Motion Of Jet Research Articles

Eulerian-Eulerian Modeling of the Features of Mean and Fluctuational Flow Structure and Dispersed Phase Motion in Axisymmetric Round Two-Phase Jets

The features of the local mean and fluctuational flow structure, carrier phase turbulence and the propagation of the dispersed phase in the bubbly and droplet-laden isothermal round polydispersed jets were numerically simulated. The dynamics of the polydispersed phase is predicted using the Eulerian–Eulerian two-fluid approach. Turbulence of the carrier phase is described using the second-moment closure while taking into account the presence of the dispersed phase. The numerical analysis was performed in a wide range of variation of dispersed phase diameter at the inlet and particle-to-fluid density ratio (from gas flow laden with water droplets to carrier fluid flow laden with gas bubbles). An increase in the concentration of air bubbles and their size leads to jet expansion (as compared to a single-phase jet up to 40%), which indicates an increase in the intensity of the process of turbulent mixing with the surrounding space. However, this makes the gas-droplet jet narrower (up to 15%) and with a longer range in comparison with a single-phase flow. The addition of finely dispersed liquid droplets to an air jet suppresses gas phase turbulence (up to 15%). In a bubbly jet, it is found that small bubbles (Stk < 0.1) accumulate near the jet axis in the initial cross-sections, while concentration of the large ones (Stk > 0.2) along the jet axis decreases rapidly. In the gas-droplet jet, the effect of dispersed phase accumulation is also observed in the initial cross-section, and then its concentration decreases gradually along the jet axis. For gas bubbles (Stk < 0.1), small turbulence attenuation (up to 6%) is shown.

Fiber trajectory tracking of centrifugal spinning and coupled-forces field effects on jet motion stability

High-speed centrifugal spinning holds excellent potential as a promising approach for nanofiber manufacturing due to its various raw materials, low environmental requirements, and high preparation efficiency. However, continuous jet movement and trajectory tracking on the action of gravity, centrifugal force, Coriolis force, viscous force, and air resistance remain significant challenges. Therefore, the present article has developed a polymer jet motion model based on the momentum equation, continuity equation, and constitutive equation of non-Newtonian fluid to explore the influence of spinning parameters on jet motion. Moreover, curved fiber trajectory in the centrifugal field, jet velocity distribution, and variation of air velocity around the nozzle have been simulated using the discrete phase model in terms of different angular velocities and solution concentrations. It is found that the angular velocity affects the formation of the jet trajectory. Furthermore, the solution concentration determines the attenuation of the jet velocity. Therefore, centrifugal spinning experiments have been carried out to verify the correctness of the results and theoretical analysis gained from the research. Scanning electron microscope observations show nanofibers with 6 wt% polyethylene oxide solution at 5500 rpm have better morphology and quality.

Hydrodynamics of the projectile entering the water under the ice hole constraint environment

The study of the water entry of the projectile passing through the ice hole can solve the special issue of water entry under marine environmental constraints. We conducted experiments to validate the effect of the ice hole constraint on the dynamics of the water entry cavity and then used the numerical simulations to investigate the cavity dynamics of the projectile passing through ice holes with different sizes and rotation degrees. The results show that the ice hole affects the evolution of the water entry cavity and the motion state of the projectile. The splash crown flows back and then contacts the projectile surface when passing through the small-sized ice hole. Cavity collapses before the pinch-off. The splash crown flows back at the hole as the hole size increases, the cavity morphology is complete, and the projectile's movement is more stable at the initial stage of water entry and after deep cavity pinch-off. Special oblique jets form when passing through irregular holes. The impact of the oblique jet on the cavity increases as the rotation degree increases. The type of hole has little effect on the water entry dynamics of the projectile, but has a significant effect on the cavity morphology and the jet motion near the hole. The size of the hole has a great effect on the motion stability of the projectile.

A Specification-Guided Framework for Temporal Logic Control of Nonlinear Systems

This article proposes a specification-guided framework for control of nonlinear systems with linear temporal logic (LTL) specifications. In contrast with well-known abstraction-based methods, the proposed framework directly characterizes the winning set, i.e., the set of initial conditions from which a given LTL formula can be realized, over the continuous state space of the system via a monotonic operator. Following this characterization, an algorithm is proposed to practically approximate the operator via an adaptive interval subdivision scheme, which yields a finite-memory control strategy. We show that the proposed algorithm is sound for full LTL specifications, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">robustly complete</i> for specifications recognizable by deterministic Büchi automaton (DBA), the latter in the sense that control strategies can be found whenever the given specification can be satisfied with additional bounded disturbances. Without having to compute and store the abstraction and the resulting product system with the DBA, the proposed method is more memory efficient, which is demonstrated by complexity analysis and performance tests. A preprocessing stage is also devised to reduce computational cost via a decomposition of the specification. We show that the proposed method can effectively solve real-world control problems, such as jet engine compressor control and motion planning for manipulators and mobile robots.

Time-dependent visibility modelling of a relativistic jet in the X-ray binary MAXI J1803−298

ABSTRACT Tracking the motions of transient jets launched by low-mass X-ray binaries (LMXBs) is critical for determining the moment of jet ejection, and identifying any corresponding signatures in the accretion flow. However, these jets are often highly variable and can travel across the resolution element of an image within a single observation, violating a fundamental assumption of aperture synthesis. We present a novel approach in which we directly fit a single time-dependent model to the full set of interferometer visibilities, where we explicitly parametrize the motion and flux density variability of the emission components, to minimize the number of free parameters in the fit, while leveraging information from the full observation. This technique allows us to detect and characterize faint, fast-moving sources, for which the standard time binning technique is inadequate. We validate our technique with synthetic observations, before applying it to three Very Long Baseline Array (VLBA) observations of the black hole candidate LMXB MAXI J1803−298 during its 2021 outburst. We measured the proper motion of a discrete jet component to be 1.37 ± 0.14 mas h−1, and thus we infer an ejection date of MJD $59348.08_{-0.06}^{+0.05}$, which occurs just after the peak of a radio flare observed by the Australia Telescope Compact Array (ATCA) and the Atacama Large Millimeter/Sub-Millimeter Array (ALMA), while MAXI J1803−298 was in the intermediate state. Further development of these new VLBI analysis techniques will lead to more precise measurements of jet ejection dates, which, combined with dense, simultaneous multiwavelength monitoring, will allow for clearer identification of jet ejection signatures in the accretion flow.

Transverse Oscillations of the M87 Jet Revealed by KaVA Observations

Recent VLBI monitoring has found transverse motions of the M87 jet. However, due to the limited cadence of previous observations, details of the transverse motion have not been fully revealed yet. We have regularly monitored the M87 jet at KVN and VERA Array (KaVA) 22 GHz from December 2013 to June 2016. The average time interval of the observation is ∼0.1 year, which is suitable for tracking short-term structural changes. From these observations, the M87 jet is well represented by double ridge lines in the region 2–12 mas from the core. We found that the ridge lines exhibit transverse oscillations in all observed regions with an average period of 0.94±0.12 years. When the sinusoidal fit is performed, we found that the amplitude of this oscillation is an order of ∼0.1 mas, and the oscillations in the northern and southern limbs are almost in phase. Considering the amplitude, it does not originate from Earth’s parallax. We propose possible scenarios of the transverse oscillation, such as the propagation of jet instabilities or magneto-hydrodynamic (MHD) waves or perturbed mass injection around magnetically dominated accretion flows.

Evolution characteristics of impact weather system and SST signals during years of anomalous Meiyu onset over the Yangtze-Huaihe River Basin

This article investigates the climatic characteristics of Meiyu over the Yangtze-Huaihe River Basin and the primary impact system based on Meiyu onset data from 1954 to 2020, precipitation during the Meiyu Period, NCEP/NCAR reanalysis data, sea surface temperature (SST) data of NOAA, and western Pacific subtropical high (sub-high) data provided by the National Climate Center. The main analytical method used is synthetic analysis. The results indicate that the Meiyu onset date has enormous interannual variation. The date of the earliest Meiyu emergence is 27 days prior to the latest. There is a strong relationship between the duration of Meiyu and rainfall. The start of Meiyu correlates with the northward motion of the South Asia High, the northward jump of the westerly jet, the northward jump of the subtropical high, and the northward motion of the low-level jet. In the early Meiyu years featured in this study, the northward jump of the aforementioned systems occurred earlier and the position of the westerly jet shifted from 34–35°N to 38–40°N, which is much further north than its position under typical climatic circumstances. From late May to early June, the subtropical high was extraordinarily powerful, the ridgeline reached 20°N, and its position was further to the north. In years with a late Meiyu onset, the position of the westerly jet and the ridgeline were further south than the climatological average from early to late June; the jump to the north was not evident until late June. In addition, SST anomalies of the Indian Ocean and Pacific Ocean are significant external forcing variables that influence the Meiyu start date. The high SST of the equatorial Indian Ocean and the equatorial tropical eastern Pacific in the autumn of the preceding year and the high SST of the equatorial Indian Ocean in the spring of that year are prophase indicators of an early Meiyu start in the Yangtze-Huaihe River Basin.

Hydrodynamic trade-offs in potential swimming efficiency of planispiral ammonoids

AbstractAmmonoid cephalopods were Earth's most abundant oceanic carnivores for hundreds of millions of years, yet their probable range of swimming capabilities is poorly constrained. We investigate potential hydrodynamic costs and advantages provided by different conch geometries using computational fluid dynamics simulations. Simulations of raw drag demonstrate expected increases with velocity and conch inflation, consistent with published experimental data. Analysis at different scales of water turbulence (via Reynolds number) reveals dynamic trade-offs between conch shape, size, and velocity. Among compressed shells, the cost of umbilical exposure makes little difference at small sizes (and/or low velocity) but is profound at large sizes (and/or high velocity). We estimate that small ammonoids could travel one to three diameters per second (i.e., a typical ammonoid with a 5-cm-diameter shell could travel 5–15 cm/s), but that large ammonoids faced greater discrepancies (a 10 cm serpenticone likely traveled &lt;30 cm/s, while a 10 cm oxycone might achieve &gt;40 cm/s). All of these velocities are proposed only for short bursts of jet propulsion, lasting only a few seconds, in the service of dodging a predator or conspecific rival. These analyses do not include phylogeny, taxonomy, second-order conch architecture (ribs, ornament, etc.), or hydrostatic consequences of internal anatomy (soft body, suture complexity). For specific paleoecological context, we consider how these results inform our reconstruction of Jurassic ammonite recovery from the end-Triassic mass extinction. Greater refinements will come with additional simulations that measure how added mass is influenced by individual shape-trait variations, ornament, and subtle body extensions during a single jet motion.

МОДЕЛИРОВАНИЕ ДВИЖЕНИЯ И НАГРЕВА ЧАСТИЦ ПОРОШКА В ПЛАЗМЕННОЙ СТРУЕ

When using special attachments in agricultural machinery, one often has to deal with the failure of the hydraulic systems for driving the working bodies due to wear of the contacting friction pairs. The process of applying gas-thermal composite coatings by plasma deposition to restore such defects is considered. The dynamics of the behavior of a single particle in a flow without taking into account the interaction of neighboring particles was studied to determine the parameters of the plasma jet, which provide precipitation of a given quality. The criterion of controlled melting of composite material particles was used. This ensures, on the one hand, obtaining the required adhesion of the coating to the treated surface, and on the other hand, it creates compressive residual stresses in the formed layer. The problem is solved under the assumption that the space is isotropic. The effects of elastic-plastic deformation are not taken into account. An algorithm is presented for the numerical solution of constitutive relations that describe the nature of the motion of a plasma jet depending on the external factors that determine it. The dependences of the particle velocity on the distance traveled by them and their temperature depending on the size of the fraction of the solid part of the filler are presented for the case of using aluminum oxide particles with a diameter of 45 μm as a filler. The regularities obtained make it possible to predict in advance the properties of deposited coatings, achieving certain features determined by the operating conditions of the restored unit.

Large Eddy Simulation of the cavitating flow around a Clark-Y mini cascade with an insight on the cavitation-vortex interaction

In this research, the Large Eddy Simulation method is utilized to predict the cavitation-vortex interaction in the flow around a Clark-Y mini cascade along with the dynamical processes of the U-type cavity, analyzed using the Lamb vector divergence transportation. To provide a novel perception of the development of the U-type cavity, various fundamental mechanisms of the periodic evolution of the U-type cavity are investigated thoroughly. The dynamical progress explicates the mechanisms that generate the high-pressure zone and low-velocity zone. This mechanism, combined with the re-entrant jet and vortex motions plays a significant role in the development of the U-type cavity. Since the Lamb vector curl associates the vorticity transport equation and is closely related to the source of vorticity of the vortex evolution, the Lamb vector curl captures the vortical structures which show good agreement with the Ω-method results. In addition, the distributions of high- and low-momentum flow in the wake of the cascade are delineated by the Lamb vector divergence. The transition from the maximum to the minimum of the lamb vector divergence in a region illustrates a quasi-cyclic behavior that is closely related to the momentum transport mechanisms and the cyclical motions of the vortex.

Broadening the scope of measurement and analysis of vibrations of an organ pipe employing intensity probe, simulations, and high-speed camera

This paper shows an integrated approach to measure, analyze, and model phenomena occurring in an organ pipe driven by pressurized air. The aim of this paper is two-fold, i.e., to measure the pressure signal and the intensity field around the mouth by means of an intensity probe and to visualize and observe the motion of the air jet, which represents the excitation mechanism of the system. This is realized through two techniques, i.e., measurements conducted on a Bourdon organ pipe and numerical simulations of the air flow in a pipe of the same geometry. Measurements were carried out in an anechoic chamber using the Cartesian robot. Simulations were performed on a server equipped with graphical cards, and the results were visualized employing ParaVIEW software. Moreover, an analysis was conducted by observing phenomena in both audio and video signals. A high-speed camera was employed to make the jet getting out from the windway visible. This was realized using the steam that produced the reaction of dry ice and hot water. This choice has been adopted to ensure safety conditions in the measurement environment. Finally, a comparison between the sound spectrum measured and the spectrum resulted from simulations was made.

Radio observations of the Black Hole X-ray Binary EXO 1846−031 re-awakening from a 34-year slumber

ABSTRACT We present radio [1.3 GHz MeerKAT, 4–8 GHz Karl G. Jansky Very Large Array (VLA), and 15.5 GHz Arcminute Microkelvin Imager Large Array (AMI-LA)] and X-ray (Swift and MAXI) data from the 2019 outburst of the candidate Black Hole X-ray Binary (BHXB) EXO 1846−031. We compute a Hardness–Intensity diagram, which shows the characteristic q-shaped hysteresis of BHXBs in outburst. EXO 1846−031 was monitored weekly with MeerKAT and approximately daily with AMI-LA. The VLA observations provide sub-arcsecond-resolution images at key points in the outburst, showing moving radio components. The radio and X-ray light curves broadly follow each other, showing a peak on ∼MJD 58702, followed by a short decline before a second peak between ∼MJD 58731–58739. We estimate the minimum energy of these radio flares from equipartition, calculating values of Emin ∼ 4 × 1041 and 5 × 1042 erg, respectively. The exact date of the return to ‘quiescence’ is missed in the X-ray and radio observations, but we suggest that it likely occurred between MJD 58887 and 58905. From the Swift X-ray flux on MJD 58905 and assuming the soft-to-hard transition happened at 0.3–3 per cent Eddington, we calculate a distance range of 2.4–7.5 kpc. We computed the radio:X-ray plane for EXO 1846−031 in the ‘hard’ state, showing that it is most likely a ‘radio-quiet’ BH, preferentially at 4.5 kpc. Using this distance and a jet inclination angle of θ = 73°, the VLA data place limits on the intrinsic jet speed of βint = 0.29c, indicating subluminal jet motion.

Constraining the Hubble constant and its lower limit from the proper motion of extragalactic radio jets

ABSTRACT The Hubble constant (H0) is a measurement to describe the expansion rate of the Universe in the current era. However, there is a 4.4σ discrepancy between the measurements from the early Universe and the late Universe. In this research, we propose a model-free and distance-free method to constrain H0. Combining Friedman–Lemaître–Robertson–Walker cosmology with geometrical relation of the proper motion of extragalactic jets, the lower limit (H0,min) of H0 can be determined using only three cosmology-free observables: the redshifts of the host galaxies, and the approaching and receding angular velocities of radio jets. Using these, we propose to use the Kolmogorov–Smirnov test (K–S test) between cumulative distribution functions of H0,min to differentiate cosmology. We simulate 100, 200, and 500 extragalactic jets with three levels of accuracy of the proper motion (μa and μr), at 10, 5, and 1 per cent, corresponding to the accuracies of the current and future radio interferometers. We perform K–S tests between the simulated samples as theoretical distributions with different H0 and power-law index of velocity distribution of jets and mock observational data. Our result suggests increasing sample sizes leads to tighter constraints on both power-law index and the Hubble constant at moderate accuracy (i.e. $10$ and $5{{\ \rm per\ cent}}$), while at $1{{\ \rm per\ cent}}$ accuracy, increasing sample sizes leads to tighter constraints on power-law index more. Improving accuracy results in better constraints in the Hubble constant compared with the power-law index in all cases, but it alleviates the degeneracy.

Curved Jet Motion. I. Orbiting and Precessing Jets

Astrophysical jets are often observed as bent or curved structures. We also know that the different jet sources may be binary in nature, which may lead to a regular, periodic motion of the jet nozzle, an orbital motion, or precession. Here we present the results of 2D (M)HD simulations in order to investigate how a precessing or orbiting jet nozzle affects the propagation of a high-speed jet. We have performed a parameter study of systems with different precession angles, different orbital periods or separations, and different magnetic field strengths. We find that these kinds of nozzles lead to curved jet propagation, which is determined by the main parameters that define the jet nozzle. We find C-shaped jets from orbiting nozzles and S-shaped jets from precessing nozzles. Over a long time and long distances, the initially curved jet motion bores a broad channel into the ambient gas that is filled with high-speed jet material whose lateral motion is damped, however. A strong (longitudinal) magnetic field can damp the jet curvature that is enforced by either precession or orbital motion of the jet sources. We have investigated the force balance across the jet and ambient medium and found that the lateral magnetic pressure and gas pressure gradients are almost balanced, but that a lack of gas pressure on the concave side of the curvature is leading to the lateral motion. Magnetic tension does not play a significant role. Our results are obtained in code units, but we provide scaling relations such that our results may be applied to young stars, microquasars, symbiotic stars, or active galactic nuclei.

Thermophysical processes in dry granulation of metallurgical slags

Mathematical model for theoretical analysis of thermophysical processes of melt drops solidification is examined during their motion inside cooling gas, applying to granulation task. The heat exchange equations during granulation, taking into account convection, heat conductivity in solid phase and Stefan conditions on the boundary of phase transition, are presented. The relationships characterizing correlation of the power exchange parameters in dispersed medium are obtained in the conditions of phase transition in melt drops inside gas phase flow. Analytical relationships allow to consider correlation of the parameters which characterize granulation process, to provide directions of efficient conduction of the processes for achieving the preset aims and to reveal the conditions for optimal technological parameters of the process. Speed of the power exchange processes determines the size of an installation and allows to make preliminary assessment during designing. Different motion modes for particles and gas are investigated. The variants for calculation of gas dynamic parameters of straight flying trajectory for a slag melt particle are suggested; they are based on solving the problem of particle motion in the gas medium, taking into account particle size, medium resistance, initial particle speed. Used relationships allow to assess the particle flying time, which is corresponded to the required time of particle cooling during its flying, and to choose programming conditions for motion of dispersed jet of slag melt. These conditions guarantee forming of solid crust on the cooled particle and possibility of size determination for a granulation system. Possible scheme of slag heat realization, allowing to utilize maximally the exergy of secondary power resources, is considered. The obtained results can be used for improvement of the existing installations fir dry granulation and for designing of the new ones, as well as for optimization of operating modes of granulators, for their efficiency rise and increase of power saving possibilities for a granulation system.&nbsp; The research was conducted within the framework of the&nbsp;State assignment, project No. FSWF-2020-0019.

Analysis of polymer jet motion in the non-isothermal melt-blown process

The motion characteristic of the polymer jet in a non-isothermal airflow field during melt blowing plays a crucial role in the process of fiber formation and has always been difficult to measure in situ. Many numerical models have been established to simulate the motion of the polymer jet during melt blowing. However, the complex interplay between the airflow field and the polymer jet in these models was usually missed. Here, a coupled air–polymer two-phase flow model in the non-isothermal airflow field was developed by the level-set method, and the temperature dependence of viscosity and density for the polymer jet were also taken into account in our model. Based on the model, the motion of the polymer jet in the melt-blowing process was simulated considering the coupled effect between the air and the polymer jet. The velocities of the polymer jet along x-direction ([Formula: see text]) and y-direction ([Formula: see text]), the whipping amplitude of the polymer jet motion, and the final diameter were discussed and verified. In addition, the effects of critical parameters, such as the inlet airflow velocity, inlet polymer flow velocity, inlet air temperature, and polymer viscosity, on the motion characteristics and temperature of the polymer jet were analyzed numerically.

Fabrication of Polyvinylpyrrolidone (PVP) Nanofibrous Membranes using Mushroom-Spinneret Needleless Electrospinning

Mushroom-spinneret is an improved spinneret design for needleless electrospinning apparatus, which has a bowl-shaped base with a mushroom-shaped cover. The mushroom spinneret can overcome some limitations that is often associated with the needleless electrospinning technique, i.e., high excitation voltages, poor stability of free liquid, and difficulty of controlling the spatial motion of multiple jets. In this study, we fabricate polyvinylpyrrolidone (PVP) nanofibrous membranes using mushroom-spinneret needleless electrospinning and determine the effect of solution concentration and applied voltage on the fiber morphology and diameter. The solution concentration had significant effect on the fibers diameter. When the solution concentration was increased from 8 wt% to 12 wt%, the average fibers diameter increased from 0.99 μm to 1.31 μm and the fibers diameter distribution became wider. Moreover, the average fiber diameter decreased from 1.31 μm to 1.16 μm when the applied voltage was increased from 30 kV to 45 kV. The coefficient of variations (CV) for all membrane samples ranged from 0.12 - 0.26, indicated uniform fibers.

Modeling of Advanced Silicon Nanomaterial Synthesis Approach: From Reactive Thermal Plasma Jet to Nanosized Particles.

A three-dimensional numerical modelling of a time-dependent, turbulent thermal plasma jet was developed to synthetize silicon nanopowder. Computational fluid dynamics and particle models were employed via COMSOL Multiphysics® v. 5.4 (COMSOL AB, Stockholm, Sweden) to simulate fluid and particle motion in the plasma jet, as well as the heat dependency. Plasma flow and particle interactions were exemplified in terms of momentum, energy, and turbulence flow. The transport of nanoparticles through convection, diffusion, and thermophoresis were also considered. The trajectories and heat transfer of both plasma jet fields, and particles are represented. The swirling flow controls the plasma jet and highly affects the dispersion of the nanoparticles. We demonstrate a decrease in both particles’ velocity and temperature distribution at a higher carrier gas injection velocity. The increase in the particle size and number affects the momentum transfer, turbulence modulation, and energy of particles, and also reduces plasma jet parameters. On the other hand, the upstream flame significantly impacts the particle’s behavior under velocity and heat transfer variation. Our findings open the door for examining thermal plasma impact in nanoparticle synthesis, where it plays a major role in optimizing the growth parameters, ensuring high quality with a low-cost technique.

Mechanism and experimental simulation of non-isothermal melt formation induced by voltage change under auxiliary heating

Over the past few decades, it has been universally acknowledged that melt-electrospinning is an attractive solvent-free production process with the aim of alleviating the solvent-related problems generated by traditional electrospinning techniques. Up to now, the temperature and applied voltage have been considered as the two most important factors affecting the melt-electrospinning process and electrospun fibers. In this paper, an auxiliary heating setup was applied to the melt electrospinning system to deeply understand the effect of heat distribution on the melt-electrospun fibers. Jet motions, morphologies, mechanical properties and inner structures of the fibers obtained under different applied voltage conditions with and without auxiliary heating were investigated. The temperature distribution in melt-electrospinning system was simulated by COMSOL Multiphysics software. The experimental results showed that a higher applied voltage results in a smaller fiber diameter, more disordered fiber mat and lower degree of strength with auxiliary heating. The simulation results of the temperature distribution in the spinneret-collector region are in good agreement with the measured values of the infrared images, which proves the feasibility and accuracy of the model.

Quasi-periodic Oscillation Analysis for the BL Lacertae Object 1823+568

We studied the optical band periodic variability of 1823+568 using the Jurkevich method, the Lomb–Scargle periodogram and the REDFIT38 software, and found evidence of quasi-periodic oscillation. An unprecedented variability with period days was identified by three different analysis methods. This quasi-periodic variability most likely results from nonballistic helical jet motion driven by the orbital motion in a binary black hole system. Considering the light-travel time effect, the real physical period is P d = 67.1 yr. Moreover, we estimated that the primary black hole mass is M ≃ 1.92 × 109 M ⊙ to 3.43 × 109 M ⊙.