Bulat Galimzyanov, Maria Doronina, Anatolii Mokshin
The viscosity of crude oil is an important physical property that largely determines the fluidity of oil and its ability to seep through porous media such as geological rock. Predicting crude oil viscosity requires the development of reliable models that can reproduce viscosity over a wide range of temperatures and pressures. Such viscosity models must operate with a set of physical characteristics that are sufficient to describe the viscosity of an extremely complex multi-phase and multi-component system such as crude oil. The present work considers empirical data on the temperature dependence of the viscosity of crude oil samples from various fields in Russia, China, Saudi Arabia, Nigeria, Kuwait and the North Sea. For the first time, within the reduced temperature concept and using the universal scaling viscosity model, the viscosity of crude oil can be accurately determined over a wide temperature range: from low temperatures corresponding to the amorphous state to relatively high temperatures, at which all oil fractions appear as melts. A novel methodology for determining the glass transition temperature and the activation energy of viscous flow of crude oil is proposed. A relationship between the parameters of the universal scaling model for viscosity, the API gravity, the fragility index, the glass transition temperature and the activation energy of viscous has been established for the first time. It is shown that the accuracy of the results of the universal scaling model significantly exceeds the accuracy of known empirical equations, including those developed directly to describe the viscosity of petroleum products.
{"title":"Unified scaling model for viscosity of crude oil over extended temperature range","authors":"Bulat Galimzyanov, Maria Doronina, Anatolii Mokshin","doi":"arxiv-2409.05917","DOIUrl":"https://doi.org/arxiv-2409.05917","url":null,"abstract":"The viscosity of crude oil is an important physical property that largely\u0000determines the fluidity of oil and its ability to seep through porous media\u0000such as geological rock. Predicting crude oil viscosity requires the\u0000development of reliable models that can reproduce viscosity over a wide range\u0000of temperatures and pressures. Such viscosity models must operate with a set of\u0000physical characteristics that are sufficient to describe the viscosity of an\u0000extremely complex multi-phase and multi-component system such as crude oil. The\u0000present work considers empirical data on the temperature dependence of the\u0000viscosity of crude oil samples from various fields in Russia, China, Saudi\u0000Arabia, Nigeria, Kuwait and the North Sea. For the first time, within the\u0000reduced temperature concept and using the universal scaling viscosity model,\u0000the viscosity of crude oil can be accurately determined over a wide temperature\u0000range: from low temperatures corresponding to the amorphous state to relatively\u0000high temperatures, at which all oil fractions appear as melts. A novel\u0000methodology for determining the glass transition temperature and the activation\u0000energy of viscous flow of crude oil is proposed. A relationship between the\u0000parameters of the universal scaling model for viscosity, the API gravity, the\u0000fragility index, the glass transition temperature and the activation energy of\u0000viscous has been established for the first time. It is shown that the accuracy\u0000of the results of the universal scaling model significantly exceeds the\u0000accuracy of known empirical equations, including those developed directly to\u0000describe the viscosity of petroleum products.","PeriodicalId":501125,"journal":{"name":"arXiv - PHYS - Fluid Dynamics","volume":"99 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kostas D. Housiadas, Evgenios Gryparis, Georgios C. Georgiou
We investigate the effect of pressure-dependent wall slip on the steady Newtonian annular Poiseuille flow employing Navier's slip law with a slip parameter that varies exponentially with pressure. The dimensionless governing equations and accompanying auxiliary conditions are solved analytically up to second order by implementing a regular perturbation scheme in terms of the small dimensionless pressure-dependence slip parameter. An explicit formula for the average pressure drop, required to maintain a constant volumetric flowrate, is also derived. This is suitably post-processed by applying a convergence acceleration technique to increase the accuracy of the original perturbation series. The effects of pressure-dependent wall slip are more pronounced when wall slip is weak. However, as the slip coefficient increases, these effects are moderated and eventually eliminated as the perfect slip case is approached. The results show that the average pressure drop remains practically constant until the Reynolds number becomes sufficiently large. It is worth noting that all phenomena associated with pressure-dependent wall slip are amplified as the annular gap is reduced.
{"title":"Annular Newtonian Poiseuille flow with pressure-dependent wall slip","authors":"Kostas D. Housiadas, Evgenios Gryparis, Georgios C. Georgiou","doi":"arxiv-2409.04890","DOIUrl":"https://doi.org/arxiv-2409.04890","url":null,"abstract":"We investigate the effect of pressure-dependent wall slip on the steady\u0000Newtonian annular Poiseuille flow employing Navier's slip law with a slip\u0000parameter that varies exponentially with pressure. The dimensionless governing\u0000equations and accompanying auxiliary conditions are solved analytically up to\u0000second order by implementing a regular perturbation scheme in terms of the\u0000small dimensionless pressure-dependence slip parameter. An explicit formula for\u0000the average pressure drop, required to maintain a constant volumetric flowrate,\u0000is also derived. This is suitably post-processed by applying a convergence\u0000acceleration technique to increase the accuracy of the original perturbation\u0000series. The effects of pressure-dependent wall slip are more pronounced when\u0000wall slip is weak. However, as the slip coefficient increases, these effects\u0000are moderated and eventually eliminated as the perfect slip case is approached.\u0000The results show that the average pressure drop remains practically constant\u0000until the Reynolds number becomes sufficiently large. It is worth noting that\u0000all phenomena associated with pressure-dependent wall slip are amplified as the\u0000annular gap is reduced.","PeriodicalId":501125,"journal":{"name":"arXiv - PHYS - Fluid Dynamics","volume":"273 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abdullah Abukhwejah, Pankaj Jagad, Ravi Samtaney, Peter Schmid
The simulation of fluid flow problems, specifically incompressible flows governed by the Navier-Stokes equations (NSE), holds fundamental significance in a range of scientific and engineering applications. Traditional numerical methods employed for solving these equations on three-dimensional (3D) meshes are commonly known for their moderate conservation properties, high computational intensity and substantial resource demands. Relying on its ability to capture the intrinsic geometric and topological properties of simplicial meshes, discrete exterior calculus (DEC) provides a discrete analog to differential forms and enables the discretization of partial differential equations (PDEs) on meshes.We present a hybrid discretization approach for the 3D incompressible Navier-Stokes equations based on DEC and Fourier transform (FT). An existing conservative primitive variable DEC discretization of incompressible Navier-Stokes equations over surface simplicial meshes developed by Jagad et al. [1] is considered in the planar dimension while the Fourier expansion is applied in the third dimension. The test cases of three-dimensional lid-driven cavity and viscous Taylor-Green three-dimensional vortex (TGV) flows show that the simulation results using this hybrid approach are comparable to literature.
模拟流体流动问题，特别是纳维-斯托克斯方程（NSE）所控制的不可压缩流，在一系列科学和工程应用中具有重要意义。在三维（3D）网格上求解这些方程所采用的传统数值方法以其中等的守恒特性、高计算强度和大量资源需求而著称。离散外部微积分（DEC）能够捕捉到简单网格的固有几何和拓扑特性，因此它提供了一种离散的微分形式，并实现了网格上偏微分方程（PDEs）的离散化。我们在平面维考虑了 Jagad 等人[1]开发的现有曲面简网格上不可压缩 Navier-Stokes 方程的保守原始变量 DEC 离散方法，而在三维应用了傅里叶展开。三维顶盖驱动空腔和粘性泰勒-格林三维涡流（TGV）的试验结果表明，采用这种混合方法的模拟结果与文献报道的结果相当。
{"title":"A Hybrid Discrete Exterior Calculus Discretization and Fourier Transform of the Incompressible Navier-Stokes Equations in 3D","authors":"Abdullah Abukhwejah, Pankaj Jagad, Ravi Samtaney, Peter Schmid","doi":"arxiv-2409.04731","DOIUrl":"https://doi.org/arxiv-2409.04731","url":null,"abstract":"The simulation of fluid flow problems, specifically incompressible flows\u0000governed by the Navier-Stokes equations (NSE), holds fundamental significance\u0000in a range of scientific and engineering applications. Traditional numerical\u0000methods employed for solving these equations on three-dimensional (3D) meshes\u0000are commonly known for their moderate conservation properties, high\u0000computational intensity and substantial resource demands. Relying on its\u0000ability to capture the intrinsic geometric and topological properties of\u0000simplicial meshes, discrete exterior calculus (DEC) provides a discrete analog\u0000to differential forms and enables the discretization of partial differential\u0000equations (PDEs) on meshes.We present a hybrid discretization approach for the\u00003D incompressible Navier-Stokes equations based on DEC and Fourier transform\u0000(FT). An existing conservative primitive variable DEC discretization of\u0000incompressible Navier-Stokes equations over surface simplicial meshes developed\u0000by Jagad et al. [1] is considered in the planar dimension while the Fourier\u0000expansion is applied in the third dimension. The test cases of\u0000three-dimensional lid-driven cavity and viscous Taylor-Green three-dimensional\u0000vortex (TGV) flows show that the simulation results using this hybrid approach\u0000are comparable to literature.","PeriodicalId":501125,"journal":{"name":"arXiv - PHYS - Fluid Dynamics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Modern machine-learning techniques are generally considered data-hungry. However, this may not be the case for turbulence as each of its snapshots can hold more information than a single data file in general machine-learning applications. This study asks the question of whether nonlinear machine-learning techniques can effectively extract physical insights even from as little as a single snapshot of a turbulent vortical flow. As an example, we consider machine-learning-based super-resolution analysis that reconstructs a high-resolution field from low-resolution data for two-dimensional decaying turbulence. We reveal that a carefully designed machine-learning model trained with flow tiles sampled from only a single snapshot can reconstruct vortical structures across a range of Reynolds numbers. Successful flow reconstruction indicates that nonlinear machine-learning techniques can leverage scale-invariance properties to learn turbulent flows. We further show that training data of turbulent flows can be cleverly collected from a single snapshot by considering characteristics of rotation and shear tensors. The present findings suggest that embedding prior knowledge in designing a model and collecting data is important for a range of data-driven analyses for turbulent flows. More broadly, this work hopes to stop machine-learning practitioners from being wasteful with turbulent flow data.
{"title":"Single-snapshot machine learning for turbulence super resolution","authors":"Kai Fukami, Kunihiko Taira","doi":"arxiv-2409.04923","DOIUrl":"https://doi.org/arxiv-2409.04923","url":null,"abstract":"Modern machine-learning techniques are generally considered data-hungry.\u0000However, this may not be the case for turbulence as each of its snapshots can\u0000hold more information than a single data file in general machine-learning\u0000applications. This study asks the question of whether nonlinear\u0000machine-learning techniques can effectively extract physical insights even from\u0000as little as a single snapshot of a turbulent vortical flow. As an example, we\u0000consider machine-learning-based super-resolution analysis that reconstructs a\u0000high-resolution field from low-resolution data for two-dimensional decaying\u0000turbulence. We reveal that a carefully designed machine-learning model trained\u0000with flow tiles sampled from only a single snapshot can reconstruct vortical\u0000structures across a range of Reynolds numbers. Successful flow reconstruction\u0000indicates that nonlinear machine-learning techniques can leverage\u0000scale-invariance properties to learn turbulent flows. We further show that\u0000training data of turbulent flows can be cleverly collected from a single\u0000snapshot by considering characteristics of rotation and shear tensors. The\u0000present findings suggest that embedding prior knowledge in designing a model\u0000and collecting data is important for a range of data-driven analyses for\u0000turbulent flows. More broadly, this work hopes to stop machine-learning\u0000practitioners from being wasteful with turbulent flow data.","PeriodicalId":501125,"journal":{"name":"arXiv - PHYS - Fluid Dynamics","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Riblets are a well-known passive drag reduction technique with the potential for as much as 9% reduction in the frictional drag force in laboratory settings, and proven benefits for large scale aircraft. However, less information is available on the applicability of these textures for smaller air/waterborne vehicles where assumptions such as periodicity and/or asymptotic nature of the boundary layer no longer apply and the shape of the bodies of these vehicles can give rise to moderate levels of pressure drag. Here, we explore the effect of riblets on both sides of a finite-size foil consisting of a streamlined leading edge and a flat body. We use high resolution two-dimensional, two-component particle image velocimetry, with a double illumination and consecutive-overlapping imaging technique to capture the velocity field in both the boundary layer and the far field. We find the local velocity profiles and shear stress distribution, as well as the frictional and pressure components of the drag force and show the possibility of achieving reduction in both the fictional and pressure components of the drag force and record cumulative drag reduction as much as 6%. We present the intertwined relationship between the distribution of the spanwise-averaged shear stress distribution, the characteristics of the velocity profiles, and the pressure distribution around the body, and how the local distribution of these parameters work together or against each other in enhancing or diminishing the drag-reducing ability of the riblets for the entirety of the body of interest.
{"title":"Localized performance of riblets with curved cross-sectional profiles in boundary layers past finite length bodies","authors":"Shuangjiu Fu, Shabnam Raayai-Ardakani","doi":"arxiv-2409.04895","DOIUrl":"https://doi.org/arxiv-2409.04895","url":null,"abstract":"Riblets are a well-known passive drag reduction technique with the potential\u0000for as much as 9% reduction in the frictional drag force in laboratory\u0000settings, and proven benefits for large scale aircraft. However, less\u0000information is available on the applicability of these textures for smaller\u0000air/waterborne vehicles where assumptions such as periodicity and/or asymptotic\u0000nature of the boundary layer no longer apply and the shape of the bodies of\u0000these vehicles can give rise to moderate levels of pressure drag. Here, we\u0000explore the effect of riblets on both sides of a finite-size foil consisting of\u0000a streamlined leading edge and a flat body. We use high resolution\u0000two-dimensional, two-component particle image velocimetry, with a double\u0000illumination and consecutive-overlapping imaging technique to capture the\u0000velocity field in both the boundary layer and the far field. We find the local\u0000velocity profiles and shear stress distribution, as well as the frictional and\u0000pressure components of the drag force and show the possibility of achieving\u0000reduction in both the fictional and pressure components of the drag force and\u0000record cumulative drag reduction as much as 6%. We present the intertwined\u0000relationship between the distribution of the spanwise-averaged shear stress\u0000distribution, the characteristics of the velocity profiles, and the pressure\u0000distribution around the body, and how the local distribution of these\u0000parameters work together or against each other in enhancing or diminishing the\u0000drag-reducing ability of the riblets for the entirety of the body of interest.","PeriodicalId":501125,"journal":{"name":"arXiv - PHYS - Fluid Dynamics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
William A. Sirignano, Wes Hellwig, Sylvain L. Walsh
An analysis takes the variable value for turbulence kinetic energy dissipation rate $epsilon$ as it might appear from a turbulent combustion computation using either Reynolds-averaged Navier-Stokes (RANS) or large-eddy simulation (LES) and relates it to both viscous dissipation rate and turbulence kinetic energy at the Kolmogorov scale. The imposed strain rate and vorticity on these smallest eddies are readily and uniquely determined from knowledge of that kinetic energy and viscous dissipation rate. Thus, a given value of $epsilon$ at a specific time and location determines the two mechanical constraints (vorticity and strain rate) on the inflow to the flamelet. It is also shown how $epsilon$ affects the sign of the Laplacian of pressure, which must be negative to allow the existence of the flamelet. Using several different flamelet models, with and without vorticity and with and without differential mass transport, different results for maximum flamelet temperature, integrated flamelet burning rate, and stoichiometric flamelet scalar dissipation rate are obtained. For a given $epsilon$ value, flamelet models that do not consider vorticity and differential diffusion produce substantial errors in the information to be provided to the resolved or filtered scales in a turbulent combustion computation.
{"title":"Flamelet Connection to Turbulence Kinetic Energy Dissipation Rate","authors":"William A. Sirignano, Wes Hellwig, Sylvain L. Walsh","doi":"arxiv-2409.04929","DOIUrl":"https://doi.org/arxiv-2409.04929","url":null,"abstract":"An analysis takes the variable value for turbulence kinetic energy\u0000dissipation rate $epsilon$ as it might appear from a turbulent combustion\u0000computation using either Reynolds-averaged Navier-Stokes (RANS) or large-eddy\u0000simulation (LES) and relates it to both viscous dissipation rate and turbulence\u0000kinetic energy at the Kolmogorov scale. The imposed strain rate and vorticity\u0000on these smallest eddies are readily and uniquely determined from knowledge of\u0000that kinetic energy and viscous dissipation rate. Thus, a given value of\u0000$epsilon$ at a specific time and location determines the two mechanical\u0000constraints (vorticity and strain rate) on the inflow to the flamelet. It is\u0000also shown how $epsilon$ affects the sign of the Laplacian of pressure, which\u0000must be negative to allow the existence of the flamelet. Using several\u0000different flamelet models, with and without vorticity and with and without\u0000differential mass transport, different results for maximum flamelet\u0000temperature, integrated flamelet burning rate, and stoichiometric flamelet\u0000scalar dissipation rate are obtained. For a given $epsilon$ value, flamelet\u0000models that do not consider vorticity and differential diffusion produce\u0000substantial errors in the information to be provided to the resolved or\u0000filtered scales in a turbulent combustion computation.","PeriodicalId":501125,"journal":{"name":"arXiv - PHYS - Fluid Dynamics","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The dissipation of energy in the impingement zone from the collision of impinging, free, equal jets of liquids was investigated by comparison with studies on the energy dissipation from the collision of impinging, free, equal sheets of liquids. Loss of energy was studied in terms of the coefficient of restitution (COR) of the collision. With few exceptions, previous analytical studies have assumed that there is no loss of energy resulting from the collision of the jets (COR = 1), and for jets with uniform velocity profiles, the sheet velocity (velocity after the collision) is equal to the jet velocity (velocity before the collision). In this study, mass and momentum balances of impinging jets with uniform velocity profiles are revised to include the impact of non-equal velocities (COR < 1). After development of the applicable theory, the COR for impinging jets is calculated from available data in the literature on jet and sheet velocities as well as the location of the stagnation point in the impingement zone. Simple empirical correlations were developed for 1) the COR of impinging jets as a function of impingement angle and 2) the relationship of the location of the stagnation point to the COR. A theoretical equation was also derived for the impact of dissipative collisions on the thickness distribution in the liquid sheet.
{"title":"Dissipative Collisions of Impinging Liquid Jets Having Uniform Velocity Profiles","authors":"Robert Demyanovich","doi":"arxiv-2409.04856","DOIUrl":"https://doi.org/arxiv-2409.04856","url":null,"abstract":"The dissipation of energy in the impingement zone from the collision of\u0000impinging, free, equal jets of liquids was investigated by comparison with\u0000studies on the energy dissipation from the collision of impinging, free, equal\u0000sheets of liquids. Loss of energy was studied in terms of the coefficient of\u0000restitution (COR) of the collision. With few exceptions, previous analytical\u0000studies have assumed that there is no loss of energy resulting from the\u0000collision of the jets (COR = 1), and for jets with uniform velocity profiles,\u0000the sheet velocity (velocity after the collision) is equal to the jet velocity\u0000(velocity before the collision). In this study, mass and momentum balances of\u0000impinging jets with uniform velocity profiles are revised to include the impact\u0000of non-equal velocities (COR < 1). After development of the applicable theory,\u0000the COR for impinging jets is calculated from available data in the literature\u0000on jet and sheet velocities as well as the location of the stagnation point in\u0000the impingement zone. Simple empirical correlations were developed for 1) the\u0000COR of impinging jets as a function of impingement angle and 2) the\u0000relationship of the location of the stagnation point to the COR. A theoretical\u0000equation was also derived for the impact of dissipative collisions on the\u0000thickness distribution in the liquid sheet.","PeriodicalId":501125,"journal":{"name":"arXiv - PHYS - Fluid Dynamics","volume":"99 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Physics-informed neural networks (PINNs) are able to solve partial differential equations (PDEs) by incorporating the residuals of the PDEs into their loss functions. Variational Physics-Informed Neural Networks (VPINNs) and hp-VPINNs use the variational form of the PDE residuals in their loss function. Although hp-VPINNs have shown promise over traditional PINNs, they suffer from higher training times and lack a framework capable of handling complex geometries, which limits their application to more complex PDEs. As such, hp-VPINNs have not been applied in solving the Navier-Stokes equations, amongst other problems in CFD, thus far. FastVPINNs was introduced to address these challenges by incorporating tensor-based loss computations, significantly improving the training efficiency. Moreover, by using the bilinear transformation, the FastVPINNs framework was able to solve PDEs on complex geometries. In the present work, we extend the FastVPINNs framework to vector-valued problems, with a particular focus on solving the incompressible Navier-Stokes equations for two-dimensional forward and inverse problems, including problems such as the lid-driven cavity flow, the Kovasznay flow, and flow past a backward-facing step for Reynolds numbers up to 200. Our results demonstrate a 2x improvement in training time while maintaining the same order of accuracy compared to PINNs algorithms documented in the literature. We further showcase the framework's efficiency in solving inverse problems for the incompressible Navier-Stokes equations by accurately identifying the Reynolds number of the underlying flow. Additionally, the framework's ability to handle complex geometries highlights its potential for broader applications in computational fluid dynamics. This implementation opens new avenues for research on hp-VPINNs, potentially extending their applicability to more complex problems.
{"title":"An efficient hp-Variational PINNs framework for incompressible Navier-Stokes equations","authors":"Thivin Anandh, Divij Ghose, Ankit Tyagi, Abhineet Gupta, Suranjan Sarkar, Sashikumaar Ganesan","doi":"arxiv-2409.04143","DOIUrl":"https://doi.org/arxiv-2409.04143","url":null,"abstract":"Physics-informed neural networks (PINNs) are able to solve partial\u0000differential equations (PDEs) by incorporating the residuals of the PDEs into\u0000their loss functions. Variational Physics-Informed Neural Networks (VPINNs) and\u0000hp-VPINNs use the variational form of the PDE residuals in their loss function.\u0000Although hp-VPINNs have shown promise over traditional PINNs, they suffer from\u0000higher training times and lack a framework capable of handling complex\u0000geometries, which limits their application to more complex PDEs. As such,\u0000hp-VPINNs have not been applied in solving the Navier-Stokes equations, amongst\u0000other problems in CFD, thus far. FastVPINNs was introduced to address these\u0000challenges by incorporating tensor-based loss computations, significantly\u0000improving the training efficiency. Moreover, by using the bilinear\u0000transformation, the FastVPINNs framework was able to solve PDEs on complex\u0000geometries. In the present work, we extend the FastVPINNs framework to\u0000vector-valued problems, with a particular focus on solving the incompressible\u0000Navier-Stokes equations for two-dimensional forward and inverse problems,\u0000including problems such as the lid-driven cavity flow, the Kovasznay flow, and\u0000flow past a backward-facing step for Reynolds numbers up to 200. Our results\u0000demonstrate a 2x improvement in training time while maintaining the same order\u0000of accuracy compared to PINNs algorithms documented in the literature. We\u0000further showcase the framework's efficiency in solving inverse problems for the\u0000incompressible Navier-Stokes equations by accurately identifying the Reynolds\u0000number of the underlying flow. Additionally, the framework's ability to handle\u0000complex geometries highlights its potential for broader applications in\u0000computational fluid dynamics. This implementation opens new avenues for\u0000research on hp-VPINNs, potentially extending their applicability to more\u0000complex problems.","PeriodicalId":501125,"journal":{"name":"arXiv - PHYS - Fluid Dynamics","volume":"273 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dolphin swimming has been a captivating area of study, yet the hydrodynamics of the dorsal fin remain underexplored. In this study, we present three-dimensional simulations of flow around a wall-mounted dolphin dorsal fin, derived from a real dolphin scan. The NEK5000 (spectral element method) is employed with a second-order hex20 mesh to ensure high accuracy and computational efficiency in the simulations. A total of 13 cases were simulated, covering angles of attack (AoA) ranging from $0^circ$ to $60^circ$ and Reynolds numbers ($text{Re}$) between 691 and 2000. Our results show that both drag and lift increase significantly with the AoA. Almost no vortex is observed at $text{AoA} = 0^circ$, whereas complex vortex structures emerge for $text{AoA} geq 30^circ$, including half-horseshoe, hairpin, arch, and wake vortices. This study offers insights that could inform the design of next-generation underwater robots, heat exchangers, and submarine sails.
{"title":"Numerical Study of Flow Past a Wall-Mounted Dolphin Dorsal Fin at Low Reynolds Numbers","authors":"Zhonglu Lin, An-Kang Gao, Yu Zhang","doi":"arxiv-2409.04147","DOIUrl":"https://doi.org/arxiv-2409.04147","url":null,"abstract":"Dolphin swimming has been a captivating area of study, yet the hydrodynamics\u0000of the dorsal fin remain underexplored. In this study, we present\u0000three-dimensional simulations of flow around a wall-mounted dolphin dorsal fin,\u0000derived from a real dolphin scan. The NEK5000 (spectral element method) is\u0000employed with a second-order hex20 mesh to ensure high accuracy and\u0000computational efficiency in the simulations. A total of 13 cases were\u0000simulated, covering angles of attack (AoA) ranging from $0^circ$ to $60^circ$\u0000and Reynolds numbers ($text{Re}$) between 691 and 2000. Our results show that\u0000both drag and lift increase significantly with the AoA. Almost no vortex is\u0000observed at $text{AoA} = 0^circ$, whereas complex vortex structures emerge\u0000for $text{AoA} geq 30^circ$, including half-horseshoe, hairpin, arch, and\u0000wake vortices. This study offers insights that could inform the design of\u0000next-generation underwater robots, heat exchangers, and submarine sails.","PeriodicalId":501125,"journal":{"name":"arXiv - PHYS - Fluid Dynamics","volume":"854 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Matilde Fiore, Enrico Saccaggi, Lilla Koloszar, Yann Bartosiewicz, Miguel Alfonso Mendez
Data-driven RANS modeling is emerging as a promising methodology to exploit the information provided by high-fidelity data. However, its widespread application is limited by challenges in generalization and robustness to inconsistencies between input data of varying fidelity levels. This is especially true for thermal turbulent closures, which inherently depend on momentum statistics provided by low or high fidelity turbulence momentum models. This work investigates the impact of momentum modeling inconsistencies on a data-driven thermal closure trained with a dataset with multiple fidelity (DNS and RANS). The analysis of the model inputs shows that the two fidelity levels correspond to separate regions in the input space. It is here shown that such separation can be exploited by a training with heterogeneous data, allowing the model to detect the level of fidelity in its inputs and adjust its prediction accordingly. In particular, a sensitivity analysis and verification shows that such a model can leverage the data inconsistencies to increase its robustness. Finally, the verification with a CFD simulation shows the potential of this multi-fidelity training approach for flows in which momentum statistics provided by traditional models are affected by model uncertainties.
{"title":"Data-driven turbulent heat flux modeling with inputs of multiple fidelity","authors":"Matilde Fiore, Enrico Saccaggi, Lilla Koloszar, Yann Bartosiewicz, Miguel Alfonso Mendez","doi":"arxiv-2409.03395","DOIUrl":"https://doi.org/arxiv-2409.03395","url":null,"abstract":"Data-driven RANS modeling is emerging as a promising methodology to exploit\u0000the information provided by high-fidelity data. However, its widespread\u0000application is limited by challenges in generalization and robustness to\u0000inconsistencies between input data of varying fidelity levels. This is\u0000especially true for thermal turbulent closures, which inherently depend on\u0000momentum statistics provided by low or high fidelity turbulence momentum\u0000models. This work investigates the impact of momentum modeling inconsistencies\u0000on a data-driven thermal closure trained with a dataset with multiple fidelity\u0000(DNS and RANS). The analysis of the model inputs shows that the two fidelity\u0000levels correspond to separate regions in the input space. It is here shown that\u0000such separation can be exploited by a training with heterogeneous data,\u0000allowing the model to detect the level of fidelity in its inputs and adjust its\u0000prediction accordingly. In particular, a sensitivity analysis and verification\u0000shows that such a model can leverage the data inconsistencies to increase its\u0000robustness. Finally, the verification with a CFD simulation shows the potential\u0000of this multi-fidelity training approach for flows in which momentum statistics\u0000provided by traditional models are affected by model uncertainties.","PeriodicalId":501125,"journal":{"name":"arXiv - PHYS - Fluid Dynamics","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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