2. The exergy approach

2.1 Introduction to the concept

2.2 Description of a system as an exergy-entropy process

2.3 Difference between energy and exergy analysis

2.4 Exergy balance

2.5 Warm and cool exergy

2.6 Radiant exergy

2.7 Exergy-entropy process of passive systems

2.8 The global environmental system

2.9 An example of heating exergy calculation

2.10 An example of cooling exergy calculation

2.11 The Human body consumes exergy for thermal comfort

 

2. The exergy approach

This chapter describes the general characteristics of a thermodynamic concept, exergy, which enables us to articulate what is consumed by all working systems, whether they are man-made systems, such as thermo-chemical engines and electricity-driven heat pumps, or biological systems, such as microbes, plants, and animals including the human body. This chapter focuses especially on its application to describing building heating and cooling systems. An example is given about the possibilities of exergy analysis to find the boundary conditions for thermal comfort of the human body.

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Figure 5a and 5b. All working systems, biological or manmade, consume exergy.

Today calculations of energy use in buildings are based solely on the energy conservation principle, the first law of thermodynamics. As shown in this chapter, through analyses and examples, the energy conservation concept alone is not adequate enough to gain a full understanding of all the important aspects of energy utilisation processes. From this point of view, the method of exergy analyses based on a combination of the first and second law of thermodynamics is presented, as the missing link needed to fill the gap in understanding and designing energy flows in buildings.

The basic principles for exergy analysis have already been stated in the nineteenth century, but the term exergy was first introduced in the mid-1950s. The difference between energy and exergy analysis is explained with examples in chapter 2.3.

By typical cases of heating and cooling, the advantages of exergy analysis are shown. The calculation examples in chapters 2.9- 2.10 suggest that to achieve an exergy optimised building design, loads on the building service system have to be reduced as much as possible. First after that, in a good building shell, further improvements on the building service system seem to be meaningful. Therefore, rational passive design seems to be a prerequisite of realising low exergy systems for heating and cooling of buildings.

The human body exergy analyses have now just started to articulate why low exergy systems are essential for creating rational and comfortable built environment. Examples of human body exergy analysis are presented in chapter 2.11.

 

2.1 Introduction to the concept

People often claim that energy is consumed; this is not only in everyday conversation but also even in scientific discussion associated with so-called energy and environmental issues. This claim, however, conflicts with the first law of thermodynamics stating that the total amount of energy is conserved even though forms of energy may change from one to another.

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Figure 6. The LowEx case building"IDIC" in Iwate, Japan has both active and passive systems for environmental control (see case JPN 5).

All macroscopic natural phenomena happening around us involve the dispersion of energy and matter, which in due course change their forms from one to another, but the total amount of energy and matter involved is never consumed but necessarily conserved.

When we use such expressions as "energy consumption", "energy saving", and even "energy conservation", we implicitly refer to "energy" as intense energy available from fossil fuels or from condensed uranium. But, it is confusing to use one of the most well-established scientific terms, energy, to mean "to be conserved" and "to be consumed" simultaneously. This is why we need to use the thermodynamic concept, exergy, to articulate what is consumed.

Active and passive systems

Over the last two decades various so-called "energy saving" measures have been conceived, developed, and implemented in building envelope systems and also their associated environmental control systems such as lighting, heating, and cooling systems. Those measures can be categorised into two groups: those for "passive" systems and those for "active" systems (Figure 6).

"Passive" systems are defined as building envelope systems to make use of various potentials to be found in the immediate environment such as the sun, wind, and others to illuminate, heat, ventilate, and cool the built environment. The history of passive systems is very long; we may say that it emerged with the evolution of human being. The recent development of material science has brought about various building materials such as low-emissivity coated glass and others; this enables us to design advanced passive systems.

"Active" systems are the systems consisting of various mechanical and electric components such as fans, pumps, heat pumps, and others, all of which work by the use of fossil fuels. Most of the active systems available these days have been developed with an assumption of the abundant use of fossil fuels so that they do not necessarily work in harmony with passive systems.

Optimal thermal environmental design with thermally-well-insulated glazing materials with other thermally-well-insulated building-envelope materials having appropriate heat capacity enables us to realise "passive" solar heating systems. However, it does not mean that active heating systems are no longer required. We need new types of active systems that can work in harmony with advanced passive systems.

Low Exergy systems

Low temperature heating systems are such kind of "active" heating systems that should fit the built environment to be conditioned primarily by "passive" heating systems. A good thermal-environmental condition within built spaces in the winter season can be provided basically with the installation of thermally-well-insulated building materials with appropriate heat capacity, which make it possible to utilise heat sources of lower temperature for heating.

In summer season, a moderate thermal-environmental condition within built spaces may be provided with a combination of nocturnal ventilation, the installation of appropriate shading devices for glass windows, and the reduction of internal heat gain in addition to the use of thermally-well insulating materials with appropriate heat capacity for building envelopes. This would allow the utilisation of cold sources with higher temperature for cooling.

The use of the exergy concept in describing various heating and cooling systems, whether they are passive or active, would enable us to have a better picture of what low temperature heating and high temperature cooling systems are.

From Shukuya and Hammache 2002

 

2.2 Description of a system as an exergy-entropy process

 

This very fundamental question in terms of life was once asked by Schrdinger some fifty years ago (Schrdinger 1945). If we could have used the wasted energy and matter, most of the so-called energy and environmental problems would have been already solved.

The most general answer to the above question would be that the energy and matter as input are different from those as output; or you may say that the energy and matter as output have something that a system in question must discard. To make the answer clearer, we use the concepts of exergy and entropy, which can express the difference in energy and matter between input and output explicitly.

Exergy and entropy, both of which are thermodynamic concepts, can show us what is the resource and what is the waste; "exergy" is the concept to articulate "what is consumed" and "entropy" is "what is disposed of". Stating in the other way, "exergy" is the concept, which quantifies the potential of energy and matter to disperse in the course of their diffusion into their environment and "entropy" is the concept which quantifies the state of dispersion, to what extent the energy and matter in question are dispersed.

Let us take a microscopic view in order to make the concepts easier to understand. Energy transfer like heat transfer is a trans-fer of the vibration of particles, which com-pose of, for example, a building envelope system as shown in Figure 7.  We assume a steady-state condition that the right-hand side of the system is warmer than the left-hand side. The particles in the warmer side of the building envelope vibrate rather strongly; that is, the energy flowing into the building envelope accompanies a certain amount of exergy. The vibration disperses in the course of energy transfer; that is, a part of the exergy is consumed as the exergy flows. As a result, the energy flo-wing out the building envelope is accom-panied with a smaller amount of exergy.

As a result of the dispersion of vibration, the state of dispersion as a whole within the system increases. This is the generation of entropy, the law of entropy increase* , which is parallel to the law of energy and mass conservation. The amount of increased entropy is proportional to that of consumed exergy and the proportional constant is the ambient temperature in the Kelvin scale as described later.

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Figure 7. Energy, exergy, and entropy flow in and out a building envelope system. The amounts of energy flowing in and out are the same under thermally steady-state condition according to the law of energy conservation; on the other hand, the amount of entropy flowing out is larger than flowing in according to the law of entropy increase. The amount of exergy flowing out is smaller than flowing in, since exergy is consumed within the system to produce entropy.

Since the steady-state condition is being assumed, the distribution of the temperature inside the building envelope is unchanged. This implies that the amount of entropy contained by the whole of the building envelope system is constant. The entropy of a substance, which is a function of temperature and pressure, remains unchanged unless the temperature and the pressure of the substance increases or decreases. As described above, a certain amount of entropy is generated due to exergy consumption within the building envelope system. This generated entropy must be discarded into the surrounding, namely outdoors, from the building envelope system, otherwise it turns out to be contradictory with our assumption of the steady-state condition and the characteristics of the entropy as a function of temperature and pressure. It is important for us to recognise that the energy flowing out the building envelope is accompanied with not only a decreased amount of exergy but also an increased amount of entropy. Disposing of the generated entropy from the system makes room for feeding on exergy and consuming it again.

We call the process described above as exergy-entropy process (Shukuya and Komuro 1996). Table 1 shows the four fundamental steps of exergy-entropy process. Any working systems perform these four steps in series and cyclically. Heating and cooling systems are no exception.

* There is a rather strong belief among scientists and engineers that entropy is one of the concepts which is most difficult to understand. I think that this is not necessarily true. Those who are interested more in the concept of entropy than described here in this article should consult, for example, a book written by Atkins [1984], which I think best describes the characteristics of entropy.

Table 1. Four Steps of Exergy-Entropy Process

1.

Feed on exergy

2.

Consume Exergy

3.

Generate Entropy

4.

Dispose of Entropy

Disposing of the generated entropy from the system makes new room for feeding on exergy and consuming it again. Thus the process cycles.

 

2.3 Difference between energy and exergy analysis

Simple examples can help to enhance the understanding of the differences in energy and exergy analyses.

A large enclosure with adiabatic boundaries containing a lot of air at the initial temperature of Ti and a small container of fuel are shown in Figure 8. It is furthermore supposed that the fuel burns in air, heating the surrounding air and environment so that there is a slightly warm mixture of combustion products and air in the final state. It is obvious that the total quantity of energy in the enclosure is the same as in the initial state. But the combination of fuel and air in the initial state has a greater potential to be useful than the warm mixture in the final state. The fuel can be used in a device to generate electricity, do work or heat rooms. But the uses for the slightly warm combustion products are much more limited. It can be stated that the initial potential has been destroyed to a large extend (Moran and Shapiro 1998).

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Figure 8. Combustion of fuel in air as an example to show the difference between energy and exergy analysis (Moran 1989, modified).

The same fact, that there is an energy quality, can be illustrated by another example evident for us from our experience in daily life (Figure 9).

It is obvious that 100 kJ electricity stored in a 12 V / 2.3 Ah car-battery is more useful, easier to transform into something useful for us, than the same amount of energy stored in 1 kg water at a temperature of 43 C in an ambient temperature of 20 C. The electricity is suitable for running a machine, like a computer, operating a light bulb of 40 W for 42 min or at least heating 1 kg of water with 23 C. The 100 kJ heat contained in the 1 kg water is only suitable for washing our hands or doing the dishes. It becomes clear that there is a difference between the types of energy. By introducing the term exergy we appreciate the fact that energy manifests itself by its quantity and its quality (Schmidt 2001).

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Figure 9. Both systems contain the same amount of energy but not the same amount of exergy.

 

2.4 Exergy balance

Let us introduce a general expression of exergy balance using the case of the above-mentioned simple building envelope system. The purpose here is to outline the structure of the exergy balance equation and we do not discuss the detailed mathematical expression. Those who are interested in the detailed mathematical expressions should refer to (Bejan 1988), (Shukuya 1994), and others, in addition to Part II of this report by (Shukuya and Hammache 2002).

Energy is the concept to be conserved so that the energy flowing in must be equal to the sum of the energy stored within the system and the energy flowing out from the system. This energy balance can be expressed as follows.

(Energy input) = (Energy stored) + (Energy output)

(1.1)

Since the steady-state condition is being assumed here, there is no energy storage and hence the above equation turns out to be the following simpler form.

(Energy input) = (Energy output)

(1.2)

Secondly, let us set up the entropy equation consistent with the above two equations. Energy flowing into the system as heat is more or less dispersed energy. Heat is a energy transfer due to dispersion, thus entropy necessarily flows into the system as heat flows in and some amount of entropy is generated inevitably within the system in the course of heat transmission. The sum of the entropy input and the entropy generated must be in part stored or in part flows out of the system. Therefore the entropy balance equation can be expressed in the following form.

(Entropy input) + (Entropy generated) = (Entropy stored) + (Entropy output)

(1.3)

Since the steady-state condition is being assumed, there is no entropy storage as well as no energy storage. Therefore, the above entropy balance equation turns out to be

(Entropy input) + (Entropy generated) = (Entropy output)

(1.4)

The fact that the outgoing entropy from the system includes the entropy generated within the system suggests that the system disposes of the generated entropy with the entropy output.

Combining the energy and entropy balance equations brings about the exergy balance equation. Entropy (or entropy rate) has a dimension of J/K (or W/K) and energy (or energy rate) has a dimension of J (or W). Therefore we need a kind of trick to combine the two equations.

Generally speaking, energy contained by a body, which has an ability to disperse, is called an energy resource. Such an energy resource exists within the environmental space, which is filled with dispersed energy. The dispersed energy level of the resource surrounded by the environmental space can be expressed as the product of the entropy contained by the resource and its environmental temperature in the Kelvin scale. The same expression applies to the waste discarded by the system. Therefore the entropy balance equation can be rewritten as follows.

(Entropy input) x Te + (Entropy generated) x Te = (Entropy output) x Te

(1.5)

Where Te is the environmental temperature. The product of entropy and environmental temperature is called "anergy", which implies dispersed energy. Using the term "anergy", the above equation can be expressed in the following form, anergy balance equation.

(Anergy input) + (Anergy generated) = (Anergy output)

(1.6)

Provided that "anergy" is a portion of energy that is already dispersed, then the other portion is not yet dispersed. Stating in another way, energy consists of two parts: the dispersed part and the part, which can disperse. The latter is "exergy". Now let us take the difference of the two equations, energy balance equation (1.2) and anergy balance equation (1.6). This operation brings about

[(Energy input) – (Anergy input)] – (Anergy generated) = [(Energy output) – (Anergy output)].

(1.7)

"Anergy generated" is such energy that originally had an ability to disperse and that has just dispersed. We can state this in the other way; that is, exergy is consumed. Anergy generation is equivalent to exergy consumption. Using the term "exergy", the above equation can be reduced to the following equation.

(Exergy input) – (Exergy consumed) = (Exergy output)

(1.8)

This is the exergy balance equation for a system under steady-state condition such as the building envelope system shown in Figure 7. Exergy consumed, which is equivalent to anergy generated, is the product of entropy generated and the environmental temperature.

(Exergy consumed) = (Environmental temperature) x (Entropy generated)

(1.9)

Exergy consumed is exactly proportional to the entropy generated with the proportional constant of environmental temperature.

2.5 Warm and cool exergy

The amount of exergy contained by a substance varies with its temperature and also with its environmental temperature. Figure 3 shows an example of thermal exergy contained by 81 m3 (= 6m x 5m x 2.7m) of air as a function of its temperature in the case of an environmental temperature of 288 K (=15 C). It should be noted that air has a certain amount of exergy both when the air temperature is higher than the environment and when the air temperature is lower than the environment. Appendix A in (Shukuya and Hammache 2002) shows a mathematical formula used to draw Figure 10.

The exergy contained by air at a temperature higher than its environment is an ability of thermal energy contained by the air to disperse into the environment. On the other hand, the exergy contained at a temperature lower than its environment is an ability of the air, in which there is a lack of thermal energy compared to the environment, to let the thermal energy in the environment flow into it. We call the former "warm" exergy and the latter "cool" exergy (Shukuya, 1996).

Either "warm" exergy or "cool" exergy described above is a quantity of state contained by a substance. We have room temperature higher than the outdoor environment when the space is heated. In such a case room air has "warm" exergy as a quantity of state. On the other hand, when we have a room temperature lower than the outdoor environment, room air has "cool" exergy as a quantity of state.

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Figure 10. Thermal exergy contained by air as a function of temperature, Tr. Air volume is assumed to be 81m3 (= 6m x 5m x 2.7m). Environmental temperature, To, is 288 K(=15 C). Air at a temperature higher than the environmental temperature has "cool" exergy and the air at a temperature lower than the environmental temperature has "warm" exergy (See Appendix A, formula A.1).

Thermal exergy, whether it is warm exergy or cool exergy, flows through walls, by a combination of convection, conduction, and radiation. The case shown in Figure 1 is when the environmental temperature, namely outdoor temperature, is lower than the indoor temperature. In this case, "warm" exergy flows in the internal surface and out the external surface of the building envelope system. If the environmental temperature is higher than the indoor temperature, namely the summer condition, the room air has "cool" exergy, which flows through the building envelope system.

The direction of energy flow changes depending on the temperature profile, whether the indoor temperature is higher or lower than the outdoor temperature, but the direction of exergy flow is always the same from the indoors to the outdoors, external environment. What changes is whether it is "warm" exergy or "cool" exergy depending on, whether indoor temperature is higher or lower than the outdoor temperature.

Space heating systems, whether they are low exergy consuming or not, are the systems that supply and consume exergy for keeping "warm" exergy as a quantity of state contained by room space in a certain desired range. Space cooling systems, on the other hand, whether they are low exergy consuming or not, are the systems that supply and consume exergy for keeping "cool" exergy as a quantity of state contained by room space in a certain desired range. As described above, exergy consumption is always accompanied with entropy generation, thus the generated entropy must be discarded constantly from the room space to the outdoor environment to keep "warm" or "cool" exergy within a desired range.

2.6 Radiant exergy

Radiant exergy transfer plays more important role in low temperature heating or high temperature cooling systems than in conventional air heating or cooling systems, because they require heat sources with a rather large surface area whose temperature is only slightly higher than room air temperature.

For this reason, it would be very important to be able to evaluate radiant exergy. Figure 11 shows an example of radiant exergy emitted by a black surface of 1 m2 in the case of environmental temperature of 20 C (=293 K) given by Takahashi et al. (2000). Appendix B shows a mathematical formula used to draw Figure 11.

Supposing that there is a radiant panel of 2 m2 with a surface temperature of 40C, this panel emits 9 W of "warm" radiant exergy. If the surface temperature decreases from 40 C to
30 C, the "warm" radiant exergy drops dramatically from 9 W down to 2 W.

In the case of cold source of the surface temperature of 6 C, the panel emits 4 W of the "cool" radiant exergy. If the surface temperature increases from 6 C to 14 C, the "cool" exergy drops dramatically from 4 W down to 0.2 W.

This suggests that low exergy systems for heating and cooling of buildings are realised provided that heating and cooling exergy requirements for room space is decreased by the installation of rational building envelope systems, thus the heating and cooling is provided at a temperature close to room temperature.

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Figure 11. An example of radiant exergy emitted by a black surface of 1 m2 when the environmental temperature is assumed to be 293 K (20C). A surface with a temperature lower than the environmental temperature emits "cool" radiant exergy and a surface with a temperature higher than the environmental temperature emits "warm" radiant exergy (See Appendix B, formula B.1).

 

2.7 Exergy-entropy process of passive systems

Here let us describe the general characteristics of six passive systems from the viewpoint of exergy-entropy process (see Shukuya, 1998 and Shukuya, 2000)). As suggested above, rational passive (bio-climatic) design would be prerequisite to realise low exergy systems for heating and cooling.

Daylighting

This is to consume solar exergy for indoor illumination. Exergy consumption occurs as solar exergy is absorbed by the interior surfaces of building envelopes. "Warm" exergy is produced as a result of solar exergy consumption for lighting; this may be consumed for space heating (Asada and Shukuya 1999). The entropy generated in the course of solar exergy consumption for lighting must be discarded into the atmosphere by ventilation cooling or mechanical cooling, hopefully by a low exergy system for cooling.

Passive heating

This is to control the rate of solar exergy consumption during daytime and nighttime by forming the built-environmental space with the appropriate materials that have low thermal conductivity and high thermal-exergy storage capacity. It is also to consume, during nighttime, the thermal exergy produced during daytime. Most of the entropy generated is discarded spontaneously through the building envelopes into the atmosphere (Shukuya and Komuro 1996).

Shading

This is to let the excess solar exergy, namely the rest of exergy necessary for daylighting, be consumed before it enters the built environment. It is also to reduce the entropy generated within the built environment so that mechanical equipment for cooling is required to consume less exergy to remove the entropy generated within the built environment. Exterior shading devices are very much attractive in this regard, since the entropy generated at the devices is effectively discarded into the atmosphere by convection (Asada and Shukuya 1999).

Ventilation cooling

(Free cooling)

This is to consume kinetic exergy of atmospheric air, which is produced by the exergy-entropy process of the global environmental system described later (Shukuya and Komuro 1996), for removing the entropy generated within the built environment, such as the entropy discarded from the body surface of the occupants and that from the lighting fixtures, electric appliances and others, into the near-ground atmosphere.

Water spraying

This is to consume the "wet" exergy contained by liquid water, which is very large compared to thermal exergy, namely "warm" or "cool" exergy, to decrease the "warm" exergy produced by solar exergy consumption and possibly to produce "cool" exergy (See (Nishikawa and Shukuya 1999), and (Saito and Shukuya 1998)). Roof spraying and uchimizu, which is to scatter rainwater on the road surface, are also due to this process. The consumption of "wet" exergy to produce "cool" exergy or to decrease "warm" exergy play a very important role in photosynthetic system of leaves (Saito and Shukuya 1998) and the temperature-regulating system of human body (Saito and Shukuya 2000).

Composting

This is to let micro organisms consume actively a large amount of exergy contained by garbage and hence turn it into fertiliser. The "warm" exergy produced as a result of micro-organisms consuming chemical exergy can be rationally consumed for maintaining the temperature inside the container at a desired level. This is realised by making the walls of a container thermally well insulated (Takahashi and Shukuya 1998). The entropy generated in the process of composting is discarded into the surrounding of the container and finally into the near-ground atmosphere.

With the view of passive (bio-climatic) design as exergy-entropy process, passive design is to design a route in which the exergy available from our immediate surroundings is rationally consumed and the generated entropy is rationally discarded into the atmosphere. Again, low exergy systems for heating and cooling would be such systems consistent with passive design described above.

 

2.8 The global environmental system

Our near-ground atmosphere receives all the entropy that is generated and discarded by all systems involving lighting, heating, and cooling of the built environment. This also applies to any living systems such as bacteria, plants, and animals, since the involved biological phenomena can be reduced to the combination of chemical and physical phenomena, although such reduction alone cannot give us an answer to why the biological phenomena are so complex or how living systems evolve.

Since the entropy contained by a substance is, as described in the previous section, a function of temperature and pressure, the near-ground atmospheric temperature must rise if the near-ground atmosphere continues to receive the entropy discarded from various systems. But, what is actually occurring in the nature is different; the average atmospheric temperature is almost constant from year to year. This is due to the fact that the atmosphere has an exergy-entropy process that works feeding on and consuming solar exergy, thereby producing the entropy, and finally disposing of the produced entropy into the Universe. We call this the global environmental system.

Figure 12 shows schematically and numerically the exergy-entropy process of the global environmental system (Shukuya and Komuro, 1996). The earth receives not only the solar exergy of 220.7 W/m2 but also the "cool" radiant exergy of 102.2 W/m2 from the Universe. These exergies are all consumed sooner or later within the upper or lower atmosphere. The figures in the squares, 176.6 W/m2 and 146.3 W/m2, show the exergy consumption in the upper and lower atmospheres respectively. The convective air current near the ground surface, a part of which can be used for ventilation, has 0.73 W/m2 of kinetic exergy. The rain drops inside the clouds before falling down towards the ground surface have 1.25 W/m2 of potential exergy; a part of this exergy may be consumed to produce electric power. These kinetic and potential exergies are produced by the solar and the "cool" radiant exergy consumption. The resultant generated entropy due to the exergy consumption is delivered first into the upper atmosphere by convection, evaporation and long-wave radiation and then into the Universe by long-wave radiation. The total amount of the entropy generation is the difference between the input and the output entropy flows across the upper boundary surface of the upper atmosphere. A portion of the 102.2 W/m2 of "cool" radiant exergy coming from the Universe enables the global environmental system to have the outgoing entropy flow of 1.239 W/(m2K). It should be recognised that the "cool" radiant exergy of 102.2 W/m2 is vitally important in addition to the solar exergy, because it is the exergy that finally sweeps away all the generated entropy within the upper and lower atmospheres, which includes the entropy generated by bio-climatically designed building envelope systems and also low exergy systems for heating and cooling.

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Figure 12. Exergy-entropy process of the global environmental system. The drawing on the top is the exergy input, output, and consumption in W/m2. The other drawing on the bottom is the entropy input, output, and generation in W/(m2K). The amounts of the exergy consumption and the entropy generation are indicated by the figures in the squares.

 

2.9 An example of heating exergy calculation

Written by Masanori Shukuya and Abdelaziz Hammache

Let us compare three numerical examples of exergy consumption during the whole process of space heating from the power plant, through the boiler to the building envelope in the steady state as shown in Figure 13. Case 1 assumes that the thermal insulation of the building envelope system is poor; that is, single window glazing and an exterior wall with only a thin insulation board, and a boiler with a moderate thermal efficiency. Case 2 meanwhile assumes that the thermal insulation of the building envelope is improved by a combination of double window glazing and an exterior wall with improved insulation, while the boiler efficiency remains unchanged. Case 3 assumes in addition that the boiler efficiency is improved to near its limit. Table 2 summarises the assumptions for calculation in the three Cases.

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Figure 13. A space heating system assumed for example calculation of exergy consumption (Shukuya, 1994).

Figure 14 shows respective three series of exergy input, exergy consumption, and exergy output from the boiler, to the water-to-air heat exchanger, to the room air, and finally to the building envelope in the three Cases.

Exergy consumption within the boiler system is the largest among the sub-systems. Consuming a lot of exergy is unavoidable when extracting thermal exergy by a combustion process from the chemical exergy contained in LNG. Because of this, one may consider that the improvement of boiler efficiency is essential. The dashed line indicated below Case 1 shows the result of the improvement of boiler efficiency from 0.8 to 0.95 in Case 1. The decrease of exergy consumption is marginal. One may, then, consider that increasing the outlet water temperature of the boiler makes exergy output from the boiler larger and hence the boiler more efficient. This, however, results in the consumption of more exergy within the water-to-air heat exchanger and also within the room air, in which the required temperature is 293 K (20 C). These facts imply that an extremely high boiler efficiency alone cannot necessarily make a significant contribution to reducing exergy consumption in a whole process of space heating.

Table 2. Assumptions for example calculation of exergy consumption

Case

Heat loss coefficient of building envelope

Thermal efficiency of boiler

1

108.7 W/K

(3.0 W/m2 K)

80 %

2

57.1

(1.59)

80

3

57.1

(1.59)

95

Heat-loss-coefficient values in the brackets are those per unit floor area. A 6.0m x 6.0m x 3.0m room with one exterior wall having a 1.5m x 6m glased window is assumed. The exterior-window and –wall U values are 6.2 and 2.67 W/m2K for Case 1; 3.6 and 1.14 for Cases 2 and 3. The number of air changes due to infiltration is 0.8 h-1 for Case 1; and 0.4 h-1 for Cases 2 and 3. The room air temperature is ideally controlled and kept constant at 293 K (20 C) in all cases while the outdoor air temperature is assumed to be constant at 273 K (0 C). Outlet air temperature, inlet and outlet water temperatures of the heat exchanger are assumed to be 303 K (30 C), 343 K (70 C), and 333 K (60 C), respectively, for all Cases. The rates of electric power supplied to a fan and a pump are 30 W and 23 W in Case 1; 16 W and 12 W in Cases 2 and 3. The ratio of the chemical exergy to the higher heating value of liquidified natural gas (LNG) is 0.94. The thermal efficiency of the power plant, that is, the ratio of produced electricity to the higher heating value of LNG supplied is 0.35.

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Figure 14. A comparison of exergy consumption for four stages of the space heating systems. Exergy consumption is the difference in exergy between input and output; for example, in Case 1, 2554 W of exergy is supplied to the boiler and 420 W of "warm" exergy is produced and delivered to the heat exchanger by hot water circulation so that their difference, namely 2134 W (=2554-420), is consumed inside the boiler.

The heating exergy load, which is the exergy output from the room air and the exergy input to the building envelope is 148 W in Case 1 and 78 W in Case 2 and 3. It is only 6 to 7 % of the chemical exergy input to the boiler so that one may regard a measure reducing the heating exergy load as marginal. But, as can be seen from the difference in the whole exergy consumption profile between Case 1 and Case 2, it is more beneficial to reduce the heating exergy load by installing thermally well-insulated glazing and exterior walls than to develop a boiler with an extremely-high thermal efficiency, in order to decrease the rate of total exergy consumption. The reduction in exergy consumption of the boiler sub-system indicated by the difference between Case 2 and Case 3 due to the improvement in boiler efficiency turns essentially meaningful together with the improvement of building-envelope thermal insulation.

Those interested in numerical calculation of the example explained above are encouraged to consult (Shukuya and Hammache 2002) Appendix E, which describes the detailed calculation procedure to obtain Figure 14

2.10 An example of cooling exergy calculation

This section describes a comparison of five numerical examples of exergy consumption during the whole process of space cooling from the power plant, through the heat pump to the building envelope in the steady state condition, much in a similar way to what was described in the heating exergy calculation example above.

A room assumed is shown in Figure 15. It is exactly the same as the one assumed for the heating calculation except that there is solar heat gain through shading devices and internal heat gain due to electric lighting and occupants.

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Figure 15. A room assumed for cooling exergy calculation. There is an external shading device, the electric lighting is in use, and the room air is conditioned by a heat-pump air conditioner. The natural-gas-fired power plant supplies the electricity for the lighting fixture in the ceiling and also for the air-conditioner.

Outdoor air temperature and room air temperature are assumed to be 33 C and 26 C. The amount of solar radiant energy incident on the window is assumed to be 500 W/m2, the density of occupancy is 5.4 persons (0.15 persons/m2 and 75 W/person are assumed) and the electric-lighting density is 480 W (13.3 W/ m2) provided that all the lighting fixtures are turned on.

Table 3 summarises five cases with miscellaneous assumptions. Case 1 is the base case in which the thermal insulation of the building envelope is moderate and the solar control is realised with an internal shading device; Case 1’ is the case where the coefficient of performance (COP) alone is improved from 2.7 to 3.2; in Case 2 the thermal insulation is improved and an external shading replaces the internal shading, but there is no improvement for the heat pump; in Case 2’ daylighting reduces the heat generation rate due to electric lighting from 480 to 160 W; in Case 3’ the outlet air temperature is raised from 16 C to 20 C and hence the COP is improved from 2.7 to 3.7.

Table 3. Assumptions for calculation.

Case Heat loss coefficient of building envelope (number of air change) Solar heat gain coefficient COP of heat pump Outlet air temperature of the internal unit of heat pump Heat generation rate due to electric lighting
1 108.7 W/K (0.8 h-1) 0.7 2.7

16 C

480 W
1’ 108.7 (0.8) 0.7 3.2 16 480
2 57.1 (0.4) 0.35 2.7 16 480
2’ 57.1 (0.4) 0.35 2.7 16 160
3’ 57.1 (0.4) 0.35 3.7 20 160

Figure 16 shows a heat pump assumed for the present calculation; this consists of an evaporator as the internal unit, a condenser as the external unit, and a compressor with a motor. The room air comes through the internal unit, is cooled down and goes out into the room air while outdoor air comes through the external unit, is heated up and goes out into the ambient air. This process is performed by the electricity rotating the motor and thereby turning the wheel of the compressor so that the working fluid is heated up being compressed and chilled down expanding through the throttling valve, while at the same time the electricity rotates the fan inside the internal unit to circulate a part of the room air through and the other fan in the external unit to circulate ambient air through.

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Figure 16. A heat pump assumed for the calculation example. Exergy is supplied through the electricity grid and a portion of it is consumed so that cool exergy is delivered into the room space while at the same time warm exergy is discarded outside to dispose of the generated entropy within both the room space and the heat pump.

The exergy balance equation of the heat pump is given in the following form.
(Exergy input to the motor and two fans) – (Exergy Consumed) = (Cool Exergy supplied to the room space) + (Warm exergy given off to the ambient air).

Exergy consumption within the heat pump is due to the compression and the expansion of the working fluid inside the conduit, the heat transfer between the working fluid and the room air at the evaporator, and the heat transfer between the working fluid and the ambient air at the condenser. Cool and warm exergies can be calculated by the equation given in the former chapters.

Figure 17 shows a comparison of Case 1, Case 1’ and Case 2. The exergy consumption pattern changes dramatically by installing an external shading device as a replacement of the internal shading device. The development of heat pumps with higher efficiency alone would be marginal. This result is very similar to the result obtained from the heating example calculation.

Figure 18 shows a comparison of Case 2, Case 2’ and Case 3’. Daylighting brings about a moderate change in exergy consumption pattern if it is carefully designed so that unnecessary electric lighting is turned off according to the level of available daylight transmitted through the window with the external shading device.

The reductions of both solar and internal heat gains would make it possible to improve the interior radiant environmental condition, namely to lower the mean radiant temperature. The outlet air temperature could then be raised and it would become possible for the heat pump to have a higher COP. This could realise another dramatic change in the whole exergy consumption pattern.

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Figure 17. A comparison of exergy consumption patterns: Case 1, Case 1’, and Case 2. The improvement of COP alone cannot change the exergy consumption pattern much, but the replacement of the internal shading device by an external one brings about a large change.

 

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Figure 18. A Comparison of exergy consumption patterns: Case 1, Case 1’, and Case 2. The improvement of COP alone cannot change the exergy consumption pattern much, but the replacement of the internal shading device by an external one brings about a large change.

2.11 Human body consumes exergy for thermal comfort

As explained in chapter 2.2. above, the exergy-entropy process of any working system consists of the following four fundamental steps: The systems first feed on exergy and then consume a portion of it or all of it to perform their purposes while at the same time producing entropy as the result of exergy consumption, and finally they discard the produced entropy into the environment. The human body, which occupies the built environment controlled by heating and cooling systems, is no exception.

We humans feed on exergy contained by food, and thereby consume it within our body so that we can sense, think and perform any physical work by contracting our muscles. In due course, we inevitably produce entropy, and it must be discarded into the built environment as symbolically shown in Figure 19.

Heating and cooling systems in buildings, whether they are active or passive, also work as exergy-entropy processes. This is what thermodynamics tells us. "Exergy" is the concept to articulate what is consumed within a system, and "entropy" is what is disposed of as waste from the system. In other words, exergy is the concept that quantifies the ability of energy and matter to disperse, and entropy is the concept that quantifies how much energy and matter are dispersed.

Exergy balance of the human body

It is vitally important to have a clear image of the exergy balance of the human body in order to understand what the low exergy systems for heating and cooling in buildings are. Therefore  a mathematical model of the human body exergy balance was developed and its numerical calculation was made and the result was related to human thermal sensation (Saito and Shukuya 2000).

In the case of the human body, "input exergy" is warm exergy and wet exergy generated by metabolism. "Warm" exergy is the ability of a portion of the sensible heat to diffuse, and "wet" exergy is the ability of the liquid water contained by the human body to disperse into the environmental space by evaporation. Both warm and wet exergies are provided by the metabolic chemical reactions occurring within the human body.

"Exergy consumed", the second term of the equation below and the most essential term in any exergy balance equation, occurs to maintain the body temperature as constant as possible. The difference in the exergy rate between the input and consumption becomes either stored or output exergy.

The actual exergy balance equation to be calculated was developed by combining the mass, energy, entropy balance equations set up for both the core and the shell of the human body, and the environmental temperature.

The general form of exergy balance equation of a system is described as follows.

Input Exergy – Exergy Consumed = Stored Exergy + Output Exergy

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Figure 19. The human body works as an exergy-entropy process.

Example of human body exergy consumption

Figure 20 shows one of the results of the numerical calculation assuming a thermally steady-state environmental condition (Saito and Shukuya, 2000; Isawa, Saito, and Shukuya, 2003). This is the relationship between the warm and wet exergy-supply rate (input), the exergy consumption rate, the rate of exergy storage, the rate of exergy output from human body and the environmental temperature with the corresponding thermal sensation (PMV*).

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Figure 20. The relationship between the rates of exergy input, exergy consumed, exergy stored within the human body and also exergy output from the human body and the environmental temperature. The dotted lines represent a case of no shivering in cold condition or no sweating in hot conditions (Isawa, Saito, and Shukuya 2003).

The assumptions made for this calculation are the following: the environmental temperature is equal both to the ambient air temperature and to the mean radiant temperature, the air movement of 0.1 m/s, the clothing insulation of 0.6 clo (= 0.093 m2K/W), and the metabolic-energy-generation rate of 1.1 met (= 64 W/m2).

The higher the environmental temperature is, the lower the input exergy rate is. The exergy consumption rate within the human body also becomes smaller as the environmental temperature becomes higher under the conditions from cold to neutral, but it reaches the lowest rate near the environmental temperature corresponding to neutral thermal sensation.

Dotted lines appearing from 0 to 13 C correspond to a case where no shivering is assumed. The difference in the input exergy between the cases with and without shivering is "warm" exergy generated by shivering in order to maintain the body temperature as constant as possible. This difference, which is warm exergy, is produced by chemical exergy consumption within the muscle cells. The reason why it becomes larger as the environmental temperature gets lower is that the human body shivers more as it gets colder and the temperature difference between the core of the human body and its environment becomes greater. The exergy consumption rate does not change much whether there is shivering or not, but instead, the absolute value of the rate of exergy storage becomes greater.

The exergy consumption rate becomes larger as the environmental temperature gets higher under the conditions from neutral to hot though the input exergy rate becomes smaller. Dotted lines appearing from 23.5 to 35 C correspond to a case where no sweating is assumed. The difference in the input exergy rate between the cases with and without sweating is equivalent to the amount of "wet" exergy generated by sweating to perform evaporative cooling over the skin surface.

The higher the environmental temperature is, the closer the input exergy rate and the exergy consumption rate are. This means that almost all of the input exergy is consumed due to sweating and evaporation in a hot environment.

It is interesting that the thermally comfortable condition is provided with the lowest exergy consumption rate within the human body. This suggests that rational heating and cooling systems in buildings would work well with low exergy consumption under a condition in which we humans consume as low amount of exergy as possible.

Low Exergy systems and human body exergy consumption

As explained in the previous section, the lowest human body exergy consumption occurs at thermally neutral condition. Exergy consumption within the human body becomes higher in a cold environment due to larger difference in temperature between the human body and its surrounding space and also becomes higher in a hot environment mainly due to sweating. These findings suggest that heating and cooling systems may also work well in such conditions where the lowest amount of exergy is consumed by those systems. That is, we may be able to establish both thermal comfort and low exergy consuming systems at the same time.

Further research on human body exergy balance has just come onto a new stage where it becomes possible to calculate more realistic cases than before, in which the environmental temperature for exergy calculation need not be presumed to be equal to the average indoor air temperature and mean radiant temperature. What follows is one of our new findings which enhances our previous finding. Figure 21 shows a new relationship between the human body exergy consumption, thermal comfort (PMV*=0), room air temperature, and mean radiant temperature. The assumptions made for this calculation are: outdoor air temperature and relative humidity of 0C and 50 %, a typical winter condition in Tokyo-Yokohama area, indoor air current and relative humidity of 0.1 m/s and 40 %, a typical winter clothing (0.9 clo), and a metabolic thermal energy generation rate at an ordinary office work (1.1 met).

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Figure 21. The relationship between exergy consumption within the human body (W/m2), room air temperature, and mean radiant temperature. The solid line descending from the upper left corner to the lower right corner indicates thermally neutral conditions (PMV*=0); this is based on ‘energy’ balance calculation. The broken line in the upper right corner is skin wetness up to the amount which most people find tolerable (W = 0.25). There is an optimal combination of room air and mean radiant temperatures which results in the lowest exergy consumption and thermal comfort (Isawa et all 2002).

As can be seen, the human-body exergy consumption rates vary with the combinations of room air temperature and mean radiant temperature. The solid line corresponds to thermally neutral conditions in which most people feel thermally comfortable. The area below the line corresponds to a rather cold environment. The lower either room air temperature or mean radiant temperature is, the higher the human body exergy consumption rate is. The reason is that the difference in temperature between the clothing surface and room air and interior wall surfaces becomes large. On the other hand, the area above the line corresponds to a rather hot environment. The higher either room air temperature or mean radiant temperature is, the slightly higher the human body exergy consumption is. This happens because sweating occurs and evaporation takes place and thereby the difference in temperature between the skin and room air and interior wall surfaces becomes large. The broken line in the upper right corner corresponds to skin wetness up to the amount which most people find tolerable.

The lowest exergy consumption rate emerges at the point where the room air temperature equals 18 C and mean radiant temperature 25 C. This suggests that the use of radiant warm exergy is more effective than the use of convective warm exergy for a heating purpose to realise both thermal comfort and as low exergy consumption within the human body as possible. Such a built environment can be provided by a moderate radiant heating system combined with passive heating strategies, for example, good thermal insulation and suitable thermal exergy storage capacity of building envelopes, solar-thermal-exergy gain through properly insulated window glazing and others.

It is interesting to see that, from the exergetic view point, there is an optimal combination of room air temperature and mean radiant temperature which results in thermally neutral conditions, namely PMV*=0, although, from the conventional energetic viewpoint, there are many combinations of room air temperature and mean radiant temperature. Some experienced scientists and engineers say that what they can see in Figure 21 is consistent with their experiences. It would be very encouraging for architects and engineers to conceive a system with as low exergy consumption as possible since it would bring about a higher quality of warmness that the occupants can sense in their given built environment. The human body exergy analyses have now just started to articulate why Low Exergy systems are essential for creating rational and comfortable built environment.