Vertical Rotor Research Articles

A CFD-Based Examination of Rotor-Rotor Separation Effects on Interactional Aerodynamics for eVTOL Aircraft

This study systematically investigates the aerodynamic interactions of a two-rotor system with a front rotor and an aft rotor aligned with the direction of flow. The rotors are 5.5 ftdiameter fixed-pitch rotors operating at approximately 12 lb/ft2 disk loading, representative of large eVTOL aircraft. Fluid flow is simulated using the commercial Navier–Stokes solver, AcuSolve, with a detached eddy simulation (DES) model. Simulations were performed nominally at 40 kt edgewise flight for nine cases corresponding to three values of longitudinal hub–hub separation (2.5R, 3R, 3.5R) and three values of vertical offset (0, 0.25 R, 0.5 R ). Aft rotor performance was compared to an isolated rotor operating in the same conditions in order to quantify the effects of rotor–rotor interaction. For the cases where the aft rotor is closest to the front rotor (2.5R longitudinal offset, zero vertical offset), the aft rotor produced 8.4% less thrust and required 13.4% higher torque than a rotor in isolation. When vertical rotor separation was increased, interactional aerodynamic effects decreased. For a 2.5R longitudinal offset, increasing the vertical offset to 0.5 R decreased the lift deficit to 4.6% and the torque penalty to 6.8%. Increasing the longitudinal offset to 3.5R (while keeping the vertical offset at zero) also reduced interactional aerodynamic effects, but reductions in lift deficit and torque penalty were smaller than those observed with 0.5R vertical offset. Reducing disk loading was found to strengthen interactional aerodynamic effects, with an 11.5% thrust deficit at 6 lb/ft2 compared to 9.0% at 12 lb/ft2. An increase in flight speed also increased interactional aerodynamic penalties from 5.4% thrust deficit at 20 kt to 12.2% at 60 kt. The increased interactional aerodynamic penalties with the reduction in disk loading and increase in flight speed were both attributed to an increase in wake skew angle and the resulting decrease in separation between the aft rotor disk and front rotor wake.

Approximation of Non-Linear Rotor Dynamic Resonance Behavior of Vertically Aligned Hydro-Units Guided by Tilting-Pad Bearings

Dynamic analyses of vertical hydro power plant rotors require the consideration of the non-linear bearing characteristics. This study investigates the vibrational behavior of a typical vertical machine using a time integration method that considers non-linear bearing forces. Thereby, the influence of support stiffness and unbalance magnitude is examined. The results show a rising influence of unbalance on resonance speed with increasing support stiffness. Furthermore, simulations reveal that the shaft orbit in the bearing is nearly circular for typical design constellations. This property is applied to derive a novel approximation procedure enabling the examination of non-linear resonance behavior, using linear rotor dynamic theory. The procedure considers the dynamic film pressure for determining the pad position. In addition, it is time-efficient compared to a time integration method, especially at high amplitudes when damping becomes small.

Resonant phenomena in nonlinear vertical rotor systems

In this paper, the study of the dynamics of a rotor system mounted on an elastic foundation rotating in rolling bearings is considered. To describe the bearing model, the Hertz theory was used, linking radial loads acting on the bearing and deformation at the points of contact between the movable housing and the bearing rings. When describing the model of rolling bearings, it is assumed that there is no kind of sliding of bodies and moving surfaces. The obtained differential equations of the rotor and the foundation do not have a common solution. Therefore, the study was conducted using numerical methods. In order to simplify the problem and increase the accuracy in solving the obtained differential equations, dimensionless quantities were used. With the increase and decrease of dimensionless quantities, the amplitudes of the rotor and the foundation are constructed. As a result, two resonances were formed: the main resonance and the second resonance. The work is connected with the physical meaning of the process considered in the problem the results obtained are the basis for the application of this mathematical model in the design of a rotary system rotating in rolling bearings.

Impact of non-synchronous whirl on post-resonance backward whirl in vertical cracked rotors

Certain heavy-duty industrial machinery uses vertical rotating shafts. Such rotating systems typically undergo transient operation phases to reach their nominal speeds; recurrent passage through resonance generally occurs during startup and coast down operations. The Non-synchronous whirl between the shaft rotational speed and its whirling in the whirl orbit in the vicinity of the resonance zones, significantly affecting the breathing mechanism of a propagating transverse crack. Therefore, the appearance of Non-synchronous whirl during the passage through resonance rotational speed activates the crack breathing mechanism. To verify this observation, Jeffcott rotor and finite element models with induced breathing cracks are considered here for geometrically symmetrical and asymmetrical vertical rotor configurations. The mathematical models associated with these systems yield linear time-varying equations of motion incorporating the angular acceleration rate. The appearance of a Non-synchronous is found activating the crack breathing mechanism, which immediately excites the post-resonance backward whirl even with small crack depths in the rotor system. Accordingly, the excitation of post-resonance backward whirl can be considered as a strong indicator of an early crack propagation phase in vertical rotors.

Numerical and experimental study on dynamic characteristics of tilting-pad journal bearings considering pivot stiffness in a vertical rotor system

Purpose The purpose of this paper is to study the influence of pivot stiffness on the dynamic characteristics of tilting-pad journal bearings (TPJBs) and the stability of the bearing-rotor system. Design/methodology/approach A theoretical numerical model is established, and the influences of pivot stiffness on TPJBs and a bearing-rotor system are analyzed. Then, two kinds of pivot structures with different stiffness are designed and the vibration characteristics are tested on the vertical rotor bearing test bench. Findings The pivot stiffness has an obvious effect on the dynamic characteristics of the TPJBs and the stability of the bearing-rotor system. As a result of appropriate pivot stiffness, the critical speed and the vibration amplification factor can be reduced, the logarithmic decay rate and the stability of the rotor system can be effectively increased. While the journal whirl orbit is smoother and the rubbing is obviously reduced when the bearings have flexible pivots. Originality/value The influence of pivot stiffness on TPJBs and a vertical rotor-bearing system is studied by theoretical and experimental methods.

Numerical and Experimental Study on the Dynamic Bearing Properties of a Four-Pad and Eight-Pad Tilting Pad Journal Bearings in a Vertical Rotor

Abstract In this paper, the dynamics of tilting pad journal bearings (TPJB) with four and eight pads are studied and compared experimentally and numerically. The experiments are performed on a rigid vertical rotor supported by two identical bearings. Two sets of experiments are carried out under a similar test setup. One set is performed on a rigid rotor with two four-pad bearings, while the other is on a rigid rotor with two eight-pad bearings. The dynamic properties of the two bearing types are compared with each other by studying the unbalance response of the system at different rotor speeds. Numerically, the test rig is modeled as a rigid rotor and the bearing coefficients are calculated based on Navier–Stokes equation. A nonlinear bearing model is developed and used in the steady-state response simulation. The measured and simulated displacement and force orbits show similar patterns for both bearing types. Compared to the measurement, the simulated mean value and range (peak-to-peak amplitude) of the bearing force deviate with a maximum of 16% and 38%, respectively. It is concluded that, unlike the eight-pad TPJB, the four-pad TPJB excites the system at the third- and fifth-order frequencies, which are due to the number of pads, and the amplitudes of these frequencies increase with the rotor speed.

Rotordynamic Characterization of Tilting-Pad Bearings With Eight Pads in Vertical Rotors

Abstract It has been documented that stiffness and damping for a four-pad bearing are dependent not only on the magnitude of the load but also on the position of the rotor in the bearing. However, eight-pad bearings are not commonly employed on horizontal turbines, and the presence of several pads in the bearing will decisively affect the dynamics of the system. This paper evaluates the stiffness and damping coefficients of tilting-pad bearings with eight pads and explores the main frequencies acting on the forced response of a vertical rotor. The bearing properties were modeled as a function of eccentricity and position in the stationary coordinate system by Navier–Stokes equations whose results are taken from commercial software. The simulated unbalanced response is compared to experimental results; the changing position of the shaft produces a periodic stiffness and damping, which is dependent on the number of pads. Cross-coupled coefficients influence is discussed, showing that their absence makes an accurate model for the mean values. The results indicate that simulation of vertical rotors with eight-pad bearings can be simplified which allow more effective simulations and dynamic analysis.

Structural and Aerodynamic Characteristics Analysis of a Small V-shaped Vertical Axis Wind Turbine Rotor

ABSTRACT A detailed comprehensive study of a proposed V-shaped turbine rotor is performed in order to examine its structural and aerodynamic characteristics. The structural analysis section of this work determined the most structurally sound blade geometry from 3 different blade geometries. Using the chosen blade profile, 8 rotor models are developed and are tested numerically. These rotor models are of different configurations, focusing on an inclination angle of 45 and 60 degrees, blade twist angle of 0 and 5 degrees and number of blades. Four rotor models are taken from the initial tests for further study, 3B45D which is a three-bladed rotor with a 45 degree inclination angle, 5B45D which is a five-bladed rotor with a 45 degree inclination angle, 5B45D (5deg) which is a five-bladed rotor with a 45 degree inclination angle and a 5 degree blade twist angle, and 5B60D which is a five-bladed rotor with a 60 degree inclination angle. From the structural study, blade design 2 held the best structural characteristics. The design showed an excellent Von-Mises at 8.8 MPa for static structural and 22.2 MPa for fatigue stress response which is well below the yield strength of ABS Plastic. Both experimental and numerical data have relatively good agreement that is within 15% difference. Overall, maximum power coefficient achieved in this study is about 0.259 numerically and 0.213 experimentally. The best performance is seen by the 3B45D rotor in both static and dynamic study considering experimental and numerical corroboration of results.

Passive Balancing of the Rotor with an Auto-Balancing Device with a Viscous Incompressible Liquid

The use of liquid auto-balancers to compensate the operational changes in the imbalance of rotary systems without stopping them is of interest because of the relative structural simplicity of these devices, which are passive direct-acting regulators that do not require power supply and control systems to move correction masses. The experience of the study of passive auto-balancing devices (SBD) indicates that the existing theory (statements) of passive automatic balancing of the fluid is idealized and inaccurately describes the processes that occur with the working bodies during their operation. In particular, the lack of studies on the effect of liquid viscosity on the efficiency of self-balancing and the reasonableness of the selection of liquid during the development of fluid SBD demanded to analyse the operation of liquid SBD in the real system, taking into account the influence of liquid properties on the efficiency of the vertical rotor balancing process. It is shown that the efficiency of balancing increases with the approach of the angular velocity to the critical one and with the increase of the external resistance. The massive forces of the working fluid have less effect on the balancing efficiency than the viscosity for liquid SBDs.

Modeling the dependence of the foam concrete structural quality coefficient on the speed and duration of mixing the foam concrete mixture

Experimental studies of the technological factors’ influence on the physical and mechanical properties of foam concrete were carried out. Additive Portland cement was used as a binder. Finely ground quartz sand of fractions 0.08-0.16 and 0.16-0.315 mm was used as a filler. Protein foaming agent Arecom-4 was used as a foaming agent. The porization time of the aerated concrete mixture was controlled using a stopwatch, and the rotation speed of the vertical rotor mixer shaft was controlled with a digital photo-tachometer. In the experiments, the following factors were varied: mixture porization time, mixing speed. The main characteristics of foam concrete were determined by testing the prototypes or their fragments according to the methods of the relevant regulatory documents using verified equipment. In the research laboratory of the DSTU, the studies on the influence of the speed and duration of mixing the foam concrete mixture on the density, strength and coefficient of the resulting foam concrete structural quality were carried out. The article presents the experimental dependences of the investigated characteristics on the speed and time of mixing the foam concrete mixture. The parameters of density and strength show a monotonic decline during pore formation, while the structural quality coefficient exhibits its maximum. The behavior of density, strength, coefficient of structural quality can be described in a single model using the parameters that reflect bonds loosening, a general decrease in the number of bonds in the material and the bonds’ change spatial distribution.

Modelling of transient and steady-state modes of a vertical rotor with an automatic balancing device

The authors of the study work out the differential equations of motion of a vertical rotor model on an elastic-dissipative suspension, balanced by a ball-type automatic balancing device. Often, the cross-section of the cavity of the body of the automatic balancing device is rectangular and during rolling the balls have two points of contact, in one of which the balls slide along the surface of the cavity. To prevent the balls from sliding, the inner surface of the cavity of the automatic balancing device is made in the shape of a torus, which provides one point of contact. The forces of gravity and the forces of resistance to the movement of the correcting weights are taken into account, and the model is drawn up for both viscous and dry friction forces inside the body of the automatic balancing device. The obtained mathematical model of the rotor makes it possible to study the transient and steady-state modes of motion of the rotor system.

Estimation of the stress state of agricultural harrows with vertical axis rotor, using mathematical models with finite elements

In this paper we simulated through mathematical models the interaction between the agricultural harrow with vertical rotor (equipped with 4 boxes per rotor) and soil. Due to the large or even very large number of mathematical models that can be developed and can receive a solution using the finite element method, there are also many new possibilities to approach and improve some already developed models. The most important benefits of using finite element modeling are: increasing the quality of projects by checking the resistance, noticing dangerous vibration problems, remedying deficiencies reported in the testing of experimental models or even in operation. Normal optimization aims to reduce material consumption, its own vibration spectrum or other mechanical qualities.By using mathematical methods, a resistance check of the subassemblies of the working member (knife), connected to the action device, is obtained.

Substantiation of the structural-functional scheme and performance of a rotary treater of periodic action for layer-by-layer seed treatment

Annotation Purpose. Improving the efficiency of pesticide use by developing a batch-type rotary seed treater for layer-by-layer seed treatment, which will improve the quality of seed treatment and environmental safety. Methods. The study used an analytical and computational method using a software environments Microsoft Office. Results. A structural-functional diagram of a rotary treater of periodic action for the layer-by-layer application of protective-stimulating-nutrient preparations to seeds has been developed, which involves the use of a seed treatment chamber with a vertical rotor installed in it, to which seeds and components of chemical preparations are sequentially applied to the seeds. A relationship has been established between the productivity of the seed treatment process and the mass of the treated seed portion, the loading time of the seed portion, the time of processing the seed portion, the drying time of the treated seed portion, the unloading time of the treated seed portion and the number of applied layers of preparations. Conclusions. The productivity of the process of layer-by-layer seed treatment increases significantly with an increase in the mass of a portion of seeds and sharply decreases with an increase in the number of applied layers of preparations. The productivity of two-layer seed treatment varies from 0.97 t/h with a mass of a portion of seeds of 10 kg to 13.62 t/h with a mass of a portion of seeds of 140 kg, the productivity of six-layer seed treatment varies from 0.4 t/h with a mass of a portion of seeds of 10 kg to 5.66 t/h with a mass of a portion of seeds of 140 kg. Keywords: portion of seeds, disinfectant, layer-by-layer processing, protective-stimulating-nutritious preparations.

Design Of Helical-Blade Rotor Of Vertical Axis Wind Turbine (VAWT)

The vertical axis wind turbine (VAWT) with helical-blade has been developed, manufactured and applied in almost all developed countries. In Indonesia, vertical axis wind turbines are still not widely applied compared to horizontal axis wind turbines. Vertical axis wind turbines with helical-blade are still very rare in Indonesia. Research and development of the vertical axis wind turbine are needed because of its advantages compared to horizontal axis wind turbine. The advantages are: can operate in various wind directions, lower noise due to smaller tip speed ratio (TSR) and for large-scale, mechanical and electrical systems of turbine can be placed on ground. The aim of this research is to design a vertical axis wind turbine rotor with helical-blade that can be applied at low speeds and changing direction wind condition, such as urban wind characteristics. Performance analysis of wind turbine rotor is done by using double-multiple stream-tube (DMS) model approach. This research yields a rotor of vertical axis wind turbine with helical-blade with rotor length and diameter are 2m and 1m respectively, the rotor blade airfoil is DU-06-W-200 with chord length is 0.2m. From analysis, the optimum tip speed ratio of the rotor is 2.6 with a maximum power coefficient is 0.57.

Vertical rotor model with hydrodynamic journal bearings

In hydropower generating plants the reliable operation of the hydropower unit (hydraulic turbine and generator) is a critical issue. Unexpected failure of the hydropower unit lead to high economic costs. A dynamic model of this type of machine is useful for condition monitoring which allows to detect failures in an early stage without the need to stop the machine. Most hydropower units over 20 MW of power has a vertical rotor and are mounted on hydrodynamic journal bearings. In vertical rotors, the load on the bearings is mainly rotatory and to provide stability tilting-pad journal bearings are used. An accurate dynamic model of hydropower unit must consider vertical tilting-pad journal bearings. The present study proposes a dynamic model of hydropower unit that considers the geometrical characteristics of vertical rotor and the behavior of the vertical tilting-pad journal bearing. The dynamic model is validated in two studies found in literature showing good agreement with published data (laboratory vertical rotor and actual hydropower unit). Then, the dynamic model is used to simulate an actual hydropower unit that was operating with an irregular pad clearance. Dynamic model was able to adequately predict waveform, orbits and spectrums of hydropower unit during operation at different power, startup, and during shutdown. It is concluded that dynamic model correctly predicts the failure in the pad clearance.

Effect of rotating unbalance on nonlinear dynamic response of flexible rotors supported on tilting pad journal bearing

The effect of orientation of rotors and rotating unbalance at disc on the dynamic response of rotor supported by four pad tilting pad journal bearing (TPJB) is studied. The orientation of the rotor taken has a horizontal rotor (HR) and a vertical rotor (VR). The rotor element modeled as the Timoshenko beam element with four degrees of freedom per node. The disc is rigid and it is centrally mounted. The nonlinear forces by the fluid film in tilting pad journal bearing were determined by solving the Reynolds equation along with each pad. The infinite short bearing assumption has taken to find pressure distribution along with pads. Indigenous MATLAB® code has developed to solve the rotor-TPJB equation. The ODE-15s solver is used to find the related response data of journal and disc centers. Orbits, phase plots, and power spectrums used to analyze the behavior of the system. The sub-synchronous vibrations dominate at lower speeds and high rpm unbalance forces become much significant and overcome bearing fluid film forces causing catastrophically change in response of the system.

The self-oscillation in the vertical rotor system mounted on elastic supports

The self-oscillation in the vertical rotor system mounted on elastic supports

An Energy-Efficiency Assessment of a Railroad Passenger-Car Power-Supply System Using Wind Generators and Photovoltaic Panels

This paper considers the use of vertical rotor centrifugal and centripetal wind turbines as sources of energy for power-supply systems of railway passenger cars, in addition to as additional sources of electrical energy, such as variable speed alterators that receive mechanical energy from wind turbines, as well as flexible PV panels located on the roof of a car. When calculating the total energy output for the supply of electric energy to consumers of passenger cars, experimental data from literature sources are used. According to the calculations, when alternative energy sources are used in addition to an existing passenger-car power-supply system, electricity consumption can be reduced by 25.5%.

Method for determining the kinematic parameters of the vertical rotor blades for the destruction of the tuberous layer

Annotation Purpose. Development of a technique for determining the velocities of collision of the blades with the tuberous layer, the trajectory of movement, the magnitude and direction of the velocities of the most characteristic points. Methods. The research was carried out using the basic provisions of theoretical mechanics, statistics, probability theory, methods of differential calculations, mathematical modeling and applied programming. The studies were carried out on a specially designed laboratory installation using a vertical rotor hydraulic drive and strain gauge equipment mounted on a tractor, as well as a set of variable connecting plates for setting the machine operating modes. Results. The calculations of the absolute collision velocities of the blades of the lower and upper beaters of the vertical rotor at the start and end points, respectively, are performed. The geometric shape of the working surfaces and the direction of rotation for the extreme points of the outer contours of the blades of the lower and upper beaters of the vertical rotor of the potato harvester are substantiated. Conclusions. Using the above technique, as well as graphical dependences, we calculated the rational kinematic parameters of the blades of the lower and upper beaters of the vertical rotor, respectively, at the start and end points, where the greatest destruction of the tuber layer. For the lower beater blade, the absolute collision speed at the angle of rotation ωнt = 120° at the starting point = 1.6 m/s, at the end point – = 1.94 m/s. For the upper beater blade, the absolute collision speed at the angle of rotation ωвt = 120° at the starting point = 1.4 m/s, at the end point – = 1.92 m/s. Therefore, according to the specified rational kinematic parameters of the blades of the lower and upper beaters of the vertical rotor, it is possible to design the geometric shape of the surfaces of the crushing working bodies of potato harvesters. Keywords: blade, breaking surface, breasts, potatoes.

Effect of Dynamic Balance Parameters on Vibration of Vertical and Horizontal Rotor System

In this paper, a rotor test device for vertical-horizontal conversion is designed. The effects of unbalanced mass, dynamic balance position and other dynamic balance parameters on the vibration response of the rotor system are experimentally analyzed, and the difference of the vibration response of the rotor system between vertical and horizontal States is compared. The test results show that the vibration of the bearing base foot will increase after the dynamic balancing rotor is installed in the vertical shafting in the horizontal state; in order to ensure the dynamic balancing accuracy, the dynamic balancing of the vertical rotor system should be carried out on the vertical system as far as possible, and the aggravation should be carried out far away from the driving end. The research results in this paper can provide necessary support for the determination of dynamic balancing process and the study of dynamic characteristics of vertical rotors.