CN100405375C

CN100405375C - Design verification and optimization method of sampling pipe network for aspirating smoke detection system

Info

Publication number: CN100405375C
Application number: CNB2005100469142A
Authority: CN
Inventors: 刘玉宝; 梅志斌; 王文青; 潘刚; 余广智; 王勇俞
Original assignee: Shenyang Fire Research Institute of MEM
Current assignee: Shenyang Fire Research Institute of MEM
Priority date: 2005-07-22
Filing date: 2005-07-22
Publication date: 2008-07-23
Anticipated expiration: 2025-07-22
Also published as: CN1719448A

Abstract

吸气式感烟火灾探测系统采样管网设计验证及优化方法，属于消防报警配套技术，为超早期吸气式感烟火灾探测器的配套设计方法。本发明方法通过对采样管网进行模拟仿真，根据流体力学的相关原理，对火灾探测器采样管网从流体运动角度进行分析建立数学模型，通过工程应用要求，确定采样管长，采样孔间距和采样孔数量，按照设定值确定初始的采样孔径，要求所有采样点具有均衡的探测灵敏度即吸气量，和不大于120秒的探测相应时间，如达不到设计要求，通过调整各采样孔孔径来优先实现。The sampling pipe network design verification and optimization method of the aspirating smoke fire detection system belongs to the supporting technology of fire alarm and is a supporting design method of the ultra-early aspirating smoke fire detector. The method of the present invention simulates the sampling pipe network, and according to the relevant principles of fluid mechanics, analyzes the fire detector sampling pipe network from the perspective of fluid movement to establish a mathematical model, and determines the sampling pipe length, sampling hole spacing and The number of sampling holes, the initial sampling aperture is determined according to the set value, and all sampling points are required to have a balanced detection sensitivity, that is, the inspiratory volume, and a corresponding detection time of no more than 120 seconds. If the design requirements cannot be met, adjust each sampling hole Aperture to achieve priority.

Description

Design verification and optimization method of sampling pipe network for aspirating smoke detection system

技术领域 technical field

本发明属于消防报警配套技术，特别涉及一种吸气式感烟火灾探测器工程管网设计验证及优化方法，为超早期吸气式感烟火灾探测器的配套设计方法。The invention belongs to the supporting technology of fire alarm, in particular to a design verification and optimization method for an engineering pipe network of an aspirating smoke detector, which is a supporting design method for an ultra-early aspirating smoke detector.

背景技术 Background technique

吸气式感烟火灾探测器采用主动吸气的工作方式，由于它能够对烟雾有较高的探测灵敏度，因此，在一些特殊的应用场合得到了广泛的应用。吸气式感烟火灾探测系统主要由气体采样管网和探测主机两部分组成：The aspirating smoke detector adopts the working mode of active aspirating, and because it can have high detection sensitivity to smoke, it has been widely used in some special applications. The aspirating smoke detection system is mainly composed of two parts: a gas sampling pipe network and a detection host:

a.气体采样管网的作用是采集被保护区域内的空气样本。气体采样管上设置采样孔，由于探测主机内吸气泵的作用，管网内产生负压，形成一个稳定的气流，被保护区域内的空气样本被抽入采样孔，通过采样管网进入探测主体。a. The function of the gas sampling pipe network is to collect air samples in the protected area. Sampling holes are set on the gas sampling pipe. Due to the function of the suction pump in the detection host, negative pressure is generated in the pipe network to form a stable air flow. The air samples in the protected area are drawn into the sampling hole and enter the detection through the sampling pipe network. main body.

b.探测主机对采集到的空气样本中的烟雾颗粒的浓度进行分析比较，当达到响应阀值时分级报警。b. The detection host analyzes and compares the concentration of smoke particles in the collected air samples, and gives a graded alarm when the response threshold is reached.

采样管网的基本组成部分是采样管。采样管沿管道壁开有一定数量的开点，可直接采样空气，为采样孔，也可以引出细管，伸入欲采样空气的位置，为毛细管。系统通过采样孔或毛细管将空气采样传递到探测器上，采样管道的另一端是末端帽(开孔)，以平衡不同采样孔的烟雾灵敏度。如图1所示。The basic component of the sampling pipe network is the sampling pipe. The sampling pipe has a certain number of openings along the pipe wall, which can directly sample air, which is called a sampling hole, and can also lead out a thin tube to extend into the position where the air is to be sampled, called a capillary. The system transmits air samples to the detector through sampling holes or capillary tubes, and the other end of the sampling pipe is an end cap (open hole) to balance the smoke sensitivity of different sampling holes. As shown in Figure 1.

本发明方法通过对采样管网进行模拟仿真，根据流体力学的相关原理，对火灾探测器采样管网从流体运动角度进行分析建立数学模型，通过工程应用要求，确定采样管长，采样孔间距和采样孔数量，按照设定值确定初始的采样孔径，要求所有采样点具有均衡的探测灵敏度(吸气量)和不大于120秒的探测相应时间(国标要求)，如达不到设计要求，通过调整各采样孔孔径来优先实现。The method of the present invention simulates the sampling pipe network, and according to the relevant principles of fluid mechanics, analyzes the fire detector sampling pipe network from the perspective of fluid movement to establish a mathematical model, and determines the sampling pipe length, sampling hole spacing and The number of sampling holes, the initial sampling aperture is determined according to the set value, and all sampling points are required to have a balanced detection sensitivity (inhalation volume) and a detection response time of no more than 120 seconds (national standard requirements). If the design requirements cannot be met, pass Adjust the aperture of each sampling hole to achieve priority.

当前国内没有相应的处理系统及方法，国外类似处理系统也只能为其本身配套的设备进行仿真计算，而不能应用于其它产品。At present, there is no corresponding processing system and method in China, and similar processing systems abroad can only perform simulation calculations for their own supporting equipment, and cannot be applied to other products.

本发明提供的吸气式感烟火灾探测器工程管网设计系统及方法可实现以下功能：The engineering pipe network design system and method of the air-breathing smoke detector provided by the present invention can realize the following functions:

1)以三维视图的方式显示采样管网的设计；1) Display the design of the sampling pipe network in a three-dimensional view;

2)可以输入房间或整个建筑的dxf文件格式图纸；2) The dxf file format drawing of the room or the whole building can be input;

3)通过图形接口设计探测器、采样管路、采样孔、毛细管，并可对采样管、采样孔、毛细管的直径进行修改；3) Design the detector, sampling pipeline, sampling hole and capillary through the graphic interface, and modify the diameter of the sampling tube, sampling hole and capillary;

4)通过图形得出弯管、管长、管径、孔径、毛细管的数量与长度等输入变量，依据数学4) Obtain input variables such as elbow, pipe length, pipe diameter, aperture, capillary quantity and length through graphics, according to mathematics

模型，可计算各采样点气样传输时间、流量比并进行优化设计；Model, which can calculate the gas sample transmission time and flow ratio of each sampling point and optimize the design;

5)图形文件，计算结果可显示、存储、打印；5) Graphic files, calculation results can be displayed, stored and printed;

6)可实现单管路和多管路的设计；6) The design of single pipeline and multiple pipelines can be realized;

7)提供详细的帮助文件。7) Provide detailed help files.

发明内容 Contents of the invention

针对现有技术的不足，本发明提供一种吸气式感烟火灾探测器工程管网设计验证及优化方法，配套超早期吸气式感烟火灾探测器使用。由于吸气式探测器采样管网的开孔应保持吸气量均等，这样对整个空间的火灾探测才能保持最佳状态，同时应保证气样传输时间在120秒内，因此需要对采样管网的各项数据进行验证计算，如果达不到上述要求，在本发明方法中，则可以通过调整孔径实现优化设计的目的。Aiming at the deficiencies of the prior art, the present invention provides a design verification and optimization method for an engineering pipe network of an aspirating smoke detector, which is used together with an ultra-early aspirating smoke detector. Since the openings of the sampling pipe network of the aspirating detector should keep the suction volume equal, so that the fire detection of the entire space can be kept in an optimal state, and at the same time, the transmission time of the gas sample should be guaranteed within 120 seconds, so the sampling pipe network needs to be adjusted If the above-mentioned requirements cannot be met, in the method of the present invention, the purpose of optimizing the design can be realized by adjusting the aperture.

本发明方法具体实现步骤如下：The concrete realization steps of the inventive method are as follows:

步骤一、输入数据；Step 1. Input data;

输入对采样管网进行仿真所需要的数据，即工程原设计的数据，在系统中重现原设计方案，包括以下内容：Input the data required for the simulation of the sampling pipe network, that is, the data of the original design of the project, and reproduce the original design scheme in the system, including the following:

1、采样管的弯折情况，每段采样管的长度；1. The bending condition of the sampling tube, the length of each sampling tube;

2、采样孔的数量，位于采样管的位置，每个采样孔的孔径；2. The number of sampling holes, the location of the sampling tube, and the diameter of each sampling hole;

3、毛细管的数量，位于采样管的位置，每个毛细管的孔径及长度；3. The number of capillaries, the position of the sampling tube, the aperture and length of each capillary;

4、末端帽的孔径。4. The aperture of the end cap.

步骤二、验证工程原设计的合理性，计算包括末端帽在内的所有采样点的吸气量，吸气百分比及吸气时间；Step 2. Verify the rationality of the original design of the project, and calculate the inhalation volume, inhalation percentage and inhalation time of all sampling points including the end cap;

验证合理性所需要的基本原理如下：The rationale required to verify plausibility is as follows:

1、管路流体动力学分析和数学模型的建立1. Pipeline fluid dynamics analysis and mathematical model establishment

如果流体经过它所占据空间各点时的运动参数不随时间改变，这样的流动称为稳定流；反之，若运动参数随时间而改变，则称为非稳定流。本系统由于探测器吸气泵的吸气能力有限，管路中气体流速不太高，可将此气体视为不可压缩流体，同时采样管网一旦确定，管路中流体参数就已确定，不随时间改变，为稳定流，符合伯努利方程的适用条件。If the motion parameters of the fluid passing through the points in the space it occupies do not change with time, such a flow is called a steady flow; conversely, if the motion parameters change with time, it is called an unsteady flow. Due to the limited suction capacity of the detector suction pump in this system, the gas flow rate in the pipeline is not too high, so the gas can be regarded as an incompressible fluid. Time changes, for a steady flow, in line with the applicable conditions of the Bernoulli equation.

伯努利方程(Bernoulli)又称流体能量方程，反映了流体动压强、流速与位置高度间的关系，是流体动力学中最重要的一个方程。稳定气流的伯努利方程如下：Bernoulli equation, also known as fluid energy equation, reflects the relationship between fluid dynamic pressure, flow velocity and position height, and is the most important equation in fluid dynamics. The Bernoulli equation for a steady airflow is as follows:

${p p}_{11} + + \frac{ρ ρ {v v}_{11}^{22}}{22} + + g g (({ρ ρ}_{a a} - - ρ ρ)) (({z z}_{22} - - {z z}_{11})) = = {p p}_{22} + + \frac{ρ ρ {v v}_{22}^{22}}{22} + + {p p}_{l l 11 - - 22}$

式中P₁、P₂——两断面的相对压力，称为静压。它不是静止流体的压力，而是与速度造成的动压相类比的一种习惯性称谓。In the formula, P ₁ and P ₂ ——the relative pressure of the two sections, called the static pressure. It is not the pressure of a static fluid, but a customary name analogous to the dynamic pressure caused by velocity.

g(ρ_a-ρ)(z₂-z₁)——高度差与高程差的乘积，称为位压。位压可正可负。ρ_a为空气密度，ρ为管路中气体密度。g(ρ _a -ρ)(z ₂ -z ₁ )—the product of height difference and elevation difference, called potential pressure. Potential pressure can be positive or negative. ρ _a is the air density, and ρ is the gas density in the pipeline.

——动压。

--Dynamic Pressure.

p_l1-2——两断面间的压力损失。p _l1-2 ——pressure loss between two sections.

当管中气体与空气间密度差甚小，或者高度差甚小时，位压项可忽略；本系统的采样管网基本位于同一水平面内，且管中气体与空气密度相差不大，可不考虑流体的位压。方程可以简化为：When the density difference between the gas and air in the pipe is very small, or the height difference is very small, the potential pressure item can be ignored; the sampling pipe network of this system is basically located in the same horizontal plane, and the density difference between the gas and air in the pipe is not large, so the fluid can be ignored bit pressure. The equation can be simplified to:

${p p}_{11} + + \frac{ρ ρ {v v}_{11}^{22}}{22} = = {p p}_{22} + + \frac{ρ ρ {v v}_{22}^{22}}{22} + + {p p}_{l l 11 - - 22} - - - - - - ((11))$

在上述的伯努利方程应用条件中要求流量沿程不变，即在所选取的有效断面之间无流体的流入或流出，但在采样管网的应用中，需要通过采样孔汇流，在这种情况下，只能按总能量守恒和转换规律列出总流的伯努利方程。In the application conditions of the above-mentioned Bernoulli equation, the flow rate is required to be constant along the course, that is, there is no inflow or outflow of fluid between the selected effective sections, but in the application of the sampling pipe network, it is necessary to flow through the sampling holes. In this case, the Bernoulli equation of the total flow can only be listed according to the total energy conservation and conversion laws.

通过以上分析，本发明方法可以通过带有汇流的伯努利方程建立采样管网的气体传输的数学模型。Through the above analysis, the method of the present invention can establish a mathematical model of the gas transmission of the sampling pipe network through the Bernoulli equation with confluence.

1.1标准采样管路气体传输的数学模型1.1 Mathematical model of standard sampling pipeline gas transmission

采样管网的计算简图如图2所示，采样管是一个等截面的吸气管，其直径为dd，截面积为AA。末端开一个点0，点径为d(0)，面积A(0)；侧壁开(n-1)个点，点的直径分别为d(i)，相应的点的面积为A(i)。由吸气装置(吸气风扇或吸气泵)在采样管与吸气装置相接(断面n)处产生一个真空度P_jn。The calculation diagram of the sampling pipe network is shown in Figure 2. The sampling pipe is a suction pipe with equal cross-section, its diameter is dd, and its cross-sectional area is AA. A point 0 is opened at the end, the point diameter is d(0), and the area is A(0); (n-1) points are opened on the side wall, and the diameters of the points are d(i), and the area of the corresponding point is A(i ). A vacuum degree P _jn is generated at the joint (section n) between the sampling pipe and the suction device by the suction device (suction fan or suction pump).

根据方程(1)，以大气液面o’-o’为基准，对于采样孔所在的管截面(1、2、……n-1)，可以列出方程组，如式(2)：According to equation (1), with the atmospheric liquid level o'-o' as the reference, for the pipe section (1, 2, ... n-1) where the sampling hole is located, a group of equations can be listed, such as formula (2):

$\begin{matrix} {P P}_{j j} ((00)) + + {P P}_{y the y} ((00)) + + {P P}_{d d} ((00)) = = {P P}_{j j} ((11)) \\ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \\ {P P}_{j j} ((00)) + + {Σ Σ}_{j j = = 00}^{i i - - 11} {P P}_{y the y} ((j j)) + + {P P}_{d d} ((i i - - 11)) = = {P P}_{j j} ((i i)) \\ {P P}_{j j} ((00)) + + {Σ Σ}_{j j = = 00}^{n no - - 22} {P P}_{y the y} ((j j)) + + {P P}_{d d} ((n no - - 22)) = = {P P}_{j j} ((n no - - 11)) \end{matrix}\} - - - - - - ((22))$

式中p_j——空气通过采样孔的局部压力损失，Pa；In the formula, p _j ——the partial pressure loss of air passing through the sampling hole, Pa;

P_d——某段采样管上的动压，Pa；P _d ——dynamic pressure on a section of sampling pipe, Pa;

P_y——沿管段上的压力损失，Pa。P _y ——pressure loss along the pipe section, Pa.

并且，and,

${P P}_{d d} ((i i)) = = \frac{{v v}^{22} ((i i)) \cdot &Center Dot; ρ ρ}{22} = = \frac{ρ ρ}{22} \cdot \cdot {((\frac{{Q Q}_{s the s} ((i i))}{AA AAA}))}^{22} = = \frac{ρ ρ}{22} \cdot \cdot {((\frac{{Σ Σ}_{j j = = 00}^{i i} Q Q ((j j))}{AA AAA}))}^{22} - - - - - - ((33))$

式中ν——采样管段i上的空气流速，m/s；In the formula, ν—the air velocity on the sampling pipe section i, m/s;

ρ——空气的密度，Kg/m³；ρ——air density, Kg/m ³ ;

Qs(i)——采样管段i处的空气流量，m³/s；Qs(i)——air flow rate at sampling pipe section i, m ³ /s;

Q(i)——采样点i的吸气量，m³/s。Q(i)——inhalation volume of sampling point i, m ³ /s.

${P P}_{j j} ((i i)) = = μ μ \cdot \cdot \frac{{v v}_{r r}^{22} ((i i)) \cdot \cdot ρ ρ}{22} = = μ μ \cdot \cdot \frac{ρ ρ}{22} \cdot \cdot {((\frac{Q Q ((i i))}{A A ((i i))}))}^{22} - - - - - - ((44))$

式中μ——采样孔入口的局部阻力系数，In the formula, μ—the local resistance coefficient at the entrance of the sampling hole,

V_r(i)——采样孔入口的空气流速，m/s。V _r (i)——air velocity at the inlet of the sampling hole, m/s.

${P P}_{y the y} ((i i)) = = ((\frac{λ λ \cdot \cdot L L ((i i))}{dd dd} + + ξ ξ)) \cdot &Center Dot; \frac{{v v}^{22} ((i i)) \cdot &Center Dot; ρ ρ}{22} = = ((\frac{λ λ \cdot \cdot L L ((i i))}{dd dd} + + ξ ξ)) \cdot \cdot \frac{ρ ρ}{22} \cdot \cdot {((\frac{{Σ Σ}_{j j = = 00}^{i i} Q Q ((j j))}{AA AAA}))}^{22} - - - - - - ((55))$

式中λ——管道的摩阻系数；In the formula, λ—the friction coefficient of the pipeline;

ξ——管道的局部阻力系数；ξ——local resistance coefficient of pipeline;

L(i)——截面i到截面(i+1)的长度，m。L(i)—the length from section i to section (i+1), in m.

于是，可以得到关于Q(0)、Q(1)、……Q(n-1)的n-1个标准采样孔方程，如下：Then, n-1 standard sampling hole equations about Q(0), Q(1), ... Q(n-1) can be obtained, as follows:

$μ μ \cdot &Center Dot; \frac{ρ ρ \cdot &Center Dot; {v v}^{22} ((00))}{22} + + {Σ Σ}_{j j = = 00}^{i i - - 11} ((\frac{λ λ \cdot &Center Dot; L L ((j j))}{dd dd} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Σ Σ}_{j j = = 00}^{i i - - 11} Q Q ((j j))}{AA AAA}))}^{22} + + {\frac{ρ ρ}{22} \cdot &Center Dot; ((\frac{{Σ Σ}_{j j = = 00}^{i i - - 11} Q Q ((j j))}{AA AAA}))}^{22} = = μ μ \cdot &Center Dot; \frac{ρ ρ \cdot &Center Dot; {v v}^{22} ((i i))}{22} - - - - - - ((66))$

1.2毛细管采样管路气体传输的数学模型1.2 Mathematical model of gas transmission in capillary sampling pipeline

毛细管采样计算简图如图3，毛细管采样是在与标准采样相同的采样管的侧壁上接直径为d1的毛细管，毛细管截面积为A1。毛细管的长度为L1(i)，毛细管的末端接直径为d(i)的堵头。The schematic diagram of capillary sampling calculation is shown in Figure 3. Capillary sampling is to connect a capillary with a diameter of d1 on the side wall of the same sampling tube as the standard sampling, and the cross-sectional area of the capillary is A1. The length of the capillary is L1(i), and the end of the capillary is connected with a plug of diameter d(i).

同样，根据流体力学能量守恒的原理，以大气液面o’-o’为基准，对于毛细管采样孔所在的管截面i，可以列出方程，如下式7：Similarly, according to the principle of energy conservation in hydrodynamics, with the atmospheric liquid surface o'-o' as the benchmark, for the tube section i where the capillary sampling hole is located, the equation can be listed, as shown in Equation 7:

${P P}_{j j} ((00)) + + {Σ Σ}_{j j = = 00}^{11} {P P}_{y the y} ((j j)) + + {P P}_{d d} ((i i)) = = {P P}_{j j}^{,,} ((i i)) + + {P P}_{y the y}^{,,} ((i i)) + + {P P}_{d d}^{,,} ((i i)) - - - - - - ((77))$

式中P_j’(i)——毛细管入口处的局部压力损失，Pa。In the formula, P _j '(i)——local pressure loss at the capillary inlet, Pa.

P_y’(i)——毛细管管道的压力损失，Pa。P _y '(i)——the pressure loss of the capillary tube, Pa.

P_d’(i)——由毛细管计算的动压，Pa。P _d '(i) - the dynamic pressure calculated from the capillary, Pa.

并且，and,

${P P}_{j j}^{' '} ((i i)) = = μ μ \cdot &Center Dot; \frac{{v v}^{' '' ' 22} ((i i)) \cdot &Center Dot; ρ ρ}{22} = = μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{Q Q ((i i))}{A A ((i i))}))}^{22} - - - - - - ((88))$

式中ν”——毛细管i入口的空气流速，m/s。In the formula, ν"—the air velocity at the inlet of capillary i, m/s.

${P P}_{y the y}^{' '} ((i i)) = = ((\frac{λ λ \cdot &Center Dot; L L 11 ((i i))}{d d 11} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ \cdot &Center Dot; {v v}^{' ' 22} ((i i))}{22} = = ((\frac{λ λ \cdot &Center Dot; L L 11 ((i i))}{d d 11} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{Q Q ((i i))}{A A 11}))}^{22} - - - - - - ((99))$

式中ν——毛细管i内的空气流速，m/s。In the formula, ν—the air velocity in the capillary i, m/s.

${P P}_{d d}^{' '} ((i i)) = = \frac{ρ ρ \cdot &Center Dot; {v v}^{' ' 22} ((i i))}{22} = = \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{Q Q ((i i))}{A A 11}))}^{22} - - - - - - ((1010))$

其余物理量如上所述。The remaining physical quantities are as above.

同样可以得到关于Q(0)、Q(1)、……Q(n-1)的毛细管方程，如下：The capillary equations about Q(0), Q(1), ... Q(n-1) can also be obtained as follows:

$μ μ \cdot \cdot \frac{ρ ρ \cdot &Center Dot; {v v}^{22} ((00))}{22} + + {Σ Σ}_{j j = = 00}^{i i - - 11} ((\frac{λ λ \cdot \cdot L L ((j j))}{dd dd} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Σ Σ}_{j j = = 00}^{i i - - 11} Q Q ((j j))}{AA AAA}))}^{22} + + \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Σ Σ}_{j j = = 00}^{i i - - 11} Q Q ((j j))}{AA AAA}))}^{22}$

$= = μ μ \cdot &Center Dot; \frac{ρ ρ \cdot &Center Dot; {v v}^{' '' ' 22} ((i i))}{22} + + ((\frac{λ λ \cdot &Center Dot; L L 11 ((i i))}{d d 11} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ \cdot &Center Dot; {v v}^{' ' 22} ((i i))}{22} + + \frac{{v v}^{' ' 22} ((i i)) \cdot &Center Dot; ρ ρ}{22} - - - - - - ((1111))$

1.3管道中压力损失的数学模型1.3 Mathematical model of pressure loss in pipeline

气体在管道中流动时，要受到与流动相反方向的流体阻力，消耗能量，成为压力损失。压力损失分为延程压力损失和局部压力损失两种。When the gas flows in the pipeline, it is subject to fluid resistance in the opposite direction of the flow, which consumes energy and becomes pressure loss. Pressure loss is divided into two types: extended pressure loss and local pressure loss.

1.3.1延程压力损失1.3.1 Elongation pressure loss

空气在整个流程上，由于克服粘性力而引起的压力损失，称为延程压力损失，如式(12)：The air pressure loss caused by overcoming the viscous force in the whole process is called the delay pressure loss, as shown in formula (12):

${P P}_{m m} = = λ λ \cdot &Center Dot; \frac{L L}{d d} \cdot &Center Dot; \frac{ρ ρ \cdot &Center Dot; {V V}^{22}}{22} - - - - - - ((1212))$

式中λ——摩阻系数，也称延程阻力系数；In the formula, λ——friction resistance coefficient, also known as extension resistance coefficient;

L——管道的延程长度；L - the extension length of the pipeline;

d——管道内径；d - the inner diameter of the pipe;

V——管道内气体的平均流速；V - the average flow velocity of the gas in the pipeline;

ρ——空气的密度，Kg/m³；ρ——air density, Kg/m ³ ;

1.3.2局部阻力1.3.2 Local resistance

当气体流过局部的管件(如弯头等)，而使气体流速的大小或方向或者两者均发生变化，致使局部的气体发生动量的交换和涡旋，而消耗能量，从而产生局部的压力降。一般局部压力损失的计算可以按照式(13)：When the gas flows through a local pipe fitting (such as an elbow, etc.), the magnitude or direction of the gas flow velocity or both changes, causing the local gas to undergo momentum exchange and vortex, which consumes energy and generates a local pressure drop. . The calculation of general local pressure loss can be according to formula (13):

${P P}_{z z} = = ξ ξ \cdot &Center Dot; \frac{ρ ρ \cdot &Center Dot; {v v}^{22}}{22} - - - - - - ((1313))$

式中ξ——局部阻力系数。Where ξ——local resistance coefficient.

局部阻力系数ξ与管道的形状、雷诺数Re有关，大多由经验公式得到。对于本工况存在以下几种局部阻力系数。The local resistance coefficient ξ is related to the shape of the pipeline and the Reynolds number Re, and is mostly obtained by empirical formulas. For this working condition, there are the following local drag coefficients.

1)弯管1) Elbow

弯管的局部阻力系数与弯管的曲率半径和管径的比值有关，可以根据《液压流体力学》的表5-4“弯头k的值”，弯管的局部阻力系数 $ξ_{1} = k \frac{θ^{*}}{90},$ 因为本发明中涉及的弯管都采用90度，所以ξ₁与k同值，查得弯管局部阻力系数ξ₁。The local resistance coefficient of the elbow is related to the ratio of the radius of curvature of the elbow to the diameter of the pipe. According to Table 5-4 "The Value of Elbow K" in "Hydraulic Fluid Mechanics", the local resistance coefficient of the elbow $ξ_{1} = k \frac{θ^{*}}{90},$ Since all the elbows involved in the present invention adopt 90 degrees, ξ ₁ has the same value as k, and the local resistance coefficient ξ ₁ of the elbow is found.

2)断面突然扩大2) The section suddenly expands

如图4所示，断面突然扩大的局部阻力系数与两个断面的面积之比有关，根据《供暖通风设计手册》中表“圆形风道锥形扩散管的局部阻力系数”可查得断面突然扩大的局部阻力系数ξ₂。As shown in Figure 4, the local resistance coefficient of the sudden expansion of the section is related to the ratio of the areas of the two sections. According to the "Heating and Ventilation Design Manual" in the table "Local resistance coefficient of circular air duct tapered diffuser pipe", the section can be found Sudden expansion of the local drag coefficient ξ ₂ .

3)T形合流三通3) T-shaped confluence tee

如图5所示，T形合流三通的局部阻力系数与主管道和支管道的长度比有关，本工程取主管道和支管道的直径相等，根据实际长度比值查《供暖通风设计手册》的表“圆风道T形合流三通”，则T形合流三通的局部阻力系数ξ₃如表一所示。As shown in Figure 5, the local resistance coefficient of the T-shaped confluent tee is related to the length ratio of the main pipe and the branch pipe. In this project, the diameters of the main pipe and the branch pipe are equal, and the "Heating and Ventilation Design Manual" is checked according to the actual length ratio. Table "Circular air duct T-shaped confluent tee", then the local resistance coefficient ξ ₃ of the T-shaped confluent tee is shown in Table 1.

表一T形合流三通的局部阻力系数ξ₃ Table 1 Local resistance coefficient ξ ₃ of T-shaped confluent tee

L3/L1L3/L1 00 0.10.1 0.20.2 0.30.3 0.40.4 0.50.5 0.60.6 0.70.7 0.80.8 0.90.9 1.01.0 支管道ξ3′branch pipeline ξ3′ -0.9-0.9 -0.52-0.52 -0.24-0.24 -0.08-0.08 0.320.32 0.420.42 0.570.57 0.720.72 0.860.86 0.990.99 1.11.1 主管道ξ3″Main pipeline ξ3″ 00 0.160.16 0.270.27 0.380.38 0.460.46 0.530.53 0.570.57 0.590.59 0.60.6 0.590.59 0.550.55

4)管道进口4) Pipeline import

如图6所示，本发明中涉及的主要的管道进口形式有3种，分别是末端帽进口、侧壁采样孔进口、毛细管末端进口。末端帽进口、侧壁采样孔进口、毛细管末端进口的局部阻力系数ξ₄′、ξ₄″、ξ₄″′，本发明所涉及的实际工程中，应符合锐缘进口的阻力系数，取值0.5。As shown in Fig. 6, there are three main pipeline inlet forms involved in the present invention, namely, the inlet of the end cap, the inlet of the sampling hole on the side wall, and the inlet of the capillary end. The local resistance coefficients ξ ₄ ′, ξ ₄ ″, ξ ₄ ″’ of the end cap inlet, the side wall sampling hole inlet, and the capillary end inlet, in the actual engineering involved in the present invention, should conform to the resistance coefficient of the sharp edge inlet, and take the value 0.5.

1.4探测器吸气能力(静压)数学模型1.4 Mathematical model of detector suction capacity (static pressure)

吸气式探测器与管网相接，通过风扇抽气产生静压，探测器一旦设计完成，它的吸气能力已经确定，在管网末端与探测器相连处所产生的静压与风速可用曲线表示。所选用的探测器的性能曲线如图7所示。The air-breathing detector is connected to the pipe network, and the static pressure is generated by fan suction. Once the design of the detector is completed, its suction capacity has been determined, and the static pressure and wind speed generated at the end of the pipe network connected to the detector can be used. express. The performance curves of the selected detectors are shown in Figure 7.

对本性能曲线进行一阶拟合。得到Perform a first-order fit to this performance curve. get

$P P = = a a \cdot &Center Dot; {V V}_{s the s} + + b b = = a a \cdot &Center Dot; \frac{{Q Q}_{s the s}}{AA AAA} + + b b . . - - - - - - ((1414))$

式中P为静压，V_s为管网与探测器连接处风速，Q_s为管网总流量，AA为主管截面积，式中a、b代表拟合参数，可用Matlab对曲线拟和，得到a＝-9.9968，b＝82.5425。In the formula, P is the static pressure, V _s is the wind speed at the connection between the pipe network and the detector, Q _s is the total flow of the pipe network, and AA is the cross-sectional area of the main pipe. In the formula, a and b represent fitting parameters, and Matlab can be used to fit the curve. This gives a=-9.9968, b=82.5425.

每一种管网的分布对应一条特定的性能曲线，他与探测器实际性能曲线的交点，就是对应此种管网的探测器工作点，联立管网的性能曲线公式(15)和探测器的性能曲线公式(14)，The distribution of each type of pipe network corresponds to a specific performance curve. The intersection point between it and the actual performance curve of the detector is the detector operating point corresponding to this pipe network. The performance curve formula (15) of the pipe network and the detector The performance curve formula (14),

P＝S·Q_s ² (15)P=S·Q _s ² (15)

式中P为采样管中的静压；In the formula, P is the static pressure in the sampling pipe;

可以得到：can get:

$S S \cdot \cdot {Q Q}_{s the s}^{22} - - a a \cdot \cdot \frac{{Q Q}_{s the s}}{AA AAA} - - b b = = 00 - - - - - - ((1616))$

这是关于Q_s的二阶非线性方程式。对它可使用弦截法求解Q_s。This is a second order non-linear equation for _Qs . It can use the chord intercept method to solve Q _s .

应用上述原理，对吸气式感烟火灾探测系统采样管网设计合理性的具体验证过程如下：Applying the above principles, the specific verification process for the rationality of the sampling pipe network design of the aspirating smoke detection system is as follows:

1、确定阻力系数。1. Determine the drag coefficient.

拟合管道入口的摩阻系数λ，一般而言，摩阻系数λ是雷诺数Re和相对粗糙度的函数，在实际的工况下，由于吸入的空气含有部分的固体颗粒，并且由于清扫周期的原因，管道简化成粗糙管，λ取0.025～0.05之间。Fit the friction coefficient λ at the inlet of the pipeline. Generally speaking, the friction coefficient λ is the Reynolds number Re and the relative roughness In actual working conditions, because the inhaled air contains some solid particles, and because of the cleaning cycle, the pipeline is simplified into a rough tube, and λ is between 0.025 and 0.05.

如果某段采样管有弯折，此段的局部阻力系数ξ₁为0.131，如果采样管是直管，局部阻力系数ξ₁是0。If a section of the sampling pipe is bent, the local resistance coefficient _ξ1 of this section is 0.131, and if the sampling pipe is straight, the local resistance coefficient _ξ1 is 0.

根据1.3.1的4)拟合管道入口局部阻力系数ξ₄′，确定空气的密度ρ＝1.204Kg/m3、毛细管上由于管径突变产生的局部阻力系数ξ₂＝0.87、采样管直径dd＝21mm，计算采样管截面积AA＝3.14dd²/4和每个采样点的面积A(i)＝3.14d(i)²/4。According to 4) of 1.3.1, fit the local resistance coefficient ξ ₄ ′ at the inlet of the pipeline, determine the density of air ρ = 1.204Kg/m3, the local resistance coefficient ξ ₂ = 0.87 on the capillary due to the mutation of the pipe diameter, and the diameter of the sampling pipe dd = 21mm, calculate the cross-sectional area of the sampling pipe AA=3.14dd ² /4 and the area of each sampling point A(i)=3.14d(i) ² /4.

2、计算每个采样点的吸气量占吸气总量的百分比QQ(i)及管网阻抗S。2. Calculate the percentage QQ(i) of the inspiratory volume of each sampling point in the total inspiratory volume and the pipe network impedance S.

假设末端帽的吸气量为1，这时第0段采样管的流量即是末端帽的吸气量1。以末端帽的吸气量是1为基础，对于普通采样孔，根据公式(6)，对于毛细管，毛细管采样是在与标准采样相同的采样管的侧壁上接直径d1为8.5mm的毛细管，毛细管截面积为A1。毛细管的长度一般L1(i)为1～6m，毛细管的末端接直径d(i)为3～8mm的堵头，根据公式11，依次循环计算其他采样孔的吸气量。这样可得到以末端帽吸气量是1为基础的，各个采样孔的吸气量为Q(0)，Q(1)，……，Q(n-1)，总吸气量Q_s＝Q(0)+Q(1)+…+Q(n-1)，则每个采样点的吸气量占吸气总量的百分比QQ(i)＝Q(i)/Q_s。Assuming that the suction volume of the end cap is 1, then the flow rate of the sampling tube in the 0th section is the suction volume of the end cap 1. Based on the suction volume of the end cap being 1, for ordinary sampling holes, according to formula (6), for capillary tubes, capillary tube sampling is to connect a capillary tube with a diameter d1 of 8.5mm on the side wall of the same sampling tube as standard sampling, The cross-sectional area of the capillary is A1. Generally, the length L1(i) of the capillary is 1-6m, and the end of the capillary is connected to a plug with a diameter d(i) of 3-8mm. According to formula 11, the suction volume of other sampling holes is calculated in turn. In this way, it can be obtained that the suction volume of the end cap is 1, the suction volume of each sampling hole is Q(0), Q(1), ..., Q(n-1), and the total suction volume Q _s = Q(0)+Q(1)+...+Q(n-1), then the percentage of inspiratory volume at each sampling point to the total inspiratory volume QQ(i)=Q(i)/Q _s .

探测器性能曲线是确定的，当管网数据确定时，这时的计算量也应该是探测器性能曲线上的一个点。根据假设管网末端帽的吸气量为1时候计算出来的Q_s和P，根据公式(15)可以计算出阻抗S。The performance curve of the detector is determined. When the pipe network data is determined, the calculation amount at this time should also be a point on the performance curve of the detector. According to the Q _s and P calculated when the suction capacity of the end cap of the pipe network is assumed to be 1, the impedance S can be calculated according to formula (15).

3、计算总吸气量Qs和每个采样点的吸气时间，验证每个采样点吸气量是否均等，采样时间是否符合要求。3. Calculate the total inspiratory volume Qs and the inspiratory time of each sampling point, and verify whether the inspiratory volume of each sampling point is equal and whether the sampling time meets the requirements.

根据公式(16)及上面已计算出的阻抗S，a，b值通过Matlab拟和得到，应用弦截法求解Qs。According to the formula (16) and the above calculated impedance S, a, b values are obtained by Matlab fitting, and the chord intercept method is used to solve Qs.

弦截法的基础是插值原理，也是使非线性方程线性化的一种方法。The chord intercept method is based on the principle of interpolation and is a method for linearizing nonlinear equations.

迭代函数的计算公式如下：The calculation formula of the iteration function is as follows:

${Q Q}_{s the s}^{((k k + + 11))} ((i i)) = = {Q Q}_{s the s}^{((k k))} ((i i)) - - \frac{{f f}_{i i} (({Q Q}_{s the s}^{((k k))} ((i i))))}{{f f}_{i i} (({Q Q}_{s the s}^{((k k))} ((i i)))) - - {f f}_{i i} (({Q Q}_{s the s}^{((k k - - 11))} ((i i))))} (({Q Q}_{s the s}^{((k k))} ((i i)) - - {Q Q}_{s the s}^{((k k - - 11))} ((i i)))) - - - - - - ((1717))$

计算时，首先任意两组初值Q_s ⁰和Q_s ¹(迭代法可任意选取)代入到式(17)，从而得到迭代公式。控制迭代误差＜10^(-13)。最终可以得到探测器的吸气量Qs，即采样管网的总吸气量。根据先前求得的吸气百分比，求得从末端帽起每点的吸气量为Q(i)＝Qs×QQ(i)。When calculating, firstly, any two groups of initial values Q _s ⁰ and Q _s ¹ (which can be selected arbitrarily in the iterative method) are substituted into formula (17), thus obtaining the iterative formula. Control iteration error <10 ^(-13) . Finally, the suction volume Qs of the detector can be obtained, that is, the total suction volume of the sampling pipe network. According to the inspiratory percentage obtained previously, the inspiratory volume at each point from the end cap is obtained as Q(i)=Qs×QQ(i).

然后可计算每个采样点的吸气时间，即每个采样点到探测器的气体传输时间，首先可算出每段采样管的气体传输时间t，t＝L(i)/v＝L(i)/(Q_g(i)/AA)，其中每段管内的气体流量Q_g(i)为从它前面进入采样管的所有采样点的流量之和，可依次计算每段采样管的气体传输时间，把每段时间依次迭加，最后可计算出末端帽的气体传输时间。Then the inspiratory time of each sampling point can be calculated, that is, the gas transmission time from each sampling point to the detector. First, the gas transmission time t of each section of the sampling tube can be calculated, t=L(i)/v=L(i )/(Q _g (i)/AA), where the gas flow Q _g (i) in each section of the pipe is the sum of the flows of all sampling points entering the sampling pipe from its front, and the gas transmission of each section of the sampling pipe can be calculated in turn Time, each period of time is superimposed in turn, and finally the gas transmission time of the end cap can be calculated.

然后可通过各采样点的吸气百分比和末端帽的气体传输时间对设计结果进行验证，判断各采样孔的吸气量是否平衡，可以用采样点的吸气百分比最大值减去最小值，如果值大于5％，可认为吸气不平衡，应按最佳气流平衡进行优化，通过判断末端帽的气体传输时间是否在所要求的时间之内(如80秒，60秒等，由具体工程设定)，来确定是否需要按传送时间进行优化。Then the design results can be verified by the inspiratory percentage of each sampling point and the gas transmission time of the end cap to judge whether the inspiratory volume of each sampling hole is balanced. The maximum value of the inspiratory percentage of the sampling point can be subtracted from the minimum value, if If the value is greater than 5%, it can be considered that the inhalation is unbalanced, and it should be optimized according to the best airflow balance. By judging whether the gas transmission time of the end cap is within the required time (such as 80 seconds, 60 seconds, etc., it is determined by the specific engineering design) set), to determine whether optimization by delivery time is required.

步骤三、对设计进行优化；Step 3, optimize the design;

(-)按最佳气流平衡优化：(-) Optimized for best airflow balance:

1、对设计进行优化是建立在计算主程序计算出采样管网总吸气量的基础上的。采样管网总吸气量已知，要使每个采样孔的吸气量平衡，可以平均分配采样孔的吸气量Q_p＝Qs/n。1. Optimizing the design is based on the calculation of the main program to calculate the total suction volume of the sampling pipe network. The total inhalation volume of the sampling pipe network is known. To balance the inhalation volume of each sampling hole, the inhalation volume of the sampling holes can be evenly distributed Q _p =Qs/n.

2、使每个采样孔的吸气量尽可能的接近Q_p，而重新安排采样孔的孔径。返回优化后的采样孔的孔径d(i)。2. Make the suction volume of each sampling hole as close to Q _p as possible, and rearrange the aperture of the sampling hole. Returns the optimized sampling hole diameter d(i).

具体实现方法如下：The specific implementation method is as follows:

由于设定每个采样点的吸气量相等，都是Q_p，所以可以得到每个采样孔的吸气量Q(0)＝Q(1)＝……＝Q(n-1)＝Q_p，每段采样管的流量分别Q_s(0)＝Qp，Q_s(i)＝(i+1)×Q_p，Q_s(n-1)＝n×Q_p。Since the inhalation volume of each sampling point is set to be equal, which is Q _p , it can be obtained that the inhalation volume of each sampling hole is Q(0)=Q(1)=...=Q(n-1)=Q _p , the flow rate of each sampling pipe is Q _s (0)=Qp, Q _s (i)=(i+1)×Q _p , Q _s (n-1)=n×Q _p .

由离探测器最近的采样孔开始，计算孔径d(n-1)，如果是普通采样孔A(n-1)的计算公式为：Starting from the sampling hole closest to the detector, calculate the aperture d(n-1). If it is an ordinary sampling hole A(n-1), the calculation formula is:

$μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((n no - - 11))}^{22}} + + ((\frac{λ λ \cdot &Center Dot; L L ((n no - - 11))}{dd dd} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((n no \cdot &Center Dot; {Q Q}_{p p}))}^{22}}{{AA AAA}^{22}} + + \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((n no \cdot &Center Dot; {Q Q}_{p p}))}^{22}}{{AA AAA}^{22}} = = P P - - - - - - ((1818))$

可以解出 $d (n - 1) = \sqrt{\frac{4 \cdot A (n - 1)}{π}},$ 式中P为采样孔处的静压；can be solved $d (no - 1) = \sqrt{\frac{4 \cdot A (no - 1)}{π}},$ Where P is the static pressure at the sampling hole;

如果是毛细管则A(n-1)的计算公式为：If it is a capillary, the calculation formula of A(n-1) is:

$μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((n no - - 11))}^{22}} + + ((\frac{λ λ \cdot &Center Dot; L L 11 ((n no - - 11))}{d d 11} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot \cdot {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + \frac{ρ ρ}{22} \cdot \cdot {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + ((\frac{λ λ \cdot \cdot L L ((n no - - 11))}{dd dd} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((n no \cdot &Center Dot; {Q Q}_{p p}))}^{22}}{{AA AAA}^{22}} + + \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((n no \cdot &Center Dot; {Q Q}_{p p}))}^{22}}{{AA AAA}^{22}}$

$= = P P - - - - - - ((1919))$

可以解出 $d (n - 1) = \sqrt{\frac{4 \cdot A (n - 1)}{π}},$ 式中P为毛细管处的静压；can be solved $d (no - 1) = \sqrt{\frac{4 &Center Dot; A (no - 1)}{π}},$ where P is the static pressure at the capillary;

然后对d(n-1)进行整合。普通采样孔的范围从2.5mm到6mm，每隔0.5mm为一个间隔；毛细管的直径范围从3mm到8mm，每隔0.5mm为一个间隔。Then d(n-1) is integrated. Ordinary sampling holes range from 2.5mm to 6mm, with an interval of 0.5mm; capillary diameters range from 3mm to 8mm, with an interval of 0.5mm.

计算其他采样点的点径，首先计算出A(i)，若第i个是普通采样孔则计算公式如20：To calculate the point diameter of other sampling points, first calculate A(i), if the i-th is a common sampling hole, the calculation formula is as follows:

$μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((i i))}^{22}} + + \frac{λ λ \cdot \cdot L L ((i i))}{dd dd} \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((((i i + + 11)) \cdot \cdot {Q Q}_{p p}))}^{22}}{{AA AAA}^{22}} + + \frac{ρ ρ}{22} \cdot \cdot \frac{{((((i i + + 11)) \cdot &Center Dot; {Q Q}_{p p}))}^{22}}{{AA AAA}^{22}} = = {P P}_{j j} ((i i + + 11)) - - - - - - ((2020))$

若第i个是毛细管则计算公式如21：If the i-th is a capillary, the calculation formula is as 21:

$μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((i i))}^{22}} + + ((\frac{λ λ \cdot &Center Dot; L L 11 ((i i))}{d d 11} + + ξ ξ)) \cdot \cdot \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + ((\frac{λ λ \cdot \cdot L L ((i i))}{dd dd} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot \cdot \frac{{((((i i + + 11)) \cdot &Center Dot; {Q Q}_{p p}))}^{22}}{{AA AAA}^{22}} + + \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((((i i + + 11)) \cdot \cdot {Q Q}_{p p}))}^{22}}{{AA AAA}^{22}}$

$= = {P P}_{j j} ((i i + + 11)) - - - - - - ((21 twenty one))$

式中的已知的P_j(i+1)根据第i+1个采样点的具体情况而确定，如果第i+1个采样点是普通采样孔，则：The known P _j (i+1) in the formula is determined according to the specific conditions of the i+1th sampling point, if the i+1th sampling point is a common sampling hole, then:

${P P}_{j j} ((i i + + 11)) = = μ μ \cdot \cdot \frac{ρ ρ}{22} \cdot \cdot \frac{{Q Q}_{p p}^{22}}{A A {((i i + + 11))}^{22}} - - - - - - ((22 twenty two))$

如果第i+1个采样点是毛细管，则：If the i+1th sampling point is a capillary, then:

${P P}_{j j} ((i i + + 11)) = = μ μ \cdot \cdot \frac{ρ ρ}{22} \cdot \cdot \frac{{Q Q}_{p p}^{22}}{A A {((i i + + 11))}^{22}} + + ((\frac{λ λ \cdot \cdot L L 11 ((i i + + 11))}{d d 11} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} - - - - - - ((23 twenty three))$

于是可以解出 $d (i) = \sqrt{\frac{4 \cdot A (i)}{π}} .$ 然后对d(i)进行整合。普通采样孔的范围从2.5mm到6mm，每隔0.5mm为一个间隔；毛细管的直径范围从3mm到8mm，每隔0.5mm为一个间隔。So it can be solved $d (i) = \sqrt{\frac{4 &Center Dot; A (i)}{π}} .$ Then d(i) is integrated. Ordinary sampling hole ranges from 2.5mm to 6mm, every 0.5mm is an interval; capillary diameter ranges from 3mm to 8mm, every 0.5mm is an interval.

计算末端帽的点径，首先计算出A(0)，若第1个是普通采样孔则计算公式如24：To calculate the point diameter of the end cap, first calculate A(0), if the first one is a common sampling hole, the calculation formula is as 24:

$μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((00))}^{22}} + + \frac{λ λ \cdot &Center Dot; L L ((00))}{dd dd} \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{{AA AAA}^{22}} + + \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{{AA AAA}^{22}} = = μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot \cdot \frac{{Q Q}_{p p}^{22}}{A A {((11))}^{22}} - - - - - - ((24 twenty four))$

若第1个是毛细管则计算公式如25：If the first one is a capillary, the calculation formula is as 25:

$μ μ \cdot \cdot \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((00))}^{22}} + + \frac{λ λ \cdot &Center Dot; L L ((00))}{dd dd} \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{{AA AAA}^{22}} + + \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{{AA AAA}^{22}} = = μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((11))}^{22}} + + ((\frac{λ λ \cdot &Center Dot; L L 11 ((11))}{d d 11} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} - - - - - - ((2525))$

于是可以解出 $d (0) \sqrt{\frac{4 \cdot A (0)}{π}} \cdot$ 然后对d(0)进行整合，范围从2.5mm到6mm，每隔0.5mm为一个间隔。So it can be solved $d (0) \sqrt{\frac{4 &Center Dot; A (0)}{π}} &Center Dot;$ Then integrate d(0), ranging from 2.5mm to 6mm, every 0.5mm is an interval.

3、根据新的d(i)再次计算包括末端帽在内的所有采样点的吸气量，吸气百分比及吸气时间，并通过各采样点的吸气百分比和末端帽的气体传输时间对优化结果进行验证。3. According to the new d(i), calculate the inspiratory volume, inspiratory percentage and inspiratory time of all sampling points including the end cap again, and compare the inspiratory percentage and the gas transmission time of each sampling point with the end cap. The optimization results are verified.

(二)按传送时间优化：(2) Optimization according to transmission time:

如果计算主程序计算出的最大采样时间超过允许范围，进行时间优化。If the maximum sampling time calculated by the calculation main program exceeds the allowable range, perform time optimization.

1、从末端帽开始，要使末端帽的采样时间最短，采样孔的孔径要取最大值，最大值取6mm，这时末端帽的吸气量假设为1，为保证各个采样孔的吸气量平衡，其他的采样孔吸气量假设依然是1，对其他采样孔的直径进行计算。计算出采样孔的孔径A(i)见公式26：1. Starting from the end cap, in order to make the sampling time of the end cap the shortest, the aperture of the sampling hole should take the maximum value, and the maximum value should be 6mm. At this time, the air suction volume of the end cap is assumed to be 1. Assuming that the suction volume of other sampling holes is still 1, calculate the diameter of other sampling holes. Calculate the aperture A(i) of the sampling hole, see formula 26:

$μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{11}{{A A ((00))}^{22}} + + {Σ Σ}_{j j = = 00}^{i i - - 11} ((\frac{λ λ \cdot &Center Dot; L L ((j j))}{dd dd} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot \cdot \frac{{((j j + + 11))}^{22}}{{AA AAA}^{22}} + + \frac{ρ ρ}{22} \cdot \cdot \frac{{i i}^{22}}{{AA AAA}^{22}} = = {P P}_{j j} ((i i)) - - - - - - ((2626))$

若第i个是普通采样孔则计算公式如27：If the i-th is an ordinary sampling hole, the calculation formula is as 27:

${P P}_{j j} ((i i)) = = μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot \cdot \frac{11}{A A {((i i))}^{22}} - - - - - - ((2727))$

若第i个是毛细管则计算公式如28：If the i-th is a capillary, the calculation formula is as 28:

${P P}_{j j} ((i i)) = = μ μ \cdot \cdot \frac{ρ ρ}{22} \cdot &Center Dot; \frac{11}{{A A ((i i))}^{22}} + + ((\frac{λ λ \cdot &Center Dot; L L 11 ((i i))}{d d 11} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot \cdot {((\frac{11}{A A 11}))}^{22} + + \frac{ρ ρ}{22} \cdot \cdot {((\frac{11}{A A 11}))}^{22} - - - - - - ((2828))$

于是可以解出 $d (i) = \sqrt{\frac{4 \cdot A (i)}{π}} \cdot$ 然后对d(i)进行整合，普通采样孔的范围从2.5mm到6mm，每隔0.5mm为一个间隔；毛细管的直径范围从3mm到8mm，每隔0.5mm为一个间隔。So it can be solved $d (i) = \sqrt{\frac{4 &Center Dot; A (i)}{π}} &Center Dot;$ Then d(i) is integrated, the range of ordinary sampling holes is from 2.5mm to 6mm, every 0.5mm is an interval; the diameter of capillary is from 3mm to 8mm, every 0.5mm is an interval.

2、根据新的d(i)再次计算包括末端帽在内的所有采样点的吸气量，吸气百分比及吸气时间，并通过各采样点的吸气百分比和末端帽的气体传输时间对优化结果进行验证。2. According to the new d(i), calculate the inspiratory volume, inspiratory percentage and inspiratory time of all sampling points including the end cap again, and compare the inspiratory percentage and the gas transmission time of each sampling point with the end cap. The optimization results are verified.

步骤四、按优化后的数据进行实际工程操作；Step 4. Carry out actual engineering operation according to the optimized data;

按优化后的数据进行实际工程施工，可以使吸气式感烟火灾探测系统工作在最佳状态，对整个设计空间进行保护。The actual engineering construction according to the optimized data can make the aspirating smoke detection system work in the best state and protect the entire design space.

附图说明 Description of drawings

图1为标准采样示意图；Figure 1 is a schematic diagram of standard sampling;

图2为采样管计算示意图；Figure 2 is a schematic diagram of the calculation of the sampling tube;

图3为毛细管采样计算示意图；Figure 3 is a schematic diagram of capillary sampling calculation;

图4为断面扩大示意图；Figure 4 is a schematic diagram of the enlarged section;

图5为T形合流三通示意图；Figure 5 is a schematic diagram of a T-shaped confluence tee;

图6为管道进口示意图；Fig. 6 is a schematic diagram of pipeline inlet;

图7为探测器特性曲线示意图。Fig. 7 is a schematic diagram of the detector characteristic curve.

具体实施方式 Detailed ways

本发明的具体实施方式如下：The specific embodiment of the present invention is as follows:

输入变量为总管长50m，在距末端帽8米处有一弯折，共10个采样孔，采样孔间隔5m，末端帽直径为4mm，其余采样孔直径3mm。The input variable is that the length of the main pipe is 50m, and there is a bend 8 meters away from the end cap. There are 10 sampling holes in total, the interval between the sampling holes is 5m, the diameter of the end cap is 4mm, and the diameter of the other sampling holes is 3mm.

通过公式6，11，16，17计算结果如下：The calculation results through formulas 6, 11, 16, and 17 are as follows:

每孔吸气量(L/m)：Q(0)＝4.489Air intake per hole (L/m): Q(0)＝4.489

Q(1)＝2.53Q(1)=2.53

Q(2)＝2.55Q(2)=2.55

Q(3)＝2.586Q(3)＝2.586

Q(4)＝2.643Q(4)＝2.643

Q(5)＝2.726Q(5)＝2.726

Q(6)＝2.837Q(6)＝2.837

Q(7)＝2.979Q(7)＝2.979

Q(8)＝3.157Q(8)＝3.157

Q(9)＝3.372 Q(9)＝3.372

吸气百分比： QQ(0)＝15.03％Inspiratory percentage: QQ(0)＝15.03%

QQ(1)＝8.47％ QQ(1) = 8.47%

QQ(2)＝8.54％ QQ(2) = 8.54%

QQ(3)＝8.66％ QQ(3) = 8.66%

QQ(4)＝8.85％ QQ(4) = 8.85%

QQ(5)＝9.13％ QQ(5) = 9.13%

QQ(6)＝9.5％ QQ(6) = 9.5%

QQ(7)＝9.98％ QQ(7) = 9.98%

QQ(8)＝10.57％ QQ(8) = 10.57%

QQ(9)＝11.29％ QQ(9) = 11.29%

气体传输时间：T(0)＝87.22Gas transit time: T(0)=87.22

T(1)＝64.09T(1)＝64.09

T(2)＝49.29T(2)＝49.29

T(3)＝38.44T(3)＝38.44

T(4)＝29.89T(4)＝29.89

T(5)＝22.87T(5)＝22.87

T(6)＝16.95T(6)＝16.95

T(7)＝11.85T(7)＝11.85

T(8)＝7.4T(8)＝7.4

T(9)＝3.48T(9)＝3.48

总吸气量：Qs＝29.869L/mTotal suction volume: Qs＝29.869L/m

计算结果采样点的吸气百分比最大值与最小值的差为6.56％，超过5％，可认为气流不平衡，应按最佳气流平衡进行优化，如果规定气体传输时间不能超过70秒，还应按最短吸气时间进行优化。The difference between the maximum value and the minimum value of the inspiratory percentage of the calculation result sampling point is 6.56%. If it exceeds 5%, it can be considered that the air flow is unbalanced and should be optimized according to the best air flow balance. If the gas transmission time cannot exceed 70 seconds, it should also be Optimized for the shortest inspiratory time.

按最佳气流平衡通过公式18～25优化后：After optimizing according to the best airflow balance through formulas 18 to 25:

孔径均为3mm。The hole diameter is 3mm.

每孔吸气量(L/m)：Q(0)＝2.815Air intake per hole (L/m): Q(0)＝2.815

Q(1)＝2.818Q(1)＝2.818

Q(2)＝2.83Q(2)＝2.83

Q(3)＝2.856Q(3)＝2.856

Q(4)＝2.901Q(4)＝2.901

Q(5)＝2.971Q(5)＝2.971

Q(6)＝3.069Q(6)＝3.069

Q(7)＝3.201Q(7)＝3.201

Q(83)＝.369Q(83)＝.369

Q(9)＝3.576Q(9)＝3.576

吸气百分比： QQ(0)＝9.26％Inspiratory percentage: QQ(0)＝9.26%

QQ(1)＝9.27％ QQ(1) = 9.27%

QQ(2)＝9.31％ QQ(2) = 9.31%

QQ(3)＝9.39％ QQ(3) = 9.39%

QQ(4)＝9.54％ QQ(4) = 9.54%

QQ(5)＝9.77％ QQ(5) = 9.77%

QQ(6)＝10.09％ QQ(6) = 10.09%

QQ(7)＝10.53％ QQ(7) = 10.53%

QQ(8)＝11.08％ QQ(8) = 11.08%

QQ(9)＝11.76％ QQ(9) = 11.76%

气体传输时间： T(0)＝106.96Gas transmission time: T(0)＝106.96

T(1)＝70.07T(1)＝70.07

T(2)＝51.63T(2)＝51.63

T(3)＝39.36T(3)＝39.36

T(4)＝30.19T(4)＝30.19

T(5)＝22.88T(5)＝22.88

T(6)＝16.84T(6)＝16.84

T(7)＝11.71T(7)＝11.71

T(8)＝7.29T(8)＝7.29

T(9)＝3.42T(9)＝3.42

总吸气量： Qs＝30.405L/mTotal suction volume: Qs＝30.405L/m

计算结果采样点的吸气百分比最大值与最小值的差为2.5％，可认为气流平衡。通过公式26～28按时间优化优化后：The difference between the maximum value and the minimum value of the inspiratory percentage of the calculation result sampling point is 2.5%, which can be considered as the air flow balance. After optimizing according to time through formulas 26-28:

孔径分别为Apertures are

d(0)＝6d(0)=6

d(1)＝6d(1)=6

d(2)＝6d(2)=6

d(3)＝5.5d(3)＝5.5

d(4)＝5d(4)=5

d(5)＝4.5d(5)＝4.5

d(6)＝4d(6)=4

d(7)＝4d(7)=4

d(8)＝3.5d(8)＝3.5

d(9)＝3.5d(9)＝3.5

每孔吸气量(L/m)：Q(0)＝4.803Air intake per hole (L/m): Q(0)＝4.803

Q(1)＝4.847 Q(1)＝4.847

Q(2)＝5.015** Q(2)＝5.015

Q(3)＝4.513** Q(3)＝4.513

Q(4)＝4.11 Q(4)＝4.11

Q(5)＝3.732 Q(5)＝3.732

Q(6)＝3.325 Q(6)＝3.325

Q(7)＝3.743** Q(7)＝3.743

Q(8)＝3.225 Q(8)＝3.225

Q(9)＝3.606** Q(9)＝3.606

吸气百分比： QQ(0)＝11.74％Inspiratory percentage: QQ(0)＝11.74%

QQ(1)＝11.85％ QQ(1) = 11.85%

QQ(2)＝12.25％ QQ(2) = 12.25%

QQ(3)＝11.03％ QQ(3) = 11.03%

QQ(4)＝10.04％ QQ(4) = 10.04%

QQ(5)＝9.12％ QQ(5)＝9.12%

QQ(6)＝8.13％ QQ(6)＝8.13%

QQ(7)＝9.15％ QQ(7) = 9.15%

QQ(8)＝7.88％ QQ(8)＝7.88%

QQ(9)＝8.81％ QQ(9)＝8.81%

气体传输时间：T(0)＝64.97Gas transit time: T(0)=64.97

T(1)＝43.35T(1)＝43.35

T(2)＝32.59T(2)＝32.59

T(3)＝25.51T(3)＝25.51

T(4)＝20.09T(4)＝20.09

T(5)＝15.63T(5)＝15.63

T(6)＝11.79T(6)＝11.79

T(7)＝8.37T(7)＝8.37

T(8)＝5.32T(8)＝5.32

T(9)＝2.54T(9)＝2.54

总吸气量： Qs＝40.921L/mTotal suction volume: Qs＝40.921L/m

计算结果采样点的吸气百分比最大值与最小值的差为4.37％，可认为气流平衡，最大气体传输时间为64.97秒，小于70秒，符合要求。The calculation results show that the difference between the maximum and minimum values of the inspiratory percentage at the sampling point is 4.37%, which can be considered as air flow balance, and the maximum gas transmission time is 64.97 seconds, which is less than 70 seconds, which meets the requirements.

Claims

1. A sampling pipe network design verification and optimization method for an aspirating smoke detection system, characterized in that the inventive method comprises the following steps:

Step 1. Input data;

Input the data required for the simulation of the sampling pipe network, that is, the data of the original design of the project, and reproduce the original design scheme in the system, including the following:

1) The bending condition of the sampling tube, the length of each sampling tube;

2) The number of sampling holes, the location of the sampling tube, and the diameter of each sampling hole;

3) The number of capillaries, the position of the sampling tube, the aperture and length of each capillary;

4) the aperture of the end cap;

Step 2. Verify the rationality of the original design of the project, and calculate the inhalation volume, inhalation percentage and inhalation time of all sampling points including the end cap;

1) Determine the drag coefficient;

2) Calculate the percentage QQ(i) of the inspiratory volume of each sampling point in the total inspiratory volume and the pipe network impedance S;

The sampling pipe is a suction pipe of equal cross-section, with a diameter of dd and a cross-sectional area of AA; a point 0 is opened at the end, the point diameter is d(0), and the area is A(0); the side wall is opened with (n-1) point, the diameter of each point is d(i), and the area of the corresponding point is A(i);

Assuming that the suction volume of the end cap is 1, then the flow rate of the sampling pipe in the 0th segment is the suction volume of the end cap 1, based on the suction volume of the end cap being 1, for ordinary sampling holes, according to the formula

μ μ \cdot \cdot \frac{ρ ρ \cdot \cdot {v v}^{22} ((00))}{22} + + {Σ Σ}_{j j = = 00}^{i i - - 11} ((\frac{λ λ \cdot \cdot L L ((j j))}{dd dd} + + ξ ξ)) \cdot \cdot \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Σ Σ}_{j j = = 00}^{i i - - 11} Q Q ((j j))}{AA AAA}))}^{22} + + \frac{ρ ρ}{22} \cdot \cdot {((\frac{{Σ Σ}_{j j = = 00}^{i i - - 11} Q Q ((j j))}{AA AAA}))}^{22} = = μ μ \cdot &Center Dot; \frac{ρ ρ \cdot &Center Dot; {v v}^{22} ((i i))}{22} - - - - - - ((66))

In the formula, μ—the local resistance coefficient of the inlet of the sampling hole;

v——air velocity on sampling pipe section i, m/s;

ρ——air density, Kg/m ³ ;

Q(i)——inhalation volume of sampling point i, m ³ /s;

λ——the friction coefficient of the pipeline;

ξ——local resistance coefficient of pipeline;

L(i)——length from section i to section (i+1), m,

For the capillary, capillary sampling is to connect a capillary with a diameter of d1 on the side wall of the same sampling tube as the standard sampling, and the cross-sectional area of the capillary is A1; the length of the capillary is L1(i), and the end of the capillary is connected with a diameter of d(i) plug; according to the formula

μ μ \cdot &Center Dot; \frac{ρ ρ \cdot &Center Dot; {v v}^{22} ((00))}{22} + + {Σ Σ}_{j j = = 00}^{i i - - 11} ((\frac{λ λ \cdot &Center Dot; L L ((j j))}{dd dd} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot \cdot {((\frac{{Σ Σ}_{j j = = 00}^{i i - - 11} Q Q ((j j))}{AA AAA}))}^{22} + + \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Σ Σ}_{j j = = 00}^{i i - - 11} Q Q ((j j))}{AA AAA}))}^{22}

= = μ μ \cdot \cdot \frac{ρ ρ \cdot \cdot {v v}^{' '' ' 22} ((i i))}{22} + + ((\frac{λ λ \cdot \cdot L L 11 ((i i))}{d d 11} +ξ +ξ)) \cdot &Center Dot; \frac{ρ ρ \cdot \cdot {v v}^{' ' 22} ((i i))}{22} + + \frac{{v v}^{' ' 22} ((i i)) \cdot \cdot ρ ρ}{22} - - - - - - ((1111)),,

In the formula, v”——the air velocity at the inlet of capillary i, m/s;

V'——air velocity in capillary i, m/s;

λ——Frictional resistance coefficient, also known as the extension resistance coefficient;

Qs(i)——air flow rate at sampling pipe section i, m ³ /s,

Calculate the suction volume of each sampling hole in turn; based on the suction volume of the end cap is 1, the suction volume of each sampling hole is Q(0), Q(1),...,Q(n- 1), the total inspiratory volume Qs=Q(0)+Q(1)+...+Q(n-1), then the inspiratory volume of each sampling point accounts for the percentage of the total inspiratory volume QQ(i)=Q (i)/Qs;

The performance curve of the detector is determined. When the pipe network data is determined, the calculation amount at this time should also be a point on the performance curve of the detector. According to the formula

P＝S·Q _s ² (15)

Calculate the impedance S; where P is the static pressure in the sampling tube;

3) Calculate the total inspiratory volume Qs and the inspiratory time of each sampling point, verify whether the inspiratory volume of each sampling point is equal, and whether the sampling time meets the requirements;

The calculation formula of the iteration function is as follows:

{Q Q}_{s the s}^{((k k + + 11))} ((i i)) = = {Q Q}_{s the s}^{((k k))} ((i i)) - - \frac{{f f}_{i i} (({Q Q}_{s the s}^{((k k))} ((i i))))}{{f f}_{i i} (({Q Q}_{s the s}^{((k k))} ((i i)))) - - {f f}_{i i} (({Q Q}_{s the s}^{((k k - - 11))} ((i i))))} (({Q Q}_{s the s}^{((k k))} ((i i)) - - {Q Q}_{s the s}^{((k k - - 11))} ((i i)))) - - - - - - ((1717))

First, select any two groups of initial values Q _s ⁰ and Q _s ¹ and substitute them into formula (17), so as to obtain the iterative formula, control the iterative error <10 ^(-13) , and finally obtain the inspiratory volume Qs of the detector, that is, the sampling pipe network The total inspiratory volume; according to the previously obtained inspiratory percentage, the inspiratory volume at each point from the end cap is obtained as Q(i)=Qs×QQ(i);

Then calculate the inspiratory time of each sampling point, that is, the gas transmission time from each sampling point to the detector, first calculate the gas transmission time t of each section of sampling pipe, t=L(i)/v=L(i)/ (Q _g (i)/AA), where the gas flow Q _g (i) in each section of the pipe is the sum of the flows of all sampling points entering the sampling pipe from its front, and the gas transmission time of each section of the sampling pipe is calculated in turn, and Each period of time is superimposed successively to calculate the gas transmission time of the end cap;

Finally, the design results are verified by the inspiratory percentage of each sampling point and the gas transmission time of the end cap to determine whether the inspiratory volume of each sampling hole is balanced, and the maximum value of the inspiratory percentage of the sampling point is subtracted from the minimum value. 5%, it is considered that the inhalation is unbalanced, and it should be optimized according to the best airflow balance. By judging whether the gas transmission time of the end cap is within the time required by the project, it is determined whether it needs to be optimized according to the transmission time;

Step 3, optimize the design;

(1) Optimized according to the best airflow balance:

1) The total suction volume of the sampling pipe network is known, and the suction volume of each sampling hole should be balanced, and the suction volume _Qp =Qs/n of the sampling holes should be evenly distributed;

2) Make the suction volume of each sampling hole close to _Qp , rearrange the aperture of the sampling hole, and return to the optimized aperture d(i) of the sampling hole;

Starting from the sampling hole closest to the detector, calculate the aperture d(n-1):

If it is an ordinary sampling hole A(n-1), the calculation formula is:

{μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((n no - - 11))}^{22}} + + ((\frac{λ λ \cdot &Center Dot; L L ((n no - - 11))}{dd dd} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot;} \frac{{((n no {\cdot &Center Dot; Q Q}_{p p}))}^{22}}{A A {A A}^{22}} + + \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((n no \cdot &Center Dot; {Q Q}_{p p}))}^{22}}{A A {A A}^{22}} = = P P - - - - - - ((1818))

but

d (no - 1) = \sqrt{\frac{4 \cdot A (no - 1)}{π}},

Where P is the static pressure at the sampling hole;

If it is a capillary, the calculation formula of A(n-1) is:

μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((n no - - 11))}^{22}} + + ((\frac{λ λ \cdot &Center Dot; L L 11 ((n no - - 11))}{d d 11} + + ξ ξ)) \cdot \cdot \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + ((\frac{λ λ \cdot &Center Dot; L L ((n no - - 11))}{dd dd} + + ξ ξ)) \cdot \cdot \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((n no \cdot \cdot {Q Q}_{p p}))}^{22}}{A A {A A}^{22}} + + \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((n no \cdot &Center Dot; {Q Q}_{p p}))}^{22}}{A A {A A}^{22}}

= = P P - - - - - - ((1919))

but

d (no - 1) = \sqrt{\frac{4 &Center Dot; A (no - 1)}{π}},

Then d(n-1) is integrated; P is the static pressure at the capillary place in the formula;

To calculate the point diameter of other sampling points, first calculate A(i):

If the i-th is an ordinary sampling hole, the calculation formula is as (20),

μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((i i))}^{22}} + + \frac{λ λ \cdot &Center Dot; L L ((i i))}{dd dd} \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((((i i + + 11)) \cdot &Center Dot; {Q Q}_{p p}))}^{22}}{A A {A A}^{22}} + + \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((((i i + + 11)) \cdot &Center Dot; {Q Q}_{p p}))}^{22}}{A A {A A}^{22}} = = {P P}_{j j} ((i i + + 11)) - - - - - - ((2020))

In the formula, P _J —— the partial pressure loss of air passing through the sampling hole, Pa, if the i-th is a capillary, the calculation formula is as (21),

μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((i i))}^{22}} + + ((\frac{λ λ \cdot &Center Dot; L L 11 ((i i))}{d d 11} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + ((\frac{λ λ \cdot &Center Dot; L L ((i i))}{dd dd} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{((((i i + + 11)) \cdot \cdot {Q Q}_{p p}))}^{22}}{A A {A A}^{22}} + + \frac{ρ ρ}{22} \cdot \cdot \frac{{((((i i + + 11)) \cdot \cdot {Q Q}_{p p}))}^{22}}{A A {A A}^{22}}

= = {P P}_{j j} ((i i + + 11)) - - - - - - ((21 twenty one))

The known P _J (i+1) in the formula is determined according to the specific conditions of the i+1th sampling point, if the i+1th sampling point is a common sampling hole, then:

{P P}_{j j} ((i i + + 11)) = = μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((i i + + 11))}^{22}} - - - - - - ((22 twenty two))

If the i+1th sampling point is a capillary, then:

{P P}_{j j} ((i i + + 11)) = = μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot \cdot \frac{{Q Q}_{p p}^{22}}{A A {((i i + + 11))}^{22}} + + ((\frac{λ λ \cdot &Center Dot; L L 11 ((i i + + 11))}{d d 11} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot \cdot {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} - - - - - - ((23 twenty three))

then solve

d (i) = \sqrt{\frac{4 \cdot A (i)}{π}},

Then integrate d(i);

To calculate the point diameter of the end cap, first calculate A(0):

If the first one is an ordinary sampling hole, the calculation formula is as (24):

μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((00))}^{22}} + + \frac{λ λ \cdot &Center Dot; L L ((00))}{dd dd} \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {A A}^{22}} + + \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {A A}^{22}} = = μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((11))}^{22}} - - - - - - ((24 twenty four))

If the first one is a capillary, the calculation formula is as (25):

μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((00))}^{22}} + + \frac{λ λ \cdot &Center Dot; L L ((00))}{dd dd} \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {A A}^{22}} + + \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {A A}^{22}} = = μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{{Q Q}_{p p}^{22}}{A A {((11))}^{22}} + + ((\frac{λ λ \cdot &Center Dot; L L 11 ((11))}{d d 11} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} + + \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{{Q Q}_{p p}}{A A 11}))}^{22} - - - - - - ((2525))

then solve

d (0) = \sqrt{\frac{4 &Center Dot; A (0)}{π}},

Then integrate d(0);

3) According to the new d(i), the inspiratory volume, inspiratory percentage and inspiratory time of all sampling points including the end cap are calculated again, and the inspiratory percentage of each sampling point and the gas transmission time of the end cap are compared with each other. The optimization results are verified again;

(2) Optimize according to transmission time: if the maximum sampling time exceeds the allowable range, perform time optimization;

1) Starting from the end cap, to make the sampling time of the end cap the shortest, the aperture of the sampling hole should take the maximum value. At this time, the inhalation volume of the end cap is assumed to be 1. In order to ensure the balance of the inhalation volume of each sampling hole, other Assuming that the suction volume of the sampling hole is still 1, calculate the diameter of other sampling holes, and calculate the aperture A(i) of the sampling hole, see formula (26):

μ μ \cdot &Center Dot; \frac{ρ ρ}{22} \cdot &Center Dot; \frac{11}{A A {((00))}^{22}} + + {Σ Σ}_{j j = = 00}^{i i - - 11} ((\frac{λ λ \cdot &Center Dot; L L ((j j))}{dd dd} + + ξ ξ)) \cdot &Center Dot; \frac{ρ ρ}{22} \cdot \cdot \frac{{((j j + + 11))}^{22}}{A A {A A}^{22}} + + \frac{ρ ρ}{22} \cdot \cdot \frac{{i i}^{22}}{A A {A A}^{22}} = = {P P}_{j j} ((i i)) - - - - - - ((2626))

If the i-th is an ordinary sampling hole, the calculation formula is as (27):

{P P}_{j j} ((i i)) = = μ μ \cdot \cdot \frac{ρ ρ}{22} \cdot &Center Dot; \frac{11}{A A {((i i))}^{22}} - - - - - - ((2727))

If the i-th is a capillary, the calculation formula is as (28):

{P P}_{j j} ((i i)) = = μ μ \cdot \cdot \frac{ρ ρ}{22} \cdot \cdot \frac{11}{A A {((i i))}^{22}} + + ((\frac{λ λ \cdot &Center Dot; L L 11 ((i i))}{d d 11} + + ξ ξ)) \cdot \cdot \frac{ρ ρ}{22} \cdot \cdot {((\frac{11}{A A 11}))}^{22} + + \frac{ρ ρ}{22} \cdot &Center Dot; {((\frac{11}{A A 11}))}^{22} - - - - - - ((2828))

then solve

d (i) = \sqrt{\frac{4 &Center Dot; A (i)}{π}},

Then integrate d(i);

2) According to the new d(i), the inspiratory volume, inspiratory percentage and inspiratory time of all sampling points including the end cap are calculated again, and the inspiratory percentage of each sampling point and the gas transmission time of the end cap are compared with each other. Verify the optimization results;

Step 4. Carry out actual engineering operation according to the optimized data;

The actual engineering construction is carried out according to the optimized data, so that the aspirating smoke detection system works in the best state.