Computational Fluid Dynamics Approach for Predicting Pipeline Response to Various Blast Scenarios: A Numerical Modeling Study

Recent industrial explosions globally have intensified the focus in mechanical engineering on designing infras-tructure systems and networks capable of withstanding blast loading.Initially centered on high-profile facilities such as embassies and petrochemical plants,this concern now extends to a wider array of infrastructures and facilities.Engineers and scholars increasingly prioritize structural safety against explosions,particularly to prevent disproportionate collapse and damage to nearby structures.Urbanization has further amplified the reliance on oil and gas pipelines,making them vital for urban life and prime targets for terrorist activities.Consequently,there is a growing imperative for computational engineering solutions to tackle blast loading on pipelines and mitigate associated risks to avert disasters.In this study,an empty pipe model was successfully validated under contact blast conditions using Abaqus software,a powerful tool in mechanical engineering for simulating blast effects on buried pipelines.Employing a Eulerian-Lagrangian computational fluid dynamics approach,the investigation extended to above-surface and below-surface blasts at standoff distances of 25 and 50 mm.Material descriptions in the numerical model relied on Abaqus’default mechanical models.Comparative analysis revealed varying pipe performance,with deformation decreasing as explosion-to-pipe distance increased.The explosion’s location relative to the pipe surface notably influenced deformation levels,a key finding highlighted in the study.Moreover,quantitative findings indicated varying ratios of plastic dissipation energy(PDE)for different blast scenarios compared to the contact blast(P0).Specifically,P1(25 mm subsurface blast)and P2(50 mm subsurface blast)showed approximately 24.07%and 14.77%of P0’s PDE,respectively,while P3(25 mm above-surface blast)and P4(50 mm above-surface blast)exhibited lower PDE values,accounting for about 18.08%and 9.67%of P0’s PDE,respectively.Utilising energy-absorbing materials such as thin coatings of ultra-high-strength concrete,metallic foams,carbon fiber-reinforced polymer wraps,and others on the pipeline to effectively mitigate blast damage is recommended.This research contributes to the advancement of mechanical engineering by providing insights and solutions crucial for enhancing the resilience and safety of underground pipelines in the face of blast events.

Computational fluid dynamics modeling of rapid pyrolysis of solid waste magnesium nitrate hydrate under different injection methods

This study developed a numerical model to efficiently treat solid waste magnesium nitrate hydrate through multi-step chemical reactions.The model simulates two-phase flow,heat,and mass transfer processes in a pyrolysis furnace to improve the decomposition rate of magnesium nitrate.The performance of multi-nozzle and single-nozzle injection methods was evaluated,and the effects of primary and secondary nozzle flow ratios,velocity ratios,and secondary nozzle inclination angles on the decomposition rate were investigated.Results indicate that multi-nozzle injection has a higher conversion efficiency and decomposition rate than single-nozzle injection,with a 10.3%higher conversion rate under the design parameters.The decomposition rate is primarily dependent on the average residence time of particles,which can be increased by decreasing flow rate and velocity ratios and increasing the inclination angle of secondary nozzles.The optimal parameters are injection flow ratio of 40%,injection velocity ratio of 0.6,and secondary nozzle inclination of 30°,corresponding to a maximum decomposition rate of 99.33%.

Flow Field Characteristics of Multi-Trophic Artificial Reef Based on Computation Fluid Dynamics

On the basis of computational fluid dynamics,the flow field characteristics of multi-trophic artificial reefs,including the flow field distribution features of a single reef under three different velocities and the effect of spacing between reefs on flow scale and the flow state,were analyzed.Results indicate upwelling,slow flow,and eddy around a single reef.Maximum velocity,height,and volume of upwelling in front of a single reef were positively correlated with inflow velocity.The length and volume of slow flow increased with the increase in inflow velocity.Eddies were present both inside and backward,and vorticity was positively correlated with inflow velocity.Space between reefs had a minor influence on the maximum velocity and height of upwelling.With the increase in space from 0.5 L to 1.5 L(L is the reef lehgth),the length of slow flow in the front and back of the combined reefs increased slightly.When the space was 2.0 L,the length of the slow flow decreased.In four different spaces,eddies were present inside and at the back of each reef.The maximum vorticity was negatively correlated with space from 0.5 L to 1.5 L,but under 2.0 L space,the maximum vorticity was close to the vorticity of a single reef under the same inflow velocity.

Application of computational fluid dynamics in design of viscous dampers-CFD modeling and full-scale dynamic testing

Computational fluid dynamics(CFD)provides a powerful tool for investigating complicated fluid flows.This paper aims to study the applicability of CFD in the preliminary design of linear and nonlinear fluid viscous dampers.Two fluid viscous dampers were designed based on CFD models.The first device was a linear viscous damper with straight orifices.The second was a nonlinear viscous damper containing a one-way pressure-responsive valve inside its orifices.Both dampers were detailed based on CFD simulations,and their internal fluid flows were investigated.Full-scale specimens of both dampers were manufactured and tested under dynamic loads.According to the tests results,both dampers demonstrate stable cyclic behaviors,and as expected,the nonlinear damper generally tends to dissipate more energy compared to its linear counterpart.Good compatibility was achieved between the experimentally measured damper force-velocity curves and those estimated from CFD analyses.Using a thermography camera,a rise in temperature of the dampers was measured during the tests.It was found that output force of the manufactured devices was virtually independent of temperature even during long duration loadings.Accordingly,temperature dependence can be ignored in CFD models,because a reliable temperature compensator mechanism was used(or intended to be used)by the damper manufacturer.

Computational fluid dynamics-discrete element method simulation of stirred tank reactor for graphene production

Liquid phase exfoliation(LPE)process for graphene production is usually carried out in stirred tank reactor and the interactions between the solvent and the graphite particles are important as to improve the production efficiency.In this paper,these interactions were revealed by computational fluid dynamics–discrete element method(CFD-DEM)method.Based on simulation results,both liquid phase flow hydrodynamics and particle motion behavior have been analyzed,which gave the general information of the multiphase flow behavior inside the stirred tank reactor as to graphene production.By calculating the threshold at the beginning of graphite exfoliation process,the shear force from the slip velocity was determined as the active force.These results can support the optimization of the graphene production process.

A simplified approach to modelling blasts in computational fluid dynamics (CFD)

This paper presents a time-efficient numerical approach to modelling high explosive(HE)blastwave propagation using Computational Fluid Dynamics(CFD).One of the main issues of using conventional CFD modelling in high explosive simulations is the ability to accurately define the initial blastwave properties that arise from the ignition and consequent explosion.Specialised codes often employ Jones-Wilkins-Lee(JWL)or similar equation of state(EOS)to simulate blasts.However,most available CFD codes are limited in terms of EOS modelling.They are restrictive to the Ideal Gas Law(IGL)for compressible flows,which is generally unsuitable for blast simulations.To this end,this paper presents a numerical approach to simulate blastwave propagation for any generic CFD code using the IGL EOS.A new method known as the Input Cavity Method(ICM)is defined where input conditions of the high explosives are given in the form of pressure,velocity and temperature time-history curves.These time history curves are input at a certain distance from the centre of the charge.It is shown that the ICM numerical method can accurately predict over-pressure and impulse time history at measured locations for the incident,reflective and complex multiple reflection scenarios with high numerical accuracy compared to experimental measurements.The ICM is compared to the Pressure Bubble Method(PBM),a common approach to replicating initial conditions for a high explosive in Finite Volume modelling.It is shown that the ICM outperforms the PBM on multiple fronts,such as peak values and overall overpressure curve shape.Finally,the paper also presents the importance of choosing an appropriate solver between the Pressure Based Solver(PBS)and Density-Based Solver(DBS)and provides the advantages and disadvantages of either choice.In general,it is shown that the PBS can resolve and capture the interactions of blastwaves to a higher degree of resolution than the DBS.This is achieved at a much higher computational cost,showing that the DBS is much preferred for quick turnarounds.

Preliminary Evaluation of Hemodynamic Effects of Fontan Palliation on Renal Artery Using Computational Fluid Dynamics

Background:The assessment of renal function is important to the prognosis of patients needing Fontan palliation due to the reconstructed compromised circulation.To know the relationship between the kidney perfusion and hemodynamic characteristics during surgical design could reduce the risk of acute kidney injury(AKI)and the postoperative complications.However,the issue is still unsolved because the current clinical evaluation methods are unable to predict the hemodynamic changes in renal artery(RA).Methods:We reconstructed a three-dimensional(3D)vascular model of a patient requiring Fontan palliation.The technique of computational fluid dynamics(CFD)was utilized to explore the changes of RA hemodynamics under different possible blood flow rates.The relationship between the kidney perfusion and hemodynamic characteristics was investigated.Results:The calculated results indicated the declined tendency of the pressure and pressure drop as the flow rate decreased.When the flow rate decreased to two-thirds of its baseline,both the pressure of left renal artery(LRA)and the pressure of right renal artery(RRA)dipped below 50%,and the pressure of RRA fell more quickly than that of LRA.Uneven distribution of WSS was observed on the trunk of RA,and the lowest WSS was found at the distal of RA.The average WSS in RA dropped to around 50%as the flow rate reached one-third of its baseline.Conclusions:As a promising approach,CFD can be utilized to quantitatively evaluate the hemodynamic characteristics of RA and contribute to offsetting the drawbacks of clinical assessments of renal function,to help realize better prognosis for the patients with Fontan palliation.

Effect of internal structure of a batch-processing wet-etch reactor on fluid flow and heat transfer

Batch-processing wet-etch reactors are the key equipment widely used in chip fabrication,and their performance is largely affected by the internal structure.This work develops a three-dimensional computational fluid dynamics(CFD)model considering heat generation of wet-etching reactions to investigate the fluid flow and heat transfer in the wet-etch reactor.The backflow is observed below and above the wafer region,as the flow resistance in this region is high.The temperature on the upper part of a wafer is higher due to the accumulation of reaction heat,and the average temperature of the side wafer is highest as its convective heat transfer is weakest.Narrowing the gap between wafer and reactor wall can force the etchant to flow in the wafer region and then facilitate the convective heat transfer,leading to better within-wafer and wafer-to-wafer etch uniformities.An inlet angle of 60°balances fluid by-pass and mechanical energy loss,and it yields the best temperature and etch uniformities.The batch with 25wafers has much wider flow channels and much lower flow resistance compared with that with 50wafers,and thus it shows better temperature and etch uniformities.These results and the CFD model should serve to guide the optimal design of batch-processing wet-etch reactors.

Numerical Study on the Aerodynamic and Fluid−Structure Interaction of An NREL-5MW Wind Turbine

A 5-MW wind turbine has been modeled and analyzed for fluid-structure interaction and aerodynamic performance.In this study, a full-scale model of a 5-MW wind turbine is first developed based on a computational fluid dynamics(CFD) approach, in which the unsteady, noncompressible Reynolds Averaged Navier-Stokes(RANS) method is used. The main focus of the study is to analyze the tower shadow effect on the aerodynamic performance of the wind turbine under different inlet flow conditions. Subsequently, the finite element model is established by considering fluid/structure interactions to study the structural stress, displacement, strain distributions and flow field information of the structure under the uniform wind speed. Finally, the fluid-structure interaction model is established by considering turbulent wind and the tower shadow effect. The variation rules of the dynamic response of the one-way and two-way fluid-structure interaction(FSI) models under different wind speeds are analyzed, and the numerical calculation results are compared with those of the centralized mass model. The results show that the tower shadow effect and structural deformation are the main factors affecting the aerodynamic load fluctuation of the wind turbine, which in turn affects the aerodynamic performance and structural stability of the blades. The structural dynamic response of the coupled model shows significant similarity, while the structural displacement response of the former exhibits less fluctuation compared with the conventional centralized mass model. The one-way fluid-structure interaction(FSI)model shows a higher frequency of stress-strain and displacement oscillations on the blade compared with the two-way FSI model.

Effect of length-width ratio of rounded rectangle aquaculture tank in dual-diagonal-inlet layout on hydrodynamics

To adapt to the change of aquaculture workshop site,optimize the shape of aquaculture tanks and improve the utilization rate of breeding space,it is necessary to determine the appropriate length width ratio parameters of aquaculture tanks.In this paper,computational fluid dynamics(CFD)technology is adopted to study the flow field performance of aquaculture tanks with different L/B ratios(L:the length;B:the width,of aquaculture tank)and different jet direction conditions(lengthways jet and widthways jet).A three-dimensional numerical calculation model of turbulence in rounded rectangle aquaculture tanks in dual-diagonal-inlet layout was established.Jet directions are arranged lengthways and widthways,and the water flow velocity,resistance coefficient change,vorticity,etc.are analyzed under two working conditions.Results show that the flow field performance in aquaculture tank decreases with the increase of the L/B ratio.The flow field performed well when L/B was 1.0-1.3,sharply dropped at 1.4-1.6,and poor at 1.7-1.9.The results provided a theoretical basis for the design and optimization in flow field performance of the industrialized circulating aquaculture tanks.

Towards implementation of alloy-specific thermo-fluid modelling for laser powder-bed fusion of Mg alloys

Multi-physics thermo-fluid modeling has been extensively used as an approach to understand melt pool dynamics and defect formation as well as optimizing the process-related parameters of laser powder-bed fusion(L-PBF).However,its capabilities for being implemented as a reliable tool for material design,where minor changes in material-related parameters must be accurately captured,is still in question.In the present research,first,a thermo-fluid computational fluid dynamics(CFD)model is developed and validated against experimental data.Considering the predicted material properties of the pure Mg and commercial ZK60 and WE43 Mg alloys,parametric studies are done attempting to elucidate how the difference in some of the material properties,i.e.,saturated vapor pressure,viscosity,and solidification range,can influence the melt pool dynamics.It is found that a higher saturated vapor pressure,associated with the ZK60 alloy,leads to a deeper unstable keyhole,increasing the keyhole-induced porosity and evaporation mass loss.Higher viscosity and wider solidification range can increase the non-uniformity of temperature and velocity distribution on the keyhole walls,resulting in increased keyhole instability and formation of defects.Finally,the WE43 alloy showed the best behavior in terms of defect formation and evaporation mass loss,providing theoretical support to the extensive use of this alloy in L-PBF.In summary,this study suggests an approach to investigate the effect of materials-related parameters on L-PBF melting and solidification,which can be extremely helpful for future design of new alloys suitable for L-PBF.

The Effect of Lateral Offset Distance on the Aerodynamics and Fuel Economy of Vehicle Queues

The vehicle industry is always in search of breakthrough energy-saving and emission-reduction technologies.In recent years,vehicle intelligence has progressed considerably,and researchers are currently trying to take advantage of these developments.Here we consider the case of many vehicles forming a queue,i.e.,vehicles traveling at a predetermined speed and distance apart.While the majority of existing studies on this subject have focused on the influence of the longitudinal vehicle spacing,vehicle speed,and the number of vehicles on aerodynamic drag and fuel economy,this study considers the lateral offset distance of the vehicle queue.The group fuel consumption savings rate is calculated and analyzed.As also demonstrated by experimental results,some aerodynamic benefits exist.Moreover,the fuel consumption saving rate of the vehicle queue decreases as the lateral offset distance increases.

Desulfurization characteristics of slaked lime and regulation optimization of circulating fluidized bed flue gas desulfurization process--A combined experimental and numerical simulation study

Circulating fluidized bed flue gas desulfurization(CFB-FGD) process has been widely applied in recent years. However, high cost caused by the use of high-quality slaked lime and difficult operation due to the complex flow field are two issues which have received great attention. Accordingly, a laboratory-scale fluidized bed reactor was constructed to investigate the effects of physical properties and external conditions on desulfurization performance of slaked lime, and the conclusions were tried out in an industrial-scale CFB-FGD tower. After that, a numerical model of the tower was established based on computational particle fluid dynamics(CPFD) and two-film theory. After comparison and validation with actual operation data, the effects of operating parameters on gas-solid distribution and desulfurization characteristics were investigated. The results of experiments and industrial trials showed that the use of slaked lime with a calcium hydroxide content of approximately 80% and particle size greater than 40 μm could significantly reduce the cost of desulfurizer. Simulation results showed that the flow field in the desulfurization tower was skewed under the influence of circulating ash. We obtained optimal operating conditions of 7.5 kg·s^(-1)for the atomized water flow, 70 kg·s^(-1)for circulating ash flow, and 0.56 kg·s^(-1)for slaked lime flow, with desulfurization efficiency reaching 98.19% and the exit flue gas meeting the ultraclean emission and safety requirements. All parameters selected in the simulation were based on engineering examples and had certain application reference significance.

Investigating the Effects of Injection Pipe Orientation on Mixing and Heat Transfer for Fluid Flow Downstream a T-Junction

At T-junctions, where hot and cold streams flowing in pipes join and mix, significant temperature fluctuations can be created in very close neighborhood of the pipe walls. The wall temperature fluctuations cause cyclical thermal stresses which may induce fatigue cracking. Temperature fluctuation is of crucial importance in many engineering applications and especially in nuclear power plants. This is because the phenomenon leads to thermal fatigue and might subsequently result in failure of structural material. Therefore, the effects of temperature fluctuation in piping structure at mixing junctions in nuclear power systems cannot be neglected. In nuclear power plant, piping structure is exposed to unavoidable temperature differences in a bid to maintain plant operational capacity. Tightly coupled to temperature fluctuation is flow turbulence, which has attracted extensive attention and has been investigated worldwide since several decades. The focus of this study is to investigate the effects of injection pipe orientation on flow mixing and temperature fluctuation for fluid flow downstream a T-junction. Computational fluid dynamics (CFD) approach was applied using STAR CCM+ code. Four inclination angles including 0 (90), 15, 30 and 45 degrees were studied and the mixing intensity and effective mixing zone were investigated. K-omega SST turbulence model was adopted for the simulations. Results of the analysis suggest that, effective mixing of cold and hot fluid which leads to reduced and uniform temperature field at the pipe wall boundary, is achieved at 0 (90) degree inclination of the branch pipe and hence may lower thermal stress levels in the structural material of the pipe. Turbulence mixing, pressure drop and velocity distribution were also found to be more appreciable at 0 (90) degree inclination angle of the branch pipe relative to the other orientations studied.

Comprehensive Examination of Solar Panel Design: A Focus on Thermal Dynamics

In the 21st century, the deployment of ground-based Solar Photovoltaic (PV) Modules has seen exponential growth, driven by increasing demands for green, clean, and renewable energy sources. However, their usage is constrained by certain limitations. Notably, the efficiency of solar PV modules on the ground peaks at a maximum of 25%, and there are concerns regarding their long-term reliability, with an expected lifespan of approximately 25 years without failures. This study focuses on analyzing the thermal efficiency of PV Modules. We have investigated the temperature profile of PV Modules under varying environmental conditions, such as air velocity and ambient temperature, utilizing Computational Fluid Dynamics (CFD). This analysis is crucial as the efficiency of PV Modules is significantly impacted by changes in the temperature differential relative to the environment. Furthermore, the study highlights the effect of airflow over solar panels on their temperature. It is found that a decrease in the temperature of the PV Module increases Open Circuit Voltage, underlining the importance of thermal management in optimizing solar panel performance.

Numerical Solutions of the Classical and Modified Buckley-Leverett Equations Applied to Two-Phase Fluid Flow

Climate change is a reality. The burning of fossil fuels from oil, natural gas and coal is responsible for much of the pollution and the increase in the planet’s average temperature, which has raised discussions on the subject, given the emergencies related to climate. An energy transition to clean and renewable sources is necessary and urgent, but it will not be quick. In this sense, increasing the efficiency of oil extraction from existing sources is crucial, to avoid waste and the drilling of new wells. The purpose of this work was to add diffusive and dispersive terms to the Buckley-Leverett equation in order to incorporate extra phenomena in the temporal evolution between the water-oil and oil-water transitions in the pipeline. For this, the modified Buckley-Leverett equation was discretized via essentially weighted non-oscillatory schemes, coupled with a three-stage Runge-Kutta and a fourth-order centered finite difference methods. Then, computational simulations were performed and the results showed that new features emerge in the transitions, when compared to classical simulations. For instance, the dispersive term inhibits the diffusive term, adding oscillations, which indicates that the absorption of the fluid by the porous medium occurs in a non-homogeneous manner. Therefore, based on research such as this, decisions can be made regarding the replacement of the porous medium or the insertion of new components to delay the replacement.

Application of Computational Fluid Dynamics and Fluid Structure Interaction Techniques for Calculating the 3D Transient Flow of Journal Bearings Coupled with Rotor Systems

Journal bearings are important parts to keep the high dynamic performance of rotor machinery. Some methods have already been proposed to analysis the flow field of journal bearings, and in most of these methods simplified physical model and classic Reynolds equation are always applied. While the application of the general computational fluid dynamics （CFD）-fluid structure interaction （FSI） techniques is more beneficial for analysis of the fluid field in a journal bearing when more detailed solutions are needed. This paper deals with the quasi-coupling calculation of transient fluid dynamics of oil film in journal bearings and rotor dynamics with CFD-FSI techniques. The fluid dynamics of oil film is calculated by applying the so-called ＂dynamic mesh＂ technique. A new mesh movement approacb is presented while the dynamic mesh models provided by FLUENT are not suitable for the transient oil flow in journal bearings. The proposed mesh movement approach is based on the structured mesh. When the joumal moves, the movement distance of every grid in the flow field of bearing can be calculated, and then the update of the volume mesh can be handled automatically by user defined function （UDF）. The journal displacement at each time step is obtained by solving the moving equations of the rotor-bearing system under the known oil film force condition. A case study is carried out to calculate the locus of the journal center and pressure distribution of the journal in order to prove the feasibility of this method. The calculating results indicate that the proposed method can predict the transient flow field of a journal bearing in a rotor-bearing system where more realistic models are involved. The presented calculation method provides a basis for studying the nonlinear dynamic behavior of a general rotor-bearing system.

Urban Green Space Planning Based on Computational Fluid Dynamics Model and Landscape Ecology Principle:A Case Study of Liaoyang City,Northeast China

As a result of environmental degradation,urban green space has become a key issue for urban sustainable development.This paper takes Liaoyang City in Northeast China as an example to develop green space planning using the computational fluid dynamics (CFD) model,landscape ecological principles and Geographical Information System (GIS).Based on the influencing factors of topography,building density and orientation,Shou Mountain,Longding Mountain and the Taizi River were selected as the urban ventilation paths to promote wind and oxygen circulation.Oxygen concentration around the green spaces gradually decreased with wind speed increase and wind direction change.There were obvious negative correlation relationships between the oxygen dispersion concentration and urban layout factors such as the building plot ratio and building density.Comparison with the field measurements found that there was significant correlation relationship between simulated oxygen concentration and field measurements (R 2=0.6415,p<0.001),moreover,simulation precision was higher than 92%,which indicated CFD model was effective for urban oxygen concentration simulation.Only less than 10% areas in Liaoyang City proper needed more green space urgently to improve oxygen concentration,mainly concentrated in Baitai and west Wensheng districts.Based on land-scape ecology principle,green space planning at different spatial scales were proposed to create a green space network system for Liaoyang City,including features such as green wedges,green belts and parks.Totally,about 2012 ha of green space need to be constructed as oxygen sources and ventilation paths.Compared with the current green space pattern,proposed green space planning could improve oxygen concentration obviously.The CFD model and research results in this paper could provide an effective way and theory support for sustainable development of urban green space.

Simulation and Analysis on the Two-Phase Flow Fields in a Rotating-Stream-Tray Absorber by Using Computational Fluid Dynamics

The flow field of gas and liquid in a φ150mm rotating-stream-tray (RST) scrubber is simulated by using computational fluid dynamic (CFD) method. The sismulation is based on the two-equation RNG κ-ε turbulence model, Eulerian multiphase model, and a real-shape 3D model with a huge number of meshes. The simulation results include detailed information about velocity, pressure, volume fraction and so on. Some features of the flow field are obtained: liquid is atomized in a thin annular zone; a high velocity air zone prevents water drops at the bottom from flying towards the wall; the pressure varies sharply at the end of blades and so on. The results will be helpful for structure optimization and engineering design.

A Computational Fluid Dynamics (CFD) Analysis of an Undulatory Mechanical Fin Driven by Shape Memory Alloy

Many fishes use undulatory fin to propel themselves in the underwater environment. These locomotor mechanisms have a popular interest to many researchers. In the present study, we perform a three-dimensional unsteady computation of an undulatory mechanical fin that is driven by Shape Memory Alloy （SMA）. The objective of the computation is to investigate the fluid dynamics of force production associated with the undulatory mechanical fin. An unstructured, grid-based, unsteady Navier-Stokes solver with automatic adaptive remeshing is used to compute the unsteady flow around the fin through five complete cycles. The pressure distribution on fin surface is computed and integrated to provide fin forces which are decomposed into lift and thrust. The velocity field is also computed throughout the swimming cycle. Finally, a comparison is conducted to reveal the dynamics of force generation according to the kinematic parameters of the undulatory fin （amplitude, frequency and wavelength）.