Using the schema of Example E.7.2 , Fig. E.7.3, find the following: (a) Make a classification of the flows in F, P and L for each component. (b) Construct the matrices [latex]A_{\mathrm{F}},A_{\mathrm{P}}{\mathrm{~and~}}A_{\mathrm{L}}.[/latex] (c) Draw the installation functional diagram. (d) Construct the installation matrices [latex]a_{\mathrm{F}},a_{\mathrm{P}}{\mathrm{~and~}}a_{\mathrm{L}}[/latex] at its maximum level of aggregation.

Question 7.8: Using the schema of Example E.7.2, Fig. E.7.3, find the foll......

Exergy Analysis and Thermoeconomics of Buildings Design and Analysis for Sustainable Energy Systems [1399314]

Using the schema of Example E.7.2, Fig. E.7.3, find the following:
(a) Make a classification of the flows in F, P and L for each component.
(b) Construct the matrices $A_{\mathrm{F}},A_{\mathrm{P}}{\mathrm{~and~}}A_{\mathrm{L}}.$
(c) Draw the installation functional diagram.
(d) Construct the installation matrices $a_{\mathrm{F}},a_{\mathrm{P}}{\mathrm{~and~}}a_{\mathrm{L}}$ at its maximum level of aggregation.

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

(a) Analogous to the development of the previous example, Table E.7.11 represents the classification of the flows in F, P and L for each component.

(b) Likewise, the matrices AF, AP and AL are shown in Table E.7.12, Tables E.7.13 and E.7.14 respectively.

(c) In the functional diagram, the fuel and product are represented for each component, see Fig. E.7.10. In this way, the installation productive structure is defined.

(d) For the installation at its maximum level of aggregation, we refer again to Fig. E.7.4. From it, we construct the following Table E.7.15.

From this Table E.7.15, we construct the matrices $a_{\mathrm{F}},a_{\mathrm{P}}{\mathrm{~and~}}a_{\mathrm{L}}$ which are grouped together in Table E.7.16, where only the columns with values different to zero are drawn.

Table E.7.11 Flows classification in F, P and L.

	Fuel	Product	Losses
S	$\dot{B}_{22}$	${\dot{B}}_{1}\,-{\dot{B}}_{2}$	$\dot{B}_{27}$
CC	$\dot{B}_{24}$	${\dot{B}}_{3}\,-{\dot{B}}_{4}$	$\dot{B}_{28}$
C	$\dot{B}_{1}\,+\dot{B}_{3}\,+\dot{B}_{6}$	$\dot{B}_{5}\,+\dot{B}_{2}\,+\dot{B}_{4}$	_
HC	${\dot{B}}_{5}\,-{\dot{B}}_{6}$	${\dot{B}}_{7}\,-{\dot{B}}_{8}$	_
V1	${\dot{B}}_{7}\,-{\dot{B}}_{8}$	$\left({\dot{B}}_{9}\,-{\dot{B}}_{10}\right)\,+\,\left({\dot{B}}_{17}\,-{\dot{B}}_{18}\right)$	_
V2	${\dot{B}}_{9}\,-{\dot{B}}_{10}$	${\dot{B}}_{11}\,-{\dot{B}}_{12}$	_
HX	${\dot{B}}_{11}\,-{\dot{B}}_{12}$	${\dot{B}}_{13}\,-{\dot{B}}_{14}$	_
T	$\left({\dot{B}}_{13}\,-{\dot{B}}_{14}\right)\,+{\dot{B}}_{26}$	${\dot{B}}_{15}\,-{\dot{B}}_{16}$	_
V3	${\dot{B}}_{17}\,-{\dot{B}}_{18}$	${\dot{B}}_{19}\,-{\dot{B}}_{20}$	_
D	${\dot{B}}_{19}\,-{\dot{B}}_{20}$	${\dot{B}}_{21}$	_

Table E.7.12 Matrix $A_{\mathrm{F}}.$

A_F =

-1

Table E.7.13 Matrix $A_{\mathrm{P}}.$

A_P =

-1

Table E.7.14 Matrix $A_{\mathrm{L}}$

A_L =

Table E.7.15 F, P and L at the maximum level of aggregation.

	$\mathrm{Fuel}_{\mathrm{T}}$	$\mathrm{Product}_{\mathrm{T}}$	$\mathrm{Losses}_{\mathrm{T}}$
T	$\dot{B}_{22}+\dot{B}_{24}\,+\,\Delta\dot{B}_{25}\,+\,\Delta\dot{B}_{26}$	${\dot{B}}_{21}+\left({\dot{B}}_{15}\:-\:{\dot{B}}_{16}\right)\:+\:{\dot{B}}_{23}$	${\dot{B}}_{27}+{\dot{B}}_{28}$