Boundary conditions for the classical solution of the Terzaghi one-dimensional consolidation equation conflict with the equation＇s initial condition. As such, the classical initial-boundary value problem for the Terz...Boundary conditions for the classical solution of the Terzaghi one-dimensional consolidation equation conflict with the equation＇s initial condition. As such, the classical initial-boundary value problem for the Terzaghi one-dimensional consolidation equation is not well-posed. Moreover, the classical boundary conditions of the equation can only be applied to problems with either perfectly pervious or perfectly impervious boundaries. General boundary conditions are proposed to overcome these shortcomings and thus transfer the solution of the Terzaghi one-dimensional consolidation equation to a well-posed initial boundary value problem. The solution for proposed general boundary conditions is validated by comparing it to the classical solution. The actual field drainage conditions can be simulated by adjusting the values of parameters b and c given in the proposed general botmdary conditions. For relatively high coefficient of consolidation, just one term in series expansions is enough to obtain results with acceptable accuracy.展开更多
In this paper,we have numerically examined the steady boundary layer of a viscous incompressible nanofluid and its heat and mass transfers above a horizontal flat sheet.The boundary conditions considered were a nonlin...In this paper,we have numerically examined the steady boundary layer of a viscous incompressible nanofluid and its heat and mass transfers above a horizontal flat sheet.The boundary conditions considered were a nonlinear magnetic field,a nonlinear velocity and convection.Such nonlinearity in hydrodynamic and heat transfer boundary conditions and also in the magnetic field has not been addressed with the great details in the literature.In this investigation,both the Brownian motion and thermophoretic diffusion have been considered.A similarity solution is achieved and the resulting ordinary differential equations (nonlinear) are worked numerically out.Upon validation,the following hydrodynamic and heat and mass transfers parameters were found:the reduced Sherwood and Nusselt numbers,the reduced skin friction coefficient,and the temperature and nanoparticle volume fraction profiles.All these parameters are found affected by the Lewis,Biot and Prandtl numbers,the stretching,thermophoretic diffusion,Brownian motion and magnetic parameters.The detailed trends observed in this paper are carefully analyzed to provide useful design suggestions.展开更多
The use of electro-osmotic chemical is an effective method to improve the clayey soil foundation.Various boundary conditions can be adopted in this method.In this work,two electrode–clay contacts,three solution condi...The use of electro-osmotic chemical is an effective method to improve the clayey soil foundation.Various boundary conditions can be adopted in this method.In this work,two electrode–clay contacts,three solution conditioners,and four anode solution supply times were used for clayey soil improvement.Based on the experimental data,electro-osmotic consolidation theory,and transport of ion theory,it is found that the electro-osmotic chemical effect of the separation of electrode–clay(E_S)is more beneficial for the transport of Ca^(2+),production of cementing material,and reduction of water content than that of electrode–clay(E_C)joining;through electrode–clay contact separation,the anode solution conditioner(NaPO3)6(E_SHMP)delayed the cementing reaction and then increased the transport of Ca^(2+)near the cathode,which increased the amount of cementing material and the electro-osmotic chemical effect;and when the anode conditioner(NaPO3)6 was used,two days of anode solution supply followed by three days cut off from the anode solution led to the highest undrained shear strength increase after the application of electro-osmotic chemical,which resolved the uneven electro-osmotic chemical effect in the E_SHMP.展开更多
The viscous flow in a wavy channel with convective boundary conditions is investigated. The channel is filled with a porous viscous fluid. Two cases of equal and different external convection coefficients on the walls...The viscous flow in a wavy channel with convective boundary conditions is investigated. The channel is filled with a porous viscous fluid. Two cases of equal and different external convection coefficients on the walls are taken into account. Effect of viscous dissipation is also considered. The governing equations are derived employing long wavelength and low Reynolds number approximations. Exact closed form solutions are obtained for the simplified equations. Important physical features for peristaltic flow caused by the wavy wave are pumping, trapping and heat transfer rate at the channel walls. These are discussed one by one in depth and detail through graphical illustrations. Special attention has been given to the effects of convective boundary conditions. The results show that for Bi1≠Bi2, there exists a critical value of Brinkman number Brc at which the temperatures of both the walls become equal. And, for Bi1>Bi2 and Br>Brc, the temperature of the cold wall exceeds the temperature of hot wall.展开更多
This paper presents an efficient numerical method for solving the Euler equations on rectilinear grids. Wall boundary conditions on the surface of an airfoil are implemented by using their first order expansions on th...This paper presents an efficient numerical method for solving the Euler equations on rectilinear grids. Wall boundary conditions on the surface of an airfoil are implemented by using their first order expansions on the airfoil chord line, which is placed along a grid line. However, the method is not restricted to flows with small disturbances since there are no restrictions on the magnitude of the velocity or pressure perturbations. The mathematical formulation and the numerical implementation of the wall boundary conditions in a finite volume Euler code are described. Steady transonic flows are calculated about the NACA 0006, NACA 0012 and NACA 0015 airfoils, corresponding to thickness ratios of 6%, 12%, and 15%, respectively. The computed results, including surface pressure distributions, the lift coefficient, the wave drag coefficient, and the pitching moment coefficient, at angles of attack from 0° to 8° are compared with solutions at the same conditions by FLO52, a well established Euler code using body fitted curvilinear grids. Results demonstrate that the method yields acceptable accuracies even for the relatively thick NACA 0015 airfoil and at high angles of attack. This study establishes the potential of extending the method to computing unsteady fluid structure interaction problems, where the use of a stationary rectilinear grid offers substantial advantages in both computer time and human work since it would not require the generation of time dependent body fitted grids.展开更多
Heat transfer of an SI engine's piston is calculated by employing three different methods based on resistor-capacitor model with the help of MATLAB code, and then the piston is thermo-mechanically analyzed using c...Heat transfer of an SI engine's piston is calculated by employing three different methods based on resistor-capacitor model with the help of MATLAB code, and then the piston is thermo-mechanically analyzed using commercial ANSYS code. The results of three methods are compared to study their effects on the piston thermal behavior. It is shown that resistor-capacitor model with less number of equations and consequently less solution time, is an appropriate method for solving problems of engine piston heat transfer. In the second part, the thermal stresses due to non-uniform temperature distribution, and mechanical stresses due to mechanical loads are calculated. Finally, the temperature distributions as a thermal load along with mechanical loads are applied to the piston to determine the total stress distribution and critical fracture zones. It is found that the amount of thermal stresses is considerable.展开更多
An iterative direct-forcing immersed boundary method is extended and used to solve convection heat transfer problems.The pressure,momentum source,and heat source at immersed boundary points are calculated simultaneous...An iterative direct-forcing immersed boundary method is extended and used to solve convection heat transfer problems.The pressure,momentum source,and heat source at immersed boundary points are calculated simultaneously to achieve the best coupling.Solutions of convection heat transfer problems with both Dirichlet and Neumann boundary conditions are presented.Two approaches for the implementation of Neumann boundary condition,i.e.direct and indirect methods,are introduced and compared in terms of accuracy and computational efficiency.Validation test cases include forced convection on a heated cylinder in an unbounded flow field and mixed convection around a circular body in a lid-driven cavity.Furthermore,the proposed method is applied to study the mixed convection around a heated rotating cylinder in a square enclosure with both iso-heat flux and iso-thermal boundary conditions.Computational results show that the order of accuracy of the indirect method is less than the direct method.However,the indirect method takes less computational time both in terms of the implementation of the boundary condition and the post processing time required to compute the heat transfer variables such as the Nusselt number.It is concluded that the iterative direct-forcing immersed boundary method is a powerful technique for the solution of convection heat transfer problems with stationary/moving boundaries and various boundary conditions.展开更多
This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary Cartesian grids. Wall boundary conditions are implemented on non moving mean wall positions by assuming the airf...This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary Cartesian grids. Wall boundary conditions are implemented on non moving mean wall positions by assuming the airfoil being thin and undergoing small deformation, but the mean angle of attack of the body can still be large and we use the full nonlinear Euler equation in the field for accurate resolution of shock waves and vorticity. The method does not require the generation of moving body fitted grids and thus can be easily deployed in any fluid structure interaction problem involving relatively small deformation of a thin body. We use the first order wall boundary conditions in solving the full Euler equation. Unsteady transonic flow is calculated about an oscillating NACA 0012 airfoil at free stream Mach number M ∞ =0.755, mean angle of attack α m =0.016, amplitude of pitching oscillation α 0 =2.51, reduced frequency κ = 0.081 4. The computed results, including surface pressure distribution, instantaneous lift and moment coefficients are compared with known experimental data. It is shown that the first order boundary conditions are satisfactory for airfoils of typical thicknesses with small deformation for unsteady calculations.展开更多
Rock bolts are widely used in rock engineering projects to improve the shear capacity of the jointed rock mass.The bolt inclination angle with respect to the shear plane has a remarkable influence on the bolting perfo...Rock bolts are widely used in rock engineering projects to improve the shear capacity of the jointed rock mass.The bolt inclination angle with respect to the shear plane has a remarkable influence on the bolting performance.In this study,a new artificial molding method based on 3D scanning and printing technology was first proposed to prepare bolted joints with an inclined bolt.Then,the effects of the bolt inclination angle and boundary conditions on the shear behavior and failure characteristic of bolted joints were addressed by conducting direct shear tests under both CNL and CNS conditions.Results indicated that rock bolt could significantly improve the shear behavior of rock joints,especially in the post-yield deformation region.With the increase of bolt inclination angle,both the maximum shear stress and the maximum friction coefficient increased first and then decreased,while the maximum normal displacement decreased monotonously.Compared with CNL conditions,the maximum shear stress was larger,whereas the maximum normal displacement and friction coefficient were smaller under the CNS conditions.Furthermore,more asperity damage was observed under the CNS conditions due to the increased normal stress on the shear plane.展开更多
地震勘探中的波动方程正演模拟受计算和存储能力的限制,只能在有限空间进行,需要对其设置边界条件。常用的完全匹配层(Perfect Match Layer,PML)是一种应用广泛的边界条件,需要对边界条件设定一定的层数,层数太大时会降低正演速度和增...地震勘探中的波动方程正演模拟受计算和存储能力的限制,只能在有限空间进行,需要对其设置边界条件。常用的完全匹配层(Perfect Match Layer,PML)是一种应用广泛的边界条件,需要对边界条件设定一定的层数,层数太大时会降低正演速度和增大内存存储。因此,文中通过将PML边界条件和改进后的梯度黏弹边界(Improved Gradient Viscoelastic Layer,IGVL)结合提出一种PML-IGVL边界条件,同时,为了减少截断误差和数值频散,将PML-IGVL边界条件应用于紧致交错网格的黏滞声波方程中进行数值模拟。均匀介质和Marmousi模型中的波场数值模拟结果表明,相对于PML边界条件,PML-IGVL边界条件使用的边界厚度更小,在相同较低边界层数下,能更好地吸收反射波,同时能节省更多的存储空间,并提高正演效率,证明了PML-IGVL边界条件的有效性和优越性,是正演模拟中一种有效的边界吸收方法。展开更多
基金Foundation item： Project（50608038） supported by the National Natural Science Foundation of China
文摘Boundary conditions for the classical solution of the Terzaghi one-dimensional consolidation equation conflict with the equation＇s initial condition. As such, the classical initial-boundary value problem for the Terzaghi one-dimensional consolidation equation is not well-posed. Moreover, the classical boundary conditions of the equation can only be applied to problems with either perfectly pervious or perfectly impervious boundaries. General boundary conditions are proposed to overcome these shortcomings and thus transfer the solution of the Terzaghi one-dimensional consolidation equation to a well-posed initial boundary value problem. The solution for proposed general boundary conditions is validated by comparing it to the classical solution. The actual field drainage conditions can be simulated by adjusting the values of parameters b and c given in the proposed general botmdary conditions. For relatively high coefficient of consolidation, just one term in series expansions is enough to obtain results with acceptable accuracy.
文摘In this paper,we have numerically examined the steady boundary layer of a viscous incompressible nanofluid and its heat and mass transfers above a horizontal flat sheet.The boundary conditions considered were a nonlinear magnetic field,a nonlinear velocity and convection.Such nonlinearity in hydrodynamic and heat transfer boundary conditions and also in the magnetic field has not been addressed with the great details in the literature.In this investigation,both the Brownian motion and thermophoretic diffusion have been considered.A similarity solution is achieved and the resulting ordinary differential equations (nonlinear) are worked numerically out.Upon validation,the following hydrodynamic and heat and mass transfers parameters were found:the reduced Sherwood and Nusselt numbers,the reduced skin friction coefficient,and the temperature and nanoparticle volume fraction profiles.All these parameters are found affected by the Lewis,Biot and Prandtl numbers,the stretching,thermophoretic diffusion,Brownian motion and magnetic parameters.The detailed trends observed in this paper are carefully analyzed to provide useful design suggestions.
基金Project(41902280)supported by the National Natural Science Foundation of ChinaProject(300102219105)supported by the Fundamental Research Funds for the Central Universities,China+1 种基金Project(LP1922)supported by the Open Foundation of State Key Laboratory of Coastal and Offshore Engineering,ChinaProject(XJKFJJ201805)supported by the Open Foundation of Shaanxi Key Laboratory of Safety and Durability of Concrete Structures,China。
文摘The use of electro-osmotic chemical is an effective method to improve the clayey soil foundation.Various boundary conditions can be adopted in this method.In this work,two electrode–clay contacts,three solution conditioners,and four anode solution supply times were used for clayey soil improvement.Based on the experimental data,electro-osmotic consolidation theory,and transport of ion theory,it is found that the electro-osmotic chemical effect of the separation of electrode–clay(E_S)is more beneficial for the transport of Ca^(2+),production of cementing material,and reduction of water content than that of electrode–clay(E_C)joining;through electrode–clay contact separation,the anode solution conditioner(NaPO3)6(E_SHMP)delayed the cementing reaction and then increased the transport of Ca^(2+)near the cathode,which increased the amount of cementing material and the electro-osmotic chemical effect;and when the anode conditioner(NaPO3)6 was used,two days of anode solution supply followed by three days cut off from the anode solution led to the highest undrained shear strength increase after the application of electro-osmotic chemical,which resolved the uneven electro-osmotic chemical effect in the E_SHMP.
文摘The viscous flow in a wavy channel with convective boundary conditions is investigated. The channel is filled with a porous viscous fluid. Two cases of equal and different external convection coefficients on the walls are taken into account. Effect of viscous dissipation is also considered. The governing equations are derived employing long wavelength and low Reynolds number approximations. Exact closed form solutions are obtained for the simplified equations. Important physical features for peristaltic flow caused by the wavy wave are pumping, trapping and heat transfer rate at the channel walls. These are discussed one by one in depth and detail through graphical illustrations. Special attention has been given to the effects of convective boundary conditions. The results show that for Bi1≠Bi2, there exists a critical value of Brinkman number Brc at which the temperatures of both the walls become equal. And, for Bi1>Bi2 and Br>Brc, the temperature of the cold wall exceeds the temperature of hot wall.
文摘This paper presents an efficient numerical method for solving the Euler equations on rectilinear grids. Wall boundary conditions on the surface of an airfoil are implemented by using their first order expansions on the airfoil chord line, which is placed along a grid line. However, the method is not restricted to flows with small disturbances since there are no restrictions on the magnitude of the velocity or pressure perturbations. The mathematical formulation and the numerical implementation of the wall boundary conditions in a finite volume Euler code are described. Steady transonic flows are calculated about the NACA 0006, NACA 0012 and NACA 0015 airfoils, corresponding to thickness ratios of 6%, 12%, and 15%, respectively. The computed results, including surface pressure distributions, the lift coefficient, the wave drag coefficient, and the pitching moment coefficient, at angles of attack from 0° to 8° are compared with solutions at the same conditions by FLO52, a well established Euler code using body fitted curvilinear grids. Results demonstrate that the method yields acceptable accuracies even for the relatively thick NACA 0015 airfoil and at high angles of attack. This study establishes the potential of extending the method to computing unsteady fluid structure interaction problems, where the use of a stationary rectilinear grid offers substantial advantages in both computer time and human work since it would not require the generation of time dependent body fitted grids.
文摘Heat transfer of an SI engine's piston is calculated by employing three different methods based on resistor-capacitor model with the help of MATLAB code, and then the piston is thermo-mechanically analyzed using commercial ANSYS code. The results of three methods are compared to study their effects on the piston thermal behavior. It is shown that resistor-capacitor model with less number of equations and consequently less solution time, is an appropriate method for solving problems of engine piston heat transfer. In the second part, the thermal stresses due to non-uniform temperature distribution, and mechanical stresses due to mechanical loads are calculated. Finally, the temperature distributions as a thermal load along with mechanical loads are applied to the piston to determine the total stress distribution and critical fracture zones. It is found that the amount of thermal stresses is considerable.
文摘An iterative direct-forcing immersed boundary method is extended and used to solve convection heat transfer problems.The pressure,momentum source,and heat source at immersed boundary points are calculated simultaneously to achieve the best coupling.Solutions of convection heat transfer problems with both Dirichlet and Neumann boundary conditions are presented.Two approaches for the implementation of Neumann boundary condition,i.e.direct and indirect methods,are introduced and compared in terms of accuracy and computational efficiency.Validation test cases include forced convection on a heated cylinder in an unbounded flow field and mixed convection around a circular body in a lid-driven cavity.Furthermore,the proposed method is applied to study the mixed convection around a heated rotating cylinder in a square enclosure with both iso-heat flux and iso-thermal boundary conditions.Computational results show that the order of accuracy of the indirect method is less than the direct method.However,the indirect method takes less computational time both in terms of the implementation of the boundary condition and the post processing time required to compute the heat transfer variables such as the Nusselt number.It is concluded that the iterative direct-forcing immersed boundary method is a powerful technique for the solution of convection heat transfer problems with stationary/moving boundaries and various boundary conditions.
文摘This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary Cartesian grids. Wall boundary conditions are implemented on non moving mean wall positions by assuming the airfoil being thin and undergoing small deformation, but the mean angle of attack of the body can still be large and we use the full nonlinear Euler equation in the field for accurate resolution of shock waves and vorticity. The method does not require the generation of moving body fitted grids and thus can be easily deployed in any fluid structure interaction problem involving relatively small deformation of a thin body. We use the first order wall boundary conditions in solving the full Euler equation. Unsteady transonic flow is calculated about an oscillating NACA 0012 airfoil at free stream Mach number M ∞ =0.755, mean angle of attack α m =0.016, amplitude of pitching oscillation α 0 =2.51, reduced frequency κ = 0.081 4. The computed results, including surface pressure distribution, instantaneous lift and moment coefficients are compared with known experimental data. It is shown that the first order boundary conditions are satisfactory for airfoils of typical thicknesses with small deformation for unsteady calculations.
基金Project(U1865203)supported by the Key Projects of the Yalong River Joint Fund of the National Natural Science Foundation of ChinaProject(51279201)supported by the National Natural Science Foundation of ChinaProjects(2019YFC0605103,2019YFC0605100)supported by the National Key R&D Program of China。
文摘Rock bolts are widely used in rock engineering projects to improve the shear capacity of the jointed rock mass.The bolt inclination angle with respect to the shear plane has a remarkable influence on the bolting performance.In this study,a new artificial molding method based on 3D scanning and printing technology was first proposed to prepare bolted joints with an inclined bolt.Then,the effects of the bolt inclination angle and boundary conditions on the shear behavior and failure characteristic of bolted joints were addressed by conducting direct shear tests under both CNL and CNS conditions.Results indicated that rock bolt could significantly improve the shear behavior of rock joints,especially in the post-yield deformation region.With the increase of bolt inclination angle,both the maximum shear stress and the maximum friction coefficient increased first and then decreased,while the maximum normal displacement decreased monotonously.Compared with CNL conditions,the maximum shear stress was larger,whereas the maximum normal displacement and friction coefficient were smaller under the CNS conditions.Furthermore,more asperity damage was observed under the CNS conditions due to the increased normal stress on the shear plane.
