- Email: [email protected]
A new duct design software tool
Building and Environment 38 (2003) 521 – 531
www.elsevier.com/locate/buildenv
A new duct design software tool E.H. Mathews∗ , D.T. Claassen Centre for Research and Commercialization, University of Potchefstroom, PO Box 2156, Faerie Glen 4, 0043, South Africa Received 30 October 2001; received in revised form 4 December 2001; accepted 25 July 2002
Abstract This article describes the features and operation of a new duct design software tool. The tool was used in a case study to establish its practicality and performance. This tool is unique in the sense that it employs an optimisation method called the T-method. As far as the authors are aware no commercial duct design software package incorporates optimisation techniques. To enhance user friendliness the program also features a CAD interface for data input and output. By using the new tool an existing duct system was redesigned with the same constraints and speci3cations set by the original designer. The design program managed to optimise the 30-section system in less than 10 s on a 50 MHz 486 personal computer. In comparison to the existing system the redesigned system yielded savings of 8% on the duct material cost while the energy cost was lowered by 3%. The life-cycle cost decreased by 5%. The redesigned system has nine transition 3ttings compared to the 3ve of the original system, which will reduce the 3nal savings. Stability problems were encountered in a few sections that had relatively large C-coe9cients, which were referenced to upstream velocities. This led to grossly oversized ducts. The problem was overcome by 3xing the diameters of the few problem sections at realistic values. This problem was analysed in a previous article by these authors (Building Environ. 33(4) (1998) 173). It must also be said that for this case study the T-method was outperformed marginally by the equal friction method, a traditional duct design method. Notwithstanding the problem with the optimisation method itself the new duct design tool speeds up the design process and provides a user-friendly way of designing duct systems. ? 2003 Elsevier Science Ltd. All rights reserved.
1. Introduction Most commercial duct design software packages use conventional design methods like equal friction and static regain. The duct design program that holds the biggest market share in the world is the Carrier e20-ii program [2]. It o@ers the user both the static regain and the equal friction methods, which can be used in combination. It also has an optional CAD interface that simpli3es the data input and produces a CAD drawing of the 3nal design. Conventional methods cannot produce optimum designs. Furthermore, many conventional procedures, including the popular static regain method, are unable to deliver a duct system design that balances at the speci3ed airBows. Optimisation procedures do not share these shortcomings, yet a literature survey showed that there is no commercial ∗ Corresponding author. Tel.: +27-12-991-5568; fax: +27-12-9915716. E-mail address: [email protected] (E.H. Mathews).
program that makes use of them. Already in 1991 a need for such a program was stated by the inBuential ASHRAE organization in their Applications Handbook [3]. A literature study suggested that the new T-method is the most promising in terms of robustness and speed and was therefore chosen for the new duct design computer tool. Section 2 gives a brief overview of the theory of the T-method. A previous article by these authors discusses the theory of the T-method in detail [1]. The duct design program follows a simple 3ve-step process to design an air-distribution network. Section 3 explains this methodology by applying the computer program to simple example. Section 4 reports on a duct design case study. It is unique because it involves a practical design problem—most examples one 3nds in literature are textbook problems with little or no bearing on reality. The air handling system for the Health & Racquet Club located in Die Strand, South Africa was used as basis for the investigation. The aim of the study was to redesign the system using the new computer design tool. In doing so the practicality and e9ciency of
0360-1323/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 3 6 0 - 1 3 2 3 ( 0 2 ) 0 0 1 3 4 - 8
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E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
Nomenclature Cc Ci
C-coe9cient of a “branch” or “straight” section referenced to the velocity of the “common” section (dimensionless) C-coe9cient of a “branch” or “straight” section referenced to its own velocity (dimensionless)
Abbreviations TB B
has the same hydraulic and 3rst cost characteristics as the whole system. Optimum fan pressure calculation: The optimum pressure drop is established for the root section. System expansion: The optimum pressure is distributed between the various sections in the network. Duct sizes are calculated in compliance with the distributed pressure drops. 3. A simple ve-step duct design methodology
Label that refers to a terminal base object Label that refers to an ordinary base object
the design program and the optimisation algorithm were established. 2. Theory of the T-method This section gives a qualitative overview of the theory of the T-method as it was presented by authors Tsal et al. [4,5]. For a mathematical understanding of this method it is imperative that the reader study the relevant papers of Tsal et al. [4,5]. 2.1. System costs The 3rst step in discussing the theory is to determine the objective function. In the case of duct design problems the objective function to be minimised is the life-cycle cost, which is the total cost of the duct system over its life span expressed in current value terms. The life-cycle cost of a duct system consists chieBy of two components namely the initial and the running costs. The former includes the cost of space occupied by ducting and equipment and the installed cost of the air distribution system itself including the ducting, fans, sound-absorbing equipment, control systems, supply and return grilles, diffusers, etc. The running cost is the sum of the energy, maintenance and operational costs. It is obvious that some of these costs would be di9cult to determine. However, for the sake of 3nding the optimum duct sizes only those components, which are a function of the duct sizes, need to be included in the objective function. For a complete analysis of the cost components in the objective function the reader is referred to the paper of Tsal et al. on the theory of the T-method [4]. The only components considered in the new duct design tool are the installed cost of the ducting and the energy cost over the lifetime of the system.
The design process is performed in 3ve steps by using this new duct design tool. For the :rst step the user prepares a drawing (in dxf format) of the layout of the system. The user draws a centre-line sketch of the duct network, placing markers along the lines to indicate air terminal positions. This drawing is placed on a separate drawing layer called Input Layer. The centre-line sketch can therefore be superimposed on the drawing of the building plan. The 3rst step is completed when the user has imported the dxf input 3le into the design tool. In the second step the program uses the information in the dxf 3le to identify duct sections in the drawing and to set up a computational structure necessary for the design calculations. It also labels the duct sections for the third step where the user speci3es certain information like the terminal airBows and constraints for the individual duct sections. Duct design calculations are performed in the fourth step and :nally an output dxf 3le is written where the duct sections are drawn to scale. To illustrate this process the program was applied to the design problem used by Tsal et al. [5]. Fig. 1 portrays the dxf input 3le prepared by the user. Note the markers and the circle, indicating the positions of the air terminals and the root node, respectively. The user then turns to the main screen of the duct design tool where he/she speci3es the input and output dxf 3le paths, selects the correct design and drawing options and sets a number of relevant defaults (Fig. 2). The user presses the Start button to commence the 3ve steps listed in the Project status box. Each item in the
2.2. General optimisation procedure The T-method follows three major steps. System condensing: The entire network is condensed into a single imaginary section, called the root section, which
Fig. 1. Input drawing for duct design tool.
E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
Fig. 2. Main screen of duct design tool.
Fig. 3. Duct network data screen.
list is checked after the relevant step has been completed. After the computational data structure has been created (step 2) the program displays the Duct network data screen (Fig. 3). It shows all the lines that were drawn on Input layer. In the right-hand corner of the screen the user can turn on the labels of the objects he wants to see. If one of the 3ve buttons in the Object data box is pressed a list of all the objects in that category appears next to the buttons. The user can then double-click with his mouse on any one of the items in order to enter certain information for that speci3c object. Fig. 4 shows the screen that would appear if the user has double-clicked on the B5 base object. A base object is de3ned as a duct run which has no change in shape, area, Bow, and friction coe9cient. After the user has speci3ed the shape of the base object, the maximum and minimum dimension constraints are selected. A dimension can also be pre-selected or 3xed at a certain value. AirBows are only speci3ed for terminal base
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Fig. 4. Base object data screen.
Fig. 5. Output drawing generated by duct design tool.
objects, that is why the airBow for B5 is greyed, which prevents any editing of the Bow. A terminal base object is de3ned as equipment that is situated at the terminating points of the duct system e.g. air di@users. At the bottom half of the screen the user can add, edit or delete element objects from the base object. An element object is de3ned as a constituent of a base object. The left-hand list box shows the current element objects of B5. The two straight objects were created from the information in the dxf input 3le while the user added a generic element object. A generic element has a 3xed C-coe9cient, which can be set by the user. The user presses the OK button of the Duct network data screen (Fig. 3) after all the design data has been entered. The program then continues to execute the T-method calculations after which it prompts the user to open the output dxf 3le in the drawing program. A portion of the 3nal output drawing created by the design tool is shown in Fig. 5.
E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
Fig. 6. Health and Racquet Club air conditioning layout.
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E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
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Table 1 Economic data Parameter
Value
Source of information and/or assumptions
Energy demand cost, Ed (R/kVA) Power factor, pf Unit energy cost, Ec (R/kWh) Operational time, Y (h)
382.8 0.8 0.05628 6300
Expected life span, a (yr) Annual interest rate, air (%) (the rate at which the building owner is able to grow his money.)
15 17
Annual electricity escalation rate, aer (%) Fan e9ciency, f (%) Motor and drive e9ciency, m (%) Installed cost per unit area, Sd (R=m2 )
5 77.5 77.5 112.4
Die Strand Municipality Typical value Die Strand Municipality Design speci3cations set by air conditioning consulting engineer: 18 h a day, 7 days a week, 50 weeks a year. Good maintenance procedures are assumed. This 3gure should ideally be obtained directly from the building owner. The author got it from the consultant engineer responsible for the project. Die Strand Municipality Air handling unit manufacturer data Air handling unit manufacturer data Installed cost of existing system divided by surface area of existing design.
Table 2 Miscellaneous data Parameter
Value
Source of information/assumptions
T , Temperature (K) v Kinematic viscosity (m2 =s) , Density (kg=m3 ) , Duct inside surface roughness (m) (Ductwork has spiral seams)
295 1.5215e-5 1.1985 0.09e-3
Typical temperature in Die Strand Heat Transfer by Mills [6] Heat Transfer by Mills [6]. ASHRAE Fundamentals Handbook (1993), [7, p. 32.5, Table 1].
4. Introduction to case study The air distribution system, as designed by the air conditioning consultants, is shown in Fig. 6. (The small system that serves the aerobic hall is not considered in this study.) Tables 1 and 2 list the design parameters. The goal of this case study is to improve this design in terms of reducing the life-cycle cost while maintaining the same layout, constraints and design speci3cations including the type of 3ttings, air quantities and the maximum air speed. The only variables in this optimisation problem are the duct diameters. (The ducts are all round and not insulated.) By adjusting them in an optimal manner it is hoped that the life-cycle cost of the system will be reduced.
5. Evaluating the existing design In order to judge the results of the system the capital, running and life-cycle costs have to be established. For the existing system (shown in Fig. 6) the installed cost of the ducting is known to be R 30751. From this 3gure we can calculate Sd, the installed cost per square metre ducting. We will assume that this 3gure also holds for the optimised system. To calculate the operating cost of the existing system over the expected system life the fan total pressure, PFan, is required. To calculate Pfan we will use the design values
for the airBow at each terminal point. This will be discussed in the next sections.
5.1. Using the new duct design tool to analyse the existing system With the new duct design tool the design process of any duct system is performed in 3ve steps. However, when analysing a system, step 5, which is to produce a CAD drawing of the 3nal results, becomes unnecessary. Fig. 6 portrays the existing air conditioning system and is a printout of the dxf 3le received from the consultant engineer. In step 1 a centre-line sketch is drawn on top of this system but on a di@erent drawing layer. Fig. 7 shows the duct centre lines along with only a few selected layers to avoid crowding the 3gure. Note the markers and the circle indicating the positions of the air terminals and the root node, respectively. The 3rst step is completed when the user has imported the appended dxf input 3le into the design tool. In step 2 the program uses the information in the dxf 3le to identify duct sections in the drawing and to set up a computational structure needed for the design calculations. Fig. 8 shows which duct sections are represented by which base objects. Note that some base objects include more than one line segment for, example B7. This is consistent with the de3nition of a base object, namely that it
E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
Fig. 7. Input 3le.
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Fig. 8. Labels of base and terminal objects.
E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
Fig. 9. Output 3le.
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E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
represents a duct run which has no change in shape, area, Bow or friction coe9cient. Step 3 involves specifying the design airBows for the terminal base objects and the 3xed dimensions for the ordinary base objects. Table 3a and b contain the duct dimensions and design Bows. In the case of the existing system step 4 involves no sizing since all the base objects have 3xed dimensions; however the pressure losses are calculated. Fig. 9 shows the 3nal drawing. 5.2. Results The only real purpose of the calculations in this case, where all the duct diameters are 3xed, is to determine Pfan, the required fan pressure di@erence. To calculate the pressure losses for the base objects, the C-coe9cients (dynamic pressure loss coe9cients) of the various 3ttings are needed (Table 4a). The 3tting data are obtained from the ASHRAE Fundamentals Handbook [7,8]. The C-coe9cients of junction 3ttings as calculated from the ASHRAE 3tting tables, Cc, are referenced to the velocity of the upstream “common” section. However, since these C-coe9cients are taken into account at the downstream “straight” and “branch” sections, Cc must be adjusted to give a C-coe9cient which is referenced to the base object’s own velocity [7,8]. Certain pressure imbalances were found during the pressure calculations (Table 4b). These imbalances will have to be recti3ed with dampers to ensure that the design airBows are achieved. Assuming that the pressure imbalances are recti3ed with dampers it was calculated that the total pressure loss between the fan discharge and the air di@user exits are 75 Pa. Other pressure losses for the existing system under consideration include the return system loss (30 Pa), the coil loss (100 Pa) and the 3lter loss (200 Pa). In addition a 3xed 30 Pa loss is assumed for each terminal base object (air diffuser). The required total pressure di@erence by the fan is therefore 435 Pa. 6. Redesigning the system 6.1. General remarks Assuming that the duct cost per square metre, Sd, remains constant the design tool is used to improve the existing design by minimising the life-cycle cost of the system. Essentially the same 3ve-step methodology as is described in Section 5 is used, therefore, Figs. 8–9 apply to Section 6 as well. 6.2. Using the new duct design tool to optimise the existing system Table 5 lists the 3nal results produced by the new duct design tool. The diameters of those objects with an asterisk have been 3xed either by the duct design tool or by the
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Table 3 Base label
Flow [m3 =s]
Length [m]
Diameter [m]
(a) Input data B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15 B16 B17 B18 B19 B20 B21 B22 B23 B24 B25 B26 B27 B28 B29 B30
9.28 3.08 2.8 2.52 2.24 1.96 1.68 1.12 0.56 6.2 5.92 5.56 5.28 4.72 4.22 3.72 3.44 3.16 2.88 2.32 1.76 1.2 0.64 0.32 0.32 0.36 0.1 0.26 0.16 0.1
0.92 1.8 4.27 4.7 4.7 4.49 7.28 5.69 5.68 3.67 3.4 2.31 5.71 3.47 3.93 4.33 4.57 4.79 4.57 5.67 5.61 5.84 5.65 3.81 3.82 2.09 1.47 2.68 5.42 1.47
1.2 1.2 0.8 0.8 0.8 0.8 0.6 0.6 0.6 1 1 1 1 1 0.85 0.85 0.85 0.85 0.85 0.7 0.7 0.5 0.5 0.35 0.35 0.35 0.25 0.35 0.35 0.25
(b) Input data Terminal base label
Flow [m3 =s]
TB1 TB2 TB3 TB4 TB5 TB6 TB7 TB8 TB9 TB10 TB11 TB12 TB13 TB14 TB15 TB16 TB17 TB18 TB19 TB20 TB21 TB22 TB23 TB24 TB25
0.56 0.56 0.56 0.28 0.28 0.28 0.28 0.28 0.32 0.32 0.56 0.56 0.56 0.56 0.28 0.28 0.28 0.5 0.5 0.56 0.28 0.1 0.16 0.1 0.28
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E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
Table 4 Base Label
Type
(a) Fitting resistance calculation B2 Junction B3 Junction B4 Junction B5 Junction B6 Junction B7 Elbow B7 Junction B8 Junction B9 Junction B10 Junction B11 Junction B12 Junction B13 Junction B14 Junction B15 Elbow B15 Junction B16 Junction B17 Junction B18 Junction B19 Junction B20 Junction B21 Junction B22 Junction B23 Junction B24 Junction B25 Junction B26 Junction B27 Junction B28 Junction B29 Elbow B29 Junction B30 Junction
Ashrae Fitting
Parameter
Cc
Ci
5-10 5-10 5-10 5-10 5-10 3-2 5-10 5-10 5-10 5-10 5-10 5-10 5-10 5-10 3-2 5-10 5-10 5-10 5-10 5-10 5-10 5-10 5-10 5-10 5-33 5-33 5-10 5-10 5-10 3-2 5-10 5-10
Vs=Vc = 0:33 Vs=Vc = 2:05 Vs=Vc = 0:90 Vs=Vc = 0:89 Vs=Vc = 0:88 r=D = 1:0 No: of Pieces = 5 Vs=Vc = 1:52 Vs=Vc = 0:67 Vs=Vc = 0:50 Vb=Vc = 0:96 Vs=Vc = 0:95 Vs=Vc = 0:94 Vs=Vc = 0:95 Vs=Vc = 0:89 r=D = 1:0 No: of Pieces = 5 Vs=Vc = 1:24 Vs=Vc = 0:88 Vs=Vc = 0:92 Vs=Vc = 0:92 Vs=Vc = 0:91 Vs=Vc = 1:19 Vs=Vc = 0:76 Vs=Vc = 1:34 Vs=Vc = 0:53 Vb=Vc = 1:02 Vb=Vc = 1:02 Vb=Vc = 0:50 Vb=Vc = 0:54 Vs=Vc = 0:72 r=D = 1:0 No: of Pieces = 5 Vs=Vc = 0:62 Vb=Vc = 0:75
0.18 0 0.01 0.01 0.01
1.64 0 0.01 0.01 0.02 0.33 0 0.11 0.4 0.47 0.01 0.01 0.01 0.01 0.33 0 0.02 0.01 0.01 0.01 0 0.05 0 0.3 0.96 0.96 2.77 2.2 0.07 0.33 0.15 0.96
0 0.05 0.1 0.44 0 0.01 0.01 0.01 0 0.01 0.01 0.01 0.01 0 0.03 0 0.09 1 1 0.68 0.65 0.04 0.06 0.54
(b) Pressure imbalances Base label
Pb [Pa]
B2 B24 B26 B28 B29 TB2 TB3 TB4 TB5 TB6 TB7 TB8 TB11 TB12 TB13 TB14 TB15 TB16 TB17 TB18 TB19 TB20 TB21 TB25
44.3 0 21.4 2.2 1.4 1.4 4 15.9 17 18.5 20.4 22.3 11 16 18.5 21.9 23.6 25.8 28.3 31.1 45 46.7 49.8 53.7
E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
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7. Results
Table 5 Final results Object label
Velocity [m/s]
Diameter [m]
Pressure drop [Pa]
B1* B2* B3* B4* B5* B6* B7* B8* B9* B10* B11* B12* B13* B14* B15* B16* B17 B18 B19 B20 B21 B22 B23 B24* B25* B26* B28* B29* B30* B27*
6.99 6.13 7.28 6.55 7.92 6.93 5.94 5.7 7.92 7.89 7.54 7.08 6.72 7.42 6.63 5.85 7.34 7.01 6.78 6.18 5.56 4.79 3.72 3.33 3.33 3.74 2.7 1.66 2.04 2.04
1.3 0.8 0.7 0.7 0.6 0.6 0.6 0.5 0.3 1 1 1 1 0.9 0.9 0.9 0.772 0.758 0.735 0.691 0.635 0.565 0.468 0.35 0.35 0.35 0.35 0.35 0.25 0.25
0.3 1.1 3 3 4.6 3.9 11.6 3.9 12.9 13.1 1.8 1.2 2.4 1.9 10.8 1.8 2.9 3 2.7 3.2 2.9 2.7 2.2 9.7 9.7 24.2 1 1.4 2.7 5.8
authors themselves. Base objects B24 to B30 were 3xed at sizes that correspond to that of the existing system for reasons of compatibility with the ceiling di@users or because they are situated in regions where high velocity noise cannot be tolerated. Objects B10, B15 and B16 had to be 3xed because it was found that they tended to become extremely oversized. For example, the diameter of B15 would otherwise exceed 1:5 m. In this case, study, it was observed that if a base object has relatively large C-coe9cients that are referenced to an upstream base object’s velocity, the base object tended to become oversized. This is a rather serious problem because it casts doubts on the T-method’s overall robustness. Nevertheless, after the troublesome bases had been 3xed, the T-method proceeded to produce a design that did in fact lower the life-cycle cost. It must be noted that many of the base objects have become 3xed during the calculations because they violated the velocity constraint of 8 m=s. This constraint was put in place because the highest velocity in the existing system is 8:2 m=s. The size of those sections that violated the velocity constraint would be assigned to the smallest multiple of 100 mm that does not violate the velocity constraint. The 3xed base objects led to pressure imbalances, which will have to be taken up by air dampers. The extra cost due to the air dampers were not taken into account.
The table below summarizes the results for the existing and the redesigned systems.
PFan (Pa) QFan (m3 =s) Duct surface area (m2 ) Capital cost (R) Operating cost (R) Total (R)
Existing system
Redesigned system
Percentage change (%)
435 9.28 273 30735 39291 70026
421 9.28 252 28368 38032 66400
−3:2 −7:7 −7:7 −3:2 −5:2
8. Conclusion An 8% saving in material cost has been achieved by using the new duct design computer tool. This 3gure can result in signi3cant savings for big systems. On the negative side, the number of transition 3ttings was increased from 5 to 9 in the process. A factor that needs consideration is that while the same maximum velocity constraint (8 m=s) was applied when the system was redesigned the average duct velocity rose from 4.9 to 5:7 m=s which will lead to higher noise levels. However, this does not pose a big problem since the system is situated in a gymnasium where other sounds may still dominate. We can not draw general conclusions from this case study. To determine if current and past system designs in general depart signi3cantly from the optimum situation a wide variety of systems needs to be designed in this fashion. However, we can say that for this case study the duct design tool performed its task and that it speeds up the design process.
References [1] Mathews EH, Claassen DT. Problems with the T-method. Building and Environment 1998;33(4):173–9. [2] Malan AG. The feasibility of developing an improved HVAC system design tool: an entrepreneurial investigation. Masters Degree thesis, University of Pretoria, 1995. [3] ASHRAE Applications Handbook, SI Ed. American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta, GA 30329, 1991. [4] Tsal RJ, Behls HF, Mangel R. T-method duct design, Part I: optimization theory. ASHRAE Transactions 1988;94(2):90–111. [5] Tsal RJ, Behls HF, Mangel R. T-method duct design, Part II: calculation procedure and economic analysis. ASHRAE Transactions 1988;94(2):112–49. [6] Mills AF. Heat transfer, international student edition. Homewood, IL: Irwin, 1992. [7] ASHRAE Fundamentals Handbook, SI Ed. American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta, GA 30329, 1993. [8] ASHRAE Fundamentals Handbook, SI Ed. American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta, GA 30329, 1989.
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A new duct design software tool E.H. Mathews∗ , D.T. Claassen Centre for Research and Commercialization, University of Potchefstroom, PO Box 2156, Faerie Glen 4, 0043, South Africa Received 30 October 2001; received in revised form 4 December 2001; accepted 25 July 2002
Abstract This article describes the features and operation of a new duct design software tool. The tool was used in a case study to establish its practicality and performance. This tool is unique in the sense that it employs an optimisation method called the T-method. As far as the authors are aware no commercial duct design software package incorporates optimisation techniques. To enhance user friendliness the program also features a CAD interface for data input and output. By using the new tool an existing duct system was redesigned with the same constraints and speci3cations set by the original designer. The design program managed to optimise the 30-section system in less than 10 s on a 50 MHz 486 personal computer. In comparison to the existing system the redesigned system yielded savings of 8% on the duct material cost while the energy cost was lowered by 3%. The life-cycle cost decreased by 5%. The redesigned system has nine transition 3ttings compared to the 3ve of the original system, which will reduce the 3nal savings. Stability problems were encountered in a few sections that had relatively large C-coe9cients, which were referenced to upstream velocities. This led to grossly oversized ducts. The problem was overcome by 3xing the diameters of the few problem sections at realistic values. This problem was analysed in a previous article by these authors (Building Environ. 33(4) (1998) 173). It must also be said that for this case study the T-method was outperformed marginally by the equal friction method, a traditional duct design method. Notwithstanding the problem with the optimisation method itself the new duct design tool speeds up the design process and provides a user-friendly way of designing duct systems. ? 2003 Elsevier Science Ltd. All rights reserved.
1. Introduction Most commercial duct design software packages use conventional design methods like equal friction and static regain. The duct design program that holds the biggest market share in the world is the Carrier e20-ii program [2]. It o@ers the user both the static regain and the equal friction methods, which can be used in combination. It also has an optional CAD interface that simpli3es the data input and produces a CAD drawing of the 3nal design. Conventional methods cannot produce optimum designs. Furthermore, many conventional procedures, including the popular static regain method, are unable to deliver a duct system design that balances at the speci3ed airBows. Optimisation procedures do not share these shortcomings, yet a literature survey showed that there is no commercial ∗ Corresponding author. Tel.: +27-12-991-5568; fax: +27-12-9915716. E-mail address: [email protected] (E.H. Mathews).
program that makes use of them. Already in 1991 a need for such a program was stated by the inBuential ASHRAE organization in their Applications Handbook [3]. A literature study suggested that the new T-method is the most promising in terms of robustness and speed and was therefore chosen for the new duct design computer tool. Section 2 gives a brief overview of the theory of the T-method. A previous article by these authors discusses the theory of the T-method in detail [1]. The duct design program follows a simple 3ve-step process to design an air-distribution network. Section 3 explains this methodology by applying the computer program to simple example. Section 4 reports on a duct design case study. It is unique because it involves a practical design problem—most examples one 3nds in literature are textbook problems with little or no bearing on reality. The air handling system for the Health & Racquet Club located in Die Strand, South Africa was used as basis for the investigation. The aim of the study was to redesign the system using the new computer design tool. In doing so the practicality and e9ciency of
0360-1323/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 3 6 0 - 1 3 2 3 ( 0 2 ) 0 0 1 3 4 - 8
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E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
Nomenclature Cc Ci
C-coe9cient of a “branch” or “straight” section referenced to the velocity of the “common” section (dimensionless) C-coe9cient of a “branch” or “straight” section referenced to its own velocity (dimensionless)
Abbreviations TB B
has the same hydraulic and 3rst cost characteristics as the whole system. Optimum fan pressure calculation: The optimum pressure drop is established for the root section. System expansion: The optimum pressure is distributed between the various sections in the network. Duct sizes are calculated in compliance with the distributed pressure drops. 3. A simple ve-step duct design methodology
Label that refers to a terminal base object Label that refers to an ordinary base object
the design program and the optimisation algorithm were established. 2. Theory of the T-method This section gives a qualitative overview of the theory of the T-method as it was presented by authors Tsal et al. [4,5]. For a mathematical understanding of this method it is imperative that the reader study the relevant papers of Tsal et al. [4,5]. 2.1. System costs The 3rst step in discussing the theory is to determine the objective function. In the case of duct design problems the objective function to be minimised is the life-cycle cost, which is the total cost of the duct system over its life span expressed in current value terms. The life-cycle cost of a duct system consists chieBy of two components namely the initial and the running costs. The former includes the cost of space occupied by ducting and equipment and the installed cost of the air distribution system itself including the ducting, fans, sound-absorbing equipment, control systems, supply and return grilles, diffusers, etc. The running cost is the sum of the energy, maintenance and operational costs. It is obvious that some of these costs would be di9cult to determine. However, for the sake of 3nding the optimum duct sizes only those components, which are a function of the duct sizes, need to be included in the objective function. For a complete analysis of the cost components in the objective function the reader is referred to the paper of Tsal et al. on the theory of the T-method [4]. The only components considered in the new duct design tool are the installed cost of the ducting and the energy cost over the lifetime of the system.
The design process is performed in 3ve steps by using this new duct design tool. For the :rst step the user prepares a drawing (in dxf format) of the layout of the system. The user draws a centre-line sketch of the duct network, placing markers along the lines to indicate air terminal positions. This drawing is placed on a separate drawing layer called Input Layer. The centre-line sketch can therefore be superimposed on the drawing of the building plan. The 3rst step is completed when the user has imported the dxf input 3le into the design tool. In the second step the program uses the information in the dxf 3le to identify duct sections in the drawing and to set up a computational structure necessary for the design calculations. It also labels the duct sections for the third step where the user speci3es certain information like the terminal airBows and constraints for the individual duct sections. Duct design calculations are performed in the fourth step and :nally an output dxf 3le is written where the duct sections are drawn to scale. To illustrate this process the program was applied to the design problem used by Tsal et al. [5]. Fig. 1 portrays the dxf input 3le prepared by the user. Note the markers and the circle, indicating the positions of the air terminals and the root node, respectively. The user then turns to the main screen of the duct design tool where he/she speci3es the input and output dxf 3le paths, selects the correct design and drawing options and sets a number of relevant defaults (Fig. 2). The user presses the Start button to commence the 3ve steps listed in the Project status box. Each item in the
2.2. General optimisation procedure The T-method follows three major steps. System condensing: The entire network is condensed into a single imaginary section, called the root section, which
Fig. 1. Input drawing for duct design tool.
E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
Fig. 2. Main screen of duct design tool.
Fig. 3. Duct network data screen.
list is checked after the relevant step has been completed. After the computational data structure has been created (step 2) the program displays the Duct network data screen (Fig. 3). It shows all the lines that were drawn on Input layer. In the right-hand corner of the screen the user can turn on the labels of the objects he wants to see. If one of the 3ve buttons in the Object data box is pressed a list of all the objects in that category appears next to the buttons. The user can then double-click with his mouse on any one of the items in order to enter certain information for that speci3c object. Fig. 4 shows the screen that would appear if the user has double-clicked on the B5 base object. A base object is de3ned as a duct run which has no change in shape, area, Bow, and friction coe9cient. After the user has speci3ed the shape of the base object, the maximum and minimum dimension constraints are selected. A dimension can also be pre-selected or 3xed at a certain value. AirBows are only speci3ed for terminal base
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Fig. 4. Base object data screen.
Fig. 5. Output drawing generated by duct design tool.
objects, that is why the airBow for B5 is greyed, which prevents any editing of the Bow. A terminal base object is de3ned as equipment that is situated at the terminating points of the duct system e.g. air di@users. At the bottom half of the screen the user can add, edit or delete element objects from the base object. An element object is de3ned as a constituent of a base object. The left-hand list box shows the current element objects of B5. The two straight objects were created from the information in the dxf input 3le while the user added a generic element object. A generic element has a 3xed C-coe9cient, which can be set by the user. The user presses the OK button of the Duct network data screen (Fig. 3) after all the design data has been entered. The program then continues to execute the T-method calculations after which it prompts the user to open the output dxf 3le in the drawing program. A portion of the 3nal output drawing created by the design tool is shown in Fig. 5.
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Fig. 6. Health and Racquet Club air conditioning layout.
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Table 1 Economic data Parameter
Value
Source of information and/or assumptions
Energy demand cost, Ed (R/kVA) Power factor, pf Unit energy cost, Ec (R/kWh) Operational time, Y (h)
382.8 0.8 0.05628 6300
Expected life span, a (yr) Annual interest rate, air (%) (the rate at which the building owner is able to grow his money.)
15 17
Annual electricity escalation rate, aer (%) Fan e9ciency, f (%) Motor and drive e9ciency, m (%) Installed cost per unit area, Sd (R=m2 )
5 77.5 77.5 112.4
Die Strand Municipality Typical value Die Strand Municipality Design speci3cations set by air conditioning consulting engineer: 18 h a day, 7 days a week, 50 weeks a year. Good maintenance procedures are assumed. This 3gure should ideally be obtained directly from the building owner. The author got it from the consultant engineer responsible for the project. Die Strand Municipality Air handling unit manufacturer data Air handling unit manufacturer data Installed cost of existing system divided by surface area of existing design.
Table 2 Miscellaneous data Parameter
Value
Source of information/assumptions
T , Temperature (K) v Kinematic viscosity (m2 =s) , Density (kg=m3 ) , Duct inside surface roughness (m) (Ductwork has spiral seams)
295 1.5215e-5 1.1985 0.09e-3
Typical temperature in Die Strand Heat Transfer by Mills [6] Heat Transfer by Mills [6]. ASHRAE Fundamentals Handbook (1993), [7, p. 32.5, Table 1].
4. Introduction to case study The air distribution system, as designed by the air conditioning consultants, is shown in Fig. 6. (The small system that serves the aerobic hall is not considered in this study.) Tables 1 and 2 list the design parameters. The goal of this case study is to improve this design in terms of reducing the life-cycle cost while maintaining the same layout, constraints and design speci3cations including the type of 3ttings, air quantities and the maximum air speed. The only variables in this optimisation problem are the duct diameters. (The ducts are all round and not insulated.) By adjusting them in an optimal manner it is hoped that the life-cycle cost of the system will be reduced.
5. Evaluating the existing design In order to judge the results of the system the capital, running and life-cycle costs have to be established. For the existing system (shown in Fig. 6) the installed cost of the ducting is known to be R 30751. From this 3gure we can calculate Sd, the installed cost per square metre ducting. We will assume that this 3gure also holds for the optimised system. To calculate the operating cost of the existing system over the expected system life the fan total pressure, PFan, is required. To calculate Pfan we will use the design values
for the airBow at each terminal point. This will be discussed in the next sections.
5.1. Using the new duct design tool to analyse the existing system With the new duct design tool the design process of any duct system is performed in 3ve steps. However, when analysing a system, step 5, which is to produce a CAD drawing of the 3nal results, becomes unnecessary. Fig. 6 portrays the existing air conditioning system and is a printout of the dxf 3le received from the consultant engineer. In step 1 a centre-line sketch is drawn on top of this system but on a di@erent drawing layer. Fig. 7 shows the duct centre lines along with only a few selected layers to avoid crowding the 3gure. Note the markers and the circle indicating the positions of the air terminals and the root node, respectively. The 3rst step is completed when the user has imported the appended dxf input 3le into the design tool. In step 2 the program uses the information in the dxf 3le to identify duct sections in the drawing and to set up a computational structure needed for the design calculations. Fig. 8 shows which duct sections are represented by which base objects. Note that some base objects include more than one line segment for, example B7. This is consistent with the de3nition of a base object, namely that it
E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
Fig. 7. Input 3le.
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Fig. 8. Labels of base and terminal objects.
E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
Fig. 9. Output 3le.
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E.H. Mathews, D.T. Claassen / Building and Environment 38 (2003) 521 – 531
represents a duct run which has no change in shape, area, Bow or friction coe9cient. Step 3 involves specifying the design airBows for the terminal base objects and the 3xed dimensions for the ordinary base objects. Table 3a and b contain the duct dimensions and design Bows. In the case of the existing system step 4 involves no sizing since all the base objects have 3xed dimensions; however the pressure losses are calculated. Fig. 9 shows the 3nal drawing. 5.2. Results The only real purpose of the calculations in this case, where all the duct diameters are 3xed, is to determine Pfan, the required fan pressure di@erence. To calculate the pressure losses for the base objects, the C-coe9cients (dynamic pressure loss coe9cients) of the various 3ttings are needed (Table 4a). The 3tting data are obtained from the ASHRAE Fundamentals Handbook [7,8]. The C-coe9cients of junction 3ttings as calculated from the ASHRAE 3tting tables, Cc, are referenced to the velocity of the upstream “common” section. However, since these C-coe9cients are taken into account at the downstream “straight” and “branch” sections, Cc must be adjusted to give a C-coe9cient which is referenced to the base object’s own velocity [7,8]. Certain pressure imbalances were found during the pressure calculations (Table 4b). These imbalances will have to be recti3ed with dampers to ensure that the design airBows are achieved. Assuming that the pressure imbalances are recti3ed with dampers it was calculated that the total pressure loss between the fan discharge and the air di@user exits are 75 Pa. Other pressure losses for the existing system under consideration include the return system loss (30 Pa), the coil loss (100 Pa) and the 3lter loss (200 Pa). In addition a 3xed 30 Pa loss is assumed for each terminal base object (air diffuser). The required total pressure di@erence by the fan is therefore 435 Pa. 6. Redesigning the system 6.1. General remarks Assuming that the duct cost per square metre, Sd, remains constant the design tool is used to improve the existing design by minimising the life-cycle cost of the system. Essentially the same 3ve-step methodology as is described in Section 5 is used, therefore, Figs. 8–9 apply to Section 6 as well. 6.2. Using the new duct design tool to optimise the existing system Table 5 lists the 3nal results produced by the new duct design tool. The diameters of those objects with an asterisk have been 3xed either by the duct design tool or by the
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Table 3 Base label
Flow [m3 =s]
Length [m]
Diameter [m]
(a) Input data B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15 B16 B17 B18 B19 B20 B21 B22 B23 B24 B25 B26 B27 B28 B29 B30
9.28 3.08 2.8 2.52 2.24 1.96 1.68 1.12 0.56 6.2 5.92 5.56 5.28 4.72 4.22 3.72 3.44 3.16 2.88 2.32 1.76 1.2 0.64 0.32 0.32 0.36 0.1 0.26 0.16 0.1
0.92 1.8 4.27 4.7 4.7 4.49 7.28 5.69 5.68 3.67 3.4 2.31 5.71 3.47 3.93 4.33 4.57 4.79 4.57 5.67 5.61 5.84 5.65 3.81 3.82 2.09 1.47 2.68 5.42 1.47
1.2 1.2 0.8 0.8 0.8 0.8 0.6 0.6 0.6 1 1 1 1 1 0.85 0.85 0.85 0.85 0.85 0.7 0.7 0.5 0.5 0.35 0.35 0.35 0.25 0.35 0.35 0.25
(b) Input data Terminal base label
Flow [m3 =s]
TB1 TB2 TB3 TB4 TB5 TB6 TB7 TB8 TB9 TB10 TB11 TB12 TB13 TB14 TB15 TB16 TB17 TB18 TB19 TB20 TB21 TB22 TB23 TB24 TB25
0.56 0.56 0.56 0.28 0.28 0.28 0.28 0.28 0.32 0.32 0.56 0.56 0.56 0.56 0.28 0.28 0.28 0.5 0.5 0.56 0.28 0.1 0.16 0.1 0.28
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Table 4 Base Label
Type
(a) Fitting resistance calculation B2 Junction B3 Junction B4 Junction B5 Junction B6 Junction B7 Elbow B7 Junction B8 Junction B9 Junction B10 Junction B11 Junction B12 Junction B13 Junction B14 Junction B15 Elbow B15 Junction B16 Junction B17 Junction B18 Junction B19 Junction B20 Junction B21 Junction B22 Junction B23 Junction B24 Junction B25 Junction B26 Junction B27 Junction B28 Junction B29 Elbow B29 Junction B30 Junction
Ashrae Fitting
Parameter
Cc
Ci
5-10 5-10 5-10 5-10 5-10 3-2 5-10 5-10 5-10 5-10 5-10 5-10 5-10 5-10 3-2 5-10 5-10 5-10 5-10 5-10 5-10 5-10 5-10 5-10 5-33 5-33 5-10 5-10 5-10 3-2 5-10 5-10
Vs=Vc = 0:33 Vs=Vc = 2:05 Vs=Vc = 0:90 Vs=Vc = 0:89 Vs=Vc = 0:88 r=D = 1:0 No: of Pieces = 5 Vs=Vc = 1:52 Vs=Vc = 0:67 Vs=Vc = 0:50 Vb=Vc = 0:96 Vs=Vc = 0:95 Vs=Vc = 0:94 Vs=Vc = 0:95 Vs=Vc = 0:89 r=D = 1:0 No: of Pieces = 5 Vs=Vc = 1:24 Vs=Vc = 0:88 Vs=Vc = 0:92 Vs=Vc = 0:92 Vs=Vc = 0:91 Vs=Vc = 1:19 Vs=Vc = 0:76 Vs=Vc = 1:34 Vs=Vc = 0:53 Vb=Vc = 1:02 Vb=Vc = 1:02 Vb=Vc = 0:50 Vb=Vc = 0:54 Vs=Vc = 0:72 r=D = 1:0 No: of Pieces = 5 Vs=Vc = 0:62 Vb=Vc = 0:75
0.18 0 0.01 0.01 0.01
1.64 0 0.01 0.01 0.02 0.33 0 0.11 0.4 0.47 0.01 0.01 0.01 0.01 0.33 0 0.02 0.01 0.01 0.01 0 0.05 0 0.3 0.96 0.96 2.77 2.2 0.07 0.33 0.15 0.96
0 0.05 0.1 0.44 0 0.01 0.01 0.01 0 0.01 0.01 0.01 0.01 0 0.03 0 0.09 1 1 0.68 0.65 0.04 0.06 0.54
(b) Pressure imbalances Base label
Pb [Pa]
B2 B24 B26 B28 B29 TB2 TB3 TB4 TB5 TB6 TB7 TB8 TB11 TB12 TB13 TB14 TB15 TB16 TB17 TB18 TB19 TB20 TB21 TB25
44.3 0 21.4 2.2 1.4 1.4 4 15.9 17 18.5 20.4 22.3 11 16 18.5 21.9 23.6 25.8 28.3 31.1 45 46.7 49.8 53.7
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7. Results
Table 5 Final results Object label
Velocity [m/s]
Diameter [m]
Pressure drop [Pa]
B1* B2* B3* B4* B5* B6* B7* B8* B9* B10* B11* B12* B13* B14* B15* B16* B17 B18 B19 B20 B21 B22 B23 B24* B25* B26* B28* B29* B30* B27*
6.99 6.13 7.28 6.55 7.92 6.93 5.94 5.7 7.92 7.89 7.54 7.08 6.72 7.42 6.63 5.85 7.34 7.01 6.78 6.18 5.56 4.79 3.72 3.33 3.33 3.74 2.7 1.66 2.04 2.04
1.3 0.8 0.7 0.7 0.6 0.6 0.6 0.5 0.3 1 1 1 1 0.9 0.9 0.9 0.772 0.758 0.735 0.691 0.635 0.565 0.468 0.35 0.35 0.35 0.35 0.35 0.25 0.25
0.3 1.1 3 3 4.6 3.9 11.6 3.9 12.9 13.1 1.8 1.2 2.4 1.9 10.8 1.8 2.9 3 2.7 3.2 2.9 2.7 2.2 9.7 9.7 24.2 1 1.4 2.7 5.8
authors themselves. Base objects B24 to B30 were 3xed at sizes that correspond to that of the existing system for reasons of compatibility with the ceiling di@users or because they are situated in regions where high velocity noise cannot be tolerated. Objects B10, B15 and B16 had to be 3xed because it was found that they tended to become extremely oversized. For example, the diameter of B15 would otherwise exceed 1:5 m. In this case, study, it was observed that if a base object has relatively large C-coe9cients that are referenced to an upstream base object’s velocity, the base object tended to become oversized. This is a rather serious problem because it casts doubts on the T-method’s overall robustness. Nevertheless, after the troublesome bases had been 3xed, the T-method proceeded to produce a design that did in fact lower the life-cycle cost. It must be noted that many of the base objects have become 3xed during the calculations because they violated the velocity constraint of 8 m=s. This constraint was put in place because the highest velocity in the existing system is 8:2 m=s. The size of those sections that violated the velocity constraint would be assigned to the smallest multiple of 100 mm that does not violate the velocity constraint. The 3xed base objects led to pressure imbalances, which will have to be taken up by air dampers. The extra cost due to the air dampers were not taken into account.
The table below summarizes the results for the existing and the redesigned systems.
PFan (Pa) QFan (m3 =s) Duct surface area (m2 ) Capital cost (R) Operating cost (R) Total (R)
Existing system
Redesigned system
Percentage change (%)
435 9.28 273 30735 39291 70026
421 9.28 252 28368 38032 66400
−3:2 −7:7 −7:7 −3:2 −5:2
8. Conclusion An 8% saving in material cost has been achieved by using the new duct design computer tool. This 3gure can result in signi3cant savings for big systems. On the negative side, the number of transition 3ttings was increased from 5 to 9 in the process. A factor that needs consideration is that while the same maximum velocity constraint (8 m=s) was applied when the system was redesigned the average duct velocity rose from 4.9 to 5:7 m=s which will lead to higher noise levels. However, this does not pose a big problem since the system is situated in a gymnasium where other sounds may still dominate. We can not draw general conclusions from this case study. To determine if current and past system designs in general depart signi3cantly from the optimum situation a wide variety of systems needs to be designed in this fashion. However, we can say that for this case study the duct design tool performed its task and that it speeds up the design process.
References [1] Mathews EH, Claassen DT. Problems with the T-method. Building and Environment 1998;33(4):173–9. [2] Malan AG. The feasibility of developing an improved HVAC system design tool: an entrepreneurial investigation. Masters Degree thesis, University of Pretoria, 1995. [3] ASHRAE Applications Handbook, SI Ed. American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta, GA 30329, 1991. [4] Tsal RJ, Behls HF, Mangel R. T-method duct design, Part I: optimization theory. ASHRAE Transactions 1988;94(2):90–111. [5] Tsal RJ, Behls HF, Mangel R. T-method duct design, Part II: calculation procedure and economic analysis. ASHRAE Transactions 1988;94(2):112–49. [6] Mills AF. Heat transfer, international student edition. Homewood, IL: Irwin, 1992. [7] ASHRAE Fundamentals Handbook, SI Ed. American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta, GA 30329, 1993. [8] ASHRAE Fundamentals Handbook, SI Ed. American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., 1791 Tullie Circle, N.E., Atlanta, GA 30329, 1989.