The exhaust outlet space arrangement is a crucial part to avoid casualties and economic losses in the event of contaminant gas leakage. To handle this problem, this work proposed a novel optimization method based on the coupling of the genetic algorithm (GA) and ant colony algorithm optimization (ACO), and the fitness function used in the optimization method is constructed as an implicit form. In this proposed optimization method, the ACO is used to obtain the implicit fitness function value, while the GA is selected to conduct the space arrangement optimization based on the iteration results transferred from ACO. With the help of this novel methodology, the influence of obstacles in space could be well considered into the space arrangement optimization, which leads to a reliable optimization result of the exhaust outlet configuration. Moreover, to validate the accuracy and efficiency of this coupling method, the optimization results are taken into the computational fluid dynamics numerical model to give a comparison with the conventional configuration. The comparison results indicate that the exhaust outlet arrangement following the optimization results shows a lower gas concentration value during the diffusion process. In addition, based on this optimal exhaust outlet space arrangement, the models with various leakage rates are also investigated and discussed in the numerical work. It is believed that the proposed method could provide an effective measure for the space arrangement optimization and the design of gas leakage protection.

At present, due to diverse practical requirements, laboratories and industrial production necessitate the utilization of various gases, such as hydrogen, nitrogen, and oxygen.1–3 Among these gases are inflammable and toxic substances that entail numerous unstable factors during usage. In the event of gas pollutant leakage, it could potentially result in significant casualties and severe economic losses.4–6 Therefore, optimizing the layout of indoor exhaust outlet and minimizing risks arising from gas pollutant leakage has gained much attention in recent studies.

For the gas leakage, many investigations attempt to study the diffusion behavior of gas pollutants by numerical simulations. Tian et al.7 proposed a computational fluid dynamics (CFD) model to simulate the hydrogen leakage and diffusion behaviors under high pressure conditions. The results gave a good description of the high-pressure hydrogen leakage and diffusion behaviors under various conditions. Lee and Lee8 established a standard for adequate ventilation to maintain gas concentration below the explosion threshold by quantifying the hydrogen leakage based on the size of the leak orifice. Xia et al.9 studied the effects of pressure and leakage diameter on the diffusion of natural gas leakage in pipelines. The results showed that the pressure and leakage diameter will affect the gas concentration but will not change the location of the concentration peak observed at the surface. Zeng et al.10 studied the continuous leakage of natural gas by establishing a scaled numerical model for gas pipelines in tunnels. The research results showed that the diffusion path of natural gas is greatly influenced by the direction of pipeline holes, and the tunnel wall has a directional effect on the diffusion of natural gas. Wang et al.11 studied the effects of heat transfer coefficient, initial pressure, and hydrogen blending ratio on natural gas leakage. Their numerical studies proved that the maximum dangerous distance of pure methane pipeline leakage is greater than that of pure hydrogen pipeline. Li et al.12 and Su et al.13 studied the effect of different hydrogen doping ratios on the diffusion characteristics of natural gas leakage. The results indicated that the explosion is more likely to occur in advance with the increase in the hydrogen doping ratio. Liu et al.14 and Yang et al.15 studied the impact of different layouts of buildings on the diffusion of natural gas leaks based on CFD models. Yu et al.16 studied the effects of leakage rate, leakage diameter, and wind speed on the distribution of natural gas leakage concentration through numerical simulations. The results discovered that the speed of wind is the main factor that affects the diffusion path of gas. Moghadam Dezfouli et al.17 proposed a new method to predict the leakage gas flow rate based on numerical simulation results. The results showed that this method could effectively predict the volumetric flow rate of gas leakage.

To handle the optimization problem of space arrangement, many optimization methods have been proposed and developed in recent decades.18–23 Among these methods, the genetic algorithm (GA) is considered as the most effective one to conduct the space arrangement optimization. Hanaei and Lakzian24 used genetic algorithms to determine the optimal location of the pressure reducing valve, and the results showed that this method could effectively reduce leakage. Yang et al.25 successfully proposed fault identification rules that can be applied to the actual operation of room air conditioning based on the random forest algorithm. Xu et al.26 proposed a method for describing gas leakage and successfully obtained a factory layout scheme based on the genetic algorithm that can determine safety factors such as gas diffusion and minimum distance. Kumar Bhargava et al.27 used genetic algorithms to determine the optimal size and position of capacitors in distribution networks to achieve power loss reduction. Lok et al.28 determined the optimal structure of metamaterials by coupling deep convolutional neural networks and genetic algorithms. The results of this work demonstrated that this method can effectively find the optimal parameters for nanoporous copper (NPC) to enhance the carbon dioxide reduction reaction (CO2RR). Cenedese et al.29 used genetic algorithms to refine the design of service stations, and they found that this approach can effectively mitigate traffic congestion on highways.

Besides the GA, another famous optimization method is the ant colony algorithm, which has been widely applied to path optimization and combinatorial optimization problems. Zhou and Huang30 proposed a method that combined Dijkstra’s algorithm and ant colony optimization for optimizing the path planning of airport automatic guidance vehicles, and the results showed that it can effectively shorten the path. Miao et al.31 proposed an improved adaptive ant colony optimization (IAACO) algorithm that enables indoor robots to effectively obtain the optimal path. Yang et al.32 developed an improved ant colony optimization planning algorithm to solve the planning problem of rescue paths in urban rescue. The results demonstrated that this approach exhibits superior robustness and feasibility compared to other currently available algorithms. Gao et al.33 combined ant colony algorithm with improved artificial potential field method to solve the problem of ship navigation safety in real-time dynamic avoidance. The results showed that this method can help improve the accuracy of path prediction and collision avoidance.

In general, the GA has proven to be a powerful tool in addressing intricate optimization problems, offering viable solutions for spatial layout optimization.34–36 Meanwhile, the Ant Colony Optimization (ACO) stands out in the realm of path optimization, utilizing its positive feedback loop and distributed search strategy to efficiently identify optimal paths.37 By judiciously coupling these two algorithms, we endeavor to harness their complementary strengths, aiming to achieve more effective and efficient resolutions to the complex optimization problems we encounter. Although many numerical studies of the gas leakage have been reported in the existing literature, few of the studies focus on the arrangement optimization of the exhaust outlet. In this work, we proposed an optimization method by coupling the genetic algorithm and ant colony algorithm to find out the optimal space arrangement of the exhaust outlet. In addition, the CFD model is established to describe the diffusion behavior of the leaking gas and give a validation of the optimization results.

This paper is organized as follows: in Sec. II A, the basic model is introduced. In Sec. II B, the theory of the ant colony algorithm and that of the genetic algorithm are presented. The discussion and results obtained from the optimization method and CFD simulation are summarized in Sec. III. Finally, the main conclusion points and findings are given in Sec. IV.

As nitrogen is widely utilized in various industries, its leakage represents a significant concern. This article examines the impact of nitrogen leakage and explores potential countermeasures, aiming to enhance safety practices and promote sustainable development across various applications.

1. Governing equations

The diffusion of nitrogen in the building also needs to follow the basic governing equations of CFD. It is necessary to satisfy the continuity equation and momentum equation. When nitrogen leaks in the building, it will be fully mixed with the air in the space during the diffusion process, so it also needs to meet the species transport equation.

The general equation of continuity could be written as follows:38,39
ρt+xi(ρui)=0,
(1)
where ui represents the partial velocity of fluid and ρ is the fluid density.
The momentum conservation is expressed as follows:39 
ρt(ρui)+xj(ρuiuj)=pxi+τijxjρgj,
(2)
where gj is the volume stress and p and τij represent the average pressure and viscosity strain tensor of the fluid, respectively. The species transport equation is described by the following equation:
(ρω)t+xi(ρuiω)=xiDρωxi,
(3)
where ω is the mass fraction and D is the diffusion coefficient.

2. Computational model

As shown in Fig. 1(a), both the length and width of the basic model is 40 m. The building structures and equipment are distributed inside the space. In addition, there is a door on the upper right as an exit, various boxes in the middle indicate that the building structure or equipment is treated as an obstacle in the calculation, nitrogen leakage is assumed at the lower left during the calculation, and this point is regarded as a leak point. Figure 1(b) is the fluent geometric model converted from the schematic diagram. The leakage point is set as mass flow inlet, and the exit point is set as pressure outlet. In addition, the fixed boundary conditions are given for the obstacle and building wall region. Figure 1(c) shows the mesh details used in the CFD model to conduct the simulation of nitrogen leakage diffusion, which is a quadrilateral element of size 0.5 m. The total number of elements is 6273, with a corresponding node count of 6906. Figure 1(d) shows that the grid map has a total of 1600 cells, which is required by the ant colony algorithm, and the obstacles are simplified into black boxes that are unreachable areas.

FIG. 1.

Illustration of the model: (a) layout of the model showing the overall arrangement, (b) CFD model for numerical analysis, (c) grid of the CFD model, and (d) grid map for ACO.

FIG. 1.

Illustration of the model: (a) layout of the model showing the overall arrangement, (b) CFD model for numerical analysis, (c) grid of the CFD model, and (d) grid map for ACO.

Close modal

1. Genetic algorithm

GA (genetic algorithm) is an optimization method, which is extended from the Darwin’s biological evolution theory. In this method, the optimization process could be carried out by the simulation of natural selection.40,41 As shown in Fig. 2, the main steps of the GA could be summarized as follows: first, the information of the optimization object needs to be encoded within a unified parameter set. Then, according to the fitness function, some individuals are selected to conduct the crossover and mutation. After the conduction of crossover and mutation, the subpopulation is generated. Finally, the crossover and mutation procedure would be repeated until the iteration number meets the requirement.

FIG. 2.

Flowchart of genetic algorithm.

FIG. 2.

Flowchart of genetic algorithm.

Close modal
In the first step, the optimized objective factors need to be encoded as follows:
Xp={r1,r2,,ri},i1,2,,n,p1,2,,pop,
(4)
where r is the individual chromosome code, n is the encoding length, and pop is the group size. To conduct the selection process, it is necessary to establish a criterion in the optimization program. This criterion of the selection is described by the fitness function quantitatively within the GA framework. It should be noticed that the construction of the fitness function is determined by the specific problem.
For the minimization problem, the fitness function is written as
Fit(f(x))=cmaxf(x),f(x)<cmax,0,otherwise,
(5)
where f(x) is the objective function, cmax is the maximum estimate of the objective function, and Fit(f(x)) is the fitness value.
For the maximization problem, the fitness function is written as
Fit(f(x))=f(x)cmin,f(x)>cmin,0,otherwise,
(6)
where cmin is the minimum estimate of the objective function.
Besides the fitness function, the GA also contains three main operations during the problem solving, including selection, crossover, and mutation. For the selection operation, it follows the elite strategy that aims to save the optimal individual from the group. For the crossover operation, it is used to produce the next generation. In this simulation, the crossover operation is described by the real number crossover method,
Pi,k+1=Pi,k(1r)+Pi+1,kr,
(7)
Pi+1,k+1=Pi+1,k(1r)+Pi,kr,
(8)
where Pi,k+1 and Pi+1,k+1 are the new individuals, Pi,k and Pi+1,k are the parent individuals, and r is a random number between 0 and 1. For the mutation operation, similar to crossover operation, it is also used to provide the next generation,
Pk+1=Pk+(PkmaxPkmin)(r0.5),
(9)
where Pk is the selected individual of generation k, Pk+1 is the individual of generation k + 1 after mutation operation, Pkmax and Pkmin are the upper and lower bounds, respectively.

2. The coupling of ant colony algorithm and genetic algorithm

Gas removal is directly related to pressure gradient and concentration gradient. The gas removal efficiency is affected by the concentration and the mass transfer distance, which could be described by the following equation:
f=miniAIMVidikeff,
(10)
where Vi is the gas concentration of the element and dikeff is the corresponding distance, respectively. The gas concentration is calculated based on the CFD model, and the corresponding distance is calculated by the ant colony algorithm. In previous studies,42–46 most of the objective functions are explicit expressions. For example, the distance could be directly calculated by the coordinates of two points, such as the expression in Eq. (10). However, this distance value is only suitable for the situations without obstacles. When the obstacles appear on the path, it is difficult to obtain the effective distance by an explicit function. In this work, to overcome this limitation, an implicit distance objective function is proposed within the GA framework. In addition, this implicit objective function is solved by the ant colony algorithm iteration. Based on this coupling method of GA and ACO, the obstacles effect could be well considered into the optimization process. Figure 3 shows the coupling flowchart of the genetic algorithm and ant colony algorithm. As shown in Fig. 3, the coordinates and concentration details derived from CFD calculations are inputted into the program when the optimization process starts. Following this, an initial population is generated, consisting of coordinate positions for five outlets. Subsequently, the fitness values for this population are computed. When the GA needs to evaluate the fitness of its solutions, the spatial layout and gas distribution data are transferred to the ACO algorithm. Then, the ACO utilizes these data to construct pheromone trails and simulate ant movements in search of optimal paths. These paths are evaluated based on their ability to avoid obstacles and efficiently traverse the search space. After evaluating the paths, selection, crossover, and mutation operations are performed based on the computed fitness values. This leads to the creation of a new generation. The entire process is repeated until the iteration criteria are met. In general, the GA serves as the outer loop, managing the population of solutions and selecting promising candidates for further evolution. Within this framework, the ACO algorithm acts as a specialized tool to solve a particular sub-problem: finding effective paths that consider obstacles.
FIG. 3.

Coupling flowchart of genetic algorithm and ant colony algorithm.

FIG. 3.

Coupling flowchart of genetic algorithm and ant colony algorithm.

Close modal

3. Ant colony

Based on the theory of the ant foraging behavior, the ant colony algorithm is established to find the optimal path for the path optimization problems, such as Traveling Salesman Problem (TSP)47–50 and mobile routing and vehicular routing problem.51–54 The utilization of the ant colony method can be summarized in three main steps: first, the necessary parameters of the algorithm should be initialized. Subsequently, each ant ought to choose the site that it will visit based on the transfer rule. Following this selection, the tabu table is updated. Once all the ants have visited all the sites, a solution path will be created. Finally, the pheromone concentration along the path is updated for the following iteration. For this method, the solving process of this method is based on the information interaction between each ant.55 Ant colony algorithm conducts path planning through information interaction between ants.

During the ACO process, for each ant, the next node selection follows the roulette wheel method, which could be expressed as
pijk=τijα(t)ηijβ(t)wIτiwα(t)ηiwβ(t),jJbest,0,otherwise,
(11)
where I is the set of all points on the next connecting line, τij(t) is the pheromone concentration value between node i and node j when the simulation time is t, and Jbest is the nodes set when the obstacle effect is considered. α is the information heuristic factor to consider the influence of the pheromone, which is 1.0 in this simulation work; β is the expected heuristic factor to consider the influence of heuristic information, which is 6.0 in this work. ηij(t) is heuristic function, which is written as
ηij(t)=1dij,
(12)
dij=(xixj)2+(yiyj)2,
(13)
where dij is the distance between the current two nodes. When an ant moves on a path, the pheromone concentrations are released by the ant on the corresponding location. The pheromone concentrations would be accumulated by all ants along this path. However, the final pheromone concentrations on each path are also dependent on the volatilization effect, which could be considered by the volatilization factor ρ. Thus, in each iteration, the pheromone concentrations are updated by the following equations:
τij(t+1)=(1ρ)τij+Δτij(t),
(14)
Δτij(t)=k=1mΔτijk(t),
(15)
where Δτijk(t) denotes the pheromone concentration released by ant k on the path ij, m is the total number of ants, Q is the pheromone constant, and Lk is the path length in the iteration.
In the existing literature, Δτijk(t) could be written as three different expressions,56,
Δτijk(t)=Q,0,otherwise,
(16)
Δτijk(t)=Qdij,0,otherwise,
(17)
Δτijk(t)=QLk,0,otherwise,
(18)
where Q is the pheromone constant and Lk is the path length found by ant k in the iteration. The determination of the pheromone concentration is used to conduct the path selection within the ACO procedure. However, the selection of the different pheromone concentration increase expressions will affect the computational accuracy and efficiency when the ACO program is performed. For the expression in Eq. (16), it does not adequately reflect this path information during the optimization procedure, which reduces the effectiveness of the solution results. To overcome this limitation, some studies attempt to use another pheromone concentration increase form shown in Eq. (17). However, in recent comparison reports,56 the utilization of Eq. (18) provides a more accurate optimization result than Eqs. (16) and (17). Due to the above reasons, among the three different expressions of the pheromone concentration increase shown in Eqs. (16)(18), Eq. (18) is the most suitable choice to update the pheromone concentration within the ACO method. In our optimization calculation, Eq. (18) is also used to determine the increase in the pheromone concentrations in each step.

To obtain the nitrogen diffusion behaviors and distribution features after the leakage, a numerical simulation of nitrogen leakage process is performed first. For the sake of observation, a monitoring point is set at the position with coordinates (34,38) to describe the nitrogen concentration evolution process quantitatively. In this work, the exhaust outlet space arrangement is used for some laboratory buildings. According to the requirements of the laboratory building, the exhaust outlet arrangement is designed for the situation of 4.0 kg/s leakage rate. In order to explore the impact of leakage rate on nitrogen diffusion, three leakage rates are deliberately selected for simulation. Figure 4 shows the mass fraction of N2 under different leakage rates.

FIG. 4.

Mass fraction curves of N2 under different leakage rates: (a) monitoring point value and (b) average value.

FIG. 4.

Mass fraction curves of N2 under different leakage rates: (a) monitoring point value and (b) average value.

Close modal

As shown in Fig. 4(a), it could be found that all of the three situations show a similar tendency of the nitrogen evolution process. For the convenience of discussion, the total nitrogen concentration curve at the monitoring point can be divided into three stages. In the first stage, when the leaking nitrogen gas diffuses to the monitoring point, the nitrogen concentration reaches about 85% with a highly increasing rate. It could be also found that the raise of the leakage rate leads to a faster increasing rate of this stage. This phenomenon is shown as the larger leakage rate curve has a higher slope in the first stage. In the second stage, due to the exhausting effect of the door, the nitrogen concentration starts to decrease. However, this exhausting effect would be weakened with the reduction in the pressure gradient. Thus, the nitrogen concentration shows an increasing trend in the third stage. It should be mentioned that the increase in the leakage rate would bring an earlier point of the initial stage. For instance, the initial point is about 75 s when the leakage rate is 4.6 kg/s. However, when the leakage rate decreases to 1.6 kg/s, the initial point is about 215 s. From Fig. 4(b), it could be found that the average concentration of nitrogen rises rapidly with the increase in leakage rate. The trend of the curves under three different leakage rates is very similar, mainly divided into two stages. The first stage is a rapid rise stage, and the second stage is a slow rise stage of concentration. This is because in the second stage, a portion of nitrogen begins to be removed from the outlet.

As shown in Fig. 5, which depicts the nitrogen concentration evolution contours, it can be observed that nitrogen initially accumulates in the vicinity of the leak point. As the nitrogen concentration increases, the gas gradually disperses further into the upper and central regions of the space, following the contours of obstacles and along the left wall. Notably, obstacles not only alter the direction of gas dispersion but also contribute to the formation of gas pockets in certain regions. These findings are consistent with trends reported in the relevant literature.57 When the nitrogen concentration reaches 84%, the oxygen content becomes lower, which would be harmful to human beings. Hence, the 84% nitrogen concentration is considered as a danger point within the analysis of nitrogen leakage. As shown in Fig. 4, the increase in the leakage rate leads to the dangerous point appearing at an earlier time. When the leakage rate is 1.6 kg/s, the danger point is reached at 244 s. However, when the leakage rate is 4.6 kg/s, the danger point is reached at 80 s. The N2 concentration contours under different leakage rates are shown in Fig. 6. As shown in Fig. 6, the model with different leakage rates shows an almost equal nitrogen distribution when the monitoring point reaches the dangerous point. This phenomenon indicates that the nitrogen distribution is related to the environmental structures instead of the leakage rate. The highest nitrogen concentration appears at the leakage point region, followed by the nitrogen concentration on the left and upper sides, and the nitrogen concentration is smaller in the right area.

FIG. 5.

Evolution of nitrogen concentration contours with a leakage rate of 2.3 kg/s.

FIG. 5.

Evolution of nitrogen concentration contours with a leakage rate of 2.3 kg/s.

Close modal
FIG. 6.

N2 concentration distribution at the dangerous time under different leakage rates.

FIG. 6.

N2 concentration distribution at the dangerous time under different leakage rates.

Close modal

According to Eq. (10), the gas diffusion efficiency is affected by the concentration gradient and the mass transfer distance. In this optimization work, to consider the hindering effect of obstacles, the corresponding distance is solved by the ant colony algorithm instead of using the straight-line distance. To give more clear insights, Fig. 7 shows the comparison of the distances obtained from the ant colony algorithm and the straight-line distance obtained from Eq. (13). For the convenience of discussion, five random points are selected to conduct the comparison in Fig. 7. The red line in Fig. 7(a) is the effective shortest path obtained by the ant colony algorithm, and the blue dashed line represents the straight-line path connecting two points. It can be observed from Fig. 7(a) that ant colony algorithm can effectively reflect the hindering effect brought by obstacles. It can be observed that the path planning obtained is largely consistent with the existing literature.37 The difference between the ant colony path and the straight-line path would be enlarged when the hindering effect is enhanced by more obstacles. Due to this reason, the path value obtained from the ant colony algorithm is higher than the straight-line one that could be observed in Fig. 7(b). Thus, the path value calculated by the ant colony algorithm is more reasonable to establish the fitness function in the GA optimization program.

FIG. 7.

A comparison of (a) the path and (b) the distance from the ant colony algorithm and the straight line.

FIG. 7.

A comparison of (a) the path and (b) the distance from the ant colony algorithm and the straight line.

Close modal

In the proposed coupling optimization method, the fitness function is related to the nitrogen concentration and the effective distance. The nitrogen concentration could be determined by the CFD simulation of the leakage diffusion, while the effective distance could be obtained by the ACO. The fitness value evolution curve with the iteration is shown in Fig. 8. As shown in Fig. 8, the fitness value decreases with iteration, which means the selection of the exhaust position reaches the optimal result gradually. The trend observed in the iteration curve obtained via the genetic algorithm aligns well with that reported in the literature.34 It can be seen from this figure that the fitness value reaches a stable state after the iteration number is 130. Consequently, the convergence of the proposed optimization solution could be ensured within 400 iterations. Actually, the selection of exhaust outlet quantity depends on the size of the building space. If the number of exhaust outlets is too few, the exhaust efficiency is hard to meet the requirements when a leakage occurs. Conversely, an excessive number of outlets may lead to unnecessary construction complexity and potential resource wastage. For this 40 × 40 m2 building space, the simulation observations have indicated that a range of 5 to 6 outlets installation could strike a balance between effective gas exhaust and resource utilization.58 The optimal arrangement of five exhaust outlets obtained from the proposed method is given in Fig. 9(a). To facilitate a more comprehensive comparison, we have included three additional models, namely “uniform layout 1,” “uniform layout 2,” and “uniform layout 3,” whose results are shown in Figs. 9(b)9(d).

FIG. 8.

Iteration curve of the genetic algorithm.

FIG. 8.

Iteration curve of the genetic algorithm.

Close modal
FIG. 9.

Layout of the model showing the overall arrangement: (a) optimized layout model, (b) uniform layout 1 model, (c) uniform layout 2 model, and (d) uniform layout 3 model.

FIG. 9.

Layout of the model showing the overall arrangement: (a) optimized layout model, (b) uniform layout 1 model, (c) uniform layout 2 model, and (d) uniform layout 3 model.

Close modal

The optimized locations are mainly concentrated at the neighbor region of the lower leakage point. As can be seen from Fig. 6, nitrogen diffusion in this building space is mainly transferred along the left side and the middle. The optimization results of the exhaust outlet arrangement are also concentrated in the nitrogen enrichment area, which also shows the rationality of the optimization results.

In order to validate the effectiveness of the optimization results, the nitrogen leakage and diffusion under different exhaust outlet arrangements are also simulated by the CFD model. As shown in Fig. 10, the nitrogen mass fraction curves at a leakage rate of 2.3 kg/s for all five scenarios are presented. Consistent with our previous findings, both uniform and optimal arrangements effectively reduce nitrogen concentration during the leakage process. However, as the leakage time progresses, the optimal layout exhibits a lower nitrogen concentration compared to the conventional uniform arrangements. This underscores the superiority of our proposed optimization method in removing leaking nitrogen. It could be found from Fig. 10 that nitrogen concentration is almost the same in the initial stage. This could be explained that nitrogen has not yet diffused from the leak point to the nearby exhaust outlet.

FIG. 10.

Mass fraction of N2 under different layouts.

FIG. 10.

Mass fraction of N2 under different layouts.

Close modal

For ease of comparison, we have extracted the nitrogen mass fractions at 250 s for all five layouts, as illustrated in Fig. 11. Notably, the nitrogen concentration under the optimal layout is 81.8%, whereas the concentrations for the three uniform layouts are 82.1%, 82.8%, and 82.3%, respectively. This further confirms the improved exhaust performance of our optimized layout.

FIG. 11.

Mass fraction of N2 at 250 s with a leakage rate of 2.3 kg/s under different layouts.

FIG. 11.

Mass fraction of N2 at 250 s with a leakage rate of 2.3 kg/s under different layouts.

Close modal

As shown in Figs. 12 and 13, the leaking nitrogen diffusion evolution trend is almost the same for the conventional uniform and optimal arrangements. The analysis of the diffusion evolution process of nitrogen leakage under uniform and optimal arrangements shows that the leaking nitrogen accumulates at the lower-left corner at the initial stage. Then, with the increase in nitrogen concentration at the leakage region, the nitrogen gas diffuses along to the top and central region. Finally, a small amount of leaking nitrogen gas would transfer to the right side along the lower side wall. However, compared with the conventional uniform configuration, leaking nitrogen can be effectively removed when it diffuses to the middle region under the optimal arrangement of the exhaust outlet. For convenience of observation and comparison, when comparing the optimal layout to the conventional uniform arrangements at 180 s, the nitrogen concentrations for the three uniform layouts are 81.2%, 81.6%, and 81.1%, respectively, whereas the optimal layout achieves a lower concentration of 80.5%. This comparison indicates that the optimal layout appears the best performance to remove the leaking nitrogen.

FIG. 12.

Nitrogen concentration contours with a leakage rate of 2.3 kg/s under optimal layout.

FIG. 12.

Nitrogen concentration contours with a leakage rate of 2.3 kg/s under optimal layout.

Close modal
FIG. 13.

Nitrogen concentration contours at time 180 s with a leakage rate of 2.3 kg/s under different layouts.

FIG. 13.

Nitrogen concentration contours at time 180 s with a leakage rate of 2.3 kg/s under different layouts.

Close modal

In this work, to handle the optimization of exhaust outlet arrangement, a novel optimization method is developed based on the coupling of the generic algorithm and ant colony algorithm. Both of these two methods are connected by an implicit fitness function. In addition, the CFD simulation is carried out to describe the gas diffusion behavior and give a validation of the optimization results. The main conclusions are summarized as follows:

  1. The CFD numerical simulation results prove that the proposed optimization method could give a better exhaust outlet arrangement, which results in a higher gas removal efficiency during the leakage process. The exhaust outlet arrangement following the optimization shows a lower gas concentration value compared with the conventional uniform arrangements.

  2. The ant colony algorithm could obtain a more accurate result of the effective path when the influence of obstacles in space needs to be considered. This provides a reliable fitness function value for the GA optimization and improves the rationality of the optimization results.

  3. It is discovered from the CFD simulation that the models with different leakage rates show an almost similar gas distribution. Due to this reason, the applicability of the proposed optimization method under different leakage rates is well validated and discussed.

Although the proposed coupling method could give a reliable optimization result for the exhaust outlet space arrangement, it still suffers from the large computational cost due to a large number of iterations. The iteration process should be optimized to reduce the iteration numbers and improve the solving efficiency in future studies.

The authors gratefully acknowledge the financial support of the basic research program of China Construction Third Bureau Group Co., Ltd. “Research on Background Control and Operation and Maintenance Support of Physical Test Facilities at the Frontier of Extremely Deep Underground Very Low Radiation Background for the Construction II Project of Jinping Large Facilities” (Grant No. 04042023ZH1929195) and thank Dr. Yehui Cui for his valuable opinions and suggestions during this paper writing process, which makes the paper more complete.

The authors have no conflicts to disclose.

Minglun Gao: Writing – original draft (equal). Shixiang Zhao: Supervision (equal); Writing – review & editing (equal). Xueke Ouyang: Conceptualization (equal); Software (equal). Jun Song: Investigation (equal). Yafen Pan: Investigation (equal). Zhongyu Wang: Investigation (equal). Xiangguo Zeng: Supervision (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
X.
Wang
,
X.
Zou
, and
W.
Gao
, “
Flammable gas leakage risk assessment for methanol to hydrogen refueling stations and liquid hydrogen refueling stations
,”
Int. J. Hydrogen Energy
54
,
1286
(
2023
).
2.
Y.
Xie
,
J.
Liu
,
Z.
Hao
,
Z.
Xu
,
J.
Qin
, and
J.
Zhu
, “
Numerical simulation and experimental study of gas diffusion in a ship engine room
,”
Ocean Eng.
271
,
113638
(
2023
).
3.
H.
Yu
,
Q.
Gao
,
L.
Pu
,
M.
Dai
, and
R.
Sun
, “
Numerical investigation on the characteristics of leakage and dispersion of cryogenic liquid oxygen in open environment
,”
Cryogenics
125
,
103514
(
2022
).
4.
L.
Jianfeng
,
Z.
Bin
,
W.
Yang
, and
L.
Mao
, “
The unfolding of ‘12.23’ Kaixian blowout accident in China
,”
Saf. Sci.
47
(
8
),
1107
1117
(
2009
).
5.
J.
Li
,
B.
Zhang
,
W.
Liu
, and
Z.
Tan
, “
Research on OREMS-based large-scale emergency evacuation using vehicles
,”
Process Saf. Environ. Prot.
89
(
5
),
300
309
(
2011
).
6.
C. P.
Lin
,
H. K.
Chang
,
Y. M.
Chang
,
S. W.
Chen
, and
C. M.
Shu
, “
Emergency response study for chemical releases in the high-tech industry in Taiwan—A semiconductor plant example
,”
Process Saf. Environ. Prot.
87
(
6
),
353
360
(
2009
).
7.
Y.
Tian
,
C.
Qin
,
Z.
Yang
, and
D.
Hao
, “
Numerical simulation study on the leakage and diffusion characteristics of high-pressure hydrogen gas in different spatial scenes
,”
Int. J. Hydrogen Energy
50
,
1335
1349
(
2024
).
8.
I.
Lee
and
M. C.
Lee
, “
A study on the optimal design of a ventilation system to prevent explosion due to hydrogen gas leakage in a fuel cell power generation facility
,”
Int. J. Hydrogen Energy
41
(
41
),
18663
18686
(
2016
).
9.
Z.
Xia
,
Z. D.
Xu
,
H.
Lu
,
H.
Peng
,
Z.
Xie
,
Y.
Jia
, and
H.
Sun
, “
Leakage analysis and prediction model of underground high-pressure natural gas pipeline considering box culvert protection
,”
Process Saf. Environ. Prot.
180
,
837
855
(
2023
).
10.
F.
Zeng
,
Z.
Jiang
,
D.
Zheng
,
M.
Si
, and
Y.
Wang
, “
Study on numerical simulation of leakage and diffusion law of parallel buried gas pipelines in tunnels
,”
Process Saf. Environ. Prot.
177
,
258
277
(
2023
).
11.
L.
Wang
,
J.
Chen
,
T.
Ma
,
R.
Ma
,
Y.
Bao
, and
Z.
Fan
, “
Numerical study of leakage characteristics of hydrogen-blended natural gas in buried pipelines
,”
Int. J. Hydrogen Energy
49
,
1166
1179
(
2024
).
12.
H.
Li
,
X.
Cao
,
H.
Du
,
L.
Teng
,
Y.
Shao
, and
J.
Bian
, “
Numerical simulation of leakage and diffusion distribution of natural gas and hydrogen mixtures in a closed container
,”
Int. J. Hydrogen Energy
47
(
84
),
35928
35939
(
2022
).
13.
Y.
Su
,
J.
Li
,
B.
Yu
, and
Y.
Zhao
, “
Numerical investigation on the leakage and diffusion characteristics of hydrogen-blended natural gas in a domestic kitchen
,”
Renewable Energy
189
,
899
916
(
2022
).
14.
A.
Liu
,
J.
Huang
,
Z.
Li
,
J.
Chen
,
X.
Huang
,
K.
Chen
, and
W. b.
Xu
, “
Numerical simulation and experiment on the law of urban natural gas leakage and diffusion for different building layouts
,”
J. Nat. Gas Sci. Eng.
54
,
1
10
(
2018
).
15.
J.
Yang
,
J.
Zhang
,
S.
Mei
,
D.
Liu
, and
F.
Zhao
, “
Numerical simulation of sudden gas pipeline leakage in urban block
,”
Energy Procedia
105
,
4921
4926
(
2017
).
16.
Q.
Yu
,
L.
Hou
,
Y.
Li
,
C.
Chai
,
J.
Liu
, and
K.
Yang
, “
Numerical study on harmful boundary of above-ground section leakage of natural gas pipeline
,”
J. Loss Prev. Process Ind.
80
,
104901
(
2022
).
17.
A.
Moghadam Dezfouli
,
M. R.
Saffarian
,
M.
Behbahani-Nejad
, and
M.
Changizian
, “
Experimental and numerical investigation on development of a method for measuring the rate of natural gas leakage
,”
J. Nat. Gas Sci. Eng.
104
,
104643
(
2022
).
18.
J.
Zhan
,
W.
He
, and
J.
Huang
, “
Comfort, carbon emissions, and cost of building envelope and photovoltaic arrangement optimization through a two-stage model
,”
Appl. Energy
356
,
122423
(
2024
).
19.
S.
Zhu
and
Y.
Li
, “
Sensitivity and optimization analysis of pillar arrangement on the thermal–hydraulic performance of vapor chamber
,”
Appl. Therm. Eng.
240
,
122246
(
2024
).
20.
Y.
Xie
,
T.
Uday
,
K.
Nutakki
,
D.
Wang
,
X.
Xu
,
Y.
Li
,
N.
Khan
,
A.
Deifalla
,
Y.
Elmasry
, and
R.
Chen
, “
Multi-objective optimization of a microchannel heat sink with a novel channel arrangement using artificial neural network and genetic algorithm
,”
Case Stud. Therm. Eng.
53
,
103938
(
2024
).
21.
Y.
Ma
,
Y.
Luo
,
C.
Zhong
,
W.
Yi
, and
J.
Wang
, “
Improved Hurst exponent based on genetic algorithm in schizophrenia EEG
,”
AIP Advances
13
(
12
),
125316
(
2023
).
22.
H. M.
Xie
,
D. Y.
Lei
,
Z. C.
Zhang
,
Y. Q.
Chen
,
Z. H.
He
, and
Y.
Liu
, “
Compact modeling of metal–oxide TFTs based on the Bayesian search-based artificial neural network and genetic algorithm
,”
AIP Adv.
13
(
8
),
085021
(
2023
).
23.
Y.
He
,
S.
Mao
,
J.
Chen
,
Y.
Yuan
,
H.
Chen
, and
Z.
Xu
, “
Optimizing speckles for dynamic objects using genetic algorithm in ghost imaging
,”
AIP Adv.
12
(
9
),
095012
(
2022
).
24.
S.
Hanaei
and
E.
Lakzian
, “
Numerical and experimental investigation of the effect of the optimal usage of pump as turbine instead of pressure-reducing valves on leakage reduction by genetic algorithm
,”
Energy Convers. Manage.
270
,
116253
(
2022
).
25.
J.
Yang
,
J.
Wu
,
X.
Yu
, and
Y.
Liang
, “
Study on fault identification rules for real refrigerant leakage in R290 room air conditioner based random forest algorithm
,”
Expert Syst. Appl.
238
,
122126
(
2024
).
26.
Y.
Xu
,
Z.
Wang
, and
Q.
Zhu
, “
An improved hybrid genetic algorithm for chemical plant layout optimization with novel non-overlapping and toxic gas dispersion constraints
,”
Chin. J. Chem. Eng.
21
(
4
),
412
419
(
2013
).
27.
A.
Kumar Bhargava
,
M.
Rani
, and
Sweta
, “
Optimal sizing and placement of capacitor on radial distribution system using genetic algorithm
,”
Mater. Today: Proc.
347
(
03
), (in press).
28.
J. Y.
Lok
,
W. H.
Tsai
, and
I. C.
Cheng
, “
A hybrid machine learning-genetic algorithm (ML-GA) model to predict optimal process parameters of nanoporous Cu for CO2 reduction
,”
Mater. Today Energy
36
,
101352
(
2023
).
29.
C.
Cenedese
,
M.
Cucuzzella
,
A. C.
Ramusino
,
D.
Spalenza
,
J.
Lygeros
, and
A.
Ferrara
, “
Optimal service station design for traffic mitigation via genetic algorithm and neural network
,”
IFAC-PapersOnLine
56
(
2
),
1528
1533
(
2023
).
30.
Y.
Zhou
and
N.
Huang
, “
Airport AGV path optimization model based on ant colony algorithm to optimize Dijkstra algorithm in urban systems
,”
Sustainable Comput.: Inf. Syst.
35
,
100716
(
2022
).
31.
C.
Miao
,
G.
Chen
,
C.
Yan
, and
Y.
Wu
, “
Path planning optimization of indoor mobile robot based on adaptive ant colony algorithm
,”
Comput. Ind. Eng.
156
,
107230
(
2021
).
32.
B.
Yang
,
L.
Wu
,
J.
Xiong
,
Y.
Zhang
, and
L.
Chen
, “
Location and path planning for urban emergency rescue by a hybrid clustering and ant colony algorithm approach
,”
Appl. Soft Comput.
147
,
110783
(
2023
).
33.
P.
Gao
,
L.
Zhou
,
X.
Zhao
, and
B.
Shao
, “
Research on ship collision avoidance path planning based on modified potential field ant colony algorithm
,”
Ocean Coastal Manage.
235
,
106482
(
2023
).
34.
Y. K.
Yi
,
M.
Anis
,
K.
Jang
, and
Y. J.
Kim
, “
Application of machine learning (ML) and genetic algorithm (GA) to optimize window wing wall design for natural ventilation
,”
J. Build. Eng.
68
,
106218
(
2023
).
35.
L.
Zhou
and
F.
Haghighat
, “
Optimization of ventilation system design and operation in office environment, Part I: Methodology
,”
Building Environ.
44
(
4
),
651
656
(
2009
).
36.
J. H.
Lee
, “
Optimization of indoor climate conditioning with passive and active methods using GA and CFD
,”
Building Environ.
42
(
9
),
3333
3340
(
2007
).
37.
L.
Xu
,
K.
Huang
,
J.
Liu
,
D.
Li
, and
Y. F.
Chen
, “
Intelligent planning of fire evacuation routes using an improved ant colony optimization algorithm
,”
J. Building Eng.
61
,
105208
(
2022
).
38.
Y.
Hajji
,
M.
Bouteraa
,
A. E.
Cafsi
,
A.
Belghith
,
P.
Bournot
, and
F.
Kallel
, “
Dispersion and behavior of hydrogen during a leak in a prismatic cavity
,”
Int. J. Hydrogen Energy
39
(
11
),
6111
6119
(
2014
).
39.
H. G.
Hussein
,
S.
Brennan
,
V.
Shentsov
,
D.
Makarov
, and
V.
Molkov
, “
Numerical validation of pressure peaking from an ignited hydrogen release in a laboratory-scale enclosure and application to a garage scenario
,”
Int. J. Hydrogen Energy
43
(
37
),
17954
17968
(
2018
).
40.
H. K.
Lo
,
E.
Chang
, and
Y. C.
Chan
, “
Dynamic network traffic control
,”
Transp. Res. A: Policy Pract.
35
(
8
),
721
744
(
2001
).
41.
S.
Katoch
,
S. S.
Chauhan
, and
V.
Kumar
, “
A review on genetic algorithm: Past, present, and future
,”
Multimedia Tools Appl.
80
,
8091
(
2021
).
42.
L.
Xue
,
X.
Zhao
,
H.
Li
,
J.
Zheng
,
X.
Lei
, and
X.
Gong
, “
Genetic algorithm-based parameter inversion and pipeline subsidence prediction
,”
J. Appl. Geophys.
215
,
105133
(
2023
).
43.
A.
Tiwari
,
N.
Kumar
, and
M. K.
Banerjee
, “
Applications of genetic algorithm in prediction of the best achievable combination of hardness and tensile strength for graphene reinforced magnesium alloy (AZ61) matrix composite
,”
Results Control Optim.
14
,
100334
(
2024
).
44.
T.
Borgonjon
and
B.
Maenhout
, “
A genetic algorithm for the personnel task rescheduling problem with time preemption
,”
Expert Syst. Appl.
238
,
121868
(
2024
).
45.
X.
Sun
,
W.
Shen
, and
B.
Vogel-Heuser
, “
A hybrid genetic algorithm for distributed hybrid blocking flowshop scheduling problem
,”
J. Manuf. Syst.
71
,
390
405
(
2023
).
46.
V.
Bertolini
,
F.
Corti
,
M.
Intravaia
,
A.
Reatti
, and
E.
Cardelli
, “
Optimizing power transfer in selective wireless charging systems: A genetic algorithm-based approach
,”
J. Magn. Magn. Mater.
587
,
171340
(
2023
).
47.
S.
Ebadinezhad
, “
DEACO: Adopting dynamic evaporation strategy to enhance ACO algorithm for the traveling salesman problem
,”
Eng. Appl. Artif. Intell.
92
,
103649
(
2020
).
48.
Ş.
Gülcü
,
M.
Mahi
,
Ö. K.
Baykan
, and
H.
Kodaz
, “
A parallel cooperative hybrid method based on ant colony optimization and 3-Opt algorithm for solving traveling salesman problem
,”
Soft Comput.
22
(
5
),
1669
1685
(
2018
).
49.
F.
Dahan
,
K.
El Hindi
,
H.
Mathkour
, and
H.
Alsalman
, “
Dynamic flying ant colony optimization (DFACO) for solving the traveling salesman problem
,”
Sensors
19
(
8
),
1837
(
2019
).
50.
S.
Chowdhury
,
M.
Marufuzzaman
,
H.
Tunc
,
L.
Bian
, and
W.
Bullington
, “
A modified ant colony optimization algorithm to solve a dynamic traveling salesman problem: A case study with drones for wildlife surveillance
,”
J. Comput. Des. Eng.
6
(
3
),
368
386
(
2019
).
51.
F.
Sui
,
X.
Tang
,
Z.
Dong
,
X.
Gan
,
P.
Luo
, and
J.
Sun
, “
ACO+PSO+A*: A bi-layer hybrid algorithm for multi-task path planning of an AUV
,”
Comput. Ind. Eng.
175
,
108905
(
2023
).
52.
K.
Dong
,
D.
Yang
,
J.
Sheng
,
W.
Zhang
, and
P.
Jing
, “
Dynamic planning method of evacuation route in dam-break flood scenario based on the ACO-GA hybrid algorithm
,”
Int. J. Disaster Risk Reduct.
100
,
104219
(
2024
).
53.
Y.
Jing
,
C.
Luo
, and
G.
Liu
, “
Multiobjective path optimization for autonomous land levelling operations based on an improved MOEA/D-ACO
,”
Comput. Electron. Agric.
197
,
106995
(
2022
).
54.
D.
Zhang
,
Y. b.
Yin
,
R.
Luo
, and
S. l.
Zou
, “
Hybrid IACO-A*-PSO optimization algorithm for solving multiobjective path planning problem of mobile robot in radioactive environment
,”
Prog. Nucl. Energy
159
,
104651
(
2023
).
55.
M.
Mavrovouniotis
,
S.
Yang
,
M.
Van
,
C.
Li
, and
M.
Polycarpou
, “
Ant colony optimization algorithms for dynamic optimization: A case study of the dynamic travelling salesperson problem [research Frontier]
,”
IEEE Comput. Intell. Mag.
15
(
1
),
52
63
(
2020
).
56.
M.
Dorigo
,
V.
Maniezzo
, and
A.
Colorni
, “
The ant system: An autocatalytic optimizing process
,”
TR91-016, Politec. Di Milano
, pp.
1
21
(
1991
).
57.
C. J.
Li
,
X. F.
Cai
,
M. Q.
Xiao
,
Y. G.
Huo
,
P.
Xu
,
S. F.
Li
, and
X. Y.
Cao
, “
Analysis on the influencing factors of radioactive tritium leakage and diffusion from an indoor high-pressure storage vessel
,”
Nucl. Sci. Tech.
33
(
12
),
151
(
2022
).
58.
M.
Siddiqui
,
S.
Jayanti
, and
T.
Swaminathan
, “
CFD analysis of dense gas dispersion in indoor environment for risk assessment and risk mitigation
,”
J. Hazard. Mater.
209–210
,
177
185
(
2012
).