Divergence Of Vector Research Articles

Flow induced acoustic characteristics analysis of propulsion pump by indirect acoustic variable method and FEM

The acoustic characteristics of water-jet propulsion pumps present significant challenges, primarily due to the interaction between flow and high-speed rotating impellers wall. Notably, such complicated turbulence induced acoustic sources by brings great difficulty to identify and control. This paper firstly analyzes the flow characteristics of the propulsion pump by using the scalable Hybrid RANS-LES model. Subsequently, an indirect acoustics variable method based on Lamb vector divergence is proposed to characterize acoustic sources caused by multiscale turbulence. The effectiveness and advantages of indirect acoustics variable method are evaluated through comparison with the acoustic finite element method and experimental results. The proposed indirect acoustics variable method demonstrates the ability to accurately quantify the contribution of turbulent flow to acoustic sources. Furthermore, the intensity of acoustic sources in different flow regions can be obtained through volume integrals, which can serve as optimization parameters in the initial hydraulic design of propulsion pumps. This study provides a novel approach for predicting turbulent noise and offers guidance for the design of low-noise propulsion systems.

A New Approach to the Use of Non-Primitive Variables in the Mechanics of Continuous Media

The problem of an approximate solution to hydrodynamic problems is the consideration of pressure. To exclude it from the equations, the transition to “non-primitive variables” (vortex and velocity vector divergence) is made. In this case, there are difficulties in the algorithmization of new equations for solving the inverse problem of hydrodynamics and a lot of internal iterative calculations. The object of this study includes equations in “non-primitive” variables. The research methods are based on the transformation without simplifications and assumptions of hydrodynamic equations into a form containing “non-primitive” variables and the demonstration of the possibilities of solving the equations. The GAMS programming language was used for approximate solutions for the first time. The aim of this paper is to demonstrate the possibility of solving the full equations in “non-primitive” variables for various conditions. The results showed the possibility of considering the compressibility of the medium when solving the inverse problem of hydrodynamics; the identity of solutions of the proposed system of equations and equations using the potential; and the possibility of using optimizing programming languages for hydrodynamics problems. The scientific novelty of this research consists of solving the full equations of hydrodynamics with the use of “non-primitive” variables but without the use of the current function. Doi: 10.28991/ESJ-2024-08-02-021 Full Text: PDF

Interfacial vorticity dynamics for Navier–Stokes–Korteweg system: General theory and application to two-dimensional near-wall cavitation bubble

A theory of interfacial vorticity dynamics is developed for the single-component liquid–vapor flows described by the Navier–Stokes–Korteweg equations. The non-ideal equation of state and surface capillarity are collectively considered via the chemical potential gradient force. Explicit formulas of the interfacial enstrophy and chemical potential fluxes are derived to elucidate their generation mechanisms from the interface, which are expressed by using the fundamental surface physical quantities. Then, the transport equation of the Lamb dilatation (namely, the Lamb vector divergence) is rigorously derived, generalizing the previous results of the Lamb-vector dynamics for single-phase incompressible viscous flows. The derived results are evaluated in a near-wall cavitation bubble combined with the van der Waals equation of state. The roles of surface shear stress and vorticity, surface chemical potential gradient, surface acceleration, surface stretching-shrinking motion and dilatational waves are emphasized in generating the interfacial enstrophy and chemical potential fluxes, featured by the strong vorticity concentration, interface deformation and inward-propagating microjet due to the longitudinal pressure difference. These distinct dynamical features observed near the bubble interface are well captured by the spatial distribution of the Lamb dilatation. Analyzing the dynamics of the Lamb dilatation based on the transport equation demonstrates the significance of the high-curvature rotating surface region and its vicinity in view of their dominance to the unsteady diffusion effect of the Lamb dilatation. The present exposition could provide new physical insights into liquid–vapor flows from the perspective of interfacial vorticity dynamics.

Noise reduction for high-lift devices on a swept wing model by droop nose

The noise of slat in the high-lift device of large aircraft is one of the main noise sources of large aircraft during take-off and landing. This paper investigates a noise reduction measure which consists in droop nose for high-lift device of three-dimensional sweep wing instead of leading-edge slat. The unsteady flow field and the far-field noise are predicted by a hybrid SA-IDDES method coupled with the integration of the Ffowcs Williams–Hawkings equation (FW-H). Based on the optimal droop nose configuration from 2D airfoil, the results of the 3D swept wing model with the droop nose on the leading edge of the inner wing are given. Numerical results show that the droop nose configuration can reduce the overall sound pressure level (OASPL) of the intermediate frequency noise, and the peak noise can be reduced by 15 dB, and the sound pressure level of the broadband noise at low and high frequencies is also partially suppressed. The maximum lift-to-drag ratio of the droop nose configuration increased by 2.7 %. In addition, the noise reduction mechanism of leading-edge droop is analyzed by combining the vortex sound theory and the generation and evolution process of the vortex structure. The leading-edge droop nose configuration fundamentally not only eliminates the vortex structure of the slat cove of the leading-edge slat configuration, but also avoids the interaction between the slat slot flow and the upper surface of the main wing. These directly lead to a thinner boundary layer vortex near the top of the main wing, and the wall pressure pulsation is smaller than that of the leading-edge slat high-lift device, thereby reducing noise. The reduction of the BEF distribution on the upper surface boundary shows again that the droop nose inhibits the vortex on the upper surface of the main wing. The change of the Lamb vector divergence reveals the noise reduction mechanism of the drooping leading edge configuration directly from the sound source.

Modulation of wake evolution, separation, and radiated noise by a cylinder with porous media cladding

In this paper, the effects of porous media parameters on circular cylinder wake flow and radiation noise are investigated using large eddy simulations and Ffowcs Williams–Hawkings acoustic analogy. We performed three-dimensional numerical simulations for flow around the cylinder coated with a porous layer of different pores per inch in a subcritical flow regime (ReD=4.7×104) to explore the control mechanism of porous media on wake and radiation noise. The results show that the application of porous media significantly alters the separation pattern behind the cylinder and stabilizes the shear layer detached from the cylinder. The existence of porous layers leads to the transformation of chaotic and irregular vortex structures into more orderly vortices. Moreover, this study also reveals that the cylinder coated with high pore density can provide the desired noise reduction. The analysis of vortex sound theory indicates that porous media reduces the interaction area and magnitude of the positive and negative Lamb vector divergences, which is beneficial for drag reduction and noise attenuation. In addition, the comparison of sound pressure contours shows that the application of porous media does not change the radiation mode of noise, but the porous media with high pore density helps to decrease the generation of noise and intensity of the sound source.

Numerical study of trailing-edge noise reduction mechanism of wind turbine with a novel trailing-edge serration

The serration assembly installed at the trailing-edge of wind turbines can reduce the turbulent boundary-layer trailing-edge noise. This work studies the aeroacoustic response and noise reduction capability of four different trailing-edge serrations, involving a novel Multi-Flapped-Serration with Iron-Shaped Edges (MFS-Iron) presented here. These four serrations are retrofitted to S809 and NACA643418 airfoils. The Large-eddy simulation (LES) method and Ffowcs Williams and Hawkings integration (FW-H) methods are respectively employed to predict the unsteady flow field and far-field noise based on optimized structured and unstructured hybrid grids. From the numerical simulation results, we explore the trailing-edge noise reduction mechanism. The results show that the proposed MFS-Iron can effectively realize noise reduction under appropriate design parameters and optimize the aerodynamic layout. When using the MFS-Iron serration, the cross-flow intensity between the serration gap is significantly reduced, and the original two groups of symmetrical horseshoe vortex are mixed into a single vortex, which has a positive impact on the suppression of high-frequency noise. By further studying the Lamb vector divergence vortex dynamics process near the surface of serrated trailing-edge, it is found that the Lamb vector divergence is directly related to the intensity of the noise source.

Fractional Vector Cross Product in Euclidean 3-Space

In this research a new definition of fractional vector cross product of two vectors in Euclidean 3-space is presented. Using this new definition the formulae for Euclidean norm, fractional triple vector cross product, curl and divergence of fractional vector cross product of an electromagnetic vector field is discussed. In particular cases, all the properties satisfy definition of standard vector cross product for standard orthogonal basis of R3. The new definition has application in radiation characteristic in micro-strip antenna and can be applied in other branches of mathematics and physics.

Large Eddy Simulation of the cavitating flow around a Clark-Y mini cascade with an insight on the cavitation-vortex interaction

In this research, the Large Eddy Simulation method is utilized to predict the cavitation-vortex interaction in the flow around a Clark-Y mini cascade along with the dynamical processes of the U-type cavity, analyzed using the Lamb vector divergence transportation. To provide a novel perception of the development of the U-type cavity, various fundamental mechanisms of the periodic evolution of the U-type cavity are investigated thoroughly. The dynamical progress explicates the mechanisms that generate the high-pressure zone and low-velocity zone. This mechanism, combined with the re-entrant jet and vortex motions plays a significant role in the development of the U-type cavity. Since the Lamb vector curl associates the vorticity transport equation and is closely related to the source of vorticity of the vortex evolution, the Lamb vector curl captures the vortical structures which show good agreement with the Ω-method results. In addition, the distributions of high- and low-momentum flow in the wake of the cascade are delineated by the Lamb vector divergence. The transition from the maximum to the minimum of the lamb vector divergence in a region illustrates a quasi-cyclic behavior that is closely related to the momentum transport mechanisms and the cyclical motions of the vortex.

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.

Прогностические маркеры исхода острого периода инфаркта миокарда

Исход острого периода инфаркта миокарда прогнозировался на основании статистического метода с применением алгоритма Data Mining «дерево решений». В качестве входных данных использовались чувствительные и специфические векторкардиографические показатели. Установлены прогностически значимые маркеры исхода острого периода инфаркта миокарда. Если возраст больного был 57 лет и более, а скорость распространения возбуждения по миокарду высоких отделов передней стенки левого желудочка замедлялась до 6,33 мв/с, прогнозировался летальный исход с точностью 92,86 %. В случае регистрации у пациента увеличения площади предсердных петель более 0,188 мм2 (в ВА2) с угловым расхождением петель QRS-P более 15,5° (в ВА1), размыкания петли QRS менее 2,834 мм (в 3-й проекции) и скорости распространения возбуждения в конечной части петли Т менее 2,338 мв/с (в ВА1) при различных значениях углового расхождения вектора QRS-Т (в ВА5) прогнозировался благоприятный исход с точностью 97,67 %.

Divergence and Curl of COVID19 Spreading in the Lower Peninsula of Michigan

This paper explores the COVID19 transmission pattern and circulation dynamics in the Euclidean space at the lower peninsula of Michigan by using the divergence and curl concept in vector field. The COVID19 transmission volume flux can be calculated for each county by using vector divergence. The results shows Wayne county had the highest divergence (162660), the Kent county had the second highest divergence (152540), and the Saginaw county had the third highest divergence (103240), the divergence is positive which means the COVID19 virus was transmitted from these counties to other places. The results also shows Monroe county had the lowest divergence (-187843), the Allegan county had the second lowest number in divergence (-90824), the divergence is negative which means the COVID19 virus was transmitted from other places to these counties. The circulation of the virus is also calculated by using vector curl. The positive curl means that the virus has circulated in a counter-clockwise direction, and the negative curl means the virus has circulated in a clockwise direction.
 
 The divergence is an operator of the COVID19 transmission vector field, which produces a scalar field giving the quantity of the transmission vector field’s source at each location. The COVID19 spreading volume density of the outward flux of transmission field is represented by divergence around a given location. 
 
 The curl is an operator of the COVID19 transmission field, which describes the circulation of a transmission vector field. The curl at a location in COVID19 transmission field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a transmission field is formally defined as the circulation density at each location of COVID19 transmission field.

Numerical study on energy conversion characteristics of molten salt pump based on energy transport theory

Molten salt pump (MSP) used in concentrating solar power (CSP) system to circulate the molten salt. The operation of MSP needs to understand the energy conversion characteristics in the flow field. In this study, the energy conversion characteristics of MSP were investigated based on energy transport theory. A significant portion of power is consumed in the propulsion of pressure between the inlet throat to the outlet throat of the impeller passage. The increase in the energy of medium by the Lamb vector divergence mainly occurs on the rear of the impeller passage. Whereas the enstrophy dissipation area is primarily located in the suction surface area at the impeller outlet. In addition, the pressure propulsion power is critical for energy transfer in the impeller, while the contribution of Lamb vector divergence and enstrophy dissipation is limited. It was observed that the distribution of the three energy transport dynamic parameters have a high degree of coincidence irrespective of the medium density, which indicates that the density of the medium does not have a significant impact on the law of energy conversion. Therefore, when the geometrical characteristics of the impeller are determined, the energy conversion characteristics of different medium do not change significantly.

Захворюваність на непухлинні хвороби, інвалідність, смертність дорослого населення радіоактивно забруднених територій України. епідеміологічні дослідження протягом 1988-2016 років

Objective: We presented a comprehensive description of the changes in the health status of the adult population of radioactively contaminated territories of Ukraine depending on gender and age at the date of the Chornobyl accident on the basis of cohort epidemiological studies after accident. Materials and methods: The epidemiological analysis of non-neoplastic morbidity, disability, mortality in the residents of radioactively contaminated territories (RCT) aged 18-60 years old at the date of the Chornobyl accident (65,189 people) was conducting during 1988-2016 for five-year observation periods and by eight classes of ICD-10. We applied the methods of mathematical and statistical analysis. Results: During 1988-2016, 90590 (100%) cases of non-neoplastic morbidity (34.94% in men and 65.06% in women), 11153 (100%) cases of disability (38.22% and61.78%, respectively), and 11586 (100%) cases of mortality(50,42% and 49,58%, respectively)were detected in the residents of the RCT for the first time as a result of epidemiological study. Most of the victims suffered from the nosological forms of the nosological forms of respiratory, circulatory and digestive systems, which made up 67.43% in the structure of non-neoplastic morbidity. Diseases of circulatory, endocrine and nervous systems (87.92%) were the main factors of disability and diseases of circulatory system (89.49%) - of mortality. The gender dependence of the development of the incidence of non-neoplastic diseases, disability and mortality due to them were established. The indices of mortality (116.08, ID/103 man-years of observation) and disability (13.57)in females significantly exceeded the males’ ones (86.57 and 11.65, respectively). But males had a higher mortality rate (16.01 vs. - 11.32). Changes in the incidence rates of non-neoplastic diseases, disability and mortality due to them throughout the observation period were characterized by a divergence of vectors: morbidity decreased, and disability and mortality increased simultaneously. The intersection of the dynamics of the mortality of non-neoplastic diseases with disability and mortality through those diseases was identified in 2008-2012. Conclusions 1. During epidemiological surveillance in 1988-2016, in the residents of RCT aged 18-60 years old on the date of the Chornobyl accident epidemiological surveillance, the non-neoplastic morbidity was formed mainly due to the significant development of diseases of the respiratory, circulatory and digestive systems, which together made up 67.43%. Non-neoplastic diseases of the circulatory, endocrine and nervous systems (87.92) were the main causes of disability, diseases of circulatory system (89.49%) - of mortality. 2. The gender dependence of the development of the morbidity of non-neoplastic diseases, disability and mortality in the residents of RCT over the thirty-year observation period was established. Diseases of the circulatory system were the main causes of disability and mortality. In males, disability and mortality were caused by the mental and behavioral disorders, diseases of respiratory and digestive systems, in females - by the diseases of nervous and urogenital systems. 3. In the residents of RCT, regardless of gender, over the years of observation, a feature of the development of morbidity, disability and mortality due to them was established, it was in the significant reduction of the incidence of diseases in 2008-2016, due to the increase of disability and mortality of the suffered, especially in 2008-2016, in comparison with the previous years, i.e. in 22-30 years after the Chornobyl accident. 4. Summarizing the obtained data, it is important to continue the epidemiological studies of the health status of the residents of RCT (non-neoplastic morbidity, disability, mortality) for the determination of the impact of radiation on the development of the main forms of non-neoplastic diseases.

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.

A Satellite Incipient Fault Detection Method Based on Local Optimum Projection Vector and Kullback-Leibler Divergence

Timely and effective detection of potential incipient faults in satellites plays an important role in improving their availability and extending their service life. In this paper, the problem of detecting incipient faults using projection vector (PV) and Kullback-Leibler (KL) divergence is studied in the context of detecting incipient faults in satellites. Under the assumption that the variables obey a multidimensional Gaussian distribution and using KL divergence to detect incipient faults, this paper models the optimum PV for detecting incipient faults as an optimization problem. It proves that the PVs obtained by principal component analysis (PCA) are not necessarily the optimum PV for detecting incipient faults. It then compares the on-line probability density function (PDF) with the reference PDF for detecting incipient faults on the local optimum PV. A numerical example and a real satellite fault case were used to assess the validity and superiority of the method proposed in this paper over conventional methods. Since the method takes into account the characteristics of the actual incipient faults, it is more adaptable to various possible incipient faults. Fault detection rates of three simulated faults and the real satellite fault are 98%, 84%, 93% and 92%, respectively.

Numerical Study on Energy Conversion Characteristics of Molten Salt Pump for Concentrating Solar Power Based on Energy Transport Theory

Molten salt pump (MSP) used to circulate the molten salt in concentrating solar power (CSP) system. The operation of MSP needs to understand the energy conversion characteristics in the flow field. In this study, the energy conversion characteristics of MSP were investigated based on energy transport theory. A significant portion of power is consumed in the propulsion of pressure between the inlet throat to the outlet throat of the impeller passage. The increase in the energy of medium by the Lamb vector divergence mainly occurs on the rear of the impeller passage. Whereas the enstrophy dissipation area is primarily located in the suction surface area at the impeller outlet. In addition, the pressure propulsion power is critical for energy transfer in the impeller, while the contribution of Lamb vector divergence and enstrophy dissipation is limited. It was observed that the distribution of energy transport dynamic parameters have a high degree of coincidence irrespective of the medium density, which indicates that the density of the medium does not have a significant impact on the law of energy conversion. Therefore, when the geometrical characteristics of the impeller are determined, the energy conversion characteristics of different medium do not change significantly.

Phantom dark energy from scalar-torsion coupling

We show that a scalar field without a kinetic term in the Lagrangian density, coupled to the covariant divergence of the torsion vector in the Einstein–Cartan theory of gravity, becomes kinetic in its general-relativistic equivalent formulation. The resulting kinetic term is negative: such a scalar field could be a source of phantom dark energy.

Poynting vector and beam divergence.

Laser beam divergence was considered using the components of the Poynting vector. A physical interpretation of the real and imaginary parts of the "longitudinal" field component (along the z axis, the direction of beam propagation) is given in an exponential representation. The longitudinal field component was shown to be the reason for the formation of laser beam divergence. This fact was used to reveal fundamental differences between Laguerre-Gaussian beams and incoherent rays in the focal region. The possibility of using selective action on the longitudinal field component to decrease the divergence of Laguerre-Gaussian beams is discussed.

Large eddy simulation of the periodic cavity evolution and the turbulence characteristics around a Delft Twist-11 hydrofoil

In the present investigation, the LES WALE method along with the Zwart cavitation model is utilised to predict the cavitating flow around a Delft Twist-11 hydrofoil and the numerical results show a reasonable agreement with the experimental data. A novel elucidation is provided to the formation of the U-type structure and the Lumley method is introduced into the numerical simulation which can offer a validation of the simulation. The evolution of the cavity structure, especially the formation and development of U-type structures, was investigated thoroughly with the assistant of the Ω method, the Lamb vector, and the vorticity transport equation (VTE). As a third-generation vortex identification, Ω = 0.52 captures the vortex structure during the cavity evolution exhaustively. The cavitation-vortex interaction impacts the cavity evolution profoundly. The primary weak vortex and the secondary weak vortex both have a significant effect on the cavity shedding and the formation of the U-type structure. Moreover, the stretching action and the vorticity bearing motion described by the Lamb vector divergence clarify the formation of the special cavity structure in depth. In virtue of the mean velocity, Reynolds stresses, Lumley triangle, and Lumley distance, the turbulence characteristics were also investigated carefully. The cavitating motion plays a significant role in the turbulence velocity fluctuation and turbulence anisotropy around a twisted hydrofoil.

Acoustic scattering in a rarefied gas: Solving the R13 equations in spherical polar coordinates

In some circumstances, sound waves in a rarefied gas can be studied using a linearised form of the regularised 13‐moment equations of Struchtrup and Torrilhon. We build solutions of those equations in spherical polar coordinates using vector spherical harmonics. We first solve a reduced system of equations (with 11 unknowns) after introduction of a force vector (divergence of the stress). We then show that the stresses themselves can be recovered by solving five additional equations. The results obtained are expected to be useful for problems such as acoustic scattering of a plane wave by a sphere in a rarefied gas.