Potential Flow Model Research Articles

Numerical prediction of stagnant and flowing zones in a blast furnace by a novel potential flow model

Several flow zones exist in an ironmaking blast furnace, including the plug flow zone at the upper part, a stagnant zone in the central bottom and a funnel flow zone near the outlet. The prediction of the stagnant zone has remained a difficulty for years, and various approaches have been attempted in the past. In this article, a new approach based on novel potential flow model was employed to predict the profile of the stagnant zone and the plug flow and funnel flow zones. The results were verified by the experimental observations in literature. The effect of the material flow resistance in the model on the stagnant and flowing zones was investigated, and the results were also compared with the traditional potential flow model. It is demonstrated that the novel potential flow model has the advantage in predicting the stagnant and flowing zones simultaneously without a need to implement extra complicated correlations. • An approach to numerically predict deadman in blast furnace is proposed. • Deadman changes with ratio of potential flow and piping flow resistances. • Predicted results accord fairly well with reality. • Material resistance surely exists within deadman in blast furnace.

Leading edge vortex formation and wake trajectory: Synthesizing measurements, analysis, and machine learning

The strength and trajectory of a leading edge vortex (LEV) formed by a pitching-heaving hydrofoil (chord $c$) is studied. The LEV is identified using the $Q$-criterion method, which is calculated from the 2D velocity field obtained from PIV measurements. The relative angle of attack at mid-stroke, ${\alpha_{T/4}} $, proves to be an effective method of combining heave amplitude ($h_0/c$), pitch amplitude ($\theta_0$), and reduced frequency ($f^*$) into a single variable that predicts the maximum value of $Q$ over a wide range of operating conditions. Once the LEV separates from the foil, it travels downstream and rapidly weakens and diffuses. The downstream trajectory of the LEV has two characteristic shapes. At low values of ${\alpha_{T/4}}$, it travels straight downstream after separating from the foil, while at higher values of ${\alpha_{T/4}} $, an accompanying Trailing Edge Vortex (TEV) forms and the induced velocity generates a cross-stream component to the vortex trajectories. This behavior is accurately predicted using a potential flow model for the LEV and TEV. Supervised machine learning algorithms, namely Support Vector Regression and Gaussian Process Regression, are used to create regression models that predicts the vortex strength, shape and trajectory during growth and after separation. The regression model successfully captures the features of two vortex regimes observed at different values of ${\alpha_{T/4}} $. However, the predicted LEV trajectories are somewhat smoother than observed in the experiments. The strengths of the vortex is often under-predicted. Both of these shortcomings may be attributed to the relatively small size of the training data set.

Assessment of one-way coupling methods from a potential to a viscous flow solver based on domain- and functional-decomposition for fixed submerged bodies in nonlinear waves

To simulate the interaction of ocean waves with marine structures, coupling approaches between a potential flow model and a viscous model are investigated. The first model is a fully nonlinear potential flow (FNPF) model based on the Harmonic Polynomial Cell (HPC) method, which is highly accurate and best suited for representing long distance wave propagation. The second model is a CFD code, solving the Reynolds-Averaged Navier–Stokes (RANS) equations within the OpenFOAM® toolkit, more suited to represent viscous and turbulent effects at local scale in the body vicinity. Two one-way coupling strategies are developed and compared in two dimensions, considering fully submerged and fixed structures. A domain decomposition (DD) strategy is first considered, introducing a refined mesh in the body vicinity on which the RANS equations are solved. Boundary conditions and interpolation operators from the FNPF results are developed in order to enforce values at its outer boundary. The second coupling strategy considers a decomposition of variables (functional decomposition, FD) on the local grid. As the FNPF simulation provides fields of variables satisfying the irrotational Euler equations, complementary velocity and pressure components are introduced as the difference between the total flow variables and the potential ones. Those complementary variables are solutions of modified RANS equations. Extensive comparisons are presented for nonlinear waves interacting with a horizontal cylinder of rectangular cross-section. The loads exerted on the body computed from the four simulation methods (standalone FNPF, standalone CFD, DD and FD coupling schemes) are compared with experimental data. It is shown that both coupling approaches produce an accurate representation of the loads and associated hydrodynamic coefficients (inertia and drag) over a large range of incident wave steepness and Keulegan–Carpenter number, for a small fraction of the computational time needed by the complete CFD simulation.

A flexible fully nonlinear potential flow model for wave propagation over the complex topography of the Norwegian coast

Coastal wave propagation and transformation are complicated due to the significant variations of water depth and irregular coastlines, which are typically present at the Norwegian fjords. A potential flow model provides phase-resolved solutions with low demands on computational resources. Many potential flow models are developed for offshore waves and lack of numerical treatments of coastal conditions. In the presented work, several modifications are introduced to a fully nonlinear potential flow model with a σ-grid for the purpose of coastal wave modelling: Shallow water breaking criteria are included in addition to deepwater breaking algorithms to approximate breaking waves over a complete range of water depth. A new coastline algorithm is introduced to detect complex coastlines and ensure robust simulations near the coast. The algorithm is compatible with structured grid arrangement in the horizontal plane and allows for high-order discretisation schemes for the free surface boundary conditions for an accurate representation of complex free surfaces. A parallelised solver for the Laplace equation is utilised to ensure fast simulations for large domains with multi-core infrastructures.The proposed model is validated against theories and experiments for various two- and three-dimensional nonlinear wave propagation and transformation cases that represent typical coastal conditions. The simulations show a good representation of nonlinear waves, and the results compare well with experiments. Furthermore, two large-scale engineering scenarios are simulated, where the applicability of the coastline algorithm and the parallel commutation capability of the model are demonstrated.

A Vortex Lattice Method for the Hydrodynamic Solution of Lifting Bodies Traveling Close and Across a Free Surface

The hydrodynamics performance of submerged and surface-piercing lifting bodies is analyzed by a potential flow model based on a Vortex Lattice Method (VLM). Such a numerical scheme, widely applied in aerodynamics, is particularly suitable to model the lifting effects thanks to the vortex distribution used to discretize the boundaries of the lifting bodies. The method has been developed with specific boundary conditions to account for the development of steady free surface wave patterns. Both submerged bodies, such as flat plates and hydrofoils, as well as planing hulls can be studied. The method is validated by comparison against available experimental data and other Computational Fluid Dynamic (CFD) results from Reynolds Averaged Navier Stokes (RANS) approaches. In all the analyzed cases, namely 2D and 3D flat plates, a NACA hydrofoil, planning flat plates and prismatic planing hulls, results have been found to be consistent with those taken as reference. The obtained hydrodynamic predictionsare discussed highlighting the advantages and the possible improvements of the developed approach.

Energy Dissipation and Nonpotential Effects in Wave Breaking

This paper presents a comparative numerical study of the energy dissipation process in the breaking of focused waves by using a potential flow model and a coupled potential/viscous flow model. An empirical eddy viscosity term is introduced to the fully-nonlinear potential (FNP) flow model to account for the breaking wave energy dissipation. The FNP model is further coupled with an incompressible two-phase NavierStokes (NS) flow solver through a one-way linkage to generate and propagate focused waves in the domain. Numerical absorbing regions are placed in front of the outlet boundaries to dampen wave reflection. The standalone FNP model and the coupled FNP+NS model are applied to deal with each scenario comparatively. This enables the accurate quantification and comparison of the energy loss of breaking waves calculated by the two numerical models. The velocity field is decomposed into potential component, which is reconstructed from the corresponding free surface elevation computed in the coupled model by using the weakly-nonlinear wave theory, and non-potential rotational component. Detailed analysis of the numerical results shows that: (1) energy loss is closely related to wave steepness, (2) mild rotational motion produced by a non-breaking wave is local in time with a short life-span, (3) strong non-potential motion triggered by wave breaking is not local in time but persists in the flow for dozens of or even many more wave periods.

Numerical Simulation of Liquid Sloshing Using a Fully Nonlinear Potential Flow Model in the Noninertial Coordinate System

Numerical Simulation of Liquid Sloshing Using a Fully Nonlinear Potential Flow Model in the Noninertial Coordinate System

Representation of 3-h Offshore Short-Crested Wave Field in the Fully Nonlinear Potential Flow Model REEF3D::FNPF

Abstract Stochastic wave properties are crucial for the design of offshore structures. Short-crested seas are commonly seen at the sites of offshore structures, especially during storm events. A long time duration is required in order to obtain the statistical properties, which is challenging for numerical simulations. In this scenario, a potential flow solver is ideal due to its computational efficiency. A procedure of reproducing accurate short-crested sea states using the open-source fully nonlinear potential flow model REEF3D::FNPF is presented in the paper. The procedure examines the sensitivity of the resolutions in space and time as well as the arrangements of wave gauge arrays. A narrow band power spectrum and a mildly spreading directional spreading function are simulated, and an equal energy method is used to generate input waves and avoid phase-locking. REEF3D::FNPF solves the Laplace equation together with the boundary conditions using a finite difference method. A sigma grid is used in the vertical direction and the vertical grid clustering follows the principle of constant truncation error. High-order discretization methods are implemented in space and time. Message passing interface is used for high performance computation using multiple processors. Three-hour simulations are performed in full-scale at a hypothetic offshore site with constant water depth. The significant wave height, peak period, kurtosis, skewness and ergodicity are examined in the numerically generated wave field. The stochastic wave properties in the numerical wave tank (NWT) using REEF3D::FNPF match the input wave conditions with high fidelity.

Mathematical modelling of diffusion flames with continuous geometric variation between counterflow and coflow regimes

This work presents a model of diffusion flames that continuously change from the counterflow regime to the coflow regime. In addition, the hydrodynamic aspects of this system are examined by means of scale modelling, asymptotic analysis and numerical simulation. The continuous change of the flame is imposed by the flow field, which is the composition of a radial fuel ejection from a cylindrical porous burner in the middle of two opposed impinging flows of oxidiser. The counterflow diffusion flame is located in the axis parallel to the incoming flows and the coflow diffusion flame, in the axis parallel to the outgoing flow. A scaling model shows that the flame length depends linearly on the stoichiometric oxidiser-fuel ratio (S), on the Péclet number based on the fuel ejection (Peb) and inversely proportional to the square root of the Péclet number based on the impinging flows (Pec), i.e., the parameter N:=cSPeb/Pec1/2 is appropriate to measure the flame length (c depends on the flame shape). A potential flow is assumed to allow analytical investigations of the flow field and flame properties. The results unveil the streamlines crossing the flame from the oxidiser side to the fuel side (oxidiser carried to the flame), up to approximately 60% of the flame length, and, from the fuel side to the oxidiser side (oxidiser carried to the flame), from this position to the flame tip. Moreover, the Navier–Stokes flow is also assumed in the analysis and the results show that the potential flow describes well the diffusion flame in the proposed geometric configuration. This result corroborates the consistency of the results and the adequate physical description provided by the potential flow model.

Experimental and numerical investigations on characteristics of coaxial liquid cone in coflow focusing

This work examines the interfacial instability and flow patterns of the liquid cone in capillary co-flow focusing. The flow field of the outermost driving flow is estimated with the potential flow model, and the startup process of the coaxial cone is analyzed. The effect of various parameters on the cone instability is studied. Moreover, the flow field inside the cone is visualized through the particle tracing method and numerical simulation, showing that flow rates have a significant impact on the size of the recirculation flow.

Hydrodynamic modeling effect analysis of a fully submerged tension leg concept integrating the DTU 10 MW offshore wind turbine

Efficient and accurate hydrodynamic load estimation is important for the dynamic response analyses of large-scale offshore wind turbines to achieve a reliable and cost-effective structural design. In this study, the hydrodynamic modeling effects based on a fully submerged tension leg platform (FSTLP) integrating the DTU 10 MW wind turbine are assessed. The linear potential flow theory combined with viscous drag force and the Morison's equation with added mass coefficients tuned by two different methods are investigated to assess their feasibility. The numerical simulations using different hydrodynamic models are performed and the results are validated by a series of hydrodynamic model tests. The dynamic motions and the structure forces of FSTLPWTs are analyzed in a range of wave-only and joint wind-wave conditions considering varying water depth. It shows that reliable predictions of the dynamic responses can be provided by the potential flow model with viscous drag force. Results obtained from Morison's equation with properly tuned added mass coefficients can match well with those provided by the potential flow model. The correct added mass coefficients are not necessarily obtained from the potential flow solutions. It is also found that the relative dominance of potential and viscous damping varies in different modes and can be affected by water depth.

Microbubble dynamics in a viscous compressible liquid subject to ultrasound

When a microbubble is subject to ultrasound, non-spherical oscillation or surface modes can be generated after many acoustic cycles. This phenomenon has wide applications, including ultrasonic cleaning, sonochemistry, and biomedical ultrasonics. Yet, the nonlinear development of the bubble shape modes over dozens of cycles is not well understood. Here, we describe a grid-free and robust model to simulate the phenomenon. A viscous pressure correction is introduced to compensate the non-zero tangential stress at the free surface in the potential flow model, based on conservation of energy. Consequently, the phenomenon is modeled using the boundary integral method, in which the compressible and viscous effects are incorporated into the model through the boundary conditions. The computations have been carried out for axisymmetric cases; however, the numerical model can be extended for three-dimensional cases in a straightforward manner. The numerical results are shown to be in good agreement for many cycles with some independent viscous and compressible theories for axisymmetric bubbles and experiments for microbubbles undergoing shape oscillation subject to ultrasound. The development of the shape oscillation of a bubble after a dozen cycles, the formation of a reentry jet and its penetration through the bubble, and the topological transformation of the bubble are simulated and analyzed in terms of the amplitude and frequency of the ultrasound. The computations and physical analysis are carried out for the development of shape modes due to a resonant volume oscillation, strong pressure wave, or the matching of the acoustic wave frequency with the shape mode frequency.

Numerical model for evaluation efficiency of coal pile wetting

Wetting the surface of coal piles is a common method of reducing dust emissions. The problem of modeling air pollution near coal after its wetting is considered. A two-dimensional mass transfer equation was used to model the process of coal dust distribution from the pile. This equation takes into account the convective and diffusion transport of coal dust in the atmosphere. The developed mathematical model takes into account different emission rates of coal dust from different parts of the coal pile. The model takes into account the effect of water evaporation from the coal pile on the rate of intensity of coal dust emission. A potential flow model was used to model the wind flow over the coal pile. Finite-difference splitting schemes have been used for numerical integration of modeling equations. Computer code based on the proposed numerical model has been developed. The developed code can be used to predict the efficiency of wetting coal piles over time. The results of a computational experiment are presented.

Lattice Boltzmann simulation of three-dimensional fluid interfacial instability coupled with surface tension

In this paper, the development of three-dimensional fluid interfacial Rayleigh-Taylor (RT) instability coupled with the surface tension was numerically studied using the mesoscopic lattice Boltzmann method. We mainly analyzed the influence of surface tension on fluid interfacial dynamics and spike/bubble late-time growth. The numerical experiments show that there exists the critical surface tension (<inline-formula><tex-math id="M3">\begin{document}$\sigma_{\rm{c}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20212061_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20212061_M3.png"/></alternatives></inline-formula>) in the three-dimensional RT instability, above which the RT phenomenon does not appear and below which it would take place. It is found that the critical surface tension increases with the fluid Atwood number and the corresponding numerical predictions show good agreements with those of the theoretical analysis <inline-formula><tex-math id="M4">\begin{document}${\sigma_{\rm{c}}}= {{({{\rho_{\rm{h}}}-{\rho_{\rm{l}}}})g}}/{{{k^2}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20212061_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20212061_M4.png"/></alternatives></inline-formula>. In addition, we can find that increasing surface tension reduces the roll-up of the interface and the complexity of interfacial structure, also preventing the breakup of the interface into the individual droplets. The late-time dynamics of phase interface change from the asymmetric development to the symmetry with respect to the middle axis. When the surface tension is sufficiently low, the spike and bubble amplitudes almost no longer change with it, and further increasing the surface tension can slow down the growth of the spike and bubble amplitudes. Furthermore, we can observe that the development of the high-Reynolds-number RT instability under different surface tensions can also be divided into four distinct stages, including the linear growth, saturated velocity growth, reacceleration, and chaotic mixing. The spike and bubble grow with approximately constant velocities at the saturated stage and their asymptotic values are consistent with those of the modified potential flow theory. In the following, the spike and bubble driven by the increasing Kelvin-Helmholtz vortices are accelerated such that their evolutional velocities exceed the solutions of the potential flow model at the reacceleration stage. The reacceleration stage cannot last infinitely and the spike and bubble velocities at the late time fluctuate with time, implying that the growth of the RT instability enters into the chaotic mixing stage. By numerical analysis, we demonstrate that the three-dimensional RT instability at the chaotic mixing stage has a quadratic growth and also report that the spike and bubble growth rates decrease with the surface tension in general.

CFD analysis of added mass, damping and induced flow of isolated and cylinder-mounted heave plates at various submergence depths using an overset mesh method

Fluid–structure interaction processes of heave damping plates in forced vertical motion are investigated using a CFD numerical model. First, a single isolated disk is considered with two submergence depths, including a case where the disk is very close to the mean water level with d/D=1/12 (d is the submergence depth and D the diameter of the disk). Then, the case of a disk attached to a vertical cylinder is analyzed, corresponding to one leg of a semi-submersible floater. The open source software OpenFOAM® is used to model the flow around the disk and to extract the relevant hydrodynamic coefficients of the structures. The dynamics of the structure and induced flow and free surface waves are tackled with the overset mesh tool implemented in OpenFOAM®. Considering the rotational symmetry of the problem, an axisymmetry model is used with wedge symmetry boundary conditions. The results are compared with experimental measurements and linearized potential flow modeling approaches with empirical correction. The CFD results of the models of both structures predict well the experimental measurements, including large oscillation periods and various amplitudes of heaving motion, where the potential model results are deteriorated.

The distribution of pantograph aerodynamic noise on train external surfaces and the influence of flow

Aerodynamic noise from the pantograph is significant when a train is running at high speeds and can be important for noise inside the train as well as at the wayside. In this work, the propagation of noise from a pantograph to the train external surfaces is studied, including the influence of the air flow. The noise emitted by the pantograph is modelled using a semi-empirical component-based approach which allows for the main factors of influence. To calculate the distribution of sound on the train external surfaces, the waveguide boundary element (2.5D BE) method is first employed, in which the pantograph is modelled by several equivalent dipole sources. Laboratory experiments are used to verify the 2.5D BE model for predicting the noise around the train due to the pantograph. The pantograph noise is found to be quite localised on the roof directly below the pantograph, where the sound pressure level on the train surface is high, but with increasing distance from the pantograph, it decreases rapidly. Moreover, the difference between the sound pressure level on the train roof and on the sides is about 20 dB in the plane of the pantograph. The influence of flow on the sound propagation is then modelled by introducing the profile of the velocity in the boundary layer into a 2D finite element model using the linearised potential flow model in COMSOL Multiphysics. The air flow causes some amplification in the sound pressure levels in the upstream direction and attenuation in the downstream direction. At high frequency the wind gradient in the boundary layer will change the direction of the sound, leading to the formation of a quiet shadow area in the upstream direction. However, despite these effects, the flow has only a small effect on the region with the highest noise levels beneath the pantograph.

Reduction of the wave propagation error of a sigma grid based numerical tank using a vertical spacing based on the constant truncation error

Numerical wave models that solve the Laplace equation for the velocity potential with a σ-grid in the vertical direction have been proven to be flexible and efficient. However, it is observed that the dispersion relation is sensitive to the variation of the vertical σ-grid arrangements. So far, there is no recommended practice to optimise the vertical σ-grid for a correct representation of the dispersion relation. In order to reduce the uncertainty of the dispersion relation and optimise the choice of the vertical grid distribution, a new method based on the constant truncation error of the finite difference scheme is presented in this article. The optimised vertical grids estimated by the novel method are applied in the fully nonlinear potential flow model REEF3D::FNPF to provide simulated wave surface elevations, which are compared with the measured time series in the long wave flume at SINTEF Ocean, Trondheim. Several different wave scenarios are considered, including regular waves, bichromatic waves, trichromatic waves as well as irregular waves. The wavemaker motions in the physical flume are used to generate waves in the numerical wave tank of REEF3D::FNPF. The proposed truncation error method is seen to effectively mitigate the dispersion (phase) error in all scenarios and the simulations show high accuracy in comparison with the experimental data.

An improved potential flow model for funnel flow prediction in a central discharging packed bed

An improved potential flow model for funnel flow prediction in a central discharging packed bed

SIMULATION OF A WATER CURTAIN APPLICATION TO PROTECT WORKERS FROM THERMAL INJURIES

Problem statement. The problem of evaluating the effectiveness of using the water curtain to reduce the risk of thermal injury to people in a fire is considered. The problem is to determine the temperature fields when supplying water for air cooling. The purpose of the article. Development of a numerical model for calculating the process of propagation of water droplets in the air, their evaporation to reduce the temperature of heated air due to fire. Methodology. For mathematical modeling of the process of propagation of water droplets in air, thermal air pollution, the convective-diffusion equation of mass transfer, the energy equation and the equation describing the motion of an ideal liquid (potential flow model) are used. The potential flow model allows you to quickly determine the field of air flow velocity in areas with a complex geometric shape. Implicit difference splitting schemes are used for numerical integration of the convective-diffusion mass transfer equation and the energy equation. Physical splitting of basic equations is used to construct a difference analogue of modeling equations. The Richardson method and the conditional approximation scheme are used to solve the aerodynamics problem of determining the velocity potential field and the components of the air velocity vector. An engineering method for calculating the process of evaporation of a drop of water based on Sreznevsky's law has been developed. Scientific novelty. An effective numerical model has been developed that allows the method of computational experiment to determine the efficiency of using the water curtain to reduce the level of thermal pollution of atmospheric air due to fire. The numerical model is based on the integration of the fundamental equations of aerodynamics, heat and mass transfer. The model takes into account the most significant physical factors that affect the process under study: the movement of heated air, the movement of water droplets in the air, evaporation of the droplet, and so on. Practical significance. Based on the built model, a computer code has been created that allows you to quickly determine the temperature fields in the air when using a water curtain. The numerical model will be useful when conducting computational experiments for the purpose of scientifically sound choice of the location of the water curtain in case of fire. Conclusions. A computer code has been created that allows a computational experiment to investigate the effectiveness of using a water curtain in a fire. The developed computer program can be implemented on low and medium power computers. The results of a computational experiment are presented.

Swimming, flying, and diving behaviors from a unified\xa02D potential model

Animals swim in water, fly in air, or dive into water to find mates, chase prey, or escape from predators. Even though these locomotion modes are phenomenologically distinct, we can rationalize the underlying hydrodynamic forces using a unified fluid potential model. First, we review the previously known complex potential of a moving thin plate to describe circulation and pressure around the body. Then, the impact force in diving or thrust force in swimming and flying are evaluated from the potential flow model. For the impact force, we show that the slamming or impact force of various ellipsoid-shaped bodies of animals increases with animal weight, however, the impact pressure does not vary much. For fliers, birds and bats follow a linear correlation between thrust lift force and animal weight. For swimming animals, we present a scaling of swimming speed as a balance of thrust force with drag, which is verified with biological data. Under this framework, three distinct animal behaviors (i.e., swimming, flying, and diving) are similar in that a thin appendage displaces and pressurizes a fluid, but different in regards to the surroundings, being either fully immersed in a fluid or at a fluid interface.