Axial Momentum Research Articles

Scaling analysis of the hydraulic behavior in reactor pressure vessel

The hydraulic behavior of coolant flow in reactor pressure vessel plays an important role in the thermal hydraulic and safety analysis of nuclear reactor system. Conventional reactor hydraulic tests were carried out by linearly down scaled facilities without tough physical principle. In this work, a scaling analysis in control volume scale for the hydraulic behavior in reactor pressure vessel is conducted to develop a theoretical basis for the down scaled hydraulic test. The mass, axial and lateral momentum conservation in reactor core is analyzed. Important scaling criteria for the reactor hydraulic test are obtained. It is found that the flow velocity should be reduced to promise the similarity of all scaling criteria. The identical velocity simulation with linear scaling method could results a distortion of about 16% to the lateral mixing criterion. This work is helpful to establish the theoretical basis for the hydraulic experiment and numerical research.

Liquid Films Falling Down a Vertical Fiber: Modeling, Simulations and Experiments

We provide a new framework for analyzing the flow of an axisymmetric liquid film flowing down a vertical fiber, applicable to fiber coating flows and those in similar geometries in heat exchangers, water treatment, and desalination processes. The problem considered is that of a viscous liquid film falling under the influence of gravity and surface tension on a solid cylindrical fiber. Our approach is different from existing ones in that we derive our mathematical model by using a control-volume approach to express the conservation of mass and axial momentum in simple and intuitively appealing forms, resulting in a pair of equations that are reminiscent of the Saint-Venant shallow-water equations. Two versions of the model are obtained, one assuming a plug-flow velocity profile with a linear drag force expression, and the other using the fully-developed laminar velocity profile for a locally uniform film to approximate the drag. These can, respectively, model high- and low-Reynolds number regimes of flow. Linear stability analyses and fully nonlinear numerical simulations are presented that show the emergence of traveling wave solutions representing chains of identical droplets falling down the fiber. Physical experiments with safflower oil on a fishing line are also undertaken and match the theoretical predictions from the laminar flow model well when machine learning methods are used to estimate the parameters.

Maximal power per device area of a ducted turbine

Abstract. The aerodynamic design of a ducted wind turbine for maximum total power coefficient was studied numerically using the axisymmetric Reynolds-averaged Navier–Stokes equations and an actuator disc model. The total power coefficient characterizes the rotor power per total device area rather than the rotor area. This is a useful metric to compare the performance of a ducted wind turbine with an open rotor and can be an important design objective in certain applications. The design variables included the duct length, the rotor thrust coefficient, the angle of attack of the duct cross section, the rotor gap, and the axial location of the rotor. The results indicated that there exists an upper limit for the total power coefficient of ducted wind turbines. Using an Eppler E423 airfoil as the duct cross section, an optimal total power coefficient of 0.70 was achieved at a duct length of about 15 % of the rotor diameter. The optimal thrust coefficient was approximately 0.9, independent of the duct length and in agreement with the axial momentum analysis. Similarly independent of duct length, the optimal normal rotor gap was found to be approximately the duct boundary layer thickness at the rotor. The optimal axial position of the rotor was near the rear of the duct but moved upstream with increasing duct length, while the optimal angle of attack of the duct cross section decreased.

Vortex Ring Theory—An Alternative to the Existing Actuator Disk and Rotating Annular Stream Tube Theories

Currently, the actuator disk theory (ADT) and the rotating annular stream-tube theory (RAST), both of which predicate on the axial momentum and generalized momentum theories, among others, are commonly used in investigating the aerodynamic characteristics of horizontal axis wind turbines (HAWTs). These theories, which are based on a rotor with an infinite number of blades, typically do not properly capture the flow physics of wind blowing past the rotors of HAWTs. A vortex ring theory (VRT) that analyzes HAWTs based solely on the characteristics of fluids flowing past obstructions is proposed. The VRT is not predicated on the assertion that the induced velocity in the wake is twice the induced velocity at the rotor. On the contrary, it splits the axial induction factor in the wake into two components, namely, the induction or interference factor due to the solidity of the rotor and the induction factor due to the wake of the rotor aw; aw and its azimuthal counterpart are determined using the Biot–Savart law. The pressure differences across the rotor segments of a HAWT are derived from the Bernoulli equation for all the three theories. Blade segment/local areas based on the blade sectional geometry of the rotor are used in the case of the VRT to estimate the local forces. All the calculations in this study are based on the design parameters of the 5 MW National Renewable Energy Laboratory’s reference offshore wind turbine. Pressure differences are plotted as functions of local radii using the calculated axial and azimuthal induction factors for each theory. The local power coefficient is plotted as a function of the local tip-speed ratio, while the local thrust coefficient is plotted as a function of the local radii for all the three theories. There is piece-wise agreement between the VRT, the ADT, the RAST and numerical and experimental data available in the literature.

Experimental investigation of swirl number influence on spiral vortex structure dynamics

The hydraulic turbines are recently forced to operate far away from the optimal conditions in order to balance fluctuations in electricity generation. In case of Francis, pump and propeller turbines, using only single control component of guide vanes, it means that in regions where the high residual swirl enters the draft tube, the flow is decelerated and convenient conditions for the vortex rope development are created. Such flow conditions are considered to be the triggering mechanism for occurrence of different forms of vortex structures in the Francis turbine draft tube, e.g. spiral or straight vortex rope at part load or full load respectively. Independently on the vortex rope shape the unsteady pressure fields develop producing periodic stress on turbine components and possibly resulting in noise, blade cracks, runner lift, power swing, etc. To study and mimic such flow conditions, a simplified device of vortex generator apparatus is employed. Thanks to its design, the vortex generator enables to change the ratio between fluxes of axial momentum and tangential moment of momentum of generated swirl. Then, the behavior of vortex structure changes in a similar way as the flow rate variation in the draft tube of Francis turbine. For above mentioned reasons the unsteady cavitating spiral vortex is experimentally studied using both high speed video record and particle image velocimetry (PIV). The main focus is on change of vortex dynamics regarding to the swirl number variation. The proper orthogonal decomposition (POD) together with the classical fast Fourier transformation (FFT) are employed to extract dominant modes and frequencies from experimental data.

Single-phase flow distribution in plate heat exchangers: Experiments and models

Abstract Maldistribution of fluid among parallel channels is one of the main issues in applications of plate heat exchangers. This paper presents an experimental and numerical investigation of the single-phase flow distribution in the brazed plate heat exchangers, but the results can be applied to plate-and-frame and plate-and-shell designs. In the experiments, the pressure profile in the heat exchanger is measured by the probes inserted into the headers. The flow distribution is determined by the measured pressure drop across the channels and the developed in-channel friction factor correlation. The experimental results indicate that in a U-type brazed plate heat exchanger, the channel flow rate first increases for the first several channels near the heat exchanger entrance due to the sudden expansion of flow in the inlet header. For the rest channels, the flow rate decreases with the distance away from the entrance/exit of the heat exchanger. Such a distribution profile is associated with the axial momentum transfer in the inlet header. The influence of the total flow rate on the distribution profile is trivial, but the maldistribution is more severe with an increased number of plates. Two distribution models presented are developed based on the principle of equal total pressure drop for all flow paths. Two models calculate the pressure profile in the headers by 3-D CFD modeling and 1-D mass and momentum conservation equation. The experimental results validate the models.

Optimization of axial water injection to mitigate the Rotating Vortex Rope in a Francis turbine

Rotating Vortex Rope (RVR) resulting from flow instabilities inside draft tube affects the hydraulic turbine's efficiency and wear. Among the passive and active RVR mitigation methods, the water injection method has been widely investigated lately. The present research focuses on the dynamics of RVR mitigation using the water injection method and the optimization of exergy loss during the water injection. The numerical simulations are performed using a reduced turbine geometry consisting of one stay vane, two guide vanes, one runner passage by applying periodic boundary conditions at side boundaries, and a complete draft tube. The pressure fluctuations, velocity field, and the RVR structure are well captured using the Shear Stress Transport - Scale Adaptive Simulation (SST-SAS) turbulence model. The results of the local swirl number during the load variation show that the onset of flow instabilities and RVR formation are created due to a decrease of the axial momentum below the runner cone. The required axial momentum flux of water injection is calculated for a stable swirl number and the local minimum ratio of dimensionless loss to the pressure recovery factor. The numerical results show that the rotating and plunging components of the pressure fluctuations inside the draft tube reduce during the water injection. The pressure recovery of the draft tube improves. The dynamics of RVR mitigation are visualized using λ2 criterion and the spectrogram of pressure probes on the draft tube wall. An optimum water flow rate and jet velocity for a fixed axial momentum are proposed. The results show that a water jet with a large radius and low velocity is more effective to mitigate the RVR and minimizing the draft tube losses.

The Rotation of the Nonrigid Earth at the Second Order. II. The Poincaré Model: Nonsingular Complex Canonical Variables and Poisson Terms

Abstract We develop a Hamiltonian analytical theory for the rotation of a Poincaré Earth model (rigid mantle and liquid core) at the second order with respect to the lunisolar potential and moving ecliptic term. Since the Andoyer variables considered in the first-order solution present virtual singularities, i.e., vanishing divisors, we introduce a set of nonsingular complex canonical variables. This choice allows for applying the Hori canonical perturbation method in a standard way. We derive analytical expressions for the first- and second-order solutions of the precession and nutation of the angular momentum axis (Poisson terms). Contrary to first-order theories, there is a part of the Poisson terms that does depend on the Earth’s structure. The resulting numerical amplitudes, not incorporated in the International Astronomical Union nutation standard, are not negligible considering current accuracies. They are at the microarcsecond level for a few terms, with a very significant contribution in obliquity of about 40 μas for the nutation argument with period −6798.38 days. The structure-dependent amplitudes present a large amplification with respect to the rigid model due to the fluid core resonance. The features of such resonance, however, are different from those found in first-order solutions. The most prominent is that it does not depend directly on the second-order nutation argument but rather on the combination of first-order arguments generating it. It entails that some first-order approaches, like those based on the transfer function, cannot be applied to obtain the second-order contributions.

On relativistic quantum mechanics of the Majorana particle: quaternions, paired plane waves, and orthogonal representations of the Poincaré group

The standard momentum operator −i∇ has the trivial domain (the null vector) if the L 2 Hilbert space consists of only real-valued functions. In consequence, it is useless in quantum mechanics of the relativistic Majorana particle which is formulated in such a Hilbert space. Instead, one can consider the axial momentum operator introduced in (2019) Phys. Lett. A 383 1242. In the present paper we report several new results which elucidate usability of the axial momentum observable. First, a new motivation for the axial momentum is given, and the Heisenberg uncertainty relation checked. Next, we show that the general solution of time evolution equation written in the axial momentum basis has a connection with quaternions. Furthermore, it turns out that in the case of massive Majorana particles, single traveling monochromatic plane waves are not possible, but there exist solutions which have the form of two plane waves traveling in opposite directions. Another issue discussed here in detail is relativistic invariance. A single real, orthogonal and irreducible representation of the Poincaré group—consistent with the lack of antiparticle—is unveiled.

Characterizing Regimes of Atmospheric Circulation in Terms of Their Global Superrotation

AbstractThe global superrotation index S compares the integrated axial angular momentum of the atmosphere to that of a state of solid-body corotation with the underlying planet. The index S is similar to a zonal Rossby number, which suggests it may be a useful indicator of the circulation regime occupied by a planetary atmosphere. We investigate the utility of S for characterizing regimes of atmospheric circulation by running idealized Earthlike general circulation model experiments over a wide range of rotation rates Ω, 8ΩE to ΩE/512, where ΩE is Earth’s rotation rate, in both an axisymmetric and three-dimensional configuration. We compute S for each simulated circulation, and study the dependence of S on Ω. For all rotation rates considered, S is on the same order of magnitude in the 3D and axisymmetric experiments. For high rotation rates, S ≪ 1 and S ∝ Ω−2, while at low rotation rates S ≈ 1/2 = constant. By considering the limiting behavior of theoretical models for S, we show how the value of S and its local dependence on Ω can be related to the circulation regime occupied by a planetary atmosphere. Indices of S ≪ 1 and S ∝ Ω−2 define a regime dominated by geostrophic thermal wind balance, and S ≈ 1/2 = constant defines a regime where the dynamics are characterized by conservation of angular momentum within a planetary-scale Hadley circulation. Indices of S ≫ 1 and S ∝ Ω−2 define an additional regime dominated by cyclostrophic balance and strong equatorial superrotation that is not realized in our simulations.

Effects of Sloped Trench Casing Treatment Combined with Air Injection on Aerodynamic Performance of a 1.5 Stage Axial Flow Compressor

A new mode, sloped trench casing treatment combined with air injection, was designed and introduced in a 1.5 stage axial compressor. To reveal the effects of this mode on the aerodynamic performance, a three-dimensional numerical simulation was carried out. Three air injection configurations were set to reflect the influence of injected flow velocity and injected mass flow rate. Results show that sloped trench casing treatment combined with air injection could improve the stall margin, total pressure ratio, and adiabatic efficiency of the compressor simultaneously. Moreover, injected flow velocity has a more significant influence on the effectiveness of extending stability than the injected mass flow rate. The optimal configuration obtains the stall margin improvement of 8.37% by using only 0.69% of the whole annulus mass flow rate. Based on a detailed analysis of the rotor flow field, it is found that the high-speed jet causes axial momentum of the incoming flow upstream the rotor blade tip to increase and load of the forepart chord of the rotor blade tip to reduce. The blockage in the tip region of the rotor passage is thus suppressed effectively, which results in the stall margin of the compressor enhanced.

Controlling the rebound on a solid surface by varying impact angles of ellipsoidal drops

Enhancing drop deposition on solid surfaces has received significant attention in various fields. Breaking the circular symmetry in typical impact dynamics has opportunities for altering the mass and momentum distributions significantly and improving the deposition. Here, we study the impact dynamics of ellipsoidal drops on nonwetted solid surfaces to reduce the bounce magnitude as a function of the impact angle and ellipticity. Experimental and numerical studies reveal that the ellipsoidal drop with the impact angle shows a strong reduction in the maximum bounce height, compared with the spherical drops. The oblique drop impact exhibits a remarkable feature of the off-axis aligning process caused by asymmetric retraction dynamics. Axial momentum analyses help us to interpret the underlying principle behind the peculiar retraction dynamics and establish a transition map of the rebound and deposition for varying angles and ellipticities. We believe that a breakup of the symmetry in the dynamics can provide practical implications for the control of drop deposition in diverse applications, such as spraying, coating, and cooling.

Helical Magnetic Cavities: Kinetic Model and Comparison With MMS Observations

AbstractMagnetic cavities are sudden depressions of magnetic field strength widely observed in the space plasma environments, which are often accompanied by plasma density and pressure enhancement. To describe these cavities, self‐consistent kinetic models have been proposed as equilibrium solutions to the Vlasov‐Maxwell equations. However, observations from the Magnetospheric Multi‐Scale (MMS) constellation have shown the existence of helical magnetic cavities characterized by the presence of azimuthal magnetic field, which could not be reconstructed by the aforementioned models. Here, we take into account another invariant of motion, the canonical axial momentum, to construct the particle distributions and accordingly modify the equilibrium model. The reconstructed magnetic cavity shows excellent agreement with the MMS1 observations not only in the electromagnetic field and plasma moment profiles but also in electron pitch‐angle distributions. With the same set of parameters, the model also predicts signatures of the neighboring MMS3 spacecraft, matching its observations satisfactorily.

Scaling of the mean transverse flow and Reynolds shear stress in turbulent plane jet

Proper scaling for the mean transverse flow and Reynolds shear stress in a turbulent plane jet is determined using a scaling patch approach. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity equation, a proper scale for the mean transverse flow in a turbulent plane jet is found as Vref=−δdUctr/dx, where δ is the jet half width and dUctr/dx is the decay rate of the mean axial velocity at the jet centerline. By seeking an admissible scaling for the mean axial momentum equation, a proper scale for the kinematic Reynolds shear stress is found as Ruv,ref=Uctr Vref, which is a mix of the velocity scales in the axial and transverse directions. Approximation functions for the scaled mean transverse flow and Reynolds shear stress are developed and found to agree well with experimental and numerical data. Similarities and differences between the scales of the mean transverse flow and Reynolds shear stress in turbulent plane jets and zero-pressure-gradient turbulent boundary layer flows are clarified.

Numerical study of suppression mechanism of two types of grooves on the TLV

In the tip clearance flow, the dominant vortex is the tip leakage vortex (TLV), which has a significant impact on the hydraulic and cavitation performance of axial flow machinery. Thus, the suppression methods of the TLV are necessary in turbomachinery. Casing groove is an effective and economical technique among many control methods. However, its mechanism is still not completely understood. In order to reveal the effect mechanism of the casing groove on the TLV, numerical investigations of gap flow with groove configurations are carried out. A NACA0009 hydrofoil with tip gap is selected as the research object. Two typical groove types (vertical groove and horizontal groove) are applied on the solid wall respectively. Efforts are made to analyze the difference of velocity distributions between the two groove cases and the smooth wall case. Combing with the vortex stability theory, the suppression mechanisms of the two types of casing groove are distinguished and uncovered. For the vertical groove, the TLV intensity is reinforced via the secondary leakage vortex (SLV) at first, and then the supply of the axial momentum in the TLV center is cut off, leading to a less stable TLV. For the horizontal groove, the dissipation effect caused by viscosity on the TLV is strong, resulting in a weakened TLV.

Twisting neutral particles with electric fields

We demonstrate that spin-orbit coupled states are generated in neutral magnetic spin 1/2 particles travelling through an electric field. The quantization axis of the orbital angular momentum is parallel to the electric field, hence both longitudinal and transverse orbital angular momentum can be created. Furthermore we show that the total angular momentum of the particle is conserved. Finally we propose a neutron optical experiment to measure the transverse effect.

Numerical simulation and self-similarity of the mean mass transfer in turbulent round jets

The paper investigates the mean mass transfer/passive scalar spreading in turbulent submerged round jets. Two regions of flow are present in the jet evolution: the Near-Field Region (NFR) and the Fully Developed Region (FDR). This group of research investigates from some years the mean evolution of turbulent rectangular jets with the new physical finding that two sub-regions (not a single one) are present in the NFR. The first region of the two is the newly discovered Undisturbed Region of Flow (URF), while the second one is the known Potential Core Region (PCR). In a recent paper we showed that the flow evolution of turbulent round jets, as far as momentum spreading is concerned, is self-similar also in the NFR. Literature shows that mass transfer spreading is self-similar only in FDR. The present paper presents new mean mass transfer results of the numerical Large Eddy Simulation (LES) in turbulent round jets. Four Reynolds numbers, from 2492 to 19,988, and two laminar Schmidt numbers, 1 and 10, are investigated. The first novel result of this paper is that mass transfer is self-similar in the NFR. The second result is that two new analytical models describe the passive scalar spreading in the URF and PCR. The third result is that two new self-similar laws describe the passive scalar spreading in the FDR. The fourth result states that the well-known power-law relationship, between passive scalar and axial momentum in the FDR, holds regardless of the modeling of turbulent viscosity and turbulent Schmidt number.

Experimental Study into the Effects of Stability between Multiple Injections on the Internal Flow and Near Field Spray Dynamics of a Diesel Nozzle

To understand the coupling effects of needle valve wobbling and residual bubbles on the nozzle internal flow and near field in diesel engines, high-speed microscopic imaging technology was employed to study the dynamics behaviors of a real-size tapered hole nozzle. Research results indicated that during the pre-injection and post-injection process, the difference in throttling effect caused by the wobbling of the needle valve is the main reason for the instability of the fuel injection quantities. As the pulse widths increases, the actual injection duration and the maximum needle valve lift increased, so that the throttling position changes from the passage between the needle valve and the needle seat to the nozzle holes, and the cavitation mode changes from geometrically induced cavitation to string cavitation. During the main injection stage, the spray cone angle and spray area ratio showed a boot-shaped trend of firstly low and then high, forming a development stage, a transformation stage and a stable stage. And in the initial stage of injection, the spray pattern is affected by the combined influences of the axial momentum and radial momentum of the injected fuel, resulting in a difference between the second spray disturbance and the primary breakup.

Effects of Rotor-Rotor Interaction on the Wake Structure and Thrust Generation of a Quadrotor Unmanned Aerial Vehicle

In this paper, the effects of rotor-rotor interaction on the wake structure and thrust generation of a quadrotor unmanned aerial vehicle (UAV) are experimentally investigated in the rotor tip Reynolds number range of 34000 - 54000. The interaction strength is manipulated by varying the number of rotating rotors and the normalized rotor separation distance. A stronger rotor-rotor interaction places the inner tip vortices between rotors closer to each other, forming an upflow region through vortex pairing and intensifying the turbulence intensity between rotors. To comprehensively evaluate the effect of interaction on the wake structure, we propose a modified Landgrebe's model that accurately describes the wake boundary of UAV, given the number of rotating rotors and the normalized rotor separation distance. The wake analysis based on the model shows that the stronger the rotor-rotor interaction, the less the wake contracts and the closer the vena contracta moves to the rotor-tip path plane. The momentum theory combined with the modified Landgrebe's model shows that the loss of axial momentum transfer due to the wake inclination is insufficient to account for the thrust loss caused by the rotor-rotor interaction. This paper shows that the shift of the inner tip vortex away from the rotational axis and the corresponding increase of induced axial velocity followed by a decrease in the local effective angle of attack is another important mechanism for the thrust loss.

Swirling turbulent pipe flows: Inertial region and velocity–vorticity correlations

Swirling pipe flows are studied here with an aim towards understanding the onset of the inertial region — where the turbulent-inertia term in the mean momentum equation is balanced by pressure gradient and viscous term is sub-dominant — as well as the clarifying the velocity–vorticity correlations that make up the turbulent inertia. To this end, we first manipulate the mean momentum equation in both axial and azimuthal directions and find some exact results in the inertial region, and carry out direct numerical simulations of swirling pipe flows at axial friction Reynolds numbers of 170 and 500. The swirl number considered in our simulations is S≈0.3, and we compare our results to non-swirling pipe flows at similar Reynolds numbers. We find that swirling produces a drag increase and an influence on the turbulence statistics similar to increasing the Reynolds number except for the streamwise turbulence intensity. An analysis on the axial and azimuthal mean momentum equations shows that swirling shifts the beginning of the inertial region wall-normal location closer to the wall. The turbulent inertia decomposition reveals that the near-wall region the velocity–vorticity correlations of the axial direction are similar to a 2D channel flow and interpreted as vorticity stretching/reorientation and dispersion, whereas in the new correlations in the azimuthal direction can also be given a similar physical meaning in the near-wall region. In the outer-region, however, the pipe axial correlations are different to the 2D-channel, and so are the azimuthal correlations. We find that the pipe has new a ‘geometric’ contribution in both axial and azimuthal directions that play an important role in contributing towards vorticity dispersion in the outer core region of a swirling pipe flow.