The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations.This paper demonstrates the viability of this a...The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations.This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields.The framework consists of a Reynolds-averaged Navier–Stokes(RANS)solver and a neuralnetwork-represented turbulence model,each accompanied by its derivative computations.For computing the sensitivities of the indirect observations to the Reynolds stress field,we use the continuous adjoint equations for the RANS equations,while the gradient of the neural network is obtained via its built-in automatic differentiation capability.We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures.We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier–Stokes equations for which no true underlying linear closure exists.The trained deep-neural-network turbulence model showed predictive capability on similar flows.展开更多
Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, ani...Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.展开更多
Partial differential equations(PDEs)play a dominant role in themathematicalmodeling ofmany complex dynamical processes.Solving these PDEs often requires prohibitively high computational costs,especially when multiple ...Partial differential equations(PDEs)play a dominant role in themathematicalmodeling ofmany complex dynamical processes.Solving these PDEs often requires prohibitively high computational costs,especially when multiple evaluations must be made for different parameters or conditions.After training,neural operators can provide PDEs solutions significantly faster than traditional PDE solvers.In this work,invariance properties and computational complexity of two neural operators are examined for transport PDE of a scalar quantity.Neural operator based on graph kernel network(GKN)operates on graph-structured data to incorporate nonlocal dependencies.Here we propose a modified formulation of GKN to achieve frame invariance.Vector cloud neural network(VCNN)is an alternate neural operator with embedded frame invariance which operates on point cloud data.GKN-based neural operator demonstrates slightly better predictive performance compared to VCNN.However,GKN requires an excessively high computational cost that increases quadratically with the increasing number of discretized objects as compared to a linear increase for VCNN.展开更多
Multiphase flows involving liquid droplets in association with gas flow occur in many industrial and sci- entific applications. Recent work has demonstrated the feasibility of using optical techniques based on laser e...Multiphase flows involving liquid droplets in association with gas flow occur in many industrial and sci- entific applications. Recent work has demonstrated the feasibility of using optical techniques based on laser extinction to simultaneously measure vapor concentration and temperature and droplet size and loading. This work introduces the theoretical background for the optimal design of such laser extinction techniques, termed WMLE （wavelength-multiplexed laser extinction）. This paper focuses on the devel- opment of WMLE and presents a systematic methodology to guide the selection of suitable wavelengths and optimize the performance of WMLE for specific applications. WMLE utilizing wavelengths from 0.5 to 10 ixm is illustrated for droplet size and vapor concentration measurements in an example of water spray, and is found to enable unique and sensitive Sauter mean diameter measurement in the range of ~1-15 ~m along with accurate vapor detection. A vapor detection strategy based on differential absorp- tion is developed to extend accurate measurement to a significantly wider range of droplet loading and vapor concentration as compared to strategies based on direct fixed-wavelength absorption. Expected performance of the sensor is modeled for an evaporating spray. This work is expected to lay the ground- work for implementing optical sensors based on WMLE in a variety of research and industrial applications involving multi-phase flows.展开更多
Unsteady cloud cavitating flow is detrimental to the efficiency of hydraulic machinery like pumps and propellers due to the resulting side-effects of vibration,noise and erosion damage.Modelling such a unsteady and hi...Unsteady cloud cavitating flow is detrimental to the efficiency of hydraulic machinery like pumps and propellers due to the resulting side-effects of vibration,noise and erosion damage.Modelling such a unsteady and highly turbulent flow remains a challenging issue.In this paper,cloud cavitating flow in a venturi is calculated using the detached eddy simulation(DES)model combined with the Merkle model.The adaptive mesh refinement(AMR)method is employed to speed up the calculation and investigate the mechanisms for vortex development in the venturi.The results indicate the velocity gradients and the generalized fluid element strongly influence the formation of vortices throughout a cavitation cycle.In addition,the cavitation-turbulence coupling is investigated on the local scale by comparing with high-fidelity experimental data and using profile stations.While the AMR calculation is able to predict well the time-averaged velocities and turbulence-related aspects near the throat,it displays discrepancies further downstream owing to a coarser grid refinement downstream and under-performs compared to a traditional grid simulation.Additionally,the AMR calculation is unable to reproduce the cavity width as observed in the experiments.Therefore,while AMR promises to speed the process significantly by refining the grid only in regions of interest,it is comparatively in line with a traditional calculation for cavitating flows.Thus this study intends to provide a reference to employing the AMR as a tool to speed up calculations and be able to simulate turbulence-cavitation interactions accurately.展开更多
Fast prediction of permeability directly from images enabled by image recognition neural networks is a novel pore-scale modeling method that has a great potential. This article presents a framework that includes (1) g...Fast prediction of permeability directly from images enabled by image recognition neural networks is a novel pore-scale modeling method that has a great potential. This article presents a framework that includes (1) generation of porous media samples,(2) computation of permeability via fluid dynamics simulations,(3) training of convolutional neural networks (CNN) with simulated data, and (4) validations against simulations. Comparison of machine learning results and the ground truths suggests excellent predictive performance across a wide range of porosities and pore geometries, especially for those with dilated pores. Owning to such heterogeneity, the permeability cannot be estimated using the conventional Kozeny–Carman approach. Computational time was reduced by several orders of magnitude compared to fluid dynamic simulations. We found that, by including physical parameters that are known to affect permeability into the neural network, the physics-informed CNN generated better results than regular CNN. However, improvements vary with implemented heterogeneity.展开更多
In view of the long stagnation in traditional turbulence modeling,researchers have attempted using machine learning to augment turbulence models.This paper presents some of the recent progresses in our group on augmen...In view of the long stagnation in traditional turbulence modeling,researchers have attempted using machine learning to augment turbulence models.This paper presents some of the recent progresses in our group on augmenting turbulence models with physics-informed machine learning.We also discuss our works on ensemble-based field inversion to provide training data for constructing machine learning models.Future and on-going research efforts are introduced.展开更多
文摘The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations.This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields.The framework consists of a Reynolds-averaged Navier–Stokes(RANS)solver and a neuralnetwork-represented turbulence model,each accompanied by its derivative computations.For computing the sensitivities of the indirect observations to the Reynolds stress field,we use the continuous adjoint equations for the RANS equations,while the gradient of the neural network is obtained via its built-in automatic differentiation capability.We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures.We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier–Stokes equations for which no true underlying linear closure exists.The trained deep-neural-network turbulence model showed predictive capability on similar flows.
文摘Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.
基金supported by the U.S.Air Force under agreement number FA865019-2-2204.
文摘Partial differential equations(PDEs)play a dominant role in themathematicalmodeling ofmany complex dynamical processes.Solving these PDEs often requires prohibitively high computational costs,especially when multiple evaluations must be made for different parameters or conditions.After training,neural operators can provide PDEs solutions significantly faster than traditional PDE solvers.In this work,invariance properties and computational complexity of two neural operators are examined for transport PDE of a scalar quantity.Neural operator based on graph kernel network(GKN)operates on graph-structured data to incorporate nonlocal dependencies.Here we propose a modified formulation of GKN to achieve frame invariance.Vector cloud neural network(VCNN)is an alternate neural operator with embedded frame invariance which operates on point cloud data.GKN-based neural operator demonstrates slightly better predictive performance compared to VCNN.However,GKN requires an excessively high computational cost that increases quadratically with the increasing number of discretized objects as compared to a linear increase for VCNN.
文摘Multiphase flows involving liquid droplets in association with gas flow occur in many industrial and sci- entific applications. Recent work has demonstrated the feasibility of using optical techniques based on laser extinction to simultaneously measure vapor concentration and temperature and droplet size and loading. This work introduces the theoretical background for the optimal design of such laser extinction techniques, termed WMLE （wavelength-multiplexed laser extinction）. This paper focuses on the devel- opment of WMLE and presents a systematic methodology to guide the selection of suitable wavelengths and optimize the performance of WMLE for specific applications. WMLE utilizing wavelengths from 0.5 to 10 ixm is illustrated for droplet size and vapor concentration measurements in an example of water spray, and is found to enable unique and sensitive Sauter mean diameter measurement in the range of ~1-15 ~m along with accurate vapor detection. A vapor detection strategy based on differential absorp- tion is developed to extend accurate measurement to a significantly wider range of droplet loading and vapor concentration as compared to strategies based on direct fixed-wavelength absorption. Expected performance of the sensor is modeled for an evaporating spray. This work is expected to lay the ground- work for implementing optical sensors based on WMLE in a variety of research and industrial applications involving multi-phase flows.
基金supported by the Office of Naval Research,USA(Grant No.N00014-18-S-B001)the Macao Young Scholars Program(Grant No.AM2022003)the Priority Postdoctoral Projects in Zhejiang Province(Grant No.341781).
文摘Unsteady cloud cavitating flow is detrimental to the efficiency of hydraulic machinery like pumps and propellers due to the resulting side-effects of vibration,noise and erosion damage.Modelling such a unsteady and highly turbulent flow remains a challenging issue.In this paper,cloud cavitating flow in a venturi is calculated using the detached eddy simulation(DES)model combined with the Merkle model.The adaptive mesh refinement(AMR)method is employed to speed up the calculation and investigate the mechanisms for vortex development in the venturi.The results indicate the velocity gradients and the generalized fluid element strongly influence the formation of vortices throughout a cavitation cycle.In addition,the cavitation-turbulence coupling is investigated on the local scale by comparing with high-fidelity experimental data and using profile stations.While the AMR calculation is able to predict well the time-averaged velocities and turbulence-related aspects near the throat,it displays discrepancies further downstream owing to a coarser grid refinement downstream and under-performs compared to a traditional grid simulation.Additionally,the AMR calculation is unable to reproduce the cavity width as observed in the experiments.Therefore,while AMR promises to speed the process significantly by refining the grid only in regions of interest,it is comparatively in line with a traditional calculation for cavitating flows.Thus this study intends to provide a reference to employing the AMR as a tool to speed up calculations and be able to simulate turbulence-cavitation interactions accurately.
文摘Fast prediction of permeability directly from images enabled by image recognition neural networks is a novel pore-scale modeling method that has a great potential. This article presents a framework that includes (1) generation of porous media samples,(2) computation of permeability via fluid dynamics simulations,(3) training of convolutional neural networks (CNN) with simulated data, and (4) validations against simulations. Comparison of machine learning results and the ground truths suggests excellent predictive performance across a wide range of porosities and pore geometries, especially for those with dilated pores. Owning to such heterogeneity, the permeability cannot be estimated using the conventional Kozeny–Carman approach. Computational time was reduced by several orders of magnitude compared to fluid dynamic simulations. We found that, by including physical parameters that are known to affect permeability into the neural network, the physics-informed CNN generated better results than regular CNN. However, improvements vary with implemented heterogeneity.
文摘In view of the long stagnation in traditional turbulence modeling,researchers have attempted using machine learning to augment turbulence models.This paper presents some of the recent progresses in our group on augmenting turbulence models with physics-informed machine learning.We also discuss our works on ensemble-based field inversion to provide training data for constructing machine learning models.Future and on-going research efforts are introduced.
