Institute of Mechanics,
Chinese Academy of Sciences
2024 Vol.14(2)
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Theoretical and Applied Mechanics Letters 14 (2024) 100497.
doi: 10.1016/j.taml.2024.100497
Abstract:
Large atmospheric boundary layer fluctuations and smaller turbine-scale vorticity dynamics are separately hypothesized to initiate the wind turbine wake meandering phenomenon, a coherent, dynamic, turbine-scale oscillation of the far wake. Triadic interactions, the mechanism of energy transfers between scales, manifest as triples of wavenumbers or frequencies and can be characterized through bispectral analyses. The bispectrum, which correlates the two frequencies to their sum, is calculated by two recently developed multi-dimensional modal decomposition methods: scale-specific energy transfer method and bispectral mode decomposition. Large-eddy simulation of a utility-scale wind turbine in an atmospheric boundary layer with a broad range of large length-scales is used to acquire instantaneous velocity snapshots. The bispectrum from both methods identifies prominent upwind and wake meandering interactions that create a broad range of energy scales including the wake meandering scale. The coherent kinetic energy associated with the interactions shows strong correlation between upwind scales and wake meandering.
Large atmospheric boundary layer fluctuations and smaller turbine-scale vorticity dynamics are separately hypothesized to initiate the wind turbine wake meandering phenomenon, a coherent, dynamic, turbine-scale oscillation of the far wake. Triadic interactions, the mechanism of energy transfers between scales, manifest as triples of wavenumbers or frequencies and can be characterized through bispectral analyses. The bispectrum, which correlates the two frequencies to their sum, is calculated by two recently developed multi-dimensional modal decomposition methods: scale-specific energy transfer method and bispectral mode decomposition. Large-eddy simulation of a utility-scale wind turbine in an atmospheric boundary layer with a broad range of large length-scales is used to acquire instantaneous velocity snapshots. The bispectrum from both methods identifies prominent upwind and wake meandering interactions that create a broad range of energy scales including the wake meandering scale. The coherent kinetic energy associated with the interactions shows strong correlation between upwind scales and wake meandering.
Theoretical and Applied Mechanics Letters 14 (2024) 100496.
doi: 10.1016/j.taml.2024.100496
Abstract:
Multi-scale system remains a classical scientific problem in fluid dynamics, biology, etc. In the present study, a scheme of multi-scale Physics-informed neural networks (msPINNs) is proposed to solve the boundary layer flow at high Reynolds numbers without any data. The flow is divided into several regions with different scales based on Prandtl’s boundary theory. Different regions are solved with governing equations in different scales. The method of matched asymptotic expansions is used to make the flow field continuously. A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale. The results are compared with the reference numerical solutions, which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows. This scheme can be developed for more multi-scale problems in the future.
Multi-scale system remains a classical scientific problem in fluid dynamics, biology, etc. In the present study, a scheme of multi-scale Physics-informed neural networks (msPINNs) is proposed to solve the boundary layer flow at high Reynolds numbers without any data. The flow is divided into several regions with different scales based on Prandtl’s boundary theory. Different regions are solved with governing equations in different scales. The method of matched asymptotic expansions is used to make the flow field continuously. A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale. The results are compared with the reference numerical solutions, which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows. This scheme can be developed for more multi-scale problems in the future.
Theoretical and Applied Mechanics Letters 14 (2024) 100503.
doi: 10.1016/j.taml.2024.100503
Abstract:
Machine-learned augmentations to turbulence models can be advantageous for flows within the training dataset but can often cause harm outside. This lack of generalizability arises because the constants (as well as the functions) in a Reynolds-averaged Navier– Stokes (RANS) model are coupled, and un-constrained re-calibration of these constants (and functions) can disrupt the calibrations of the baseline model, the preservation of which is critical to the model’s generalizability. To safeguard the behaviors of the baseline model beyond the training dataset, machine learning must be constrained such that basic calibrations like the law of the wall are kept intact. This letter aims to identify such constraints in two-equation RANS models so that future machine learning work can be performed without violating these constraints. We demonstrate that the identified constraints are not limiting. Furthermore, they help preserve the generalizability of the baseline model.
Machine-learned augmentations to turbulence models can be advantageous for flows within the training dataset but can often cause harm outside. This lack of generalizability arises because the constants (as well as the functions) in a Reynolds-averaged Navier– Stokes (RANS) model are coupled, and un-constrained re-calibration of these constants (and functions) can disrupt the calibrations of the baseline model, the preservation of which is critical to the model’s generalizability. To safeguard the behaviors of the baseline model beyond the training dataset, machine learning must be constrained such that basic calibrations like the law of the wall are kept intact. This letter aims to identify such constraints in two-equation RANS models so that future machine learning work can be performed without violating these constraints. We demonstrate that the identified constraints are not limiting. Furthermore, they help preserve the generalizability of the baseline model.
Theoretical and Applied Mechanics Letters 14 (2024) 100511.
doi: 10.1016/j.taml.2024.100511
Abstract:
Identification of underlying partial differential equations (PDEs) for complex systems remains a formidable challenge. In the present study, a robust PDE identification method is proposed, demonstrating the ability to extract accurate governing equations under noisy conditions without prior knowledge. Specifically, the proposed method combines gene expression programming, one type of evolutionary algorithm capable of generating unseen terms based solely on basic operators and functional terms, with symbolic regression neural networks. These networks are designed to represent explicit functional expressions and optimize them with data gradients. In particular, the specifically designed neural networks can be easily transformed to physical constraints for the training data, embedding the discovered PDEs to further optimize the metadata used for iterative PDE identification. The proposed method has been tested in four canonical PDE cases, validating its effectiveness without preliminary information and confirming its suitability for practical applications across various noise levels.
Identification of underlying partial differential equations (PDEs) for complex systems remains a formidable challenge. In the present study, a robust PDE identification method is proposed, demonstrating the ability to extract accurate governing equations under noisy conditions without prior knowledge. Specifically, the proposed method combines gene expression programming, one type of evolutionary algorithm capable of generating unseen terms based solely on basic operators and functional terms, with symbolic regression neural networks. These networks are designed to represent explicit functional expressions and optimize them with data gradients. In particular, the specifically designed neural networks can be easily transformed to physical constraints for the training data, embedding the discovered PDEs to further optimize the metadata used for iterative PDE identification. The proposed method has been tested in four canonical PDE cases, validating its effectiveness without preliminary information and confirming its suitability for practical applications across various noise levels.
Theoretical and Applied Mechanics Letters 14 (2024) 100510.
doi: 10.1016/j.taml.2024.100510
Abstract:
The flow field near a spur dike such as down flow and horseshoe vortex system(HVS) are susceptible to the topographic changes in the local scouring process, resulting in variation of the sediment transport with time.In this study, large eddy simulations with fixed-bed at different scouring stages were conducted to investigate the changes in flow field. The results imply that the bed deformation leads to an increase in flow rate per unit area, which represent the capability of sediment transportation by water, in the scour hole. Moreover, the intensity of turbulent kinetic energy (TKE) and bimodal motion near the sand bed induced by the HVS were also varied. However, the peak moments between the two sediment transport mechanisms were different. Hence, understanding the complex feedback mechanism between topography and flow field is essential for the local scour problem.
The flow field near a spur dike such as down flow and horseshoe vortex system(HVS) are susceptible to the topographic changes in the local scouring process, resulting in variation of the sediment transport with time.In this study, large eddy simulations with fixed-bed at different scouring stages were conducted to investigate the changes in flow field. The results imply that the bed deformation leads to an increase in flow rate per unit area, which represent the capability of sediment transportation by water, in the scour hole. Moreover, the intensity of turbulent kinetic energy (TKE) and bimodal motion near the sand bed induced by the HVS were also varied. However, the peak moments between the two sediment transport mechanisms were different. Hence, understanding the complex feedback mechanism between topography and flow field is essential for the local scour problem.
Theoretical and Applied Mechanics Letters 14 (2024) 100501.
doi: 10.1016/j.taml.2024.100501
Abstract:
This research comprehensively investigates the flow and thermal characteristics of a pulsating impinging jet over a dimpled surface. It analyzes the impact of key parameters (e.g., inlet velocity pulsation functions, pulsation frequency, amplitude, dimple pitch, dimple depth, Reynolds number) on flow patterns and heat transfer. Validated computational fluid dynamics (CFD) and the Re-Normalization Group (RNG) turbulence model are employed to accurately simulate complex turbulent flow behavior. Local and average heat transfer coefficients are calculated and compared to steady impingement cases, revealing the potential benefits of pulsation for heat transfer enhancement. The study also examines how pulsationinduced flow modulation and thermal mixing affect heat transfer mechanisms. Results indicate that combining fluctuating flow with a dimpled surface can improve heat transfer rates. In summary, increasing pulsation amplitude consistently enhances heat transfer, while the effect of frequency varies between impinging and wall jet zones.
This research comprehensively investigates the flow and thermal characteristics of a pulsating impinging jet over a dimpled surface. It analyzes the impact of key parameters (e.g., inlet velocity pulsation functions, pulsation frequency, amplitude, dimple pitch, dimple depth, Reynolds number) on flow patterns and heat transfer. Validated computational fluid dynamics (CFD) and the Re-Normalization Group (RNG) turbulence model are employed to accurately simulate complex turbulent flow behavior. Local and average heat transfer coefficients are calculated and compared to steady impingement cases, revealing the potential benefits of pulsation for heat transfer enhancement. The study also examines how pulsationinduced flow modulation and thermal mixing affect heat transfer mechanisms. Results indicate that combining fluctuating flow with a dimpled surface can improve heat transfer rates. In summary, increasing pulsation amplitude consistently enhances heat transfer, while the effect of frequency varies between impinging and wall jet zones.
Theoretical and Applied Mechanics Letters 14 (2024) 100508.
doi: 10.1016/j.taml.2024.100508
Abstract:
In this paper, a liquid-solid origami composite design is proposed for the improvement of impact resistance. Employing this design strategy, Kresling origami composite structures with different fillings were designed and fabricated, namely air, water, and shear thickening fluid (STF). Quasi-static compression and drop-weight impact experiments were carried out to compare and reveal the static and dynamic mechanical behavior of these structures. The results from drop-weight impact experiments demonstrated that the solid-liquid Kresling origami composite structures exhibited superior yield strength and reduced peak force when compared to their empty counterparts. Notably, the Kresling origami structures filled with STF exhibited significantly heightened yield strength and reduced peak force. For example, at an impact velocity of 3 m/s, the yield strength of single-layer STF-filled Kresling origami structures increased by 772.7% and the peak force decreased by 68.6%. This liquid-solid origami composite design holds the potential to advance the application of origami structures in critical areas such as aerospace, intelligent protection and other important fields. The demonstrated improvements in impact resistance underscore the practical viability of this approach in enhancing structural performance for a range of applications.
In this paper, a liquid-solid origami composite design is proposed for the improvement of impact resistance. Employing this design strategy, Kresling origami composite structures with different fillings were designed and fabricated, namely air, water, and shear thickening fluid (STF). Quasi-static compression and drop-weight impact experiments were carried out to compare and reveal the static and dynamic mechanical behavior of these structures. The results from drop-weight impact experiments demonstrated that the solid-liquid Kresling origami composite structures exhibited superior yield strength and reduced peak force when compared to their empty counterparts. Notably, the Kresling origami structures filled with STF exhibited significantly heightened yield strength and reduced peak force. For example, at an impact velocity of 3 m/s, the yield strength of single-layer STF-filled Kresling origami structures increased by 772.7% and the peak force decreased by 68.6%. This liquid-solid origami composite design holds the potential to advance the application of origami structures in critical areas such as aerospace, intelligent protection and other important fields. The demonstrated improvements in impact resistance underscore the practical viability of this approach in enhancing structural performance for a range of applications.
Theoretical and Applied Mechanics Letters 14 (2024) 100512.
doi: 10.1016/j.taml.2024.100512
Abstract:
Inspired by the excellent adhesion performances of setae structure from organisms, micro/nano-pillar array has become one of the paradigms for adhesive surfaces. The micropillar arrays are composed of the resin pillars for adhesion and the substrate with different elastic modulus for supporting. The stress singularity at the bi-material corner between the pillars and the substrate can induce the failure of the micropillar-substrate corner and further hinder the fabrication and application of micropillar arrays, yet the design for the stability of the micropillar array lacks systematical and quantitative guides. In this work, we develop a semi-analytical method to provide the full expressions for the stress distribution within the bi-material corner combining analytical derivations and numerical calculations. The predictions for the stress within the singularity field can be obtained based on the full expressions of the stress. The good agreement between the predictions and the FEM results demonstrates the high reliability of our method. By adopting the strain energy density factor approach, the stability of the pillar-substrate corner is assessed by predicting the failure at the corner. For the elastic mismatch between the pillar and substrate given in this paper, the stability can be improved by increasing the ratio of the shear modulus of the substrate to that of the micropillar. Our study provides accurate predictions for the stress distribution at the bi-material corner and can guide the optimization of material combinations of the pillars and the substrate for more stable bioinspired dry adhesives.
Inspired by the excellent adhesion performances of setae structure from organisms, micro/nano-pillar array has become one of the paradigms for adhesive surfaces. The micropillar arrays are composed of the resin pillars for adhesion and the substrate with different elastic modulus for supporting. The stress singularity at the bi-material corner between the pillars and the substrate can induce the failure of the micropillar-substrate corner and further hinder the fabrication and application of micropillar arrays, yet the design for the stability of the micropillar array lacks systematical and quantitative guides. In this work, we develop a semi-analytical method to provide the full expressions for the stress distribution within the bi-material corner combining analytical derivations and numerical calculations. The predictions for the stress within the singularity field can be obtained based on the full expressions of the stress. The good agreement between the predictions and the FEM results demonstrates the high reliability of our method. By adopting the strain energy density factor approach, the stability of the pillar-substrate corner is assessed by predicting the failure at the corner. For the elastic mismatch between the pillar and substrate given in this paper, the stability can be improved by increasing the ratio of the shear modulus of the substrate to that of the micropillar. Our study provides accurate predictions for the stress distribution at the bi-material corner and can guide the optimization of material combinations of the pillars and the substrate for more stable bioinspired dry adhesives.
Theoretical and Applied Mechanics Letters 14 (2024) 100515.
doi: 10.1016/j.taml.2024.100515
Abstract:
The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential equation. In this paper, the emerging computational science paradigm of physics-informed neural networks is studied for the first time for solving both linear and nonlinear variants of the governing dynamics. Unlike conventional methods, the proposed neural network provides rapid simulations of arbitrarily high resolution in particle size, predicting values on arbitrarily fine grids without the need for model retraining. The network is assigned a simple multi-head architecture tailored to uphold monotonicity of the modelled cumulative distribution function over particle sizes. The method is theoretically analyzed and validated against analytical results before being applied to real-world data of a batch grinding mill. The agreement between laboratory data and numerical simulation encourages the use of physics-informed neural nets for optimal planning and control of industrial comminution processes.
The breakage of brittle particulate materials into smaller particles under compressive or impact loads can be modelled as an instantiation of the population balance integro-differential equation. In this paper, the emerging computational science paradigm of physics-informed neural networks is studied for the first time for solving both linear and nonlinear variants of the governing dynamics. Unlike conventional methods, the proposed neural network provides rapid simulations of arbitrarily high resolution in particle size, predicting values on arbitrarily fine grids without the need for model retraining. The network is assigned a simple multi-head architecture tailored to uphold monotonicity of the modelled cumulative distribution function over particle sizes. The method is theoretically analyzed and validated against analytical results before being applied to real-world data of a batch grinding mill. The agreement between laboratory data and numerical simulation encourages the use of physics-informed neural nets for optimal planning and control of industrial comminution processes.
Theoretical and Applied Mechanics Letters 14 (2024) 100505.
doi: 10.1016/j.taml.2024.100505
Abstract:
This paper studies a single degree of freedom system under free vibration and controlled by a general semi-active damping. A general integral of squared error is considered as the performance index. A one-time switching damping controller is proposed and optimized. The Pontryagin Maximum Principle is used to prove that no other form of semi-active damping can provide the better performance than the proposed one-time switching damping.
This paper studies a single degree of freedom system under free vibration and controlled by a general semi-active damping. A general integral of squared error is considered as the performance index. A one-time switching damping controller is proposed and optimized. The Pontryagin Maximum Principle is used to prove that no other form of semi-active damping can provide the better performance than the proposed one-time switching damping.
Theoretical and Applied Mechanics Letters 14 (2024) 100502.
doi: 10.1016/j.taml.2024.100502
Abstract:
In this paper, two lifting mechanism models with opposing placements, which use the same hydraulic hoist model and have the same angle of 50 degrees, have been developed. The mechanical and hydraulic simulation models are established using MATLAB Simscape to analyze their kinetics and dynamics in the lifting and holding stages. The simulation findings are compared to the analytical calculation results in the steady state, and both methods show good agreement. In the early lifting stage, Model 1 produces greater force and discharges goods in the container faster than Model 2. Meanwhile, Model 2 reaches a higher force and ejects goods from the container cleaner than its counterpart at the end lifting stage. The established simulation models can consider the effects of dynamic loads due to inertial moments and forces generated during the system operation. It is crucial in studying, designing, and optimizing the structure of hydraulic-mechanical systems.
In this paper, two lifting mechanism models with opposing placements, which use the same hydraulic hoist model and have the same angle of 50 degrees, have been developed. The mechanical and hydraulic simulation models are established using MATLAB Simscape to analyze their kinetics and dynamics in the lifting and holding stages. The simulation findings are compared to the analytical calculation results in the steady state, and both methods show good agreement. In the early lifting stage, Model 1 produces greater force and discharges goods in the container faster than Model 2. Meanwhile, Model 2 reaches a higher force and ejects goods from the container cleaner than its counterpart at the end lifting stage. The established simulation models can consider the effects of dynamic loads due to inertial moments and forces generated during the system operation. It is crucial in studying, designing, and optimizing the structure of hydraulic-mechanical systems.
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