Irrotational Flow Field Research Articles

Forced vibration characteristics of lock gate structure

The influence of fluid on the lock gate structure in a dam-reservoir system subjected to sinusoidal excitation is investigated. The gate’s material is considered homogeneous, isotropic, prismatic, and elastic, and the gate is analysed using Mindlin’s plate theory. The fluid is considered non-viscous, incompressible, and has an irrotational flow field. The method of separation of variables with the Fourier half range cosine series is used to solve the fluid domain’s Laplace equation. The fluid’s infinite length is curtailed near the gate, controlling the calculations without affecting the results too much. Both the domains are interacted with each other by transferring the fluid’s pressure to the gate and the gate’s acceleration to fluid. At the fluid’s free surface, undisturbed and linearised, conditions are considered. The Newmark-beta time integration approach is used to solve the forced vibration equations using developed FORTRAN computer code. A study has been performed to assess the dynamic pressure variation due to fluid. The present results may be valuable if the lock gate is subjected to any terrible natural phenomena.

Free Vibration Analysis of Stiffened Lock Gate Coupled with Reservoir Fluid considering Linearised Free Surface Condition

The effect of surrounding reservoir fluid on the stiffened lock gate structure is investigated using the finite element method. A single stiffener is used to stiffen the plate, which is placed edge to edge along the height on the plate's center nodal line. Mindlin’s plate bending and Euler’s beam theories are used to formulate plate and stiffener, respectively. The stiffened lock gate material is assumed to be isotropic, homogeneous, uniformly thick and elastic in nature. The fluid is assumed to be incompressible and inviscid, resulting in an irrotational flow field. The fluid domain's top free surface is assumed to be linear based on Airy’s linear wave theory. The far boundary of the fluid domain is truncated numerically close to the lock gate to control the size of computation without influencing the results, very much. It is truncated by solving the Laplace equation using Fourier half range cosine series expansion in the finite element formulation. Pressure and displacement are considered as nodal variables for the fluid domain and the lock gate, respectively. The interaction between the fluid domain and the lock gate is established by finite element formulation and transformed into a computer code, written in FORTRAN. The natural frequencies of clamped and simply supported stiffened lock gates are evaluated by the varying extent of the fluid. Both stiffened and unstiffened gates are compared. The results are beneficial to the engineers/designers when the gate structure is subjected to cataclysmic events.

Supersonic separation technology for carbon dioxide and hydrogen sulfide removal from natural gas

Abstract A cleaner approach was proposed for removing CO2 and H2S from highly acid natural gas by supersonic separation technology. For this purpose, different structures of Laval nozzles and supersonic swirling separation devices were designed. The mathematical models of gas flow in the nozzle were established, and the supersonic flow characteristics of CH4–H2S–CO2 ternary mixture were accurately predicted by adding the real gas state equation and the transport equation to describe the rotational and irrotational flow field. The effects of nozzle structure, swirl angle of static vanes and inlet parameters on the refrigeration performance of the nozzle and the separation characteristics of the swirl device were systematically investigated. The results show that the average temperature at the nozzle outlet can be as low as 135.2 K under the condition of inlet temperature 293.15 K, inlet pressure 4 MPa and 20 mol % acid gas. It indicates that the refrigeration effect produced by high speed expansion of acid natural gas in the supersonic nozzle can provide a favorable liquefying environment for the acid components, which confirms the feasibility of capturing acid components by supersonic separation device. Better refrigeration performance can be achieved in the nozzle with higher outlet Mach number, but the pressure recovery capacity of the device will be suppressed accordingly. As swirl angle increases from 73.90° to 81.79°, the maximum tangential velocity in the nozzle rises from 119.6 m/s to 212.5 m/s, the separation performance of the swirl device increases, while the pressure and temperature at the same location decrease slightly. However, the increase of swirl intensity will restrict the flow capacity of the separator. For the given supersonic swirling separation device, it shows a good adaptability in separation performance when changing the inlet parameters.

Free Vibration Analysis of Lock Gate Structure

ABSTRACTThe effect of fluid on the natural frequencies of a vertical rectangular lock gate is investigated. The fluid is assumed to be inviscid and incompressible having an irrotational flow field. The far boundary of fluid domain is truncated near the lock gate structure by solving the Laplace equation using Fourier half range cosine series expansion. The formulation of lock gate structure is governed using Mindlin’s plate theory. The coupled interaction between the fluid domain and the lock gate structure is established using finite element method (FEM) and a computer code is written using FORTRAN. Convergence study and validation of the formulation are carried out to minimise the computational error. The natural frequencies of lock gate coupled with and without fluid are determined for undisturbed and linearised free surface conditions. By varying extent of fluid domain, the effect on the natural frequencies of lock gate is evaluated. The results of natural frequencies obtained may be useful to the designer when the reservoir lock gate structure is exposed to the natural disasters.

The unusual fluid dynamics of particle electrophoresis

The classical problem of the electrophoretic motion of a spherical particle has been treated theoretically by Overbeek in his 1941 PhD thesis and almost 40 years later by O’Brien & White. Although both approaches used identical assumptions, the details are quite different. Overbeek solved for the pressure, velocity fields as well as the electrostatic potential, whereas O’Brien & White obtained the electrophoretic mobility without the need to consider the pressure and velocity explicitly. In this paper, we establish the equivalence of these two approaches that allow us to show that the tangential component of the fluid velocity has a maximum near the surface of the particle and outside the double layer, the velocity decays as 1/r3, where r is the distance from the sphere, instead of 1/r in normal Stokes flow. Associated with this behavior is that of an irrotational outer flow field. This is consistent with the fact that a sphere moving with a constant electrophoretic velocity experiences zero net force. A study of the forces on the particle also provides a physical explanation of the independence of the electrophoretic mobility on the electrostatic boundary conditions or dielectric permittivity of the particle. These results are important in situations where inter-particle interaction is considered, for instance, in electrokinetic deposition.

The shape and motion of gas bubbles in a liquid flowing through a thin annulus

We study the shape and motion of gas bubbles in a liquid flowing through a horizontal or slightly inclined thin annulus. Experimental data show that in the horizontal annulus, bubbles develop a unique ‘tadpole-like’ shape with a semi-circular cap and a highly stretched tail. As the annulus is inclined, the bubble tail tends to vanish, resulting in a significant decrease of bubble length. To model the bubble evolution, the thin annulus is conceptualised as a ‘Hele-Shaw’ cell in a curvilinear space. The three-dimensional flow within the cell is represented by a gap-averaged, two-dimensional model, which achieved a close match to the experimental data. The numerical model is further used to investigate the effects of gap thickness and pipe diameter on the bubble behaviour. The mechanism for the semi-circular cap formation is interpreted based on an analogous irrotational flow field around a circular cylinder, based on which a theoretical solution to the bubble velocity is derived. The bubble motion and cap geometry is mainly controlled by the gravitational component perpendicular to the flow direction. The bubble elongation in the horizontal annulus is caused by the buoyancy that moves the bubble to the top of the annulus. However, as the annulus is inclined, the gravitational component parallel to the flow direction becomes important, causing bubble separation at the tail and reduction in bubble length.

Particle Based Simulation for Solitary Waves Passing over a Submerged Breakwater

This research develops a two-dimensional numerical model for the simulation of the flow due to a solitary wave passing over a trapezoidal submerged breakwater on the basis of generalized vortex methods. In this method, the irrotational flow field due to free surface waves is simulated by employing a vortex sheet distribution, and the vorticity field generated from the submerged object is discretized using vortex blobs. This method reduces the difficulty in capturing the nonlinear deformation of surface waves, and also concentrates the computational resources in the compact region with vorticity. This numerical model was validated by conducting a set of simulations for irrotational solitary waves and then compared with the results of a relevant research. The comparisons exhibit good agreement. The rotational flows induced by different incident wave height were simulated and analyzed to study the effect of vorticity on the deformation and the breaking of solitary waves.

On the flow field about an electrophoretic particle

The flow field about an electrophoretic body is theoretically investigated by analytical methods. An effective boundary condition for the electric potential at particle surface is derived. This condition, which generalizes the one obtained by Levich [Physicochemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, 1962), Chap. 9, p. 475], captures the effect of (convective and electromigratory) surface current in the Debye layer and is valid as far as it is legitimate to neglect ion-concentration gradient in the bulk liquid. Conditions for negligible concentration gradients are also presented and discussed. The effect of surface current determines a deviation from Morrison's “classical” theory, which predicts irrotational flow-field for any particle shape with electrophoretic velocity given by the well-known Smoluchowski formula and always directed along the applied electric field. It is shown here that in the presence of the above effect the irrotationality of the flow field is not preserved if the particle surface has non-uniform curvature. However, irrotational flow-field still subsists for a sphere and a cylinder and is analytically determined in terms of a new non-dimensional parameter, referred to as the electrophoretic number. The case of spheroidal objects is also examined in detail. In this case the flow field, though not strictly irrotational, is shown to be nearly approximated by an irrotational flow-field, which is also determined over wide ranges of electrophoretic number and spheroid aspect ratio. The quality of this approximation is expressed as a relative error on the Helmholtz-Smoluchowski condition and numerically evaluated both in longitudinal and transverse configuration. The limiting cases of spheroid degenerating into a needle and a disk are also addressed. In all above cases the respective mobilities deviate from Smoluchowski's formula and depend on the electrophoretic number. An important effect of surface ion-transport in the double layer is anisotropy of electrophoretic mobility for non-spherical objects. That always bears a bias of the electrophoretic velocity with respect to the applied electric field when the latter is not collinear with a symmetry axis of the body. For a cylinder, bias is always toward the axis. For a spheroid, it is generally toward the polar axis; however, bias toward the equatorial axis is predicted for moderately oblate spheroids. In general, the bias angle is remarkable, which is of potential consequence in technical applications of electrophoresis. Comparison of results of the present theory with experimental work from the literature is presented and discussed.

Dynamic interaction of multiple buoyant jets

AbstractAn array of closely spaced round buoyant jets interact dynamically due to the pressure field induced by jet entrainment. Mutual jet attraction can result in a significant change in jet trajectories. Jet merging also leads to overlapping of the passive scalar fields associated with the individual jets, resulting in mixing characteristics that are drastically different from those of an independent free jet. A general semi-analytical model for the dynamic interaction of multiple buoyant jets in stagnant ambient conditions is proposed. The external irrotational flow field induced by the buoyant jets is computed by a distribution of point sinks with strength equal to the entrainment per unit length along the unknown jet trajectories and accounting for boundary effects. The buoyant jet trajectories are then determined by an iterative solution of an integral buoyant jet model by tracking the changes in the external entrainment flow and dynamic pressure fields. The velocity and concentration fields of the jet group are obtained by momentum or kinetic energy superposition for merged jets and plumes, respectively. The modelling approach is supported by numerical solution of the Reynolds-averaged Navier–Stokes equations. The model shows that jet merging and mixing can be significantly affected by jet interactions. Model predictions of the multiple jet trajectories, merging height, as well as the centreline velocity and concentration of the buoyant jet group are in good agreement with experimental data for: (i) a clustered momentum jet group; (ii) a turbulent plume pair; and (iii) a rosette buoyant jet group. Dynamic interactions between a jet group are shown to decrease with the addition of an ambient cross-flow.

A new method of retrieving typhoon's sea level pressure fields and central positions from scatterometer-derived sea surface winds

First, UWPBL model(the university of washington planetary boundary layer model) is used to retrieve YaGi typhoon sea level pressure from sea surface wind data of SeaWinds which are obtained from QuikSCAT(called direct retrieving) and these strength results are analyzed. Then the variational method is used to decompose the sea surface winds field into two parts: vortex and irrotational environmental flow field, the UWPBL model is used again to retrieve YaGi typhoon sea level pressure from the vortex flow field, the results of typhoon central positions are analyzed by comparing the results with the results of direct retrieving, NCEP data and typhoon annual reports. It turns out that the accuracy of the typhoon sea level pressure central position is obviously improved. This method offers a new idea for the study of typhoon from microwave scatterometer data.

An iterative scheme for axisymmetric supercavitating flow

This article presents a numerical investigation of axisymmetric supercavitating flow. It is assumed that such a flow field could be estimated by a potential flow that neglects the viscosity effects and rotational motion of the fluid and assumes the flow as an irrotational flow field. One of the most adequate methods for modelling potential fields is the boundary element method, which is employed in this article. A novel iterative scheme is used to capture the free surface of an axisymmetric supercavity. This numerical algorithm is based on updating an initial guess for the cavity's boundary; the convergence criterion is the pressure amount on the free surface of the cavity, which converges to a constant value. To obtain finite lengths for supercavities, a cavity closure model is applied. The results are in good agreement with similar analytical and numerical solutions as well as the existing experimental data for supercavities characteristic properties and the drag coefficient on cavitators. The present iterative numerical algorithm is reliable for predicting the characteristics of a supercavitating flow. Moreover, the feasibility of the cavity capturing in a flow field with low cavitation number is especially attractive.

Coordinate mapping of analytical contaminant transport solutions to non-uniform flow fields

Existing analytical solutions to 2D and 3D contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. An approximate method is developed herein for coordinate mapping of 2D (vertically-averaged) transport solutions to non-uniform steady-state irrotational and divergence-free flow fields in single-layer aquifers. The method enables existing analytical transport solutions to be applied to aquifer systems with wells, non-uniform saturated thickness, surface water features, and (to a limited degree) heterogeneous hydraulic conductivity and recharge. This mass-conservative coordinate mapping approach is inexact in its approximation of the dispersion process but is still sufficiently accurate for many simple flow systems. The degree of model error is directly proportional to the variation of velocity magnitude within the domain. These mapped analytical solutions are compared to numerical simulation results and the coordinate mapping errors are investigated. The methods described herein may be used in the traditional capacity of analytical transport models, i.e., screening and preliminary site assessment, without sacrificing accuracy by assuming locally uniform flow conditions or applying an ad-hoc coordinate transformation. The solutions benefit from the traditional advantages of analytical methods, particularly the removal of artifacts due to spatial and temporal discretization: no time-stepping or numerical discretization is required.

Bright solitary waves of atomic Bose-Einstein condensates under rotation

We analyze the rotation of bright solitary waves formed of atomic Bose-Einstein condensates with attractive atomic interactions. By employing a variational technique and assuming an irrotational quadrupolar flow field, we map out the variational solutions in the rotating frame. In particular, we show that rotation has a considerable stabilizing effect on the system, significantly raising the critical threshold for collapse of the bright solitary waves.

On decomposition of typhoon flow field

The present paper is concerned with characteristics of flow structures of typhoons, and the double variational method is applied. First, the typhoon flow field is decomposed into two parts: the maximum asymmetric vortex and irrotational environmental flow field. Then the maximum asymmetric vortex is also decomposed into two parts: the maximum symmetric vortex and β-gyres. Finally, typhoon Pearl(2006) is simulated by WRF model(weather research and forcasting model), and flow fields at various times at 500hPa are decomposed using the above method. It turns out that the decomposed flow fields are useful for researches on motion and track prediction of typhoons.

MAST solution of advection problems in irrotational flow fields

A new numerical–analytical Eulerian procedure is proposed for the solution of convection-dominated problems in the case of existing scalar potential of the flow field. The methodology is based on the conservation inside each computational elements of the 0th and 1st order effective spatial moments of the advected variable. This leads to a set of small ODE systems solved sequentially, one element after the other over all the computational domain, according to a MArching in Space and Time technique. The proposed procedure shows the following advantages: (1) it guarantees the local and global mass balance; (2) it is unconditionally stable with respect to the Courant number, (3) the solution in each cell needs information only from the upstream cells and does not require wider and wider stencils as in most of the recently proposed higher-order methods; (4) it provides a monotone solution. Several 1D and 2D numerical test have been performed and results have been compared with analytical solutions, as well as with results provided by other recent numerical methods.

Effect of flow on solutions of rod-coil block co-polymers

An elongational flow field is imposed on a solution of block copolymers consisting of semirigid macromolecules with rigid, rodlike sequences of units in combination with random coil (flexible) units. The problem is formulated according to the lattice treatment of Matheson and Flory. In this formulation, the system consists of rigid blocks whose lengths and locations are fixed by the structure within each macromolecule. These blocks are separated by random coiled units. An excess free energy other than the equilibrium Gibbs free energy of the quiescent solution has to be considered due to the flow field that tends to align the rods. This excess free energy is calculated from the potential energy of rods when a steady-state, homogeneous and irrotational flow field is applied to the solution. The effects of composition, polymer–solvent interaction, size of the co-polymer and flow rates are investigated. Depending on the size and number of rods, some of the chains studied exhibit a biphasic region at equilibrium that shifts to lower concentrations with increasing flow. Longer chains with shorter rods that are isotropic at equilibrium, exhibit a biphasic region at finite values of flow. The degree of orientation increases sharply when the system is biphasic. For larger flows, the orientation function is very close to unity which is perfect orientation.

An explicit unconditionally stable numerical solution of the advection problem in irrotational flow fields

A new methodology for the Eulerian numerical solution of the advection problem is proposed. The methodology is based on the conservation of both the zero‐ and the first‐order spatial moments inside each element of the computational domain and leads to the solution of several small systems of ordinary differential equations. Since the systems are solved sequentially (one element after the other), the method can be classified as explicit. The proposed methodology has the following properties: (1) it guarantees local and global mass conservation, (2) it is unconditionally stable, and (3) it applies second‐order approximation of the concentration and its fluxes inside each element. Limitation of the procedure to irrotational flow fields, for the 2‐D and 3‐D cases, is discussed. The results of three 1‐D and 2‐D literature tests are compared with those obtained using other techniques. A new 2‐D test, with radially symmetric flow, is also carried out.

Wave field with a submerged porous breakwater

The flow field of linear waves passing a submerged porous breakwater has been solved analytically in this paper. The permeable breakwater is considered to be aniso‐tropic but homogeneous. The hypothesis of equivalent work is assumed in the porous field to ensure the existence of velocity potential in an irrotational flow field. The boundary value problem is then solved by the method of separation of variables. The eigenvalues in the boundary value problem with porous media are in general, complex. There are two series solutions of eigenvalues in the water column containing the porous breakwater. The range of each mode of eigenvalues, even in porous media, has been given explicitly. Orthogonality of the velocity potentials has been proved and the convergence of the series solution verified. The corresponding flow field has then been studied by varying wave and structure properties and justified by experiments. Since wave reflection can occur on both sides of the porous breakwater, partial standing waves, as well as a resonance, similar to harbor seiche, may be found in the corresponding flow region.

A note on impulsive sphere motion beneath a free-surface

A general framework is presented for solving the impulsive oblique motion of a spherical body in close proximity and below a free-surface. The fluid is considered to be impulsive and the flow as incompressible. The irrotational flow field is deduced from a velocity potential. The full nonlinear problem is reduced to a sequence of boundary-value problems by employing a small-time expansion technique. The mixed boundary conditions are of a Dirichlet type on the undisturbed free-surface and of a Neumann type on the equilibrium spherical shape. The solution is obtained by employing a Green's function and the method of multipoles expansions. General expressions, correct to each order in the small-time, are given for the free-surface deflections and the pressure force experienced by the moving sphere.

New numerical method for constructing quasiequilibrium sequences of irrotational binary neutron stars in general relativity

We propose a new numerical method to compute quasi-equilibrium sequences of general relativistic irrotational binary neutron star systems. It is a good approximation to assume that (1) the binary star system is irrotational, i.e. the vorticity of the flow field inside component stars vanishes everywhere (irrotational flow), and (2) the binary star system is in quasi-equilibrium, for an inspiraling binary neutron star system just before the coalescence as a result of gravitational wave emission. We can introduce the velocity potential for such an irrotational flow field, which satisfies an elliptic partial differential equation (PDE) with a Neumann type boundary condition at the stellar surface. For a treatment of general relativistic gravity, we use the Wilson--Mathews formulation, which assumes conformal flatness for spatial components of metric. In this formulation, the basic equations are expressed by a system of elliptic PDEs. We have developed a method to solve these PDEs with appropriate boundary conditions. The method is based on the established prescription for computing equilibrium states of rapidly rotating axisymmetric neutron stars or Newtonian binary systems. We have checked the reliability of our new code by comparing our results with those of other computations available. We have also performed several convergence tests. By using this code, we have obtained quasi-equilibrium sequences of irrotational binary star systems with strong gravity as models for final states of real evolution of binary neutron star systems just before coalescence. Analysis of our quasi-equilibrium sequences of binary star systems shows that the systems may not suffer from dynamical instability of the orbital motion and that the maximum density does not increase as the binary separation decreases.