1. Introduction
Air purification in polar enclosed vessel cabins has become a significant challenge, particularly during long-distance voyages with self-sustaining capabilities [1, 2]. The interior environment of these enclosed spaces is typically compromised by various pollution sources [3–5], including the volatilization of ship paint or oil [6], diesel combustion [7], human movement [8], cooking activities [9], and wall deposition [10]. These factors contribute to the accumulation of indoor aerosol contamination, which poses potential risks to both physical and mental health [11], including cardiovascular and pulmonary issues [12]. Ultrafine particles are particularly concerning, as they are linked to general health deterioration [13, 14] and can adversely affect the cardiovascular and respiratory systems [15].
Negative air ions (NAIs) have been demonstrated to reduce aerosol particle concentrations by charging the particles and enhancing their deposition [16, 17], improving air quality and benefiting human health [18–20]. Furthermore, air ionization plays a biologically and physiologically essential role [21], promoting blood oxygen levels [22], cognitive function [23, 24], respiratory health [25, 26], and alleviating physiological stress [27], depression [28–30], atypical seasonal affective disorder symptoms [31] and fatigue caused by muscle overload [32]. Nonetheless, some studies suggest potential negative effects, such as impacts on cardiac function [33] and respiratory symptoms [34].
Despite the promising potential of NAIs for improving indoor air quality [35, 36], current research exhibits two significant limitations. First, most studies focus on short-term, static conditions [25, 37–39], neglecting the dynamic equilibrium between continuous particle generation and ion-induced deposition in real-world operational environments. Second, although NAIs (4.0×102–1.0×106 ions/cm3) demonstrate excellent efficacy in removing specific particles (whose aerodynamic diameters are from 0.15 to 10 μm) [40–44], their performance under variable air circulation rates (3.0–12.0 AC/h) remains poor characteristics [45]. These gaps substantially limit the predictive accuracy for polar voyages where ventilation constraints are critical factors [46].
To address this research gap, this study introduces a transient numerical simulation that integrates aerosol transport, ionization dynamics, and airflow patterns, methodologically advancing beyond conventional steady-state approaches [47–49]. The model has been empirically validated using operational data from the “Xuelong” research vessel, successfully capturing ion-particle interactions across 16 cabins under varying particle concentrations. Furthermore, the negative-ion-enhanced particle removal efficiency is systematically evaluated in ten enclosed cabins of a polar icebreaker under different air circulation rates (3.0–12.0 AC/h). This investigation explores the particle removal effectiveness enhanced by NAIs during early design phases and retrofitting processes and provides essential theoretical calculations for ion-particle interactions in enclosed vessel cabins.
2. Numerical Simulation of Ion-particle Removal
2.1. Particle Removal Mechanisms
During the early stage of planet formation, aerosol particles are primarily charged by a diffusion charging mechanism [50]. The electrostatic force enables fine particles to overcome the bouncing barrier and forms large aggregates [51] such as flue-gas particles ranging from 0.01 to 10.0 μm [52], fine particles between 0.3 and 1.0 μm [53], or metallic particles from 0.35 to 0.6 μm [54]. Particles smaller than 1.0 μm may deposit more readily due to the electrostatic charge [55].
Fig. 1 illustrates the particle removal mechanisms in an enclosed vessel cabin. The removal mechanisms can be categorized into six groups: the air ventilation supplied into the cabin with filtered recirculated air and outdoor air [56–59], the interception by the high-efficiency particulate air (HEPA) filters [60, 61], the ion-enhanced particle recombination [62, 63], the diffusive deposition onto surfaces [64, 65], the gravitational deposition onto surfaces [66–69], and the electrostatic deposition caused by ion-induced electric fields [70].
2.3. Model Assumptions
The transient numerical model is established based on the principles of mass conservation for ions and particles, alongside the various mechanisms of particle removal. The model assumes that the air within enclosed cabins behaves as a fully mixed homogeneous system, characterized by isotropic and uniform spatial distributions of particle and ion concentrations [48, 71, 72]. In the numerical model, the particle-particle interaction is considered primarily through their influence on ion-particle combination processes, aerosol charge effects, and deposition mechanisms, rather than explicit particle-particle collision dynamics. Some dynamic environmental variables may significantly influence the ion-particle interaction processes [73]. It is assumed that both ventilation and thermal stability are adequately controlled and realized within vessel cabins, while the effects of air humidity on ion generation and particle recombination are excluded from consideration.
2.4. Model Description
Given a fully mixed space with a volume of V (m3) and a ventilation rate of Q (m3/h). The ion balance of both negative ion concentration n (ions/m3) and positive ion concentration p (ions/m3) can be described by considering the internal generation, the removal by opposite polarity and aerosol particles, the discharge by air ventilation, and the removal deposited onto surfaces. The balance equations for both NAIs and positive air ions [45, 57] can be expressed as
where n and p are negative ion concentration and positive ion concentration, ions/m3; t represents the service time, s; qn and qp denote the indoor generation rate of negative and positive ions, respectively, ions/(m3·s); α is the recombination rate of ions with opposite polarity, α ≈ 1.5 × 10−12 m3/s; β means the combination rate of ions with aerosol particles (particles/m3), β ≈ 1.0 – 2.0×10−12 m3/s; A represent the aerosol number concentration of large-size particles, respectively, particles/m3; no and po are the negative and positive ion concentrations entering the cabin from external environment, respectively, ions/m3; N is the air circulation rate per hour, AC/h; and λi denotes the ion removal rate from space onto surface due to electrostatic deposition, s−1.
The air circulation rate per hour N is defined as
where Q denotes the air ventilation flowrate, m3/h; and V means the cabin volume, m3.
In the presence of airborne ions, the constant ion removal rate from space onto the surface due to electrostatic deposition is calculated by
where b is the ion mobility, and b = 2.4×10−6 m2/(V·s) [74, 75]; ε0 represents the permittivity of free space, and ε0 = 8.854×10−12 C2/(N·m2); qe is the total ionic space charge density, C/m3; qc is the charge on the aerosol particles, -; e denotes the elementary charge, and e = 1.6×10−19 C; and B represents the number concentration of small-size particles, particles/m3.
The total ionic space charge qe is represented by
The charge on the aerosol particles qc [76] is calculated by
where dp means the particle diameter, m; k is the Boltzmann constant, and k =1.381×10−23 J/K; T denotes the absolute temperature, e.g. 300 K; c is the thermal speed of ions, e.g. 300 m/s; and t represents the average amount of time when the particle stays in the space, s.
Without indoor human activities, particles larger than 1.0 μm are primarily removed by gravitational deposition [56, 77, 78], whereas particles smaller than 1.0 μm are mainly removed by electrostatic deposition [53, 55, 79–81]. And thus, two concentration balance equations for large-size (>1.0 μm) and small-size (<1.0 μm) particles, can be expressed by the Eqs. (7) and (8), respectively.
where q is the generation rate of indoor aerosol particles, particles/(m3·s); Ao and Bo denote the aerosol particles entering cabin from outside, particles/s; λ means the aerosol particles removal rate deposited onto surface from space, s−1; Sp is the sticking probability which is defined as a ratio of the adhesion force between particles and surfaces, and the drag force acting on particles, −; vgp and vdp denote the deposition velocities of the gravity, and the Brownian and eddy diffusion [82], respectively, m/s.
For the small-size particles, the gravitational deposition could be neglected, and the diffusion deposition velocity is approximately a constant like (1.875 ± 0.187)×10−2 m/s [83]. For the large-size particles, the gravity deposition velocity increases with the enlarging particle diameters [84, 85].
The particles with large-size diameters usually exhibit poor electrostatic deposition and a short residence time in air aerosols. If the electrostatic interaction amongst particles is sufficiently small, the removal of static electricity can be disregarded, and λA=0.
The aerosol particle removal rate λB [86] due to the electric field is expressed by
where Dp and Di denote the diffusion coefficients of aerosol particles and airborne ions, respectively, Dp =1.3×10−10 m2/s and Di =1.0×10−7 m2/s [57].
The sticking probability or collision efficiency Sp [87] can be expressed by
where kd is the surface adhesion constant, m2/s2; Ea represents the surface activation energy of adhesion, J; vp,avg denotes the average of particle velocity, m/s; Ro is the gas constant, J/(mol·K); and Tsur is the surface temperature, K.
The surface adhesion constant kd and the surface adhesion activation energy Ea can be achieved from the experimental data [88]. The sticking probability usually exhibits linearly proportional to the particle diameters [89].
The baseline ratio between average mass concentration and number concentration [90] with the particle diameters dp >10 nm and dp>100 nm can be approximately estimated by
where np and mp represent average particle number concentration and mass particle concentration, respectively, particles/m3 and μg/m3.
For the situations with particle emission source, the particle removal efficiency ηA and ηB [20, 91] can be expressed by
where η represents the removal efficiency, %; A and B denote large-size particle concentration and small-size particle concentration, respectively, particles/m3; and the subscript 0 and t mean the initial time t=0 and the service time t.
For the situations with ionizers, the negative-ion-enhanced particle removal efficiency ηt is computed by
where represents the negative-ion-enhanced particle removal efficiency at the service time t, %; denotes the particle concentration at the service time t when the ionizer is turned off, particles/m3; and indicates the particle concentration at the service time t when the ionizer is running, particles/m3.
2.4. Solver of the Simulation Model
The pseudocode of the numerical simulation of ion-particle removal is illustrated in Table 1. A system of differential equations is created by combining Eqs. (1) and (2) with Eqs. (7) and (8). A medium-order method is employed to solve this system of four differential equations represented as . With respect to a single independent time variable t and include the derivatives of four dependent variables: negative ion concentration n, positive ion concentration p, large-size particle concentration A, and small-size particle concentration B.
As a versatile solver of ordinary differential equations, the MATLAB function ode45 is leveraged to solve the differential equation system from t=0 to t=n with initial conditions [n0, p0, A0, B0]. The function ode45 is implemented on the basis of an explicit Runge-Kutta (4,5) algorithm with the Dormand-Prince pair, incorporating a variable time step to enhance computational efficiency. The solver of the simulation model adequately describes the methodology used to solve the system of differential equations modeling the interaction between ions and particles in enclosed spaces. To ensure that the obtained solutions contribute to achieving the research objectives, several measures can be implemented to enhance the robustness and reliability of the model and solver. These measures include evaluating a range of operating conditions, adjusting hyperparameters, and addressing other relevant details (such as variable time steps).
For the range of operating conditions evaluated by the numerical simulation, the solver can provide robust solutions in each calculating loop. The ion-particle removal mechanisms are described by one equation with multiple initial conditions, which is subject to typical initial value problems. The solver is computed by starting from an initial condition y0, as well as a period of time (t0, tf), and the solution is obtained iteratively. At the first such step, the initial condition provides the necessary information that allows the integration to proceed. The final result is that the solver returns a vector of time steps t=[ t0, t1, t2, ..., tf ] as well as the corresponding solution at each step y=[y0, y1, y2, ..., yf ].
The solver hyperparameters are set to the default values, which also leverage the integration settings defined by the option. For example, use the AbsTol and RelTol options to specify absolute and relative error tolerances with 1×10−6 and 1×10−3, respectively.
In addition, the solver time step is based on the mass balance equations for both ions and particles that need to take the smallest step. For most of calculating loops, the variable time steps are in the range from 0.0025 to 1.0512 s. In this case, the solver can take small time steps like 0.0025 s to satisfy the mass balance equation for one initial condition. The other equations, if solved on their own, would leverage different step sizes. For the numerical simulation of ion-particle removal, the time step with 1 s is sufficient to represent the dynamic process of ion-particle interactions. Thus, the results obtained from the model could make sense to reveal the ion-particle removal mechanisms.
2.5. Model Validation
The numerical model is validated using experimental data from Fletcher et al. [43]. These data are collected in a climatically controlled 32 m3 test chamber (4.25×3.35×2.50 m). The chamber is equipped with a HEPA-filtered ventilation system (air circulation rate of 1.0–15.0 AC/h) and a WM 120 Aircare ionizer (Air Ion Technologies Limited, UK). The ionizer is installed 0.2 m from the rear wall along the chamber's central axis, with built-in fans ensuring proper air recirculation. For data acquisition, the experimental setup employed an Inti ITC-201A ion counter (Andes Electrical Corporation, Japan) with a high temporal resolution of 0.5 s sampling interval for ion concentration measurements, complemented by a Kanomax Geo-a laser particle counter (Optical Sciences, UK) that recorded particle concentrations in the 0.3–5.0 μm size range at 5-minute intervals. This comprehensive instrumentation provides robust validation data for the numerical model across multiple timescales and particle size distributions.
Iterative calibration of hyper parameters in the model (e.g., ion generation rate and outdoor ion concentration) is performed using experimental data from the literature [45] until high fidelity is achieved. The calibrated parameter assignments are listed in Table S1 in the supplementary materials.
As illustrated in Fig. 2, the validation identifies two ventilation-driven regimes. At low ventilation (3.0 AC/h), ion and particle concentrations increase over time, indicating insufficient air exchange to offset continuous particle generation and ion depletion. Higher ventilation rates (6.0–12.0 AC/h) produce exponential decay profiles, reflecting dynamic equilibrium described by concentration balance Eq. (7), where ventilation removal dominates for large particles (>1.0 μm) due to negligible gravitational settling (≈10−5 m/s). This explains the observed inverse proportionality between ventilation rate and steady-state particle concentration, with each doubling of ventilation roughly halving particle levels, consistent with first-order decay kinetics.
Simulations agree well with experiments at 3.0 and 6.0 AC/h, capturing generation, depletion, and ventilation-driven removal, but diverge at 12.0 AC/h. This discrepancy arises from: (a) increased turbulence and flow heterogeneity at high ventilation, invalidating the well-mixed assumption; (b) intensified nonlinear ion-particle interactions and recombination due to reduced residence times, poorly represented by linear kinetics; (c) overlooked removal mechanisms like turbulent impaction and electrostatic deposition that become significant at high ventilation; and (d) differences in temporal resolution between simulations and experiments affecting transient concentration profiles.
As the ventilation rates increase from 3.0 to 12.0 AC/h, the correlation coefficient for negative ion concentrations decreases from 0.842 to 0.020. A phenomenon is attributed to dynamic equilibrium effects under high ventilation rates. Particle concentration correlations remain above 0.709, confirming the model’s reliability in characterizing particle dynamics. This stronger correlation demonstrates the model’s effectiveness in representing the behavior of particles within 0.3–5.0 μm. The more detailed similarity between simulated and experimental data are illustrated in Table S2 in the supplementary materials.
To make sure the numerical simulations align with the actual processes in polar vessel cabins, the model is enhanced by the following three measures.
The fundamental physical mechanisms embedded in the model, encompass ion diffusion processes, ventilation removal dynamics, and ion-particle interactions. These mechanisms exhibit universal applicability across diverse enclosed environments.
The key numerical parameters such as the ventilation rate, temperature, and negative ion generation rate are obtained from the actual processes in polar vessel cabins. The details are listed in Sections 3.1, 4.2 and 5.2.
Moreover, the model incorporates a particle size-dependent removal mechanism, significantly improving its ability to simulate complex aerosol mixtures under real-world scenarios. The predictive accuracy in experimental conditions (as illustrated in Fig. 2 and Table S2), further underscores its robustness and adaptability. Consequently, it is well-suited for numerical simulations of negative-ion-enhanced particle removal in polar vessel cabins and other enclosed marine environments.
3. Discussion on Different Ion Generation Rate
3.1. Assignment of Model Parameters
To analyze the effectiveness of negative-ion-enhanced particle removal, the following assumptions are made for the model parameters to ensure that the numerical model can accurately reflect the actual processes inside the polar vessel cabins.
The generation rate qA of indoor aerosol particles larger than 1.0 μm is assigned as 1.0×105 particles/(m3·s), and the generation rate qB of indoor aerosol particles smaller than 1.0 μm is given as 1.0×107 particles/(m3·s). These values are based on field investigation on real-world vessels. The air dry-bulb temperature T is assumed to be constant at 295 K, which is in accordance with the standard air temperature in vessel cabins under winter conditions [92]. It is also consistent with the findings from Wu et al. [2], which shows that controlling the temperature at 22.5 °C can effectively reduce the concentrations of PM2.5 and PM10 in polluted rooms. The air circulation rate N is defined as 6.0 AC/h. This is determined based on the existing ventilation system design of the crew quarters on research vessels and the minimum ventilation rate required during long voyages [92]. The generation rates of indoor negative ion qn are defined as 2.0×108, 2.0×109, 2.0×1010, 2.0×1011, 2.0×1012 and 2.0×1013 ions/(m3·s). These values are statistically achieved from the nameplate performance indicators of common ionizers.
3.2. Negative Ion Concentration
Negative ion concentration varies against different generation rates of negative ion. In general, with the increasing negative ion generation, the negative ion concentration increases, while the time to fully charge the indoor air aerosol becomes short. As shown in Fig. S1(a) in the supplementary materials, when the generation rate is 2.0×108 ions/(m3·s), the negative ion concentration typically reaches around 3.6×1010 ions/m3 at the service time t=400 s. When the generation rate is 2.0×1013 ions/(m3·s), the negative ion concentration tends to be approximately 21.45×1012 ions/m3 at the service time t=5 s.
In general, the concentration of negative ions rises with the increasing negative ion generation rate, which enhances the electrical conductivity of the air. This enhancement facilitates the effective distribution of ions within the enclosed cabins, thereby increasing the likelihood of aerosol particles being charged and thus prone to be removed.
3.3. Particle Number Concentration
The indoor particle number concentrations decrease with the increasing generation rates of negative ions. As illustrated in Fig. S1(b) in the supplementary materials, at the service time t=1800 s, the generation rates of negative ions qn increase with a 10-fold growth rate from 2.0×108 to 2.0×1013 ions/(m3·s). The cabin particle number concentrations are 52.91×108, 46.82×108, 33.25×108, 15.98×108, 5.62×108 and 1.73×108 particles/m3, respectively.
As the generation rates of negative ions rise, the particle number concentrations tend to stabilize for shorter periods of time. When the generation rates are less than 2.0×1010 ions/(m3·s), it takes longer stabilizing time more than 600 s. When the generation rates are greater than 2.0×1011 ions/(m3·s), it takes less time than 400 s.
When the generation rates of negative ions are greater than 2.0×1010 ions/(m3·s), the variation curve of indoor particle number concentrations gradually flattens out and reaches relatively stable values at about 1200 s. Their concentrations are 16.5×108 particles/m3 for qn = 2.0×1011 ions/(m3·s), 5.81×108 particles/m3 for qn = 2.0×1012 ions/(m3·s), and 1.78×108 particles/m3 for qn = 2.0×1013 ions/(m3·s).
The findings above indicate that larger generation rates of negative ion contribute to higher removal efficiency of indoor aerosol particle pollutants. Additionally, the longer service time will bring a more significant removal effect of aerosol particle pollutants. The removal effects of aerosol particles under NAIs are the comprehensive interaction of multiple mechanisms. The small particle contaminants are continuously charged, condensed, and deposited over the service time. Once the previously formed smaller aerosol particles recombination, the older aerosol particles progressively grow larger. Throughout the whole process, the concentrations of both negative ions and particles tend to remain constant over a period of service time, despite the fact that they are continuously eliminated under the influence of the ion-particle interactions.
4. Case 1: A Scientific Research Vessel with Sixteen Cabins
4.1. Particle Concentration Level in Sixteen Cabins
The scientific research vessel “Xuelong” conducted two Antarctic voyages on the 31st (October to November 2014) and the 34th (February to April 2018). During these two trips, the PM2.5 concentrations in the various cabins ranged from 0.71 to 95.28 μg/m3, with an average of 13.91 μg/m3 [2]. This value is lower than the 24-hour limit of 15 μg/m3 but greater than the recommended annual limit of 5 μg/m3 [93]. Taken the Biological Lab A as an example, the particle number concentration is 2.16 ×106 particles/m3 for particles larger than 1.0 μm, 1.05 ×104 particles/m3 for particles greater than 5.0 μm, and 2.50 ×108 particles/m3 for particles smaller than 1.0 μm. More details about the particle number concentration is displayed in Table S3 in the supplementary materials.
The common air filters are utilized to intercept the particles larger than 1.0 μm, and the air ventilation plays an essential role in replacing the rest of the particles smaller than 1.0 μm. In this case, the air circulation rates N multiplied by the small-size particle number concentration B can be employed to approximately estimate the generation rate of particles smaller than 1.0 μm qB.
4.2. Definition of Model Parameters
In each cabin, the air circulation rate is defined as 6.0 AC/h, and the air dry-bulb temperature is assumed to be constant at 295 K, consistent with the model settings in Section 3. The ionizer presents the potential to 2.0×1010 ions/(m3·s) of negative ions. This generation rate can achieve a high efficiency of particle removal. It is assumed that no particles larger than 1.0 μm are transmitted into or generated within each cabin. The generation rate of particles smaller than 1.0 μm is determined through Eq. (16).
4.3. Results under Various Particle Generation Rates
4.3.1. Ion dynamics and system response
Fig. 3 summarizes the transient negative ion concentration, particle number concentration, and negative-ion-enhanced removal efficiency at the service time t=1800 s. As demonstrated in the analysis of Biological Lab A, the application of NAIs results in a significant reduction in particle concentration under elevated cabin concentrations, achieving a negative-ion-enhanced particle removal efficiency of 41.37%. This process exhibits two characteristic phenomena: (1) effective particle removal through ion-particle interactions, and (2) reduction of steady-state NAI concentration to 6.18×1011 ions/m3 due to ion-induced particle removal, markedly lower than in low-particle cabins (6.55×1011 ions/m3). These results establish a dynamic equilibrium between particle and NAI concentrations where high particle loading accelerates NAI depletion.
This observation aligns with the findings by Li et al. [94], who reported a negative correlation between NAI concentrations and air quality. Specifically, when particle concentrations are low and air quality is deemed good, the concentrations of NAIs are significantly higher than during conditions marked by high particle concentrations and poor air quality. The results suggest implementing real-time NAI monitoring to optimize removal efficiency via feedback control - for instance, automatically boosting ionizer output or adjusting ventilation rates when NAI levels fall below threshold concentrations (<6.2×1011 ions/m3).
The system's practical applications include: (1) establishing NAI-based control parameters for marine cabin air quality management, and (2) validating predictive “ ion-particle ” dynamic equilibrium models for purification performance.
4.3.2. Particulate removal performance characteristics
Fig. 3b documents consistent particle removal efficiencies of 38.24–41.37% across all test conditions, with Biological Lab A showing the most substantial absolute reduction from 45.30×108 to 26.56×108 particles/m3. The minimal efficiency variation (±1.6%) despite a twenty-fold range in initial particle concentrations (0.34×108 to 45.30×108 particles/m3) confirms system operation in an ion-saturated regime. This performance stability indicates that the removal process is fundamentally constrained by ion availability rather than particle concentration under the specified experimental conditions. The system's robust performance across diverse loading scenarios suggests particular suitability for marine environments where particle generation rates may fluctuate significantly during different operational phases.
4.3.3. Compliance with air quality standards
Fig. 4 illustrates the relationship between particle number concentrations and WHO limits in the sixteen cabins of the “Xuelong” vessel. By using Eq. (12), the WHO annual limit of 5 μg/m3 can be converted to 2.5 ×108 particles/m3 of particle number concentration, and the WHO 24-hour limit of 15 μg/m3 to 7.5 ×108 particles/m3. The particle number concentrations in all sixteen cabins were reduced under negative air ionization. Notably, the particle number concentration in Physical Lab C (PhyC) decreased from 10.43×108 particles/m3 to 6.24×108 particles/m3, shifting from exceeding the WHO 24-hour limit to exceeding the WHO annual limit. Additionally, three cabins, including Staff Quarter 1 (Staff1), the Lecture Hall (Lect), and the Physical Ocean Lab (Physi), showed an obvious improvement in concentration levels from exceeding the WHO annual limit to falling below the annual limit.
These results indicate that within a particle number concentration range of 2.5×108 to 4.05×108 particles/m3, the use of an ionizer with a generation rate of 2.0×1010 ions/(m3·s) effectively reduces indoor particle pollution levels below the WHO annual limit. For particle number concentrations ranging from 7.50×108 to 10.43×108 particles/m3, the ionizer can also effectively reduce pollution levels, and bring them below the WHO 24-hour limit. However, for particle number concentrations in the range of 4.73×108 to 7.50×108 particles/m3 or even up to 45.3×108 particles/m3, the negative ion with the generation rate of 2.0×1010 ions/(m3·s) exhibits effective reductions in particle concentration levels.
5. Case 2: A Polar Icebreaker with Ten Cabins
5.1. Description of Ten Cabins
The polar icebreaker is a four-story structure, each deck is 3.0 meters high, and the cabin clearance height is 2.1 meters. As listed in Table 2, ten cabins include four office rooms, two staff quarters, a lecture hall, a meeting room, and two restaurants. Each cabin gets its air supply from the top of the middle of the cabin, which is then recirculated upward around the top of the cabin. The supply air volume in each cabin is determined by the designed thermal load, and the air circulation rate is calculated by dividing the supply air volume by the cabin area.
5.2. Assignment of Model Parameters
In each cabin, the air circulation rate is obtained from the field data. Similar to the scientific research vessel “Xuelong”, the air dry-bulb temperature is supposed to remain constant at 295 K, and an ionizer is installed to produce negative ions of 2.0×1010 ions/(m3·s). No particles larger than 1.0 μm are flowed into or generated in each cabin, and the generation rate of particles smaller than 1.0 μm is defined as 6.0×105 particles/m3.
5.3. Results under Different Air Circulation Rates
5.3.1. Removal efficiency at standard circulation rate
As illustrated in Fig. 5, comprehensive analysis of three operational parameters - steady-state negative ion concentration, resultant particle concentration, and removal efficiency - revealed several critical aspects of system performance under varying ventilation conditions. The captain's cabin served as an exemplary case study for examining the fundamental relationship between air circulation rates and particle removal efficiency through NAIs. For the moderate air circulation rate of 6.15 AC/h, the system achieved optimal performance with 39.40% removal efficiency. This represents the most favorable balance between sufficient air exchange to maintain particle suspension and adequate residence time for effective ion-particle interactions through electrostatic attraction and agglomeration. The particle concentration reduction from 3.35×108 to 2.03×108 particles/m3 demonstrates significant air quality improvement while achieving compliance with WHO annual limits (2.50×108 particles/m3).
5.3.2. Efficiency-circulation rate relationship
Analysis revealed a well-defined inverse correlation between circulation rates and removal efficiency. Higher circulation rates (>9.35 AC/h) substantially diminished removal efficiency to 26.26–31.44% due to reduced particle residence time, which limits ion attachment probability. This effect was particularly pronounced at rates exceeding 10 AC/h, where rapid air exchange flushed out both particles and ions before complete neutralization. Conversely, lower circulation rates (5.12–6.15 AC/h) enhanced efficiency to 39.40–42.67% by extending interaction duration. The primary cause for this effect is that NAIs can drive particles to settle down more easily by accelerating their recombination process.
5.3.3. Ion concentration stability across operating conditions
The negative ion concentration maintained a stable 6.50×1011 ions/m3 across all tested circulation rates, confirming system operation in an ion-saturated regime. This stability indicates the ion generation rate of 2.0×1010 ions/(m3·s), sufficiently compensated for both ventilation losses and particle neutralization effects, even at 12.04 AC/h. The consistent ion concentration suggests system performance is primarily limited by particle dynamics rather than ion availability in this configuration.
5.3.4. Practical implications for marine applications
The identified optimal circulation range of 5–7 AC/h corresponds well with typical ship cabin conditions, enabling NAI implementation without major ventilation modifications. The stable performance across this range provides operational flexibility for temporary ventilation increases. The captain's cabin results (39.40% efficiency at 6.15 AC/h) establish a valuable benchmark for comparable marine environments, suggesting similar performance could be expected in spaces with equivalent size (3.5×4.2×2.1 m) and occupancy patterns.
Totally, the case studies of the scientific research vessel and the polar icebreaker provide compelling evidence of the efficiency of NAIs in enhancing air quality.
6. Conclusion
This study reveals the potential of NAIs in enhancing particle removal efficiency within enclosed spaces and explores their significant positive correlation. Based on actual operational data from the “Xuelong” research vessel and polar icebreakers, it can be found that the efficiency of particle removal exhibits a slight upward trend with increasing particle generation rates, while it presents a minor decline as air circulation rate increases. However, this study exhibits two potential limitations. Firstly, some environmental parameters such as humidity and temperature might be simplified to constant values in the model. Secondly, potential secondary effects such as ozone generation and static charge accumulation on insulating surfaces, require systematic assessment through more rigorous controlled experiments and field measurements. Future work will focus on the effect of thorough environmental parameters and secondary ionization on negative-ion-enhanced particle removal.
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