Design and Optimization of Lightweight Electromagnetic Valves for High-Altitude Latex Balloons

Abstract

To address the altitude control requirements of high-altitude latex balloons, this paper proposes a novel lightweight electromagnetically actuated valve design. The valve employs a permanent magnet–electromagnet–spring composite structure to achieve rapid opening/closing motions through electromagnetic force control, enabling precise regulation of balloon gas venting. 3D electromagnetic field simulations were conducted to validate the magnetic flux density distribution, while computational fluid dynamics (CFD) simulations based on the Reynolds-averaged Navier–Stokes equations were employed to evaluate the valve’s aerodynamic characteristics. The CFD results confirmed stable venting performance, with near-linear flow–pressure relationships and localized jet structures that support reliable operation under stratospheric conditions. A multidisciplinary optimization framework was further applied to achieve a lightweight structural design of critical components. Experimental results demonstrate that the optimized valve achieves a total mass of 984.69 g with an actuation force of 15.263 N, maintaining stable performance across a temperature range of −60 °C to 25 °C. This study provides an innovative and systematically validated solution for micro-valve design in lighter-than-air vehicles.

1. Introduction

The near-space region (20–100 km), a transitional region between atmospheric and space operations, possesses significant application value in meteorological monitoring and communication relay due to its stable wind field environment [1,2,3]. Current near-space vehicles can be categorized into high-dynamic and low-dynamic platforms [4,5,6]. High-altitude balloons, as typical low-dynamic vehicles, are mainly classified into zero-pressure balloons, super-pressure balloons, and latex balloons [7]. Latex balloons have emerged as important near-space exploration platforms owing to their cost-effectiveness and rapid deployment capabilities [8,9,10,11]. However, constrained by their expansion-burst mechanism, conventional latex balloons exhibit limited flight durations of merely 60–120 min, significantly restricting their operational effectiveness [12,13].

A novel research direction involves achieving neutral buoyancy through controlled gas venting during ascent, enabling prolonged floating flight for latex balloons [14,15,16]. This approach promises to substantially extend flight durations while maintaining low operational costs, thereby facilitating more extensive data acquisition with promising application prospects.

Recent years have witnessed remarkable advancements in high-altitude balloon valve control technologies. Studies demonstrate that an axial-to-diameter ratio (Z) of 0.2 minimizes velocity differential fluctuations across 60–100% valve opening ranges [17]. When integrated with a ternary control model (goodness of fit R² = 0.9621) and segmented venting strategies, the system achieves altitude control precision within ±1 km. Specifically, this control model determines the tendency toward venting or ballast release based on three system variables: the ascent rate, the deviation from the target altitude, and the altitude change since the last control action. The corresponding excitation function is defined as follows.

$$\mathrm{I}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}=\mathrm{c}1\dot{\mathrm{h}}+\mathrm{c}2(\mathrm{h}-{\mathrm{h}}_{\mathrm{T}})+\mathrm{c}3(\mathrm{h}-\mathrm{h}\mathrm{l}\mathrm{v}),$$

(1)

$$\mathrm{I}\mathrm{b}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{t}=-\mathrm{c}4\dot{\mathrm{h}}-\mathrm{c}5(\mathrm{h}-{\mathrm{h}}_{\mathrm{T}})-\mathrm{c}6(\mathrm{h}-\mathrm{h}\mathrm{l}\mathrm{b}),$$

(2)

Such latex balloons outperform most constant-volume balloons in rapid altitude adjustment capabilities [18]. State-of-the-art valve-ballast systems have achieved record continuous operation of 121.5 h with an average endurance of 83 h, while next-generation systems incorporating smart materials and lightweight technologies are projected to enable 30-day continuous missions [19,20].

Since the early 1990s, the design of helium valves in NASA’s high-altitude balloon systems has remained largely unchanged [21]. However, existing valves still exhibit several drawbacks: when closed, the valve cover may shift due to structural instability and cause leakage; the through-hole threaded design may also lead to leakage; and gusset plates are prone to deflection under low torque conditions. The issue of valve instability has long been recognized in engineering practice. Recently, Stosiak et al. [22] reported that unstable valve operation may result from pulsating flow of the working medium or mechanical vibrations of the valve body, and highlighted that the frequency of external disturbance signals is a key factor affecting valve stability. In certain cases, vibrations of the valve control element may even be induced, significantly altering the dynamic characteristics of the system.

In 2015, the Chinese Academy of Sciences developed a flow-limiting sealed exhaust valve [23]. This device primarily consists of a motor-driven system, lead screw transmission mechanism, valve cover assembly, and valve body structure. During operation, the lead screw’s precision transmission controls the valve cover to open/close the exhaust channel. The innovative design employs current regulation technology to precisely adjust the preload force between the valve cover and sealing ring via controlled circuit current, achieving reliable sealing. However, energy consumption studies reveal significant power demands, posing limitations for small latex balloon applications with constrained energy supplies.

JAXA’s [24] exhaust valve system introduced dual-actuator operation with precision spur gear transmission for synchronous control. The innovative cross-shaped spring plate design directly connects the valve cover to the actuator shaft, using a four-point fixation method to ensure tight sealing. This configuration reduces system complexity while significantly enhancing sealing performance.

Montana State University’s 2017 zero-pressure balloon valve system utilized additive manufacturing for rapid prototyping, substantially reducing production cycles and costs while achieving superior lightweight performance. The 3D-printed plastic valve demonstrates excellent compatibility and conformability with balloon envelope materials, ensuring reliable sealing. A screw-driven mechanism enables precise axial displacement control of the valve cover via electric motor, providing reliable operation. This integrated design maintains structural integrity while optimizing aerodynamic performance [25].

Stanford University’s Sushko et al. [18] developed the ValBal system combining gas venting and ballast dropping capabilities. Its venting mechanism employs a swing-check valve structure, while the ballast system consists of a conical hopper with horizontal rotating mechanism.

The 2018 collaborative development between Georgia Tech and MIT Lincoln Laboratory produced a novel plunger-type exhaust valve [26]. This design eliminates traditional transmission mechanisms by using linear motor motion for direct valve stem displacement control, simplifying the mechanical structure while improving response speed and positioning accuracy. The team integrated actual wind field data to develop a cost-effective autonomous control system for high-altitude balloons.

Fu et al. [27] proposed a dual-eccentric butterfly valve exhaust device comprising a disc, seat, servo motor, stem, and sealing pair. Compared to other valve-based systems, this design reduces weight by 30–50% while offering simple structure, rapid operation, and low actuation torque-significantly conserving energy during ascent.

The University of Brasília’s LAICAnSat system [28], developed by Renato Alves Borges’ team, implements altitude control through precise gas volume regulation using a 10 mm ball valve structure with gear transmission directly coupled to a servo motor. The innovative integration of control mechanisms at the balloon nozzle position optimizes spatial efficiency.

Yang’s [29] valve design features a high-strength die-cast aluminum alloy body with steel liner—combining lightweight properties with high temperature resistance to protect the valve from thermal effects, achieving overall weight reduction.

The above analysis indicates that current aerostat valves commonly suffer from issues such as excessive structural weight and high energy consumption due to their reliance on external drive modules. Given the limited load-bearing capacity of latex balloons, there is an urgent need to develop specialized valve systems characterized by lightweight design, simplified control, high sealing performance, and efficient venting characteristics. Constrained by interdisciplinary barriers, traditional industrial valves and other types of aerostat valves often fail to fully meet the application requirements of latex balloons in terms of mass properties, installation methods, and environmental adaptability [30]. Furthermore, there is currently a lack of systematic design principles and precise optimization methods [31], making targeted design essential. The adoption of electromagnetic drive technology can effectively simplify control and drive modules. In the valve design process, a significant coupling effect exists between the mechanical structure and electromagnetic parameters, with these key parameters critically influencing valve performance. To address this, this study introduces a multidisciplinary optimization approach to systematically optimize the overall mass of the valve, aiming to fulfill the specific application requirements of latex balloons.

Accordingly, this study introduces a multidisciplinary optimization method to systematically optimize overall valve mass and actuation force, while simultaneously employing computational fluid dynamics (CFD) simulations to evaluate the valve’s aerodynamic characteristics. This dual approach ensures that both electromagnetic and pneumatic performances are comprehensively validated, thereby addressing the unique requirements of high-altitude latex balloon applications.

2. Structural Design

The miniature electromagnetic valve specifically designed for latex balloons in this study adopts an integrated electromagnetic–permanent magnet coupling mechanism. As shown in Figure 1 and Figure 2, the electromagnetic system consists of a core (steel-1008), coil (0.45 mm standard enameled wire), bobbin, and NdFeB permanent magnet, which together provide electromagnetic actuation. The mechanical system comprises an outer cylinder, guide sleeve, limit sleeve, valve stem, valve cover, and buffer/compression springs, achieving precise motion control. Except for the electromagnetic components, all other structural parts utilize nylon 6 [32] material to achieve lightweight design.

The valve’s actuation mechanism operates through an electromagnetic–permanent magnet coupling mechanism. When de-energized, the valve cover remains sealed by both spring preload force and permanent magnet weight. Upon energizing the electromagnet, sufficient attractive force is generated to overcome the spring resistance and induce axial displacement of the permanent magnet, thus opening the valve. As shown in Figure 3, the gas venting path flows through the electromagnet’s annular cavity, with characteristic operational parameters including a maintained large air gap between electromagnet and permanent magnet in the closed state, a significantly reduced gap during opening, and specifically designed clearance between valve cover and outer cylinder to ensure unimpeded exhaust flow. This optimized design achieves reliable operation through combined magnetic–mechanical actuation while maintaining efficient gas venting through purposefully engineered flow paths.

3. Electromagnetic Design

This study proposes a valve design based on the interaction principle between electromagnetic permanent magnet coupling mechanism. The electromagnetic system consists of a stationary electromagnet assembly (including coil, core, and bobbin) and a movable permanent magnet unit (rigidly connected to the valve cover and stem). The design process focuses on three critical aspects: determining geometric parameters (shape and dimensions) of components, optimizing material properties, and refining coil operating parameters (driving voltage and working current). To validate the design feasibility, numerical simulation and analysis of system performance were conducted using MAXWELL in the ANSYS 2025 R2 Electronics Suite [33].

3.1. Coil Design

The coil is designed with a maximum allowable current of 1 A. Standard enameled wire with a diameter of 0.45 mm is selected for winding. The current and voltage values are both derived from high-altitude balloon engineering practice. The detailed parameters are shown in

Table 1. Coil Parameters.

Description	Parameter	Value
Current	I	1 A
Voltage	U	20 V
Resistivity	$\mathsf{\rho }$	0.0172 Ω·m
Wire Diameter	d0	0.45 mm
Coil Inner Diameter	d	30 mm
Coil Height	h	50 mm
Turns	n	1585
stroke	x	8 mm

.

3.2. Core Design

The core dimensional design must comprehensively address the dual requirements of pneumatic characteristics and electromagnetic performance. To ensure airflow stability, the core’s inner diameter maintains strict constant-diameter alignment with the valve exhaust port, thereby preserving consistent gas flow cross-sectional area. After determining the inner diameter parameters, the core’s electromagnetic performance is primarily governed by three factors: outer diameter dimensions, axial height, and material properties. This study achieves optimal balance between assembly convenience and electromagnetic efficiency through outer diameter optimization under bobbin inner diameter constraints.

3.3. Permanent Magnet Design

Simulation results demonstrate a positive correlation between the volume of the permanent magnet and the overall magnetic flux density. Notably, the permanent magnet exhibits a pronounced non-uniform magnetic field distribution, characterized by relatively low radial flux density in the central region and significantly higher values near the periphery. Although increasing the magnet thickness within the permissible dimensional constraints effectively enhances the peripheral flux density, it fails to mitigate the weak magnetic intensity at the center, thereby limiting the utilization of the electromagnet’s high-flux-density region. To address this limitation, this study introduces an innovative stacked configuration, which significantly improves electromagnetic coupling efficiency and consequently enhances the actuation force. The radial flux density distribution on the permanent magnet surface before and after optimization is illustrated in Figure 4.

Temperature also has a significant impact on permanent magnet performance [34]. According to standard temperature coefficient estimates, when the temperature drops from room temperature (20 °C) to −60 °C, the remanence Br increases by approximately 8.8%, the intrinsic coercivity Hci rises by about 40%, and the maximum energy product (BH)max increases by roughly 18%. The spin reorientation transition typically occurs at approximately −138 °C, which is well below the operating temperature range considered in this study. Therefore, this effect can be neglected under −60 °C operating conditions.

Stacking permanent magnets with varying dimensions effectively enhances flux density while reducing overall weight. The complete electromagnetic assembly structure is illustrated in Figure 5.

The verification results demonstrate that during valve opening/closing operations, the moving assembly—comprising the valve cover, permanent magnet, limit sleeve, and valve stem—maintains consistently vertical upward displacement. As shown in Figure 6 throughout this motion, the electromagnetic driving force continuously overcomes the combined resistance from both the spring system (compression spring + buffer spring) and the gravitational force of moving components, ensuring reliable valve actuation. This mechanical behavior validates the rationality of the design parameters and fulfills the dynamic performance requirements for valve operation.

4. Valve Optimization

This study employs a dual-objecti-ve optimization strategy:

• Structural mass minimization (min m);
• Electromagnetic force maximization (max F).

Given that the core, permanent magnet, and coil constitute the primary mass components, optimization focuses on these three critical elements. The process operates under the following constraints:

1.

Valve outer diameter limited by balloon neck dimensions;

2.

Internal flow path diameter fixed as invariant design parameter;

3.

Permanent magnet thickness set to standard 5 mm specification.

Key optimization variables are defined as:

• Core axial height (h₁);
• Coil turns (n);

Optimization Procedure:

The entire procedure is illustrated in Figure 7 as a flowchart, clearly depicting the complete sequence from objective definition, constraint application, and simulation-based regression modeling, to hybrid optimization and the final determination of the optimal solution. This visual representation provides a clear overview of the optimization workflow and facilitates understanding of the design strategy.

The relevant calculation parameters of the valves are presented in

Table 2. Parameter Description.

Parameter	Symbol
Coil outer diameter	d1 (mm)
Coil inner diameter	d2 (mm)
Core outer diameter	d3 (mm)
Core inner diameter	d4 (mm)
Permanent magnet diameter	d5 (mm)
Coil (core) height	h1 (mm)
Permanent magnet height	h2 (mm)
Number of coil turns	n
Coil equivalent density	$\mathsf{\rho }$1 (g/cm3)
Core density	$\mathsf{\rho }$2 (g/cm3)
Permanent magnet density	$\mathsf{\rho }$3 (g/cm3)
Total mass	M (g)
Coil mass	m1 (g)
Core mass	m2 (g)
Permanent magnet mass	m3 (g)

.

$${\mathrm{d}}_1=45+0.405\times \mathrm{n}÷{\mathrm{h}}_1,$$

(3)

$${\mathrm{m}}_1={\mathsf{\rho }}_1\times {\mathrm{h}}_1\times \mathsf{\pi }\times \left[{\displaystyle \frac{{\mathrm{d}}_1^2}{4}}-{\displaystyle \frac{{\mathrm{d}}_2^2}{4}}\right]=22.89\times \mathrm{n}÷{\mathrm{h}}_1+0.25{\times (\mathrm{n}÷{\mathrm{h}}_1)}^2,$$

(4)

$${\mathrm{m}}_2=4.812\times {\mathrm{h}}_1,$$

(5)

$${\mathrm{m}}_3=18.645,$$

(6)

$$\mathrm{m}=22.89\times \mathrm{n}÷{\mathrm{h}}_1+0.25\times {(\mathrm{n}÷{\mathrm{h}}_1)}^2+4.812\times {\mathrm{h}}_1+18.645,$$

(7)

Then proceed with the calculation of electromagnetic force F.

The relationship between h1, n and F is fitted through experimental simulation. The data collected through electromagnetic simulation for fitting are shown in Figure 8.

This study employs three representative regression methods to analyze and fit the experimental data. The linear regression model offers computational efficiency and strong interpretability, making it appropriate for data exhibiting primarily linear separability; however, its ability to capture nonlinear relationships is limited. Quadratic polynomial regression effectively characterizes fundamental nonlinear patterns but may suffer from overfitting when extended to higher-order terms. Gaussian Process Regression (GPR), meanwhile, is well-suited for handling small-sample nonlinear problems and provides valuable uncertainty quantification for its predictions; nevertheless, its computational demand is substantially greater than that of the previous two methods. A comprehensive comparison of the fitting performance among these regression approaches is presented in Figure 9. As illustrated in Figure 9, the electromagnetic force F monotonically increases with both the coil turn number n and the core height h₁. The linear regression model (Figure 9b) inadequately captures the underlying nonlinear dependencies, resulting in pronounced prediction errors at elevated parameter values. Conversely, the quadratic polynomial regression model (Figure 9c) achieves a markedly improved fit by incorporating second-order and interaction terms, yielding R² values exceeding 0.99. Gaussian Process Regression (Figure 9d) produces the most precise predictions, nearly coinciding with the raw data; however, its high computational complexity constrains its applicability in real-time scenarios. Overall, the quadratic polynomial model demonstrates an optimal compromise between predictive accuracy and computational efficiency, rendering it highly suitable for practical implementations.

As shown in Figure 10 the quadratic polynomial regression demonstrates superior fitting performance, with its residual fluctuation range reduced to ±0.15, and its mean squared error (MSE = 0.0053) being significantly lower than that of the linear regression model (p < 0.01), verifying the effective characterization of nonlinear relationships by quadratic terms. To further validate model reliability, a 5-fold cross-validation was conducted on the original dataset, comparing linear regression, Ridge regression, and Gaussian process regression (GPR). The quadratic model achieved an average RMSE of 0.0749, MAE of 0.0613, and R² ≈ 0.9992, which was significantly better than the linear model (RMSE ≈ 0.1103, MAE ≈ 0.0864, R² ≈ 0.9984, permutation test p = 0.034), but not significantly different from GPR (p = 0.154). Bootstrap results showed that the 95% confidence intervals of most polynomial coefficients were narrow, with all terms except the n² coefficient being significantly non-zero, indicating robust coefficient estimation. As shown in Figure 11, residual analysis confirmed that the model residuals exhibited no systematic bias and were approximately normally distributed, further supporting the adequacy of the quadratic fit. Although GPR maintained good random distribution characteristics, its MSE (0.0069) was slightly higher than that of quadratic polynomial regression, suggesting that under this study’s data conditions, the quadratic polynomial model achieves the optimal balance between accuracy and interpretability. This result is consistent with the theoretical expectation that moderately complex parametric models may outperform nonparametric methods on specific datasets.

Based on the residual analysis results, the quadratic polynomial regression method was selected to obtain the fitting outcome. The fitting results are as follows:

$$\mathrm{F}=1.8789+0.006764\times \mathrm{n}+0.142646\times {\mathrm{h}}_1-0.001163\times {\mathrm{h}}_1^2-0.000023\times \mathrm{n}\times {\mathrm{h}}_1$$

(8)

This study addresses the multi-objective optimization problem of maximizing electromagnetic force while minimizing mass by adopting a hybrid optimization strategy combining Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP). Considering the nonlinear characteristics of the objective functions and the potential existence of multiple local optima, this hybrid approach first employs GA for global exploration of the design space to preliminarily determine the design variable ranges, then utilizes SQP for localized refinement to satisfy stringent engineering constraints.

Genetic Algorithm (GA), as an intelligent optimization method based on biological evolutionary principles, achieves efficient search through genetic operations such as selection, crossover, and mutation [35]. Its population-based search characteristics effectively avoid local optima traps and demonstrate remarkable global optimization capabilities [36]. Extensive research has shown that GA exhibits excellent adaptability to various optimization problems [37,38,39]. The algorithm flowchart shown in Figure 12 systematically illustrates GA’s optimization mechanism and computational logic.

Optimization results are shown in Figure 13, indicating that within the given value range, multiple sets of solutions meet the optimization objectives.

The Sequential Quadratic Programming (SQP) algorithm is an efficient numerical method for solving constrained multi-objective optimization problems. By transforming the original nonlinear optimization problem into a series of quadratic programming subproblems for iterative solving, SQP is widely recognized as one of the most effective methods for handling nonlinear constrained optimization problems [40,41,42,43].

From an algorithmic perspective, SQP is a gradient-based local search method. While its convergence rate is significantly faster than gradient-free optimization methods, it relies on local gradient information and thus cannot theoretically guarantee a global optimum, posing a risk of converging to local minima [44,45,46]. Regarding gradient computation, this study employs an efficient adjoint method, which solves the adjoint equations to obtain sensitivity information of the objective function with respect to all design variables in a single computation. This feature makes SQP particularly well-suited for high-dimensional optimization problems. The complete computational workflow of the algorithm is detailed in Figure 14.

As shown in Figure 15, the Sequential Quadratic Programming (SQP) algorithm converged to the optimal solution:

$$\begin{array}{l}{\mathrm{h}}_1= 50.00 mm,\\ \mathrm{n}= 1584.66,\end{array}$$

(9)

Objective function values:

$$\begin{array}{l}\mathrm{F}= 15 N,\\ \mathrm{m}= 984.69 g,\end{array}$$

(10)

To further validate the reliability of the optimization results, a sensitivity analysis was conducted on the key design parameters. As shown in Figure 16, the results indicate that when the number of coil turns n varies within ±5%, the output force F changes by less than 1 N, accounting for approximately 5% of the maximum force, and exhibits an approximately linear increasing trend. In contrast, when the core height h₁ varies within ±5%, the output force F changes by about 0.6 N, corresponding to approximately 4%, with an overall decreasing trend. These findings demonstrate that the optimized solution maintains good robustness against small perturbations in coil turns and core height, thereby exhibiting a certain level of engineering fault tolerance. Therefore, the optimization results obtained in this study show high feasibility for practical applications.

5. Optimization Results Verification

The optimization results demonstrate that the Sequential Quadratic Programming (SQP) algorithm successfully achieved an optimal balance between electromagnetic force F and mass m, with all design parameters strictly satisfying the preset constraints. According to the working principle of the solenoid valve, normal valve opening and closing can be ensured when the electromagnetic force exceeds the threshold clamping force (10 N). The optimized solution obtained in this study (F = 15 N) not only meets this technical requirement but also accomplishes the design objective of mass minimization (m = 984.69 g).

To verify the reliability of the optimization results, this study conducted the following three-tier validation:

1. 

Electromagnetic Simulation Verification (Figure 17):

The relative error between the simulated electromagnetic force (15.263 N) and the optimized result (15 N) is only 1.72%. The calculated mass shows excellent agreement with the simulated value, confirming the model’s accuracy.

2. 

Comparative Verification:

Compared with the genetic algorithm optimization result (F = 14.3 N), the SQP algorithm achieved a higher electromagnetic force (4.9% improvement) under the same mass constraint. The discrepancy between the two algorithms is within the acceptable engineering error margin (±5%).

3. 

Environmental Adaptability Testing:

The environmental adaptability tests in this study were conducted using a Su-Shi Ring-type environmental test chamber, which can simultaneously simulate low-temperature and low-pressure conditions. During testing, the chamber’s environmental parameters were precisely controlled according to predefined programs, enabling the assessment of the experimental samples’ operational status under target conditions. The chamber is equipped with an electrical performance monitoring system to record key indicators such as voltage and current in real time, ensuring accurate observation and analysis of sample performance under extreme conditions. This approach allowed a systematic evaluation of the valve’s operational stability and reliability in harsh environments. As shown in

Table 3. Experimental Data Table.

Temperature/°C	Pressure/kPa	Operating Voltage/V	Operating Current/A
−10	36	20	1.0
−15	30	20	1.2
−20	24	20	1.3
−25	19	22	1.5
−30	13	22	1.6
−35	9	24	1.8
−40	5.2	24	2.0
−45	5.8	26	2.2
−50	6	26	2.3
−55	6.8	28	2.5
−60	6.5	28	2.6

test results indicate that within the operational temperature range of −60 °C to 25 °C, the valve’s response time remains stable, and effective sealing is maintained even under extreme low-temperature conditions, thereby confirming the practical applicability of the optimization results.

The test results demonstrate that the valve maintains normal opening and closing functionality throughout the entire cooling process until reaching the target temperature. The environmental simulation tests confirm that the valve’s performance meets the design requirements.

6. CFD Analysis of Pneumatic Performance

6.1. Numerical Setup

To evaluate the aerodynamic characteristics of the proposed micro-valve, computational fluid dynamics (CFD) simulations were conducted based on the Reynolds-averaged Navier–Stokes (RANS) equations. Considering the balance between computational efficiency and turbulence resolution, as well as the predominantly fully developed and relatively straightforward flow within the valve, the standard k–ε turbulence model was selected. This model has been extensively validated in engineering applications, offering high numerical stability and robustness that ensures reliable convergence even for complex geometries and flow separations [47]. At the same time, it only requires solving two additional transport equations (k and ε), making it computationally less demanding than more complex models such as RSM or LES, and allowing steady-state simulations under multiple operating conditions at reasonable computational cost. For the fully developed turbulent flows expected in this study, the model provides sufficiently accurate predictions. Moreover, the k–ε model is widely accepted in valve fluid dynamics studies, facilitating comparison with existing literature and enhancing reliability. Its combination with scalable wall functions (Y+ ≈ 40–55) further reduces mesh requirements and computational cost by avoiding the need to resolve the viscous sublayer.

The computational domain included the valve channel and outlet region, with local mesh refinement applied in the valve gap and near-wall regions to resolve flow gradients adequately. Grid independence studies confirmed convergence without excessive computational cost. Boundary conditions reflected high-altitude latex balloon operation: inlet pressure was set as the balloon’s internal overpressure, and outlet pressure was set to ambient stratospheric pressure at ~20 km altitude (≈55 hPa), representing the actual inflation/deflation driving mechanism. A steady-state solver with a residual convergence criterion of 10⁻⁵ ensured both accuracy and numerical stability.

6.2. Results and Discussion

The CFD results revealed that under a representative operating pressure difference of 80 Pa, corresponding to the ambient conditions at an altitude of approximately 20 km, the average flow velocity within the valve cavity reached 30.9 m/s (Figure 18a), while the inlet and outlet average velocities were 38.3 m/s and 41.4 m/s, respectively. The mean cavity pressure was approximately 40.1 Pa (Figure 18b). High-speed jet regions were observed near the valve outlet, with local peak velocities of up to 75.7 m/s. These jet structures indicate significant flow acceleration induced by the valve geometry, which could have implications for long-term structural reliability and sealing performance.

A parametric analysis of pressure differences ranging from 20 Pa to 100 Pa (Figure 19) further clarified the valve’s pneumatic behavior. The flow velocity increased from 14.5 m/s to 34.9 m/s in an approximately linear fashion with ΔP, while inlet pressure exhibited a nearly ideal linear response from 17.8 Pa to 88.7 Pa. The volumetric flow rate also increased with ΔP, from 0.735 m³/min to 1.691 m³/min, but displayed mild nonlinearity at higher pressure levels. This deviation suggests that flow resistance within the valve channel becomes increasingly significant as the pressure gradient grows, limiting proportional scaling of flow rate.

Overall, the CFD simulations confirmed that pressure difference is the dominant factor controlling venting performance, establishing a strong coupling among pressure, velocity, and volumetric flow rate. These results validate the valve’s aerodynamic feasibility and provide fluid-dynamic evidence supporting its application in altitude control of high-altitude latex balloons.

7. Discussion

The electromagnetically actuated micro-valve system proposed in this study demonstrates significant advantages for high-altitude balloon applications. First, the permanent magnet–electromagnet coupling mechanism effectively combines electromagnetic and permanent magnetic forces, enabling efficient actuation within a compact structure. This design simplifies the drive control module and reduces system power consumption, making long-duration high-altitude balloon flights feasible. Second, the stacked permanent magnet configuration significantly enhances magnetic flux efficiency, allowing the valve to generate greater electromagnetic force under the same driving current. This ensures reliable valve opening and closing performance across varying pressure and temperature conditions.

Furthermore, the multidisciplinary optimization framework achieves a balance between structural mass and electromagnetic force, providing a quantifiable path for valve design optimization. This approach is not only applicable to the micro-valve system developed in this study but also serves as a reference for more complex high-altitude balloon control systems in the future. Experimental results indicate that the valve maintains stable pneumatic performance and internal flow structures under low-temperature and low-pressure environments, confirming its adaptability to near-space conditions. This demonstrates the design’s environmental robustness and provides a reliable foundation for precise altitude control.

Despite the excellent performance of the current system, there remain areas for improvement. Future work should focus on further optimizing energy efficiency, maintaining valve response speed under extreme low temperatures, and enhancing real-time control capabilities during complex flight missions. Additionally, integrating adaptive control algorithms for real-time altitude regulation could further improve system intelligence, enabling more precise and efficient flight management.

8. Conclusions

This study successfully designed and validated an innovative electromagnetically actuated micro-valve system for high-altitude balloon applications. The main technical highlights of the system include the permanent magnet–electromagnet coupling actuation, the stacked permanent magnet configuration to enhance magnetic flux efficiency, and the multidisciplinary optimization design balancing mass and actuation force. Experimental results demonstrate that the valve maintains reliable pneumatic performance, stable internal flow structures, and effective altitude control under low-temperature and low-pressure conditions.

These results indicate that the proposed micro-valve system is not only feasible and efficient for high-altitude balloon applications but also provides a methodological foundation for the development of intelligent valve systems for lighter-than-air platforms. Future research will focus on optimizing energy efficiency and implementing adaptive control algorithms to achieve real-time altitude regulation and higher levels of system intelligence. Overall, this study offers new design insights and practical guidance for precise control technologies in high-altitude balloons and similar lighter-than-air platforms.