Flow Field Structure Research Articles

Numerical study on transient coke deposition and heat transfer characteristics of hydrocarbon fuel in a mini-channel under varying wall heat flux

Dynamic coke deposition has significant influence on flow and heat transfer characteristics of regenerative cooling using hydrocarbon fuel. In the present work, the effect of coke deposition on flow and heat transfer performance of hydrocarbon fuel, n-Decane is numerically investigated under different heating modes including the constant heat flux (CHF), the periodic heat flux (PHF) and staged heat flux (SHF). The results show that as the heating mode varies from CHF to SHF, locally high temperature zones are formed. The flow field structure is varied by dynamic heating condition and coke deposition. The reaction rate of n-Decane also varies periodically with heat flux, resulting in an irregular “S” shaped density distribution. The two main coke precursors i.e., propylene and aromatics are highly sensitive to temperature due to secondary reactions. The thickness of coke deposition increases significantly with time regardless of the heating modes, which indicates that coke deposition process is irreversible. Compared with CHF heating mode, the thickness of coke deposition increases by nearly 25% for the SHF heating mode. Coking mechanism undergoes transition from catalytic coke to lateral coke with increasing temperature. For the CHF heating mode, the heat transfer coefficient increases from 1200 W/(m2·K) to 4400 W/(m2·K) along the flow direction. The PHF and SHF heating modes render higher Nusselt number and heat transfer coefficient than the CHF heating mode as the periodically varying wall heat flux results in locally higher heat flux and smaller temperature difference between the fluid and solid zones. In addition, the thermal conductivity and flow velocity in the regenerative cooling channel are also enhanced for the PHF and SHF heating modes. However, coke deposition leads to serious heat transfer deterioration for PHF and SHF with a decrease of up to 13% in heat transfer coefficient adjacent to the outlet section of the cooling channel. The new heat transfer correlation considering chemical reaction and coke deposition effects of supercritical hydrocarbon fuel is established for different wall heating conditions.

Enhanced photoelectrochemical water splitting via 3D flow field structure: Unveiling the decisive role of interfacial mass transfer

The efficiency of photoelectrochemical water splitting is not only related to the electrode material, but also influenced by the mass transport at the electrode surface. Here, we design a novel photoelectrochemical water splitting reactor, which generates a turbulent flow (0–145 mL/min) at the electrode/electrolyte interface. It was revealed that the reactor has a significant effect on the electrolyte flow, and the flow rate on the photocurrent density was more significant during the transition period of the flow state and the high flow rate. The 3D flow field structure improved the water splitting reaction of TiO2 photoelectrode by 130% at the flow rate of 130 mL/min, and consequently, the TiO2 exhibited a photocurrent density of 0.142 mA·cm−2 at 1.23 V versus the reversible hydrogen electrode. Then we changed the temperature (20–90 °C) of the electrolyte, and electrochemical impedance spectra results indicated that the ion transport impedance decreased with increasing electrolyte temperature in the experimental range. The photocurrent density increased by about 2.2 times at 90 °C compared to that at 20 °C. This work provided insights of the structure design on the photoelectrode/electrolyte interface in solar water splitting and revealed the non-negligible effect of interfacial mass transport in photoelectrochemical performance.

Large eddy simulation of non-premixed flame behavior and NOx emission characteristics in a staged combustor with multi-swirling flows

This study utilizes Large Eddy Simulation (LES) to investigate flame characteristics and NOx emission generation in a concentric staged combustor with three distinct pilot swirler arrangements. We examine the effects of multi-swirling flow on the instantaneous flow field and flame characteristics using the Proper Orthogonal Decomposition (POD) method, and assess how variations in swirler structures influence thermoacoustic instability. Furthermore, a comparison of NOx emissions between two pilot swirler configurations, with similar mean flow field and flame characteristics, highlights the precessing vortex core's role in NOx emissions. Compared to a single-swirler setup, a double-swirler configuration produces a more distinct single precessing vortex core, thereby amplifying thermoacoustic instability. The extended venturi structure in the double-swirler setup mitigates the development of the swirl-induced vortex core, reducing thermoacoustic instability. However, the expansion section in this setup impedes initial fuel and air mixing, leading to an extended flame length, which in turn results in higher NOx emissions due to a more concentrated temperature distribution. With similar mean flow field and flame structure, the double-swirler combustor proves more effective in reducing NO emissions than the triple-swirler combustor.

Swirl-induced motion prediction with physics-guided machine learning utilizing spatiotemporal flow field structure

PurposeHigher energy conversion efficiency of internal combustion engine can be achieved with optimal control of unsteady in-cylinder flow fields inside a direct-injection (DI) engine. However, it remains a daunting task to predict the nonlinear and transient in-cylinder flow motion because they are highly complex which change both in space and time. Recently, machine learning methods have demonstrated great promises to infer relatively simple temporal flow field development. This paper aims to feature a physics-guided machine learning approach to realize high accuracy and generalization prediction for complex swirl-induced flow field motions.Design/methodology/approachTo achieve high-fidelity time-series prediction of unsteady engine flow fields, this work features an automated machine learning framework with the following objectives: (1) The spatiotemporal physical constraint of the flow field structure is transferred to machine learning structure. (2) The ML inputs and targets are efficiently designed that ensure high model convergence with limited sets of experiments. (3) The prediction results are optimized by ensemble learning mechanism within the automated machine learning framework.FindingsThe proposed data-driven framework is proven effective in different time periods and different extent of unsteadiness of the flow dynamics, and the predicted flow fields are highly similar to the target field under various complex flow patterns. Among the described framework designs, the utilization of spatial flow field structure is the featured improvement to the time-series flow field prediction process.Originality/valueThe proposed flow field prediction framework could be generalized to different crank angle periods, cycles and swirl ratio conditions, which could greatly promote real-time flow control and reduce experiments on in-cylinder flow field measurement and diagnostics.

The swirl and pyrolysis reaction synergistically enhance solid-solid heat transfer and product separation in cyclone pyrolyzer

Cyclone pyrolyzer is a novel type of downer that combines centrifugal force field and double-layer cyclone vortex. Research on transfer behavior is helpful to optimize the pyrolyzer to meet the needs of pyrolysis. In this study, the Computational Particle Fluid Dynamics (CPFD) model is used to analyze the transfer behavior of binary particles, and finds that the swirl and reaction have a synergistic effect. This effect can increase the heating rate of the particles to the range of flash pyrolysis, and its mechanism lies in the flow field structure of the pyrolyzer. Due to the centrifugal force field, the particles gather to the near wall. The rapid swirl, which facilitates intense gas-solid heat transfer, leads to the rapid heating and pyrolysis of biomass particles. As the pyrolysis proceeds, the mass of the biomass particles becomes smaller and they are more easily affected by the gas flow in pyrolyzer. Under the action of gas flow, char particles serve as new heat carrier to form the inner cycle of particles, which strengthens the heating process. The pyrolysis products are discharged from the exhaust port in time with the flow field of the pyrolyzer to achieve separation from the heat carrier and inhibit the occurrence of secondary reactions.

Investigation of longitudinal airflow characteristics in an aircraft cabin based on angle of attack

As an important means of transportation, an aircraft’s environmental control system plays an important role in ensuring the health and thermal comfort of the cabin environment. To guarantee sufficient lift during flight, the aircraft cabin needs to have a certain angle of attack with the horizontal direction. In this study, the flow field, temperature field and vortex structure characteristics of the cabin were analysed using a scaled 28-row cabin model and computational fluid dynamics (CFD) under different angles of attack (15° and 8°) conditions. The results show that the velocity and temperature in the local area in the longitudinal section were increased when the angle of attack was increased. Compared with the horizontal state (angle of attack 0°), the longitudinal airflow under the condition of a larger angle of attack was enhanced. The overall trend of forward airflow is presented in this paper. The longitudinal airflow would strengthen the separation of the large vortex at the top of the cabin. The vortex structure shows high instability in different times and spaces.

A numerical and experimental investigation into the mixing mechanism of hydrogen transverse jets into an air swirl flow

As a clean fuel with the advantages of abundant reserves, high calorific value, renewability, and zero carbon emissions, hydrogen has broad application prospects in the fields of energy and power. Moreover, the mixing characteristics of hydrogen and air play a crucial role in determining combustion performance. A novel mixing method of hydrogen transverse jets into an air swirl flow was investigated via numerical and experimental approaches. The Schlieren technique and high-speed photography were employed in the experiments. The effects of various swirl numbers and jet momentum flux ratios on the flow field structure, its transient characteristics, and mixing properties were studied. The research results indicate that the complex vortex structure in the mean flow field is jointly affected by the swirl number and the jet momentum flux ratio. An increase in the jet momentum flux ratio has distinct effects on the flow unsteadiness for different swirl numbers, and there exists a critical value of the jet momentum flux ratio that substantially affects the degree of mixing and a characteristic length suitable for normalization of the axial coordinates when describing the centerline concentration decay. This study provides a reference and basis for further research on combustion in air swirl flows of hydrogen transverse jets.

Kinematics and aerodynamic analysis in the turning flights of butterflies

This study investigates the free-turning flight of butterflies (Idea leuconoe) and analyze the influence of body posture and asymmetric motions of left and right wings on aerodynamics and the asymmetric flow field structure. Three high-speed cameras were used in the biological experiment to observe the turning flight motions, and varied motion angles were calculated. The results showed that the body started to tilt to the right at 0.3 cycles and the flapping amplitude of the inner wing increased by 20.31% relative to the outer wing during a cycle. The outer wing showed a forward-then-backward deviation, whereas the inner wing exhibited the opposite trend. A three-dimensional numerical model with six degrees of freedom and prescribed motion functions was constructed to simulate the flight of butterflies. The results revealed that the roll angle was the primary factor influencing the direction of aerodynamic forces and had a similar mechanism as the banked turn of a fixed wing. During the downstroke, the outer wing provided the normal force while the inner wing contributed to the vertical force, and both wings generated horizontal thrust during the upstroke. The asymmetric wing motions and the lateral inflow velocity were the two major factors affecting the flow field structure. The difference in flapping amplitudes caused the inner wing to generate greater vertical-normal resultant force first. The asymmetric forewing-deviation angle and the lateral flow influenced the direction of the spanwise flow to enhance the strength of the leading-edge vortex and stabilize the attached flow for the outer wing.

Experimental Investigation on a convex Mode-2 internal solitary wave and its induced flow field

The second mode internal solitary wave (Mode-2 ISW) and its wave-induced flow field structure are investigated by conducted physical experiments in a large stratified fluid flume. The Mode-2 ISW is generated by the method of the gravity collapse of fluid, and the measurements of its wave-flow structure are obtained by the combined method of conductivity probe array and particle image velocimetry (PIV). The flow field structure and its influencing factors were analysed quantitatively. The results reveal the characteristic of the Mode-2 ISW waveform and density field and the effect of the wave amplitude on the flow and shear characteristics of induced flow field.

Supersonic cooling film flow evolution on a curved wall under hypersonic flow

Curvature plays a crucial role in evolving supersonic cooling film flow-field structures. Flow-field structural images were captured using nanotracer-based planar laser scattering,, and wall pressure values were obtained using experimentally validated numerical simulations. A supersonic cooling film is tangentially injected at the Mach number of Maj = 2.3 into a laminar boundary layer at a mainstream of Ma = 6. The supersonic cooling film inhibits mixing-layer instability on the convex curved wall (CV) and promotes it on the concave curved wall (CC). After increasing the total incoming pressure, the reduction ratio of static pressure (RSP) between the supersonic cooling film and the mainstream flow causes a delay in the position of the mixing-layer instability, smaller-scale vortex structures, and decreased flow velocity of the typical vortex structures on the CC and CV. The wall pressure increases for the CV and decreases for the CC, indicating that the supersonic cooling film suppresses the changes in wall pressure due to curvature. The supersonic cooling film suppresses the decrease in the impulses for bulk dilatation (Ip) due to convex curvature and the increase in Ip due to concave curvature. The growth rate of Ip on the CC increases from −15% to −8% and decreases on the CV from 31% to 12% in the bending impulse (IΦ) range of |IΦ| = 1.337–3.624 for a total inlet pressure of 0.5 MPa. Increasing the RSP could control the Ip values on curved surfaces more effectively. The results of this study can be applied to cooling the infrared optics window on hypersonic vehicles.

Flow2Mesh: A flow-guided data-driven mesh adaptation framework

Mesh adaptation is crucial in numerical simulation, providing optimal resource allocation for accurately capturing physical phenomena. However, when applied to Computational Fluid Dynamics (CFD) problems with complex multi-scale properties, existing adaptation methods face huge challenges due to the high computational cost of solving auxiliary partial differential equations (PDEs) and the difficulty in aligning the flow features with mesh geometric features. In this work, an end-to-end data-driven mesh adaptation framework, Flow2Mesh, is proposed to address these challenges by adopting a hybrid modeling strategy to construct the mapping from pixelated flow-fields to graph-based meshes. It achieves a rapid and accurate one-step mesh adaptation via a perceptual feature network (PFN) and a mesh movement network (MMN). PFN extracts the global perceptual features from flow-fields to enhance flow feature representation and mesh resolution independence. In MMN, these features are utilized to deform the initial mesh to a topology-invariant adaptive mesh by a proposed physically driven mesh convolutional network. It considers the inherent mesh geometric information for efficient node feature aggregation and alignment of mesh density with a flow-field structure. To generate high-quality adaptive meshes, various mesh-related losses are designed to regularize the mesh movement and alleviate the mesh tangling. Experiments in CFD scenarios demonstrate the generalization of our model to different design parameters and mesh configurations. It takes three orders of magnitude less time to generate similar meshes than the PDE-based method. The results exhibit the potential of Flow2Mesh to be a flexible and reliable tool for rapid mesh adaptation in scientific and industrial fields.

Spectral feature extraction of rocket exhaust plume using spectral proper orthogonal decomposition

The spectral characterization of flow-field parameters provides a new perspective for understanding the spatiotemporal evolution of unsteady supersonic exhaust plumes and for extracting typical structures. In this study, a large-eddy simulation is performed to calculate the three-dimensional unsteady supersonic plume flow field of rocket engines, and a spectral proper orthogonal decomposition (SPOD) method with a spatiotemporal separation is established. This approach is used to extract the coherent structural features of the unsteady exhaust plume flow field and analyze the mode space structure at different frequencies. The three-dimensional reconstruction and denoising of the exhaust plume flow-field parameters can be achieved via the frequency- and time-domain reconstructions of the SPOD algorithm and oblique projection method, respectively. The ground rocket exhaust plume of ballistic evaluation motor-II is analyzed. The results indicate that the SPOD method can effectively extract the single-frequency mode structure of the reactive supersonic flow field, and that low-order behavior appears in the m = 0 and m = 1 azimuth modes. The potential core exhibits a high-frequency wave-packet structure that is affected by shock waves and shear layers. Time-domain reconstruction based on the oblique projection method facilitates the capture of the dynamic characteristics of the flow field. For the first-order SPOD mode, the frequency- and time-domain reconstruction errors are 3.3% and 1.5%, respectively. The frequency-domain reconstruction method exhibits a 4% improvement in denoising ability compared to low-pass filters. This study provides a novel method for the spectral characterization and spatiotemporal feature extraction of supersonic exhaust plume flow fields.

Numerical Simulation of wind load on Inflated Membrane Structure

The fluid-structure interaction (FSI) program were used to simulate the condition that inflated membrane structure transport process in incoming flow. A comparison between the results from numerical simulation and from the ground simulation test was used to validate the computational method. Due to the analysis of flow field and membrane structure’s deformation, the law of force variation of inflated membrane structure during FSI was discussed, and the causes of deformation instability in FSI problems were preliminary discussed. Possible ways to reduce the sensitivity of envelope deformation caused by constraint position were explored, and the effect of this improved method on the surface stress of the envelope was investigated.

Energetic and dynamic characterization of pollutant dispersion in varied building layouts through an augmented analysis procedure

This work presents a post-data analysis procedure, namely, proper orthogonal decomposition (POD)–dynamic mode decomposition (DMD)–discrete Fourier transform analysis, for evaluating the dominant features of the flow fields from both energetic and dynamic perspectives. The large-eddy simulation (LES) was first employed to reproduce the flow field surrounding three types of building layouts. Subsequently, both POD and DMD were conducted according to LES simulation results. The extracted modes were classified into three types based on the POD and DMD: Type-1 mode: energetically and dynamically significant mode, Type-2 mode: energetically significant and dynamically insignificant mode, and Type-3 mode: energetically insignificant and dynamically significant mode. The findings indicate that Type-1 mode governs the primary velocity field and the predominant vortex patterns observed at the rear of the building arrays, as the reduction of inter-building widths leads to a shorter flow separation region. Type-2 mode is characterized by the presence of small-scale vortices and the high turbulent kinetic energy region, which periodically triggers pollutant increase in the vicinity of structures. Type-3 mode demonstrates a minimal energetic influence on the flow field; nevertheless, it significantly contributes to the consistent build-up of pollutants within the far-wake region. The present study also investigates the predominant coherent structures of flow fields concerning various building layouts and highlights the influence of passage widths on the efficiency of pollutant removal. This comprehensive analysis enables a systematic exploration of flow patterns within various building layouts, offering potential solutions for pollutant dispersion challenges in metropolitan areas.

Experimental and numerical studies on vertical water entry of a cylinder under the influence of current

When a moving object penetrates the free surface, it is often accompanied by complex multiphase flow phenomena. In this work, the complicated impact cavity and flow characteristics of water entry by a cylinder are investigated both experimentally and numerically for different current velocities. A high-speed photography technique is employed to capture the cavity contours under both calm water and flowing water. Under the same working conditions, a three-dimensional simulation using a volume of fraction model is conducted to provide detailed flow field structures and motion behaviors for experimental results. The primary results are as follows: the effect of current causes the cavities to no longer develop symmetrically. The cavity on the upstream side is compressed close to the cylinder surface, while the cavity on the downstream side expands. The asymmetrical distribution of cavities causes different wetting states on both sides of the cylinder. The ensuing pressure difference prompts the cylinder to deflect which is quite different that without considering current. Vortices generated on the upstream side disappear faster, while those generated on the downstream side expand significantly along the flow direction.

Influence of the Trailing Edge Shape of Impeller Blades on Centrifugal Pumps with Unsteady Characteristics

The flow field structure and pressure pulsation characteristics in two series of trailing edges of a centrifugal pump are investigated using the SST k-w turbulence model. Series 1 involves varying the impeller exit angle, and Series 2 involves varying the impeller exit shape. The entropy generation rate analysis method is used to evaluate the numerical simulation results. Vortex cores within the flow field are identified by applying the Ω criterion. The influence of different trailing edge configurations on the energy loss characteristics of the pumps is explored. The dynamic mode decomposition (DMD) method is used to analyze pressure pulsations at the volute considering unsteady flows in centrifugal pumps with different trailing edge shapes. The findings suggest that different trailing edge shapes can be used to adjust the energy loss proportions in various components of the pump. In Series 1, the efficiency remains nearly constant with changes in the outlet angle on both sides of the trailing edge. In Series 2, the efficiency is enhanced by 1.18% with the elliptical edge shape on both sides (EBS) compared to the original trailing edge (OTE) shape. In Series 1 and Series 2, greater entropy generation rates are accompanied by greater pressure pulsations at the pump outlet. The DMD results demonstrate a noticeable impact of the different trailing edges on the pressure distribution of various modes within the volute. Moreover, the impeller outlet pressure inhomogeneity coefficient changes under different modes. This study holds great significance for selecting the appropriate trailing edges for centrifugal pumps.

Study on the Hydrodynamic Performance of Swing-Type Flapping Hydrofoil Bionic Pumps Affected by Foil Camber

The flapping hydrofoil bionic pump is an innovative hydrodynamic device that utilizes flapping hydrofoil technology. Flapping hydrofoil bionic pumps are crucial in addressing issues like inadequate river hydropower and limited water purification capabilities in flat river network regions. Optimizing the foil characteristics is essential for enhancing the hydrodynamic efficiency of the flapping hydrofoil bionic pump. This study investigates the impact of foil camber parameters on the hydrodynamic performance of swing-type asymmetric flapping bionic pumps. The NACA series standard foils with varying cambers are analyzed using the overlapping grid technology and finite volume method. The thrust coefficient, flow rate, pumping efficiency, and flow field structure of the flapping hydrofoil bionic pump are examined under pressure inlet conditions with the foil camber. The findings indicate that increasing the foil’s curvature within a specific range can greatly enhance the maximum values of thrust coefficient, propulsive efficiency, and pumping efficiency of the flapping hydrofoil bionic pump. Specifically, when the foil curvature is 6%c, the maximum value of the instantaneous thrust coefficient of the flapping hydrofoil bionic pump is significantly improved by 31.25% compared to the symmetric foil type under the condition of an oscillating frequency of f = 1 HZ. The flapping hydrofoil bionic pump achieves its maximum pumping efficiency when the oscillation frequency is within the range of f ≤ 2.5 Hz. This efficiency is 11.7% greater than that of the symmetric foil, and it occurs when the foil curvature is 8%c. Within the frequency range of f > 2.5 Hz, the flapping hydrofoil bionic pump that has a foil curvature of 6%c exhibits the highest enhancement in pumping efficiency. It achieves a maximum increase of 12.8% compared to the symmetric foil type. Nevertheless, the average head was less than 0.4 m, making it suitable for ultra-low-head applications.

Propulsion curve analysis and optimisation of biomimetic pectoral fin with three degree of freedom based on multi-layer perception

This paper aims to improve the swimming efficiency of biomimetic robotic fish by optimising its propulsion curve with three degree of freedom (DOF), in which the key is to minimise the resistance during swing backstroke of the pectoral fin. For this purpose, a reference point on the pectoral fin is first selected, and then an 8-shaped propulsion curve is constructed to coordinate rowing and flapping motions. Meanwhile, a propulsion curve of feathering motion is also given correspondingly. On this basis, the overall curvature and curve offset are proposed as measurement parameters for the deformation of the propulsion curve and the proportion of abdominal/dorsal circles in the propulsion curve, respectively. As the motion law of feathering is given in a sinusoidal pattern, a data set of hydrodynamic parameters is obtained for pectoral fin propulsion under different motion parameter conditions by computational fluid dynamics(CFD) numerical simulation. Once again, a propulsion curve optimisation model is established based on multi-layer perception(MLP), which uses the hydrodynamic parameters data set as input. The results show that the resistance of swing backstroke reached the minimum when overall curvature is π/10 and curve offset is 0.4, which is enhanced by 30.13% and 33.33% at thrust and lift direction compared to the existing design, respectively. Furthermore, the flow field structure and hydrodynamic parameters around the robotic fish are calculated by CFD. The results show that two sets of vortex rings are generated around the fish body during a propulsion cycle. The vortex rings detached towards the lower and upper sides of the fish body such that the lift is minimal, the thrust direction is relatively stable, and the resistance is minimal during the swing backstroke. The experimental results indicate that it can raise propulsion efficiency during the pectoral fin propulsion process, verifying the effectiveness of this method.

Reconstruction and prediction of the rotor wake flow field in hovering state

A clear understanding of the flow structure and evolution of the rotor wake flow field is one of the key problems to be solved in the development of rotor aerodynamics. The tip vortices are the primary structure of the rotor wake flow field. A theoretical model of the vortex ring was established to verify the feasibility of flow field reconstruction. Particle image velocimetry (PIV) is used to measure the two-dimensional velocity field in the rotor wake. Because of the wandering motion of tip vortices, a new conditional average algorithm is proposed to deal with the flow field. On this basis, it is proposed that the plane interval of the rotor wake flow field reconstructed by interpolation should be less than 20 deg. The vortex core radius is obtained by the analysis method based on the circulation. A Back Propagation (BP) neural network was established to predict the axial and radial positions of the tip vortices and the radius of the vortex core. The inputs are the vortex ages measured by the experiment, and the outputs are the position and radius of the vortex core under any vortex ages. The predicted values were in good agreement with the experimental results. The study provides further analytical methods and new insights for the characteristics and evolution of tip vortices.

Hydrodynamic analysis of the upright swimming of seahorse

The seahorse is the only creature in the ocean that can maintain an upright posture while swimming. This paper mainly discusses the hydrodynamic characteristics and the flow field structure of the seahorse when it swims upright. Using a three-dimensional seahorse model, numerical simulations of self-propelled swimming are conducted by establishing the kinematic equations of its dorsal fin. The focus is on elucidating the effects of the undulation frequency and the inclination angle on swimming performance. The results indicate that a higher undulation frequency of the dorsal fin leads to better acceleration performance, or in other words, greater hydrodynamic forces. The inclination angle of the seahorse's body also directly affects its hydrodynamics and the flow field structure. Unlike other fish that swim horizontally, the seahorse generates forward and upward thrust as the flow field simultaneously spreads backward and downward. Since the upright posture makes the forward thrust much smaller than the upward one, the seahorse has low efficiency in forward propulsion when swimming upright. As the inclination angle decreases, the forward thrust gradually increases and exceeds the upward force, which allows for a rapid improvement in the swimming velocity. The simulation findings of this study are consistent with previous experimental observations.