Gas Torque Research Articles

Pebble-driven migration of low-mass planets in the 2D regime of pebble accretion

Pebbles drifting past a disk-embedded low-mass planet develop asymmetries in their distribution and exert a substantial gravitational torque on the planet, thus modifying its migration rate. Our aim is to assess how the distribution of pebbles and the resulting torque change in the presence of pebble accretion, focusing on its 2D regime. First, we performed 2D high-resolution multi-fluid simulations with Fargo3D but found that they are impractical for resolving pebble accretion due to the smoothing of the planetary gravitational potential. To remove the smoothing and directly trace pebbles accreted by the planet, we developed a new code Deneb which evolves an ensemble of pebbles, represented by Lagrangian superparticles, in a steady-state gaseous background. For small and moderate Stokes numbers, $ St pebble accretion creates two underdense regions with a front-rear asymmetry with respect to the planet. The underdensity trailing the planet is more extended. The resulting excess of pebble mass in front of the planet then makes the pebble torque positive and capable of outperforming the negative gas torque. Pebble accretion thus enables outward migration (previously thought to occur mainly for $ St in a larger portion of the parameter space. It occurs for the planet mass pl oplus $ and for all the Stokes numbers considered in our study, $ St $, assuming a pebble-to-gas mass ratio of $Z=0.01$. If some of the observed planets underwent outward pebble-driven migration during their accretion, the formation sites of their progenitor embryos could have differed greatly from the usual predictions of planet formation models. To enable an update of the respective models, we provide a scaling law for the pebble torque that can be readily incorporated in N-body simulations.

On the evolution of pebble-accreting planets in evolving protoplanetary discs

ABSTRACTWe examine the migration of luminous low-mass cores in laminar protoplanetary discs where accretion occurs mainly because of disc winds and where the planet luminosity is generated by pebble accretion. Using 2D hydrodynamical simulations, we determine the eccentricities induced by thermal forces as a function of gas and pebble accretion rates, and also evaluate the importance of the torque exerted by the solid component relative to the gas torque. For a gas accretion rate $\dot{M}= 2\times 10^{-8}\, \mathrm{ M}_\odot$ yr−1 and pebble flux $\dot{M}_{\mathrm{ peb}}=170\, \mathrm{ M}_\oplus$ Myr−1, we find that embryo eccentricities attain values comparable to the disc aspect ratio. The planet radial excursion in the disc, however, causes the torque exerted by inflowing pebbles to cancel on average and migration to transition from outward to inward. This is found to arise because the magnitude of thermal torques decreases exponentially with increasing eccentricity, and we provide a fitting formula for the thermal torque attenuation as a function of eccentricity. As the disc evolves, the accretion luminosity becomes at some point too small to make the core eccentricity grow such that the solid component can exert a non-zero torque on the planet. This torque is positive and for gas accretion rates $\dot{M} \lesssim 5\times 10^{-9}$M⊙ yr−1 and pebble fluxes $\dot{M}_{\rm {peb}} \lesssim 120\, \mathrm{ M}_\oplus $ Myr−1, it is found to overcome the gas torque exerted on cores with mass $m_\mathrm{ p}\lesssim \, 1\,\mathrm{ {M}}_\oplus$, resulting in outward migration.

Analysis of circumferential gas force on star-wheel in a single screw expander

Service life of a star-wheel directly affects operation stability of a single screw expander. In addition, since star-wheel tooth of a single screw expander is prone to wear, circumferential force of the star-wheel rotor is investigated in this paper. Geometric gap models between the meshing pair with a single line envelope profile at different rotation angles are established and meshed section pressure fields and velocity fields of a referent tooth flank are simulated. Circumferential gas torque calculation model of a referent tooth and multi-tooth are established, and torque influencing factors are analyzed. Results indicate that the pressure difference between the expansion cavity and low-pressure cavity as well as gap geometry shape have a significant influence on the pressure field and velocity field. Both gas forces that act on the meshed section and the unmeshed section of the tooth have significant effects on the circumferential torque. Due to multi-tooth coupling, total gas torque periodically changes with the star-wheel rotation angle. Moreover, the negative values indicate that the gas torque on the left side of the star-wheel is greater than that on the right side. Unbalanced gas torque can cause star-wheel teeth deviation towards the side with less force. This consequently results in wear increase.

A design approach for controlled blade-off in overspeeding turbines

Following a shaft failure or loss of load in a gas turbine engine, the turbine overspeeds due to the continuing expansion through the stage(s). The overspeed may result in hazardous conditions which have to be prevented. Several mitigation methods include the control system’s response by shutting the fuel flow, mechanical friction to reduce turbine acceleration, and blade release at a predetermined rotational speed. The release of the blades not only terminates the gas torque which accelerates the disk, but also increases the disk burst speed at reduced centrifugal load. In this manuscript, a design space exploration is presented to avoid disk burst by blade-off in a civil large turbofan engine through a parametric design of blade firtree and disk post system. The firtree design parameters used in the study are the contact angle between the blade firtree and the disk post, firtree bottom flank angle, firtree flank length and firtree thickness with respect to the disk post. The LS-DYNA finite element software was used in the simulations to generate possible failure scenarios. These were ‘disk burst’ and ‘blade-off’. Blade-off conditions manifested in two ways as a function of design parameters. The first type was blade release from serrations without disk post failure, and the second type was blade escape with disk post failure. Following the design space exploration, the effect of several design and material parameters on the design space was investigated. These parameters are; the contact friction coefficient between the blade firtree and disk post, firtree serration number, and the strain hardening behavior of the material.

Effects of misfire on the dynamic behavior of gasoline Engine Crankshafts

Misfire faults caused by the malfunction of single cylinder increases the emission level and fuel consumption of internal combustion. So, the detection of misfire is required.In this paper, we studied the effect of misfire on the dynamic response of the crankshaft in order to propose a method based on the torsional vibration signal of crankshaft acceleration for misfire detection. For this, a torsional model of a four cylinder crankshaft excited by the acyclism phenomena is proposed. The external forces are the inertia and gas torque of each engine cylinder. The equations of motion are obtained by using Lagrange method and computed with the help of Newmark algorithm. Three kind of misfire faults of the first cylinder are modeled through the gas pressure variation inside this cylinder and induced in the excitation torques: missing combustion, pre-ignition and delayed ignition. After that, the vibration responses of the crankshaft is computed and processed in order to highlight the effect of misfire defects on the crankshaft vibration signals. In fact, appearance of sidebands around the acyclism frequency in the frequency domain allow detecting the misfire and the time acceleration signal allows identifying the kind of defect.

Multidisciplinary methodology for turbine overspeed analysis

ABSTRACTIn this paper, an integrated approach to turbine overspeed analysis is presented, taking into account the secondary air system dynamics and mechanical friction in a turbine assembly following an unlocated high-pressure shaft failure. The axial load acting on the rotating turbine assembly is a governing parameter in terms of overspeed protection since it governs the level of mechanical friction which acts against the turbine acceleration due to gas torque. The axial load is dependent on both the force coming from secondary air system cavities surrounding the disc and the force on the rotor blades. It is highly affected by secondary air system dynamics because rotor movement modifies the geometry of seals and flow paths within the network. As a result, the primary parameters of interest in this study are the axial load on the turbine rotor, the friction torque between rotating and static structures and the axial position of the rotor.Following an initial review of potential damage scenarios, several cases are run to establish the effect of each damage scenario and variable parameter within the model, with comparisons being made to a baseline case in which no interactions are modelled. This allows important aspects of the secondary air system to be identified in terms of overspeed prevention, as well as guidelines on design changes in current and future networks that will be beneficial for overspeed prevention.

Accuracy analysis of narrow groove theory for spiral grooved gas seals: A comparative study with numerical solution of Reynolds equation

This study examined the accuracy of narrow groove theory for spiral grooved gas seals. Designed for compressible fluids, a finite difference method was proposed to solve the two-dimensional compressible Reynolds equation. The predictions of narrow groove theory were compared with those of the Reynolds equation. The typical performance parameters including gas film force, leakage, gas film stiffness, and torque were analyzed. The results show that the predictions of narrow groove theory generally agree with those of finite difference method when the number of grooves is more than eight. The gas film force, leakage, and gas film stiffness were slightly overestimated by narrow groove theory, with better accuracy for gas film force, leakage, and torque than for gas film stiffness. Although some cases showed deviation for gas film stiffness of as much as 52%, most deviations can be effectively ignored. Therefore, it is feasible to use narrow groove theory for qualitative analysis such as groove shape optimization. The present analysis provides the optimum groove parameters for the investigated seal.

Electric motor-based crankshaft stop position control to suppress range extender start vibration in electric vehicle

Range-extended electric vehicles have the most complex noise and vibration problems since certain control strategies often make range extenders (REs) shut down or restart for the sake of better fuel consumption. This paper deals with this uncomfortable riding experience, especially during the range extender start phase. A control-oriented nonlinear model for the start–stop vibration analysis, including range extender mount system, engine–clutch–motor shaft system, engine inertia torque and force, engine friction torque, engine gas torque, engine manifold pressure, electric motor torque, and range extender controller, is thus built. In the developed model, a new estimation method for gas torque is proposed, where the initial crank angle is considered and the relevant equations are simplified. The method has proven to predict gas torque accurately without using a complex calculation process. According to the developed model, the active control method, crankshaft stop position control (CSPC) has been proposed. The crankshaft stop position is analyzed as well as the crankshaft movement with different speeds at top dead center is discussed, which lead to the design of the target curves for crankshaft movement during the stop phase. Based on the set-up model, CSPC is finally applied through the cascade control of the motor to evaluate the control effectiveness. The simulation outcomes demonstrate that CSPC can help the crankshaft to finally stop at the optimal initial crank angle, which effectively lessens the vibration in the next start phase.

Gas torque compensation control for range extender start-stop vibration reduction in electric vehicle

One of the key challenges with the development of range extended electric vehicles is the noise, vibration and harshness behavior, specifically the uncomfortable ride experience during the range extender starting and stopping. This article focuses on providing an active control method to address this critical noise, vibration and harshness issue. A control-oriented nonlinear model for the start-stop vibration analysis, including range extender mount system, engine-clutch-motor shaft system, engine inertia torque and force, engine friction torque, engine gas torque, engine manifold pressure, electric motor torque and range extender controller, is thus built. In the developed model, a new estimation method for gas torque is proposed, where the initial crank angle is considered as well as the relevant equations are simplified. The method is proved to predict gas torque accurately without the expense of complex calculation process. Based on the model, the mount system vibration response has been analyzed that the excitation of range extender block on vehicle body in x-direction is the most prominent. The concept of the active control method, gas torque compensation control, is thus introduced in detail to reduce such a system vibration during start-stop phase. According to the control principle, the torque compensation coefficient for gas torque compensation control is determined and the compensation speed range is analyzed. In order to evaluate the control effectiveness, gas torque compensation control is implemented in the set-up model. The simulation outcomes demonstrate that gas torque compensation control is effective in reducing the vibration generated during start-stop transitions.

MIGRATION TRAPS IN DISKS AROUND SUPERMASSIVE BLACK HOLES

ABSTRACT Accretion disks around supermassive black holes (SMBHs) in active galactic nuclei (AGNs) contain stars, stellar mass black holes, and other stellar remnants, which perturb the disk gas gravitationally. The resulting density perturbations exert torques on the embedded masses causing them to migrate through the disk in a manner analogous to planets in protoplanetary disks. We determine the strength and direction of these torques using an empirical analytic description dependent on local disk gradients, applied to two different analytic, steady-state disk models of SMBH accretion disks. We find that there are radii in such disks where the gas torque changes sign, trapping migrating objects. Our analysis shows that major migration traps generally occur where the disk surface density gradient changes sign from positive to negative, around 20–300R g, where R g = 2GM/c 2 is the Schwarzschild radius. At these traps, massive objects in the AGN disk can accumulate, collide, scatter, and accrete. Intermediate mass black hole formation is likely in these disk locations, which may lead to preferential gap and cavity creation at these radii. Our model thus has significant implications for SMBH growth as well as gravitational wave source populations.

Gas dynamics analysis of a rotary compressor based on CFD

The different pulsation of pressure between the upper and lower space of the shell in a rotary compressor used for refrigerator and air conditioner room could be a cause of the axial movement of the rotor. In this paper, the gas dynamics analysis of a rotary compressor was carried out. In order to analyze the mechanisms of the fluctuation of the axial force in rotor system and the functions of the gas force and the gas torque on the rotor system, a three-dimensional dynamic numerical model was built up by the method of CFD (computational fluid dynamics) and dynamic grid technique. The simulated results were compared by theoretical cycle and calorimeter performance experiment. Good agreement was found between the simulated results and experimental results for the rotary compressor system.

Considerations Regarding Validation through Simulation of Some Board System Information’s for Powertrain Performance Optimization

The authors present in this paper the opportunities offered by the use of software platforms (MULTISIM) in the validation of informational systems for optimizing economical consumption. So after some research (based on identification methodology system type) a physical-mathematical model can be developed that offers the possibility to optimize fuel consumption in the economy pole depending on specific correlations of operating regimes. Resulted relationships allow designing of information systems by proposing solutions which acquire information on movement speed, engine RPM in load (by determining the actual torque through correlations of exhaust gas temperature, moment and torque).Having these relationships we can design, for example, system version with discrete components or with digital system for surveillance engine operation.

Mechanical Property of Internal Meshing Rotary Compressor

The internal-meshing rotary mechanism is widely used in the oil pumps and cyclonical pin wheels application. The working principle of the internal meshing rotary compressor is very different with the current institutions applications. while, the mechanical property method of the internal meshing rotary pump can’t be entirely and directly used in the rotary compressor because of the different working principles. In order to simplify the study of the internal-meshing rotary compressors, the forces acted on the inner and outer gears are computed. The gas force and torque related to the rotating angle are derived, and then compared with other rotary compressors. The result shows that the internal meshing rotary compressor’s mechanical parameters vary periodically and the period is 2π/Z2and this type of compressor has perfect mechanical property compared with other compressors.

Mathematical modeling and analysis of gas torque in twin-rotor piston engine

The gas torque in a twin-rotor piston engine (TRPE) was modeled using adiabatic approximation with instantaneous combustion. The first prototype of TRPE was manufactured. This prototype is intended for high power density engines and can produce 36 power strokes per shaft revolution. Compared with the conventional engines, the vector sum of combustion gas forces acting on each rotor piston in TRPE is a pure torque, and the combustion gas rotates the rotors while compresses the gas in the compression chamber at the same time. Mathematical modeling of gas force transmission was built. Expression for gas torque on each rotor was derived. Different variation patterns of the volume change of working chamber were introduced. The analytical and numerical results is presented to demonstrate the main characteristics of gas torque. The results show that the value of gas torque in TRPE falls to be less than zero before the combustion phase is finished; the time for one stroke is 30° in terms of the rotating angle of the output shaft; gas torque in one complete revolution of the output shaft has a period which is equal to 60° and it is necessary to put off the moment when gas torque becomes zero in order to export the maximum energy.

Analysis and Exploration for Automotive Engine Vibration Signal

In Modern society, most of car engines are multi cylinder four stroke engines, rotate speed is an important parameter of the engine, engine running status is a comprehensive expression of engine operation condition. It is also the result of the interaction by the gas torque, load torque and inertia moment. So the speed measurement is of great significance. Car engine speed measurement method has a lot of kinds, this article is based on the vibration method to measure, different methods used in vibration signal acquisition, analysis, processing and implementation. The vibration of the automobile engine output signals are continuous changes over time, we can say is a continuous signal. The vibration of the automobile engine output signals are continuous changes over time, we can say at this time is a continuous signal, when we use vibration sensor to gather the signals, a certain number of sampling points that are in different time, same time interval the vibration data resulting from the sampling theorem. At this time we deal with discrete time signals [1, 3]. Because of various vibration interference, The useful information we want to extract has been hidden in a lot of vibration under the disturbance signal, therefore, we carried out on the vibration signal analysis and processing, converting vibration wave in the frequency domain analysis, combining the new method of machinery vibration signal feature extraction, using short time Fourier transform, multiple correlation theory and Hilbert Huang transform combined with the application, making us in post-processing can extract the characteristic signal under the strong noise background [4]. The original signal frequency is obtained, based on related formulas to calculate car engine speed.

Fault Detection of Inline Reciprocating Diesel Engine: A Mass and Gas-Torque Approach

Early fault detection and diagnosis for medium-speed diesel engines are important to ensure reliable operation throughout the course of their service. This work presents an investigation of the diesel engine combustion-related fault detection capability of crankshaft torsional vibrations. Proposed methodology state the way of early fault detection in the operating six-cylinder diesel engine. The model of six cylinders DI Diesel engine is developed appropriately. As per the earlier work by the same author the torsional vibration amplitudes are used to superimpose the mass and gas torque. Further mass and gas torque analysis is used to detect fault in the operating engine. The DFT of the measured crankshaft’s speed, under steady-state operating conditions at constant load shows significant variation of the amplitude of the lowest major harmonic order. This is valid both for uniform operating and faulty conditions and the lowest harmonic orders may be used to correlate its amplitude to the gas pressure torque and mass torque for a given engine. The amplitudes of the lowest harmonic orders (0.5, 1, and 1.5) of the gas pressure torque and mass torque are used to map the fault. A method capable to detect faulty cylinder of operating Kirloskar diesel engine of SL90 Engine-SL8800TA type is developed, based on the phases of the lowest three harmonic orders.

Adaptive Cylinder Balancing of Internal Combustion Engines

For internal combustion engines with electronic fuel-injection systems, differences in fuel injector performance may result in significant discrepancies between the fuel amounts injected into the individual cylinders. In order to avoid excessive torsional vibrations of the crankshaft due to nonuniform cylinder-wise torque contributions, it is important to calibrate the fuel injectors. This can be done using angular speed measurements of the crankshaft to reconstruct the gas torque applied on the flywheel and relating it to the cylinder firings. For engines with a high number of cylinders, an accurate engine model is essential for successful cylinder balancing. This is due to closely spaced cylinder firings and the fact that the crankshaft dynamics cannot be ignored, partly due to the increased length of the crankshaft, and partly because analysis of higher frequency components is required to obtain sufficient information for balancing the cylinder-wise torque contributions. The need for accurate models forms a major obstacle to the implementation of cylinder balancing methods for such engines. In this paper an online adaptive cylinder balancing method is proposed which can be applied to engines with unknown crankshaft dynamics. The procedure identifies the engine-specific phase-angle diagrams which relate the amplitudes and phases of the relevant torque frequencies to the cylinder firings. The identified model is applied to balance the cylinder-wise torque contributions of the engine with the objective of minimizing torsional vibrations. The proposed method is evaluated using both simulations on twelve and eighteen cylinder V-engine generator sets and experiments on a full-scale 6 MW six cylinder common-rail diesel power plant engine. The results show that the adaptive cylinder balancing procedure achieves a more efficient reduction of torsional vibrations than methods based on a fixed engine model, in which a rigid crankshaft is assumed.

Analysis, Design, and Modeling of a Rotary Vane Engine (RVE)

This paper introduces a mathematical model to analyze the dynamic behavior of a novel rotary vane engine (RVE). The RVE can be considered to have a number of advantages when compared to a majority of other reciprocating engine types. The advantages are found in the simple structure and the small number of moving parts. In this paper the geometrical structure and dynamical behavior of engines with a different number of work units is considered in detail. This has been examined through a study of torque transmission with a particular reference to how this is affected by the noncircular geometry of gear pitch curves. Using the Coulomb friction model, consideration has been given to the mechanical power loss due to friction in different parts of the engine, which must be taken into account. The study also proposes a possible method for balancing of asymmetric cogwheels. The analysis concludes that by using an appropriate design and arrangement of cogwheels and all moving parts, vibration can be attenuated due to impulsive gas torque.

Rotor Tooth Profile of Screw Compressor.

The rotors of a screw compressor engage peculiarly with each other in comparison with helical gears. In order to obtain a compressor with high performance, it is necessary to clarify the peculiarity of the rotor tooth profile following the peculiar engagement. In this study, the peculiarity is investigated. The results of the investigation are as follows. (1) The trailing tooth profile of the rotor is fundamentally fixed. (2) The leading tooth profile of the rotor can be determined arbitrarily. (3) The volume of the rotor tooth space is fixed almost independently of the rotor tooth profile. (4) A blow hole occurs in the trailing tooth profile which is not a roulette. It is impossible to avoid a blow hole in the practical tooth profile. (5) If gas torque promotes the progressive rotation of the female rotor, the female rotor tooth thickness must be altered thin.

Engine Fault Analysis: Part II---Parameter Estimation Approach

The general fault analysis problem can be divided into two parts: fault detection and diagnosis (location). Fourier series, autocorrelation, and other techniques have been used for fault detection. However, these approaches cannot be utilized for locating the faults. In this paper a methodology is presented to locate faulty cylinder(s). The procedure involves the development of a mathematical model of the engine dynamics. This model takes into consideration the cylinder gas pressure, engine inertia, and load. The resultant torque is computed by using parameter estimation techniques. The parameter estimation technique employed can determine time-varying parameters without prior knowledge of the structure of the parameter. In the problem at hand, this is an important requirement. The resultant torque is the net of the cylinder gas torque and the frictional torque. The model and the estimation procedure have been verified by performing tests on a single-cylinder engine. A discriminant function has been defined to classify the performance of each cylinder. Our results indicate that the amplitude of the resultant torque can be used to identify the faulty cylinder(s). We have verified this approach by tests and studies on a six-cylinder engine. In our experiments we have studied cases involving one or two faulty cylinders.