Boundary Vorticity Flux Research Articles

Impeller optimization using a machine learning-based algorithm with dynamic sampling method and flow analysis for an axial flow pump

Design optimization for widely used axial flow pumps presents a formidable challenge due to the significant impact of numerous parameters associated with impeller geometry on hydraulic performance. The expansive design space raises concerns about the cost and time implications of the optimization process. This paper introduces a machine learning-based algorithm with a dynamic sampling approach to enhance the hydraulic performance of axial flow pumps. The focus is on an axial flow pump designed for China’s South-to-North Water Diversion Project. Optimization involves selecting 15 design variables governing impeller geometry, considering meridional shape and mean blade profiles. The optimization process predicts hydraulic performance using CFD methods, with a primary objective of maximizing efficiency at the axial flow pump’s design point while maintaining pump head around the design value. The results indicate that the proposed machine learning-based algorithm exhibits commendable convergence, delivering a notable improvement in performance. For instance, the optimized axial flow pump displays 2% efficiency increase compared to the initial design. Further analysis employing concepts like entropy generation rate and boundary vorticity flux reveals that the optimized pump has more uniform flow near the pressure side of the impeller blade. Additionally, design optimization effectively suppresses flow separation at the blade trailing edge near the impeller hub. This study offers valuable insights and a practical tool for the design optimization of axial flow pumps.

New Insights into Flow for a Low-Bypass-Ratio Transonic Fan with Optimized Rotor

In this paper, a three-dimensional aerodynamics optimization system is built and applied to optimize a rotor blade to balance the conflicts between stall margin, total pressure ratio, adiabatic efficiency, and mass flow rate for the high-loading and transonic-flow fan. A novel flow diagnostic method based on vorticity dynamics theory is utilized to analyze the reasons for the improvement in aerodynamic performance in the optimized transonic fan. In the established aerodynamic optimization method, use the blade profile camber line curvature and its leading edge metal angle as the optimization variables, which are optimized by modifying the coordinates of their control points and introducing a genetic algorithm. Finally, the vorticity dynamics parameters, such as the boundary vorticity flux (BVF), azimuthal vorticity and skin-friction lines are used to diagnose the key flow features in the optimized and baseline fan passage. The results indicate that, by controlling skillfully the blade camber line curvature in the optimization improves the aerodynamic performance of the fan stage, increasing the total pressure ratio by 1.90% while increasing the mass flow rate and adiabatic efficiency by 5.82% and 4.45%, respectively. The formulas from the vorticity dynamics diagnosis method indicate a close link between the aerodynamic performance and vorticity dynamic parameters for the axial fan/compressor passage flow, and that both azimuthal vorticity and boundary vorticity flux have significant influence on fan stage performance. Moreover, the boundary layer separation flow on the rotor blade surface is accompanied by a spike of entropy and static pressure, and their derivative/gradient also suffer drastic changes under the effect of shock waves. Detailed flow information can be obtained about the on-wall with high accuracy based on the vorticity dynamics diagnosis method, which provides researchers with a novel method for the turbomachinery aerodynamic design and analysis in the aero-engine engineering development field.

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.

Numerical study on flow separation and force evolution in liquid nitrogen cavitating flow

In this paper, a two-phase flow model and the improved thermal cavitation model are used to study the flow characteristics and the evolution of vorticity force for liquid nitrogen cavitation flow. The results are validated against the experimental data from NASA, which shows that the flow re-attachment occurs in the area where the boundary vorticity flux begins to decrease from its positive value. Alternatively, the flow separation occurs near the area with low boundary vorticity fluxes. Besides, the boundary vorticity flux changes typically from negative to positive around the cavity. The development of the cavity affects the surrounding vortex structure, which leads to the evolution of vorticity force and the fluctuations of lateral force and drag force. The results show that the drag force is magnified by the cavitation, and it first decreases and then increases in a typical cycle of cavity evolution. The negative resistance unit is mainly produced in the front of the cavity, and the positive resistance unit is also made in the rear of the cavity. When the attached cavity is shed, the positive drag elements decrease, and the drag force drops to its minimum. When the attached cavity is growing, the positive resistance elements behind the cavity increase, making the resistance force gradually increase. For the lateral force, the existence of the cavity produces lift elements pointing out of the surface outside the cavity, and the unsymmetrical distribution of the cavity leads to the fluctuation of the lateral force.

The Lyman–Huggins interpretation of enstrophy transport

The Lighthill–Panton and Lyman–Huggins interpretations of vorticity dynamics are extended to the dynamics of enstrophy. There exist two competing definitions of the vorticity current tensor, which describes the flow rate of vorticity in the fluid interior, and the corresponding boundary vorticity flux, which represents the local vorticity creation rate on a boundary. It is demonstrated that each definition of the vorticity current tensor leads to a consistent set of definitions for the enstrophy current, boundary enstrophy flux and the enstrophy dissipation term. This leads to two alternative interpretations of vorticity and enstrophy dynamics: the Lighthill–Panton and Lyman–Huggins interpretations. Although the kinematic evolution of the vorticity and enstrophy fields are the same under each set of definitions, the dynamical interpretation of the motion generally differs. For example, we consider the Stokes flow over a rotating sphere, and find that the flow approaches a steady state where, under the Lyman–Huggins interpretation, there is no enstrophy creation or dissipation. Under the Lighthill–Panton interpretation, however, the steady-state flow features a balance between the continuous generation and subsequent dissipation of enstrophy. Moreover, the Lyman–Huggins interpretation has previously been shown to offer several benefits in understanding the dynamics of vorticity, and therefore it is beneficial to extend this interpretation to the dynamics of enstrophy. For example, the Lyman–Huggins interpretation allows the creation of vorticity, and therefore enstrophy, to be interpreted as an inviscid process, due to the relative acceleration between the fluid and the boundary.

Performance of seal vibrissa-inspired bionic surface in suppressing aerodynamic forces and vortex shedding around a circular cylinder

In this study, circular cylinders with bionic surfaces were developed to control the flow fields around cylindrical structures such as stay cables of bridges. The bionic cylinder geometries were characterized by slanted elliptical governing sections and wave surfaces. Wind tunnel experiments were conducted to identify the surface pressure distributions, aerodynamic forces, and flow field characteristics of bionic circular cylinders at a Reynolds number (Re) of 3.8 × 104. The results show that the aerodynamic forces of the bionic cylinders are sensitive to the wind attack angle (γ) and wave surface wavelength. The control effects were excellent at γ = 0°, 90°, and 180°, whereas they vanished at γ = 45° and 135° compared with a baseline circular cylinder. When the wavelength range of the bionic cylinder is 4D–5D, the maximum reductions in the mean drag and fluctuating lift were 27% and 93%, respectively. The vortex formation region was elongated, and the alternative vortex shedding process was suppressed. Proper orthogonal decomposition was performed to determine the coherent structure of the wake field and the boundary vorticity flux analysis demonstrates the difference in the strength of the wake vortex from the viewpoint of boundary vorticity diffusion between the fluid and wall. Spatial–temporal correlation analysis of the velocity profiles behind different cross-sections shows that the wave surface troughs contribute significantly to disrupting the flow consistency in the spanwise direction.

Improved Prediction of Aerodynamic Loss Propagation as Entropy Rise in Wind Turbines Using Multifidelity Analysis

Several physics-based enhancements are embedded in a low-fidelity general unducted rotor design analysis tool developed, py_BEM, including the local Reynolds number effect, rotational corrections to airfoil polar, stall delay model, high induction factor correction, polar at large angle of attack, exergetic efficiency calculation and momentum-based loss. A wind turbine rotor is analyzed in high fidelity designed from py_BEM using a 3D blade generator. It is a design derived from the NREL Phase VI rotor. Three design variations are analyzed using steady 3D CFD solutions to demonstrate the effect of geometry on aerodynamics. S809 and NACA 2420 airfoil properties are used for calculating the aerodynamic loading. Momentum, vorticity and energy transport are explained in depth and connected to entropy production as a measure of performance loss. KE dissipation downstream of the rotor is shown to be a significant contributor of entropy rise. Wake analysis demonstrates mixing with the free stream flow, which begins after 3 diameters downstream of the rotor and extends to about 25 diameters until the decay is very small. Vorticity dynamics is investigated using a boundary vorticity flux technique to demonstrate the relationship between streamwise vorticity and lift generated in boundary layers. Drag components are accounted as well. It is demonstrated using rothalpy that shaft power is not only torque multiplied by rotational velocity but a viscous power loss term must also be included. A multifidelity analysis of wind turbine aerodynamics is demonstrated by capturing flow physics at several levels.

Numerical study on the flow and noise control mechanism of wavy cylinder

Generation of noise caused by the flow around a cylinder and its control are important in various engineering applications. Based on computational fluid dynamics with acoustic analogy and the vortex dynamics theory analysis, this study aims at investigating the ability of the wavy cylinder in improving aerodynamic performance and reducing aerodynamic noise. Noise control mechanisms with different Reynolds numbers are analyzed. The results show that the wavy cylinder is helpful for the reduction of the average drag coefficient and is efficient in suppressing fluctuation of the lift coefficient; consequently, the overall noise of the wavy cylinder is reduced. Specifically, the tonal noise is significantly suppressed or even eliminated under proper configurations. To explore the underlying noise suppression mechanisms, the process of vorticity generation around the wavy cylinder surface is examined in detail. The vorticity distribution on the surface of the wavy cylinder is profoundly improved, and the distribution of the boundary vorticity flux and boundary enstrophy flux is also remarkably weakened. As a result, the generation of vorticity near the wavy cylinder wall is diminished. These directly lead to a significant contraction of the vortex structure distribution in the wavy cylinder wake, especially for some large-scale vortex structures. Moreover, periodic vortex shedding is significantly suppressed in the case with high Reynolds numbers, which might be the main reasons for noise reduction. The interaction area of the positive and negative Lamb vector divergence, which is closely related to the noise generation, is decreased. This contributes to drag reduction and noise attenuation. This indicates that drag reduction and noise suppression are closely bounded in the wavy cylinder.

Unstable flow characteristics in vaneless region with emphasis on the rotor-stator interaction for a pump turbine at pump mode using large runner blade lean

In this study, the unstable flow characteristics in vaneless region of the pump-turbine with different runner blade lean has been numerically investigated by using a modified SST k-ω partially averaged Navier-Stokes model. Results on the characteristic curves show good agreements between the experiment and simulation, and indicate that with the increase of blade lean angle (θ of 0°, 2°, 4°, 6°, 10° and 15°), the positive slope on characteristic curve is gradually alleviated. It is noted that the runner with large blade lean (θ of 15°) can suppress the peak value region of boundary vorticity flux at blade trailing edge from the crown side to mid-span section, and the unstable flow near the mid-span in runner blade-to-blade passage as well as in vaneless region. It is confirmed that the runner with large blade lean spatially and temporally changes the flow near the blade trailing edge and in vaneless region, and is beneficial to improve the flow stability. Finally, the proper orthogonal decomposition analysis reveals that the runner model with large blade lean effectively alleviates the dominant flow oscillation with the low frequency of 0.088fn (or 0.044fn), corresponding to the unstable flow evolution in vaneless region.

Mechanism analyses of the unsteady vortical cavitation behaviors for a waterjet pump in a non-uniform inflow

The waterjet pump is widely applied in the high-speed marine vessels to exploit various kinds of resources in the vast ocean. The transient cavitating flows in a waterjet pump are numerically investigated under a non-uniform inflow for the purpose of revealing the correlation mechanism between the cavitation and the vorticity diffusion as well as the exited pressure fluctuations. The unsteady numerical simulation is conducted by using the Reynold-Averaged Navier-Stokes (RANS) method coupled with a homogenous cavitation model. Both the hydrodynamic performance and the cavitation performance are well predicted by the present numerical approach when compared with the available experimental data. The cavitation occurrence would cause larger pulsations to the hydrodynamic characteristics and the nonuniformity together with perpendicularity at the impeller inlet plane. As the blade passes through the non-uniform inflow, the instantaneous cavitation dynamics behaviors include the cavity generation, development and extinction, and the dominant frequency corresponds to the impeller rotating frequency. Based on analyses of the boundary vorticity flux, the cavitation is an important mechanism for vorticity diffusion from the blade into the mainstream with the major contributor of the variable density due to cavitation. Furthermore, combined computational and theoretical analysis illustrates that the cavity volume variations would cause the flow-rate fluctuations and the cavity volume acceleration is the major source for the pressure fluctuations inside the mixed-flow waterjet pump.

Noise control for high-lift devices by slat wall treatment

A novel wall treatment method, termed as the Slat Cove Wavy Wall (SCWW), is proposed to improve both the aero-acoustic and the aerodynamic performances of high-lift devices. By this treatment, a wavy pattern is imposed on the wall in the slat cove. In the present work, slats with three different SCWWs are designed and applied to a straight wing composed by 30P30N airfoil. Numerical simulations and analyses are conducted to unveil the underlying mechanisms of noise reduction. The unsteady flow field and the far-field noise are predicted by a hybrid SA-IDDES method followed by the integration of the Ffowcs Williams and Hawkings equation. The modified high-lift device is proved to be able to improve the aero-acoustic performance by reducing the low-frequency components of the radiated noise. Meanwhile, the aerodynamic performance is maintained or improved under proper design parameters. The boundary layer separation in the slat cove is accelerated by the SCWW, which transforms low-frequency periodic vortex shedding to high-frequency turbulent flow. This results in the sound energy shift from low-frequency noise to high-frequency broadband noise. The SCWW method is proved to be effective in redistribution of boundary vorticity flux on the slat lower surface. To reveal the mechanism of the SCWW's drag and noise reduction, the vortex dynamic processes near the slat lower surface in terms of the Lamb vector divergence are further investigated. It is found that the Lamb vector divergence is directly related to both the noise source and the drag. The interaction area of positive and negative Lamb vector divergence can be balanced and decreased by SCWW, resulting in the drag and noise reduction. As expressed by the vortex dynamic processes, this feature implies the SCWW method is of great potential in noise attenuation.

Boundary Vorticity Analysis and Shedding Dynamics of Transient Cavitation Flow Around a Twisted Hydrofoil

AbstractThe objective of this paper is to investigate the dynamic characteristics of transient cavitating flow over a twisted NACA0009 hydrofoil. The large eddy simulation (LES) approach is selected for the computation of fluid flow and the Zwart model is used for the mass transfer due to cavitation. Moreover, the skin-friction coefficient and boundary-vorticity flux (BVF) are used to study the flow separation. Numerical results show that the attached shear layer separates from the boundary layer and then squeezes to form the separation line under the obstruction of the reentrant jet. The analysis based on the terms of vorticity transport equation demonstrates that vortex stretching and vortex dilatation terms dominate the evolution of the multiscale vortex. Moreover, the secondary shedding induced by the side-entrant jet enhances the instability of partial cavities and the underlying mechanism is comprehensively revealed. Furthermore, the feature of the pressure fluctuation indicates that high pressure generated by the cavity collapse at the tail simultaneously propagates to the leading edge and downstream of the hydrofoil. This enhances the intensity of the reentrant jet and side-entrant jet, promoting occurrences of flow separation near the suction surface and cavity shedding to a certain extent.

Redesign of Axial Fan Using Viscous Inverse Design Method Based on Boundary Vorticity Flux Diagnosis

Abstract The inverse design method for turbomachinery can directly acquire a blade geometry with specific aerodynamic parameters, such as pressure loading on the blade surfaces. The difference between the inverse design and direct analysis design is that the management of the flow field is controlled by aerodynamic parameters instead of geometric parameters. Although the inverse design has been studied since the 1940s, it is far from being mature enough in comparison with the analysis method. In this work, the inverse problem method is improved by two aspects: the calculation accuracy and the strategy to determine the pressure loading distribution. The application of a high-quality mesh auto-generation and deformation technique to the inverse design is introduced. The no-slip wall boundary conditions, similar to the analysis model, and high-quality mesh, enable the use of an advanced turbulence model in the inverse design. These methods improve the accuracy of the inverse design. The loading distribution in the inverse design is obtained based on the boundary vorticity flux diagnosis. An axial fan is redesigned as an example of the inverse design method. The internal flow loss analysis based on the entropy production theory verifies the effectiveness of the inverse design used in this study.

The generation and diffusion of vorticity in three-dimensional flows: Lyman's flux

Abstract

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.

Investigation of flow separation in a centrifugal pump impeller based on improved delayed detached eddy simulation method

The mechanism of flow separation in the impeller of a centrifugal pump with a low specific speed was explored by experimental, numerical, and theoretical methods. A novel delayed Reynolds-averaged Navier–Stokes/large eddy simulation hybrid algorithm combined with a rotation and curvature correction method was developed to calculate the inner flow field of the original pump for the large friction loss in the centrifugal impeller, high adverse pressure gradient, and large blade curvature. Boundary vorticity flux theory was introduced for internal flow diagnosis, and the relative velocity vector near the surface of the blade and the distribution of the dimensionless pressure coefficient was analyzed. The validity of the numerical method was verified, and the location of the backflow area and its flow features were determined. Finally, based on flow diagnosis, the geometric parameters influencing the flow state of the impeller were specifically adjusted to obtain a new design impeller. The results showed that the distribution of the boundary vorticity flux peak values, the skin friction streamline, and near-wall relative velocities improved significantly after the design change. In addition, the flow separation was delayed, the force applied on the blade was improved, the head under the part-load condition was improved, and the hydraulic efficiency was improved over the global flow ranges. It was demonstrated that the delayed Reynolds-averaged Navier–Stokes/large eddy simulation hybrid algorithm was capable to capture the separation flow in a centrifugal pump, and the boundary vorticity flux theory was suitable for the internal flow diagnosis of centrifugal pump.

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.

Twisted Contact Structures in Turbulent Flows

The “hairpin” vortical structure initiated from a conceptual model of Theodorsen refers to a Ω-shaped vortex with two streamwise-oriented legs connected via a raised spanwise-oriented arch. Both computational and experimental studies in flow visualization revealed considerable disagreement as to the underlying hairpin vortex generation mechanism as well as its interpretation. The goal of this paper is to give a deeper insight of this key issue closely related to the turbulence as a dynamic stochastic phenomenon involving the origin and its generation mechanism. The topological concept of twisted contact structures associated with vorticity concentrations in wall-bounded flows strongly contorted at the starting-time is used to explain the genuine structured turbulence of Lagrangian nature at sufficiently large Reynolds numbers. The dynamical stochastic models of starting impact permit to identify two intrinsic scales for describing the starting impact-wall twist relationship generating a local turbulence mechanism. The inertia scale (rate of inertia, e) and circulation scale (azimuthal wave length, π) are measures for impact and twist, respectively, the turbulence lying in their dynamics like a torsion pendulum mechanism. The intrinsic scales of molecular nature have an interesting correspondence in macro-flow field through two relativistic well-known parameters: Mach number and Reynolds number playing the role of some reduced amplitudes and frequencies of the compressibility waves generated by the starting impact/shock. The maximum amplitude 2/3M∞= defines a critical Reynolds number 25200Re1/22/310/scraNm≡=⋅ρ (a0 –sound velocity of air at rest), numerically equal to the maximum impact pressure where the frictional shearing stress is near annulled, and its inverse value is the equilibrium kinematic viscosity 2201.510/ms−=⋅ν or the stable minimum circulation at a contact surface. These reference dimensional quantities are used to a more comprehensive definition of the current Reynolds numbers as the ratio of 20(/)V∞ν contact to (/)Vl∞ outer flow frequencies. Then, it is shown that the wave behavior of wall-bounded flows have a universal character (regardless of much diversity of flow cases) where the wall torsion pressure and the frictional wave drag are more realistic models than Lighthill’s boundary vorticity flux (BVF) mechanism and semi-empirical Prandtl’s wall law.

Passing-over leading-edge vortex: The thrust booster in heaving airfoil

The thrust generated by heaving airfoil in incompressible flow is studied both numerically and theoretically. It is found that the behaviors of leading-edge vortex (LEV) under different airfoil’s transverse velocities have an important influence on the thrust. When this velocity is small, the LEV is advected downstream regularly; however, as transverse velocity increases, the LEV can be pushed back to the leading edge again and pass over it to the opposite side of the airfoil. In cases with the LEV passing over the leading edge, the maximum transient thrust can be enhanced by several times compared with that in the single-stroke motion. The reason and critical condition for the occurrence of passing-over leading-edge vortex (PO-LEV) are found. Based on the source of the pressure Poisson equation, a near-field force theory is developed and used together with the boundary vorticity flux (BVF) theory to clarify the thrust enhancement mechanisms.