Boundary conditions for momentum and vorticity have been precisely derived, paying attention to the physical meaning of each mathematical expression of terms rigorously obtained from the basic equations: Navier-Stokes...Boundary conditions for momentum and vorticity have been precisely derived, paying attention to the physical meaning of each mathematical expression of terms rigorously obtained from the basic equations: Navier-Stokes equation and the equation of vorticity transport. It has been shown first that a contribution of fluid molecules crossing over a conceptual surface moving with fluid velocity due to their fluctuating motion is essentially important to understanding transport phenomena of momentum and vorticity. A notion of surface layers, which are thin layers at both sides of an interface, has been introduced next to elucidate the transporting mechanism of momentum and vorticity from one phase to the other at an interface through which no fluid molecules are crossing over. A fact that a size of δV, in which reliable values of density, momentum, and velocity of fluid are respectively defined as a volume-averaged mass of fluid molecules, a volume-averaged momentum of fluid molecules and a mass-averaged velocity of fluid molecules, is not infinitesimal but finite has been one of the key factors leading to the boundary conditions for vorticity at an interface between two fluids. The most distinguished characteristics of the boundary conditions derived here are the zero-value conditions for a normal component of momentum flux and tangential components of vorticity flux, at an interface.展开更多
In this paper,by applying theoretical method to the governing equations of compressible viscous flow,we derive the theoretical formula of the boundary dilatation flux(BDF)on a flexible wall,which generalizes the most ...In this paper,by applying theoretical method to the governing equations of compressible viscous flow,we derive the theoretical formula of the boundary dilatation flux(BDF)on a flexible wall,which generalizes the most recent work of Mao et al.(Acta Mechanica Sinica 38(2022)321583)for a stationary wall.Different boundary sources of dilatation are explicitly identified,revealing not only the boundary generation mechanisms of vortex sound and entropy sound,but also some additional sources due to the surface vorticity,surface angular velocity,surface acceleration and surface curvature.In particular,the generation mechanism of dilatation at boundary due to the coupled divergence terms is highlighted,namely,the product of the surface velocity divergence(▽_(■B)·U)and the vorticity-induced skin friction divergence(V_(■B)·τ_(ω)).The former is attributed to the surface flexibility while the latter characterizes the footprints of near-wall coherent structures.Therefore,by properly designing the surface velocity distribution,the dilatation generation at the boundary could be controlled for practical purpose in near-wall compressible viscous flows.展开更多
To improve the performance of complex viscous engineering flows,the focus should be on local dynamics(local processes and structures)measured by the space-time derivatives of the primary-variable fields,rather than th...To improve the performance of complex viscous engineering flows,the focus should be on local dynamics(local processes and structures)measured by the space-time derivatives of the primary-variable fields,rather than these fields themselves.In the context of optimal flow management such as optimal configuration design and flow control,the local fluid dynamics on solid wall is of most direct relevance.For large Reynolds-number flows,we show that the on-wall local dynamics is highlighted by the balance between tangential pressure gradient and vorticity creation rate at the wall(boundary vorticity flux,BVF),namely the on-wall coupling of the compressing and shearing processes.This basic concept is demonstrated by previously unpublished and newly obtained numerical examples for external and internal flows,including the role of BVF as a faithful marker of the local appearance of boundary-layer separation and wall curvature discontinuity,and the use of BVF-based formulas to optimize the integrated performance of airfoil and compressor rotor blade.展开更多
To optimize the aerodynamic performance of the automobile cooling fan(ACF), the internal flow field of the original fan was numerically simulated. According to the theory of boundary vorticity dynamics(BVD), the distr...To optimize the aerodynamic performance of the automobile cooling fan(ACF), the internal flow field of the original fan was numerically simulated. According to the theory of boundary vorticity dynamics(BVD), the distribution laws of the boundary vorticity flux(BVF) on the blade surface and the circumferential vorticity(CV) at the wake plane of the fan were analyzed, and the underlying various negative factors, such as vortex shedding, separated flow and complicated secondary flow, on the fan blade surface and its dynamic source were diagnosed. Combined with the velocity triangle theory, the mathematical relationship between the BVF diagnosis and the geometrical characteristics of the blade profile(hereinafter referred to as profile) is used to guide the design improvement of the blade. The analysis found that at the same speed, the extension and rotation of the profile could match a smaller input torque at the same flow rate and pressure rise, thereby improving the efficiency of the fan. The test results confirmed the above conclusion. The peak efficiency of the improved fan has been increased by 2.3%, and the aerodynamic performance in the low-flow-rate has been improved. The conclusion of the study shows the applicability of the BVD theory in the diagnosis and design improvement of ACF internal flow.展开更多
Why the stall of an airfoil can be significantly delayed by its pitching-up motion？ Various attempts have been proposed to answer this question over the past half century, but none is satisfactory. In this letter we ...Why the stall of an airfoil can be significantly delayed by its pitching-up motion？ Various attempts have been proposed to answer this question over the past half century, but none is satisfactory. In this letter we prove that a chain of vorticity-dynamics processes at accelerating boundary is fully responsible for the causal mechanism underlying this peculiar phenomenon. The local flow behavior is explained by a simple potential-flow model.展开更多
This paper presents a critical evaluation of the physical aspects of lift generation to prove that no lift can be generated in a steady inviscid flow.Hence,the answer to the recurring question in the paper title is ne...This paper presents a critical evaluation of the physical aspects of lift generation to prove that no lift can be generated in a steady inviscid flow.Hence,the answer to the recurring question in the paper title is negative.In other words,the fluid viscosity is necessary in lift generation.The relevant topics include D’Alembert’s paradox of lift and drag,the Kutta condition,the force expression based on the boundary enstrophy flux(BEF),the vortex lift,and the generation of the vorticity and circulation.The physi-cal meanings of the variational formulations to determine the circulation and lift are discussed.In particular,in the variational formulation based on the continuity equation with the first-order Tikhonov regularization functional,an incompressible flow with the artificial viscosity(the Lagrange multiplier)is simulated,elucidating the role of the artifi-cial viscosity in lift generation.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.展开更多
This review attempts to elucidate the physical origin of aerodynamic lift of an airfoil using simple formulations and notations,particularly focusing on the critical effect of the fluid viscosity.The evolutionary deve...This review attempts to elucidate the physical origin of aerodynamic lift of an airfoil using simple formulations and notations,particularly focusing on the critical effect of the fluid viscosity.The evolutionary development of the lift problem of a flat-plate airfoil is reviewed as a canonical case from the classical inviscid circulation theory to the viscous-flow model.In particular,the physical aspects of the analytical expressions for the lift coefficient of the plate-plate airfoil are discussed,including Newton’s sine-squared law,Rayleigh’s lift formula,thin-airfoil theory and viscous-flow lift formula.The vortex-force theory is described to provide a solid foundation for consistent treatment of lift,form drag,Kutta condition,and downwash.The formation of the circulation and generation of lift are discussed based on numerical simulations of a viscous starting flow over an airfoil,and the evolution of the flow topology near the trailing edge is well correlated with the realization of the Kutta condition.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.展开更多
文摘Boundary conditions for momentum and vorticity have been precisely derived, paying attention to the physical meaning of each mathematical expression of terms rigorously obtained from the basic equations: Navier-Stokes equation and the equation of vorticity transport. It has been shown first that a contribution of fluid molecules crossing over a conceptual surface moving with fluid velocity due to their fluctuating motion is essentially important to understanding transport phenomena of momentum and vorticity. A notion of surface layers, which are thin layers at both sides of an interface, has been introduced next to elucidate the transporting mechanism of momentum and vorticity from one phase to the other at an interface through which no fluid molecules are crossing over. A fact that a size of δV, in which reliable values of density, momentum, and velocity of fluid are respectively defined as a volume-averaged mass of fluid molecules, a volume-averaged momentum of fluid molecules and a mass-averaged velocity of fluid molecules, is not infinitesimal but finite has been one of the key factors leading to the boundary conditions for vorticity at an interface between two fluids. The most distinguished characteristics of the boundary conditions derived here are the zero-value conditions for a normal component of momentum flux and tangential components of vorticity flux, at an interface.
文摘In this paper,by applying theoretical method to the governing equations of compressible viscous flow,we derive the theoretical formula of the boundary dilatation flux(BDF)on a flexible wall,which generalizes the most recent work of Mao et al.(Acta Mechanica Sinica 38(2022)321583)for a stationary wall.Different boundary sources of dilatation are explicitly identified,revealing not only the boundary generation mechanisms of vortex sound and entropy sound,but also some additional sources due to the surface vorticity,surface angular velocity,surface acceleration and surface curvature.In particular,the generation mechanism of dilatation at boundary due to the coupled divergence terms is highlighted,namely,the product of the surface velocity divergence(▽_(■B)·U)and the vorticity-induced skin friction divergence(V_(■B)·τ_(ω)).The former is attributed to the surface flexibility while the latter characterizes the footprints of near-wall coherent structures.Therefore,by properly designing the surface velocity distribution,the dilatation generation at the boundary could be controlled for practical purpose in near-wall compressible viscous flows.
基金supported in part by Natural Science Foundation of China,Project No.10572005.
文摘To improve the performance of complex viscous engineering flows,the focus should be on local dynamics(local processes and structures)measured by the space-time derivatives of the primary-variable fields,rather than these fields themselves.In the context of optimal flow management such as optimal configuration design and flow control,the local fluid dynamics on solid wall is of most direct relevance.For large Reynolds-number flows,we show that the on-wall local dynamics is highlighted by the balance between tangential pressure gradient and vorticity creation rate at the wall(boundary vorticity flux,BVF),namely the on-wall coupling of the compressing and shearing processes.This basic concept is demonstrated by previously unpublished and newly obtained numerical examples for external and internal flows,including the role of BVF as a faithful marker of the local appearance of boundary-layer separation and wall curvature discontinuity,and the use of BVF-based formulas to optimize the integrated performance of airfoil and compressor rotor blade.
基金funded by the Basic Scientific Research Funds of Central Universities and the National Science and Technology Major Project(2017-Ⅱ-0007-0021)。
文摘To optimize the aerodynamic performance of the automobile cooling fan(ACF), the internal flow field of the original fan was numerically simulated. According to the theory of boundary vorticity dynamics(BVD), the distribution laws of the boundary vorticity flux(BVF) on the blade surface and the circumferential vorticity(CV) at the wake plane of the fan were analyzed, and the underlying various negative factors, such as vortex shedding, separated flow and complicated secondary flow, on the fan blade surface and its dynamic source were diagnosed. Combined with the velocity triangle theory, the mathematical relationship between the BVF diagnosis and the geometrical characteristics of the blade profile(hereinafter referred to as profile) is used to guide the design improvement of the blade. The analysis found that at the same speed, the extension and rotation of the profile could match a smaller input torque at the same flow rate and pressure rise, thereby improving the efficiency of the fan. The test results confirmed the above conclusion. The peak efficiency of the improved fan has been increased by 2.3%, and the aerodynamic performance in the low-flow-rate has been improved. The conclusion of the study shows the applicability of the BVD theory in the diagnosis and design improvement of ACF internal flow.
基金supported by the National Natural Science Foundation of China(10921202,11221062,11521091,and 11472016)
文摘Why the stall of an airfoil can be significantly delayed by its pitching-up motion？ Various attempts have been proposed to answer this question over the past half century, but none is satisfactory. In this letter we prove that a chain of vorticity-dynamics processes at accelerating boundary is fully responsible for the causal mechanism underlying this peculiar phenomenon. The local flow behavior is explained by a simple potential-flow model.
文摘This paper presents a critical evaluation of the physical aspects of lift generation to prove that no lift can be generated in a steady inviscid flow.Hence,the answer to the recurring question in the paper title is negative.In other words,the fluid viscosity is necessary in lift generation.The relevant topics include D’Alembert’s paradox of lift and drag,the Kutta condition,the force expression based on the boundary enstrophy flux(BEF),the vortex lift,and the generation of the vorticity and circulation.The physi-cal meanings of the variational formulations to determine the circulation and lift are discussed.In particular,in the variational formulation based on the continuity equation with the first-order Tikhonov regularization functional,an incompressible flow with the artificial viscosity(the Lagrange multiplier)is simulated,elucidating the role of the artifi-cial viscosity in lift generation.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.
文摘This review attempts to elucidate the physical origin of aerodynamic lift of an airfoil using simple formulations and notations,particularly focusing on the critical effect of the fluid viscosity.The evolutionary development of the lift problem of a flat-plate airfoil is reviewed as a canonical case from the classical inviscid circulation theory to the viscous-flow model.In particular,the physical aspects of the analytical expressions for the lift coefficient of the plate-plate airfoil are discussed,including Newton’s sine-squared law,Rayleigh’s lift formula,thin-airfoil theory and viscous-flow lift formula.The vortex-force theory is described to provide a solid foundation for consistent treatment of lift,form drag,Kutta condition,and downwash.The formation of the circulation and generation of lift are discussed based on numerical simulations of a viscous starting flow over an airfoil,and the evolution of the flow topology near the trailing edge is well correlated with the realization of the Kutta condition.The presented contents are valuable for the pedagogical purposes in aerodynamics and fluid mechanics.
