Entire Cylinder Research Articles

Gas dynamics and heat exchange of stationary and pulsating air flows during cylinder filling process through different configurations of the cylinder head channel (applicable to piston engines)

Piston machines are used in distributed generation, are in demand as auxiliary energy sources in hybrid systems and are indispensable devices in compressor technology. The purpose of this article is to develop a method for improving the quality of the cylinder filling process based on an experimental study of the gas dynamics and heat transfer of stationary and pulsating flows in an intake system with profiled channels in a piston machine's cylinder head. Experiments were carried out on full-scale models of piston machines with thermal anemometry and thermal imaging. The article examines three cross-sectional shapes for the intake port in the cylinder head: circle (basic design), square and triangle. It is established that profiled channels in a piston machine's intake system have a significant impact on the gas-dynamic, flow and heat-exchange characteristics of both stationary and pulsating air flows. It is shown that the use of profiled channels leads to a more uniform distribution of air flow throughout the entire cylinder volume and a significant reduction in stagnation zones, which should lead to a reduction in specific fuel consumption. It is established that air flow through an intake system with square and triangular ducts increases up to 30 % compared to the basic system, which should lead to an increase in power. It is found that the use of square and triangular channels leads to an increase in the flow turbulence intensity by 3…30 % and an increase in the heat transfer coefficient to 25 % in a piston machine's intake system. On the practical side, the installation of a cylinder head with profiled channels should improve the technical, economic and environmental characteristics of piston machines.

Water flow in two Cactaceae species: standardization of the method and test under different drought conditions

AbstractInvestigating water flow in the vascular system of plants is important to identify the water path and conduction capacity of different plant species, mainly in succulent species living in dry regions. This study aimed to standardize a method to track water flow in the xylem of Mammillaria bocasana and Echinocereus reichenbachii var. fitchii (Cactaceae) and test it under different drought conditions. The plants were kept under greenhouse conditions to perform the split root method, water flow tracing, and different drought treatments. The plants of each species were separated into three treatments: constant irrigation, drought with water and dye, and drought with dye. Plants were cut 24 h after staining, total and lumen diameters were taken, and the relative theoretical hydraulic conductivity was calculated. The absorption method was adequate for the tracing of water flow, and it worked in all the treatments of the drought experiment. Conducting elements, including wide-band tracheids, were stained violet and were located near the vascular cambium. In Mammillaria bocasana, half of the vascular cylinder was stained, while in Echinocereus reichenbachii var. fitchii, the entire cylinder was stained due to the cortical bundles. M. bocasana had a higher lumen diameter and relative theoretical hydraulic conductivity than E. reichenbachii var. fitchii. With the absorption staining method, the flow of water was traced, and differences in conduction under water stress conditions between the two species of cacti were detected. These results suggest that cacti species living under water stress solve the water movement in different ways.

Vortex shedding from a square cylinder interacting with an undular bore wave train

In this work, we studied the wave-induced vortex generation and shedding from a semi-submerged vertical square cylinder interacting with an upcoming undular bore wave train under a shallow water configuration. This unsteady and rapid process was investigated by means of numerical and experimental approaches. A numerical simulation, solving the full turbulent viscous Navier–Stokes equations, was carried out in order to study and characterize both the undular bore wave properties and the vortex dynamics triggered during this unsteady interaction. Starting with fluid at rest, the undular bore was generated by the impulsive translational motion of a piston wavemaker at laboratory scale in both a numerical and an experimental wave tank. When the undular bore impinges on the cylinder, filamentary vortex structures were formed at the four cylinder's edges synchronized with the propagating wave motion, leading to the vortex shedding phenomena at a frequency that matched the wave instantaneous frequency. These vortices extended along the entire cylinder span under the water column, from the free surface to the seabed. At the trailing edge of the cylinder, a pairing process of two shed vortices was observed, similar to a Lamb–Oseen vortex pair. These vortices were present during the whole undular bore wave train dynamic forcing. An overall agreement was found with the experimental version of the bore–cylinder interaction, carried out in a physical wave tank. Laser sheet bore profiling and particle image velocimetry measurements of the velocity field confirmed undular bore properties, the onset of vortex formation, subsequent shedding, and pairing in the experiments performed in similar conditions with the numerical approach.

Cooling enhancement for engine parts using jet impingement

A computational study has been performed to evaluate the use of jet impingement for cooling applications in the automotive industry. The current study uses an entire internal combustion engine cylinder with its components as a computational domain. An unsteady numerical solution for the Navier-Stokes equations was carried out using Improved Delayed Detached Eddy Simulation (IDDES). The volume of fluid approach is proposed to track and locate the liquid jet surface that is in contact with the air. The conjugate heat transfer approach is used to link the heat transfer solution between the fluid and the solid. The boundary conditions that are employed in the study are provided from lab experiments and one-dimensional simulations. The cooling jet in this study targets the hottest region in the piston, i.e., the region underneath the exhaust valve. Three nozzle sizes with flows at different Reynolds numbers are chosen to examine the thermal characteristics of the cooling jet. The computational study reveals that for a specific Reynolds number, the smaller diameter nozzle provides the highest heat transfer coefficient around the impingement point. The maximum relative velocity location at the impingement point slightly leads the location of the maximum Nusselt number. The maximum temperature in the piston decreases by 7% to 11% as the nozzle diameter changes from 1.0 to 3.0 mm for a jet Reynolds number of 4,500. If a correct selection is made for the nozzle size, the cooling jet can be efficiently used to reduce the temperature and alleviate the thermal stresses in the piston in the region underneath the exhaust valve where the maximum temperature occurs.

Wake of wavy elliptic cylinder at a low Reynolds number: wavelength effect

Effects of the spanwise wavelength (λ) of a sinusoidal wavy cylinder with elliptic cross-section on wake structures and fluid forces are numerically investigated at a Reynolds number Re = 100. A wide range of the wavelength, $0.43 \le \lambda /{D_m} \le 8.59$ , is considered with a wave amplitude of a/Dm = 0.048, where Dm is the hydraulic diameter of the wavy cylinder. Based on vortical structures, Strouhal number (St) and wake closure length (Lc), fluid forces, streamline topologies and spatio-temporal evolutions of the near wake, five distinct flow patterns (I–V) are identified depending on λ/Dm. The drag force reaches its minimum in pattern III, the fluctuating lift force is zero in flow patterns III and IV. Distinct from the classical flow where alternate vortex shedding occurs synchronously over the entire cylinder span, flow pattern IV has alternate vortex shedding over a one half-wavelength of the wavy elliptic cylinder, antiphased with that over the other half-wavelength, thus leading to zero fluctuating lift over one complete wavelength. A thorough comparison of the wakes is made between the wavy elliptic cylinder and wavy circular or square cylinder, distinguishing the underlying flow physics behind the salient behaviours observed.

Gas Leakage Detection and Booking Using IoT

There is a rapid development in technology which influencing the human life in several aspects due to rapid development in different fields but we still need to adopt that technology such that we can make human life easier to live. In our Country it is not possible to supply LPG through Pipes to each and every home as production of LPG is too short. At present we are having a system Advance LPG cylinder booking through IVRS or online which is most difficult for the illiterate and busy schedule people to book the LPG cylinder in advance. Another Major problem LPG cylinder users facing is “They don’t know exactly the status of LPG gas completion” makes even more delay in booking the cylinder which is uncomfortable most of the times. Now a day we are having a IVRS system in which customer needs to go through few steps in accordance with the Automatic voice which also includes selecting options. Most of the illiterate people can’t even complete the booking due to this reason and also most of the times these landline phones are either busy due to congested calls or phones not working due to some technical issues. This paper proposes a system that will make entire LPG cylinder booking procedure automated without human intervention. This system continuously measures the weight of the cylinder and once it reaches minimum threshold it will automatically sends message to the authorized LPG Agent so that they can deliver the LPG cylinder in time. Along with the Automated cylinder booking we also designed feature related to the safety of the user in which it continuously monitor the leakage of LPG gas and alerts the user regarding leakage to avoid major accidents which costs human lives mostly.

Cylinder Pressure Feedback Control for Ideal Thermodynamic Cycle Tracking: Towards Self-learning Engines

To meet increasingly strict future greenhouse gas and pollutant emission targets, development time and costs of heavy-duty internal combustion engines will reach unacceptable levels. This is mainly due to increased system complexity and need to guarantee robust performance under a wide range of real-world conditions. Cylinder Pressure Based Control is a major contributor to achieve these goals in advanced, highly-efficient engine concepts. Current Cylinder Pressure Based Control approaches use combustion and air-path parameters as feedback signals. These signals are not directly linked to engine efficiency; therefore, compensation for changing ambient conditions, engine ageing or differences in fuel qualities is a non-trivial problem. Contrary to other methods, the method presented in this paper aims to realise an idealised thermodynamic cycle by directly control of the entire cylinder pressure curve. From measured in-cylinder pressure, a new set of feedback signals is derived using principle component decomposition. With these signals, optimal fuel path settings are determined. The potential of this method is demonstrated for a dual fuel Reactivity Controlled Compression Ignition (RCCI) engine, which combines very high efficiency and ultra low nitrogen oxides and particle matter emission. For the studied RCCI engine, it is shown that the newly proposed optimisation method gave the same optimal fuel path settings as existing methods. This is an important step towards self-learning engines.

End boundary effects on wakes dynamics of inclined circular cylinders

We perform direct numerical simulations to characterize the three-dimensional wake dynamics of long inclined circular cylinders with inhomogeneous end boundary conditions. Three Reynolds numbers, Re=100, 200 and 300, corresponding to the regimes of laminar flow, mode A* wake, and mode B wake, respectively, are considered to reveal the roles of the intrinsic secondary instabilities and the extrinsic end boundary effects in shaping the three-dimensional flows. At Re=100, the end boundary effects are felt over the entire cylinder span by inducing oblique vortex shedding, which is associated with stronger spanwise flow in the wake than a parallel shedding. The Strouhal number of the oblique shedding is related to that of the parallel shedding of straight cylinder by the cosine law, considering the combined inclination angle and oblique angle. At Re=200, the intrinsic secondary instability results in large-scale vortex dislocation, precluding the propagation of the end boundary effects towards further span. Nevertheless, for the inclined cases, oblique shedding is still observed within limited span from the upstream end boundary. The oblique vortices feature intact and straight vortex cores, and are related to the two-dimensional flow at Re=200 (that are void of vortex dislocations) from the viewpoint of cosine law. Further along the span, the oblique vortices destabilizes with the formation of small-scale vortices, and the flow transitions to the typical mode A* wake. At Re=300, the highly three-dimensional flow near the end boundary creates disturbances that travel along the cylinder span, creating vortex dislocations for cases with low inclination angles. For high inclination angle, oblique vortex shedding is again observed over the cylinder span, and is not disrupted by vortex dislocations of either intrinsic or extrinsic causes. The present study offers renewed insights into the three-dimensional wake dynamics of inclined cylinders, and lays the foundation for the designs of long flexible engineering structures and related flow control techniques.

Comparative vegetative anatomy of three Elaeocarpus species from the Western Ghats, Southern India.

The vegetative anatomy of Elaeocarpus angustifolius Blume, Elaeocarpus tuberculatus Roxb., and Elaeocarpus variabilis Zmarzty were investigated to illustrate anatomical variations. Plant materials were free-hand sectioned using a razor blade and stained with different staining solutions. The maceration technique was used to assess stomatal characteristics. Elaeocarpus leaves have abaxial epidermis with paracytic stomata and curved anticlinal walls in E. angustifolius, straight walls in other two species. Trichomes were absent in E. angustifolius.havMesophyll dorsiventral, midvein cortex contains starch grains, and vascular tissues enclosed by thick-walled sclerenchymatous cells. The petioles of all the three species possess unicellular epidermal hairs, collenchymatous hypodermis, and cortex containing druses and crystals, and vascular tissue enclosed by sclerenchymatous fibers. Water-storage cells are absent in petioles of E. angustifolius. Anatomical features of Elaeocarpus stem include epidermal hairs, epidermis covered by thin cuticle, the collenchymatous hypodermis and vascular integrity with entire cylinder enclosed by sclerenchymatous fibers. Pith contains water-storage cells. Starch grains absent in the pith cells of E. tuberculatus. The roots of Elaeocarpus possess unicellular root hairs, cortex 12-14 layered in E. tuberculatus and E. variabilis and 10-12 layerd E. angustifolius, Endodermis O-thickened and pericycle single-layered in all the examined Elaeocarpus species. Vascular bundles are arranged radially. Lignin deposition occurred in stellar region of roots. Water-storage cells present in the stelar regions of E. variabilis. The study revealed significant anatomical differences between the three Elaeocarpus species and most of these anatomical features may be used as markers for the identification of these species. RESEARCH HIGHLIGHTS: Comparative anatomy of three south Indian Elaeocarpus was studied. Leaf mesophyll layers varied in all the Elaeocarpus species. Crystals was present in petiole of all examined Elaeocarpus species. Starch grains was absent in stems of E. tubercuatus, but present in E. variabilis. Water-storage cells observed in stellar region of E. variabilis.

Bubble Cutting by Cylinder – Elimination of Wettability Effects by a Separating Liquid Film

AbstractExperiments and simulations are presented for the interaction of single bubbles rising in a viscous liquid against a horizontal cylinder (Ø = 4 mm) of varying wettability. The slide‐off of small and the cutting of larger bubbles into two daughter bubbles observed in the experiment are reproduced by phase‐field simulations. It is shown that in the entire process bubble and cylinder are separated by a liquid film, which eliminates any influence of cylinder wettability. Before the mother bubble splits, a thinning gas thread develops below the cylinder. The rupture of this gas thread can lead to a different number of satellite bubbles depending on the conditions.

Determining the global manifold structure of a continuous-time heterodimensional cycle

<p style='text-indent:20px;'>A heterodimensional cycle consists of two saddle periodic orbits with unstable manifolds of different dimensions and a pair of connecting orbits between them. Recent theoretical work on chaotic dynamics beyond the uniformly hyperbolic setting has shown that heterodimensional cycles may occur robustly in diffeomorphisms of dimension at least three. We consider the first explicit example of a heterodimensional cycle in the continuous-time setting, which has been identified by Zhang, Krauskopf and Kirk [<i>Discr. Contin. Dynam. Syst. A</i> <b>32</b>(8) 2825-2851 (2012)] in a four-dimensional vector-field model of intracellular calcium dynamics.</p><p style='text-indent:20px;'>We show here how a boundary-value problem set-up can be employed to determine the organization of the dynamics in a neighborhood in phase space of this heterodimensional cycle, which consists of a single connecting orbit of codimension one and an entire cylinder of structurally stable connecting orbits between two saddle periodic orbits. More specifically, we compute the relevant stable and unstable manifolds, which we visualize in different projections of phase space and as intersection sets with a suitable three-dimensional Poincaré section. In this way, we show that, locally near the intersection set of the heterodimensional cycle, the manifolds interact as described by the theory for three-dimensional diffeomorphisms. On the other hand, their global structure is more intricate, which is due to the fact that it is not possible to find a Poincaré section that is transverse to the flow everywhere. More generally, our results show that advanced numerical continuation techniques enable one to investigate how abstract concepts â€" such as that of a heterodimensional cycle of a diffeomorphism â€" arise and manifest themselves in explicit continuous-time systems from applications.</p>

Coating flow on a rotating cylinder in the presence of an irrotational airflow with circulation

A detailed analysis of steady coating flow of a thin film of a viscous fluid on the outside of a uniformly rotating horizontal circular cylinder in the absence of surface-tension effects but in the presence of a non-uniform pressure distribution due to an irrotational airflow with circulation shows that the presence of the airflow can result in qualitatively different behaviour of the fluid film from that in classical coating flow. Full-film solutions corresponding to a continuous film of fluid covering the entire cylinder are possible only when the flux and mass of fluid do not exceed critical values, which are determined in terms of the non-dimensional parameters $F$ and $K$ representing the speed of the far-field airflow and the circulation of the airflow, respectively. The qualitative changes in the behaviour of the film thickness as $F$ and $K$ are varied are described. In particular, the film thickness can have as many as four stationary points and, in general, has neither top-to-bottom nor right-to-left symmetry. In addition, when the circulation of the airflow is in the same direction as the rotation of the cylinder the maximum mass of fluid that can be supported on the cylinder is always less than that in classical coating flow, whereas when the circulation is in the opposite direction the maximum mass of fluid can be greater than that in classical coating flow.

From tip to toe – dressing centrioles in γTuRC

Centrioles are microtubule-based cylindrical structures that assemble the centrosome and template the formation of cilia. The proximal part of centrioles is associated with the pericentriolar material, a protein scaffold from which microtubules are nucleated. This activity is mediated by the γ-tubulin ring complex (γTuRC) whose central role in centrosomal microtubule organization has been recognized for decades. However, accumulating evidence suggests that γTuRC activity at this organelle is neither restricted to the pericentriolar material nor limited to microtubule nucleation. Instead, γTuRC is found along the entire centriole cylinder, at subdistal appendages, and inside the centriole lumen, where its canonical function as a microtubule nucleator might be supplemented or replaced by a function in microtubule anchoring and centriole stabilization, respectively. In this Opinion, we discuss recent insights into the expanded repertoire of γTuRC activities at centrioles and how distinct subpopulations of γTuRC might act in concert to ensure centrosome and cilia biogenesis and function, ultimately supporting cell proliferation, differentiation and homeostasis. We propose that the classical view of centrosomal γTuRC as a pericentriolar material-associated microtubule nucleator needs to be revised.

Enhanced Stability of Stable Isotopic Gases.

Pure gases and mixtures containing stable isotopes are used in a wide variety of applications including health care, food authentication, geochemistry, and environmental monitoring. It is therefore important to understand the role of moisture, which is one of the most critical impurities in compressed gas mixtures and pure gases, in their stability. Gaseous carbon dioxide (CO2) was used as a proxy for the evaluation of the effects of its isotopic composition, when in contact with moisture throughout the depletion of a cylinder’s contents, as well as pressure regulation and long-term stability. To accentuate the detrimental effects of moisture on CO2 isotopic stability, enriched 18O-water was added to natural-abundance, gaseous carbon dioxide. The δ18O–CO2 changed from −23.16‰ vs Vienna Pee Dee Belemnite (VPDB) to +109‰ vs VPDB. It was further demonstrated that with appropriate cylinder preparation to reduce residual moisture, source material purity with low moisture content, and pressure regulation (from 57.0 down to 0.5 bar), both δ13C and δ18O remained consistent within ±0.04 and ±0.06‰, respectively, throughout the entire cylinder contents. Pressure reduction using a dual-stage regulator yielded statistically consistent results at the 99% confidence level from delivered pressures of 0.1–0.8 bar. Furthermore, the isotopic values remained consistent during a 1 year shelf-life study, illustrating the ability to utilize and regulate pressurized gases as working reference standard gases.

Broadband cloaking of multiple truncated cylinders in water waves using the arrangement defects

Cloaking based on scattering cancellation is investigated for a surface-piercing truncated cylinder surrounded by several annularly arranged small truncated cylinders in water waves. The cloaking condition of a body in water waves corresponds to the absence of scattered waves radiating to infinity; that is, the cloaked structure appears invisible to a far-field observer. The effects of three kinds of defects of the outer cylinders on cloaking are considered: a radial location defect, a circumferential location defect, and a size defect. The higher-order boundary element method is combined with the wave interaction theory to accurately study this wave–structure interaction problem. Both the scattered wave energy of the entire structure and the wave drift force on the inner cylinder are calculated and analyzed for the different defects. The symmetry of the defect effects and the cloaking-wavenumber offset caused by a radial position defect of the entire outer cylinder array are first identified. The radial location defect is successfully adopted to control the cloaking frequencies over a wide band.

Modelling and analysis of slip conditions in hydrodynamic lubrication of a piston skirt-cylinder contact

Purpose After more than a century of agreement with the postulate of non-slip condition (adhesion to the wall), the study of fluid-solid boundary conditions has shown renewed interest over the past two decades. Although numerous studies have not yet been arrived to a complete description of slip phenomena, however, it appears that the influence of wetting and/or surface roughness results in a weak interaction between fluid and solid; thus, the presence of the slip phenomenon is observed at the fluid-solid interface. The purpose of this paper is to highlight the presence of the slip phenomenon at the lubricated piston skirt-cylinder contact. Design/methodology/approach For this proposal, a modified Reynolds equation and operating characteristics are determined by taking into account the slip conditions at the interface between oil-film and entire cylinder surface. Findings The findings indicate that the operating characteristics are strongly influenced when the slip conditions are taken into account at the interface between oil-film and cylinder surface. The friction force and dissipated power might be reduced to improve diesel engine performances. Originality/value Various research studies have been conducted to model the slip phenomenon in different lubricated contacts over the past two decades. However, there are no studies available concerning the piston-cylinder system. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-11-2019-0483/

DESIGN AND FABRICATION OF MULTI ENGINE AIR COMPRESSOR

A compressor is used to get high pressure air for many industrial and commercial purpose. The triangular air compressor with the common compression chamber is a reciprocating type compressor, which delivers air at high pressure with less vibration and less power consumption than the existing ones. Triangular air compressor with common compression chamber uses three cylinders and the entire cylinder and all the cylinders will have their own connecting red, crank shaft, pistons and chain sprockets and it is driven by a chain drive. During operation the pistons will move in phase from BDC to TDC and hence the air is compressed in the common compression head. This common in the compression chamber will have one inlet and outlet valve. From this valve, air is intake and delivered. The common compression head will be is a triangular shape with angle of 60* from one side to another. The compressor is mechanical equipment which is used to increase the pressure with the help of the piston. Need to improve the performance of compressor by several methods. The main aim of the project is to make tri-cylinder, air compressor to generate large amounts of air with less power and low vibration. In Tri cylinder, air compressor the three cylinders are kept at 120 degrees to each other. The three cylinders are placed radically and equally apart such that the cylinder opening tends to meet on a common triangular compression chamber. The three pistons are made to compress air simultaneously onto the common triangular chamber over shorter stroke and the isothermal efficiency will be better than single cylinder with one piston. The motor is connected to the chain drive to drive the three crankshafts which are used to move the piston. If space is smaller the pressure will be more and bigger lower. If compressor is made to work at 1400 rpm air taken will be147.18 × 1400 = 206052 litters at 7 atmospheres pressure .The advantage with triangular compressor will be low vibration, smaller unit giving more output and so cheaper to make, ideal for air compressor is Airconditioning and Refrigeration, Vacuum pumps and general purpose usage.

Applying PIV to study a fluid flow in the vicinity of a circular streamlined cylinder

The round cylinder streamlining by a turbulent water flow in a hydrodynamic pipe is investigated experimentally. Using the optical method of PIV (Particle Image Velocimetry) the averaged velocity fields near the cylinder are obtained and, on their basis, the geometric characteristics of the vortex zone of the near wake are calculated for the non-cavitation and cavitation flow regimes in the critical region of Reynolds numbers. The use of two mirrors, set at a certain angle to each other, allows obtaining a picture of the velocity fields around the entire cylinder, rather than around half of it, as it is done in most of the works. Using vector patterns of averaged velocity fields, the angles of the boundary layer separation from the cylinder surface along the reverse flow are determined in the considered flow regimes. An asymmetrical separation of the boundary layer from different sides of the streamlined cylinder was obtained. It is shown that the increase in the Reynolds number for the non-cavitation flow regimes leads to a more than two times decrease in the vortex zone behind the cylinder, and, accordingly, to a displacement of the separation angles downstream. Cavitation increases the vortex zone behind the cylinder and displaces the separation angles upstream.

Low-frequency dynamics of the flow around a finite-length square cylinder

Fluctuating pressure on the side faces, lee-ward face and free end of a finite-length square cylinder is measured simultaneously, together with the velocity in its free-end shear flow, to reveal their inherent connection. The width (d) of the tested model is 40 mm, and the aspect ratio is 5. All experiments are conducted in a low-speed wind tunnel at an oncoming flow velocity (U∞) of 10 m/s. The corresponding Reynolds number based on U∞ and d is 27,000. It is found that, the fluctuating pressure on the side faces and free end has remarkable low-frequency instability with the frequency of about 1/10 of the well-known spanwise Karman vortex shedding. Besides, a high-frequency component, corresponding to Karman vortex shedding, is also found in the fluctuating pressure on cylinder side faces. The low-frequency instability is in phase over the entire cylinder span, while the high-frequency component tends to be out of phase, especially at the lower part of the cylinder. The free-end shear flow flaps at the low frequency and strongly correlates with the modes of spanwise vortex shedding. Particularly, when the free-end shear flow flaps to its lower position, alternate spanwise vortex shedding with high pressure fluctuation occurs; when it flaps to its upper position, the occurrence probability of co-shedding with low pressure fluctuation increases significantly especially near the cylinder free end.

Ways for detection of the exact number of limit cycles of autonomous systems on the cylinder

For real autonomous systems of differential equations with continuously differentiable right-hand sides, the problem of detecting the exact number and localization of the second-kind limit cycles on the cylinder is considered. To solve this problem in the absence of equilibria of the system on the cylinder, we have developed our previously proposed ways consisting in a sequential two-step application of the Dulac – Cherkas test or the Dulac test. Additionally, a new way has been worked out using the generalization of the Dulac – Cherkas or Dulac test at the second step, where the requirement of constant sign for divergence is replaced by the transversality condition of the curves on which the divergence vanishes. With the help of the developed ways, closed transversal curves are found that divide the cylinder into subdomains surrounding it, in each of which the system has exactly one second-kind limit cycle.The practical efficiency of the mentioned ways is demonstrated by the example of a pendulum-type system, for which, in the absence of equilibria, the existence of exactly three second-kind limit cycles on the entire phase cylinder is proved.