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Development of Design and Calculation of Urban Drainage Pipe System
Abstract: In the context of municipal construction and environmental management projects, rainwater and sewer systems often constitute a significant portion of the investment. Therefore, designing an urban drainage piping system in a rational manner under various technical conditions that meet regulatory requirements is a critical issue in the design process. This paper discusses the methods and problems involved in the development of design and calculation for sewer systems from three perspectives: optimized design under fixed pipelines, planar layout of pipelines, and runoff models. It highlights that further research and improvement in design and calculation methods are still needed in the future.
Keywords: drainage system; optimization design; layout; runoff model
Introduction: The drainage system is an essential and indispensable infrastructure in modern cities. It serves as the backbone for urban water pollution control, drainage, and flood prevention. Among these, the investment in rainwater and sewer systems in residential areas and industrial and mining enterprises typically accounts for about 70% of the total investment in the drainage system [1]. Hence, minimizing the capital cost of the pipeline system while meeting the stipulated technical conditions during the design phase is a crucial issue in the design work.
The traditional method of designing and calculating drainage systems involves designers using reliable data to determine a more reasonable sewage pipeline layout based on alignment principles. Subsequently, they calculate the design flow of each section, using hydraulic calculation diagrams or tables along with relevant design requirements as control conditions. Starting from upstream to downstream, they perform hydraulic design on each pipe section, determining the pipe diameter, slope, and elevation and depth of inspection wells at the end. Usually, adjustments are made based on experience regarding pipe diameter and slope to achieve economic and reasonable results. However, the degree of reasonableness is limited by the designer's personal capacity. Moreover, most calculations rely on repetitive chart and table access, leading to low efficiency, long duration, and not conducive to design optimization.
Since the 1960s, the international community has gradually established mathematical models for various water supply and drainage engineering systems or processes based on empirical summaries and mathematical analysis. As a result, water supply and drainage projects have entered a stage marked by quantitative and semi-quantitative "reasonable design and management." Simultaneously, research and practical applications have been carried out for various types of water supply and drainage systems [2].
To explore optimal design and calculation methods for sewer systems, many domestic and foreign scientific research, design, and teaching institutions, as well as individuals, have conducted extensive work and published numerous articles. Research results show that computer-aided design and calculation not only free designers from the laborious task of consulting charts but also optimize the entire drainage pipeline system and improve design quality. Compared to traditional methods, the optimal solution can reduce construction costs by more than 10% [3].
The drainage pipeline system is a large and complex system. According to existing research results, the design and calculation of the drainage pipeline system mainly involve three aspects: (1) optimization of pipe diameter and buried depth; (2) optimization of pipeline layout; and (3) establishment of stormwater runoff models.
Condensate drainage systems often include overflow facilities to limit the amount of water delivered to a local wastewater treatment plant. Since overflowed rainwater is also discharged into nearby rivers, the effect of combined flow drainage systems on the drainage area is essentially similar to that of split-flow rainwater systems [4].
Optimized Design of Piping System under a Given Pipeline: A considerable amount of groundbreaking work has been done both domestically and internationally on the optimization design of pipe diameter and depth when the pipeline layout has already been established. Optimization methods are generally divided into two categories: indirect optimization and direct optimization. Indirect optimization, also known as analytical optimization, is based on an optimization mathematical model and obtains the optimal solution through optimization calculations. Direct optimization is based on changes in performance indices, tunable parameters, and calculations and comparisons to obtain the optimal or satisfactory solution [5].
1.1 Direct Optimization Method: In the optimization design of drainage pipes, the direct optimization method is considered [6–8]. Although the hydraulic calculation formula for drainage pipes is very simple, the optional size of the pipe diameter is not continuous, and it cannot be arbitrarily chosen. The maximum fullness limit is related to the pipe diameter, and the minimum design flow rate, the change in flow rate (which increases with the design flow rate), and its constraints on the pipe diameter, which can be described using mathematical formulas. Therefore, it is difficult to establish a complete mathematical model to solve the optimization problem using indirect optimization methods. In contrast, the direct optimization method has the advantages of being direct, intuitive, and easy to verify.
1.2 Indirect Optimization Method: Indirect optimization methods involve the use of mathematical tools to simplify and abstract the design and calculation of drainage piping systems into an easy-to-solve mathematical model, provided that appropriate conditions are selected. Depending on the time of day and the mathematical method used, indirect optimization methods fall into the following categories:
1.2.1 Linear Programming: Linear programming is one of the most commonly used algorithms in optimization methods that solves many problems in sewer design and can also be used for sensitivity analysis of drainage pipes. Its disadvantage is that it treats pipe diameter as a continuous variable, which may lead to a contradiction between calculated diameter and commercially available specifications [9]. Additionally, all objective functions and constraints are linearized into linear functions, resulting in a large preprocessing workload and difficulty in ensuring accuracy.
1.2.2 Nonlinear Programming Method: Dajani and Gemmell established a nonlinear programming model in 1972 to address the nonlinear characteristics of the objective function and constraints in the optimal design of the drainage system [10]. This method is based on the principle of derivation, where the point at which the derivative of the objective function is zero is the optimal solution sought. It can handle commercially available pipe sizes, but if it cannot be proven that the pipe cost function is a single-peak function, the result obtained may be a local optimal solution rather than a global one.
1.2.3 Dynamic Programming: In 1975, Mays and Yen introduced dynamic programming into the optimization design of sewer systems [11]. This method is still widely used both domestically and internationally. It is divided into two branches in application: one uses the buried depth of each node as a state variable and conducts a full-scale search through slope decisions. The advantage of this method is that it directly uses standard diameters, and the optimization constraint has nothing to do with the initial solution. However, it requires that the interval of the state points be very small, significantly increasing storage and computational time [12]. To save computing time, Mays and Yen introduced the quasi-difference dynamic programming method in 1976. The pseudo-dynamic programming method reduces the scope of the iterative process, significantly decreasing computational time and storage, but there is a risk of omitting the optimal solution during the iterative process, especially in complex terrain or gentle slope conditions [13–14].
The other branch is based on the pipe diameter as a state variable, conducting a search through flow rate and fullness decision-making [15]. Due to the limited number of standard pipe diameters, this method offers significant advantages in terms of computer storage and computation time compared to the method of embedding node depth into decision variables. Some of the standard pipe diameters selected for the initial dynamic planning may not necessarily be feasible. Therefore, a feasible pipe diameter method was developed. Through mathematical analysis, this method uses the maximum and minimum pipe diameter and the standard pipe diameter between each of the pipe diameters satisfying the constraint conditions to form a feasible pipe diameter set, then applies dynamic programming for calculation. The feasible caliber method improves the precision of the calculation and significantly reduces the computational workload and computer memory [16].
Dynamic programming is an effective method for solving multi-stage decision-making optimization problems. There is insufficient evidence to prove whether the "post-validation" state of the phase state is valid when using node depth or pipe diameter as the state variable. "Post-effectiveness" refers to the fact that when given the state of a certain phase, subsequent phases are not influenced by the state of the previous phases. Therefore, the optimal design of sewer systems using dynamic programming is not necessarily the best solution.
1.2.4 Genetic Algorithm: A genetic algorithm is an optimization technique that has developed rapidly in recent years. It is a stochastic optimization algorithm proposed by natural genetics in simulated biology [17]. It still uses the specification pipe diameter as the state variable and searches for many points in the feasible solution space simultaneously. Through iterative operations such as selection, hybridization, and mutation, a satisfactory solution is finally obtained. Generally, the optimal design scheme can be obtained when solving the optimal design of small and medium-sized pipeline systems. Although the search method has a certain degree of randomness, when solving the problem of large-scale pipeline systems, the genetic algorithm can still obtain a feasible solution approaching the optimal solution [18].
In summary, both indirect and direct optimization methods are applied in the process of optimizing the design of drainage pipe systems and are constantly improving and perfecting. Both methods share common design specifications and requirements, such as diameter, flow rate, gradient, and fullness of the hydraulic relationship, with the goal of achieving the minimum cost.
2 Planes for Planar Optimization of Pipelines: Researchers have pointed out that they have solved the problem of drainage system optimization in a given pipeline and found that they are more suitable for the optimization of different alignment schemes. However, since the design under the given pipeline is the basis of the pipeline layout, coupled with the immature design and optimization of the planned pipeline, there has been little progress in optimizing the layout of the system.
The earliest study in this area is JCLiebman (1976). In his study, considering hydraulic factors, he assumed that each pipe diameter is the same, using the cost of excavation as the preferred basis, choosing an initial arrangement, and then using the trial algorithm to gradually adjust. Since then, Argaman (1973) and Mays (1976) introduced the concept of a Drainage Line in a plan layout that uses a drain at a node in the drainage area that is equally spaced from the final outlet node (i.e., inspection well) wire connection. For any drainage line, the upstream flow will flow downstream of the drainage line [19]. In this way, the optimal problem of pipeline layout is transformed into the shortest path problem, which can be solved by dynamic programming. This model has taken into account the hydraulic factors, but due to the introduction of drainage lines, the search scope of the optimization process is limited to a small part of the feasible area of the floorplan. Even those with rich design experience may be able to exclude the optimal program. Coupled with its maximum storage and calculation of the characteristics of a long time, this method is still unable to achieve.
In 1982, Walters made some improvements to this method, which was applied to the design of highway drainage systems. Over time, researchers found that the urban drainage system can be abstracted as a decision-making map made up of points and lines, and then turned to looking for a plane-optimized arrangement from the graph theory. In 1983, PRBhave and JF Borlow applied the algorithm of minimum generation in network graph theory to the optimization of the drainage system layout. Assuming that each pipe in the system has the same weight (Weight), to avoid the hydraulic factor, using the weight method to solve. In 1986, S. Tekel and H. Belkaya applied three kinds of weights to solve: (1) the reciprocal of the slope of each pipe section; (2) the pipe length of each pipe section; (3) according to the smallest slope design when the amount of cut. The three kinds of weights are respectively calculated by using the shortest spanning tree algorithm to find the pipeline layout plan, then the pipe diameter, depth, and the optimal design of pumping stations are optimized. Finally, the plane plan with the lowest investment cost is taken as the optimal design plan.
For all feasible pipeline laying paths in the drainage system, the actual weights of each pipe section cannot be calculated until the scheme is determined, so it belongs to the variable weight problem in graph theory. However, until now, there is no effective solution to the problem. In China, Li Guiyi (1986) proposed a simple gradient method, and Chen Sen-fa (1988) proposed a hierarchical optimization method [20]. These methods also failed to achieve satisfactory results. Recently, the emergence of genetic algorithms has provided possible conditions for the optimal layout of drainage piping systems, because the computational mechanism of genetic algorithms has no special requirements on objective functions and constraints. GAWalters has applied genetic algorithms to study urban water supply and drainage, farmland irrigation, cables, and gas pipelines [21].
3 Study on Rainfall Runoff Model: The design of stormwater canals in China has been using inference formula methods, which were piloted in 1974 and revised in the outdoor drainage design code in 1987. The inference formula method assumes that the flow in the canal is uniform and calculates the travel time of the flow in the pipeline. Assuming that the flow velocity of rainwater on the ground is equal to the flow velocity of the water in the canal, the rainfall duration equals the surface catchment time. The maximum design flow of the next pipe section is obtained from the storm formula. Select a feasible pipe diameter as the design pipe diameter, and obtain the required hydraulic gradient (or choose a feasible hydraulic gradient) from the hydraulic formula to find the feasible pipe diameter.
The inference formula method uses the open channel uniform flow formula for hydraulic calculation, and its greatest advantage is simplicity and speed. Due to the use of historical maximum rainfall data, it can be biased toward safe design. However, many studies have shown that the assumptions based on the derivation formula in the inference formula method are not reasonable and have some imperfections, mainly in the following aspects [22]: (1) The spatial variation of rainfall is not considered. Because the actual storm intensity is unevenly distributed in the rainfall area, when the catchment area is larger, the rainfall duration taken is longer, and the design flow of the downstream pipe section calculated by the formula will be greatly deviated. (2) Theoretically, overly simplistic assumptions are made, and users may borrow parameters and constants published elsewhere without checking to save time. Due to the lack of sufficient design information examples, there is a certain degree of blindness. (3) Only the peak flow can be calculated, and the complete runoff process cannot be deduced. For the design of rainwater regulation tanks, the overflow flow calculation of the combined drainage pipe cannot meet the requirements. (4) The assumption that the design recurrence period is directly converted from design torrential rains to the design recurrence period of drainage pipelines has not been fully substantiated. Marsalek (1978), Wenzel and Vookes (1978, 1979) pointed out that the selection of rainfall duration, duration distribution, and pre-rain soil moisture content has a great impact on the relationship between peak flow rate and frequency. Some functions exist between these parameters. (5) It cannot meet the calculation requirements of runoff water quality. Because high pollution concentration of rainfall does not necessarily occur in the high flow process line. Even for confluence pipelines, there is still a significant amount of contaminants in the combined effluent from the system.
In recent 20 years, with the increasingly prominent problems of urban runoff pollution, it is becoming more and more important to establish various high-accuracy urban hydrological and hydraulic computational models. Much progress has been made abroad in this area, and many models have been widely used in the planning, design, and management of stormwater piping systems. Currently, the most famous programs in the West are [23] the Wallingford Procedure of the UK Department of Environment and the National Water Commission, the Storage, Treatment, Overflow, Runoff Mode of the Corps of Engineers Hydrographic Center, STORM), the EPA's Storm Water Management Mode SWMM and others. These models can simulate the rainfall and runoff processes in the city with relatively accurate quantities (rainfall and runoff) and quality (water quality of rainfall and runoff water and water quality of receiving water bodies). Their development is closely linked with the project. After a period after the accumulation of experience, the government departments will organize and coordinate the introduction of stereotype software for design and management selection [24].
The study of urban runoff models in China started late, and there are currently some research results that are combined with the actual situation in our country. Such as the proliferation of rainwater pipe network simulation simplification and motion wave reduction [25], surface runoff system simulation techniques include: flow method, instantaneous unit line method, and improved reasoning method [26].
4 Conclusion: Both domestic and foreign countries have made great achievements in the theoretical calculation and engineering application of the drainage piping system design, and many problems still waiting to be solved still exist. With the development of computing technology and system methods, it is an inevitable trend to study and design drainage pipe system design and calculation software better.
★ Correspondence: 200092 School of Environmental Science and Engineering, Tongji University Tel: (021) References 1 Gu Guowei. Research on Water Pollution Control Technology. Shanghai: Tongji University Press, 1997 2 Fu Guowei. Introduction to Water Supply and Drainage System Optimization (1). China Water and Wastewater, 1987, 3 (4): 45-50 50 James, S J. Optimal design of sanitary sewers. Computing in civil engineering proceeding of the fourth conference, Edited by W Tracy Lenocker, Published by the American Society of Civil Engineers 1986: 162 ~ 177 4 MJ Hall [English], translated by Zhan Daojiang etc. Urban Hydrology. Nanjing: Hohai University Press, 1989 5 Peng Yongzhen, Cui Foyi. Computer programming of water supply and drainage engineering. Beijing: China Building Industry Publishing House, 1994 6 Wang Boren. Calculation of sewer system and optimization options. China Water & Wastewater, 1985,1 (2): 1 ~ 5 7 Peng Yongzhen, Wang Shuying, Wang Fuzhen. Global Optimization of Drainage Network Calculation Program. , 1994,10 (5): 41 ~ 438 Zhang Lianmin. Flow rate control method for optimal design of sewer network. China Water & Wastewater, 199 4,10 (5): 41 ~ 43 9 Shen Yi.Application of Microcomputer in Sewage Pipeline Optimal Design. Ministry of Communications First Flight Engineering Prospecting and Design Institute, 1988 10 Li GY and Matthew, GS R. New approach for optimization of urban drainage systems. Journal of environmental engineering, ASCE, 1990, 116 (5): 927-944 11 Kuo JT and Yen B C. Hwang, GP P. Optimal design for storm sewer system with pumping stations. Journal of water resource planning and management, Journal of Xi'an Institute of Metallurgy and Architecture, 1993,25 (3): 305 ~ 310 13 Li Guiyi.Drainage network optimization design.China water supply and drainage (2): 18 ~ 23 14 Ouyang Jianxin, Chen Xinshang. Discrete Optimization of Penalty Function for Drainage System Design. Water Supply and Drainage, 1996,22 (5): 19-21 21 Ding Hongda. Dynamic Planning of Gravity Flow and Rainfall Water Pipe System Analysis. Water Supply and Drainage, 1983,9 (5): 2 ~ 7 16 Lu Shaoming, Liu Suiqing. Optimized Design of Feasible Pipe Diameter for Urban Sewer Network. Journal of Tongji University, 1996,24 (3): 275-280 17 Simpson AR, Dandy GC and Murphy L J. Genetic algorithms compared to other techniques for pipe optimization. Journal of water resource planning and management, 1994,120 (4): 423 ~ 443 18 Zhang Jinguo, Li Shuping. Genetic algorithm for drainage system optimization design. China Water and Wastewater, 1997 , 13 (3): 28 ~ 30 19 Li Guiyi. Optimization design of drainage channel system. Information Technology Station of Tongji University, 1986 20 Chen Senfa. Hierarchical Optimization Design of Urban Sewer Network System Layout. China Water Supply and Drainage, 1988,4 ( 3): 6 ~ 10 21 Walters GA and Lohbeck T K. Optimal layout of tree network using genetic algorithms. Engineering Optimization, 1993, 22: 27 ~ 48 22 Hydrology Bureau of Ministry of Water Conservancy and Electric Power. 23 Wang Wenyuan, Wang Chao. Enlightenment from the Development of Foreign Urban Drainage Systems. China Water and Wastewater, 1998,14 (2): 45 ~ 47 24 Harry van Mameren and Francois Clemens. Guidelines for hydrodynamic calculations on urban drainage in the and principles. Water science and technologies, 1997,36 (8): 247 ~ 252 25 Cen Guoping. DYNAMIC WAVE SIMULATION AND EXPERIMENT OF RAINWAY NETWORK Journal of Water Supply and Drainage, 1995,21 (10): 11 ~ 13 26 Zhou Yuwen, Meng Shaolu. Study on the process of in-line flow of rainwater network by instantaneous unit line method. In municipal construction and environmental management project construction, rainwater and sewer systems often occupy a larger proportion of investment. Therefore, how to design urban drainage piping system rationally under the various technical conditions that meet the stipulations is an important issue in the design. The methods and the problems to be solved in the development of design and calculation of sewer system are discussed from the aspects of the optimized design under the fixed pipeline, the plane layout of the pipeline and the runoff model. It can be seen that in the future still need to devote a lot of energy to study and improve its design and calculation methods. Keywords drainage system optimization design layout layout runoff model Introduction The drainage system is an indispensable and important infrastructure in the modern city. It is also the backbone project of urban water pollution control and city drainage waterlogging prevention and flood control. Among them, the investment of rainwater and sewer systems in residential areas and industrial and mining enterprises generally accounts for about 70% of the total drainage system investment [1]. Therefore, it is an important issue in the design work to minimize the capital cost of the pipeline system under various technical conditions that meet the stipulations in the design. The design and calculation method of the traditional drainage system is as follows: After the designers have mastered the relatively complete and reliable design basis data, they can determine a more reasonable sewage pipeline layout according to the principle of pipeline alignment and layout. And then calculate the design flow of each design section, hydraulic calculation diagram or hydraulic calculation table and the relevant design requirements as the control conditions, from upstream to downstream, followed by hydraulic design of each section of the pipe, calculate the pipe diameter, slope and In the inspection wells at the end of the elevation and depth of embedding. Calculation, generally only by experience on the pipe diameter and slope, etc. for proper adjustment, in order to achieve the purpose of economic and reasonable, but the reasonable degree by the designer's personal capacity constraints; the other hand, the majority of calculations using repeated access Figure and table methods, work efficiency is low, a long time, is not conducive to the optimization of the design. Since the 1960s, the international community has gradually established mathematical models of various water supply and drainage engineering systems or processes on the basis of experience summaries and mathematical analyzes. As a result, water supply and drainage projects marked by quantitative and semi-quantitative " Reasonable design and management "stage. At the same time, optimized research and practice have been carried out for various types of water supply and drainage systems [2]. In order to explore the optimal design and calculation method of sewer system, many domestic and foreign scientific research, design, teaching units and individuals have done a lot of work and published a large number of articles. From the research results, the design and calculation of drainage pipes by computer not only free designers from the heavy labor of consulting charts, speed up the design progress, but also optimize the entire drainage pipe system and improve the design quality. Compared with the traditional method, the optimal solution determined can reduce the construction cost by more than 10% [3]. The drainage pipeline system is a huge and complex system. According to the existing research results, the design and calculation of the drainage pipeline system mainly involves three aspects: (1) Pipeline diameter-buried depth Optimization design; (2) optimization of pipeline layout; and (3) establishment of stormwater runoff model. Condensate drainage systems often have overflow facilities to limit the amount of water delivered to a local wastewater treatment plant. Since the overflowed rainwater is also discharged into the river nearby, the effect of the combined flow drainage system on the drainage area is actually the same from that of the split-flow rainwater system [4]. Optimized Design of Piping System under a Given Pipeline A great deal of groundbreaking work has been done at home and abroad for the optimization design of the pipe diameter-depth under the condition that the pipeline layout has been established. Optimization methods are generally divided into two types: indirect optimization and direct optimization. The indirect optimization method, also called analytic optimization, is based on the optimization mathematical model, and obtains the optimal solution through optimization calculation. The direct optimization method is based on the change of the performance index, Tunable parameters of choice, calculation and comparison, to get the optimal solution or satisfactory solution [5]. 1.1 Direct Optimization Method In the optimization design of drainage pipe, the direct optimization method is considered [6-8]: Although the hydraulic calculation formula for drainage pipe calculation is very simple, but the optional size of the pipe diameter is not continuous, can not be arbitrary The choice of pipe diameter; the maximum fullness limit is related to the pipe diameter; the minimum design flow rate, the change of the flow rate (which increases with the design flow rate), and its constraints on the pipe diameter, To use mathematical formulas to describe. Therefore, it is difficult to establish a complete mathematical model to solve the optimization problem to solve with indirect optimization method. In contrast, direct optimization method to solve this problem has the advantages of direct, intuitive and easy to verify. 1.2 Indirect optimization method Indirect optimization method is that: With the development of optimization technology, although there are a number of constraints in the design and calculation of drainage piping system, as long as the appropriate choice of some of the conditions, the rational use of mathematical tools It can be simplified, abstracted as easy to solve the mathematical model, by calculating the optimal solution. Depending on the time of day and the mathematical method used, the indirect optimization methods fall into the following categories: 1.2.1 Linear Programming The LFS is one of the most commonly used algorithms in optimization methods that solves many of the problems in the design of sewers , But also can be built on the drainage pipe sensitivity analysis. Its disadvantage is that the pipe diameter as a continuous variable to deal with, there is a calculated diameter and the diameter of the commercially available specifications of the contradiction [9]. And all the objective functions and constraints are linearized into a linear function, the pre-processing workload is large, the accuracy is difficult to be guaranteed. 1.2.2 Nonlinear programming method Dajani and Gemmell established a nonlinear programming model in 1972 in order to meet the nonlinear characteristics of the objective function and constraints in the optimal design of the drainage system [10]. The method is based on the principle of derivation, that is, the point at which the derivative of the objective function is zero is the optimal solution sought. It can handle commercially available pipe sizes, but when it can not be proved that the pipe cost function is a single-peak function, the result obtained may be a local optimal solution rather than a global optimal solution. 1.2.3 Dynamic Programming In 1975, Mays and Yen firstly introduced dynamic programming into the optimization design of sewer system [11]. At present, this method is still widely used at home and abroad. It is divided into two branches in the application: one is to use the buried depth of each node as a state variable, and conduct full-scale search by slope decision. The advantage of this method is that it directly uses the standard diameter and the optimization constraint has nothing to do with the initial solution, However, it is required that the interval of the state points is very small, which greatly increases the storage and calculation time [12]. In order to save computing time, Mays and Yen introduced the quasi-difference dynamic programming method in 1976. Pseudo-dynamic programming method is based on the dynamic programming method to reduce the scope of the introduction of the iterative process can significantly reduce the computational time and storage, but in the iterative process may omit the optimal solution, but also in complex terrain conditions Fell, gentle slope conditions are limited [13 ~ 14]. The other is based on the tube diameter as a state variable, through the flow rate and fullness decision-making search [15]. Due to the limited number of standard pipe diameters, there are significant advantages in terms of computer storage and calculation time compared with the method of embedding node depth into decision variables. Some of the standard pipe diameters selected for the pipe diameter of each pipe section in the initial dynamic planning are not necessarily feasible pipe diameters. Therefore, a feasible pipe diameter method is developed. Through mathematical analysis, this method uses the maximum and minimum pipe diameter and the standard pipe diameter between each of the pipe diameters satisfying the constraint conditions to form a feasible pipe diameter set, and then applies the dynamic programming Calculate. The feasible caliber method can improve the precision of calculation and reduce the computational workload and computer memory [16]. The dynamic programming method is an effective method to solve the optimization problem of multi-stage decision-making. There is not enough evidence to prove the "post-validation" state of the phase state whether using the node depth or the pipe diameter as the state variable. No post-effectiveness "refers to the fact that when given the state of a certain phase, the subsequent phases are not influenced by the state of the previous phases). Therefore, the optimal design of sewer system using dynamic programming is not necessarily the best solution. 1.2.4 Genetic Algorithm Genetic algorithm is an optimization technique developed rapidly in recent years. It is a stochastic optimization algorithm proposed by natural genetics in simulated biology [17]. It still uses the specification pipe diameter as the state variable, and searches for many points in the feasible solution space at the same time. Through the iterative operation factors such as selection, hybridization and mutation, the satisfactory solution is finally obtained. Generally, the optimal design scheme can be obtained when solving the optimal design of small and medium-sized pipeline system. Although the search method has a certain degree of randomness, when solving the problem of large-scale pipeline system, the genetic algorithm can still obtain the feasible solution approaching the optimal solution Program [18]. In short, in the process of the optimization design of drainage pipe system, both the indirect optimization method and the direct optimization method are applied and are constantly improving and perfecting. Common to both of these methods are the design specifications and requirements of the diameter, flow rate, gradient, fullness of the hydraulic relationship between the constraints, in order to achieve the minimum cost as the goal. 2 PLANES FOR PLANAR OPTIMIZATION OF PIPELINES Researchers have pointed out at the same time that they have solved the problem of drainage system optimization in a given pipeline and have found that they are more suitable for the optimization of different alignment schemes. However, since the design under the given pipeline is the basis of the pipeline layout, coupled with the immature design and optimization of the planned pipeline, there has been little progress in optimizing the layout of the system. The earliest study in this area is JCLiebman (1976). In his study, taking into account the hydraulic factor, assuming that each pipe diameter is the same, with the cost of excavation as the preferred basis, choose an initial arrangement, and then use the trial algorithm to gradually adjust. Since then Argaman (1973) and Mays (1976) have introduced the concept of a Drainage Line in a plan layout that uses a drain at a node in the drainage area that is equally spaced from the final outlet node (ie inspection well) Wire connection. For any drainage line, the upstream flow will flow downstream of the drainage line [19]. In this way, the optimal problem of pipeline layout is transformed into the shortest path problem, which can be solved by dynamic programming. This model has taken into account the hydraulic factors, but due to the introduction of drainage lines, the searching scope of the optimization process is limited to a small part of the feasible area of ​​the floorplan. Even those with rich design experience may be able to put the optimal The program is excluded. Coupled with its maximum storage and calculation of the characteristics of a long time, this method is still unable to achieve. In 1982, Walters made some improvements to this method, which was applied to the design of highway drainage system. Over time, the researchers found that the urban drainage system can be abstracted as a decision-making map made up of points and lines, and then turned to looking for a plane-optimized arrangement from the graph theory. In 1983, PRBhave and JF Borlow applied the algorithm of minimum generation in network graph theory to the optimization of the drainage system layout. Assuming that each pipe in the system has the same weight (Weight), to avoid the hydraulic factor, using the weight method to solve. In 1986, S. Tekel and H. Belkaya applied three kinds of weights to solve: (1) the reciprocal of the slope of each pipe section; (2) the pipe length of each pipe section; (3) , According to the smallest slope design when the amount of cut. The three kinds of weights are respectively calculated by using the shortest spanning tree algorithm to find the pipeline layout plan, then the pipe diameter, depth and the optimal design of pumping stations are optimized. Finally, the plane plan with the lowest investment cost is taken as the optimal design plan. For all feasible pipeline laying paths in drainage system, the actual weights of each pipe section can not be calculated until the scheme is determined, so it belongs to the variable weight problem in graph theory. However, until now, There is no effective solution to the problem. In China, Li Guiyi (1986) proposed a simple gradient method, and Chen Sen-fa (1988) proposed a hierarchical optimization method [20]. These methods also failed to achieve satisfactory results. Recently, the emergence of genetic algorithms has provided possible conditions for the optimal layout of drainage piping systems, because the computational mechanism of genetic algorithms has no special requirements on objective functions and constraints. GAWalters has applied genetic algorithms to study urban water supply and drainage, farmland irrigation, cables, and gas pipelines [21]. 3 Study on Rainfall Runoff Model The design of stormwater canal in China has been using inference formula method, which was piloted in 1974 and the outdoor drainage design code revised in 1987 are all the same. The inference formula method is based on the assumption that the water flow in the canal is uniform and the prevailing time of the water flow in the pipeline is obtained. Assuming that the flow velocity of rainwater on the ground is equal to the flow velocity of the water in the canal, the rainfall duration equals to the time of surface catchment, The maximum design flow of the next pipe section is obtained from the rainstorm formula. Select a feasible pipe diameter as the design pipe diameter, and obtain the required hydraulic gradient (or choose a feasible hydraulic gradient) from the hydraulic formula to find the feasible pipe diameter. The inference formula method uses open channel uniform flow formula for hydraulic calculation, the biggest advantage is simple and rapid. Due to the use of the history of the largest rainfall data, can be biased in favor of security design. However, many researches have shown that the reasoning based on the derivation formula in the inference formula method is not reasonable and there are some imperfections, mainly in the following aspects: (1) The spatial variation of rainfall is not considered. Because the actual rainstorm intensity is unevenly distributed in the rainfall area, when the catchment area is larger, the rainfall taken takes longer, and the design flow of the downstream pipe section calculated by the formula will be greatly deviated. (2) In theory, we made a simplistic assumption that users may borrow parameters and constants published elsewhere to save time without checking. Due to the lack of sufficient examples of design information, there is a certain degree of blindness. (3) The peak flow can only be calculated, and the complete runoff process can not be deduced. For the design of rainwater regulating tank, the overflow flow calculation of the combined drainage pipe can not meet the requirements. (4) The assumption that the design recurrence period directly from design torrential rains is converted into the design recurrence period of drainage pipelines has not been fully substantiated. Marsalek (1978), Wenzel and Vookes (1978, 1979) pointed out that the selection of rainfall duration, duration distribution and early soil moisture content have a great impact on the relationship between peak flow rate and frequency. Some functions exist between these parameters relationship. (5) Can not meet the calculation requirements of runoff water quality. Because of the high pollution concentration of rainfall does not necessarily occur in the Gao Hongfeng process line. Even for confluent pipelines, there is still a significant amount of contaminants in the combined effluent from the system. In recent 20 years, with the increasingly prominent problems of urban runoff pollution, it is more and more important to establish all kinds of urban hydrological and hydraulic computational models with high accuracy. Much progress has been made abroad in this area and many models have been widely used in the planning, design and management of stormwater piping systems. Currently, the most famous programs in the West are [23] the Wallingford Procedure of the UK Department of Environment and the National Water Commission, the Storage, Treatment, Overflow, Runoff Mode of the Corps of Engineers Hydrographic Center, STORM), the EPA's Storm Water Management Mode SWMM and others. These models can simulate the rainfall and runoff processes in the city with relatively accurate quantities (
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1. Graphite Block Heat Exchanger - Structural Features: Made of impregnated or molded impervious graphite, offering high corrosion resistance and
thermal conductivity. Common types include cylindrical block-type (e.g., Cylindrical Block Graphite Heat Exchanger)
and shell-and-tube graphite heat exchangers. - Applications: Ideal for corrosive media like strong acids or alkalis, such as heat exchange in phosphoric acid production. 2. Ceramic Block Heat Exchanger - Structural Features: Fabricated from monolithic ceramic blocks with elongated cross-sectional channels. The overlapping
arc-shaped channel walls enhance fluid flow efficiency. - Applications: Suitable for high-temperature or high-wear environments in chemical and energy industries. Classification by Structural Design
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1. Block-and-Hole Heat Exchanger - Composed of multiple perforated graphite blocks stacked together, allowing fluid exchange through interconnected channels (e.g., *Cylindrical Block Graphite Heat Exchanger*). 2. Shell-and-Tube Block Structure - Modular shell-and-tube designs, including fixed-tube and floating-head types. Examples include *Complex Shell-and-Tube Graphite Heat Exchanger*. 3. Monolithic Block Heat Exchanger - Single-piece structures formed by casting or injection molding, eliminating welds and enhancing pressure resistance (e.g., ceramic or metal monolithic blocks). Classification by Special Functions
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1. High-Pressure Thread-Locked Ring Heat Exchanger - Design Features: Employs threaded locking rings for sealing, suitable for high-pressure hydrogen environments (e.g., hydrogenation reaction systems). Corrosion resistance is improved via optimized materials like hydrogen-resistant steel. 2. Corrosion-Resistant Block Heat Exchanger - Examples include *Double-Side Corrosion-Resistant Cylindrical Block Graphite Heater*, designed for strong acid media. Classification by Manufacturing Process
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1. Modular Assembly Type - Multiple modules connected via bolts or adhesives, facilitating maintenance (common in graphite heat exchangers). 2. Integrated Monolithic Type - Molded in one piece for high structural integrity, such as cast ceramic or metal blocks. Application Scenarios
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- Chemical Industry: Graphite and ceramic block exchangers handle corrosive media (e.g., sulfuric acid, phosphoric acid). - Energy & High-Pressure Systems: Thread-locked ring exchangers are used in petroleum hydrogenation and high-pressure steam systems. - High-Temperature Environments: Ceramic blocks excel in waste heat recovery from high-temperature exhaust gases.