Circumferential Velocity Component Research Articles

Amplification of Secondary Flow at the Initiation Site of Intracranial Sidewall Aneurysms.

The initiation of intracranial aneurysms has long been studied, mainly by the evaluation of the wall shear stress field. However, the debate about the emergence of hemodynamic stimuli still persists. This paper builds on our previous hypothesis that secondary flows play an important role in the formation cascade by examining the relationship between flow physics and vessel geometry. A composite evaluation framework was developed to analyze the simulated flow field in perpendicular cross-sections along the arterial centerline. The velocity field was decomposed into secondary flow components around the centerline in these cross-sections, allowing the direct comparison of the flow features with the geometrical parameters of the centerline. Qualitative and statistical analysis was performed to identify links between morphology, flow, and the formation site of the aneurysms. The normalized mean curvature and curvature peak were significantly higher in the aneurysmal bends than in other arterial bends. Similarly, a significant difference was found for the normalized mean velocity ( ), the circumferential ( ), and radial ( ) velocity components between the arterial bends harboring the aneurysm than in other arterial bends. In contrast, the difference of means for the normalized axial velocity is insignificant ( ). Thirty cases with aneurysms located on the ICA were analyzed in the virtually reconstructed pre-aneurysmal state by an in-silico study. We found that sidewall aneurysm formation on the ICA is more probable in these arterial bends with the highest case-specific curvature, which are accompanied by the highest case-specific secondary flows (circumferential and radial velocity components) than in other bends.

A scrutiny of streamline calculation in analytical solutions of Oseen flow past cylinders and spheres

The problems associated with the calculation of streamlines in the analytical solutions of Oseen's equation for the creeping flow past cylinders and spheres are addressed in this paper. First, the analytical solutions to Oseen flow past cylinders and spheres are presented. Then, the solutions and their computer implementation are validated against existing data. To examine the correctness of the streamlines obtained as contours of the stream function, the true streamlines are calculated by directly integrating the velocity components. The comparison shows that the stream function proposed by past researchers is correct for the cylinder flow whereas it is incorrect for the sphere flow. Thus, the streamline patterns of the sphere flow as predicted by the stream function, both approximate and full formulations, are erroneous. In particular, it overpredicts the separation angle and the size of the recirculation zone. The correctness of the stream function for flow around a cylinder is mathematically proved. Additionally, it is rigorously shown why the stream function for flow around a sphere is incorrect. Specifically, the analysis shows that while the circumferential velocity component derived from the stream function is accurate for the cylinder, it is incorrect for the sphere.

Transport enhancement in the laminar rotating disk boundary layer

Enhanced momentum and heat transport in a three-dimensional rotating disk boundary layer due to the consideration of a wavy disk surface is an already known fact in the literature. Such a transport enhancement is primarily associated with two fundamental attributes of the wavy disk: the increased surface area and the enhanced convection due to the surface undulations. However, there exists no further information about their individual role, mutual interaction, and individual share in enhancing the convective transport in the rotating disk boundary layer. This study aims to investigate these facts in detail by considering radially heterogeneous different wavy configurations on the disk surface. It is revealed that the said attributes contribute non-trivially to enhance the transport phenomena. Their impactful role is identified due to the strengths of circumferential and crossflow velocity components, the magnitude of flow swirl angle, and hence due to the coefficients of skin friction and their inter relationship. In this regard, a fundamental benchmark regarding the relative strength of the two coefficients of skin friction is identified from the flat disk case. Decisive observations regarding the impact of surface undulations and the increased surface area of the wavy disk on the enhanced convective transport are made with the aid of this benchmark. It is observed that the enhanced transport phenomena, especially the heat transfer, mainly depend upon the further dominance of the circumferential velocity component. In the situations of increased dominance of rotational flow Kw>Kf, the increased convection and surface area collectively contribute to enhance the thermal transport while in a reverse situation Kw<Kf the convection contributes adversely by even reducing the impact of the increased surface area. In the neutral situation where the dominance of rotational velocity is neither increased nor decreased (i.e., Kw≈Kf), any increase in the transport phenomena is wholly due to the increased surface area. Therefore, the presence of surface undulations or increase in surface area is not the only criterion for an optimum rise in the transport phenomena, rather the impact of surface undulations on the velocity profiles is important which is manipulated due to their positioning on the disk surface. It is observed that the presence of surface undulations in the central and intermediate regions on the disk surface causes to increase the gradients of the crossflow velocity while their presence in the near rim location causes to enhance the gradients of the circumferential velocity. Thus, the configurations that have higher undulations in the near rim region outperform the other configurations.

Flow and Performance Characterization of Rotating Detonation Combustor Integrated with Various Convergent Nozzles

In this study, convergent nozzles of various area ratios (ARs) are used downstream of an annular rotating detonation combustor (RDC) to increase the operating pressure and approach sonic conditions at the nozzle throat. Reactant methane and oxygen-enriched air (67% O2 and 33% N2 by volume) are supplied in counterflow arrangement from two separate plenums located at the base of the RDC annulus. Based on experimentation, a total mass flow rate of 0.32 kg/s was chosen to achieve stable, single-wave mode RDC operation for all test cases, allowing for one-to-one comparisons. The internal performance of the RDC was characterized by ion probes and pressure measurements (wall static and oscillating) in supply plenums and across different axial locations of the combustor. Particle image velocimetry (PIV) at 100 kHz was utilized to measure axial and circumferential velocity components within a two-dimensional region of interest located downstream of the converging nozzle exit. Results show higher internal performance of the RDC with increasing AR of the convergent nozzle. PIV measurement illustrated that the flow oscillation amplitudes decrease with an increasing AR of the converging nozzle. The exit flow contained significant nonuniformity and unsteadiness even with a converging nozzle of AR 2.0, indicating incomplete choking of the flow at the nozzle throat.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ВИХРЕВОГО ДВИЖЕНИЯ ДВУХФАЗНОГО ПОТОКА В ДЕЗИНТЕГРАТОРНОЙ МЕЛЬНИЦЕ

Mathematical models and the results of their numerical calculations play an important role at the modern level of automation of technological processes. The development of mathematical models to determine the design-technological or energy-power parameters of the operation of grinding equipment allows to obtain numerical information about the rational modes of its operation. In this study, numerical results were obtained from calculating a mathematical model of the vortex motion of a two-phase flow for the second stage of grinding depending on the physical and mechanical characteristics of the material being ground (ρp) and the current radius Rk of the grinding chamber of the unit. A method for numerically determining the speed characteristics of unit operating modes for materials with different physical and mechanical properties is presented. In the work, using the analysis of graphs of the sought functions of the mathematical model of the vortex motion of a two-phase flow, the velocity fields are presented in the form of diagrams of the radial, circumferential (tangential) and axial velocity components, which characterize the intensity of the flow dynamics inside the original design of the grinding chamber of the mill. In the process of mathematical modeling, it was established that the radial and circumferential (tangential) components of the two-phase flow velocities at current radii in the range Rk = 0.1–0.2 m reach their maximum values, both for solid particles of the crushed material and for the carrier phase – air. It has been determined that for the circumferential component of the velocity of a two-phase flow in a vortex at Rk = 0.3 m, its maximum is observed for both solid particles and the carrier phase – up = uo = 112.1 m/s.

Cross-Diffusion and Higher-Order Chemical Reaction Effects on Hydromagnetic Copper–Water Nanofluid Flow Over a Rotating Cone in a Porous Medium

Spin coating of engineering components with advanced functional nanomaterials which respond to magnetic fields is growing. Motivated by exploring the fluid dynamics of such processes, a mathematical model is developed for chemically reactive Cu–H2O magnetohydrodynamic (MHD) nanofluid swirl coating flow on a revolving vertical electrically insulated cone adjacent to a porous medium under a radial static magnetic field. Heat and mass transfer is included and Dufour and Soret cross-diffusion effects are also incorporated in the model. Thermal and solutal buoyancy forces are additionally included. To simulate chemical reaction of the diffusing species encountered in manufacturing processes, a higher-order chemical reaction formulation is also featured. Via suitable scaling transformations, the governing nonlinear coupled partial differential conservation equations and associated boundary conditions are reformulated as a nonlinear ordinary differential boundary value problem. MATLAB-based shooting quadrature with a Runge–Kutta method is deployed to solve the emerging system. Concentration, temperature and velocity variations for various nondimensional flow parameters have been visualized and analyzed. In addition, key wall characteristics, i.e., radial and circumferential skin friction, Nusselt number and Sherwood number, have also been computed. Validation with earlier studies is also included. The simulations indicate that when compared to a lower-order chemical reaction, a higher-order chemical reaction allows a greater rate of heat and mass transfer at the cone surface. Increasing Dufour (diffuso-thermal) and Soret numbers generally reduces radial and circumferential skin friction and also Nusselt number, whereas it elevates the Sherwood number. Both skin friction components are also suppressed with increasing Richardson number. Strong deceleration in the tangential and circumferential velocity components is induced with greater magnetic field.

On the Unsteady Rotationally Symmetric Flow Between a Stationary and a Finite Rotating Disk With a Given Change in the Axial Velocity

Abstract We consider the scenario of an unsteady viscous flow between two coaxial finite disks, one stationary and the other rotating with an axial velocity changing impulsively from zero to a constant value. The three-dimensional (3D) incompressible Navier–Stokes equations are analytically solved by postulating the polynomial profiles for the axial and circumferential velocity components and by employing the open-end condition of zero pressure difference and an integral approach. It is shown that the time-dependent squeezing of the fluid between the disks and the edge effects of the finite open-ended disks in the flow domain are determined by the compressing Reynolds number and the rotating Reynolds number for the case of laminar flow at low Reynolds numbers and small aspect ratios. The general explicit formulae are derived for the velocity and pressure distributions as a function of the compressing and rotating Reynolds numbers in this unsteady flow process (and the steady-state solutions are then obtainable as the compressing Reynolds number vanishes). A simple theoretical relationship between the radial and axial pressure gradients is deduced to hinge the radial and circumferential velocity components together. The values of the compression and rotation Reynolds numbers suitable to this theory are also suggested for the problem of rotating disk flows at low Reynolds numbers. The validity of the theoretical predictions for the circumferential, radial, and axial velocity components is partially verified through comparison with previous steady experimental and numerical results. These analytical results have the immediate engineering applications of fluid flows with varying gap widths, including wet brakes, wet clutches, hydrostatic bearings, face seals, and rotating heat exchangers.

Circumferential velocities in laminar and turbulent counter-vortex flow

Knowledge of the parameters of fluid movement is essential in the designing and operating various technological processes in various technical applications. These processes play a special role in hydro engineering, where the structures of water works are directly subjected to static and dynamic forces from the side of the water flow. The operation of hydraulic turbines, spillway and water transport systems, and other hydraulic structures is directly connected with understanding the behavior of a fluid in various regimes of movement. This report is devoted to the study of a special type of fluid and gas flow, which is called counter-vortex flow. The report compares the results of the distribution of circumferential velocities with a laminar and turbulent pattern of fluid movement. The results of the laminar flow regime were obtained using a mathematical model, and the turbulent regime on a physical model using laser technologies. Such a comparison allows one to assess two approaches in determining the kinematic structures of a complicated flow. The parameters for the viscous fluid laminar flow were determined based on the traditional system of Navier-Stokes equations by determining the dependence of the circumferential component of the total velocity at the given initial circulations and angular flow velocity. A physical model was made and equipped with a set of measuring equipment to obtain the distribution of velocities in the turbulent flow. The comparison showed that the distributions of velocities for the considered flow regimes depending on the channel radius have close coincidence. In contrast, the transformation length-wise of the active zone of the flow is significant.

INLET RECIRCULATION IN PARTLOAD REGIMES – RADIAL PUMP

Partload regimes of all types of centrifugal pumps are strongly and unfavorably affected by an influence of an inlet recirculation. This negative phenomenon usually occurs at pump suctions, when a circumferential velocity component of the fluid flow (derived from a rotational speed of a rotor) is dominant over an axial velocity component. Such physical effect goes hand in hand with a creation of a pump-head instability, a decrease of an overall efficiency, an excessive noise and pressure pulsations and even a possible cavitation formation. The introduced technical problem was tested/examined for a radial centrifugal pump Ns375 with a volute (spiral casing) and an axial intake domain with two potential countermeasures. Both, a physical experiment and transient numerical simulations were employed and compared on crucial levels.

Simulation and Modeling of Ported Shroud Effects on Radial Compressor Stage Stability Limits

The design features of a centrifugal compressor must guarantee high performance and a wide operating range. The ported shroud was developed specifically to extend the operating limit. It is a passive flow control device based on a cavity for flow recirculation to avoid blade passage blocking in near surge conditions. A CFD simulation campaign using a simplified model identified the differences in the performance of the centrifugal compressor with ported shroud, compared to the baseline case. The use of a stability criterion to determine the limit mass flow rate, developed in a previous study by the authors, highlighted and quantified the extension of the surge margin in the case with ported shroud for different rotational speeds. An increase in the surge margin of 11% was detected at design speed, but with a lower trend at higher speeds. An in-depth flow analysis showed the main physical mechanisms in the compressor that occur for different operating conditions: at near surge conditions the cavity recirculates the low momentum flow located in the inducer region; it re-energizes the mainstream decreasing the circumferential velocity component; an improvement of up to 7% of the pressure ratio was obtained. Instead, at best efficiency conditions the flow recirculation worsens the performance by reducing the flow incidence at the rotor leading edge. Finally, using unsteady simulations with a complete 3D model and with the application of the stability criterion it was possible to confirm that the ported shroud can effectively extend the operating range.

The Effect of J-Groove on Vortex Suppression and Energy Dissipation in a Draft Tube of Francis Turbine

The vortex rope in the draft tube is considered as the major contributor to pressure pulsation at partial load (PL) conditions, which causes the hydro unit to operate unstably. Based on the prototype Francis turbine HLA551-LJ-43 in the laboratory, J-grooves are designed on its conical section in this paper. We used numerical simulation to study the effect of the J-grooves on vortex suppression and energy dissipation in the draft tube. Four typical operating conditions were chosen to analyze the vortex suppression; the corresponding flow ratios Q* are 100%, 82%, 69%, and 53%, respectively. Entropy production theory is used to calculate the energy losses and assess the effect of the J-groove on energy dissipation under part-load conditions. By comparing entropy production, circumferential and axial velocity components, swirl intensity, pressure pulsation, and vortex distribution in a draft tube with and without J-grooves at different operating conditions, it can be concluded that the entropy production on the wall containing a conical section with J-grooves is obviously smaller than that without J-grooves, the effects of J-grooves on reducing circumferential velocity component Vu, pressure pulsation, and weakening vortex intensity and vortex rope in the conical section are obvious, especially at part load and deep part-load operating conditions. Using J-grooves shows better performance on vortex control and energy dissipation in the draft tube of a Francis turbine at partial load conditions.

Measurement of ejection velocity of rock fragments under dynamic compression and insight into energy partitioning

High-speed three-dimensional digital image correlation (3D-DIC) technique was utilised to examine the ejection velocity characteristics of rock fragment in dynamic compression tests . The fragment velocity components of fragment were extracted from velocity fields distributed within the fragment area. By identifying the peak resultant velocity, the initial fragment ejection velocity was determined. The kinetic energy of fragments was evaluated with the initial ejection velocity and the mass of the fragments in each size group. Results show that the fragment movement is successively accelerated by stress-wave propagation, crack opening and Poisson's effect which contribute to the axial, circumferential and radial velocity component of fragment, respectively. The variance in circumferential velocity of two neighbouring fragment areas indicates the formation of fragments. The peak value of radial velocity , which is the chief component in ejection velocity reveals the time when ejection taking place. The initial ejection velocity of fragment gradually decreases with increasing size, but increases significantly as strain rate increases . The kinetic energy of fragments ejection comprises 12%∼24% of absorbed energy at strain rate of 69∼100 s -1 , and the percentage further increases with increasing strain rates. Ignoring the kinetic energy of fragments will lead to overestimation of dissipated energy consumed by rock fragmentation in dynamic compression. • High-speed 3D-DIC was applied to identify three-dimensional velocity patterns of rock fragments under dynamic compression. • Strain recovery, fragment formation and ejection were revealed by velocity components of fragments, respectively. • Ejection velocity of fragment gradually decreases with increasing size, but increases significantly as strain rate increases. • Kinetic energy of fragments ejection takes more than 20% of absorbed energy with the strain rate above 85 s -1 .

Effects of Front Plate Geometry on Brush Seal in Highly Swirling Environments of Gas Turbine

Advanced brush seal technology has a significant impact on the performance and efficiency of gas turbine engines. However, in highly inlet swirling environments, the bristles of a brush seal tend to circumferentially slip, which may lead to aerodynamic instability and seal failure. In this paper, seven different front plate geometries were proposed to reduce the impact of high inlet swirl on the bristle pack, and a three-dimensional porous medium model was carried out to simulate the brush seal flow characteristics. Comparisons of a plane front plate with a relief cavity, plane front plate with axial drilled holes, anti-“L”-type plate and their relative improved configurations on the pressure and flow fields as well as the leakage behavior were conducted. The results show that the holed front plate can effectively regulate and control the upstream flow pattern of the bristle pack, inducing the swirl flow to move radially inward, which results in decreased circumferential velocity component. The anti-“L” plate with both axial holes and one radial hole was observed to have the best effect on reducing the swirl of those investigated. The swirl velocity upstream the bristle pack can decline 50% compared to the baseline model with plane front plate, and the circumferential aerodynamic forces on the bristles, which scale with the swirl dynamic head, are reduced by a factor of 4. This could increase the bristle stability dramatically. Moreover, the front plate geometry does not influence the leakage performance significantly, and the application of the axial hole on the front plate will increase the leakage slightly by around 3.5%.

Discontinuous solutions of the unsteady boundary-layer equations for a rotating disk of finite radius

Abstract

Experimental Studies into the Effect that the Rotor Rotation and Flow Swirling Upstream of Seals Have on the Leakage Flowrate

The results from experiments for studying the effect of rotor rotation on the leakage through different types of seals are presented. It is shown from a comparative study of models involving a stalled rotor and rotor rotating with a 50 Hz frequency that the rotor rotation has hardly any effect on the leakage flowrate, so that the rotation may not be taken into account in calculations of leakage flowrate through the steam turbine end and diaphragm seals. The article presents results from experiments for studying the dependence of leakage flowrate on the flow parameters, namely, the change of the velocity vector axial and circumferential components in the annular inlet channel upstream of a single annular throttle orifice. During the experiments, the velocity axial and circumferential components were varied independently and in a very significant range. The accomplished studies have shown that the change of both the axial and circumferential velocity components has hardly any effect on the leakage flowrate. It can be concluded from an analysis of the obtained results that the influence of flow parameters upstream of the seal on the leakage flowrate is so insignificant that its neglect in the previously developed calculation procedures for determining the leakage flowrate in the steam turbine seals, which are still in use at present, is quite substantiated and justified. At present, studies are being carried out that allow the flow structure in different places of turbine machinery flow paths, including the turbine seals, to be analyzed by calculation. It should be noted that it is possible by using the modern calculation methods not only to determine the vortex structure in the seal neighborhood but also to estimate the leakage flowrate, leakage losses, and even the stage efficiency for different configurations of the chamber upstream of the seal. Nonetheless, care should be taken in dealing with practical recommendations on changing the seal configurations that are based solely on the calculation results. The soundness of such recommendations must be confirmed by the relevant experimental investigations.

Numerical Simulation of Double Surface Liquid Ejector with Flow Swirl for Centrifugal Pump

Many systems with liquid ejectors and centrifugal pump are known. Often, jet pumps are used to provide a self-priming mode, as well as an acceptable pressure level for cavitation-free operation. The main disadvantage of such systems is the relatively low efficiency associated with the peculiarities of energy transfer in ejector. To increase efficiency double surface jet pump with driving and suction flow swirl (with circumferential component of velocity) is proposed. The active flow swirling is ensured by using of multi-nozzle tangential nozzle inlet and passive flow part by a special blade system. Combination of these factors makes it possible to improve the efficiency of energy conversion process. In comparison with the known design increases pump efficiency by 10 % – 15 %. Flow swirl also permits to reduce horizontal overall size by increasing the diffuser angle and reducing the mixing chamber length. These positive effects can be achieved by using methods and recommendations given in this paper. The paper also includes ANSYS CFX numerical simulation study results of double surface jet pump and analysis of the impact of nozzle position, length of the mixing chamber and other geometry parameters on pump performance. The results allow optimize the constructive solutions.

ВЛИЯНИЕ ТУРБУЛЕНТНЫХ ПУЛЬСАЦИЙ НА ПРОЦЕСС ФРАКЦИОННОГО РАЗДЕЛЕНИЯ МЕЛКОДИСПЕРСНЫХ ПОРОШКОВ НИТРИДОВ МЕТАЛЛОВ

This paper presents a numerical study of a two-phase swirling turbulent flow in a separation element of a vortex chamber. The paper considers a process of fractional separation in the separation chamber with three particular features in its design. The main feature is the separation mobile element located at the outlet of the separation area. Changes in the position of this element can affect the boundary size and the sharpness of the separation. The second feature of the considered separation chamber is the presence of a rotating element along the vertical axis. This element helps to align the field of the circumferential velocity component. The third feature of this chamber is the presence of a branch pipe for the auxiliary gas flow supply intended to push the particles away from the chamber wall and to blow the separated particles in order to prevent them from agglomeration. In this work, the trajectories of the motion of fine nitride particles are calculated taking into account the turbulent diffusion effect. A possibility to control the boundary size of the particles, when moving the separation element located at the outlet of the vortex chamber, is demonstrated. Numerical study results show that the turbulent pulsations cause significant changes in the separation process and affect the boundary size and the sharpness of the separation.

Разработка и внедрение новой математической модели тангенциальных выходных устройств центробежных компрессоров

Various engineering techniques are used for optimal gas-dynamic design of centrifugal compressors. This includes a universal modelling method that consists of software programs developed at Peter the Great St. Petersburg Polytechnic University. Tangential exit nozzles are elements of the centrifugal compressor flow path. The analysis of the results of the tangential exit nozzle calculations using the current mathematical model showed a need of improvement. The following main provisions formed a basis for a new model: the size of the passage is determined using the flow rate equation at the entrance and exit of the output unit (the calculated cross sections should be increased by 25–35% according to the recognized recommendations by Russian experts); the real nature of the flow in the output unit is taken into account by introducing an empirical coefficient in the equation of the circumferential component of velocity; the output diffuser is designed taking into account the optimal angle of expansion of an equivalent conical diffuser; the scroll tongue is shifted from a section with an angle of expansion of 0° to a section with an angle of expansion of 30°, which aids levelling the circumferential flow parameters and reduces total losses. To simplify the calculation process, a constant density along the scroll length is adopted in the mathematical model. The circumferential component of velocity is also determined approximately using the flow continuity equation without taking viscosity into account. Losses in scrolls and annular chambers are calculated in the radial and meridional planes. In the radial plane, the main losses are friction losses, whereas in the meridional plane, the main losses are due to expansion. For a trapezoid scroll, these pressure losses are determined depending on the scroll’s expansion angle. In the off-design operating modes, incidental losses due to impact flow around the scroll tongue are added. The presented model was implemented in the new version of the universal modeling method. The mathematical model was identified by the results of the commissioning test of the turboexpanders and turbochargers.

Developing the complex method for flow investigation in a hydro-turbine model using laser anemometry and video recording

The complex technique using laser and video equipment in test conditions at the setups of the Laboratory of water turbines of the Leningrad Metal Plant has been developed to conduct laser measurements of velocity fields and video recording of cavitation phenomena based on the integration of the laser systems (“LAD - 0xx" and “Track-07 S”), created at the Kutateladze Institute of Thermophysics SB RAS (IT SB RAS) and JSC “IOIT.” The Doppler anemometer allowed to achieve experimental distribution of the circumferential, axial, and radial velocity components at each point along the radius of the suction tube cone section of test experimental setup which has give information about vortex structure in suction turbine. The developed PTV method is described. The investigation of cavitation behind the turbine blade at test setup at velocities of 8-10 m/s is presented.

On the movement of two layers of viscous liquids on the outer surface of a horizontal rotating cylinder

The plane motion of thin layers of viscous immiscible liquids on the outer surface of a horizontal cylinder rotating at a constant angular velocity in a field of gravity and inertia is explored. In the case of sufficiently slow motion, neglecting the inertial terms of the Navier-Stokes equations, circumferential and radial velocity components were obtained, as well as an interrelated system of evolution equations for the inner and outer layers in a gravitational field. The problem of determining the type of surfaces of two layers in the case of unsteady motion of liquids on the outer surface of a rotating cylindrical shell is solved.