Transverse Oscillations Research Articles

Investigation of Pobeda furnace bubbling zone physics using cold modeling method Part 3. The hydro-gas dynamics of combined blowing of liquid by gas using bottom and lateral lances

Hydro-gas regularities of liquid combined blowing by gas were studied using cold modeling method at Archimedes criterion for lateral Arl = 12÷120 and bottom blowing Arb = 5÷60 simulating Pobeda bubbling unit. The blowing was performed simultaneously by bottom lance vertically fixed in centre of reactor and by the lateral lance which was attached at an angle 5° to the horizontal axis. The quantitative estimation of instantaneous and average circulation velocities (Vav) of liquid flow elements in different bath areas, depending on the location of blowing zone and Archimedes criterion, was performed. The liquid motion trajectory was determined. A vortex zone was revealed near the liquid surface and the reactor shell, where instantaneous velocity of the liquid flow elements changes from 69.9 to 181.1 mm/s and Vav = 123.8 mm/s. The circulation flows fade in the bulk of liquid and Vav decreases from 123.8 to 47.0 and 54.1 mm/s. It was shown that, in general, circulation velocity depends on the blowing intensity and appears to be higher for the zone of overlapping of lateral and bottom streams. The dynamic blowing conditions, which ensure the direct contact of lateral and bottom jets leading to their interflow and increased spatter formation, were identified. The characteristics of 3 types of surface oscillations for interface phases “pure liquid- gas-liquid layer”, as well as the estimation of the lateral and bottom blowing impact on the type of oscillation were provided. It has been noted that the introduction of the bottom blowing (Arb = 5) causes the wave-like motion of liquid (the 2nd type) along with the transverse oscillations of the 1st type, and at higher values of Arb = 25 the angular oscillations of the 3rd type develop. It has been shown that the presence of a lateral jet at the combined blowing decreases angles of bath swinging to 8–12° to horizontal axis. For the estimation of oscillation intensity, Δhl = (hl )max – (hl )min value, which means the difference between maximum (hl )max and minimum (hl )min height of liquid for the full-wave oscillations (τ), was introduced. The height of liquid (hl ) was plotted as a function of τ, Arl , Arb, Δhl was determined on the basis of obtained graph values, which varied upon modeling over the range of 7.7–69.5 mm. The relation between the liquid circulation velocity and the oscillation value (Δhl ) was established for different bath zones and dynamic conditions of the blowing. The impact of all oscillations types on potential erosive lining wear of Pobeda bubbling unit and the completeness of adoption of charging material nearby the bath surface was investigated.

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.

A Statistical Study of Short-period Decayless Oscillations of Coronal Loops in an Active Region

Coronal loop oscillations are common phenomena in the solar corona, which are often classified as decaying and decayless oscillations. Using the high-resolution observation measured by the Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter, we statistically investigate small-scale transverse oscillations with short periods (<200 s) of coronal loops in an active region (AR), i.e., NOAA AR 12965. A total of 111 coronal loops are identified in EUI 174 Å images, and they all reveal transverse oscillations without any significant decaying, regarded as decayless oscillations. Oscillatory periods are measured from ∼11 to ∼185 s, with a median period of 40 s. Thus, they are also termed short-period oscillations. The corresponding loop lengths are measured from ∼10.5 to ∼30.2 Mm, and a strong dependence of oscillatory periods on loop lengths is established, indicating that the short-period oscillations are standing kink-mode waves in nature. Based on the coronal seismology, kink speeds are measured to be ∼330–1910 km s−1, and magnetic field strengths in coronal loops are estimated to be ∼4.1–25.2 G, while the energy flux carried by decayless kink oscillations lies in the range from roughly 7 to 9220 W m−2. Our estimations suggest that the wave energy carried by short-period decayless kink oscillations cannot support the coronal heating in the AR.

Suddenly switching-on interaction in the relativistic strophotron

The equations of motion in the transition layer of a free-electron laser of the relativistic strophotron type are studied. Two types of strophotrons are considered: electric and magnetic. It is shown, that the condition of a suddenly switching-on interaction: smallness of the transition layer at the entrance compared to the distance traveled by the electron in longitudinal direction in one period of transverse oscillations in strophotron is realistic and feasible.

On the Countering of Free Vibrations by Forcing: Part II—Damped Oscillations and Decaying Forcing

The present two-part paper concerns the active vibration suppression for the simplest damped continuous system, namely the transverse oscillations of an elastic string, with constant tension and mass density per unit length and friction force proportional to the velocity, described by the telegraph or wave-diffusion equation, in two complementary parts. The initial part I considers non-resonant and resonant forcing, by concentrated point forces or continuous force distributions independent of time, with phase shift between the forced and free oscillations, in the absence of damping, in which case the forced telegraph equation reduces to the forced classical wave equation. The present and final part II uses the forced wave-diffusion equation to model the effect of damping, both as amplitude decay and phase shift in time, for non-resonant and resonant forcing by a single point force, with constant magnitude or magnitude decaying exponentially in time at an arbitrary rate. Assuming a finite elastic string fixed at both ends, the free oscillations are (i) sinusoidal modes in space-time with exponential decay in time due to damping. The non-resonant forced oscillations at an applied frequency distinct from a natural frequency are also (ii) sinusoidal in space-time, with constant amplitude and a phase shift such that the work of the applied force balances the dissipation. For resonant forcing at an applied frequency equal to a natural frequency, the sinusoidal oscillations in space-time have (iii) a constant amplitude and a phase shift of π/2. In both cases, the (ii) non-resonant or (iii) resonant forcing dominates the decaying free oscillations after some time. Even by optimizing the forcing to minimize the total energy of oscillation, it remains below the energy of the free oscillation alone, but only for a short time—generally a fraction of the period. A more effective method of countering the damped free oscillations is to use forcing with amplitude decaying exponentially in time; by suitable choice of the forcing decay relative to the free damping, the total energy of oscillation over all time can be reduced to no more than 1/16th of the energy of the free oscillation.

Stereoscopic observation of simultaneous longitudinal and transverse oscillations in a single filament driven by two-sided-loop jet

ABSTRACT We report the first observations of simultaneous large-amplitude longitudinal and transverse oscillations of a quiescent filament trigged by a two-sided-loop jet formed by the magnetic reconnection between the filament and an emerging loop in the filament channel, recorded by the Solar Dynamics Observatory and the Solar TErrestrial RElations Observatory. The north arm of the jet firstly pushed the filament mass moving northwardly along the magnetic field lines consisting of the coronal cavity, then some elevated filament mass fell back and started to oscillate longitudinally at the bottom of the cavity (i.e. the magnetic dip). The northernmost part of the filament also showed transverse oscillation simultaneously. The amplitude and period of the longitudinal (transverse) oscillation are 12.96 (2.99) Mm and 1.18 (0.33) h, respectively. By using the method of filament seismology, the radius of curvature of the magnetic dip is about 151 Mm, consistent with that obtained by the 3D reconstruction (166 Mm). Using different physical parameters of the observed longitudinal and transverse oscillations, the magnetic field strength of the filament is estimated to be about 23 and 21 Gauss, respectively. By calculating the energy of the moving filament mass, the minimum energy of the jet is estimated to be about $1.96 \times 10^{28} \operatorname{erg}$. We conclude that the newly formed jet can not only trigger simultaneous longitudinal and transverse oscillations in a single filament, but also can be used as a seismology tool for diagnosing filament information, such as the magnetic structure, magnetic field strength, and magnetic twists.

Acoustic response in the transition region to transverse oscillations in a solar coronal loop

Context. Magnetohydrodynamic (MHD) waves play an important role in the dynamics and heating of the solar corona. Transverse (Alfvénic) oscillations of loops commonly occur in response to solar eruptions and are mostly studied in isolation. However, acoustic coupling has been shown to be readily observable in the form of propagating intensity variations at the loop footpoints. Aims. We extend the modelling of wave coupling between a transverse loop oscillation and slow magnetoacoustic waves in a structured loop to include a lower atmosphere. Methods. We achieve this with combined analytical modelling and fully non-linear MHD simulations. Results. Transverse loop oscillations result in the excitation of propagating slow waves from the top of the transition region and the lower boundary. The rate of excitation for the upward propagating waves at the lower boundary is smaller than for waves at the top of the transition region due to the reduced local sound speed. Additionally, slow waves are found to propagate downwards from the transition region, which reflect at the lower boundary and interfere with the upward propagating waves. Resonances are present in the normal mode analysis but these do not appear in the simulations. Due to the presence of the transition region, additional longitudinal harmonics lead to a narrower slow wave profile. The slow wave field is anti-symmetric in the direction of wave polarisation, which highlights the importance that the loop orientation has on the observability of these waves. The ponderomotive effect must be accounted for when interpreting intensity oscillations. Evidence is found for an additional short-period oscillation, which is likely a hybrid mode.

Numerical investigation of noise suppression and amplification in forced oscillations of single and tandem cylinders in high Reynolds number turbulent flows

The noise generated by a three-dimensional turbulent wake behind an oscillating single or tandem cylinder(s) is studied using detached eddy simulation and the Ffowcs Williams-Hawkings (FW-H) method. This hybrid methodology is validated using some experimental data of a turbulent flow past a single or tandem stationary cylinder(s) and some numerical data (obtained from a direct numerical simulation) of a laminar flow past tandem oscillating cylinders. For an oscillating cylinder at a fixed Reynolds number Re=120,000, the sound energy is suppressed compared to that of a stationary cylinder provided the value of oscillation frequency approaches 57% of the original vortex-shedding frequency of the stationary cylinder. This noise reduction arises from the structural oscillations suppressing the noise generated by the vortex shedding from the stationary cylinder—the additional source of noise stemming from the structural oscillations is too small to compensate for the mechanism responsible for the noise suppression. The noise generated by the cylinder motion includes contributions from the loading and thickness noise, whereas the noise generated by vortex shedding from the stationary cylinder only includes the loading noise. The flow past tandem stationary cylinders exhibits a larger number of spectral peaks in the sound pressure power spectrum and the peaks occur at a lower frequency compared to the flow past a single cylinder. The drag force fluctuations result in the propagation of the sound pressure in the in-line direction, whereas the lift force fluctuations result in the propagation of the sound pressure in the transverse direction. Five different scenarios of stationary and/or oscillating tandem cylinders are studied. The second and third invariants of the velocity gradient tensor are used to visualize the distinct vortex structures in the wake for the five different scenarios of tandem cylinders. A single cylinder oscillating in the transverse direction exhibits a larger sound pressure level (SPL) than the streamwise oscillation of the same cylinder. In contrast, the streamwise (in-line) oscillation of one or the other cylinder in a tandem array results in a larger SPL than the transverse oscillation of one or the other cylinder. Finally, the SPL is more sensitive to the oscillations of the rear (downstream) cylinder than the front (upstream) cylinder.

Asymptotic Study of Longitudinal Velocity Influence and Nonlinear Elastic Characteristics of the Oscillating Moving Beam

Mathematical models of the nonlinear transversal oscillations for a beam moving along its axis have been studied. These models deal with the nonlinearity of body elastic properties and with the influence of physical–mechanical and kinematic parameters on the oscillation amplitude and frequency of the moving one-dimensional nonlinear systems as well. A procedure for studying both cases, non-resonance and resonance oscillation regimes, has been developed. The paper focuses on the influence of the longitudinal velocity, nonlinear elastic material properties, and external periodical perturbations on the dynamical process of beam transversal oscillation. The obtained mathematical model could be applied to describe the oscillation behavior of the different types of pipelines (liquid or gas). The proposed results allow the estimation of the influence of these parameters on the amplitude and frequency of the oscillations. Mathematical analysis realized by asymptotic methods enables the prediction of the resonance phenomena and proposal of a numerical algorithm to plan the most effective operation regime. Applications of this approach in engineering, particularly to construct the corresponding elements of industrial environments and pipelines, are also discussed.

Longitudinal and transverse oscillations of the impact device tool under impulsive loads

The destruction process of the rock by the tool of the impact device occurs with an impulsive load on the tool from the recoil reaction from the side of the rock, not only in the axial, but also in the transverse direction. A model of the tool part of the impact device is considered, which takes into account the transverse and longitudinal tool oscillations. The tool model has the form of a rod for longitudinal loading and a beam of constant cross section for transverse loading. Transverse and longitudinal oscillations of the tool sections are considered independent. When calculating transverse oscillations, the tool is considered as a cantilever beam with a rigid mount at one end. The calculation scheme of longitudinal oscillations is represented by a rod with reduced elastic resistance at the end. Impulsive loads are modeled by the initial velocity distribution on the contact part of the tool. The initial-boundary value problem with wave equations of the second and fourth orders is formulated. The solution of the initial-boundary value problem by the Fourier method, realized in the Mathcad system, is proposed.

Effect of corner radius on flow topology and heat transfer from free oscillating tandem cylinders at low Reynolds number

Flow-induced vibration (FIV) on two tandem cylinders with forced convection is numerically investigated at a constant Re = 150. Elastically mounted cylinder with four different values of corner radii (r* = r/R: r = radius of fillet; R = radius of circle) = 0 (square cylinder), 0.25, 0.75, and 1 (circular cylinder) with two spacing ratio (L/D) = 4 and 2 is studied. Transverse oscillations are generated from the cylinder having non-dimensional mass (m*) = 10. The structural damping coefficient is assigned a zero value with varying reduced velocity Ur=2−10. The two-dimensional incompressible Navier–Stokes and energy equations are solved together with Newton's second law governing the motion of the cylinders. Both cylinders' surfaces are maintained at a higher constant temperature of T*=1, and incoming flow is set to be at T*=0 with Prandtl number (Pr) = 0.7. The effect of r* and L/D is observed on the flow structure and FIV parameters. Flow characteristics at L/D=4 such as steady flow, reattachment, and unsteady flow are examined. A “shift” in vibrational amplitude is noted from r* = 1 and 0.75 to r* = 0 and 0.5, respectively. The downstream cylinder (DC) experiences a hike in vibration amplitude due to the impingement of vortex shedding from the upstream cylinder (UC). r* = 1 has 18.1% higher vibrational amplitude than r* = 0 at their respective lock-in regimes for DC. For L/D=2, vortices from upstream and downstream cylinders interact to form C(2S) and 2S types of vortex shedding. Different regimes, such as single body, reattachment, and co-shedding, have been observed while changing L/D. r* = 0.75 results in 13.3% higher oscillation amplitude as compared to r* = 0.5 for DC. The average Nusselt number (Nuavg) strongly depends on flow topology, corner radius, and vibrational amplitude A/D. At low L/D, heat transfer from the downstream cylinder is plummeted due to rolling of shear layers over the cylinder. There is a significant change in Nuavg due to higher vibration; for example, increase in 10.71% change is observed from Ur=2 to Ur=6 for r*=1 and L/D=4. Corner radii also alter the Nuavg as a decrease in 27.39% from r* = 1 to r* = 0 at Ur=10 and L/D=4 (UC).

Динамика процессов взаимодействия элементов гусеничного движителя при наезде первого опорного катка на неровность

The article focuses on the dynamics of high-speed tracked vehicle caterpillar drive elements and their interaction when moving over unevenness. Such movements are accompanied by the previously insufficiently studied effect of the caterpillar drive free branch capturing by the drive wheel gear rim in its front location, which leads to the destruction of the structural elements of the power unit. The paper presents the results of dynamic wave processes in a caterpillar drive obtained using mathematical modeling. The model, in which the dynamic system is presented as an elastic rod on an inertialess elastic foundation, takes into account the inertial dynamic loads in the caterpillar drive formed by the soil microprofile. It also allows us to analyze with satisfactory accuracy the dynamic excitation process of transverse vibrations in a free branch. The computational and experimental results of studying the dynamic process of free-branch transverse wave oscillations (when the first roller wheel hits an unevenness) demonstrate that due to the significant inertial force influence, the caterpillar oscillations amplitude increases significantly, which increases the likelihood of its capture by the drive wheel gear rim. The free branch transverse oscillations amplitude does not significantly depend on the design parameters. The determining factor is the pretensioning force. When the first track roller hits an unevenness, it is not a controllable value and, in the limiting case, can be reduced to zero. To reduce the likelihood of the drive wheel being caught by the gear rim, it is necessary to introduce an additional track tensioning mechanism and an appropriate control system into the design of the caterpillar mover with the front location of the drive wheels.

Апаратурно-методичний комплекс досліджень петрофізичних властивостей тріщинуватих порід-колекторів вуглеводнів

We have developed the apparatus-methodical complex of laboratory investigations of fractured reservoir rocks of hydrocarbons. Basing on the study of variability of acoustic properties in different-oriented directions for measuring of raw pieces of core, it was possible to develop the apparatus for the express-diagnostics of the inner structure of the rock. The results of analysis of anisotropy of acoustic properties of the core give us the possibility to choose the specimens with abnormal properties on which one can conduct further investigations for determination of the factors of heterogeneity of rocks. Measuring of the velocity of longitudinal and transverse oscillations with recording their wave pictures is conducting in the acoustic bath. The acoustic system is equipped with corresponding adapter for connection to the computer that enables us to keep up the recording of all parameters of measuring. To estimate the permeability of microfractures and the influence of composite taut state upon them we have developed the device for studying radial filtration the results of which allow us to estimate the rock permeability due to the change in the structure and microfractures size depending upon the value and the character of the taut state. To measure deformational-strength parameters the corresponding plant was developed and produced, which was additionally equipped with a meter for the measuring of deformation, that allows to measure the values of contact strength, elasticity module and the boundary of rock strength while one-axis charging. The parameters are determined at arbitrary points of the core cuts, and the velocity of charging is half-automatically regulated at a wide bounds. The device is equipped with the electron controller that allows us not only to measure the value of contact strength, but to conduct observations on a display as to the changes in deformation depending on the charging value in real time and to put down the parameters of investigations into corresponding data base. Obtained characteristic of rocks is not only parametric basis for interpretation of materials of charging, but for the estimation of the changes in volume, type of porous space and permeability, and also for modelling of formation conditions of fractured reservoir, and on the whole, for prediction of zones (plots) where a dense rock with corresponding mechanical parameters should acquire the properties of the collector. The usage of the complex for the studying of fracturing in oil geology allows us to widen the prognosis and discovery of new fields and to improve production and exploitation possibilities of already acting ones.

EFFICACY OF POROUS MEDIA ON FLUID-INDUCED VIBRATION OF A FLUCTUATING CYLINDER

In this research, the numerical simulation of the vibrations caused by the release of the vortex from the surface of the two-degrees-of-freedom circular cylinder, under the elastic support with the porous cover, has been done. The laminar flow around the cylinder is considered and the Reynolds number is &amp;#60; 250. The effect of the porous layer is investigated by considering its different thicknesses. In order to solve continuity and momentum equations for incompressible, unsteady, and two-dimensional flow, the finite volume numerical method based on the SIMPLE algorithm has been used. In addition, to simulate the fluid-structure interaction, the solver of the equations of motion of the rigid body in the flow direction and perpendicular to it is coupled with the computational fluid dynamics solver. The efficacy of the porous coat on the locking zone was investigated by comparing the transverse-longitudinal displacement diagrams and aerodynamic coefficients. The results show that, by adding the porous layer, the amplitude of transverse and longitudinal oscillations, the length of vortices, the drag and lift force are reduced. Up to 97&amp;#37; reduction of transverse vibrations in the porous state has been observed.

Estimation of seismic resistance of multi-storey buildings based on a continuum model

A dynamic continuum plate model of a multi-story building is proposed in the form of a cantilevered orthotropic plate, developed in the framework of Timoshenko’s theory of plates, which describes seismic vibrations of buildings. Formulas are given for determining the reduced moduli of elasticity, shear, and density of a plate model of a building. Transverse natural and forced oscillations of a nine-story building under nine-point seismic impacts are considered. Numerical results are obtained.

Effect of the composition of multicomponent powders on the mechanical and tribotechnical properties of coatings obtained by laser additive technologies

The paper presents the results of metallographic studies and tribotechnical tests of samples of medium-carbon steel 34KhNi3MoA and coatings obtained by laser surfacing of a powder multicomponent charge based on iron and cobalt in a ratio of 3:1 with additives of nano particles of tantalum carbide. The samples were processed with a circular defocused beam and with transverse beam oscillations normal to the scanning speed. Comparative tests for friction and wear were carried out in a pair with a hardened 40Kh steel counterplate. The load and sliding speed during the tests varied discretely. Turbine oil TP 22C was used as a lubricant. It is shown that the introduction of additives of nano-tantalum carbide into the charge reduces friction losses, increases the wear resistance of coatings compared to the charge without carbides and the base material. The wear resistance of coatings with an increase in the amount of the hardening phase increases compared to the original steel. It has been established that the technology of laser surfacing with multicomponent coatings with nano particles of tantalum carbide can be used to restore worn surfaces of shaft necks, turbine blades, thrust discs, shut-off valves and other parts operating at high temperatures and in corrosive environments.

Seismic stress state of a high earth dam using the spectroscopic method

The reliable and safe operation of earth dams located in seismic regions of the Republic of Uzbekistan requires engineers and researchers to constantly improve the design normative methods for their calculation in order to identify safety margins and stability under various types of loads. A method is proposed for calculating the seismic stress state of an earth dam (on the example of the Pskem HPP being designed), based on the spectral method, in accordance with the current standards for the design of hydro-technical structures in seismic areas. Structural and piecewise non-homogeneous physical and mechanical characteristics of soils of the structure body were provided by Hydroproject JSC of the Republic of Uzbekistan. The results of the calculations show that under a horizontal seismic impact, the dam performs transverse oscillations. It was determined that the maximum vertical stresses are observed in the lower part of the upper slope, where the maximum hydrostatic pressure is reached. The maximum shear stresses appear at the base of the dam and on the surface of the downstream slope, where the risk of loss of strength under shear is greater..

Transverse vibrations of underground pipeline with pinched ends

The study of transverse oscillations of extended underground structures from the action of constant harmonic forces is of practical interest. Transverse vibrations of an underground cylindrical structure of finite length under the action of a system of concentrated forces that change according to a harmonic law are considered. The environment surrounding the structure is assumed to be elastic, while the interaction of the “environment-structure” system is studied. When considering the problem, the Fourier method and the results of solving the problem of vibrations of an unbounded cylindrical structure in an elastic medium from the action of concentrated harmonic forces were used. The problem of transverse vibrations of a cylindrical rod of finite length interacting with an elastic homogeneous medium is solved by the method of compensating loads. In this case, the structure is considered a source of waves radiated into space and satisfying the conditions of radiation to infinity. The resulting solution is approximate and reliable within the length of the rod. The analysis of the influence of soil conditions and geometric dimensions on the amplitude of oscillations of an underground structure was carried out according to the graphs of the amplitude-frequency characteristic of the object.

Modeling and mitigation of long-range wakefields for advanced linear colliders

The luminosity requirements of TeV-class linear colliders demand use of intense charged beams at high repetition rates. Such features imply multi-bunch operation with long current trains accelerated over the km length scale. Consequently, particle beams are exposed to the mutual parasitic interaction due to the long-range wakefields excited by the leading bunches in the accelerating structures. Such perturbations to the motion induce transverse oscillations of the bunches, potentially leading to instabilities such as transverse beam break-up. Here we present a dedicated tracking code that studies the effects of long-range transverse wakefield interaction among different bunches in linear accelerators. Being described by means of an efficient matrix formalism, such effects can be included while preserving short computational times. As a reference case, we use our code to investigate the performance of a state-of-the-art linear collider currently under design and, in addition, we discuss possible mitigation techniques based on frequency detuning and damping.

Effects of recess ratio on combustion characteristics of LOX/methane swirl coaxial injectors

To explore the effects of recess ratio on the flame spatial structure and combustion efficiency of LOX/methane swirl coaxial injectors, visual combustion experiments with injectors featuring varied recess ratios were carried out based on an optically accessible combustor. The instantaneous spray and flame images were obtained using the red background light imaging technique. Liquid oxygen was tangentially injected into the center post of the injector at a temperature of 121.5 K, while gaseous methane was axially introduced into the coaxial annulus at a temperature of 290.5 K. With the recess ratio increasing from 0 to 0.83, the flame transforms from a steady state to an oscillating state at the frequency of 3144 Hz to 3281 Hz. A strong relationship between flame length and combustion efficiency is identified firstly. The combustion efficiency of stable flame is higher than that of the oscillating flame. There is a specific recess ratio between 0.33 and 0.54, corresponding to the maximum combustion efficiency, which causes the transition of the flame from a steady state to an oscillating state simultaneously. The combustion efficiency of the injector critical recess ratio (RR = 0.73) is the lowest. Both the spray and flame without recess appear to exhibit axial and transverse coupled oscillation. The transverse oscillation of spray and flame is gradually suppressed with larger recess ratio. As opposed to the oscillation region area, the amplitude of spray oscillation may be the main influence factor of flame oscillation scale. In addition, the relationship between self-pulsation, flame oscillation and combustion instability has been further verified.