Convection Velocity Research Articles

A physics-informed neural network based simulation tool for reacting flow with multicomponent reactants

The reacting flow involves nonlinear partial differential equations which are mostly solved numerically for autocatalytic reaction between multi reactants. One-dimensional convection-diffusion-reaction equations are widely used for modeling reacting flows. This paper developed a method to solve the convection-diffusion-reaction equations using a neural network model, called the physics-informed neural network. It was applied to solve the nonlinear reacting flow for forward as well as inverse problems. To enhance accuracy and to eliminate non-physical oscillations, a derivative constraint of the spatial dimension was employed. In order to avoid the slow training speed caused by the derivative constraint, a new neural network connection structure is proposed. For validation, three different forward reacting flow problems involving steep fronts were analyzed, including the convection reaction, and steady and unsteady convection-diffusion-reaction systems. For the inverse problem, except for the kinetic parameters, the unknown convection velocity and diffusion coefficients were correctly predicted, demonstrating the capability of the proposed method for identifying reacting flow parameters. Moreover, under the guidance of the improved algorithm, the sensitivity of the reacting flow to certain kinetic parameter was investigated.

On the energetics of a tidally oscillating convective flow

ABSTRACT This paper examines the energetics of a convective flow subject to an oscillation with a period $t_{\rm osc}$ much smaller than the convective time-scale $t_{\rm conv}$, allowing for compressibility and uniform rotation. We show that the energy of the oscillation is exchanged with the kinetic energy of the convective flow at a rate $D_R$ that couples the Reynolds stress of the oscillation with the convective velocity gradient. For the equilibrium tide and inertial waves, this is the only energy exchange term, whereas for p modes there are also exchanges with the potential and internal energy of the convective flow. Locally, $\left| D_R \right| \sim u^{\prime 2} / t_{\rm conv}$, where $u^{\prime}$ is the oscillating velocity. If $t_{\rm conv} \ll t_{\rm osc}$ and assuming mixing length theory, $\left| D_R \right|$ is $\left( \lambda_{\rm conv} / \lambda_{\rm osc} \right)^2$ smaller, where $\lambda_{\rm conv}$ and $\lambda_{\rm osc}$ are the characteristic scales of convection and the oscillation. Assuming local dissipation, we show that the equilibrium tide lags behind the tidal potential by a phase $\delta(r) \sim r \omega_{\rm osc} / \left( g(r) t_{\rm conv}(r) \right)$, where g is the gravitational acceleration. The equilibrium tide can be described locally as a harmonic oscillator with natural frequency $\left( g/r \right)^{1/2}$ and subject to a damping force $-u^{\prime}/t_{\rm conv}$. Although $\delta(r)$ varies by orders of magnitude through the flow, it is possible to define an average phase shift $\overline{\delta }$ which is in good agreement with observations for Jupiter and some of the moons of Saturn. Finally, $1 / \overline{\delta }$ is shown to be equal to the standard tidal dissipation factor.

On wall pressure fluctuations in conical shock wave/turbulent boundary layer interaction

The structure and the frequency spectra of wall pressure fluctuations beneath a planar turbulent boundary layer interacting with a conical shock wave at Mach number $M_\infty =2.05$ and Reynolds number $\textit {Re}_\theta \approx 630$ (based on the upstream boundary layer momentum thickness) are examined to elucidate the effects of pressure gradient and flow separation on the characteristics of the wall pressure fluctuations, by exploiting a direct numerical simulation database. Upstream of the interaction, in the zero pressure gradient region, wall pressure statistics compare well with canonical compressible boundary layers in terms of fluctuation intensities and frequency spectra. Across the main interaction zone (APG1), the root-mean-square of wall pressure fluctuations becomes very large (corresponding to approximately 173.3 dB), with maximum increase approximately 12.7 dB from the incoming level. In the second adverse pressure gradient zone (APG2), the root-mean-square of wall pressure fluctuations attains a second peak (corresponding to $164.7$ dB), with an increase of 8.4 dB from the upstream level. Both the APG1 and APG2 regions feature a substantial fraction of flow reversal events, which are, however, scattered and interspersed with regions of attached flow. The wall pressure power spectral density exhibits a broadband and energetic low-frequency component associated with the global unsteadiness of the separation bubble/conical shock system. Analysis of the two-point correlations and wavenumber/frequency spectra of wall pressure fluctuations further suggests that the typical eddies become more elongated along the spanwise direction, as the flow in the separated region tends to escape the centreline, and the convection velocity is significantly reduced.

Effect of Monodisperse Coal Particles on the Maximum Drop Spreading after Impact on a Solid Wall

The effect of coal hydrophilic particles in water-glycerol drops on the maximum diameter of spreading along a hydrophobic solid surface is experimentally studied by analyzing the velocity of internal flows by Particle Image Velocimetry (PIV). The grinding fineness of coal particles was 45–80 μm and 120–140 μm. Their concentration was 0.06 wt.% and 1 wt.%. The impact of particle-laden drops on a solid surface occurred at Weber numbers (We) from 30 to 120. It revealed the interrelated influence of We and the concentration of coal particles on changes in the maximum absolute velocity of internal flows in a drop within the kinetic and spreading phases of the drop-wall impact. It is explored the behavior of internal convective flows in the longitudinal section of a drop parallel to the plane of the solid wall. The kinetic energy of the translational motion of coal particles in a spreading drop compensates for the energy expended by the drop on sliding friction along the wall. At We = 120, the inertia-driven spreading of the particle-laden drop is mainly determined by the dynamics of the deformable Taylor rim. An increase in We contributes to more noticeable differences in the convection velocities in spreading drops. When the drop spreading diameter rises at the maximum velocity of internal flows, a growth of the maximum spreading diameter occurs. The presence of coal particles causes a general tendency to reduce drop spreading.

Continuous counter-current electrophoretic separation of oleosomes and proteins from oilseeds

Oilseeds, with their high content of oil and protein, will play an important role in the transition to plant based foods. Currently, seed oil extraction involves elevated temperatures and the use of organic solvents, which degrade the quality of both oils and proteins. To take full advantage of the oilseeds, a gentler process is needed. We here propose a mild alkaline extraction followed by a continuous electrophoretic separation process that is based on differences in electrophoretic mobility and recovers intact oleosomes and proteins from the seeds. Rapeseed oleosomes and proteins are both negatively charged at pH ≥ 5, yet exhibit significantly different electrophoretic mobility. Therefore, separation can be achieved by imposing a counter-current hydrodynamic flow rate between their electrophoresis rate. Thus, the compounds with higher mobility, oleosomes, are retained by the electric field, and the compounds with lower mobility, proteins, go along with the flow. The separation was modeled using the Nernst-Planck equation and demonstrated using a PDMS-based microfluidic system. Both the modeling and the experimental studies confirmed that the direction and rate of migration of the compounds can be steered by the electric field strength and the convective flow velocity. The proposed electrophoretic approach is feasible and scaleable, and may be a novel path to separate differently charged components under mild conditions, thereby preserving their original native properties.

Tidal dissipation due to the elliptical instability and turbulent viscosity in convection zones in rotating giant planets and stars

ABSTRACT Tidal dissipation in star–planet systems can occur through various mechanisms, among which is the elliptical instability. This acts on elliptically deformed equilibrium tidal flows in rotating fluid planets and stars, and excites inertial waves in convective regions if the dimensionless tidal amplitude (ϵ) is sufficiently large. We study its interaction with turbulent convection, and attempt to constrain the contributions of both elliptical instability and convection to tidal dissipation. For this, we perform an extensive suite of Cartesian hydrodynamical simulations of rotating Rayleigh–Bénard convection in a small patch of a planet. We find that tidal dissipation resulting from the elliptical instability, when it operates, is consistent with ϵ3, as in prior simulations without convection. Convective motions also act as an effective viscosity on large-scale tidal flows, resulting in continuous tidal dissipation (scaling as ϵ2). We derive scaling laws for the effective viscosity using (rotating) mixing-length theory, and find that they predict the turbulent quantities found in our simulations very well. In addition, we examine the reduction of the effective viscosity for fast tides, which we observe to scale with tidal frequency (ω) as ω−2. We evaluate our scaling laws using interior models of Hot Jupiters computed with mesa. We conclude that rotation reduces convective length-scales, velocities, and effective viscosities (though not in the fast tides regime). We estimate that elliptical instability is efficient for the shortest period Hot Jupiters, and that effective viscosity of turbulent convection is negligible in giant planets compared with inertial waves.

Turbulence-supported Massive Star Envelopes

The outer envelopes of massive (M ≳ 10 M ⊙) stars exhibit large increases in opacities from forests of lines and ionization transitions (particularly from iron and helium) that trigger near-surface convection zones. One-dimensional (1D) models predict density inversions and supersonic motions that must be resolved with computationally intensive three-dimensional (3D) radiation hydrodynamic (RHD) modeling. Only in the last decade have computational tools advanced to the point where ab initio 3D models of these turbulent envelopes can be calculated, enabling us to present five 3D RHD Athena++ models (four previously published and one new 13 M ⊙ model). When convective motions are subsonic, we find excellent agreement between 3D and 1D velocity magnitudes, stellar structure, and photospheric quantities. However, when convective velocities approach the sound speed, hydrostatic balance fails as the turbulent pressure can account for 80% of the force balance. As predicted by Henyey, we show that this additional pressure support leads to a modified temperature gradient, which reduces the superadiabaticity where convection is occurring. In addition, all five models display significant overshooting from the convection in the Fe convection zone. As a result, the turbulent velocities at the surface are indicative of those in the Fe zone. There are no confined convection zones as seen in 1D models. In particular, helium convection zones seen in 1D models are significantly modified. Stochastic low-frequency brightness variability is also present in the 13 M ⊙ model with comparable amplitude and characteristic frequency to observed stars.

A Model of High Latitude Ionospheric Convection Derived From SuperDARN EOF Model Data

AbstractForecasting of the effects of thermospheric drag on satellites will be improved significantly with better modeling of space weather effects on the high‐latitude ionosphere, in particular the Joule heating arising from electric field variability. We use a regression analysis to build a model of the ionospheric convection drift velocity which is driven by relatively few solar and solar wind variables. The model is developed using a solar cycle's worth (1997–2008 inclusive) of 5‐min resolution Empirical Orthogonal Function (EOF) patterns derived from Super Dual Auroral Radar Network (SuperDARN) line‐of‐sight observations of the convection velocity across the high‐latitude northern hemisphere ionosphere. At key stages of development of the model, we use the percentage of explained variance P to see how well the model reproduces the EOF data. The final model is driven by four variables: (a) the interplanetary magnetic field component By, (b) the solar wind coupling parameter epsilon ε, (c) a trigonometric function of day‐of‐year, and (d) the monthly F10.7 index. The model can reproduce the EOF velocities with a characteristic P = 0.7. The model and EOF data compare best around the solar maximum of 2001. is lower around solar minimum, due to occasional limitations in the geographical and temporal coverage of the SuperDARN measurements. This may indicate the need to modify our model around the minimum of the solar cycle. Our model has the potential to be used to forecast the ionospheric electric field using the real‐time solar wind data available from spacecraft located upstream of the Earth.

Near-field flow characteristics of a free coaxial jet

Detailed planar PIV measurements are reported of the flow field in the near-field of a free coaxial air jet. Measurements were performed at outer to inner jet velocity ratios of ru(=Uo/Ui)=∞, 2, 1, and 0.5, while keeping Uo constant. Mean velocity distributions and turbulent stress distributions compared well to those reported in the literature at similar ru. The spatial organization of the generated vortices, analyzed based on the instantaneous vorticity and swirling strength distributions, revealed distinct spatial wavelengths. Associated Strouhal numbers (assuming vortex convection velocities) were higher than those reported in the literature for different nozzle geometries. Our results point at the importance of the nozzle geometry and associated flow exit conditions on the vortex generation frequency. In addition, for the present nozzle geometry and jet exit flow conditions, the outer and inner jet are strongly coupled.

A numerical investigation of hydrogen impingement-effusion array jet for a heat sink cooling using solid/porous fins: A thermo-hydrodynamic analysis

Increasing the aim of hydrogen use as fuel in vehicles motivates applying it to other critical requirements, such as cooling, owing to its thermal properties. Therefore, the effect of applying hydrogen impingement jets for cooling a hot surface of electrical devices, such as a prismatic battery, is investigated in this numerical study. The dependent variables are the volumetric flow rate, the jet distance from the target to the jet diameter, the coolant type, and the fins configuration, called in-line and staggered, and types, as solid or porous. The convective heat transfer coefficient, thermal resistance, pressure drop, and temperature and velocity distribution for the studied cases are considered. The simulation is conducted using the SST k-ω turbulence model, SIMPLE algorithm, and second-order method for discretization differential equations. Applying hydrogen as the coolant decreases the maximum temperature up to 2% and increases heat transfer by about 10%, while it mitigates the pressure drop by a factor of 1/12 if compared to air coolant. Further, inserting porous fins improves heat transfer by about 10% and 17%, respectively for air and hydrogen coolant in comparison with the case without fins. The fin decreases the temperature on the root and makes the recirculation zones.

Combined Experimental and Numerical Investigation of a Hypersonic Turbulent Boundary Layer by Means of FLDI and Large-Eddy Simulations

This work investigates a hypersonic turbulent boundary layer over a 7° half angle cone at a wall-to-total temperature ratio of 0.1, M∞=7.4 and Re∞m=4.2×106 m−1, in terms of density fluctuations and the convection velocity of density disturbances. Experimental shock tunnel data are collected using a multi-foci Focused Laser Differential Interferometer (FLDI) to probe the boundary layer at several heights. In addition, a high-fidelity, time-resolved Large-Eddy Simulation (LES) of the conical flowfield under the experimentally observed free stream conditions is conducted. The experimentally measured convection velocity of density disturbances is found to follow literature data of pressure disturbances. The spectral distributions evidence the presence of regions with well-defined power laws that are present in pressure spectra. A framework to combine numerical and experimental observations without requiring complex FLDI post-processing strategies is explored using a computational FLDI (cFLDI) on the numerical solution for direct comparisons. Frequency bounds of 160 kHz <f<1 MHz are evaluated in consideration of the constraining conditions of both experimental and numerical data. Within these limits, the direct comparisons yield good agreement. Furthermore, it is verified that in the present case, the cFLDI algorithm may be replaced with a simple line integral on the numerical solution.

Thermal behavior of CMC solutions under simulation of radio frequency pasteurization

Pasteurization and enzyme-inactivation are an economical and convenient way to provide safety and shelf-life stability. However, long heating time and non-uniform temperature distribution are the main issues of traditional thermal processing for enzyme-inactivation. Because of the volumetric heating and high heating rate, radio frequency (RF) treatment is considered as one of the most promising physical enzyme-inactivating methods. A 6 kW, 27.12 MHz RF heating system was applied to explore the effect of cylindrical container dimension and solution concentration on the thermal behavior of high-viscosity liquid food. Carboxymethylcellulose (CMC) solution as a non-Newtonian fluid was selected as a model liquid food in this study. The target temperature for enzyme inactivation was 70 °C. The experimental results showed that the electrode gap, container length, and container diameter affected the heating rate and uniformity of the liquid food. Furthermore, when the concentration of CMC solution increased from 0.5% to 2.0%, the heating rate of the solution firstly increased and then decreased, while the heating uniformity index of the solution increased from 0.008 ± 0.001 to 0.056 ± 0.002. The simulation results showed that the higher electric field strength led to a higher heating rate, temperature, and velocity of natural convection of the solution at the ends of the container. Then, the recirculation zones from the ends to the center of the container were formed, which was diminished with the increasing concentration solution, resulting in the increased maximum temperature difference of solution. The results of this research may provide useful data for subsequent continuous flow studies and information on potential RF enzyme-inactivation in high-viscosity liquid foods.

Relaxation Fluidic Oscillators: Design Parameters, New Operating Modes, and Characteristics of Their Internal and External Flows

AbstractFluidic oscillators are no-moving-part actuators that can be used to produce pulsating jets. The characteristics of these devices and of the flow fields they produce are of particular interest in the field of heat transfer, as pulsating impinging jets have been shown to improve heat transfer compared to steady jets. In this study, special focus is given to these characteristics as a preparation for a subsequent thermal study that will evaluate the performance of these pulsed jets against steady jets. The functioning of the device in response to different operating and design parameters is first considered. It was shown that a transition between different operating modes is possible, depending on both the inlet mass flowrate and the width of the feedback channel of the device. This was followed by a study of the velocity fields of the pulsed jets produced by the device. More specifically, attention is given to the developing characteristics and flow structures of the pulsating free jets of air which are then compared to equivalent steady jets. Finally, by taking advantage of the periodic aspect of the flow, the phase-averaged velocity field was reconstructed. Vortex dipoles were detected, tracked and their convection velocity computed from the same data and compared to a theoretical value from the literature. A proper orthogonal decomposition (POD) of the synchronized raw data was then performed to further highlight the presence of these vortex structures and other flow instabilities.

Rotation Reduces Convective Mixing in Jupiter and Other Gas Giants

Recent measurements of Jupiter’s gravitational moments by the Juno spacecraft and seismology of Saturn’s rings suggest that the primordial composition gradients in the deep interior of these planets have persisted since their formation. One possible explanation is the presence of a double-diffusive staircase below the planet’s outer convection zone, which inhibits mixing across the deeper layers. However, hydrodynamic simulations have shown that these staircases are not long-lasting and can be disrupted by overshooting convection. In this Letter, we suggests that planetary rotation could be another factor for the longevity of primordial composition gradients. Using rotational mixing-length theory and 3D hydrodynamic simulations, we demonstrate that rotation significantly reduces both the convective velocity and the mixing of primordial composition gradients. In particular, for Jovian conditions at t ∼ 108 yr after formation, rotation reduces the convective velocity by a factor of 6, and in turn, the kinetic energy flux available for mixing gets reduced by a factor of 63 ∼ 200. This leads to an entrainment timescale that is more than 2 orders of magnitude longer than without rotation. We encourage future hydrodynamic models of Jupiter and other gas giants to include rapid rotation because the decrease in the mixing efficiency could explain why Jupiter and Saturn are not fully mixed.

A numerical solver for investigating the space charge effect on theelectric field in liquid argon time projection chambers

This paper reports the development of a numerical solver aimed to simulate the interaction between the space charge (i.e. ions) distribution and the electric field in liquid argon time projection chamber (LArTPC) detectors. The ion transport equation is solved by a time-accurate, cell-centered finite volume method and the electric potential equation by a continuous finite element method. The electric potential equation updates the electric field which provides the drift velocity to the ion transport equation. The ion transport equation updates the space charge density distribution which appears as the source term in the electric potential equation. The interaction between the space charge distribution and the electric field is numerically simulated within each physical time step. The convective velocity in the ion transport equation can include the background flow velocity in addition to the electric drift velocity. The numerical solver has been parallelized using the Message Passing Interface (MPI) library. Numerical tests show and verify the capability and accuracy of the current numerical solver. It is planned that the developed numerical solver, together with a Computational Fluid Dynamics (CFD) package which provides the flow velocity field, can be used to investigate the space charge effect on the electric field in large-scale particle detectors.

Heat Transport and Convective Velocities in Compositionally Driven Convection in Neutron Star and White Dwarf Interiors

We investigate heat transport associated with compositionally driven convection driven by crystallization at the ocean–crust interface in accreting neutron stars, or growth of the solid core in cooling white dwarfs. We study the effect of thermal diffusion and rapid rotation on the convective heat transport, using both mixing length theory and numerical simulations of Boussinesq convection. We determine the heat flux, composition gradient, and Péclet number, Pe (the ratio of thermal diffusion time to convective turnover time) as a function of the composition flux. We find two regimes of convection with a rapid transition between them as the composition flux increases. At small Pe, the ratio between the heat flux and composition flux is independent of Pe, because the loss of heat from convecting fluid elements due to thermal diffusion is offset by the smaller composition gradient needed to overcome the reduced thermal buoyancy. At large Pe, the temperature gradient approaches the adiabatic gradient, saturating the heat flux. We discuss the implications for cooling of neutron stars and white dwarfs. Convection in neutron stars spans both regimes. We find rapid mixing of neutron star oceans, with a convective turnover time of the order of weeks to minutes depending on rotation. Except during the early stages of core crystallization, white dwarf convection is in the thermal-diffusion-dominated fingering regime. We find convective velocities much smaller than recent estimates for crystallization-driven dynamos. The small fraction of energy carried as kinetic energy calls into question the effectiveness of crystallization-driven dynamos as an explanation for observed magnetic fields in white dwarfs.

Aerodynamic noise reduction of a blunt flat plate by trailing-edge blowing

This study investigates the influence of air blowing on the aerodynamic noise generated by a flat plate with a blunt trailing edge. The uniform blowing was applied through evenly spaced holes along the span at the base of the flat plate. Acoustic pressure measurements were conducted in an anechoic wind tunnel using a free-field microphone at Reynolds numbers ranging from 2.8×105 to 6.5×105. Particle image velocimetry measurements were performed to obtain time-resolved evolution and statistics of the flow velocity field, providing a detailed understanding of the noise reduction mechanisms. The results demonstrated that air blowing effectively reduces both the amplitude and bandwidth of tonal and broadband noise within a limited frequency range. This phenomenon was attributed to the stabilization of separated shear layers over a longer distance by air blowing and a decrease in turbulent kinetic energy in the near-wake region. It was shown that air blowing suppresses the tonal peak of vertical velocity fluctuations and narrows the wake width, which accounts for the increase of vortex shedding frequency and a potential drag reduction. Generally, the effects of air blowing on vortex shedding at the blunt trailing edge are analogous to those of a splitter plate. The unaffected convective velocity of the large-scale vortex structures and the enhanced spanwise coherence in the vortex formation region provide further evidence to this analogy.

Flow field characteristics of a 127-pin rod bundle with hexagonal spacer grids

A determination of nominal flow phenomena in liquid metal fast reactor (LMFR) fuel assemblies is critical toward generation-IV reactor development. Axially positioned spacer grids are used to maintain the geometry of hexagonal rod bundles and simultaneously introduce perturbations in the flow. Three-dimensional (3D) printed asymmetric honeycomb spacer grids were installed in a prototypical 127-pin LMFR fuel assembly model to study complex fluid dynamics interactions induced by the spacer grid and rods. To characterize flow dynamics in this intricate geometry, time-resolved particle image velocimetry (TR-PIV) using the matched-index-of-refraction method was employed to obtain non-intrusive velocity measurements for three axial planes (one near-wall and two interior planes) at a Reynolds number of 6000. The statistical TR-PIV results compared sub-channel-dependent normalized time-averaged velocity, velocity fluctuations, Reynolds stress, vorticity, and turbulence kinetic energy distributions. TR-PIV line profiles characterized downstream spacer grid flow dynamics. Two-point spatial and spatial–temporal cross-correlation fields revealed local coherent structures and quantified convection velocities of traveling vortices. Spatial–temporal decomposition using dynamic mode decomposition (DMD) applied to the near-wall vorticity fields extracted turbulent structures and flow instabilities in the wake region of the spacer grid, along with their decay and frequency rates. Reduced-order velocity fields from DMD reconstructions identified the most energy-containing coherent structures persistent in the near-wall region. This research provides experimental data sets and analyses of flow behavior in rod bundles with hexagonal spacer grids. The results are critical toward LMFR design and geometry optimization, crucial for the validation of computational fluid dynamics and reduced-order flow models.

Analysis of CO2 Migration in Horizontal Saline Aquifers during Carbon Capture and Storage Process

The storage of CO2 has become an important worldwide problem, considering that an excess of CO2 in the Earth’s atmosphere causes dramatic changes in its climate. One possible solution is to remove the excess of CO2 from the atmosphere, capture it in the process of creation, and store it safely, negating the possibility of its return into the atmosphere. This is the process of Carbon Capture and Storage (CCS). In the following paper, the authors investigate horizontal saline aquifers and their ability to store CO2. The authors’ application of sensitivity analysis on horizontal migrations uncovered that CO2 permeability and aquifer porosity have a considerable impact on horizontal migrations. During the migration process, CO2 can reach tens of kilometers from its injection point. By introducing effective CO2 density to the conduction velocity term, the authors showcase that the convection-diffusion equation for compressible fluids can be replaced with the equation for incompressible fluids. The buoyancy factor in convective velocity is as density dependent as in conduction velocity. By means of introducing an effective density to the aforementioned term, the process of transport via variable convective velocity can be substituted for a process which is effective, constant, and not density dependent.

Periodic large-scale structural characteristics of two-phase flow in tight lattice bundles

This paper investigated the two-phase flow characteristics in a double sub-channel tight lattice (P/D = 1.06). Compared to the prototype, the test channel was magnified by 2.7 times. A self-developed 16 × 32 wire-mesh sensor was utilized to measure the phase distribution at two fully developed positions of the test channel (Z/Dh = 86.86, 115.8). The flow conditions are 0.036 m/s < jg < 1.04 m/s and 0.93 m/s < jl <1.86 m/s at Z/Dh = 115.8, including the bubbly flow (B), the cap-bubbly flow (CB), and the slug flow (S). Combined with the pseudo-side view of the flow pattern and the power spectrum, the coherent structure of the gas phase under the bubbly flow and the cap-bubbly flow was confirmed. For the bubbly flow, the coherent structure is in the form of bubble clusters consisting of discrete bubbles. These bubble clusters are staggered on both sides of the gap but do not traverse across the gap, which is speculated to be caused by the large-scale vortex of the liquid flow field. For the cap-bubbly flow, the coherent structure is in the form of cap-shaped bubbles. In this study, the cap-shaped bubbles are confined in the center of the subchannels and staggered in adjacent subchannels, which is attributed to the compact arrangement of rod bundles and the inter-subchannel liquid cross-flow caused by the cap-shaped bubbles. The characteristic parameters, including the pulsation frequency f, convection velocity v, wavelength λ, and amplitude A were defined to characterize the coherent structure. Data analysis results show that the coherent structure frequency under the bubbly flow increases with the increase of the liquid-phase velocity and the coherent structure frequency under the cap-bubbly flow increases with the increase of the gas-phase velocity. In addition, the coherent structure is suppressed under three flow conditions, including the bubbly flow with low liquid velocity (jl < 1.3 m/s), the B-CB transition, and the slug flow.