Transient Model Research Articles

Prediction and Analysis of Transient Turbine Tip Clearance Using Long Short-Term Memory Neural Network

Abstract The transient turbine tip clearance (δ) throughout the engine process is crucial to modern high-performance aero engines. However, there is still a lack of efficient and accurate transient prediction models of tip clearances with active thermal control (ATC) system, especially for the tip clearances of the complex turbine structures with various parameters. This study develops a transient prediction model for the tradeoff between computational efficiency and accuracy, which includes an offline dataset generation process and an online δ prediction process. The offline dataset is first generated using an in-house finite element analysis code, which is validated against a transient tip clearance experiment, and data splicing and sensitivity analysis are applied to enrich the sample features and reduce the input parameters' dimensionality. Then, the long short-term memory neural network (LSTM) is employed to learn the transient tip clearances' timing information. The time consumption for the transient prediction model is significantly shorter than that for the tip clearance calculation method by three orders, and the maximum relative error is as low as 3.59%. In addition, the transient characteristics, including the overshoot value (σ) and the response time (ts), are investigated with different jet Reynolds numbers (Rec) and temperatures (Tfc) of ATC cooling flow. The ts decreases with larger Rec and smaller Tfc due to a more significant cooling effect. However, the σ increases with the increase of Rec and Tfc due to the different sensitivity of cooling parameters. This study provides a reference for the transient tip clearance prediction and the adjustments in the cooling strategies.

Influence of particle parameters on the melting/migration of silicon particles and turbulent heat transfer during CCZ monocrystalline silicon growth

The Continuous Czochralski (CCZ) is a promising approach for preparing low-cost high-quality monocrystalline silicon in the photovoltaic field. To investigate the coupled mechanism of silicon particles melting/migration and melt turbulent heat transfer during the CCZ monocrystalline silicon growth, based on the Euler–Lagrange framework, a three-dimensional transient heat-mass transfer model is developed using the LES method considering the heat exchange between the silicon particles and the silicon melt as well as the particles size change. In addition, we investigated the effects of key silicon particle parameters such as feeding temperature, particle size and feeding speed, on the silicon particles melting/migration and melt turbulent heat transfer. The results show that appropriately increasing the feeding temperature and speed contributes to achieve more concentrated particles distribution and weaken the movement of silicon particles towards the crystalline interface simultaneously, which conduce to eliminate the adverse impact of continuous feeding on monocrystalline silicon growth. And the feeding temperature has a great effect on the temperature fluctuation near the crystalline interface. In addition, when the feeding speed exceeds 1.5m/s, increasing feeding speed has no significant effect on the particles distribution and melting process. Besides, the feeding particle size has a significant effect on the maximum penetration depth of particles. The small silicon particles prefer moving to the crystalline interface driven by thermophoretic force, which is detrimental to the high-quality CCZ monocrystalline silicon growth.

A new analytical model for transient heat transfer modeling of geothermal monotube heat exchangers

In this study, we present a new analytical model for the analysis of transient heat transfer (the model is solved after Laplace transformation) in geothermal monotube heat exchangers (GHE). The model accounts for various factors, including the heat exchanger's geometric parameters, the nature of the fluid (air and water), flow characteristics (laminar and turbulent), and heat transfer boundary conditions. Initially, the model's performance is validated by comparing its results with those obtained from computational fluid dynamics simulations using OpenFOAM. This validation process ensures the reliability and accuracy of the model. Additionally, an analysis of the heat transfer mechanisms and key modeling parameters identified from the comparison is provided. In the subsequent section, the analysis is extended by comparing the proposed model to four existing analytical models available in the literature. These reference models employ distinct approaches to simulate heat transfer to the ground. By examining a range of cases, the performance of the model is systematically evaluated against these conventional methods. This work closes by an analysis of the analytical models and the impact on the accuracy of the results highlighting the advantages of the proposed method in geothermal applications.

Integrated Time-Dependent Analysis of a Hydraulic Structure on Soft Foundations during Construction

An integrated model that considers multiphysics is necessary to accurately analyze the time-dependent response of hydraulic structures on soft foundations. This study develops an integrated superstructure–foundation–backfills model and investigates the time-dependent displacement and stress of a lock head project on a soft foundation during the construction period. Finite element analyses are conducted, incorporating a transient thermal creep model for concrete and an elasto-plastic consolidation model for the soil. The modified Cam-clay model is employed to describe the elasto-plastic behavior of the soil. Subsequently, global sensitivity analyses are conducted to determine the relative importance of the model parameters on the system’s response, using Garson’s and partial derivative algorithms based on the backpropagation (BP) neural network. The results indicate that the integrated system exhibits pronounced time-dependent displacement and stress, with dangerous values appearing during specific periods. These values are easily neglected, highlighting the importance of integrated time-dependent analysis. Construction activities, particularly the backfilling process, could cause a sudden change in stress and significantly impact the stress redistribution of the superstructure. Additionally, the mechanical properties of concrete have a significant impact on the stress on the superstructure, while the mechanical properties of the soil control the settlement of the integrated system.

A new approach to predict pump transient phenomena in Molten salt reactor Experiment (MSRE) by missing data identification and regeneration

Molten Salt Reactor Experiment (MSRE) is being extensively used for validating the computational tools for Molten Salt Reactors (MSRs). The pump transient tests were performed during the operation of MSRE to obtain the reactivity response to flow perturbation. The transient flow rate during this set of tests is required as input to predict the reactivity response. Since the primary loop of MSRE was not equipped with a flow rate meter, the transient flow rate, which is the crucial factor for the reactivity change in MSRE, is missing. Achieving an accurate simulation of the reactivity response to the MSRE pump transient tests necessitates a precise estimation of the transient flow rate.This paper endeavors to reconstruct the missing flow rate with the aim of offering a valuable input for simulating reactivity responses in the pump transient test series. In order to obtain an accurate transient flow rate, we employed a centrifugal pump transient model based on the affinity laws and solved the model for the MSRE secondary pump to validate the underlying assumptions of the model. In addition, we constructed the homologous pump head curves based on the water test data for the same purpose. The affinity law approximation is proved to be adequate in predicting the MSRE pump startup transient with the root-mean-square error (RMSE) in the normalized flow rate to be 0.03. On the other hand, for the MSRE pump coastdown transient, the preliminary results indicate that neither the affinity law approximation nor the homologous head curve is sufficient to provide acceptable predictions. To overcome this noticeable modeling deficit, we propose an innovative approach based on a straightforward data mining technique to regenerate the MSRE pump coastdown homologous relations using the measured data of the secondary pump. These relations are transferred to the primary pump and used to simultaneously solve for the impeller speed and the flow rate of the pump in the primary pump coastdown. With the new approach, the estimated RMSE in the normalized pump speed for the primary pump coastdown is reduced 0.0052. This excellent agreement validates the accurate calculations for the flow rate during the pump coastdown transient. We also performed an uncertainty analysis to quantify the confidence interval of the predicted quantities, which further justifies the robustness of the proposed approach.

Transient surrogate modeling of modally reduced structures with discontinuous loads and damping

AbstractIn this work, a surrogate model for structural, transient and discontinuously excited finite element method simulations is developed. This allows to reduce the computational effort of repeated calculations of identical models under different load cases. The architecture of the surrogate combines fully connected neural network layers with long short-term memory layers. For the reproduction of different damping ratios, a categorical variable is added to the continuous input data. Based on a recursive flow of the predicted data back to the input layer, long-term dependencies do not vanish due to short-input sequences. The system dimension is reduced by applying the model-order reduction technique for modal decomposition. The high accuracy of the surrogate and the reduction of computational costs are shown on an academic example of a cantilever beam and a real-world example of a robot. The advantages of our approach are illustrated in comparison with state-of-the-art surrogates for transient finite element analysis. By using the surrogate proposed in this study, oscillations due to discontinuous excitation of mechanical structures can be reproduced. For this purpose, only short-input sequences are necessary since the excitation of the oscillations does not have to be part of the input sequence during the whole duration of the oscillations. Due to the categorical variable for the damping ratio, the surrogate can account for the influence of different damping in parameter studies.

Transient Temperature at Tool–Chip Interface during Initial Period of Chip Formation in Orthogonal Cutting of Inconel 718

Machining nickel-based super alloys such as Inconel 718 generates a high thermal load induced via friction and plastic deformation, causing these alloys to be among most difficult-to-cut materials. Localized heat generation occurring in machining induces high temperature gradients. Experimental techniques for determining cutting tool temperature are challenging due to the small dimensions of the heat source and the chips produced, making it difficult to observe the tool–chip interface. Therefore, theoretical analysis of cutting temperatures is crucial for understanding heat generation and temperature distribution during cutting operations. Periodic heating and cooling occurring during cutting and interruption, respectively, are modeled using a hybrid analytical and finite element (FE) transient thermal model. In addition to identifying a transition distance associated with initial period of chip formation (IPCF) from apparent coefficient of friction results using a sigmoid function, the transition temperature is also identified using the thermal model. The model is validated experimentally by measuring the tool–chip interface temperature using a two-color pyrometer at a specific cutting distance. Due to the cyclic behavior in interrupted cutting, where a steady-state condition may or may not be achieved, transient thermal modeling is required in this case. Input parameters required to identify the heat flux for the transient thermal model are obtained experimentally and the definitions of heat-flux-reducing factors along the cutting path are associated with interruptions and the repeating IPCF. The thermal model consists of two main parts: one is related to identifying the heat flux, and the other part involves the determination of the temperature field within the tool using a partial differential equation (PDE) solved numerically via a 2D finite element method.

Thermal-force coupling simulation of carbon fibre-reinforced poly-ether-ether-ketone thermoplastic composites during the laser-assisted automated tape placement process

To reveal the thermal-force coupling characteristics of the laser in-situ consolidation (ISC) of carbon fibre-reinforced poly-ether-ether-ketone (CF/PEEK) composites, a two-dimensional transient thermal-force model of CF/PEEK composites was constructed using COMSOL Multiphysics finite element simulation software to calculate the temperature history and the thermal stress variation of CF/PEEK composites during the laser-assisted automated tape placement (LATP) process. The results show that the temperature field formed on the surface of each layer by the laser spot during LATP is stable, and the temperature gradient at the front of the spot movement direction is higher than that at the back edge. The maximum stresses in the laminate occur on both sides of the first CF/PEEK layer and the stresses are unevenly distributed along the length and thickness directions of the lay-up. The composite material on both sides of the laminate tends to ‘shrink’ compared to its original position.

Thermodynamic and economic analyses of a modified adiabatic compressed air energy storage system coupling with thermal power generation

With the proposal of "Carbon peaking and carbon neutrality", Adiabatic Compressed Air Energy Storage (A-CAES) has emerged as a significant component within China's energy storage infrastructure. But its thermodynamic efficiency and economical return need yet to be raised. The present paper proposed a modified system coupling with thermal power plant to utilize the excess compression heat. Utilizing advanced transient modeling software, an A-CAES plant is modeled and validated. The operation performance of the coupled system is compared with non-coupled system, which shows that the system efficiency is raised from 54.8 % to 76.7 % and the investment return rate is improved from 9.18 % to 10.43 %.

Thermohydraulic performance analysis and optimization of stripe patterned hybrid-wetting surface condensation by 3D steady simulation

The configuration parameters of stripe patterned hybrid-wetting surfaces (SPHWSs) had a significant effect on the thermohydraulic performance of condensation. By using Taguchi-GRA method modified by entropy weight for optimization, Nusselt number (Nu) and thermal performance factor (TPF) reached the highest increment of 225.9% and 252.8% at vapor mass fraction (ω) equal to 15%, respectively, and the maximum reduction of Fanning friction coefficient (f) was −41.7% at ω = 30%, as compared without SPHWSs. A 3D steady CFD-aided method based on pseudo transient under-relaxation model was developed to predict Nu, f, and TPF of SPHWSs for different configuration parameters, including oblique pattern angle (β), hydrophilic (Wi) and hydrophobic (Wo) pattern width, hydrophilic (θi), and hydrophobic (θo) contact angle. The result indicated that the simulation was in good agreement with the experimental data. θi had a more pronounced effect on the thermohydraulic performance compared to other factors. Notably, the droplet reached a specific dynamic force balance at θi = 60°, effectively restraining near-wall erratic flow and enabling cost-optimal heat transfer.

MSD-based transient fluid model of liquid circular angular accelerometer for vibration-induced error analysis

This paper investigates the errors induced by linear vibration in the fluidic system of liquid circular angular accelerometers (LCAAs). A two-dimensional mass-spring-damper model is proposed to analyze the pressure difference between both sides of LCAA transducer subjected to linear vibration in both transient and steady states, where the compressibility of fluid is taken into account. The complex flow patterns of fluid are simplified to the positional changes of fluid particles. Springs and dampers are utilized to simulate the forces inside the fluid and between the fluid and the tube wall. Simulations are carried out based on the linear acceleration step excitation to explore the influence of model parameters, LCAA structure parameters and fluid parameters. The proposed model is validated by comparing the characteristics of the simulated pressure difference with their corresponding theoretical values, and is further verified by the comparison with the results from computational fluid dynamics method. Furthermore, the pressure difference under linear acceleration excitations in various forms is analyzed. The results indicate that the abrupt changes in linear acceleration are the primary cause of pressure difference oscillation, and the compressibility of fluid leads to increased pressure difference.

Evaluating the maximum drilling length of horizontal geothermal wells utilizing temperature constraints

The geothermal industry faces a significant challenge in exploring and developing resources due to elevated temperatures in downhole environments. Successful drilling in high-temperature geothermal wells requires precise thermal management. This research assesses constraints on horizontal section length and temperature during geothermal horizontal well drilling, aiming to formulate effective wellbore temperature management guidelines.The study utilizes thermal resistance analysis to establish a tailored transient heat transfer model for high-temperature horizontal geothermal well drilling. Parameters such as circulation time, horizontal section length, flow rate, drilling fluid properties, formation thermal conductivity, and drill string thermal conductivity are thoroughly investigated. Treating input parameters as triangular distributions, Monte Carlo simulation techniques conduct sensitivity analysis. Tornado diagrams quantitatively determine key parameter impacts on bottom-hole temperature. The research introduces a procedural framework for geothermal well drilling, aiding engineers in swiftly identifying operational parameter combinations for effective wellbore temperature management. This workflow provides practical guidance for geothermal resource development, ensuring drilling safety in diverse conditions.

Effects by geothermal gradient on thermal response tests for boreholes

A thermal response test (TRT) on a borehole provides information needed in the design of ground heat exchangers for ground source heat pump systems. Conventional analysis of TRT data sets uses the late-time period to estimate the ground thermal conductivity and the effective borehole resistance. During this quasi-steady-state period, the transient average fluid temperature has a logarithmic linear trend, which is consistent with conventional heat transfer models that assume a uniform undisturbed ground temperature. As the depth of the borehole increases the undisturbed ground temperature increases with depth following the geothermal gradient. This paper focuses on how the geothermal gradient affects a TRT. As the geothermal gradient increases, the required time to reach the conventional logarithmic linear trend may increase beyond any practical testing duration in coaxial boreholes. Then, conventional analysis methods based on a quasi-steady-state period incorrectly estimate the ground thermal conductivity. The magnitude of this effect is controlled through a dimensionless parameter |qratio|, which includes the geothermal gradient and other test parameters. In place of conventional models, a transient model that includes the geothermal gradient and fluid thermal storage can estimate the ground thermal conductivity and local borehole resistance within the typical TRT testing duration.

Thermal performance of packed-bed latent heat storage tank integrated with flat-plate collectors under intermittent loads of building heating

Packed-bed latent heat storage (PBLHS) system has been widely studied in the solar energy application area due to its properties of solving the time-space mismatch of energy supply and demand. The paper delves into the cyclic thermal performance of PBLHS tanks, seamlessly integrated with flat-plate collectors, to manage building heat loads effectively. A 1D transient mathematic model of PBLHS integrated with the solar collector for a building is established using MATLAB which is validated with the experimental results from the literature. Based on this model, the effect of different sizes, flow rates, inlet temperature thresholds and different heating months are discussed. The results show that: 1). Building heat load can have a significant influence on the thermal performance of the PBLHS system. 2). The optimal size of the tank for a 96 m2 house is 1.0*1.0 m and the optimal flow rate is 0.05 kg/s 3). The weather data can significantly affect the thermal performance of PBLHS, the storage tank heating durations for one week in different heating months are 108.4h, 73.6h,70.8h and 81.7h. These insights are pivotal for the optimal design of PBLHS tanks, paving the way for more efficient building heating solutions.

Numerical analysis and process optimization of electron beam melting for superalloys

This study aims to determine the optimal parameters for the electron beam melting process by employing a modified transient three-dimensional thermal model. The validity of the thermal model is confirmed through experimental results. Moreover, the proposed method establishes mathematical relationships between the resulting molten pool temperature and process parameters. A broader range of process parameters for a new Ni–Co-based superalloy was achieved by investigating the effects of scanning velocities (10–100 mm/s), scanning radius (20–60 mm), and melting mass (1500–3100 g) on temperature at various electron beam power levels (10–30 kW). Regression models were established between scanning velocities-temperature, and scanning radius-temperature under different electron beam power levels. These models laid the foundation for real-time automatic control of molten pool temperature. Significantly, orthogonal experimental design and response surface method are employed to conduct a multi-objective optimization based on sixteen experiments and three parameters. The results of multi-objective optimization indicate that with a smelting mass of 1.5 kg, an electron beam power of 11 kW, a scanning radius of 60 mm, and a scanning velocity of 75 mm/s, the energy consumption is 34.95 kW h, and the theoretical mass loss of Ni element is 0.002 kg. The desirability is 91.2 %.

Adaptive state-of-health temperature sensitivity characteristics for durability improvement of PEM fuel cells

To obtain the temperature sensitivity characteristics of the proton exchange membrane fuel cell under different degradation levels, accelerated durability tests and temperature sensitivity tests of the fuel cell are first performed, and the temperature characteristics under different degradation states are analyzed by electrochemical impedance spectroscopy and polarization curve. Besides, an adaptive state-of-health transient thermal model of fuel cells is developed to investigate the effect of operating temperature on the internal gas concentration and hydrothermal distribution characteristics of the fuel cell from a mechanistic perspective. The experimental results of temperature sensitivity validate that the adaptive state-of-health transient thermal model can effectively monitor the steady and transient performance of the fuel cell. Subsequently, a mathematical model is proposed to describe the relationship among the load current, state of health, and optimal temperature using the temperature sensitivity test data and the transient thermal model of the adaptive state of health, which provides important insights into the optimal temperature range tailored to the current state of health of fuel cells to ensure efficient and stable operation of fuel cells all the time and contributes to the fine design of an optimal degradation adaptive temperature control strategy.

Study on geothermal energy self-recycling extraction and ScCO2 storage in the horizontal well annuli with fracture network system

With the extensive exploitation of fossil fuels, a substantial number of production and injection wells have been or are on the verge of being abandoned. However, many of these wells present viable opportunities for geothermal energy extraction, as they are situated in geothermal reservoirs with favourable temperatures. In alignment with carbon neutrality policies, supercritical CO2 (ScCO2) has emerged as the preferred working fluid for geothermal extraction, facilitating subsequent storage. This study has developed three transient models to characterize the heat and mass transfer processes of ScCO2 circulating within a horizontal wellbore and the reservoir's fracture network. Finite element method and Comsol Multiphysics 6.1 software are employed to solve these models. Results show that ScCO2 efficiently flows from the annuli into the hydraulic fracture network and then circulates back through the annuli completing a self-recycling heat extraction process. The findings reveal several key insights: (a) Lower injection mass flow rates and flow rates lead to more efficient extraction of thermal energy within horizontal wellbores. (b) Low-temperature ScCO2 enhance thermal energy recovery. (c) The larger the coverage area of the fracture network, the more effective the heat extraction. (d) The efficiency of heat extraction and ScCO2 storage in the horizontal well-fracture network self-circulation system is 3 to 5 times and 6 to 7 times higher than that of the horizontal well self-recycling and injection-production systems. (e) Periodic thermal extraction proves to be more efficient than continuous methods. (f) The cumulative heat production of the vertical dual well injection-production system is the highest, reaching 2.45 × 1011 kJ. But it's still lower than the self-circulating system. The heat extraction effect of the diagonal dual well injection-production system is the lowest, which is 1.83 × 1011 kJ. (g) Three developed transient models facilitate efficient heat extraction and ScCO2 storage reservoir screening and evaluation. In conclusion, the self-recycling system has achieved efficient heat extraction and carbon dioxide storage, providing a theoretical basis for future energy conversion and management.

Transient optical properties change and dense plasma dynamics during water breakdown induced by ultrashort laser pulses

We propose a nonlinear transient coupling model to study the plasma dynamics during the interaction between ultrashort laser pulses and water. We conduct a quantitative characterization of the transient optical properties, energy deposition, and dense plasma dynamics in water with near-infrared ultrashort laser pulses by simulating the spatiotemporal coupling of the laser field with the plasma while calculating the time-varying relative permittivity. The results show that the free electron density in the dense plasma exceeds ≈1.0×1026 m−3, the plasma will move in the reverse direction of the laser pulse propagation, and the velocity is related to the incident laser intensity. An empirical model is established to quantify this reverse movement of dense plasma in the laser field taking into account the energy deposition. We also validate our coupling model by comparing the breakdown thresholds with experimental results and find excellent agreement.

Detailed modeling and numerical analysis of thermo mechanical stresses in the crystalline silicon and thin film PV modules under varying climatic conditions

The present manuscript provides an in-depth analysis of the modeling and simulation of thermo-mechanical stresses in photovoltaic panels using finite element (FEM) analysis. It covers important aspects such as the choice of the model, including governing equations, boundary conditions, and simplifying assumptions. The study mainly focuses on evaluating the impact of environmental conditions on the thermo-mechanical stresses of first-generation c-Si and second-generation thin-film CdTe and a-Si PV panels in five different climatic zones in Algeria. The proposed transient 3D numerical model is validated against experimental measurements by other researchers and the tabulated values of the nominal operating temperature of the cell (NOCT). The obtained results indicate that the first principle stress for the c-Si cell is lower compared to CdTe and a-Si cells; this can be explained by looking at the thickness, as well as the Young modulus of the solar cell. Consequently, in regions or countries with hot climatic conditions or large temperature gradients, it is recommended to use PV panels based on first-generation c-Si cells with glass-glass as the front and back covers.

Transient Mechanism Analysis of Three-Dimensional Zinc-Nickel Single Flow Battery Based on Different Negative Electrode Structures

On the basis of the mass, momentum, charge conservation equations, in addition to coupled with the global reaction kinetic equations, a transient three-dimensional mechanistic analytical model of zinc-nickel single flow batteries (ZNBs), which comprehensively takes into account the hydrogen and oxygen evolution side reactions, the polarization distribution, as well as the structural effects of the pole lugs, is developed in this paper. After grid independence validation and experimental verification, the polarization distribution, side-reaction current density, and battery efficiency of ZNBs at high current density and multiple cycles of charging and discharging were comparatively analyzed based on this model with different anode materials of nickel sheet (NS) and porous nickel foam (NF). Subsequently, the effects of changes in negative electrode porous nickel foam thickness and porosity on battery polarization, side-reaction current density and battery efficiency were further investigated. Finally, the performance of the battery under the optimal battery state was studied. The results showed that the NF negative electrode effectively reduced the battery polarization, suppressed the battery side reactions as well as improved the battery efficiency under high current density and multiple cycles of charging and discharging, which improved the efficiency and stability of the battery.