Boundary Vorticity Flux Research Articles

Numerical investigation of attached cavitating flow in thermo-sensitive fluid with special emphasis on thermal effect and shedding dynamics

This study aims to investigate the unsteady cavitation shedding dynamics flow around a NACA 0015 hydrofoil in thermo-sensitive fluid with thermal effect. The thermal effects are captured by a coupled solution of the continuity, momentum and energy equations, and the numerical results show a reasonable agreement with the available experiments. Time evolution process of the vortex structure is investigated. The ability and limitation of B-factor is analysed to evaluate the thermal effect, which can provide guidance for the further improvement of B-factor. The re-entrant jet and vortex structure show strong coherent relationship with the flow separation. The re-entrant jet promotes the formation of vortex structure, which in turn affects the separation flow of the flow field. Skin friction coefficient and boundary vorticity flux are applied to displace the flow separation on the hydrofoil surface. The results showed that the streamwise velocity decreases sharply in the vicinity of the collision between the re-entrant jet and the main stream, the skin friction streamline suddenly breaks off and separation or re-attachment line occurs. The intensity of the re-entrant jet inside the cavity becomes gradually weaker, the strength of the vortex is also weakened, which causes the skin friction coefficient in this region to be almost zero, and the phenomenon of flow separation and re-attachment is indistinct.

Energy dissipation caused by boundary layer instability at vanishing viscosity

A qualitative explanation for the scaling of energy dissipation by high-Reynolds-number fluid flows in contact with solid obstacles is proposed in the light of recent mathematical and numerical results. Asymptotic analysis suggests that it is governed by a fast, small-scale Rayleigh–Tollmien–Schlichting instability with an unstable range whose lower and upper bounds scale as$Re^{3/8}$and$Re^{1/2}$, respectively. By linear superposition, the unstable modes induce a boundary vorticity flux of order$Re^{1}$, a key ingredient in detachment and drag generation according to a theorem of Kato. These predictions are confirmed by numerically solving the Navier–Stokes equations in a two-dimensional periodic channel discretized using compact finite differences in the wall-normal direction, and a spectral scheme in the wall-parallel direction.

Expressions of force and moment exerted on a body in a viscous flow via the flux of vorticity generated on its surface

Nonlinear and viscous contributions in the equation of a vorticity evolution in three-dimensional flow are represented in the divergent form. The concept ”vorticity transfer tensor” which describes transference of the vorticity in a flow is introduced. The vortex flux for all the flow points and from the body surface are defined (the vortex flux from the body surface in general case is not the same as the boundary vorticity flux used in the literature). Exact expressions of force and moment via the vortex flux from the body surface for non stationary viscous incompressible flow under the no-slip boundary condition are derived directly from Navier–Stokes equations without applying the conservation law in the whole flow region. The expressions contain only surface integrals, and are valid for calculating force and moment for each body of the system in infinite or bounded space. They are most useful when meshless vortex methods are applied for the flow simulation. That is demonstrated in the numerical example of the flow around the sphere. The formulas obtained can also be useful for checking the accuracy of the computations which are performed in natural variables.

Flow Diagnosis and Optimization Based on Vorticity Dynamics for Transonic Compressor/Fan Rotor

This paper presents two optimized rotors. The first rotor is as part of a 3-blade row optimization (IGV-rotor-stator) of a high-pressure compressor. It is based on modifying blade angles and advanced control of curvature of the airfoil camber line. The effects of these advanced blade techniques on the performance of the transonic 1.5-stage compressor were calculated using a 3D Navier-Stokes solver combined with a vortex/vorticity dynamics diagnosis method. The first optimized rotor produces a 3-blade row efficiency improvement over the baseline of 1.45% while also improving stall margin. The throttling range of the compressor is expanded largely because the shock in the rotor tip area is further downstream than that in the baseline case at the operating point. Additionally, optimizing the 3-blade row block while only adjusting the rotor geometry ensures good matching of flow angles allowing the compressor to have more range. The flow diagnostics of the rotor blade based on vortex/vorticity dynamics indicate that the boundary-layer separation behind the shock is verified by on-wall signatures of vorticity and skin-friction vector lines. In addition, azimuthal vorticity and boundary vorticity flux (BVF) are shown to be two vital flow parameters of compressor aerodynamic performance that directly relate to the improved performance of the optimized transonic compressor blade. A second rotor-only optimization is also presented for a 2.9 pressure ratio transonic fan. The objective function is the axial moment based on the BVF. An 88.5% efficiency rotor is produced.

Flow control of the wake vortex street of a circular cylinder by using a traveling wave wall at low Reynolds number

Abstract In the present study, a traveling wave wall (TWW) was employed to manipulate the vortex shedding behind a fixed circular cylinder based on a 2-D CFD numerical simulation method at a low Reynolds number of 200. The study mainly focused on four types of TWW propagation directions combined with nine different wave velocities to eliminate vortex shedding, and the lift and drag coefficients and vortex shedding modes at different propagation directions or velocities were analyzed in detail to access the effectiveness of the TWW flow control method. The control mechanism of eliminating wake stemming from the flow around a TWW-controlled circular cylinder was revealed by the boundary vorticity flux (BVF) and relative flow fields. The results show that the type of downstream propagating TWW can effectively eliminate the alternating wake. When the ratio of the wave velocity to the oncoming velocity is 2.0, the fluctuations of the lift coefficients descended to the lowest point. The averages of the drag coefficients decreased with increasing wave velocity and descended to the lowest point when the ratio of the wave velocity to the oncoming velocity was 5.0. Owing to the capture of small-scale vortices, there was a relatively larger level of vorticity in the wave valley of the TWW cylinder. The relative flow fields showed that the vortex shedding from the cylinder was completely eliminated and that the goal of eliminating the oscillating wake and suppressing the potential vortex-induced vibration (VIV) of flow around a cylinder was achieved.

Three-dimensional numerical simulation of a vortex ring impinging on a circular cylinder

A vortex ring impinging on a three-dimensional circular cylinder is studied using large eddy simulation for a Reynolds number based on the initial translational speed and diameter of the vortex ring. We have investigated the evolution of vortical structures and identified three typical evolution phases. When the primary vortex approaches the cylinder closely, a secondary vortex is generated and its segment parts move inward to the primary vortex ring. Then two large-scale loop-like vortices are formed, which evolve in opposite directions. Thirdly, the two loop-like vortices collide with each other, forming complicated small-scale vortical structures. Moreover, a series of hairpin vortices are generated due to the deformation and stretching of the tertiary vortex. The trajectories of the primary and secondary vortices and the relevant speeds of evolution are discussed. The total kinetic energy and enstrophy are investigated with the purpose of revealing the properties that are relevant to the three evolution phases. The boundary vorticity flux is further studied with the aim of analyzing the generation of vorticity and the connection with the pressure gradient on the cylinder surface.

Numerical Study of a Vortex Ring Interacting with a Three-dimensional Convex Surface

A vortex ring impinging on a three-dimensional bump is studied using Large Eddy Simulation (LES) for a Reynolds number Re = 4×10 4 based on the initial diameter and translational speed of the vortex ring. The evolution of vortical structures are investigated and an array of flow phenomena are discovered, such as the generation and deformation of secondary vortex ring, formation of loop-like vortices, interaction of vortex rings and the instability and breakdown of vortical structures. The total enstrophy of the flow reasonably elucidates some typical phases of flow evolution. Based on the Fourier analysis of the vertical vorticity, the azimuthal instabilities of the primary vortex ring are studied. Furthermore, the mechanism of vorticity generation on the bump surface has been revealed based on analysis of the boundary vorticity flux.

Large Eddy Simulation of a Vortex Ring Impacting a Bump

AbstractA vortex ring impacting a three-dimensional bump is studied using large eddy simulation for a Reynolds number Re = 4 × 104 based on the initial diameter and translational speed of the vortex ring. The effects of bump height and vortex core thickness for thin and thick vortex rings on the vortical flow phenomena and the underlying physical mechanisms are investigated. Based on the analysis of the evolution of vortical structures, two typical kinds of vortical structures, i.e., the wrapping vortices and the hair-pin vortices, are identified and play an important role in the flow state evolution. The boundary vorticity flux is analyzed to reveal the mechanism of the vorticity generation on the bump surface. The circulation of the primary vortex ring reasonably elucidates some typical phases of flow evolution. Further, the analysis of turbulent kinetic energy reveals the transition from laminar to turbulent state. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to the flow evolution and the flow transition to turbulent state.

The Optimal Hydraulic Design of Centrifugal Impeller Using Genetic Algorithm with BVF

Derived from idea of combining the advantages of two-dimensional hydraulic design theory, genetic algorithm, and boundary vorticity flux diagnosis, an optimal hydraulic design method of centrifugal pump impeller was developed. Given design parameters, the desired optimal centrifugal impeller can be obtained after several iterations by this method. Another 5 impellers with the same parameters were also designed by using single arc, double arcs, triple arcs, logarithmic spiral, and linear-variable angle spiral as blade profiles to make comparisons. Using Reynolds averaged N-S equations with a RNGk-εtwo-equation turbulence model and log-law wall function to solve 3D turbulent flow field in the flow channel between blades of 6 designed impellers by CFD code FLUENT, the investigation on velocity distributions, pressure distributions, boundary vorticity flux distributions on blade surfaces, and hydraulic performance of impellers was presented and the comparisons of impellers by different design methods were demonstrated. The results showed that the hydraulic performance of impeller designed by this method is much better than the other 5 impellers under design operation condition with almost the same head, higher efficiency, and lower rotating torque, which implied less hydraulic loss and energy consumption.

The Impeller Improvement of the Centrifugal Pump Based on BVF Diagnostic Method

Selecting one IS 150-125-250 centrifugal pump as reference model, impeller with 3D blades has been designed using two-dimensional theory. Numerical simulations using Reynolds averaged N-S equations with a RNG k-ε two-equation turbulence model and log-law wall function are used to estimate the hydraulic performance of pump and obtain BVF distributions on impeller blade pressure surfaces and suction surfaces. The results show that, compared with IS150-125-250 pump, the designed one shows better performance in a wide operation range with the maximal efficiency 2.8% increase. With the help of boundary vorticity flux diagnostic, further improvement is realized. Local defect areas on blade surfaces are identified and inlet blade angle distribution modification and wrapping angle change of designed impeller are carried out on local defect areas. The vortices that exist in designed impeller disappear after modification and it flows more smoothly in the modified impeller with slight hydraulic performance improvement than in the original designed one. BVF diagnostic can be further embedded in optimal design method to perform an automatic optimal design without manual trial-and-error procedures.

Numerical analysis of cavitation within slanted axial-flow pump

In this paper, the cavitating flow within a slanted axial-flow pump is numerically researched. The hydraulic and cavitation performance of the slanted axial-flow pump under different operation conditions are estimated. Compared with the experimental hydraulic performance curves, the numerical results show that the filter-based model is better than the standard k -ɛ model to predict the parameters of hydraulic performance. In cavitation simulation, compared with the experimental results, the proposed numerical method has good predicting ability. Under different cavitation conditions, the internal cavitating flow fields within slanted axial-flow pump are investigated. Compared with flow visualization results, the major internal flow features can be effectively grasped. In order to explore the origin of the cavitation performance breakdown, the Boundary Vorticity Flux (BVF) is introduced to diagnose the cavitating flow fields. The analysis results indicate that the cavitation performance drop is relevant to the instability of cavitating flow on the blade suction surface.

Hydraulic design, numerical simulation and BVF diagnosis of high efficiency centrifugal pump

Under the Two-dimensional Flow Theory and the Velocity Coefficient Theory, a centrifugal-pump impeller has been designed, based on the parameters of IS150-125-250 centrifugal pump. And self-compiled programs have been used to complete the hydraulic design of the whole flow passage of centrifugal pump. The space bending and twisting characteristics of the design blade are more obvious. Then, numerical simulation is applied to the inner flow field of the two pumps using RANS (Reynolds Averaged N-S) Equation with a standard k-ε two-equation turbulence model. The compare of the numerical simulation data of two centrifugal pumps, getting from 13 working points including design condition, shows that, the design pump has higher head and efficiency in the range of lower flow rate. Based on the numerical results of the inner flow of the design pump and model pump, the boundary vorticity flux (BVF) diagnostics has been used to analyze the BVF distribution of suction surface and pressure surface of two pumps. The result shows that, the BVF distribution of the design pump is more uniform and smooth, with smaller peak value.

Numerical Simulation and Flow Diagnosis of Axial-flow Pump at Part-load Condition

The paper demonstrates the flow behavior in a high specific speed axial-flow pump at part-load condition by numerical methods. The unsteady Reynolds averaged NavierStokes equations (URANS) with the filter-based model were solved by using the computational fluid dynamics code ANSYS CFX and the hydraulic performance of axial-flow pump was estimated. At part-load condition numerical results show that parameters of hydraulic performance predicted by the filter-based model are proved to match with the experiment results better than that of the standard k-ε model. Furthermore, we analyzed the internal flow field within the axial-flow pump in fully developed stall and in deep stall, respectively, and compared the obtained typical flow features with the flow visualization experimental results in (I. Goltz, 2003). The boundary vorticity flux (BVF) was introduced to diagnose the internal flow field inside blade passage at part-load condition and to find out the root of the instability vortices. Based on the BVF diagnosis, the differences about the numerical results of flow fields in deep stall were further analyzed between the standard k-ε model and the filter-based model. It show that the filter-based model is more practical to capture the unsteady flow structures than the standard k-ε model.

Vorticity Dynamics in Axial Compressor Flow Diagnosis and Design—Part II: Methodology and Application of Boundary Vorticity Flux

In a companion paper (2008, “Vorticity Dynamics in Axial Compressor Flow Diagnosis and Design,” ASME J. Fluids Eng., 130, p. 041102), a study has been made on the critical role of circumferential vorticity (CV) in the performance of axial compressor in through-flow design (TFD). It has been shown there that to enhance the pressure ratio, the positive and negative CV peaks should be pushed to the casing and hub, respectively. This criterion has led to an optimal TFD that indeed improves the pressure ratio and efficiency. The CV also has great impact on the stall margin as it reflects the end wall blockage, especially at the tip region of the compressor. While that work was based on inviscid and axisymmetric theory, in this paper, we move on to the diagnosis and optimal design of fully three-dimensional (3D) viscous flow in axial compressors, focusing on the boundary vorticity flux (BVF), which captures the highly localized peaks of pressure gradient on the surface of the compressor blade, and thereby signifies the boundary layer separation and dominates the work rate done to the fluid by the compressor. For the 2D cascade flow we show that the BVF is directly related to the blade geometry. BVF-based 2D and 3D optimal blade design methodologies are developed to control the velocity diffusion, of which the results are confirmed by Reynolds-averaged Navier–Stokes simulations to more significantly improve the compressor performance than that of CV-based TFD. The methodology enriches the current aerodynamic design system of compressors.

Turbulent drag reduction by traveling wave of flexible wall

A direct numerical simulation of channel turbulent flow and its control by spanwise traveling waves of flexible wall shows that such an on-wall open-loop vorticity creation control can effectively reduce the friction drag for any incompressible Newtonian fluid. The control effect is similar to that of existing transverse-wave controls by spanwise near-wall oscillating flow/wall oscillation and traveling body-force wave. The main physical mechanism is the change of boundary vorticity flux due to wall acceleration, which forces the streamwise vorticity generated at the wall to be confined in a thin generalized Stokes layer and hence alleviates the low-speed streaks, suppresses the streamwise vortices and hairpin vortices in viscous sublayer, associated with a regularized wall skin-friction pattern. A new potential is revealed toward reducing the power input in open-loop control by waves, which is worth further exploring: the optimization of imposed wave pattern.

Interactions between a solid surface and a viscous compressible flow field

This paper presents a general theory and physical interpretation of the interaction between a solid body and a Newtonian fluid flow in terms of the vorticity ω and the compression/expansion variable Π instead of primitive variables, i.e. velocity and pressure. Previous results are included as special simplified cases of the theory. The first part of this paper shows that the action of a solid wall on a fluid can be exclusively attributed to the creation of a vorticity-compressing ω–Π field directly from the wall, a process represented by respective boundary fluxes. The general formulae for these fluxes, applicable to any Newtonian flow over an arbitrarily curved surface, are derived from the force balance on the wall. This part of the study reconfirms and extends Lighthil's (1963) assertion on vorticity-creation physics, clarifies some currently controversial issues, and provides a sound basis for the formulation of initial boundary conditions for the ω-Π variables.The second part of this paper shows that the reaction of a Newtonian flow to a solid body can also be exclusively attributed to that of the ω-Π field created. In particular, the integrated force and moment formulae can be expressed solely in terms of the boundary vorticity flux. This implies an inherent unity of the action and reaction between a solid body and a ω-Π field.In both action and reaction phases the ω-Π coupling on the wall plays an essential role. Thus, once a solid wall is introduced into a flow, any theory that treats ω and Π separately will be physically incomplete.