Boundary Conditions for Momentum and Vorticity at an Interface between Two Fluids

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.

Boundary Vorticity Flux and Engineering Flow Management

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the on-wall coupling of the compressing and shearing processes.This basic concept is demonstrated by previously unpublished and newly obtained numerical examples for external and internal flows,including the role of BVF as a faithful marker of the local appearance of boundary-layer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.

THE FORCING OF ANOMALOUS DIVERGENT WIND AND TRANSIENT VORTICITY FLUXES TO THE ANOMALY OF STATIONARY WAVES

The forcing of anomalous divergent wind and transient vorticity fluxes to the anomaly of stationary waves of DJF (December—January—February) 1982/1983 is studied.The results show that the anomaly of the transient vorticity flux convergence tends to cancel or dissipate the anomaly of the vorticity sources generated by divergent wind.The stationary wave anomalies are maintained by both of these forcings.It is also found that,for the DJF 1982/1983 case,both of the vorticity source anomaly over the tropical and equatorial eastern Pacific and that over the midlatitude North Pacific are important to maintain the atmospheric circulation anomaly over the Pacific/North America region.

THEORY AND CONSERVATION THEOREM OF VORTICITY FLUX IN TRANSPORT

According to the theory of the transport and vorticity dynamics,the paper establishes the theory of vorticity flux and the conservation theorem between the vorticity flux and vortex strength in a plane flow.The theory of vorticity flux is a basic one in research on turbulence.

Causal mechanism behind the stall delay by airfoil's pitching-up motion

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.

Diagnosis and Design Improvement of the Internal Flow Field in an Automotive Cooling Fan Based on Boundary Vorticity Dynamics, Part Ⅰ: Blade Profile Scaling and Rotation

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.

MAINTENANCE MECHANISMS OF THE STATIONARY WAVE ANOMALY TELECONNECTION PATTERNS IN THE UPPER TROPOSPHERE

The spatial structure and temporal variations of the stationary wave anomalies in the upper troposphere during the Northern Hemisphere winter are studied with the ECMWF data of 1980— 1988 and PCA(principal component analysis)method.The vorticity source anomalies of the main teleconnection patterns are analyzed,and their roles in the maintenance of the stationary wave anomaly teleconnection patterns are investigated with the harotropic model.The results show that the anomalies of transient vorticity flux convergences tend to cancel the anomaly of vorticity sources generated by divergent winds.The stationary wave anomaly patterns caused by divergent wind anomalies only are very different from observations.However,if the anomalous transient vorticity flux convergences are also included in the vorticity sources,the simulated patterns will be greatly improved.