Model Calculations Research Articles

Modeling and Performance Analysis of Variable Cycle Engine with Ceramic Matrix Composite Turbine Blades

To meet the requirements of future aircraft for power systems, the turbine inlet temperatures of aero engines are gradually increasing. Ceramic matrix composite (CMC), with its higher thermal limit, has become the preferred material for the turbine blades of variable cycle engines (VCEs). However, the impact of CMC turbine blades on the performance of a VCE is still unknown. In this research project, the comprehensive cooling-efficiency characteristics of CMC are determined through a fluid–solid coupling calculation; a cooling calculation model for turbine blades is established, and cooling airflow solution and control technology (CSCT) for an air system is developed. Additionally, a VCE simulation model is established to analyze the influence of CMC turbine blades on the cooling airflow of the air system and the overall performance of the engine. The results show that, for the design condition, the CMC turbine blade can reduce the cooling airflow of the air system by approximately 10%, and the net thrust is increased by 6.07–7.98%. For the off-design conditions, with the CSCT, the specific fuel consumption can be reduced by 3.06–5.73% while ensuring that the engine net thrust remains unchanged. A comprehensive analysis of the performance for both the design point and off-design points indicates that the use of CMC for high-pressure turbine (HPT) guide vanes and rotor blades yields significant performance benefits, while the performance improvement from the use of CMC for low-pressure turbine (LPT) rotor blades is minimal.

A 3D DEM modeling of soil-rock mixture considering spatial distribution orientation of blocks

Spatial distribution orientations of blocks can cause significant errors in the discrete element model (DEM) calculation of soil-rock mixture (SRM). To avoid this error, spherical harmonic (SH) series whose harmonization degrees fixed at 15 were proposed for block reconstruction. This research refers to the case-history of a deep excavation rift valley spanning from the Mabian to Zhaojue section of the Leshan-Xichang Expressway, mainly containing moderately-weathered silty mudstone, in the Leshan City, Sichuan Province, China. The appropriate degree of finite-term SH series is selected by the volume, surface area. 100 blocks were scanned on site, and sphericity and angularity of the blocks were calculated. The sphericity and angularity of 50 reconstructed blocks were considered for the error analysis of SH method. Moreover, stochastic polyhedron method was considered for comparing different block reconstructions. The maximum block placement angle was defined to control the spatial distribution orientations of the blocks. Large scale direct tests were carried. Numerical simulations of large-scale direct shear tests were conducted to study the influence of the spatial distribution orientations of the blocks on the mechanical properties of the SRMs. The results revealed that the finite-term SH series fixed at 15 accurately reflected the shape characteristics and mechanical behaviors of actual blocks. The spatial distribution orientations of the blocks had a minimal impact on the friction angle and cohesion of SRM constructed through the SH method. The SRMs developed via the SH method exhibited marginal variations in contact force and anisotropy index of contact across diverse block placement strategies. The evolution of coordination number was closer when employing the SH method under varied block placement methods. Blocks reconstructed by the SH method, could mitigate errors in DEM calculation caused by the spatial distribution orientations of the blocks.

High‐precision numerical simulation method for thermal–mechanical coupling in rubbers

AbstractImproving the precision of numerical simulations in thermal–mechanical coupling for amorphous polymer materials is crucial for their effective utilization. To enhance the precision of rubber numerical simulations, this study proposed a method considering the temperature and strain rate to establish tensile testing conditions based on the principle of time–temperature equivalence. Additionally, to obtain more precise parameters for hyperelastic constitutive equations, stress relaxation experiments were conducted to determine a set of stress values under complete rubber stress relaxation, which were used to fit the hyperelastic components of the hyper‐viscoelastic algorithm. A finite element model of rubber rebound was established, and a hyperelastic model based on loss factor and a hyperelastic model based on Prony series (hyper‐viscoelastic) were used to calculate the temperature changes caused by rubber rebound coefficient and energy dissipation during the rebound process at 110, 120, and 130°C. We compared the calculation results of these two algorithms with experimental data to verify their accuracy. The research results show that the average error of the rebound coefficient of the hyperelastic algorithm at three temperatures is 3.63%, and the average error of the rebound coefficient of the hyper‐viscoelastic algorithm at these three temperatures is 0.93%. The comparison with the rebound test results shows that the hyper‐viscoelastic method is more accurate and better captures the viscoelastic hysteresis of rubber, but the model calculation time is longer. In addition, at the moment of rebound sample impact, the maximum temperature rise amplitude of the hyperelastic algorithm sample impact position is 2.60, 1.75, and 0.91°C, which are 110, 120, and 130°C, respectively; The maximum heating amplitudes of the hyper‐viscoelastic algorithm are 2.05, 1.35, and 0.61°C. The hyper‐viscoelastic algorithm is closer to the actual test results.Highlights Applied the principle of time–temperature equivalence. Determination of material parameters using the hyper‐viscoelastic algorithm. Calculated the temperature change during the rubber rebound process.

Contribution of Protonation to the Dielectric Relaxation Arising from Bacteriopheophytin Reductions in the Photosynthetic Reaction Centers of Rhodobacter sphaeroides

The pH dependence of the free energy level of the flash-induced primary charge pair P+IA− was determined by a combination of the results from the indirect charge recombination of P+QA− and from the delayed fluorescence of the excited dimer (P*) in the reaction center of the photosynthetic bacterium Rhodobacter sphaeroides, where the native ubiquinone at the primary quinone binding site QA was replaced by low-potential anthraquinone (AQ) derivatives. The following observations were made: (1) The free energy state of P+IA− was pH independent below pH 10 (–370 ± 10 meV relative to that of the excited dimer P*) and showed a remarkable decrease (about 20 meV/pH unit) above pH 10. A part of the dielectric relaxation of the P+IA− charge pair that is not insignificant (about 120 meV) should come from protonation-related changes. (2) The single exponential decay character of the kinetics proves that the protonated/unprotonated P+IA− and P+QA− states are in equilibria and the rate constants of protonation konH +koffH are much larger than those of the charge back reaction kback ~103 s−1. (3) Highly similar pH profiles were measured to determine the free energy states of P+QA− and P+IA−, indicating that the same acidic cluster at around QB should respond to both anionic species. This was supported by model calculations based on anticooperative proton distribution in the cluster with key residues of GluL212, AspL213, AspM17, and GluH173, and the effect of the polarization of the aqueous phase on electrostatic interactions. The larger distance of IA− from the cluster (25.2 Å) compared to that of QA− (14.5 Å) is compensated by a smaller effective dielectric constant (6.5 ± 0.5 and 10.0 ± 0.5, respectively). (4) The P* → P+QA− and IA−QA → IAQA− electron transfers are enthalpy-driven reactions with the exemption of very large (>60%) or negligible entropic contributions in cases of substitution by 2,3-dimethyl-AQ or 1-chloro-AQ, respectively. The possible structural consequences are discussed.

Melt Characteristics of a Deposited Layer on Rail Surface under Different Contact Models for Electromagnetic Launching

Understanding the melting of the deposited layer is crucial for the armature’s melting process and sliding electrical contact performance. This study first establishes contact models for both the boundary lubrication state (BLS) and squeezed-film lubrication state (SFLS). A three-dimensional magnetic diffusion model is then constructed to simulate interface current distribution in these contact states. It is discovered that the maximum current density on the surface of the armature shows a decreasing trend as the thickness of the deposited layer grows. Then, a calculation model for the deposited layer’s melting thickness under BLS is developed. For SFLS, Reynolds and energy equations are used to construct models for liquid film thickness and the deposited layer’s melting thickness. The results indicate that the deposited layer’s melting thickness under BLS is significantly greater than that under SFLS. Specifically, the melting thickness decreases with launching displacement in BLS and increases under SFLS. In SFLS, the deposited layer’s melting can suppress armature melting, though it remains nearly equivalent to that observed with polished rail. These findings provide a foundation for deposited layer control technology, which is essential for enhancing sliding electric contact performance and launching efficiency.

Determination of PAH Contamination in Breast Milk Samples from Hungarian Volunteering Mothers, Using HPLC–FLD

(1) The evidence is mounting that polycyclic aromatic hydrocarbons (PAHs) are a class of hazardous organic compounds with established carcinogenic and toxic properties. Humans may be exposed to PAHs through several different routes, including diet, inhalation, and dermal contact. There is also a possibility that they could transfer into breast milk following maternal exposure, which could potentially endanger breastfeeding infants. (2) The objective of this study was to ascertain the concentration of polycyclic aromatic hydrocarbons (PAHs) in breast milk samples from 50 Hungarian mothers, employing high-performance liquid chromatography with fluorescence detection (HPLC–FLD). An Incremental Life Risk Calculation (IRCL) model estimated the carcinogenic risk to infants. (3) Total PAH concentrations ranged from 0 to 78 ng/mL, with fluorene (5.3 ng/mL), phenanthrene (3.2 ng/mL), and pyrene (2.5 ng/mL) being the most abundant. PAHs were detected in 48 of the 50 samples, with phenanthrene present in 92% of samples. Dibenzo (a,h)anthracene was not detected. (4) According to the model measurements, most of the samples were within acceptable risk levels; however, 2 samples out of 50 posed a higher risk. Statistical analysis of questionnaires completed by the mothers indicated that factors such as diet, residence, and education may influence PAH levels in breast milk.

Математична модель камери згоряння газотурбінного двигуна, який працює на етанолі

Ethanol is one of the most promising alternative fuels for Ukraine. To convert existing projects of power and cogeneration plants based on gas turbine engines (GTEs) operating on petroleum products and natural gas to ethanol, as well as for their design and performance calculation, it is necessary to have a mathematical model of the working process of GTE combustor. The object of the study is the working process of the GTE combustor fueling on ethanol. The subject of the study is a mathematical model of the working process of GTE combustor fueling on ethanol. The work aims to improve a mathematical model of the working process of a GTE combustor fueling on ethanol by changing the algorithm for calculation of the fuel air ratio, considering thermal dissociation, and a correctly formulated equivalent chemical reaction path of the combustion process. To achieve the aim, the following tasks were solved: based on the use of experimental values of specific isobaric heat capacities of combustion products, which are a function of temperature and pressure, a mathematical model of the working process of the GTE combustor was improved ("simplified" mathematical model); based on the solution of the system of equations of chemical thermodynamics, a mathematical model of the working process of the GTE combustor was developed ("complex" mathematical model); the results of calculation by "simplified" mathematical model of the working process of the GTE combustor were compared with the "complex" one. The following results were obtained: the difference in the calculation of the combustion products' thermodynamic parameters between the developed mathematical models was less than 1.2% for the three modes of the General Electric CF6-80A engine. Conclusion: the "simplified" mathematical model of the working process of the GTE combustor fueling on ethanol was improved. A feature of the model is the implicit consideration of the effect of thermal dissociation and correctly formulated equivalent chemical reaction path of the combustion process by using experimental values of specific isobaric heat capacities of combustion products. This will improve the accuracy of fuel air ratio calculation and other thermodynamic parameters of GTE combustor mathematical models fueling on ethanol, without significantly complicating the model algorithm.

Quantum Chemical Model Calculations of Adhesion and Dissociation between Epoxy Resin and Si-Containing Molecules

There is no doubt that when solid surfaces are modified, the functional groups and atoms directly bonded to solid atoms play a major role in adsorption interactions with molecules or resins. In this study, the adhesion and dissociation between epoxy resin and molecules containing Si atoms were analyzed. The analysis, conducted in contact with the solid surface of silicon, utilized quantum chemical calculations based on a molecular model. We compared some Si-containing molecular models to test quantum chemical calculations that contribute to the study of adhesion and dissociation between epoxy resins and solid surfaces somehow other than simple potential energy curve calculations. The AFIR (artificial force induced reaction) method, implemented in the GRRM (global reaction route mapping) program, was employed to separate an epoxy resin model molecule and three types of silicon compounds (Si(CH3)2(OH)2, Si(CH3)4, and (CH3)2SiF2) in three directions, determining their minimum dissociation energy when changing the applied energy by 2.5 kJ/mol. In systems with weak hydrogen bonds, such as Si(CH3)4 or (CH3)2SiF2, the energy required for dissociation was not large; however, in systems with strong hydrogen bonds, such as Si(CH3)2(OH)2, dissociation was more difficult in the vertical direction. Although anisotropy due to hydroxyl groups was calculated in the horizontal direction, dissociation remained relatively easy.

Lateral Shear Stress Calculation Model Based on Flow Velocity Field Distribution from Experimental Debris Flows

AbstractDebris flows continuously erode the channel downward and sideways during formation and development, which changes channel topography, enlarges debris flow extent, and increases the potential for downstream damage. Previous studies have focused on debris flow channel bed erosion, with relatively little research on lateral erosion, which greatly limits understanding of flow generation mechanisms and compromises calibration of engineering parameters for prevention and control. Sidewall resistance and sidewall shear stress are key to the study of lateral erosion, and the distribution of the flow field directly reflects sidewall resistance characteristics. Therefore, this study has focused on three aspects: flow field distribution, sidewall resistance, and sidewall shear stress. First, the flow velocity distribution and sidewall resistance were characterized using laboratory debris flow experiments, then a debris flow velocity distribution model was established, and a method for calculating sidewall resistance was developed based on models of flow velocity distribution and rheology. A calculation method for the sidewall shear stress of debris flow was then developed using the quantitative relationship between sidewall shear stress and sidewall resistance. Finally, the experiment was validated and supplemented through numerical simulations, enhancing the reliability and scientific validity of the research results. The study provides a theoretical basis for the calculation of the lateral erosion rate of debris flows.

A BIM-integrated Thailand building energy code framework for building envelope thermal requirements in a conceptual design stage

This work presents the development of a building energy code (BEC) of Thailand compliance framework during conceptual design stages (CDS) using building information modeling (BIM) through visual programming language (VPL). The proposed method included five steps: (i) establish a commercial building reference; (ii) develop a BIM base model; (iii) create a BIM overall thermal transfer value (OTTV) and roof thermal transfer value (RTTV) calculation model with VPL scripts; (iv) test the BIM framework with various scenarios; and (v) verify the results with Thailand BEC software. The findings revealed an insignificant difference between the results from the BIM calculation model and those estimated by the Thailand BEC software. This study demonstrated that using BIM with VPL for OTTV and RTTV calculations during the CDS may be implemented automatically, which could help designers make timely decisions to comply with Thailand’s BEC, considering building design, materials, and fenestration ratios.

Real‐time reliability evaluation method for IGBT module in MMC based on junction temperature and bond wire failure online monitoring

AbstractThe lack of an MMC reliability evaluation approach that incorporates data on essential components' health monitoring in the already related research prevents reliability from being further improved. Therefore, this article proposes a real‐time reliability evaluation method of the multi‐state IGBT module in MMC through iterative calculation of the Markov chain model. The degradation process of the IGBT module is divided into multiple states based on the monitored bond wire failure, and the failure rate of the IGBT module is updated in real time using the accumulated monitoring data of junction temperature. The proposed method can more accurately reflect the real state of MMC compared with the binary state evaluation method. Besides, a multi‐channel high‐speed data acquisition board is designed to measuring the gate voltage and collector voltage of the IGBT for the health evaluation of IGBT modules in MMC; the typically measured results validate the effectiveness of the data acquisition board.

Seasonal Variations of PM2.5 Pollution in the Chengdu–Chongqing Urban Agglomeration, China

During the development of the Chengdu–Chongqing Urban Agglomeration (CCUA) in China, PM2.5 pollution severely threatened public health, presenting a significant environmental challenge. This study employs a novel spatial interpolation method known as High Accuracy Surface Modeling (HASM), along with the geographical detector method, local and regional contributions calculation model, and the Hybrid Single–Particle Lagrangian Integrated Trajectory model to analyze the seasonal spatial distribution of PM2.5 concentrations and their anthropogenic driving factors from 2014 to 2023. The transport pathway and potential sources of seasonal PM2.5 concentrations were also examined. The results showed the following: (1) HASM was identified as the most suitable interpolation method for monitoring PM2.5 concentrations in the CCUA; (2) The PM2.5 concentrations exhibited a decreasing trend across all seasons, with the highest values in winter and the lowest in summer. Spatially, the concentrations showed a pattern of being higher in the southwest and lower in the southeast; (3) Industrial soot (dust) emissions (ISEs) and industry structure (IS) were the most important anthropogenic driving factors influencing PM2.5 pollution; (4) The border area between the eastern part of the Tibet Autonomous Region and western Sichuan province in China significantly contribute to PM2.5 pollution in the CCUA, especially during winter.

Influence of cork-rubber gasket on the circular propagation of train-induced vibration waves in high-speed railway shield tunnels

Shield tunnels are constructed by assembling segment, and this construction method will produce a large number of joints. As the component with the largest contact area in the joints of the shield tunnel, the cork-rubber gasket has a significant effect on the transmission of train-induced vibration waves between the segments. In order to study the influence of cork-rubber gasket on the transmission of train-induced vibration waves in the circumferential direction, based on the hammering test of high-speed railway shield tunnel, a dynamic calculation model for high-speed railway shield tunnel was constructed, and the influence of elasticity modulus of cork-rubber gasket on the propagation of train-induced vibration waves was investigated. The results show that: (1) the longitudinal joints of high-speed railway shield tunnels can weaken high-frequency vibration waves more than low-frequency vibration waves; (2) the lower the modulus of elasticity of cork-rubber gasket is, the greater the attenuation of the peak of the temporal range of vibration acceleration of train-induced vibration waves after they pass through the longitudinal joints; (3) compared with the cork-rubber gasket of high elasticity, the cork-rubber gasket with low elasticity can improve the damping effect of the longitudinal joints on low-frequency bands (0–500 Hz) effectively. This research offers new methodologies for optimising vibration isolation in shield tunnels and contributes to the advancement of tunnel design for high-speed rail systems.

Modeling net-charge fluctuations in heavy-ion collisions at the LHC

Abstract The analysis of Pb+Pb data for net-charge fluctuations at LHC energies
within the HYDJET++ model is presented. The strongly intensive
quantities $D$ and $\Sigma$ are used to get rid of the effects related
to volume fluctuations of the system. We employ two versions of the
HYDJET++ for the analysis. The first one is the standard or default
version, whereas the second one represents its further modification,
which takes into account explicit event-by-event conservation of the
electric net-charge of produced particles. Inclusion of the canonical
net-charge conservation in the model allows one for better description
of the experimental data obtained by the ALICE and the CMS
Collaborations. Comparison with calculations of other models is also
presented.

An optimal global biochar application strategy based on matching biochar and soil properties to reduce global cropland greenhouse gas emissions: findings from a global meta-analysis and density functional theory calculation

Biochar has been extensively utilized to amend soil and mitigate greenhouse gas (GHG) emissions from croplands. However, the effectiveness of biochar application in reducing cropland GHG emissions remains uncertain due to variations in soil properties and environmental conditions across regions. In this study, the impact of biochar surface functional groups on soil GHG emissions was investigated using molecular model calculation. Machine learning (ML) technology was applied to predict the responses of soil GHG emissions and crop yields under different biochar feedstocks and application rates, aiming to determine the optimum biochar application strategies based on specific soil properties and environmental conditions on a global scale. The findings suggest that the functional groups play an essential role in determining biochar surface activity and the soil’s capacity for adsorbing GHGs. ML was an effective method in predicting the changes in soil GHG emissions and crop yield following biochar application. Moreover, poor-fertility soils exhibited greater changes in GHG emissions compared to fertile soil. Implementing an optimized global strategy for biochar application may result in a substantial reduction of 684.25 Tg year−1 CO2 equivalent (equivalent to 7.87% of global cropland GHG emissions) while simultaneously improving crop yields. This study improves our understanding of the interaction between biochar surface properties and soil GHG, confirming the potential of global biochar application strategies in mitigating cropland GHG emissions and addressing global climate degradation. Further research efforts are required to optimize such strategies.Graphical

Biogenic silica dynamics in coastal wetland sediments: A key driver of silicon and carbon biogeochemical cycling

AbstractBiogenic silica (biogenic Si) is a bioactive component crucial for the biogeochemical cycling of Si in terrestrial and aquatic ecosystems. Its formation and dissolution dynamics are intricately linked to carbon (C) cycling. However, knowledge about the source, composition, and factors controlling the distribution of biogenic Si in coastal wetland sedimentary environments is still limited. To address this lack of knowledge, we introduced a suite of geometric models for biogenic Si biovolume calculation and investigated biogenic Si assemblages, along with biogenic Si and biogenic Si‐occluded C contents, in sediments from representative coastal wetlands along the west coast of Bohai Bay. Our analysis showed that sedimentary biogenic Si predominantly derived from phytoliths (78.1% ± 5.8%), diatoms (18.2% ± 4.8%), and sponge spicules (3.7% ± 2.9%). Notably, phytolith assemblages were primarily composed of forms derived from the Poaceae family. The biogenic Si‐occluded C content (0.035–1.870 g kg−1) within these wetland sediments was consistent across both sites, accounting for 0.97–5.71% of the total organic C pool. Structural equation modeling indicated that total organic C, pH, and amorphous aluminum oxides either directly or indirectly influenced the biogenic Si content in coastal wetlands sediments. These results demonstrate the critical role that biogenic Si plays in the Si biogeochemical cycle and provide valuable information that advances our understanding of the biogeochemical interactions between Si and C in coastal wetland ecosystems.

Dyeing behaviour of iron(III)-gallic acid complexes on wool as function of pH-dependent iron(III)-complex stoichiometry

Iron complexes with polyphenolics e.g. gallotannins and flavonoids have been used since ancient times for coloration of textiles, painting and preparation of inks. The composition of iron gall inks on historical artefacts has been investigated with modern instrumental methods. However the dyeing behaviour of iron-complexes with polyphenols still bases on empirical knowledge. In this study Fe(III)-complexes with gallic acid were used as model system to elucidate their pH dependent sorption and dyeing behaviour on wool. At dyebath pH 3 high sorption of Fe(III)-gallic acid complexes was observed, however darker dyeings were obtained at dyebath pH 4. Model calculations for the complex species present in the dyebath indicated the presence of the binary complex [Fe(III)(GA2−)]+ as main species at pH 3, while at pH 4 the ternary species [Fe(III)(GA2−)2]- prevails. The dye sorption bases on Van-der-Waals forces, while ionic interactions between Fe(III)-complex and keratin are of minor relevance. The elaborated theoretical model also explains the influence of dyebath pH in dyeing with gallotannins, polyphenols and flavonoids in presence of iron salts and thus is of particular relevance for improved utilisation of these natural colorants.

Simplified calculation models for evaluating the post-earthquake axial load-carrying capacity of RC bridge piers

This study aims to develop simplified calculation models of the post-earthquake axial load-carrying capacity of reinforced concrete columns to determine the post-earthquake traffic flow capacity of the bridges for the evaluation and design process. To this end, the maximum and residual drift ratios are first determined as the engineering demand parameters for the simplified calculation model for the evaluation and design process, respectively. Then, the optimal models describing the relationships between the maximum/residual drift ratio and the post-earthquake axial load-carrying capacity are selected. The analysis results show the normal cumulative model in the coordinate system of ln(x)-y is the optimal relationship model. On this basis, the effects of high-sensitivity parameters (i.e. the axial compressive ratio and shear span ratio) on the post-earthquake axial load-carrying capacity are investigated. Results indicate that the axial compressive ratio negatively affects, while the shear span ratio positively affects the post-earthquake axial load-carrying capacity. Finally, the simplified calculation models of the post-earthquake axial load-carrying capacity are developed from the optimal model and the effects of the high-sensitivity parameters, and with validated high accuracy. The simplified calculation models provide engineers and policymakers with a tool to predict the post-earthquake traffic flow capacity of bridges.

Optimal Flexibility Dispatching of Multi-Pumped Hydro Storage Stations Considering the Uncertainty of Renewable Energy

With the continuous increase in the penetration rate of renewable energy, the randomness and flexibility demand in the power system continues to increase. The main grid side of the power system vigorously develops pumped hydro storage (PHS) resources. However, the current PHS station scheduling method of a fixed time period and fixed power has lost a certain flexibility supply. In this paper, an optimal dispatching model of multi-pumped hydro storage stations is proposed to supply flexibility for different regions of the state grid in east China. Firstly, the credible predictable power (CPP) of renewable energy is calculated and the definition of flexibility demand of a power system is given. The calculation model for flexibility demand is established. Secondly, considering the regional allocation constraint in the state grid in east China, a non-centralized model of multi-PHS within the dispatch scope is established. In the model, the constraints of storage capacity of different hydropower conversion coefficients of each PHS station is considered. The flexibility supply model of PHS stations to each region of the state grid in east China is established to realize reasonable flexibility allocation. Then, by combining the PHS station models and the flexibility demand calculation model, the optimal dispatching model for the flexibility supply of multi-PHS stations is established. Finally, based on the network dispatching example, the effectiveness and superiority of the proposed strategy are verified by a case study.

Proton dose calculation with LSTM networks in presence of a magnetic field

Objective.To present a long short-term memory (LSTM) network-based dose calculation method for magnetic resonance (MR)-guided proton therapy.Approach.35 planning computed tomography (CT) images of prostate cancer patients were collected for Monte Carlo (MC) dose calculation under a perpendicular 1.5 T magnetic field. Proton pencil beams (PB) at three energies (150, 175, and 200 MeV) were simulated (7560 PBs at each energy). A 3D relative stopping power cuboid covering the extent of the PB dose was extracted and given as input to the LSTM model, yielding a 3D predicted PB dose. Three single-energy (SE) LSTM models were trained separately on the corresponding 150/175/200 MeV datasets and a multi-energy (ME) LSTM model with an energy embedding layer was trained on either the combined dataset with three energies or a continuous energy (CE) dataset with 1 MeV steps ranging from 125 to 200 MeV. For each model, training and validation involved 25 patients and 10 patients were for testing. Two single field uniform dose prostate treatment plans were optimized and recalculated with MC and the CE model.Results.Test results of all PBs from the three SE models showed a mean gamma passing rate (2%/2 mm, 10% dose cutoff) above 99.9% with an average center-of-mass (COM) discrepancy below 0.4 mm between predicted and simulated trajectories. The ME model showed a mean gamma passing rate exceeding 99.8% and a COM discrepancy of less than 0.5 mm at the three energies. Treatment plan recalculation by the CE model yielded gamma passing rates of 99.6% and 97.9%. The inference time of the models was 9-10 ms per PB.Significance.LSTM models for proton dose calculation in a magnetic field were developed and showed promising accuracy and efficiency for prostate cancer patients.