Automatic calculation of resistance balance in the air duct system

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This post was last edited by “Hasty Passerby” on October 23, 2018, at 09:18. Automatic calculation of resistance balance in duct systems. I. Introduction: In air conditioning and ventilation systems, since the ducts within the same system are interconnected as a whole, they must adhere to the principle of resistance balance among various branches. Once the structural configuration and dimensions of the duct system are determined, under the action of a given fan, the airflow rates through each section are automatically distributed according to this resistance balance principle. Failing to perform resistance balance calculations during design calculations can result in the actual air volume distribution in the system not matching the design specifications. Of course, we can also distribute the air volume by adjusting the air valves, but this in turn results in excess air pressure in the non-most-unfavorable circuits. Therefore, it is practical to consider the resistance balance of each loop during design calculations. However, many designers rely solely on empirical estimates or manual calculations using reference tables when performing hydraulic calculations for air ducts and balancing resistances; this is time-consuming and laborious, and does not yield ideal results. The calculation software designed by the author uses EXCEL as its working platform and VBA as the development tool, thereby ensuring the efficiency of program execution. II. Basic steps for the automatic calculation of resistance balance. The process of automatically calculating the resistance balance in a duct system follows essentially the same calculation steps as those used in conventional design, and mainly includes the following: ① Enter and save the logical relationships between various nodes as well as the relevant parameters of each duct segment; thereafter, determine the assumed wind speed for each duct segment based on technical requirements ； ②Automatically calculate the equivalent hydraulic diameter and friction loss of the pipe section based on the assumed wind speed ； ③Use the node backtracking method to automatically determine the paths and resistance losses of each loop in the system, and identify the most unfavorable loop in the system ； ④Automatically balance the resistance for non-harmful loops ； ⑤Verify the calculation results. In the above processes, only those with a relatively small amount of work, namely ① and ⑤, require manual intervention, while all other steps are completed automatically by the computer. This not only ensures its computing speed and accuracy, but also allows for appropriate manual adjustments as needed. III. Key calculation points: To achieve an automatic calculation of the resistance balance in the air duct system, it mainly relies on the following core points. 1. Definition of key terms: To facilitate understanding of this article, the author first provides the following definitions for some of the key terms that appear in it. Rules for numbering nodes. In order to easily query the various loops of the air duct system based on the logical relationships between the nodes, we assign a numerical identifier to each node. The following assumption is made regarding these node numbers: they are numbered from smallest to largest in the direction of decreasing air volume; in other words, for supply air systems, the node numbers increase in the direction of airflow. 2. Automatic sorting of various system circuits: The automatic sorting of the system’s various circuits is a prerequisite for achieving automatic calculation of resistance balance, and it is also one of the key steps in this program. The process is essentially one of automatically sorting according to the magnitude of the resistance loss in each loop. Sorting can effectively address the following two issues: ① The most unfavorable loop in the system can be directly identified based on the sorting results ； ②It indeed reduces the repeated calculations when balancing the resistance of each loop. The specific steps for the automatic sorting of various loops in the system are as follows: ① Automatically select the end nodes. When system parameters are entered, all nodes other than the system’s starting point are listed in the “Nodes” column of the table used for calculating the resistance balance in the duct system, in descending order of their numbers; the corresponding preceding node is listed in the “Preceding Node” column, as shown in Figure 2. When automatically selecting terminal nodes, the computer checks the number of times each node in the node column appears as a repeat in the preceding node column; if the count is 0, it is a terminal node, if it is 1, it is an ordinary node, and otherwise it is a branching point. ②Search for the loop path corresponding to each terminal node in sequence, and simultaneously calculate its resistance loss value. First, the end node is used to identify its immediate predecessor node; then, the immediate predecessor node’s own immediate predecessor and the resistance loss associated with that pipe segment are determined. This process is repeated until the corresponding immediate predecessor node is the starting node of the system, at which point the search for that loop is complete. The resistance losses of all pipe segments in the loop are added together to obtain the total resistance loss for that loop. In fact, this process is one of iteration and recursion; the author refers to this method as the reverse search method. ③Arrange all loops in descending order based on the resistance loss value. The loop at the front at this point is the most unfavorable loop of that duct system. 3. Resistance balance of each circuit: Resistance balance is the most complicated and yet the most crucial step in the entire duct design process. In this paper, the author balances each loop in descending order of loop resistance value, and does not make further adjustments to the sections that have already been balanced, which effectively solves the problem of repeated calculations during the balancing process. For ease of calculation, we assume that the ratio of resistance values for each duct segment in the duct network that needs to be adjusted remains constant before and after adjustment. The relationship between diameter and resistance value before and after adjustment is given by: D = D(P/P)0.225 (1) Where D1 and D2 represent the diameters of the duct segments before and after resistance balance ； P, P: Resistance values of the corresponding duct branches on the most unfavorable loop before and after resistance balancing. When the resistance balance is calculated automatically, the paths of the pipe segments and their resistance losses that have already been adjusted in the loop are excluded, and for the unadjusted branches, the diameter D after resistance balance is calculated for each pipe segment using equation (1). From this diameter D, the corresponding velocity V and the pipe segment resistance ΔP are determined. 4. Verification of calculation results: Since the above calculations are based on the assumption that the air ducts are circular tubes of any diameter, in actual design they may be either circular or rectangular tubes, and their diameters must be standard ones. Therefore, during verification, it is first necessary to convert the diameter of the air ducts into standard diameters with similar hydraulic diameters, and to calculate the corresponding wind speed V and duct section resistance ΔP. At the same time, it is assumed that the wind speed in a pipe section can be any value when resistance is in balance; however, in reality, there are certain limits on the wind speed. When the wind speed exceeds these limits, it is necessary to adjust the wind speed in that pipe section in accordance with technical requirements, and the pipe diameter as well as the resistance of the pipe section must be calculated accordingly. The branches that require the installation of resistance-regulating valves, along with the resistance values of those valves, are then printed out. It is also necessary to check whether, after achieving resistance balance, the total (equivalent) diameter of the main pipe sections in the system is greater than the total (equivalent) diameter of the branch pipe sections, in accordance with the established rule. For each loop that has been verified, its resistance value must be recalculated to determine whether the most unfavorable loop has changed, and whether the difference in resistance between the other loops and the most unfavorable loop exceeds the allowable range. If the above situations occur, the results need to be adjusted again. IV. Conclusions 1. Using the method proposed in this paper, combined with computers, for the automatic balancing of the resistance in air conditioning and ventilation duct systems offers advantages such as speed, accuracy, and simplicity ； 2. How to enhance human-computer interaction is an issue that requires further exploration ； 3. During the automatic balancing process, it is possible to further incorporate technical and economic comparisons in order to optimize the duct design; this requires further research and resolution. 4. This paper is based on a constant air volume system as a model; it also provides some insights into the duct design and valve control when a variable air volume system is used for duct systems.