A ventilation calculation method for double-walled pipe structures

By splitting the double-wall pipe into a single-layer pipe component, calculating the single-layer compression loss value and establishing an association relationship, the problem of lack of pressure loss calculation of the double-wall pipe is solved, and the accuracy and economicality of fan selection is achieved.

CN120180628BActive Publication Date: 2025-08-22NANTONG COSCO KHI SHIP ENG
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Patent Information

Application Number
CN202510660522.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-05-22
Publication Date
2025-08-22
Estimated Expiration
2045-05-22

AI Technical Summary

Technical Problem

The lack of a double-wall pipe pressure loss calculation method in the prior art has led to engineers who need to use experience to estimate the fan selection, which may lead to insufficient or excessive ventilation, poor economic benefits and high cost.

Method used

By splitting the double-wall tube into a single-layer tube component, the single-layer compression loss value is calculated, and the correlation relationship is established. The double-wall pressure loss value is obtained by using CFD simulation to form a correlation number table, and the double-wall pressure loss value is directly calculated.

Benefits of technology

The accuracy of the pressure loss calculation of double-wall pipes is achieved, repeated simulation work is avoided, the accuracy of fan selection is improved, and the project cost is reduced.

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Abstract

The present invention discloses a ventilation calculation method for a double-walled pipe structure, which relates to the technical field of double-walled pipe structures for dual-fuel systems. The method comprises the following steps: first, separating a single-layer pipe component from the pipeline components of the double-walled pipe, and obtaining the pressure loss coefficient corresponding to the single-layer pipe component, and obtaining the single-layer pressure loss value corresponding to the single-layer pipe component; establishing a model for the double-walled pipe, and simulating the double-wall pressure loss value corresponding to the double-walled pipe in the annular ventilation space of the double-walled pipe; then, comparing and analyzing the single-layer pressure loss value and the double-wall pressure loss value under different air volumes, obtaining the correlation between the two, and repeating the above steps to obtain the corresponding correlation between different double-walled pipes; when calculating the ventilation of the double-walled pipe structure, first obtain the corresponding single-layer pressure loss value, and then directly obtain the double-wall pressure loss value based on the pre-obtained correlation. Parameterizing the pressure loss calculation of the double-walled pipe avoids the need for repeated full system simulation work for new engineering projects, thereby achieving the effect of efficiently solving the problem of accurate fan selection at the beginning of the project.
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Description

Technical Field

[0001] The present invention relates to the technical field of double-walled pipe structures of dual-fuel systems, and in particular to a ventilation calculation method for double-walled pipe structures. Background Art

[0002] With increasingly stringent international environmental regulations, ships are increasingly adopting green and clean energy sources such as LNG and methanol in addition to traditional fuel oil. Regulations require structural protection when gas and other pipelines pass through the engine room area. This system consists of an inner and outer pipe, forming an annular space. A fan provides ventilation within this annular space. This ensures that if the inner pipe ruptures or leaks, the gas can be promptly discharged from the pipeline, ensuring safe operation of the dual-fuel system. Fresh air is provided by the fan. Fan selection involves two technical parameters: air volume and duct pressure drop. Air volume is easily calculated by multiplying the duct volume by the number of ventilation cycles, while duct pressure drop is calculated by accumulating the local pressure drops of each component. Currently, empirical data on pressure drop coefficients is available only for single-wall pipes. There are no relevant pressure drop calculation methods for double-wall pipes. Specific engineering calculations require engineers to rely on their own experience to make estimates. If the estimated fan volume is insufficient, the minimum ventilation requirements stipulated by regulations will not be met. If the volume is too high, the fan will be oversized, resulting in poor economic benefits and significantly increased technical costs.

[0003] Therefore, accurate calculation of the pressure loss of double-wall pipes plays a vital role in the calculation of ventilation systems. The accuracy of the calculation results will be of great significance to the entire system design and fan selection. Summary of the Invention

[0004] The purpose of the present invention is to provide a ventilation calculation method for a double-walled pipe structure, which parameterizes the pressure loss calculation of the double-walled pipe, avoids the need for repeated full system simulation work in new engineering projects, and effectively solves the accurate selection of fans at the beginning of the project.

[0005] The above technical objectives of the present invention are achieved through the following technical solutions:

[0006] A ventilation calculation method for a double-walled pipe structure includes the following steps:

[0007] First, separate the single-layer pipe components from the double-wall pipe components, and obtain the corresponding pressure loss coefficient of the single-layer pipe components, and obtain the corresponding single-layer pressure loss value △P of the single-layer pipe components. single ;

[0008] A model is established for the double-walled pipe. In the annular ventilation space of the double-walled pipe, the double-wall pressure loss value △P corresponding to the double-walled pipe is obtained by simulation. double ;

[0009] Then, compare and analyze the single-layer pressure loss value △P under different air volumes single and double-wall pressure loss △P double , and get the correlation between the two.

[0010] Repeat the above steps to obtain the corresponding correlation relationship of different double-walled pipes;

[0011] When calculating ventilation for a double-walled pipe structure, the corresponding single-layer pressure loss value is first obtained, and then the double-wall pressure loss value is directly obtained based on the pre-obtained correlation relationship.

[0012] Furthermore, the corresponding relationship is,

[0013] △P double =ζ(i)*△P single +P constant ;

[0014] ζ(i) is the correlation coefficient, P constant is the fitting quantity.

[0015] Furthermore, the correlation relationship of double-walled pipes with different parameters is recorded as a correlation coefficient table, and the correlation coefficient table records at least correlation coefficients ζ(i) corresponding to different double-walled pipes.

[0016] Furthermore, P constant It has different values ​​in different ranges.

[0017] Furthermore, when υ≤υ(i), P constant =0, when υ>υ(i), P constant is a non-zero constant, and υ(i) is the discrete dividing value.

[0018] Furthermore, when υ(i)<υ≤5 m / s, P constant Take 10~20Pa.

[0019] Furthermore, the single-layer pressure loss value corresponding to the single-layer tube component is obtained by the following steps:

[0020] A model is established for the single-layer pipe component, and the corresponding physical parameters are set. The ventilation volume data is adjusted and the single-layer pressure loss value corresponding to the single-layer pipe component is output. The obtained single-layer pressure loss value is a data set related to the air volume.

[0021] Furthermore, the corresponding physical parameters set in the single-layer pipe component model are substituted into the pipeline model of the double-wall pipe.

[0022] Furthermore, when a single-layer tube component is modeled, the corresponding pressure loss coefficient is obtained in advance through a ventilation pressure loss coefficient table, so that the output results of the pressure loss coefficient in the model under different air volume conditions match the ventilation pressure loss coefficient table.

[0023] Furthermore, the method for establishing the double-walled pipe model includes establishing a model for the complete path of the ventilation duct and establishing a simulation calculation model based on the complete path of the ventilation duct.

[0024] In summary, the present invention has the following beneficial effects:

[0025] The completed simulation results for double-walled and single-layer tubes show significantly higher pressure loss for double-walled tubes than for single-layer tubes at all wind speeds, with no apparent inherent correlation between the two. If a complete double-walled tube model is established for each engineering calculation, it would take a long time and significantly delay engineering applications.

[0026] This application is based on the empirical data of single-layer pipes. As a theoretical support, it analyzes the changes in pressure loss of double-wall pipes under the dual friction resistance of the inner and outer pipe walls during ventilation, and finds a practical solution to the current technical bottleneck of the lack of pressure loss calculation method for double-wall pipes.

[0027] With the help of CFD simulation, the pressure loss calculation of double-wall pipes was parameterized, avoiding the need for repeated full-system simulation work in new engineering projects. This effectively solved the problem of accurate fan selection at the beginning of the project and avoided the need to adjust the fan specifications when deficiencies were discovered during later debugging, which would lead to rework of the project. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a schematic diagram of the gas pipeline ventilation system;

[0029] Figure 2 This is a diagram of the double-walled pipe structure;

[0030] Figure 3 It is a table of single-layer pipe pressure loss coefficients in the ventilation calculation method of double-wall pipe structure;

[0031] Figure 4 It is a CFD simulation software for double-wall pipe structure ventilation calculation method to simulate and calculate the straight pipe section;

[0032] Figure 5 It is a CFD simulation software for double-walled pipe structure ventilation calculation method to simulate the elbow section;

[0033] Figure 6 It is a CFD simulation software for double-wall pipe structure ventilation calculation method to simulate and calculate the elbow section;

[0034] Figure 7 It is a double-wall pipe straight section pressure loss curve and single-layer pipe pressure loss curve in the double-wall pipe structure ventilation calculation method;

[0035] Figure 8It is a double-wall pipe elbow or elbow section pressure loss curve and single-layer pipe pressure loss curve in the double-wall pipe structure ventilation calculation method;

[0036] Figure 9 It is a double-wall pipe ventilation correlation coefficient table in the double-wall pipe structure ventilation calculation method. DETAILED DESCRIPTION

[0037] The specific embodiments of the present invention are further described below in conjunction with the accompanying drawings. This embodiment does not constitute a limitation of the present invention. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0038] A ventilation calculation method for a double-walled pipe structure, wherein the double-walled pipe structure in this embodiment is based on the following environment;

[0039] like Figure 1 As shown, the engine room is equipped with dual-fuel equipment. A gas pipe enters the engine room area from the air supply port and connects to the dual-fuel equipment to ensure fuel supply. A double-walled pipe is installed outside the engine room section of the gas pipe. One end of the double-walled pipe draws fresh air from the air inlet in the safe area outside the engine room, supplies it to the double-walled pipe structure through a single-layer pipe. The fresh air then passes through the internal piping of the dual-fuel equipment and is then drawn out through the single-layer pipe by the double-walled pipe fan in the safe area. This continuous replacement of fresh air ensures safe use of the gas pipe in the engine room and meets regulatory requirements.

[0040] like Figure 2 As shown, the interior of the double-walled pipe structure is a gas pipe, and the annular space is a ventilation pipe formed by the outer and inner pipes of the double-walled pipe. The double-walled pipe can be a completely straight pipe section structure. When fresh air flows through the double-walled pipe structure, the fluid rubs against the outer wall of the inner pipe and the inner wall of the outer pipe. By adding the friction of the outer wall of the inner pipe on the basis of the friction of the inner wall of the single-layer pipe, the calculation of the pressure loss of the straight pipe section is solved. The double-walled pipe structure can also be a bend or elbow section structure. When fresh air flows through the bend or elbow of the double-walled pipe, in addition to the double wall friction of the outer wall of the inner pipe and the inner wall of the outer pipe similar to that of the straight pipe section, it also includes the effect of variable cross-section or variable direction turbulence, so as to solve the calculation of the pressure loss of the bend or elbow.

[0041] The ventilation calculation method of the double-walled pipe structure includes the following steps:

[0042] Step S10, establishing a pipe segment model of a double-wall pipe;

[0043] Specifically,

[0044] Step S11: Model the complete path of the ventilation duct (in AVEVA AM12 software) to ensure that the path meets the actual ship design requirements and calculate the volume of the ventilation duct;

[0045] Step S12: establishing a simulation calculation model (in CFD simulation software) based on the complete path of the ventilation duct, and establishing models for each component in the duct, including straight pipes, curved pipes or elbows, inner pipe brackets, tees, etc.

[0046] Step S20: separate the single-layer pipe components from the double-wall pipe components, obtain the pressure loss coefficient corresponding to the single-layer pipe components, and obtain the single-layer pressure loss value ΔP corresponding to the single-layer pipe components. single ;

[0047] In this embodiment, the single-layer pressure loss value corresponding to the single-layer tube component is obtained by the following steps:

[0048] Step S21: Create a CFD simulation software model for the single-layer tube component.

[0049] In step S22, the corresponding pressure loss coefficient is obtained in advance through the ventilation pressure loss coefficient table in the manual such as the "Practical Handbook of Ship Design", and then the corresponding physical parameters such as material, elastic modulus, Reynolds number, roughness, etc. are set according to the single-layer pipe setting of the CFD simulation software, and the ventilation volume data is continuously adjusted so that the output results of the pressure loss coefficient in the model under different air volume conditions match the ventilation pressure loss coefficient table;

[0050] And output the single-layer pressure loss value corresponding to the single-layer tube component, and obtain the single-layer pressure loss value △P single It is a data set related to air volume, namely △P single ={△P1,△P2,△P3,△P N Based on this set, we can draw the single-layer tube pressure loss coefficient curve Curve 1 under different air volumes.

[0051] like Figure 3 As shown, based on the elbow and bend pressure loss coefficient table widely used in engineering to calculate the ventilation pressure loss value of single-layer pipes, the pressure loss coefficient value of single-layer pipes can be easily obtained by calculating the corresponding cross-sectional ratio, curvature, etc. of the pipe; the data in this table is used as the basic data for this application to simulate the pressure loss of double-wall pipes and find the inherent connection between the pressure loss calculation of double-wall pipes and single-layer pipes, thereby obtaining a double-wall pipe pressure loss coefficient table with the same function as the single-layer pipe pressure loss coefficient table;

[0052] In some embodiments, the straight pipe and elbow or bend specifications of 1 / 2"~8" inner pipe diameter and 21 / 2"~12" outer pipe diameter used in the applicable ASME standard to be calculated are selected. Figure 3 Find the corresponding pressure loss coefficient in the ventilation pressure loss coefficient table, and then accurately simulate the single-layer pipe pressure loss coefficient in the CFD software to make the result consistent with Figure 3 The listed data are equivalent, the parameters set in the software are used as the material parameters under this specific specification, and the single-layer pressure loss value △P corresponding to the single-layer pipe under this condition is output.single .

[0053] Step S30: Substitute the corresponding physical parameters of the single-layer pipe component model set in step S20 into the double-wall pipe model. By setting the wind speed, model unit length, etc. in the annular ventilation space of the double-wall pipe, the ventilation volume data is continuously adjusted to simulate the double-wall pressure loss value ΔP corresponding to the double-wall pipe. double ; The obtained △P double It is also a data set related to air volume, namely △P double ={△P 1 , △P 2 , △P 3 , △P N Based on this set, we can draw the curve 2 of the pressure loss coefficient of the double-walled pipe under different air volumes;

[0054] In some embodiments, a double-walled tube model can be directly established in the completed single-layer tube simulation calculation to directly integrate it into the model required for double-walled tube calculation;

[0055] Step S40: plot Curve 1 and Curve 2 on the same graph, and compare and analyze the single-layer pressure loss values ​​△P under different air volumes at the same air volume setting value. single and double-wall pressure loss △P double , we can get that, under different air volume conditions, the double-walled tube curve 2 will be above the single-layer tube curve 1, and the double-walled tube pressure loss curve is a multi-segment line (υ-△P) (初始) , compare the coincidence and dispersion of pressure loss values ​​and obtain the correlation between them;

[0056] Specifically, in certain sections, the pressure loss of the double-walled pipe is close to the single-layer pipe curve (υ-△P), and the inherent connection between the pressure loss of the double-walled pipe and the single-layer pipe is established. The coefficient ζ(i) is artificially set to move the single-layer pipe curve closer to the double-walled pipe curve, that is, the pressure loss value of the double-walled pipe is fitted to the pressure loss value area of ​​the single-layer pipe, and an area with a large overlap is obtained; that is, the obtained ζ(i) is used as the correlation coefficient of the components of the unit length of the pipeline, thereby obtaining the pressure loss coefficient of the double-walled pipe;

[0057] Depending on the air volume, the pressure loss curve will gradually separate from curve 1 in some specific areas, resulting in failure of curve fitting. On this basis, it is necessary to set a constant, or set a constant for each flow segment to eliminate the separation of the curves, that is, P constant .

[0058] Specifically, the corresponding association relationship can be set as,

[0059] △P double=ζ(i)*△P single +P constant ;

[0060] ζ(i) is the correlation coefficient, P constant is the fitting quantity; among them, P constant There are different values ​​in different ranges; the acquisition of this value is currently based on the complete simulation results. The current simulated wind speed is not higher than 5 m / s in the double-walled pipe. When υ(i)<υ≤5 m / s, P constant Take 10~20Pa;

[0061] That is, when υ≤υ(i), P constant =0, when υ>υ(i), P constant is a non-zero constant, υ(i) is the discrete boundary value; that is, when υ≤υ(i), △P double =ζ(i)*△P single ; When υ>υ(i), △P double =ζ(i)*△P single +P constant .

[0062] After setting ζ(i), re-apply the parameter setting value in the CFD simulation software to further obtain the new pressure loss curve (υ-△P) after fitting the double-walled pipe. (新) , so that the new pressure loss curve of the double-walled pipe coincides with the single-layer pipe curve (υ-△P) in a large range, and no discreteness occurs in the high wind speed area as much as possible.

[0063] In actual simulations, combined with the actual air volume in the duct, as the air volume gradually increases, the flow velocity has a dramatic impact on the pressure drop, and turbulence is more obvious. In engineering applications, it is best to control the design air volume within a relatively stable flow field range. Based on commonly used double-walled pipe information, the simulation results under a wind speed of 5 m / s were selected. The double-walled pipe curve 2 is relatively linear with the single-layer pipe curve 1.

[0064] As attached Figure 7 and 8 For branch pipe sections, elbows or bends, curve 2 and curve 1 have two different slope values ​​κ2 and κ1. The two straight lines have only one intersection point, and gradually show a trend of separation beyond the intersection point. The farther away from the intersection point, the more obvious the separation. For example, when going to the right high-speed air volume area, the difference between the two straight lines will be greater, that is, P constant =(κ2-κ1)*υ As the compensation amount of the two curve fitting, the larger it is, the more discrete the fitting curve will be in the high wind speed area;

[0065] In order to obtain the double-wall pipe pressure loss data more accurately and take into account the discrete effect, in this embodiment, the discrete boundary value υ(i) is determined to be 2.5 m / s, and P is taken. constantThe value is 10Pa, and the mathematical calculation model is adjusted to:

[0066] When υ≤2.5m / s, △P double =ζ(i)*△P single ;

[0067] When υ>2.5m / s, △P double =ζ(i)*△P single +10.

[0068] Figure 7 The straight section pressure loss curve of the double-walled pipe and the single-layer pipe in this embodiment are shown in FIG. Figure 8 The double-wall pipe elbow or elbow section pressure loss curve and the single-layer pipe pressure loss curve drawn in this embodiment are obtained from the curves. It is found that the curves have a high degree of overlap within a certain wind speed range (below 5 m / s in this embodiment), thereby guiding the selection of fans within this area as much as possible. The high wind speed area is discrete and is not recommended as a reference for fan selection; under specific high wind speed conditions, continuing to use this correlation coefficient method to calculate pipeline pressure loss may result in a deviation from the actual value.

[0069] Step S50, repeat the above steps, and then substitute the elbow or bend pipe section, first obtain the model setting environment based on the empirical data of the single-layer pipe elbow or elbow pipe section, and after judging that the simulation results are the same as the empirical calculation, substitute the parameters into the double-wall pipe pipeline model, and draw a curve of the air volume based on the simulated pressure loss data to find the fitting correlation coefficient ζ(i) (and P constant Data), obtain the corresponding correlation relationship of different double-walled pipes;

[0070] like Figure 9 As shown in the figure, the correlation relationship of double-walled pipes with different parameters is recorded as a correlation coefficient table. The correlation coefficient table records at least the correlation coefficient ζ (i) corresponding to different double-walled pipes, which closely combines the pressure loss coefficient of double-walled pipes with that of single-layer pipes, providing convenience for engineering calculations.

[0071] Double-wall pipes with different parameters include straight pipe sections, curved pipes or elbow sections within the commonly used inner and outer pipe ranges of double-wall pipe projects. Based on the curves and correlation coefficients of straight pipes, curved pipes or elbows, a pressure loss coefficient table of straight pipe sections, curved pipes or elbow sections within the commonly used inner and outer pipe ranges of double-wall pipe projects is formulated as the empirical data of double-wall pipe pressure loss; Figure 4 The simulation calculated the pressure loss value △P of the double-wall pipe straight section under various wind speed data. double - straight pipe; Figure 5 The simulation calculated the pressure loss value △P of the double-wall pipe elbow section under various wind speed data. double -elbow; Figure 6 The simulation calculated the pressure loss value △P of the double-wall pipe elbow section under various wind speed data. double-Bend; that is, the pressure loss value △P of different parts of double-wall pipe double .

[0072] Step S60, when calculating ventilation of the double-walled pipe structure, first obtain the corresponding single-layer pressure loss value, and then directly obtain the double-wall pressure loss value based on the correlation coefficient table pre-obtained in step S50;

[0073] Taking elbow as an example, according to the double-wall pipe diameter in the correlation coefficient table, find the corresponding single-layer pipe diameter, and then according to the attached Figure 3 The required ratio of elbow bending radius R and circular cross-section diameter d R / d and wind speed ω in the pipe are used to obtain the pressure loss coefficient ξ and single-layer pressure loss value △P of the elbow assembly under this wind speed. single ; According to the data in the correlation coefficient table, specify the correlation coefficient ζ and calculate △P double =△P single *ζ.

[0074] This embodiment first establishes a complete pipe model in which fresh air enters the single-layer ventilation duct and double-wall ventilation duct structure from the air inlet and is drawn out by the fan; secondly, the annular space formed between the inner pipe and the outer pipe, as well as the ventilation-related physical structural characteristics such as straight pipes, curved pipes or elbows and elastic supports in the annular space are analyzed; then the required ventilation volume and pressure loss value in the double-wall pipe structure are calculated, and the ventilation volume and pressure loss value are used as basic parameters to complete the selection of the double-wall pipe fan; it provides a more accurate ventilation calculation method for the double-wall pipe structure in the annular space, and provides a more accurate reference for the selection of double-wall pipe fans, avoiding the risk of unnecessary energy consumption caused by over-selection of double-wall pipe fans and the risk of ventilation not meeting regulatory requirements due to under-selection, and has good engineering application guidance benefits.

[0075] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art may make various modifications or equivalent substitutions to the present invention within the essence and protection scope of the present invention, and such modifications or equivalent substitutions should also be deemed to fall within the protection scope of the technical solution of the present invention.

Claims

1. A ventilation calculation method for a double-walled pipe structure, characterized by: The following steps are included: First, separate the single-layer pipe components from the double-wall pipe components, and obtain the corresponding pressure loss coefficient of the single-layer pipe components, and obtain the corresponding single-layer pressure loss value △P of the single-layer pipe components. single ; A model is established for the double-walled pipe. In the annular ventilation space of the double-walled pipe, the double-wall pressure loss value △P corresponding to the double-walled pipe is obtained by simulation. double ; Then, compare and analyze the single-layer pressure loss value △P under different air volumes single and double-wall pressure loss △P double , we get the correlation between the two, the corresponding correlation is, △P double =ζ(i)*△P single +P constant ; Wherein, ζ(i) is a correlation coefficient, and the correlation relationship of double-walled pipes with different parameters is recorded as a correlation coefficient table, and the correlation coefficient table records at least the correlation coefficients ζ(i) corresponding to different double-walled pipes; P constant is the fitting quantity, P constant It has different values ​​in different ranges. When υ≤υ(i), P constant =0, when υ>υ(i), P constant is a non-zero constant, υ(i) is the discrete boundary value; when υ(i)<υ≤5 m / s, P constant Take 10~20Pa; Repeat the above steps to obtain the corresponding correlation relationship of different double-walled pipes; When calculating ventilation for a double-walled pipe structure, the corresponding single-layer pressure loss value is first obtained, and then the double-wall pressure loss value is directly obtained based on the pre-obtained correlation relationship.

2. A ventilation calculation method for a double-walled pipe structure according to claim 1, characterized in that: The single-layer pressure loss value corresponding to the single-layer tube component is obtained by the following steps: A model is established for the single-layer pipe component, and the corresponding physical parameters are set. The ventilation volume data is adjusted and the single-layer pressure loss value corresponding to the single-layer pipe component is output. The obtained single-layer pressure loss value is a data set related to the air volume.

3. The ventilation calculation method for a double-walled pipe structure according to claim 2, characterized in that: The corresponding physical parameters set in the single-layer pipe component model are substituted into the double-wall pipe model.

4. The ventilation calculation method for a double-walled pipe structure according to claim 1, characterized in that: When establishing a model for a single-layer tube component, the corresponding pressure loss coefficient is obtained in advance through the ventilation pressure loss coefficient table, so that the output results of the pressure loss coefficient in the model under different air volume conditions match the ventilation pressure loss coefficient table.

5. The ventilation calculation method for a double-walled pipe structure according to claim 1, characterized in that: The method for establishing the double-wall pipe model includes establishing a model for the complete path of the ventilation duct and establishing a simulation calculation model based on the complete path of the ventilation duct.

Citation Information

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