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Axiomatic design and HVAC systems: An efficient design decision-making criterion
Energy and Buildings 41 (2009) 146–153
Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Axiomatic design and HVAC systems: An efficient design decision-making criterion Miguel Cavique a,*, A.M. Gonc¸alves-Coelho b a b
Department of Mechanical Engineering, School of Technology of Setu´bal, Polytechnic Institute of Setu´bal, Campus do IPS, Estefanilha, 2914-508 Setu´bal, Portugal UNIDEMI, Department of Mechanical and Industrial Engineering, Faculty of Science and Technology, The New University of Lisbon, Campus de Caparica, 2829-516 Caparica, Portugal
A R T I C L E I N F O
A B S T R A C T
Article history: Received 17 October 2007 Received in revised form 7 August 2008 Accepted 8 August 2008
Axiomatic design (AD) is a theory that helps to develop new design objects and allows one to evaluate the quality of designs. The aim of this paper is to apply this theory to the design of heat ventilation and airconditioning (HVAC) systems and to come to conclusions about the design quality of some specific applications. The focus is the comfort and energy consumption in commercial buildings in South European climates. The discussion contains a brief description of variable air volume (VAV) systems and dedicated outdoor air systems (DOAS) with terminal units, such as fan-coils, induction units and chilled ceilings. Occasionally, the DOAS design should include over-cooled outdoor air in order to ensure an extra cooling means. According to the AD’s first axiom, ideal systems are independent or decoupled. Our conclusion is that VAV and DOAS with induction units are coupled designs, and on the other end, DOAS with fan-coils or chilled ceilings are decoupled designs. In addition, over-cooling outdoor air (OA) flow couples the OA flow with the indoor heat removable needs. ß 2008 Elsevier B.V. All rights reserved.
Keywords: VAV DOAS Comfort Energy Axiomatic design
1. Introduction In the heat ventilation and air-conditioning (HVAC) design, the focus can be either comfort or energy savings. ASHRAE standard 90.1-2004 [1] focuses on energy savings, which is fundamental to sustainability. However, the commitment to save energy may lead to poor design in terms of thermal comfort and healthy environments. Regarding comfort, the setting of an HVAC system is an ergonomic problem with balancing solutions being proposed in standards. ISO standard 7730-2005 [2] for thermal comfort ranks the customer’s needs in several ranges, according to the building’s quality. In terms of ventilation, European standard EN 13779-2004 [3] sets up a classification according to the ventilation needs. These ranges have a key role in design. For example, ISO 7730 prescribes an indoor temperature hysteresis of 1.5 8C for category B buildings, and EN 13779 states the range of 36–54 m3/h for the outdoor airflow per person in class 2 indoor air quality (IDA2). While these standards define ranges, the ASHRAE 62.1 [4] suggests minimum ventilation
* Corresponding author. Tel.: +351 265 79 0000; fax: +351 265 721 869. E-mail addresses: [email protected] (M. Cavique), [email protected] (A.M. Gonc¸alves-Coelho). Abbreviations: A, design matrix; AD, axiomatic design; AHU, air handling unit; CC, chilled ceiling; DOAS, dedicated outdoor air system; DP, design parameters; EA, exhaust air; EN, Standard of the European Committee for Standardization; FC, fancoil; FR, function requirements; HVAC, heat ventilation and air-conditioning; ISO, International Organization for Standardization; IU, induction units; OA, outside air; PM, airborne particle matter; RA, recirculation air; Ts, temperature supply; VAV, variable air volume. 0378-7788/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2008.08.002
bounds for acceptable environments. Although the ventilation systems are classified in single or dual duct HVAC systems [5], we will limit this analysis to the variable air volume system (VAV) and dedicated outdoors air system (DOAS) single duct systems. All HVAC system designs should fulfil thermal comfort needs and indoor air quality, which can be achieved by adjusting some parameters, taking energy savings into consideration. The design process is crucial in the accomplishment of those goals. It is therefore important to discuss the application of design theories in the HVAC system design. Axiomatic design (AD) [6] is a design theory that allows one to describe any design object in four different domains: the customer domain, the functional domain, the physical domain and the process domain [6]. Fig. 1 depicts the mapping between those four domains. Product design, for example, maps the relationships between the functional requirements described by vector {FR}, belonging to the functional domain, and the design parameters described by vector {DP}, belonging to the physical domain. Product design can be mathematically expressed by the following design equation: fFRg ¼ ½A:fDPg
(1)
where [A] is the design matrix. Different sets of DP can satisfy the functional requirements of Eq. (1), which means that one can choose between different design solutions. According to AD, a good design must fulfil the independence axiom, which states that changing the value of any DP should not affect more that one FR. As a result, the number of DPs must be equal or higher than the number of FRs. If the number of DPs is
M. Cavique, A.M. Gonc¸alves-Coelho / Energy and Buildings 41 (2009) 146–153
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Fig. 1. The product design process as mapping.
lower than the number of FRs, then the system is coupled, since it is impossible to fulfil all FRs independently. In this case, one must decouple the system by adding new DPs. If the number of DPs is higher than the number of FRs, then the system is either coupled or redundant. In redundant systems, it might be possible to aggregate DPs, or to fix a set of DPs at constant values [6]. Some installations need redundant designs because they can fulfil the FRs by using different combinations of DPs. A good design should be ‘‘uncoupled’’, i.e. characterized by a diagonal design matrix [A], or ‘‘decoupled’’, i.e. with a lower or upper triangular matrix that can be ‘‘tuned’’ by choosing the right adjustment order of DPs values. All other shapes of matrix [A] result in poor design, in other words a ‘‘coupled design’’ [7], since any change in the required value of a FR generally imposes changes in several DPs. The AD’s information axiom states that the best solution in a set of known independent solutions is the one with the minimum information content. The information axiom will not be discussed here, and details about this matter can be found elsewhere [6]. According to axiomatic design, a FR at some level of abstraction can be decomposed into independent child FRs belonging to the following level. The union of these child functions should fulfil the parent FR. FRs are verbalized ranges of a desired solution. To help defining a solution there are some verbalized bounds, called constraints, which appear in the decomposition process by influencing the chosen DPs. Each FR will require the choice of a DP that performs it, which will influence the choice of all the subsequent children FRs. This is called the zigzagging process performed between the functional and the physical domains until one reaches the most detailed DP (Fig. 2) [7]. FRs and DPs may be merged in the same plan as depicted in Fig. 7. 2. Typical HVAC systems 2.1. Variable air volume Fig. 3 depicts a VAV system, with only two arbitrary spaces in order to simplify the image. We will call ‘‘space’’ to any independent building area with its own temperature control, and ‘‘zone’’ to a group of spaces climatized by a single system [8]. The system has an air-handling unit (AHU) that supplies a variable airflow (1) at constant temperature, the purpose of which is to fulfil the heat removal needs of different zones. Each space has a VAV box (2) that controls the cooled airflow by setting the position of a damper inside each VAV box. There are various types of VAV boxes, such as the reheating coil type, the induction type, or the fan-assisted type [9], the application details of which will not be discussed here. In a partial load condition, the airflow passing through each VAV box can be adjusted so that the indoor air can attain the required temperature. As a result, the airflow supplied by the AHU must also be adjusted. The AHU uses the outside air (OA) and mixes it with recirculation air (RA) taken from all spaces.
Fig. 2. The zigzagging process.
Fig. 3. The VAV system.
Subsequently, the AHU treats the airflow by filtration, heating, cooling and humidification, and supplies it to the building at a predetermined temperature (Ts). Exhaust air (EA) flow is released to the atmosphere at an OA flow similar rate. Varying the AHU fan speed (N) causes the variation of the airflow through the AHU, which affects energy consumption, since the energy that is delivered to the flow depends on the third power of fan speed. A common method to adjust the airflow is by setting a constant pressure value in a specific section of the duct (P) and controlling the fan speed accordingly. Other more expensive control methods are based on the VAV boxes monitoring allowing resetting the static pressure set point [1]. VAV is known to be an energy efficient system [9] especially when the load varies significantly, as in the cases of perimeter facade areas or shopping areas. Nevertheless, moist removal in VAV systems may be difficult during working periods with high chilling water temperature [9]. Another important aspect of any HVAC system is the OA flow delivered to the building, which usually depends on the number of people in the building. In the case of a VAV system, the OA flow may be set according to any condition related to the number of people in the building, such as the occupancy timetable or the CO2 concentration. Nevertheless, zones with low heat loads will receive low supply airflow and consequently a low OA fraction. Therefore, spaces with high human occupancy and low heat loads tend to receive an insufficient OA flow. Using free cooling raises OA to 100% of the supplied airflow, avoiding insufficient OA flow and reducing energy consumption during middle seasons. A design challenge arises when using VAV in low footprint buildings, due to the scarce space available for ducts.
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The commonly used VAV system keeps the supplied air at constant temperature and varies the supplied airflow depending on the pressure. In addition, the outdoor airflow rate is kept constant according to the value stated in the design specifications. VAV is the most usual air-conditioning system in the United States of America. 2.2. Dedicated outdoor air system DOAS is extensively used in the EU countries in association with fan-coils, chilled ceilings or induction units. Chilled ceilings and induction units are more common in the northern countries, while systems that use fan-coils as terminal units are especially used in southern countries, although they are common all over the EU. Fig. 4 depicts a DOAS serving two generic spaces, each one with its terminal unit. The DOAS uses a detached ventilation system to supply the necessary outdoor air. A DOAS is characterised by treating the outside air in a dedicated AHU, delivering it into each space at a constant flow. Design specifications define the total OA flow and a similar EA flow, keeping them constant during system operation. Each space receives a predetermined constant OA flow and the sum of the partial flows determines the total outside air that the AHU has to deliver. The OA flow is usually set to a specific value, but it is possible to design a DOAS for which the OA flow varies according to any zone parameter, as for example the return air CO2 concentration. Free cooling is also possible, making the AHU supply air temperature equal to the outside air temperature. In a DOAS, the terminal units are sets of fan-coils, induction units or chilled ceilings, the role of which is to remove the internal heat load [9]. Fan-coils (FC) (1) treat the outdoor air supplied by the AHU after it is mixed with the return air from the space they climatize, so that it attains the required temperature. A FC usually has a low efficiency filter, an air–water heat exchanger, and a fan that is able to supply the airflow at an external pressure drop. The AHU’s supply temperature (Ts) is usually equal to the comfort temperature. In this case, the outdoor air does not introduce any sensible load into the room [9]. The energy efficiency of a system with fan-coils can be poor due to the efficiency of motors and fans and because of unnecessary latent cooling removal. Fan-coil efficiency increases by resorting to more efficient fans and motors, by using coils with the appropriate sensible heat ratio (SHR) and by adjusting the chiller water temperature. A DOAS plus fan-coils is widely used in general applications, such as hotels, offices and residential buildings. Induction units (IU) (1) are terminal units that receive a cooled OA flow from a central AHU, called primary air (PA), mixing it with return air from the space they treat (Fig. 5). A duct system at medium or high-pressure supplies the primary airflow, adjusted by a duct damper to a unit plenum, so that the air flows through induction
Fig. 4. The DOAS plus fan-coils.
Fig. 5. The DOAS plus induction units.
nozzles that cause a lower pressure inside the unit. This induces a secondary airflow coming from the room. The secondary airflow passes in the unit coil where it is cooled and after that mixed with the PA. Finally, the resulting mixture of both flows is supplied into the room [9]. The induction units have a heating and/or cooling coil and usually work at a temperature that does not remove any latent cooling. Therefore, in order to remove the latent heat, the PA should be supplied dryer than the indoor air. As a result, the PA temperature must be lower than the indoor air, but not cool enough to remove more heat than the space heat load. The usual cooling capacity of the primary airflow is about one-half of the coils in the IUs. Because of the lack of latent cooling capacity of the terminal units, the system does not allow for opening windows, for it would cause moisture intake. In order to increase IU duty, the AHU may cool the PA to an even lower temperature than space comfort temperature, allowing the PA to remove more sensible and latent heat from the space. The DOAS plus IU has energy advantages compared to FC systems because it uses chilled water at a higher temperature and does not have the energy consumption of fans. Nevertheless, it imposes an increase in the air duct pressure of more than 70 Pa in order to cause the air to flow against the IU internal resistance. The average coil temperature might be higher than the room dew point, causing a water inlet temperature of around 16 8C with an inlet to outlet difference of 2–3 8C. Compared to the FCs, this shorter inlet to outlet difference introduces an increase in the pumping energy consumption. The duty of an induction unit depends on the PA flow, and consequently of the OA flow. Therefore, the heat load determines the OA flow, so that it is not possible to define the OA flow in an independent manner. The resultant OA airflow is usually higher than the proposed value in the low ranges of EN13779. In most plants with induction units, the noise level is usually lower than in plants with DOAS plus FC. The OA flow is usually higher and the energy consumption lower. Chilled ceilings (CC) (1 in Fig. 6) are ceiling panel structures entrenched to chilled water pipes [9] that remove sensible heat through radiant and convection heat transfer. Given that the CC temperature is close to the water temperature, and the panel temperature should be above room dew point in order to avoid condensation, then the chilled water temperature must be between 16 and 18 8C. In such conditions, a CC panel removes 60–80 W/m2 of space heat load and reduces the mean radiant thermal temperature. The thermal comfort depends on the air temperature and on the mean radiant temperature. Decreasing mean radiant temperature allows increasing the indoor air set point. As radiative systems have a slow thermal response, chilled ceilings are especially suitable for general steady heat load applications [9]. Due to moisture inlet and condensation, the building envelope should be airtight and window opening and natural ventilation are not allowed.
M. Cavique, A.M. Gonc¸alves-Coelho / Energy and Buildings 41 (2009) 146–153
Fig. 6. The DOAS plus chilled ceilings.
In some applications, cooling OA to a temperature lower than the comfort temperature allows the system to remove more sensible and latent heat from the space. The main arguments to use CC are the low noise level in the ambience and the high thermal comfort, which depends mostly on the low residual velocity. The axiomatic design theory allows comparing the typical HVAC systems presented. 3. HVAC systems analysis Standards suggest bounded values for noise level, humidity and airborne particle matter per unit volume (PM) for common commercial HVAC. The developer must also define a cost limit. Consequently, in the context of commercial HVAC, the noise level, humidity, PM and the cost value are constraints. As shown in Fig. 7, there is only one FR to fulfil at the top level (level zero): ‘‘provide climatization to the commercial building’’. This choice leads to the selection of a ‘‘commercial building HVAC system’’ in the physical domain. The decomposition of the top level FR at level one leads to the following child functions: ‘‘ensure appropriate thermic comfort’’, ‘‘ensure healthy environment’’ and ‘‘ensure
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energy efficiency’’. The corresponding DPs are ‘‘active system’’, ‘‘ventilation system’’ and ‘‘efficient solutions’’, depicted in Fig. 7, in which rectangles represent the FRs and ovals represent the DPs. Focusing on the active and ventilation system, we carry out the decomposition of ‘‘efficient solutions’’ just until level two. At this level, in order to set up ‘‘efficient solutions’’ one needs to perform the functions of ‘‘adjust flows’’ and ‘‘recover heat’’, as well as use ‘‘efficient equipment’’ and define ‘‘efficient working conditions’’. The ‘‘active system’’ FRs at level two are to ‘‘provide the appropriate temperature’’ and to ‘‘provide appropriate residual velocity’’. The corresponding DPs are the ‘‘temperature control system’’ and the ‘‘Indoor flow supply system’’. Humidity is a constraint in the present context, especially important in systems using CC or IU. Healthy environments are strong related to indoor air quality techniques. These techniques are dilution, filtration, and local exhaust of polluted air. Special applications use local exhausts techniques, but they are seldom used in commercial buildings. PM is a constraint in commercial buildings, this being controlled by filtration equipment. Therefore, the child ‘‘ventilation system’’ FR is to ‘‘ensure dilution of pollution’’, performed by the ‘‘outdoor air control system’’. Fig. 7 sketches the decomposition process until level two, valid for the commercial HVAC systems studied. In the following levels, interesting differences between systems occur, which are presented in the next sections. 3.1. VAV system As represented in Fig. 8, the VAV ‘‘temperature control system’’ ensures the necessary airflow at each space through the VAV box. The AHU has a battery that adjusts the temperature of the supply airflow and the AHU ensures the total air supply flow to the building. A correct selection of diffusers guarantees a correct indoor residual air velocity, avoiding the draught effect. Although the total OA flow is provided by the AHU, the spaces OA fraction
Fig. 7. HVAC common DPs and FRs’ decomposition.
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Fig. 8. VAV system’s level 2 decomposition.
remain dependent of the VAV box airflow. The FRs and DPs of two generic spaces, m and n (visible) depicted in the figure, expose the influence of one space system on the behaviour of the other. Eq. (2) contains the VAV’s design matrix, where ‘‘X’’ stands for a strong relationship between an FR and a DP, while a ‘‘x’’ in the matrix represents a weak relationship. In the matrix, dashed lines plotted horizontally separate the FRs levels, and vertical dashed lines separate the DPs levels. The VAV system is coupled, as there are more FRs than DPs in the design equation. The off-diagonals elements on Eq. (2) show that: In order to ‘‘ensure dilution of pollution’’, FR2.3 depends on DP2.1, the ‘‘temperature control system’’. In order to ‘‘adjust airflows’’, FR2.4 depends slightly on DP2.1, the ‘‘temperature control system’’. In order to ‘‘ensure total supply airflow’’, FR3.4 depends on DP3.1 and DP3.2, the ‘‘VAV boxes airflow’’. In order to ‘‘ensure space supply air velocity’’, both FR3.5 and FR3.6 have a weak dependency of the matching DP3.1 and DP3.2, the ‘‘VAV boxes airflow’’. In order to ‘‘provide space OA’’, both FR3.7 and FR3.8 depend on a set of DP3.1 and DP3.2, the ‘‘VAV boxes airflow’’.
(2)
Note that, according to ASHRAE 62.1, ensuring dilution of pollution is a bounded parameter. It is therefore a constraint, which explains why FR3.7 to FR3.9 would vanish from the design equation, giving raise to a decoupled design. 3.2. DOAS Fig. 9 depicts the decomposition process of the DOAS plus FCs, starting at the DPs of level 2 and ending on the FRs and DPs at level 3. It states that the ‘‘temperature control system’’ should adjust each space air supply temperature using the FC’s cooling capacity. The FC’s flow is the design parameter to ensure the space supply airflow, which has an important effect in the residual air velocity. The AHU adjusts the supply air temperature in the battery, not running over the FCs’ cooling capacity. The AHU is also responsible for ensuring the total OA airflow, suitably provided to each space. Eq. (3) represents the DOAS plus FCs’ design equation, in which the upper off-diagonal elements state the relation between FCs’ cooling capacity and FCs’ flow. The lower off-diagonals elements represent the influence of varying the FC speed into the supply air velocity.
(3)
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Fig. 9. DOAS plus FC’s level 2 decomposition.
Fig. 10. DOAS plus IU’s level 2 decomposition.
Designing a FC system at an established speed solves this coupling problem. Consequently, this design practice eliminates the off-diagonal elements of the matrix, and the design becomes independent. The design establishes, therefore, a FC flow that allows choosing the diffuser for a determined air supply velocity. Fig. 10 depicts the decomposition process of a DOAS plus IU, showing that the number of DPs is lower than the number of FRs. This system design is therefore coupled. Eq. (4) states that the temperature control must adjust the spaces’ air supply temperature using the IU’s cooling capacity. The AHU adjusts a constant PA
flow at a certain temperature, which is regulated in the battery. The temperature of the PA must not be too low that reduces any space air temperature under the set point temperature. For each building, a difficult balance has to be set in order to establish a lower bound for the PA temperature. The regulated PA flow at each IU ensures the induction airflow. The IU supply airflow and the selected diffuser determine the space air velocity. The matrix off-diagonals ‘‘OA’’ represent the use of over-cooled outside air in order to improve the IUs’ cooling capacity. Adjusting the AHU air supply temperature will consequently change the IU
Fig. 11. DOAS plus CC’s level 2 decomposition.
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cooling capacity and adjusting space air temperature will depend on AHU supply air temperature.
the different spaces, the damper minimum setting will be too large to allow any energy benefits. Therefore, this suggestion should be applied to systems whose spaces have a similar thermal behaviour. Nevertheless, if at each space the OA flow needs vary according to the thermal load, a common VAV can be tuned to work correctly. The DOAS plus IU equation has one DP less for each space, which gives raise to a coupled design. This coupling problem may be solved by introducing a nozzle control for each IU that would adjust the OA flow while maintaining the induction effect. Nevertheless, the coupling between PA temperature and IUs’ duty persists. In order to solve this coupling problem, the PA temperature should be close to the indoor air temperature. As the OA depends on IUs’ primary flow, the indoor air quality is defined by the temperature control system. Therefore, the IDA rating cannot be pre-defined. This analysis has exposed the main characteristics of the common HVAC systems, but it is important to notice that in an HVAC project multiple systems might be part of a solution. In each zone, a solution may be found by merging systems that match its weaknesses, as occurs when one use fan-coils in perimeter areas, while leaving IU or CC to climatize the steadier central spaces. 4. Conclusions
(4) Fig. 11 depicts the decomposition process of a DOAS plus CC. In these systems, the operative temperature [2] expresses the thermal comfort that depends on the mean radiant surfaces temperature and on the indoor dry air temperature. Eq. (5) states that the temperature control must ensure the space operative temperature through the CC’s cooling capacity. The AHU adjusts the supply air temperature and ensures the total OA flow. As the relevant elements of the design matrix are in the diagonal, the DOAS plus CC is an independent design, if no overcooled OA is used as a cooling method.
(5)
3.3. Systems discussion Applying axiomatic design to HVAC systems allows changing the way we look at HVAC systems. To solve the VAV coupling problem, one must introduce one more DP for each space, in order to provide the OA flow independently at each space. A possible solution is to introduce a minimum position for the VAV damper that would ensure the necessary OA flow regardless of the load conditions. However, if there are large load dissimilarities between
This work exposes the application of axiomatic design (AD) to the common design of HVAC systems. According to AD, a design must be either independent or decoupled. The object of this work is the application of AD to the design of commercial HVAC systems to be used in EU southern climates, studying its behaviour during cooling season. In commercial applications, noise, humidity and the airborne particle matter are system constraints. This evaluation centres on the classification of VAV and DOAS, defining the correct application for those systems. The terminal units that were considered in this study in order to create a system with the DOAS were the fan-coils (FC), the induction units (IU) and the chilled ceiling (CC). VAV couples indoor air supply to the spaces’ heat loads, and therefore it cannot undertake the supply of the required outdoor airflow in every space permanently. For that reason, it is appropriate for zones where the space thermal loads vary according to the outdoor air (OA) requirements. The use of free cooling techniques increases the yearly OA flow delivery to the building, reducing the shortage of OA flow that may occur in some spaces. DOAS plus FC is an independent design, as any function can be accomplished independently by varying just one DP. As a result, the DOAS plus FC may have the indoor air quality varied independently of thermal quality. The space noise constraint defines the FC’s speed that might stay unchanged during system operation. Otherwise, some minor coupling occurs between the supply airflow and the FC’s duty. A DOAS plus IU is a coupled design, as the thermal load at each space defines its outdoor airflow. However, a DOAS plus IU needs a high primary airflow rate that usually leads to good indoor air quality. Nevertheless, the function ‘‘Provide OA space n OA’’ probably cannot be fulfilled at every space for any predetermined OA flow. As primary air (PA) contributes to remove the space heat as well as the IU coil, the PA temperature setting might be careful not to develop a coupled design. DOAS plus CC is an independent design, so that the CC panels remove space loads independently of the DOAS that deliver the necessary outdoor air. As a conclusion, both VAV and DOAS plus IU are coupled designs, in contrast with DOAS plus FC and DOAS plus CC, which are decoupled designs. In addition, a special care must be taken when using over-cooled OA flow in order to increase CC
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or IU internal duties, since this would couple the outdoor air needs with the thermal loads, hence yielding to coupled designs. References [1] ASHRAE Standard 90.1-2004, Energy Standard for Buildings Except Low-Rise Residential Buildings. [2] ISO 7730-2005, Ergonomics of the thermal environment — Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria.
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[3] EN13779-2004, Ventilation for non-residential buildings – Performance requirements for ventilation and room-conditioning systems. [4] ASHRAE 62.1-2004, Ventilation for Acceptable Indoor Air Quality. [5] 62.1 User’s Manual, ANSI/ASHRAE Standard 62.1-2004, Ventilation for Acceptable Indoor Air Quality. [6] N.P. Suh, The Principles of Design, Oxford University Press, 1990. [7] N.P. Suh, Axiomatic Design: Advances and Applications, Oxford University Press, 1998. [8] SHRAE Handbook, Fundamentals, 2005. [9] ASHRAE Handbook, HVAC Systems and Equipment, 2004.
Contents lists available at ScienceDirect
Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild
Axiomatic design and HVAC systems: An efficient design decision-making criterion Miguel Cavique a,*, A.M. Gonc¸alves-Coelho b a b
Department of Mechanical Engineering, School of Technology of Setu´bal, Polytechnic Institute of Setu´bal, Campus do IPS, Estefanilha, 2914-508 Setu´bal, Portugal UNIDEMI, Department of Mechanical and Industrial Engineering, Faculty of Science and Technology, The New University of Lisbon, Campus de Caparica, 2829-516 Caparica, Portugal
A R T I C L E I N F O
A B S T R A C T
Article history: Received 17 October 2007 Received in revised form 7 August 2008 Accepted 8 August 2008
Axiomatic design (AD) is a theory that helps to develop new design objects and allows one to evaluate the quality of designs. The aim of this paper is to apply this theory to the design of heat ventilation and airconditioning (HVAC) systems and to come to conclusions about the design quality of some specific applications. The focus is the comfort and energy consumption in commercial buildings in South European climates. The discussion contains a brief description of variable air volume (VAV) systems and dedicated outdoor air systems (DOAS) with terminal units, such as fan-coils, induction units and chilled ceilings. Occasionally, the DOAS design should include over-cooled outdoor air in order to ensure an extra cooling means. According to the AD’s first axiom, ideal systems are independent or decoupled. Our conclusion is that VAV and DOAS with induction units are coupled designs, and on the other end, DOAS with fan-coils or chilled ceilings are decoupled designs. In addition, over-cooling outdoor air (OA) flow couples the OA flow with the indoor heat removable needs. ß 2008 Elsevier B.V. All rights reserved.
Keywords: VAV DOAS Comfort Energy Axiomatic design
1. Introduction In the heat ventilation and air-conditioning (HVAC) design, the focus can be either comfort or energy savings. ASHRAE standard 90.1-2004 [1] focuses on energy savings, which is fundamental to sustainability. However, the commitment to save energy may lead to poor design in terms of thermal comfort and healthy environments. Regarding comfort, the setting of an HVAC system is an ergonomic problem with balancing solutions being proposed in standards. ISO standard 7730-2005 [2] for thermal comfort ranks the customer’s needs in several ranges, according to the building’s quality. In terms of ventilation, European standard EN 13779-2004 [3] sets up a classification according to the ventilation needs. These ranges have a key role in design. For example, ISO 7730 prescribes an indoor temperature hysteresis of 1.5 8C for category B buildings, and EN 13779 states the range of 36–54 m3/h for the outdoor airflow per person in class 2 indoor air quality (IDA2). While these standards define ranges, the ASHRAE 62.1 [4] suggests minimum ventilation
* Corresponding author. Tel.: +351 265 79 0000; fax: +351 265 721 869. E-mail addresses: [email protected] (M. Cavique), [email protected] (A.M. Gonc¸alves-Coelho). Abbreviations: A, design matrix; AD, axiomatic design; AHU, air handling unit; CC, chilled ceiling; DOAS, dedicated outdoor air system; DP, design parameters; EA, exhaust air; EN, Standard of the European Committee for Standardization; FC, fancoil; FR, function requirements; HVAC, heat ventilation and air-conditioning; ISO, International Organization for Standardization; IU, induction units; OA, outside air; PM, airborne particle matter; RA, recirculation air; Ts, temperature supply; VAV, variable air volume. 0378-7788/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2008.08.002
bounds for acceptable environments. Although the ventilation systems are classified in single or dual duct HVAC systems [5], we will limit this analysis to the variable air volume system (VAV) and dedicated outdoors air system (DOAS) single duct systems. All HVAC system designs should fulfil thermal comfort needs and indoor air quality, which can be achieved by adjusting some parameters, taking energy savings into consideration. The design process is crucial in the accomplishment of those goals. It is therefore important to discuss the application of design theories in the HVAC system design. Axiomatic design (AD) [6] is a design theory that allows one to describe any design object in four different domains: the customer domain, the functional domain, the physical domain and the process domain [6]. Fig. 1 depicts the mapping between those four domains. Product design, for example, maps the relationships between the functional requirements described by vector {FR}, belonging to the functional domain, and the design parameters described by vector {DP}, belonging to the physical domain. Product design can be mathematically expressed by the following design equation: fFRg ¼ ½A:fDPg
(1)
where [A] is the design matrix. Different sets of DP can satisfy the functional requirements of Eq. (1), which means that one can choose between different design solutions. According to AD, a good design must fulfil the independence axiom, which states that changing the value of any DP should not affect more that one FR. As a result, the number of DPs must be equal or higher than the number of FRs. If the number of DPs is
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Fig. 1. The product design process as mapping.
lower than the number of FRs, then the system is coupled, since it is impossible to fulfil all FRs independently. In this case, one must decouple the system by adding new DPs. If the number of DPs is higher than the number of FRs, then the system is either coupled or redundant. In redundant systems, it might be possible to aggregate DPs, or to fix a set of DPs at constant values [6]. Some installations need redundant designs because they can fulfil the FRs by using different combinations of DPs. A good design should be ‘‘uncoupled’’, i.e. characterized by a diagonal design matrix [A], or ‘‘decoupled’’, i.e. with a lower or upper triangular matrix that can be ‘‘tuned’’ by choosing the right adjustment order of DPs values. All other shapes of matrix [A] result in poor design, in other words a ‘‘coupled design’’ [7], since any change in the required value of a FR generally imposes changes in several DPs. The AD’s information axiom states that the best solution in a set of known independent solutions is the one with the minimum information content. The information axiom will not be discussed here, and details about this matter can be found elsewhere [6]. According to axiomatic design, a FR at some level of abstraction can be decomposed into independent child FRs belonging to the following level. The union of these child functions should fulfil the parent FR. FRs are verbalized ranges of a desired solution. To help defining a solution there are some verbalized bounds, called constraints, which appear in the decomposition process by influencing the chosen DPs. Each FR will require the choice of a DP that performs it, which will influence the choice of all the subsequent children FRs. This is called the zigzagging process performed between the functional and the physical domains until one reaches the most detailed DP (Fig. 2) [7]. FRs and DPs may be merged in the same plan as depicted in Fig. 7. 2. Typical HVAC systems 2.1. Variable air volume Fig. 3 depicts a VAV system, with only two arbitrary spaces in order to simplify the image. We will call ‘‘space’’ to any independent building area with its own temperature control, and ‘‘zone’’ to a group of spaces climatized by a single system [8]. The system has an air-handling unit (AHU) that supplies a variable airflow (1) at constant temperature, the purpose of which is to fulfil the heat removal needs of different zones. Each space has a VAV box (2) that controls the cooled airflow by setting the position of a damper inside each VAV box. There are various types of VAV boxes, such as the reheating coil type, the induction type, or the fan-assisted type [9], the application details of which will not be discussed here. In a partial load condition, the airflow passing through each VAV box can be adjusted so that the indoor air can attain the required temperature. As a result, the airflow supplied by the AHU must also be adjusted. The AHU uses the outside air (OA) and mixes it with recirculation air (RA) taken from all spaces.
Fig. 2. The zigzagging process.
Fig. 3. The VAV system.
Subsequently, the AHU treats the airflow by filtration, heating, cooling and humidification, and supplies it to the building at a predetermined temperature (Ts). Exhaust air (EA) flow is released to the atmosphere at an OA flow similar rate. Varying the AHU fan speed (N) causes the variation of the airflow through the AHU, which affects energy consumption, since the energy that is delivered to the flow depends on the third power of fan speed. A common method to adjust the airflow is by setting a constant pressure value in a specific section of the duct (P) and controlling the fan speed accordingly. Other more expensive control methods are based on the VAV boxes monitoring allowing resetting the static pressure set point [1]. VAV is known to be an energy efficient system [9] especially when the load varies significantly, as in the cases of perimeter facade areas or shopping areas. Nevertheless, moist removal in VAV systems may be difficult during working periods with high chilling water temperature [9]. Another important aspect of any HVAC system is the OA flow delivered to the building, which usually depends on the number of people in the building. In the case of a VAV system, the OA flow may be set according to any condition related to the number of people in the building, such as the occupancy timetable or the CO2 concentration. Nevertheless, zones with low heat loads will receive low supply airflow and consequently a low OA fraction. Therefore, spaces with high human occupancy and low heat loads tend to receive an insufficient OA flow. Using free cooling raises OA to 100% of the supplied airflow, avoiding insufficient OA flow and reducing energy consumption during middle seasons. A design challenge arises when using VAV in low footprint buildings, due to the scarce space available for ducts.
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The commonly used VAV system keeps the supplied air at constant temperature and varies the supplied airflow depending on the pressure. In addition, the outdoor airflow rate is kept constant according to the value stated in the design specifications. VAV is the most usual air-conditioning system in the United States of America. 2.2. Dedicated outdoor air system DOAS is extensively used in the EU countries in association with fan-coils, chilled ceilings or induction units. Chilled ceilings and induction units are more common in the northern countries, while systems that use fan-coils as terminal units are especially used in southern countries, although they are common all over the EU. Fig. 4 depicts a DOAS serving two generic spaces, each one with its terminal unit. The DOAS uses a detached ventilation system to supply the necessary outdoor air. A DOAS is characterised by treating the outside air in a dedicated AHU, delivering it into each space at a constant flow. Design specifications define the total OA flow and a similar EA flow, keeping them constant during system operation. Each space receives a predetermined constant OA flow and the sum of the partial flows determines the total outside air that the AHU has to deliver. The OA flow is usually set to a specific value, but it is possible to design a DOAS for which the OA flow varies according to any zone parameter, as for example the return air CO2 concentration. Free cooling is also possible, making the AHU supply air temperature equal to the outside air temperature. In a DOAS, the terminal units are sets of fan-coils, induction units or chilled ceilings, the role of which is to remove the internal heat load [9]. Fan-coils (FC) (1) treat the outdoor air supplied by the AHU after it is mixed with the return air from the space they climatize, so that it attains the required temperature. A FC usually has a low efficiency filter, an air–water heat exchanger, and a fan that is able to supply the airflow at an external pressure drop. The AHU’s supply temperature (Ts) is usually equal to the comfort temperature. In this case, the outdoor air does not introduce any sensible load into the room [9]. The energy efficiency of a system with fan-coils can be poor due to the efficiency of motors and fans and because of unnecessary latent cooling removal. Fan-coil efficiency increases by resorting to more efficient fans and motors, by using coils with the appropriate sensible heat ratio (SHR) and by adjusting the chiller water temperature. A DOAS plus fan-coils is widely used in general applications, such as hotels, offices and residential buildings. Induction units (IU) (1) are terminal units that receive a cooled OA flow from a central AHU, called primary air (PA), mixing it with return air from the space they treat (Fig. 5). A duct system at medium or high-pressure supplies the primary airflow, adjusted by a duct damper to a unit plenum, so that the air flows through induction
Fig. 4. The DOAS plus fan-coils.
Fig. 5. The DOAS plus induction units.
nozzles that cause a lower pressure inside the unit. This induces a secondary airflow coming from the room. The secondary airflow passes in the unit coil where it is cooled and after that mixed with the PA. Finally, the resulting mixture of both flows is supplied into the room [9]. The induction units have a heating and/or cooling coil and usually work at a temperature that does not remove any latent cooling. Therefore, in order to remove the latent heat, the PA should be supplied dryer than the indoor air. As a result, the PA temperature must be lower than the indoor air, but not cool enough to remove more heat than the space heat load. The usual cooling capacity of the primary airflow is about one-half of the coils in the IUs. Because of the lack of latent cooling capacity of the terminal units, the system does not allow for opening windows, for it would cause moisture intake. In order to increase IU duty, the AHU may cool the PA to an even lower temperature than space comfort temperature, allowing the PA to remove more sensible and latent heat from the space. The DOAS plus IU has energy advantages compared to FC systems because it uses chilled water at a higher temperature and does not have the energy consumption of fans. Nevertheless, it imposes an increase in the air duct pressure of more than 70 Pa in order to cause the air to flow against the IU internal resistance. The average coil temperature might be higher than the room dew point, causing a water inlet temperature of around 16 8C with an inlet to outlet difference of 2–3 8C. Compared to the FCs, this shorter inlet to outlet difference introduces an increase in the pumping energy consumption. The duty of an induction unit depends on the PA flow, and consequently of the OA flow. Therefore, the heat load determines the OA flow, so that it is not possible to define the OA flow in an independent manner. The resultant OA airflow is usually higher than the proposed value in the low ranges of EN13779. In most plants with induction units, the noise level is usually lower than in plants with DOAS plus FC. The OA flow is usually higher and the energy consumption lower. Chilled ceilings (CC) (1 in Fig. 6) are ceiling panel structures entrenched to chilled water pipes [9] that remove sensible heat through radiant and convection heat transfer. Given that the CC temperature is close to the water temperature, and the panel temperature should be above room dew point in order to avoid condensation, then the chilled water temperature must be between 16 and 18 8C. In such conditions, a CC panel removes 60–80 W/m2 of space heat load and reduces the mean radiant thermal temperature. The thermal comfort depends on the air temperature and on the mean radiant temperature. Decreasing mean radiant temperature allows increasing the indoor air set point. As radiative systems have a slow thermal response, chilled ceilings are especially suitable for general steady heat load applications [9]. Due to moisture inlet and condensation, the building envelope should be airtight and window opening and natural ventilation are not allowed.
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Fig. 6. The DOAS plus chilled ceilings.
In some applications, cooling OA to a temperature lower than the comfort temperature allows the system to remove more sensible and latent heat from the space. The main arguments to use CC are the low noise level in the ambience and the high thermal comfort, which depends mostly on the low residual velocity. The axiomatic design theory allows comparing the typical HVAC systems presented. 3. HVAC systems analysis Standards suggest bounded values for noise level, humidity and airborne particle matter per unit volume (PM) for common commercial HVAC. The developer must also define a cost limit. Consequently, in the context of commercial HVAC, the noise level, humidity, PM and the cost value are constraints. As shown in Fig. 7, there is only one FR to fulfil at the top level (level zero): ‘‘provide climatization to the commercial building’’. This choice leads to the selection of a ‘‘commercial building HVAC system’’ in the physical domain. The decomposition of the top level FR at level one leads to the following child functions: ‘‘ensure appropriate thermic comfort’’, ‘‘ensure healthy environment’’ and ‘‘ensure
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energy efficiency’’. The corresponding DPs are ‘‘active system’’, ‘‘ventilation system’’ and ‘‘efficient solutions’’, depicted in Fig. 7, in which rectangles represent the FRs and ovals represent the DPs. Focusing on the active and ventilation system, we carry out the decomposition of ‘‘efficient solutions’’ just until level two. At this level, in order to set up ‘‘efficient solutions’’ one needs to perform the functions of ‘‘adjust flows’’ and ‘‘recover heat’’, as well as use ‘‘efficient equipment’’ and define ‘‘efficient working conditions’’. The ‘‘active system’’ FRs at level two are to ‘‘provide the appropriate temperature’’ and to ‘‘provide appropriate residual velocity’’. The corresponding DPs are the ‘‘temperature control system’’ and the ‘‘Indoor flow supply system’’. Humidity is a constraint in the present context, especially important in systems using CC or IU. Healthy environments are strong related to indoor air quality techniques. These techniques are dilution, filtration, and local exhaust of polluted air. Special applications use local exhausts techniques, but they are seldom used in commercial buildings. PM is a constraint in commercial buildings, this being controlled by filtration equipment. Therefore, the child ‘‘ventilation system’’ FR is to ‘‘ensure dilution of pollution’’, performed by the ‘‘outdoor air control system’’. Fig. 7 sketches the decomposition process until level two, valid for the commercial HVAC systems studied. In the following levels, interesting differences between systems occur, which are presented in the next sections. 3.1. VAV system As represented in Fig. 8, the VAV ‘‘temperature control system’’ ensures the necessary airflow at each space through the VAV box. The AHU has a battery that adjusts the temperature of the supply airflow and the AHU ensures the total air supply flow to the building. A correct selection of diffusers guarantees a correct indoor residual air velocity, avoiding the draught effect. Although the total OA flow is provided by the AHU, the spaces OA fraction
Fig. 7. HVAC common DPs and FRs’ decomposition.
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Fig. 8. VAV system’s level 2 decomposition.
remain dependent of the VAV box airflow. The FRs and DPs of two generic spaces, m and n (visible) depicted in the figure, expose the influence of one space system on the behaviour of the other. Eq. (2) contains the VAV’s design matrix, where ‘‘X’’ stands for a strong relationship between an FR and a DP, while a ‘‘x’’ in the matrix represents a weak relationship. In the matrix, dashed lines plotted horizontally separate the FRs levels, and vertical dashed lines separate the DPs levels. The VAV system is coupled, as there are more FRs than DPs in the design equation. The off-diagonals elements on Eq. (2) show that: In order to ‘‘ensure dilution of pollution’’, FR2.3 depends on DP2.1, the ‘‘temperature control system’’. In order to ‘‘adjust airflows’’, FR2.4 depends slightly on DP2.1, the ‘‘temperature control system’’. In order to ‘‘ensure total supply airflow’’, FR3.4 depends on DP3.1 and DP3.2, the ‘‘VAV boxes airflow’’. In order to ‘‘ensure space supply air velocity’’, both FR3.5 and FR3.6 have a weak dependency of the matching DP3.1 and DP3.2, the ‘‘VAV boxes airflow’’. In order to ‘‘provide space OA’’, both FR3.7 and FR3.8 depend on a set of DP3.1 and DP3.2, the ‘‘VAV boxes airflow’’.
(2)
Note that, according to ASHRAE 62.1, ensuring dilution of pollution is a bounded parameter. It is therefore a constraint, which explains why FR3.7 to FR3.9 would vanish from the design equation, giving raise to a decoupled design. 3.2. DOAS Fig. 9 depicts the decomposition process of the DOAS plus FCs, starting at the DPs of level 2 and ending on the FRs and DPs at level 3. It states that the ‘‘temperature control system’’ should adjust each space air supply temperature using the FC’s cooling capacity. The FC’s flow is the design parameter to ensure the space supply airflow, which has an important effect in the residual air velocity. The AHU adjusts the supply air temperature in the battery, not running over the FCs’ cooling capacity. The AHU is also responsible for ensuring the total OA airflow, suitably provided to each space. Eq. (3) represents the DOAS plus FCs’ design equation, in which the upper off-diagonal elements state the relation between FCs’ cooling capacity and FCs’ flow. The lower off-diagonals elements represent the influence of varying the FC speed into the supply air velocity.
(3)
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Fig. 9. DOAS plus FC’s level 2 decomposition.
Fig. 10. DOAS plus IU’s level 2 decomposition.
Designing a FC system at an established speed solves this coupling problem. Consequently, this design practice eliminates the off-diagonal elements of the matrix, and the design becomes independent. The design establishes, therefore, a FC flow that allows choosing the diffuser for a determined air supply velocity. Fig. 10 depicts the decomposition process of a DOAS plus IU, showing that the number of DPs is lower than the number of FRs. This system design is therefore coupled. Eq. (4) states that the temperature control must adjust the spaces’ air supply temperature using the IU’s cooling capacity. The AHU adjusts a constant PA
flow at a certain temperature, which is regulated in the battery. The temperature of the PA must not be too low that reduces any space air temperature under the set point temperature. For each building, a difficult balance has to be set in order to establish a lower bound for the PA temperature. The regulated PA flow at each IU ensures the induction airflow. The IU supply airflow and the selected diffuser determine the space air velocity. The matrix off-diagonals ‘‘OA’’ represent the use of over-cooled outside air in order to improve the IUs’ cooling capacity. Adjusting the AHU air supply temperature will consequently change the IU
Fig. 11. DOAS plus CC’s level 2 decomposition.
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cooling capacity and adjusting space air temperature will depend on AHU supply air temperature.
the different spaces, the damper minimum setting will be too large to allow any energy benefits. Therefore, this suggestion should be applied to systems whose spaces have a similar thermal behaviour. Nevertheless, if at each space the OA flow needs vary according to the thermal load, a common VAV can be tuned to work correctly. The DOAS plus IU equation has one DP less for each space, which gives raise to a coupled design. This coupling problem may be solved by introducing a nozzle control for each IU that would adjust the OA flow while maintaining the induction effect. Nevertheless, the coupling between PA temperature and IUs’ duty persists. In order to solve this coupling problem, the PA temperature should be close to the indoor air temperature. As the OA depends on IUs’ primary flow, the indoor air quality is defined by the temperature control system. Therefore, the IDA rating cannot be pre-defined. This analysis has exposed the main characteristics of the common HVAC systems, but it is important to notice that in an HVAC project multiple systems might be part of a solution. In each zone, a solution may be found by merging systems that match its weaknesses, as occurs when one use fan-coils in perimeter areas, while leaving IU or CC to climatize the steadier central spaces. 4. Conclusions
(4) Fig. 11 depicts the decomposition process of a DOAS plus CC. In these systems, the operative temperature [2] expresses the thermal comfort that depends on the mean radiant surfaces temperature and on the indoor dry air temperature. Eq. (5) states that the temperature control must ensure the space operative temperature through the CC’s cooling capacity. The AHU adjusts the supply air temperature and ensures the total OA flow. As the relevant elements of the design matrix are in the diagonal, the DOAS plus CC is an independent design, if no overcooled OA is used as a cooling method.
(5)
3.3. Systems discussion Applying axiomatic design to HVAC systems allows changing the way we look at HVAC systems. To solve the VAV coupling problem, one must introduce one more DP for each space, in order to provide the OA flow independently at each space. A possible solution is to introduce a minimum position for the VAV damper that would ensure the necessary OA flow regardless of the load conditions. However, if there are large load dissimilarities between
This work exposes the application of axiomatic design (AD) to the common design of HVAC systems. According to AD, a design must be either independent or decoupled. The object of this work is the application of AD to the design of commercial HVAC systems to be used in EU southern climates, studying its behaviour during cooling season. In commercial applications, noise, humidity and the airborne particle matter are system constraints. This evaluation centres on the classification of VAV and DOAS, defining the correct application for those systems. The terminal units that were considered in this study in order to create a system with the DOAS were the fan-coils (FC), the induction units (IU) and the chilled ceiling (CC). VAV couples indoor air supply to the spaces’ heat loads, and therefore it cannot undertake the supply of the required outdoor airflow in every space permanently. For that reason, it is appropriate for zones where the space thermal loads vary according to the outdoor air (OA) requirements. The use of free cooling techniques increases the yearly OA flow delivery to the building, reducing the shortage of OA flow that may occur in some spaces. DOAS plus FC is an independent design, as any function can be accomplished independently by varying just one DP. As a result, the DOAS plus FC may have the indoor air quality varied independently of thermal quality. The space noise constraint defines the FC’s speed that might stay unchanged during system operation. Otherwise, some minor coupling occurs between the supply airflow and the FC’s duty. A DOAS plus IU is a coupled design, as the thermal load at each space defines its outdoor airflow. However, a DOAS plus IU needs a high primary airflow rate that usually leads to good indoor air quality. Nevertheless, the function ‘‘Provide OA space n OA’’ probably cannot be fulfilled at every space for any predetermined OA flow. As primary air (PA) contributes to remove the space heat as well as the IU coil, the PA temperature setting might be careful not to develop a coupled design. DOAS plus CC is an independent design, so that the CC panels remove space loads independently of the DOAS that deliver the necessary outdoor air. As a conclusion, both VAV and DOAS plus IU are coupled designs, in contrast with DOAS plus FC and DOAS plus CC, which are decoupled designs. In addition, a special care must be taken when using over-cooled OA flow in order to increase CC
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or IU internal duties, since this would couple the outdoor air needs with the thermal loads, hence yielding to coupled designs. References [1] ASHRAE Standard 90.1-2004, Energy Standard for Buildings Except Low-Rise Residential Buildings. [2] ISO 7730-2005, Ergonomics of the thermal environment — Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria.
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[3] EN13779-2004, Ventilation for non-residential buildings – Performance requirements for ventilation and room-conditioning systems. [4] ASHRAE 62.1-2004, Ventilation for Acceptable Indoor Air Quality. [5] 62.1 User’s Manual, ANSI/ASHRAE Standard 62.1-2004, Ventilation for Acceptable Indoor Air Quality. [6] N.P. Suh, The Principles of Design, Oxford University Press, 1990. [7] N.P. Suh, Axiomatic Design: Advances and Applications, Oxford University Press, 1998. [8] SHRAE Handbook, Fundamentals, 2005. [9] ASHRAE Handbook, HVAC Systems and Equipment, 2004.