Vortex Trajectories Research Articles

An Experimental Investigation of Rotor–Box Aerodynamic Interaction1

Abstract Multirotor unmanned aerial vehicles (UAVs) are a promising means of package delivery. Such applications generally involve carrying bulky payloads under the vehicle. Understanding the aerodynamic interaction effects of payloads on the vehicle is the key to design such systems, in the low Reynolds number regime of small UAVs. High-speed particle image velocimetry (PIV), force, and torque measurements have been used with a rotor and a cubic box to investigate the rotor–box interactions and configurations typical of multirotor UAVs. The observed rotor and vehicle performance trends are explained by the mean flow field captured through PIV. Conditions similar to ground-effect operation are developed for the rotor at a high level of rotor-box overlap. A slight improvement in the vehicle performance is observed at conditions where the box is just out of the rotor wake. Some basic instantaneous flow phenomena due to rotor–box interaction have been identified. The interactions have been classified into three distinct modes based on observations at a range of box positions relative to the rotor. An empirical tip vortex trajectory model for isolated rotors is found to be instrumental in predicting the interaction mode at a given box position.

One-dimensional modeling for tip clearance leakage vortex trajectory and stall-onset prediction in subsonic centrifugal impellers

Two one-dimensional models are established for the tip leakage vortex trajectory and rotating stall-onset point prediction respectively for subsonic centrifugal impellers. The goal of modeling is to supply an effective estimation strategy of the stall-onset point for use in the one-dimensional performance prediction stage. The tip leakage vortex trajectory prediction is a critical part of the stall-onset prediction. The proposed one-dimensional model (one-dimensional tip leakage vortex trajectory model) to predict the tip leakage vortex trajectory is based on blade loading, i.e. the velocity difference between the pressure and suction surfaces. The loading function considers the effect of radial rotation, blade turning, and passage width variation. Compared with the computational fluid dynamics results, the current model shows reasonable accuracy, with an average relative error below 12.35%. The one-dimensional prediction model (Model II) is developed to determine the stall-onset point, where the interface between the tip leakage flow and the main flow spills from the blade leading edge. In this model, the momentum balance analysis is applied to identify the position of the interface. The parameter of the tip leakage vortex trajectory in Model II is determined by one-dimensional tip leakage vortex trajectory model. The effective origin of the tip leakage flow is correlated with the rotational speed and tip clearance. The effectiveness of Model II is validated with the experimental and computational fluid dynamics results using three impellers. Compared with the conventional model (Model I), Model II shows better accuracy, with a maximum error of about 7.42%.

Vortical lift on retreating rotor blades at high advance ratios

A retreating helicopter rotor blade encounters reverse flow over large portions of the rotor disk in high advance ratio flights. Measurements of flow velocity and loads are described for a two-bladed teetering rotor for advance ratios ranging from 0.6 to 1.2 in a low speed wind tunnel. The tip vortex trajectory is separately mapped. A pressure extraction technique is used to map the static pressure field on the lower surface of the rotor blade near sharp edge. The reverse flow region shows a proof of an attached, helical Sharp Edge Vortex (SEV). The proximity of the SEV to the rotor blade creates sharp excursions in the static pressures at the sharp edge. The negative lift generated by the vortex is comparable to the sectional bound circulation. The presence of the SEV explains the shift in the center of pressure from 75 to 70% of chord. Stereo particle image velocimetry, a pressure extraction technique, and load measurements provide closure in estimating aerodynamic loads. As the blade approaches 270 $$^\circ$$ azimuth vortex strength stops growing and its core detaches from the blade surface but the vortex stays close to the blade. Flow on blunt edge of the blade in reverse flow is found to be largely attached, unlike expectations of vortex shedding.

Chaotic few-body vortex dynamics in rotating Bose-Einstein condensates

We investigate a small vortex-lattice system of four co-rotating vortices in an atomic Bose--Einstein condensate and find that the vortex dynamics display chaotic behaviour after a system quench introduced by reversing the direction of circulation of a single vortex through a phase-imprinting process. By tracking the vortex trajectories and Lyapunov exponent, we show the onset of chaotic dynamics is not immediate, but occurs at later times and is accelerated by the close-approach and separation of all vortices in a scattering event. The techniques we develop could potentially be applied to create locally induced chaotic dynamics in larger lattice systems as a stepping stone to study the role of chaotic events in turbulent vortex dynamics.

Measuring topology from dynamics by obtaining the Chern number from a linking number

Integer-valued topological indices, characterizing nonlocal properties of quantum states of matter, are known to directly predict robust physical properties of equilibrium systems. The Chern number, e.g., determines the quantized Hall conductivity of an insulator. Using non-interacting fermionic atoms in a periodically driven optical lattice, here we demonstrate experimentally that the Chern number determines also the far-from-equilibrium dynamics of a quantum system. Extending a respective proposal to Floquet systems, we measure the linking number that characterizes the trajectories of momentum-space vortices emerging after a strong quench. We observe that it directly corresponds to the ground-state Chern number. This one-to-one relation between a dynamical and a static topological index allows us to experimentally map out the phase diagram of our system. Furthermore, we measure the instantaneous Chern number and show that it remains zero under the unitary dynamics.

Wake dynamics and surface pressure variations on two-dimensional normal flat plates

The relationship between vortex dynamics and surface pressure fluctuations on the leeward face of a two-dimensional normal thin flat plate was studied using Direct Numerical Simulations for incompressible flow at a Reynolds number of 1200. The vortex shedding frequency was observed in the spectra of pressure fluctuations on both faces of the plate, while a lower frequency spectral peak was only evident on the leeward pressure fluctuations. Local sharp peaks of low pressure in the separated shear layers coincide with increases in the leeward face pressure fluctuations. These observations are tied to the vortex dynamics using the invariant Q, commonly used for vortex identification. Q is also proportional to the source term for the Poisson equation for the instantaneous pressure. The pressure, which is the only contributor to the plate drag, varies significantly in response to alterations to the vortex shedding, which can be observed in differences of vortex trajectories. At minimum drag, the pressure fluctuations are small, which is attributed to lower values of Q associated with weaker vortices.

Effect of circumferential static pressure nonuniformity caused by volute on tip leakage flow in a centrifugal compressor

For a centrifugal compressor with volute, the flow field is circumferentially nonuniform because of the volute asymmetrical structure and leads to a circumferential difference in the tip leakage flow. In this work, the compressor performance and the casing wall static pressure distribution are measured, and the results are compared with the time-averaged results of the unsteady calculation to verify the reliability of the simulation. The results show a relationship between the tip leakage vortex trajectory and the high static pressure region in the diffuser, based on which a prediction model is established for the reverse propagation of pressure waves caused by a volute tongue. Influenced by the volute asymmetric structure, the trajectory, shape, and strength of the tip leakage vortex at different circumferential positions differs significantly. The tip leakage vortex trajectory affected by the high static pressure is more inclined to a circumferential direction because the tip leakage flow velocity flowing out of the suction surface is reduced, and the tip leakage flow with low velocity is subjected to the high-pressure gradient in a passage. Moreover, the tip leakage vortex breakdown in different passages differs significantly. A tip leakage vortex core more inclined towards the streamwise direction is more likely to break down than a tip leakage vortex core inclined towards the circumferential direction because of the larger reverse pressure gradient.

Spatial–Temporal Evolution of Tip Leakage Vortex in a Mixed-Flow Pump With Tip Clearance

Tip clearance in pump induces tip leakage vortex (TLV), which interacts with the main flow and leads to instability of flow pattern and decrease of pump performance. In this work, the characteristics of TLV in a mixed-flow pump are investigated by the numerical simulation using shear stress transport (SST) k–ω turbulence model with experimental validation. The trajectory of the primary tip leakage vortex (PTLV) is determined, and a power function law is proposed to describe the intensity of the PTLV core along the trajectory. Spatial–temporal evolution of the TLV in an impeller revolution period T can be classified into three stages: splitting stage, developing stage, and merging stage. The TLV oscillation period TT is found as 19/160 T, corresponding to the frequency 8.4 fi (fi is impeller rotating frequency). Results reveal that the TLV oscillation is intensified by the sudden pressure variation at the junction of two adjacent blades. On analysis of the relative vorticity transport equation, it is revealed that the relative vortex stretching item in Z direction is the major source of the splitting and shedding of the PTLV. The dominant frequency of pressure and vorticity fluctuations on the PTLV trajectory is 8.4 fi, same as the TLV oscillation frequency. This result reveals that the flow instability in the PTLV trajectory is dominated by the oscillation of the TLV. The blade number has significant effect on pressure fluctuation in tip clearance and on blade pressure side, because the TLV oscillation period varies with the circumferential length of flow passage.

Propagation dynamics of off-axis noncanonical vortices in a collimated Gaussian beam**Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2017B14914), China Postdoctoral Science Foundation (Grant No. 2016M601586), and the National Natural Science Foundation of China (Grant Nos. 11874140 and 11404092).

It is widely accepted that an off-axis noncanonical vortex moves across the free-space diffracting Gaussian beam without rotation. But our analysis shows that the vortex swirls a while before it approaches infinite. By neglecting the divergence of the host beam, we focus on this rotation characteristics of the vortices in linear homogeneous media. For the symmetrical host beam, it is found that the vortex moves along an elliptical trajectory, while the topological charge and the angular momentum of the vortex core relative to the beam axis are conserved. For the asymmetrical host beam, the vortex trajectory is rather complicated, since the noncanonical parameter varies as the light propagates, resulting in topological charge inversion. But we find that the vortices are always confined in a rectangular area, and the rotation direction is determined by the topological charge.

Optical vortex trajectory as a merit function for spatial light modulator correction

Spatial light modulator (SLM) is a modern device extensively used for laser beam shaping. Over the years, its quality has been significantly improved. Nevertheless, there is still a need to correct its imperfections. In this paper we propose two criteria which allow to examine correction effectiveness of SLM. One is based on the Laguerre–Gauss transform and the second uses optical vortex dynamics which exposes a high sensitivity to any beam imperfections. It is based on the vortex internal scanning method, where the shape of vortex trajectory provides information about SLM correction quality. In this paper we test its sensitivity to astigmatism, which was introduced manually by SLM, after proper correction.

The interaction between a spatially oscillating jet emitted by a fluidic oscillator and a cross-flow

This experimental study investigates the fundamental flow field of a spatially oscillating jet emitted by a fluidic oscillator into an attached cross-flow. Dominant flow structures, such as the jet trajectory and dynamics of streamwise vortices, are discussed in detail with the aim of understanding the interaction between the spatially oscillating jet and the cross-flow. The oscillating jet is ejected perpendicular to the cross-flow. A moveable stereoscopic particle image velocimetry (PIV) system is employed for the plane-by-plane acquisition of the flow field. The three-dimensional, time-resolved flow field is obtained by phase averaging the PIV results based on a pressure signal from inside the fluidic oscillator. The influence of velocity ratio and Strouhal number is assessed. Compared to a common steady wall-normal jet, the spatially oscillating jet penetrates to a lesser extent into the cross-flow’s wall-normal direction in favour of a considerable spanwise penetration. The flow field is dominated by streamwise-oriented vortices, which are convected downstream at the speed of the cross-flow. The vortex dynamics exhibits a strong dependence on the Strouhal number. For small Strouhal numbers, the spatially oscillating jet acts similar to a vortex-generating jet with a time-dependent deflection angle. Accordingly, it forms time-dependent streamwise vortices. For higher Strouhal numbers, the cross-flow is not able to follow the motion of the jet, which results in a quasi-steady wake that forms downstream of the jet. The results suggest that the flow field approaches a quasi-steady behaviour when further increasing the Strouhal number.

Analysis of tip-leakage flow in an axial fan at varying tip-gap sizes and operating conditions

Detailed and comprehensive analyses of the tip vortex system of a ducted axial fan are performed based on highly resolved large-eddy simulations. Various tip gap sizes, which are typically found in technical fans, and two operating conditions are considered. The Reynolds number based on the tip speed of the blade and the diameter of the fan D0 is Re=9.36×105, the Mach number is M=0.136, and the rotational speed Ω=3000 rpm. The chosen tip clearances s are s/Do=0.001,0.005,0.01 and the design and off-design operating conditions are defined by the flow rate coefficients Φ=0.195 and Φ=0.165, respectively. The conservation equations of a compressible, viscous fluid are integrated on a multi-block structured mesh with 140 × 106 grid points in a rotating frame of reference for a single out of five blades using periodic boundary conditions in the circumferential direction and prescribed undisturbed inflow conditions based on experimental data. The results show that increasing the tip-gap size results in several vortices in the tip-gap region, i.e., tip leakage, separation and induced vortices, which enlarge the diameter and the strength of the main tip vortex and decrease the efficiency of the fan. For the off-design operating condition, the tip-gap vortex for the smallest tip-gap size decays faster than for the design operating condition. Increasing the tip-gap width, changes the direction of the tip-leakage vortex trajectory. The angle between the blade chord and the tip-leakage vortex is decreased at design condition, while the opposite behavior is observed for the off-design condition, in which the tip-leakage vortex moves further away from the suction side of the blade. Furthermore, the interaction between the axial flow and the main tip leakage vortex convecting downstream of the blade leads to an enhanced turbulent mixing at larger tip-gap size. For the largest tip clearance, i.e., s/Do=0.01, spiral vortex breakdown occurs at the design operating condition caused by the interaction of the main tip vortex with the secondary vortex generated in the tip-gap region. At off-design operating conditions, a larger tip-leakage-loss coefficient is obtained due to a more intensive turbulent mixing, where the maximum loss coefficient occurs at around midchord.

Aeroelastic Study for HART II Rotor Using Unstructured Mixed Meshes

In the present study, aeroelastic response of HART II rotor blade has been numerically investigated using a coupled CFD/CSD method. Aerodynamic forces were calculated from a Navier–Stokes CFD flow solver based on unstructured mixed meshes. In the mixed meshes methodology, body-fitted prismatic/tetrahedral mesh was used in the near-body flow region to handle complex geometries easily. Cartesian mesh was used in the off-body flow region and high-order accurate weighted essentially non-oscillatory scheme was employed to implement high-order spatial accuracy. In the FEM-based CSD solver, an elastic deformation of the rotor blade was obtained on the basis of nonlinear Euler–Bernoulli beam theory. The coupling between the CFD and CSD solver was performed in a loosely coupled manner by exchanging the aerodynamic loads and elastic deformation of the rotor blade. An overset mesh technique was adopted to simulate rotating motion of the rotor blade and to exchange flow information between two different meshes. In addition, spring analogy was used to implement elastic deformation of the rotor blade. Coupled CFD/CSD method was applied to the HART II rotor in forward flight to examine aerodynamic performance and aeroelastic effect of the rotor. Aerodynamic loads and elastic deformation of the rotor blade were calculated and compared with experimental results and other research efforts. Overall, the present results were in good agreement with the experimental data. In addition, adaptive fine mesh was used to capture tip vortex trajectory and BVI (blade–vortex interaction) phenomenon more accurately.

On Stability of the Thomson’s Vortex N-gon in the Geostrophic Model of the Point Vortices in Two-layer Fluid

A two-layer quasigeostrophic model is considered. The stability analysis of the stationary rotation of a system of N identical point vortices lying uniformly on a circle of radius R in one of the layers is presented. The vortices have identical intensity and length scale is $$\gamma ^{-1}>0$$ . The problem has three parameters: N, $$\gamma R$$ and $$\beta $$ , where $$\beta $$ is the ratio of the fluid layer thicknesses. The stability of the stationary rotation is interpreted as orbital stability. The instability of the stationary rotation is instability of system reduced equilibrium. The quadratic part of the Hamiltonian and eigenvalues of the linearization matrix are studied. The parameter space $$(N,\gamma R,\beta )$$ is divided on three parts: $$\varvec{A}$$ is the domain of stability in an exact nonlinear setting, $$\varvec{B}$$ is the linear stability domain, where the stability problem requires the nonlinear analysis, and $$\varvec{C}$$ is the instability domain. The case $$\varvec{A}$$ takes place for $$N=2,3,4$$ for all possible values of parameters $$\gamma R$$ and $$\beta $$ . In the case of $$N=5$$ , we have two domains: $$\varvec{A}$$ and $$\varvec{B}$$ . In the case $$N=6$$ , part $$\varvec{B}$$ is curve, which divides the space of parameters $$(\gamma R, \beta )$$ into the domains: $$\varvec{A}$$ and $$\varvec{C}$$ . In the case of $$N=7$$ , there are all three domains: $$\varvec{A}$$ , $$\varvec{B}$$ and $$\varvec{C}$$ . The instability domain $$\varvec{C}$$ takes place always if $$N=2n\geqslant 8$$ . In the case of $$N=2\ell +1\geqslant 9$$ , there are two domains: $$\varvec{B}$$ and $$\varvec{C}$$ . The results of research are presented in two versions: for parameter $$\beta $$ and parameter $$\alpha $$ , where $$\alpha $$ is the difference between layer thicknesses. A number of statements about the stability of the Thomson N-gon is obtained for the systems of interacting particles with the general Hamiltonian depending only on distances between the particles. The results of theoretical analysis are confirmed by numerical calculations of the vortex trajectories.

Numerical investigation of tip flow dynamics and main flow characteristics with varying tip clearance widths for an axial-flow pump

The effects of varying tip clearance widths on tip flows dynamics and main flows characteristics for an axial-flow pump are studied employing computational fluid dynamics method. An analysis is presented for the distributions of turbulent kinetic energy, mean axial velocity, and mean vorticity magnitude at the specific flow rate of 0.7 Q BEP , focusing on flow patterns in the tip region with different tip clearance widths and associated flows. From the simulation results we find that the flow structure of tip vortex and its transportation strongly depend on the tip clearance width, especially for the extension of tip leakage vortex, appearance of induced vortex and the area of tip separation vortex. For a small clearance of 0.15 mm at 0.7 Q BEP, there is no tip separation vortex at the tip. When tip clearance width becomes larger, a tip separation vortex attaches more on the surface of blade tip as well as vortex intensity of tip flows increases. For tip clearances of 0.9 and 1.2 mm, there is a small part of induced vortex near the blade leading edge. Meanwhile, no induced vortex can be captured for tip clearances of 0.15 and 0.45 mm. The relative angle between the blade chord and tip leakage vortex trajectory reduces gradually when tip clearance width increases from 0.45 to 1.2 mm. Additionally, the radial position of tip leakage vortex core moves inwards as tip clearance width increases. Furthermore, a larger tip clearance width has greater effects on the main-stream characteristics especially near the shroud, which is due to more energy being exchanged between tip flows and main flows. At the flow rate 0.7 Q BEP, both the efficiency and head of the pump reduce with an increasing tip clearance because of greater energy loss.

On the Interactions of a Rotor Blade Tip Flow With Axial Casing Grooves in an Axial Compressor Near the Best Efficiency Point

Experiments in a refractive index-matched axial turbomachine facility show that semicircular skewed axial casing grooves (ACGs) reduce the stall flowrate by 40% but cause a 2.4% decrease in the maximum efficiency. Aiming to elucidate mechanism that might cause the reduced efficiency, stereo-PIV measurements examine the impact of the ACGs on the flow structure and turbulence in the tip region near the best efficiency point (BEP), and compare them to those occurring without grooves and at low flowrates. Results show that the periodic inflow into the groove peaks when the rotor blade pressure side (PS) overlaps with the downstream end of the groove, but diminishes when this end faces the suction side (SS). Entrainment of the PS boundary layer and its vorticity generates a vortical loop at the entrance to the groove, and a “discontinuity” in the tip leakage vortex (TLV) trajectory. During exposure to the SS, the backward tip leakage flow separates at the entrance to the groove, generating a counter-rotating circumferential “corner vortex,” which the TLV entrains into the passage at high flowrates. Interactions among these structures enlarge the TLV and create a broad area with secondary flows and elevated turbulence near the groove's downstream corner. A growing shear layer with weaker turbulence also originates from the upstream corner. The groove also increases the flow angle upstream of the blade tip and varies it periodically. Accordingly, the circulation shed from the blade tip and strength of leakage flow increase near the blade leading edge (LE).

Suction control of flow separation of a low-aspect-ratio wing at a low Reynolds number

Suction-based flow control is explored as one of means of enhancing the performance of a low aspect ratio (AR) wing. Large-eddy simulation (LES) was performed to investigate the flow past a three-dimensional (3D) NACA0012 profile wing tip at a chord-based Reynolds number of 35966, such configurations and flow conditions are typical of those utilized in a small unmanned air system (UAS). The flow separation appears at an angle of attack a = 15°, which is used as the example for our investigation. After validating of our numerical results, the suction distribution was designed and mounted near the wing root, and two different control parameters, suction coefficients and angles, were investigated to assess the benefits of flow control and to determine their effectiveness. Our results show that suction control can improve the lift, and the suction coefficient has larger effect on the aerodynamic performances of the wing than that of the suction angle. The lift enhancement is attributed to the standing vortex near the leading edge and the trajectory of wing tip vortex is also affected during the suction control.

Topology of interacting coiled vortex rings

Pairs of nested vortex rings, one with coils, are evolved numerically to compare their topological numbers to those of recent experiments reported in Scheeler et al. (Science, vol. 357, 2017, pp. 487–491). Included are the twist $Tw$, writhe $Wr$ and self-linking ${\mathcal{L}}_{S}$ numbers, plus centreline helicities ${\mathcal{H}}_{c}$. The questions are: can the experimental numbers be validated and do these numbers have roles in the dynamics of the global helicities ${\mathcal{H}}$ and enstrophies $Z$ with respect to cascades? Topological analysis of the experiments $t=0$ analytic centreline vortex trajectories validates only the writhe measurements, not their values of $Tw$ and ${\mathcal{L}}_{S}$, which obey $Tw\lesssim {\mathcal{L}}_{S}=m\gg Wr$ for $m$-coil rings. Not $Tw\ll Wr$. To suggest why the large twists do not contribute to ${\mathcal{H}}$, it is noted that the mapping of the coiled rings onto the mesh is to a first approximation a single pair of Clebsch potentials, whose self-helicity ${\mathcal{H}}_{S}\equiv 0$. Numerical rings with circulations $\unicode[STIX]{x1D6E4}$, including some single rings, show small initial helicities with ${\mathcal{H}}(0)\approx {\mathcal{H}}_{c}\sim (\text{1 to 2})Wr\unicode[STIX]{x1D6E4}^{2}$$\ll {\mathcal{L}}_{S}\unicode[STIX]{x1D6E4}^{2}$. For time and velocity scales that are consistent with the experiments, as the coils evolve, their $Tw$, $Wr$, ${\mathcal{L}}_{S}$ numbers and their helicities are nearly static until reconnection. Nonetheless, $Wr$ and $Tw$ retain important complementary roles in the dynamics of the global helicity ${\mathcal{H}}$ and enstrophy $Z$, with the evolution of the torsion $\unicode[STIX]{x1D70F}(s)$ profile showing the beginnings of a cascade to small scales.

Entrapping of a vortex pair interacting with a fixed point vortex revisited. II. Finite size vortices and the effect of deformation

We investigate the evolution of a pair of two-dimensional, opposite-signed, finite-size vortices interacting with a fixed point vortex. The present paper builds on the accompanying study by Koshel et al. [“Entrapping of a vortex pair interacting with a fixed point vortex revisited. I. Point vortices,” Phys. Fluids 30, 096603 (2018)] focusing on the motion of a pair of point vortices impinging on a fixed point vortex. Here, by contrast, the pair of opposite-signed finite-size vortices, or vortex dipole for simplicity, can deform. This deformation has an impact on the dynamics. We show that, as expected, finite size vortices behave like point vortices if they are distant enough from each other. This allows one to recover the rich and diverse set of possible trajectories for the dipole. This includes the regimes of intricate bounded motion when the finite-size vortices remain stable near the fixed vortex for a long time. On the other hand, we show that large finite-size vortices can deform significantly and deviate from the trajectories of equivalent point vortices. When the shear that the vortices induce on each other is large enough, the finite size vortices may break into smaller structures or may even be completely strained out.

Entrapping of a vortex pair interacting with a fixed point vortex revisited. I. Point vortices

The problem of a pair of point vortices impinging on a fixed point vortex of arbitrary strengths [E. Ryzhov and K. Koshel, “Dynamics of a vortex pair interacting with a fixed point vortex,” Europhys. Lett. 102, 44004 (2013)] is revisited and investigated comprehensively. Although the motion of a pair of point vortices is established to be regular, the model presents a plethora of possible bounded and unbounded solutions with complicated vortex trajectories. The initial classification [E. Ryzhov and K. Koshel, “Dynamics of a vortex pair interacting with a fixed point vortex,” Europhys. Lett. 102, 44004 (2013)] revealed that a pair could be compelled to perform bounded or unbounded motion without giving a full classification of either of those dynamical regimes. The present work capitalizes upon the previous results and introduces a finer classification with a multitude of possible regimes of motion. The regimes of bounded motion for the vortex pair entrapped near the fixed vortex or of unbounded motion, when the vortex pair moves away from the fixed vortex, can be categorized by varying the two governing parameters: (i) the ratio of the distances between the pair’s vortices and the fixed vortex and (ii) the ratio of the strengths of the vortices of the pair and the strength of the fixed vortex. In particular, a bounded motion regime where one of the pair’s vortices does not rotate about the fixed vortex is revealed. In this case, only one of the pair’s vortices rotates about the fixed vortex, while the other oscillates at a certain distance. Extending the results obtained with the point-vortex model to an equivalent model of finite size vortices is the focus of Paper II [J. N. Reinaud et al., “Entrapping of a vortex pair interacting with a fixed point vortex revisited. II. Finite size vortices and the effect of deformation,” Phys. Fluids 30, 096604 (2018)].