Boundary Vorticity Dynamics Research Articles

A Boundary-Vorticity Perspective on Lift Enhancement at Ultra-Low Reynolds Numbers

The ultra-low Reynolds number flow over airfoils is considered from the perspective of boundary vorticity dynamics in this paper. The dynamic balance between the streamwise pressure gradient and vorticity creation rate at the wall is highlighted by the boundary vorticity flux. It is a localized feature with a high peak generally indicating impending boundary layer separation. Two interesting features of ultra-low Reynolds number flows are considered. Firstly, the higher values of lift coefficient with decreasing Reynolds number is seen to be due to delayed boundary layer separation. The peak in boundary vorticity flux clearly predicts the separation event. Secondly, the lift enhancement achieved by certain optimal airfoils due to a vortex trapped in the airfoil cavity is considered. An interesting double-peak in boundary vorticity flux seen for the optimal airfoil enhances the lift. An alternative interpretation of the lift enhancement is also provided by examining the Lamb vector-field.

Vorticity dynamics diagnosis of the internal flow field in a high-load counter-rotating compressor

AbstractA high-load counter-rotating compressor is optimised based on the method of coupling aerodynamic optimisation technology and computational fluid dynamics, and the flow structures in the passage are analysed and evaluated by vorticity dynamics diagnosis. The results show that the aerodynamic performance of optimised compressor are obviously improved at both design point and off-design point. By comparing the distribution characteristics of vorticity dynamics parameters on the blade surface before and after the optimisation, it is found that BVF (boundary vorticity flux) and circumferential vorticity can effectively capture high flow loss regions such as shock waves and secondary flow in the passage. In addition, the BEF (Boundary enstrophy flux) diagnosis method based on the theory of boundary enstrophy flux is developed, which expands the application scenario of the boundary vorticity dynamics diagnosis method. The change of vorticity dynamics parameters shows blade geometric parameters’ influence on the passage’s viscous flow field, which provides a theoretical basis for the aerodynamic optimisation design.

Lie derivatives of fundamental surface quantities in incompressible viscous flows

Lie derivative is an important concept in differential geometry. From the perspective of theoretical fluid dynamics, the present paper evaluates and interprets the Lie derivatives of the fundamental surface physical quantities (including skin friction, surface vorticity, and surface pressure) with respect to a characteristic velocity field in near-wall incompressible viscous flows. It is found that the Lie derivatives are directly associated with the boundary enstrophy flux, an orthogonal pair of skin friction and surface vorticity, and an orthogonal pair of surface enstrophy gradient and its conjugate vector, while components of the Lie derivatives in skin-friction-surface-vorticity orthogonal frame are related to four on-wall coupling scalar quantities (associated with the skin friction divergence and the surface vorticity divergence). The derived theoretical results are first evaluated in a laminar oblique Hiemenz flow and a turbulent channel flow. Then, features of the Lie derivatives are explored in a typical skin friction structure generated by a complex separated flow over a hill model. The present exposition provides a unique perspective of the Lie derivatives to the boundary vorticity dynamics and near-wall flow physics.

Boundary vorticity dynamics of two-phase viscous flow

From the Navier–Stokes–Korteweg equations, the exact relations between the fundamental surface physical quantities for the two-phase viscous flow with the diffuse interface are derived, including density gradient, shear stress, vorticity, pressure, enstrophy flux, and surface curvature. These theoretical results provide a solid foundation of the boundary/interfacial vorticity dynamics and a new tool for the analysis of complex interfacial phenomena in two-phase viscous flows. To demonstrate the application of the developed results, simulation of a droplet impacting and spreading on a solid wall is conducted by using a recently developed well-balanced discrete unified gas kinetic scheme, focusing on the spreading process when the separation bubbles form inside the droplet. The distributions of shear stress, pressure, and enstrophy flux at the interface and the wall are analyzed, particularly near the moving contact points and other characteristic points. This example gives an unique perspective to the physics of droplet impingement on a wall.

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

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

Numerical analysis of thermo-sensitive cavitating flows with special emphasises on flow separation and enstrophy conversion

The objectives of this paper are to investigate the flow separation and its effects on the characteristics of enstrophy conversion in a thermo-sensitive cavitating flow. Simulated results indicate the correlation exists in the flow separation and re-entrant-jets can be well depicted by the application of boundary vorticity dynamics theory (BVDT). The distributions and first-order moment of the wall vorticity demonstrate that the shedding, collapse and reattachment of cavity enhance the effect of vorticity. To reveal the evolution mechanism and distribution characteristics of enstrophy, various terms of enstrophy are established. As demonstrated by the results, the enstrophy production term (EPT) dominates the entire energy evolution process, and it is distributed in the interface of the cavity where intensive mass transfer exists. The enstrophy viscosity dissipation term (EVDT) always reduces enstrophy and inhibits energy loss. The impacts of the other two terms on absolute enstrophy are limited due to the smaller numerical integration. Furthermore, the attachment sheet cavity suppresses the development of various terms because of the stationary flow field. Whereas the multiscale detachment or collapse of cavity lead to a rapid increase in enstrophy, which manifests as the energy loss becomes evident.

A boundary vorticity diagnosis of the flows in a model pump-turbine in turbine mode

In the present study, the internal flow field in a model pump-turbine operating in turbine mode was numerically studied. By recognizing that appearance of boundary vorticity flux (BVF)’s peaks might act as the precursors of flow separation in turbomachines, flow diagnosis based on the boundary vorticity dynamics was then performed. It was shown that the effect of the BVF distribution at the condition in design operating zone is to weaken the axial vorticity component ωz, as well as to enhance the radial and circumferential vorticity components ωr and ωθ. Thus, the peaks of the axial BVF component σz led to the strong weakening of ωz, which is responsible for the flow separations. Geometric optimization for the runner was then achieved by modifying the inlet angle of the blade from 14° to 16°. The optimization successfully suppressed the occurrence of the flow separations and improved the moment on the runner at design operating condition by 4%, which was achieved by the redistribution of the axial BVF component generated by pressure σpz on the pressure side. The fact that only an accurate steady simulation is required for the analysis indicates the great potential application of this method in engineering practice.

A study of boundary vorticity dynamics and identification of large-scale structures in flow field based on two-dimensional flow around a bluff body

A method based on decomposition of acceleration field and Lie derivative is introduced to identify shearing and rotational domains. This method is validated on two typical kinds of model flows. Vorticity dynamics of flow around bluff body is studied, illustrated by numerical examples of flow around an elliptic cylinder, a slanted elliptic cylinder and an elliptic cylinder with a pair of bumps on the front side. To explain the generation of vortical structures and how they evolve into inner flow field, boundary vorticity dynamics analysis is performed. Boundary vorticity flux as well as the enstrophy diffusion flux creates vorticity sources and vorticity sinks, which generate or consume boundary vorticity, then shearing layers are generated and interact with each other finally create vortices. The results provide potential in accurate flow control by boundary deformation, and show that relevant theoretical conclusions can be effectively applied in revealing the flow mechanisms.

Design Improvement of the Splitter Blade in the Centrifugal Pump Impeller Based on Theory of Boundary Vorticity Dynamics

Design Improvement of the Splitter Blade in the Centrifugal Pump Impeller Based on Theory of Boundary Vorticity Dynamics

English

The true problem of turbulence dynamics is the problem of its origin and successive development from some initial conditions (IC) at some boundary conditions (BC) to an ultimate state restored, in a statistical sense, as fully developed turbulence. Since this intricate route is unknown up to now, a second approach is used quite frequently. That is, turbulent flows are studied as they are disregarding their origin, and without looking into some of the details of the mechanisms of turbulence production and sustenance. The last approach has been mainly represented by Kolmogorov's papers which have kept the turbulence community quite busy until now. This fractional/ local approach aiming to describe theoretically the extremely complicated details of the visible fluctuating motion superimposed on a main motion, i.e. its noise, to the detriment of the essential aspects of turbulence (the origin and its self-sustaining mechanism), was however worth developing both mathematical and experimental analysis methods for the representation/ decomposition of the flow field. On the other hand, the extremely detailed decompositions became to some extent less useful by obscuring the physics of turbulence. In this paper, we propose a holistic approach for the entire evolution of turbulence phenomenon as being created and governed by boundary vorticity dynamics, which in our opinion mostly responds to Leonardo da Vinci's questions: where the turbulence is generated, where the turbulence maintains for long, and where the turbulence comes to rest. In contrast to the previous approaches, here we will try firstly to understand the hidden causes of various existing visible facts and then to explain them.

English

English

A vorticity dynamics view of “effective slip boundary” with application to foil-flow control

Effective slip boundary (ESB) formed on textured surfaces provides a very promising method to control complex separated flow. It is becoming technically feasible due to the rapid development of new materials and other innovative technologies. In this paper, we explore the underlying physical mechanisms and guiding principle of this new control strategy by theory of boundary vorticity dynamics. We illustrate the theory by a numerical study of using textured surface to control separated foil-flow. Unlike traditional control strategy working on existing boundary layers, this new strategy aims at weakening or even eliminating the boundary layer itself by manipulating its origin. Significant ESB control effects are observed on suppressing separation, enhancing lift, and reducing drag at stall angle of attack.

Boundary Vorticity Dynamics Since Lighthill's 1963 Article: Review and Development

In his well-known 1963 article: “Introduction. Boundary Layer Theory,” Lighthill explained for the first time how to describe quantitatively the vorticity creation rate from a solid surface and how this creation rate is dominated by the tangent pressure gradient. This was the first cornerstone of boundary vorticity dynamics, which has now been developed to a complete theory on the vorticity creation from solid or fluid boundaries and the reaction of the created vorticity to the boundaries. In this paper we present a general formulation of boundary vorticity dynamics, briefly review the theoretical progress for Newtonian fluid since 1963, examine the effect of variable viscosity and turbulence on the vorticity creation, and, of many applications, exemplify the use of the theory in aerodynamic diagnosis and optimization.