J],\,[M F_{2}=-450\,M J],\,[M F_{8}=-136\,{M}J],\,[M F_{11}=-40\,M J] and [M F_{12}=-1~M J]).
- Malfunctions usually cause dysfunctions. These effects are mostly experienced by equipment upstream from the anomaly site. So the boiler CB is the component that experiences the greatest dysfunctions [{D}{ F}_{1}=D{F}_{1,2}+D{F}_{1,3}+D{ F}_{1,6}+D{F}_{1.10}+D{F}_{1.11}+D{F}_{1,12}={}6.702\,M{ J}].
- For its part, the RS component is the one that induces the greatest amount of dysfunctions [{ D}{ F}_{1,10}+{ D}{ F}_{2,10}+{ D}{ F}_{6,10}+{ D}{ F}_{8,10}=7864\;{M}{J}].
- The dysfunctions generated by HX \left[\sum_{i}D F_{i,6}=1239\,M J\right] are notable but do not have as much effect because this equipment is located at the beginning of the energy chain.
- According to Eq. (9.32) the sum for all components reflects the impact on fuel as a conse-quence of the intrinsic anomalies, that is, \Delta F_{T}=6296\,M J.
Table E.9.6 Accumulated values of the flows exergy during the heating period.
| [GJ] | B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 | B9 | B10 | B11 | |
| FREE | 122.9 | 100.1 | 372.3 | 351.8 | 192.0 | 180.3 | 153.3 | 38.9 | 29.8 | 182.9 | 169.2 | |
| REAL | 122.9 | 99.2 | 369.8 | 348.4 | 190.7 | 179.1 | 151.9 | 38.8 | 29.8 | 181.7 | 166.7 | |
| B12 | B13 | B14 | B15 | B16 | B17 | B18 | B19 | B20 | B21 | B22 | B23 | B24 |
| 57.6 | 122.7 | 111.6 | 37.2 | 28.3 | 0.2 | 6.5 | 2.3 | 149.1 | 0.04 | 0.2 | 5.8 | 0.03 |
| 57.7 | 121.4 | 109.2 | 36.2 | 27.5 | 0.2 | 6.4 | 2.3 | 155.3 | 0.05 | 0.2 | 5.6 | 0.03 |
Table E.9.7 MF and DF values.
| MF and DF diagnosis | ||||||||||||||||
| M F_{} | DF_0 | [D F] | \Delta P_{S} | |||||||||||||
| ① | -1214 | -1396 | _ | 557 | -24 | _ | _ | 1255 | _ | -486 | _ | 6617 | -34 | -21 | _ | _ |
| ② | -450 | -9 | _ | _ | -80 | _ | _ | -48 | _ | 52 | _ | 480 | 104 | _ | _ | _ |
| ③ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ |
| ④ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ |
| ⑤ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ |
| ⑥ | 206 | -12 | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | -10 | _ | _ | _ |
| ⑦ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ |
| ⑧ | -136 | -14 | _ | _ | 87 | _ | _ | 32 | _ | -23 | _ | -15 | -25 | _ | _ | _ |
| ⑨ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ |
| ⑩ | 1093 | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ |
| ⑪ | -40 | -6 | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ |
| ⑫ | -1 | -15 | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | -129 |
| ⑬ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ | _ |
| ⓪ | ① | ② | ③ | ④ | ⑤ | ⑥ | ⑦ | ⑧ | ⑨ | ⑩ | ⑪ | ⑫ | ⑬ | |||