An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant ...An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two- and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two- and three-dimensional turbulent buoyant flows.展开更多
A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows： a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components o...A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows： a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components of conformation tensor are first computed together with the velocity and pressure to describe the change of morphology of polymer chain coils in flow fields. Macroscopic quantities of viscoelastic flow are then calculated based on the conformation tensor. Comparisons between the numerical simulations and experiments for stress patterns and velocity profiles are carried out to prove the validity of the method.展开更多
The effect of pre-shear flow on the subsequent crystallization process of polymeric melt was investigated and a flow-induced crystallization （FIC） model based on the conformation tensor incorporating the pre-shear e...The effect of pre-shear flow on the subsequent crystallization process of polymeric melt was investigated and a flow-induced crystallization （FIC） model based on the conformation tensor incorporating the pre-shear effect was proposed. The model is capable of predicting the overshoot phenomena of the stress and the flow-induced free energy change of the polymeric system at high pre-shear rates. Under the condition of flow, the increase in the activated nuclei number was contributed by the flow-induced free energy change, which showed an overwhelming effect on the nuclei formation during the pre-shear process at high shear rates. The half crystallization time （t1/2） of polypropylene （PP） as functions of pre-shear rate and pre-shear time at different crystallization temperatures was predicted and compared with the experiment data. Both numerical and experimental results showed that t1/2 of PP decreased dramatically when the flow started but leveled off at long times. It was found that two transformation stages in t1/2 existed within a wide range of shear rates. For the first stage where the melting polymer experienced a relatively weak shear flow, the acceleration of crystallization kinetics was mainly contributed by the steady value of free energy change while in the second stage for high shear rates, strong overshoot in flow-induced free energy change occurred and the crystallization kinetics was thus significantly enhanced. The overshoots in stress and flow-induced free energy change reflected an important role of flow on the primary nucleation especially when the flow was strong enough.展开更多
In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional...In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional curvature.展开更多
One kind of tensor denotation of nth Beltrami axisymmetric and nonaxisymmetric spherical vortices, their classification and symmetries were discussed. Chaotic Phenomena will occur in the dynamic system of the nonaxisy...One kind of tensor denotation of nth Beltrami axisymmetric and nonaxisymmetric spherical vortices, their classification and symmetries were discussed. Chaotic Phenomena will occur in the dynamic system of the nonaxisymmetric Beltrami spherical vortices. From these aspects, it is shown that the tensor denotation has more meaningful characters and nonaxisymmetric Beltrami shperical vortices are various and very complex.展开更多
Direct numerical simulation of decaying homogeneous isotropic turbulence （DHIT） of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we dire...Direct numerical simulation of decaying homogeneous isotropic turbulence （DHIT） of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase ＂strain generation resistance＂ and ＂vorticity generation resistance＂, i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.展开更多
A transonic turbulent separation flow in a converging-diverging transonic diffuser was studied,when there existed a separation bubble on the top wall of the diffuser triggered by strong shock-wave-boundary-layer-inter...A transonic turbulent separation flow in a converging-diverging transonic diffuser was studied,when there existed a separation bubble on the top wall of the diffuser triggered by strong shock-wave-boundary-layer-interaction(SWBLI).To capture the essential behavior of this complex flow,the current study utilized an anisotropic turbulence model developed on the basis of a statistical partial average scheme.The first order moment of turbulent fluctuations,retained by a novel average scheme,and the turbulent length scale,can be determined from the momentum equations and mechanical energy equation of the fluctuation flow,respectively.The two physical quantities were readily used to construct the nonlinear anisotropic eddy viscosity tensor and to significantly improve the computational results.Comparisons between the computational results and experimental data were carried out for velocity profiles,pressure distribution,skin friction coefficient,Reynolds stress as well as streamline vectors distribution.Without using any empirical coefficients and wall functions,the numerical results were in good agreement with the available experimental data,further confirming that the nonlinear anisotropic eddy viscosity tensor is the decisive factor for the success of the computational results.展开更多
Polymer chain coils with entanglement is a crucial scale of structures in polymer materials since their relaxationtimes are matching practical processing times.Based on the phenomenological model of polymer chain coil...Polymer chain coils with entanglement is a crucial scale of structures in polymer materials since their relaxationtimes are matching practical processing times.Based on the phenomenological model of polymer chain coils and a new finiteelement approach,we have designed a computer software including solver,pre-and post-processing modules,and developeda digital analysis technology for the morphology of polymer chain coils in flow fields(DAMPC).Using this technology wemay simulate the morphology development of chain coils in various flow fields,such as simple shear flow,elongational flow,and any complex flow at transient or steady state.The applications made up to now show that the software predictions arecomparable with experimental results.展开更多
By studying a fully nonlinear flow deforming conformal metrics on a compact and connected manifold, we prove the long time existence and the exponential convergence of the solutions of the flow for any initial metric ...By studying a fully nonlinear flow deforming conformal metrics on a compact and connected manifold, we prove the long time existence and the exponential convergence of the solutions of the flow for any initial metric g0 with the Schouten tensor Ag0 ∈ Γk.展开更多
A new kind of Universal Serendipity Element (USE) - the Tensor Universal Serendipity Element (TUSE) is constructed by using both tensor force finite elements and the basic idea of USE. The formulation of shape functio...A new kind of Universal Serendipity Element (USE) - the Tensor Universal Serendipity Element (TUSE) is constructed by using both tensor force finite elements and the basic idea of USE. The formulation of shape functions and their derivatives for TUSE is presented. TUSE can be used to study steady and unsteady transonic flow fields when combined with Taylor-Galerkin Finite Element Methods, the NND scheme in FDM, and four-stage Runge-Kutta methods. As numerical examples the transonic flow in cascades and one kind of complex unsteady transonic axisymmetric how in engineering are studied. It is shown that the algorithm presented in this paper is efficient and robust.展开更多
On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form...On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.展开更多
The continuum approach in fluid flow modeling is generally applied to porous geological media, but has limited applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely dis...The continuum approach in fluid flow modeling is generally applied to porous geological media, but has limited applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely distributed in the matrix, it may be difficult or erroneous to use a porous medium fluid flow model with continuum assumptions to describe the fluid flow in fractured rocks at small or even large field scales. A discrete fracture fluid flow approach incorporating a stochastic fracture network with numerical fluid flow simulations could have the capability of capturing fluid flow behaviors such as inhomogeneity and anisotropy while reflecting the changes of hydraulic features at different scales. Moreover, this approach can be implemented to estimate the size of the representative elementary volume (REV) in order to find out the scales at which a porous medium flow model could be applied, and then to determine the hydraulic conductivity tensor for fractured rocks. The following topics are focused on in this study: (a) conceptual discrete fracture fluid flow modeling incorporating a stochastic fracture network with numerical flow simulations; (b) estimation of REV and hydraulic conductivity tensor for fractured rocks utilizing a stochastic fracture network with numerical fluid flow simulations; (c) investigation of the effect of fracture orientation and density on the hydraulic conductivity and REV by implementing a stochastic fracture network with numerical fluid flow simulations, and (d) fluid flow conceptual models accounting for major and minor fractures in the 2 D or 3 D flow fields incorporating a stochastic fracture network with numerical fluid flow simulations.展开更多
文摘An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two- and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two- and three-dimensional turbulent buoyant flows.
基金This work was financially supported by the National Natural Science Foundation of China(Nos.20204007 and 50390090)the Doctoral Foundation of National Education Committee of China(No.20030248008)the 863 Project of China(No.2002AA336120).
文摘A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows： a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components of conformation tensor are first computed together with the velocity and pressure to describe the change of morphology of polymer chain coils in flow fields. Macroscopic quantities of viscoelastic flow are then calculated based on the conformation tensor. Comparisons between the numerical simulations and experiments for stress patterns and velocity profiles are carried out to prove the validity of the method.
基金supported by the National Natural Science Foundation of China(No.10590355)the Shanghai Leading Academic Discipline Project(No.B202)
文摘The effect of pre-shear flow on the subsequent crystallization process of polymeric melt was investigated and a flow-induced crystallization （FIC） model based on the conformation tensor incorporating the pre-shear effect was proposed. The model is capable of predicting the overshoot phenomena of the stress and the flow-induced free energy change of the polymeric system at high pre-shear rates. Under the condition of flow, the increase in the activated nuclei number was contributed by the flow-induced free energy change, which showed an overwhelming effect on the nuclei formation during the pre-shear process at high shear rates. The half crystallization time （t1/2） of polypropylene （PP） as functions of pre-shear rate and pre-shear time at different crystallization temperatures was predicted and compared with the experiment data. Both numerical and experimental results showed that t1/2 of PP decreased dramatically when the flow started but leveled off at long times. It was found that two transformation stages in t1/2 existed within a wide range of shear rates. For the first stage where the melting polymer experienced a relatively weak shear flow, the acceleration of crystallization kinetics was mainly contributed by the steady value of free energy change while in the second stage for high shear rates, strong overshoot in flow-induced free energy change occurred and the crystallization kinetics was thus significantly enhanced. The overshoots in stress and flow-induced free energy change reflected an important role of flow on the primary nucleation especially when the flow was strong enough.
基金supported by the National Natural Science Foundation of China under the grant numbers 11126073the Fundamental Research Funds for the Central Universities of SCUT under the grant number 2012ZB0017
文摘In this article, we study the steady, shrinking, and expanding Kahler-Ricci solitons with vanishing Bochner-Weyl tensor and prove that, under this condition, the Ricci solitons must have constant holomorphic sectional curvature.
文摘One kind of tensor denotation of nth Beltrami axisymmetric and nonaxisymmetric spherical vortices, their classification and symmetries were discussed. Chaotic Phenomena will occur in the dynamic system of the nonaxisymmetric Beltrami spherical vortices. From these aspects, it is shown that the tensor denotation has more meaningful characters and nonaxisymmetric Beltrami shperical vortices are various and very complex.
基金supported by the National Natural Science Foundation of China (Grant No. 10872060)the Fundamental Research Funds for the Central Universities (Grant No. HIT.BRET2.2010008)
文摘Direct numerical simulation of decaying homogeneous isotropic turbulence （DHIT） of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase ＂strain generation resistance＂ and ＂vorticity generation resistance＂, i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.
基金Aerospace Power Foundation(6141B09050397)Foudamental Reasearch Foundation of North China University of Technology(110052971921/042).
文摘A transonic turbulent separation flow in a converging-diverging transonic diffuser was studied,when there existed a separation bubble on the top wall of the diffuser triggered by strong shock-wave-boundary-layer-interaction(SWBLI).To capture the essential behavior of this complex flow,the current study utilized an anisotropic turbulence model developed on the basis of a statistical partial average scheme.The first order moment of turbulent fluctuations,retained by a novel average scheme,and the turbulent length scale,can be determined from the momentum equations and mechanical energy equation of the fluctuation flow,respectively.The two physical quantities were readily used to construct the nonlinear anisotropic eddy viscosity tensor and to significantly improve the computational results.Comparisons between the computational results and experimental data were carried out for velocity profiles,pressure distribution,skin friction coefficient,Reynolds stress as well as streamline vectors distribution.Without using any empirical coefficients and wall functions,the numerical results were in good agreement with the available experimental data,further confirming that the nonlinear anisotropic eddy viscosity tensor is the decisive factor for the success of the computational results.
基金This work was supported by the research grants from the National Natural Science Foundation of China(No.50290090No.20204007+2 种基金No.20174024)National 863 project of China(No.2002AA336120)the Doctoral Foundation of National Education Committee of China(
文摘Polymer chain coils with entanglement is a crucial scale of structures in polymer materials since their relaxationtimes are matching practical processing times.Based on the phenomenological model of polymer chain coils and a new finiteelement approach,we have designed a computer software including solver,pre-and post-processing modules,and developeda digital analysis technology for the morphology of polymer chain coils in flow fields(DAMPC).Using this technology wemay simulate the morphology development of chain coils in various flow fields,such as simple shear flow,elongational flow,and any complex flow at transient or steady state.The applications made up to now show that the software predictions arecomparable with experimental results.
基金Research supported by NSFC (10771189 and 10831008)
文摘By studying a fully nonlinear flow deforming conformal metrics on a compact and connected manifold, we prove the long time existence and the exponential convergence of the solutions of the flow for any initial metric g0 with the Schouten tensor Ag0 ∈ Γk.
基金The project supported by the National Natural Science Foundation of China
文摘A new kind of Universal Serendipity Element (USE) - the Tensor Universal Serendipity Element (TUSE) is constructed by using both tensor force finite elements and the basic idea of USE. The formulation of shape functions and their derivatives for TUSE is presented. TUSE can be used to study steady and unsteady transonic flow fields when combined with Taylor-Galerkin Finite Element Methods, the NND scheme in FDM, and four-stage Runge-Kutta methods. As numerical examples the transonic flow in cascades and one kind of complex unsteady transonic axisymmetric how in engineering are studied. It is shown that the algorithm presented in this paper is efficient and robust.
文摘On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.
基金ChinaCommitteeofEducation theUniver sityofArizonaandtheMetropolitanWaterDistrictofSouthernCaliforni a.
文摘The continuum approach in fluid flow modeling is generally applied to porous geological media, but has limited applicability to fractured rocks. With the presence of a discrete fracture network relatively sparsely distributed in the matrix, it may be difficult or erroneous to use a porous medium fluid flow model with continuum assumptions to describe the fluid flow in fractured rocks at small or even large field scales. A discrete fracture fluid flow approach incorporating a stochastic fracture network with numerical fluid flow simulations could have the capability of capturing fluid flow behaviors such as inhomogeneity and anisotropy while reflecting the changes of hydraulic features at different scales. Moreover, this approach can be implemented to estimate the size of the representative elementary volume (REV) in order to find out the scales at which a porous medium flow model could be applied, and then to determine the hydraulic conductivity tensor for fractured rocks. The following topics are focused on in this study: (a) conceptual discrete fracture fluid flow modeling incorporating a stochastic fracture network with numerical flow simulations; (b) estimation of REV and hydraulic conductivity tensor for fractured rocks utilizing a stochastic fracture network with numerical fluid flow simulations; (c) investigation of the effect of fracture orientation and density on the hydraulic conductivity and REV by implementing a stochastic fracture network with numerical fluid flow simulations, and (d) fluid flow conceptual models accounting for major and minor fractures in the 2 D or 3 D flow fields incorporating a stochastic fracture network with numerical fluid flow simulations.
