Forchheimer方程作为非达西渗流中广泛应用的基本方程之一,方程中A、B系数的确定一直是孔隙介质渗流领域中的热点及难点,不同学者根据渗流试验结果提出了不同的Forchheimer方程A、B系数的经验公式,但对于均质以及混合粒径的非均质条件...Forchheimer方程作为非达西渗流中广泛应用的基本方程之一,方程中A、B系数的确定一直是孔隙介质渗流领域中的热点及难点,不同学者根据渗流试验结果提出了不同的Forchheimer方程A、B系数的经验公式,但对于均质以及混合粒径的非均质条件下评价各经验公式适用性的研究较少。因此在渗流阻力试验的基础上,采用归一化目标函数和线性回归法评价了Forchheimer方程经验公式的适用性,为不同孔隙介质条件下Forchheimer方程经验公式的选取提供参考。结果表明:对于均质孔隙介质,Sidiropoulou公式对水力梯度有着很好的预测效果;对于2种混合粒径孔隙介质,在使用平均粒径的基础上,还应考虑混合粒径的质量比和大小因素,Macdonald公式的预测效果受混合粒径的质量比和大小影响较小,Kadlec and Knight公式对于水力梯度的预测结果较为稳定;对于5种混合粒径孔隙介质,使用d60作为特征粒径进行预测的效果较好,Kadlec and Knight公式对于系数A的预测效果较好,Ergun公式对于系数B的预测效果较好。研究结果能够为工程中均质及非均质松散砂砾石孔隙介质渗流计算的Forchheimer方程的选取提供依据。展开更多
We present an efficient deep learning method called coupled deep neural networks(CDNNs) for coupling of the Stokes and Darcy–Forchheimer problems. Our method compiles the interface conditions of the coupled problems ...We present an efficient deep learning method called coupled deep neural networks(CDNNs) for coupling of the Stokes and Darcy–Forchheimer problems. Our method compiles the interface conditions of the coupled problems into the networks properly and can be served as an efficient alternative to the complex coupled problems. To impose energy conservation constraints, the CDNNs utilize simple fully connected layers and a custom loss function to perform the model training process as well as the physical property of the exact solution. The approach can be beneficial for the following reasons: Firstly, we sample randomly and only input spatial coordinates without being restricted by the nature of samples.Secondly, our method is meshfree, which makes it more efficient than the traditional methods. Finally, the method is parallel and can solve multiple variables independently at the same time. We present the theoretical results to guarantee the convergence of the loss function and the convergence of the neural networks to the exact solution. Some numerical experiments are performed and discussed to demonstrate performance of the proposed method.展开更多
A three-dimensional Darcy Forchheimer mixed convective flow of a couple stress hybrid nanofluid flow through a vertical plate by means of the double diffusion Cattaneo-Christov model is presented in this study.The inf...A three-dimensional Darcy Forchheimer mixed convective flow of a couple stress hybrid nanofluid flow through a vertical plate by means of the double diffusion Cattaneo-Christov model is presented in this study.The influence of highorder velocity slip flow,as well as a passive and active control,is also considered.The motive of the research is to develop a computational model,using cobalt ferrite(Co Fe_(2)O_(4))and copper(Cu)nanoparticles(NPs)in the carrier fluid water,to magnify the energy and mass communication rate and boost the efficiency and performance of thermal energy conduction for a variety of commercial and biological purposes.The proposed model becomes more significant,with an additional effect of non-Fick's mass flux and Fourier's heat model to report the energy and mass passage rate.The results are obtained through the computational strategy parametric continuation method.The figures are plotted to reveal the physical sketch of the obtained solution,while the statistical assessment has been evaluated through tables.It has been observed that the dispersion of Cu and Co Fe_(2)O_(4)NPs to the base fluid significantly enhances the velocity and thermal conductivity of water,which is the most remarkable property of these NPs from the industrial point of view.展开更多
This paper investigates the spatial behavior of the solutions of the Forchheimer equations in a semi-infinite cylinder.Using the energy estimation method and the differential inequality technology,the differential ine...This paper investigates the spatial behavior of the solutions of the Forchheimer equations in a semi-infinite cylinder.Using the energy estimation method and the differential inequality technology,the differential inequality about the solution is derived.By solving this differential inequality,it is proved that the solutions grow polynomially or decay exponentially with spatial variables.展开更多
文摘Forchheimer方程作为非达西渗流中广泛应用的基本方程之一,方程中A、B系数的确定一直是孔隙介质渗流领域中的热点及难点,不同学者根据渗流试验结果提出了不同的Forchheimer方程A、B系数的经验公式,但对于均质以及混合粒径的非均质条件下评价各经验公式适用性的研究较少。因此在渗流阻力试验的基础上,采用归一化目标函数和线性回归法评价了Forchheimer方程经验公式的适用性,为不同孔隙介质条件下Forchheimer方程经验公式的选取提供参考。结果表明:对于均质孔隙介质,Sidiropoulou公式对水力梯度有着很好的预测效果;对于2种混合粒径孔隙介质,在使用平均粒径的基础上,还应考虑混合粒径的质量比和大小因素,Macdonald公式的预测效果受混合粒径的质量比和大小影响较小,Kadlec and Knight公式对于水力梯度的预测结果较为稳定;对于5种混合粒径孔隙介质,使用d60作为特征粒径进行预测的效果较好,Kadlec and Knight公式对于系数A的预测效果较好,Ergun公式对于系数B的预测效果较好。研究结果能够为工程中均质及非均质松散砂砾石孔隙介质渗流计算的Forchheimer方程的选取提供依据。
基金Project supported in part by the National Natural Science Foundation of China (Grant No.11771259)the Special Support Program to Develop Innovative Talents in the Region of Shaanxi Province+1 种基金the Innovation Team on Computationally Efficient Numerical Methods Based on New Energy Problems in Shaanxi Provincethe Innovative Team Project of Shaanxi Provincial Department of Education (Grant No.21JP013)。
文摘We present an efficient deep learning method called coupled deep neural networks(CDNNs) for coupling of the Stokes and Darcy–Forchheimer problems. Our method compiles the interface conditions of the coupled problems into the networks properly and can be served as an efficient alternative to the complex coupled problems. To impose energy conservation constraints, the CDNNs utilize simple fully connected layers and a custom loss function to perform the model training process as well as the physical property of the exact solution. The approach can be beneficial for the following reasons: Firstly, we sample randomly and only input spatial coordinates without being restricted by the nature of samples.Secondly, our method is meshfree, which makes it more efficient than the traditional methods. Finally, the method is parallel and can solve multiple variables independently at the same time. We present the theoretical results to guarantee the convergence of the loss function and the convergence of the neural networks to the exact solution. Some numerical experiments are performed and discussed to demonstrate performance of the proposed method.
基金Deanship of Scientific Research at King Khalid University for funding this work through Large Groups Project under grant number(RGP.2/155/43)。
文摘A three-dimensional Darcy Forchheimer mixed convective flow of a couple stress hybrid nanofluid flow through a vertical plate by means of the double diffusion Cattaneo-Christov model is presented in this study.The influence of highorder velocity slip flow,as well as a passive and active control,is also considered.The motive of the research is to develop a computational model,using cobalt ferrite(Co Fe_(2)O_(4))and copper(Cu)nanoparticles(NPs)in the carrier fluid water,to magnify the energy and mass communication rate and boost the efficiency and performance of thermal energy conduction for a variety of commercial and biological purposes.The proposed model becomes more significant,with an additional effect of non-Fick's mass flux and Fourier's heat model to report the energy and mass passage rate.The results are obtained through the computational strategy parametric continuation method.The figures are plotted to reveal the physical sketch of the obtained solution,while the statistical assessment has been evaluated through tables.It has been observed that the dispersion of Cu and Co Fe_(2)O_(4)NPs to the base fluid significantly enhances the velocity and thermal conductivity of water,which is the most remarkable property of these NPs from the industrial point of view.
基金Supported by Innovation Team Project of Humanities and Social Sciences in Colleges and Universities of Guangdong Province(Grant No.2020WCXTd008)Research Team Project of Guangzhou Huashang College(Grant No.2021HSKT01).
文摘This paper investigates the spatial behavior of the solutions of the Forchheimer equations in a semi-infinite cylinder.Using the energy estimation method and the differential inequality technology,the differential inequality about the solution is derived.By solving this differential inequality,it is proved that the solutions grow polynomially or decay exponentially with spatial variables.
