Flow Of Ideal Fluid Research Articles

On one analytical solution to the problem of flow around a tandem from two profiles by a flow of ideal incompressible fluid

On one analytical solution to the problem of flow around a tandem from two profiles by a flow of ideal incompressible fluid

Ideal and non-ideal planar compressible fluid flows in radial equilibrium

Two-dimensional compressible flows in radial equilibrium are investigated in the ideal dilute-gas regime and the non-ideal single-phase regime close to the liquid–vapour saturation curve and the critical point. Radial equilibrium flows along constant-curvature streamlines are considered. All properties are therefore independent of the tangential streamwise coordinate. A differential relation for the Mach number dependency on the radius is derived for both ideal and non-ideal conditions. For ideal flows, the differential relation is integrated analytically. Assuming a constant specific heat ratio $\gamma$ , the Mach number is a monotonically decreasing function of the radius of curvature for ideal flows, with $\gamma$ being the only fluid-dependent parameter. In non-ideal conditions, the Mach number profile also depends on the total thermodynamic conditions of the fluid. For high molecular complexity fluids, such as toluene or hexamethyldisiloxane, a non-monotone Mach number profile is admissible in single-phase supersonic conditions. For Bethe–Zel'dovich–Thompson fluids, non-monotone behaviour is observed in subsonic conditions. Numerical simulations of subsonic and supersonic turning flows are carried out using the streamline curvature method and the computational fluid dynamics software SU2, respectively, both confirming the flow evolution from uniform flow conditions to the radial equilibrium profile predicted by the theory.

(Invited) Experimental and Data Analysis Platforms to Better Understand the Corrosion and Discharge of Powdered Zn

Zinc anodes have been a cornerstone of many commercial and pre-commercial battery technologies including primary and secondary alkaline cells, Zn-air batteries and Zn-ion batteries. To maximize the performance of devices at both the lab and commercial scales, moderate surface area (mm-sized) Zn powder is used – either immobilized onto a diffusion electrode or incorporated into a slurry. Unlike nano-sized materials, micron-sized materials are poorly characterized by traditional electrochemical techniques like thin-film rotating disk electrodes, because the roughness introduced by the relatively large particles disrupts the ideal fluid flow near the surface, negating the mathematical description of the electrode behavior. This leads many researchers to try and characterize the Zn behavior in more application-like cells. The downside of doing this is that there is a strong influence of the counter electrode, electrolyte solution and the efficacy of the specific individual in assembling the cells. Therefore, there is a need to develop new platforms that have the ability to determine the electrochemical properties of powdered Zn – most notably achievable capacity and corrosion current – and to develop analytical models to describe their behavior.Over the past several years, our group has been developing new platforms to understand how Zn behaves during discharge and charge, including 1-D cells and cells that mimic the geometry of a primary alkaline battery [1]. However, those platforms have their limitations. In this talk, another new cell, coined the “gravity cell” will be discussed. The gravity cell has a small well where Zn (either as raw powder or in slurry form) is gravity deposited onto an indium foil current collector. Typically, a gel electrolyte is placed on top of the Zn bed, followed by liquid electrolyte, which also contains the counter and reference electrodes. The gravity cell is used to both discharge the Zn powder and to measure its corrosion characteristics. This can be done as a function of mass loading, which introduces limitations into the behavior as the Zn discharges from the Zn/gel interface towards the current collector. This type of discharge, limited by Ohmic resistance, requires new mathematical frameworks to extract the desired parameters. This talk will focus on the design of the cell as well as the derivation of the mathematical framework. Then, data will be shown using several types of Zn powder both in the presence and absence of surfactants that aim to reduce the corrosion rate.

Steady-State Flows of Ideal Incompressible Fluid with Velocity Pointwise Orthogonal to the Pressure Gradient

Steady-State Flows of Ideal Incompressible Fluid with Velocity Pointwise Orthogonal to the Pressure Gradient

Lagrangian reduction and wave mean flow interaction

How does one derive models of dynamical feedback effects in multiscale, multiphysics systems such as wave mean flow interaction (WMFI)? We shall address this question for hybrid dynamical systems, defined as systems whose motion can be expressed as the composition of two or more Lie-group actions. Hybrid systems abound in fluid dynamics. Examples include: the dynamics of complex fluids such as liquid crystals; wind-driven waves propagating with the currents moving on the sea surface; turbulence modelling in fluids and plasmas; and classical–quantum hydrodynamic models in molecular chemistry. From among these examples, the motivating question here is: How do wind-driven waves produce ocean surface currents?The paper first summarises the geometric mechanics approach for deriving hybrid models of multiscale, multiphysics motions in ideal fluid dynamics. It then illustrates this approach for WMFI in the examples of 3D WKB waves and 2D wave amplitudes governed by the nonlinear Schrödinger (NLS) equation propagating in the frame of motion of an ideal incompressible inhomogeneous Euler fluid flow. The results for these examples tell us that the mean flow in WMFI does not create waves, although it does transport the waves. However, feedback in the opposite direction is possible, since the 3D WKB and 2D NLS wave dynamics discussed here do in fact create circulatory mean flow.

Blockage coefficient of cylindrical blocker and diffusion resistance of membrane channels.

This study deals with potential flow of ideal fluid in an infinite cylindrical tube in the presence of a blocking object. The blockage effect of the object on the flow can be characterized by a lump parameter, blockage coefficient, which accounts for the object shape and size. For a cylindrical blocking object, analytical results for the blockage coefficient are known only in three limiting cases: for a long thin cylinder and for small and large blocking disks. We propose a simple analytical expression for the blockage coefficient of a cylindrical blocker of arbitrary length and radius that reduces to the known asymptotic results in the corresponding limits.

Some exact solutions that describe an ideal fluid flow with a free boundary

The study is aimed at constructing exact solutions that describe unsteady flows of an ideal fluid with a free boundary. Currently existing examples of solutions of this kind have a linear or quadratic initial field of velocities. The object of the present study is flows with a cubic initial velocity field. Several exact solutions are obtained by using a method based on the complex Hopf equation for the complex velocity. One of the main problems in solving the Euler equations in the domain with a free boundary is to study the positions of singular points because these points can reach the free boundary with time, which may lead to solution destruction. In the present case, singularities can be found explicitly. However, as the initial velocity field is defined by a third-power polynomial, one has to study the Riemann surfaces for the function of complex velocity in order to determine the mutual positions of the singularities and flow domain. It is shown that any initial velocity field defined by a cubic polynomial yields one of seven flows described in the paper with time. It is of interest that there are examples of flows that exist for a finite time and break down when the singularities reach the free boundary. Using a certain modification of the Hopf equation, we obtain a two-parameter family of exact solutions that describe fluid flows with a free boundary. Two examples of this family are considered. In one of them, the solution breaks down within a finite time. The second example is of interest because the motion of a singular point in the fluid leads to the formation of a narrow channel with free boundaries.

Theoretical investigation of dam-break waves in frictional channels with power-law sections

Both the hydraulic resistance and the channel cross-sectional geometry have significant effect on the propagation of the dam-break waves. Analytical models including either of them have been available. However, it is not feasible to assess the comprehensive influence using the existing solutions. The present study considers a resistance-dominated wave tip region followed by an ideal fluid flow region in a dry horizontal channel whose cross-sectional shape is controlled by a power-law index n. Laboratory experiments and numerical simulations are conducted to measure/predict the water surface profiles of the dam-break flows in five types of flumes. The water depth, location and celerities of the wave front predicted by the analytical model agree well with the experimental and numerical results. The quantitative effects of the bottom resistance and the channel cross-sectional shape on the wave properties are investigated. Results show that the spatio-temporal variation in the wave feature of the dam-break flows strongly depends on the channel cross-sectional geometry; while the retardation effect of the bottom resistance becomes more significant as n increases. Furthermore, the derived analytic solution as well as the experimental data can be used for evaluating numerical solutions considering the hydraulic resistance and cross-sectional geometry.

A novel grid-stiffening concept for locally reinforcing window openings of composite fuselage panels using streamline stiffeners

Streamlines are smooth and continuous curves that naturally never intersect with each other and fit the shape of the body that exists in an ideal fluid flow. These features can be exploited to employ the streamlines as reference trajectories for stiffening panels with cutouts. Moreover, the streamline stiffeners can properly be placed to locally reinforce the cutouts leading to integrated curvilinear grid-stiffening concepts that can be implemented in composite fuselage panels with window openings. In this paper, based on this new concept, the buckling performance of grid-stiffened fuselage panels with reinforced window openings is addressed. Two common shapes of commercial aircraft fuselage windows are considered. Grid-stiffened panels with different grid patterns subjected to in-plane uniaxial and biaxial compressive loads are investigated. Analysis and design optimization studies are conducted. In the optimization study, a panel with streamline fibres and stiffeners is considered where the layup of the skin is optimized for maximum buckling load. The buckling performance of the panels with streamline fibres and stiffeners constructed based on the proposed concept is compared with that obtained for traditional panels with straight fibres and stiffeners. It is shown that the proposed grid-stiffening concept offers substantial improvements in the buckling capacity compared with the conventional grid-stiffening approach baseline.

Numerical method for steady ideal 2‐D flows of finite vorticity with applications to vertical‐axis wind turbine aerodynamics

AbstractThis paper presents a new method for approximately modeling 2‐D ideal steady fluid flows with finite vorticity induced by actuator curves of arbitrary shape. An actuator curve is an infinitesimally thin region containing a body force density acting on the flow, while the rest of the flow is force‐free. The approach can be used for any flow satisfying this description, but, like other actuator methods, it is naturally suited for modeling turbines or propellers. We derive a weak formulation of the governing equations in the Lagrange streamfunction and solve it using finite elements. Compared to related methods such as the actuator cylinder (AC) approach, our formulation is uniquely suited for computations involving wake–wake or wake–turbine interactions. We validate the method by computing the flow through a single Darrieus vertical‐axis wind turbine (VAWT) and comparing with previous work. To demonstrate the ability to simulate interacting actuators of arbitrary configuration, we simulate a three‐VAWT array. The turbines are modeled in a freestream, and the loading is chosen to represent ideal airfoils. The standard VAWT results are consistent with previous work, validating the method. The three‐VAWT array demonstrates a higher efficiency than the single VAWT (0.56 vs. 0.52), with differing optmal tip speed ratios for the upwind and downwind turbines (upwind: 3.9, downwind: 3.1. The optimum for a single turbine is 3.6). The flow field of the three‐VAWT array shows expected features such as an acceleration of flow between the two counter‐rotating upwind turbines.

Twenty-six moment equations for the Enskog–Vlasov equation

The Enskog–Vlasov equation is a phenomenological kinetic equation that extends the Enskog equation for the dense (non-ideal) hard-sphere fluid by adding an attractive soft potential tail to the purely repulsive hard-sphere contribution. Simplifying assumptions about pair correlations lead to a Vlasov-like self-consistent force field that adds to the Enskog non-local hard-sphere collision integral. Within the limitations imposed by the underlying assumptions, the extension gives the Enskog–Vlasov equation the ability to give a unified description of ideal and non-ideal fluid flows as well as of those fluid states in which liquid and vapour regions coexist, being separated by a resolved interface. Furthermore, the Enskog–Vlasov fluid can be arbitrarily far from equilibrium. Thus the Enskog–Vlasov model equation provides an excellent, although approximate, tool for modelling processes with liquid–vapour interfaces and adjacent Knudsen layers, and allows us to look at slip, jump and evaporation coefficients from a different perspective. Here, a set of 26 moment equations is derived from the Enskog–Vlasov equation by means of the Grad moment method. The equations provide a meaningful approximation to the underlying kinetic equation, and include the description of Knudsen layers. This work focuses on the – rather involved – derivation of the moment equations, with only a few applications shown.

Translationally invariant exact steady flows of gas and fluid

Abstract New exact 3-D steady translationally invariant (or z-invariant) flows of isentropic gas and ideal incompressible fluid are constructed. New exact solutions for steady magnetohydrodynamics equations are derived. We show that Euler equations for steady z-invariant flows of isentropic gas are equivalent to a coupled system of a partial differential equation of second order for the streamfunction ψ(x, y) which contains an arbitrary differentiable function H(ψ) and a transcendental equation connecting gas density ρ(x, y) with function ψ(x, y) and depending on equation of state p(ρ) = cρ γ and on the function H(ψ). We prove that functions ψ(x, y) and ρ(x, y) satisfy a universal nonlinear equation that is independent of equation of state p = p(ρ) and of the function H(ψ).

Energy balance for forced two-dimensional incompressible ideal fluid flow.

Cheskidov et al. (2016 Commun. Math. Phys. 348, 129-143. (doi:10.1007/s00220-016-2730-8)) proved that physically realizable weak solutions of the incompressible two-dimensional Euler equations on a torus conserve kinetic energy. Physically realizable weak solutions are those that can be obtained as limits of vanishing viscosity. The key hypothesis was boundedness of the initial vorticity in [Formula: see text], [Formula: see text]. In this work, we extend their result, by adding forcing to the flow. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

On air entrapment onset and surface velocity in high-speed turbulent prototype flows

In a free-surface spillway, the upstream flow is non-aerated and the flow becomes a strong air-water mix downstream of the onset location of air entrapment. Field observations were conducted over a steep spillway chute, and detailed quantitative measurements were undertaken in real-world high-speed flows with strong turbulence and very high Reynolds numbers within the range 107 to 108. The data showed that the onset of air entrapment is a complicated transient three-dimensional process in high-speed strongly-turbulent flows. A robust optical flow (OF) technique was applied and provided physically-meaningful surface velocities in the non-aerated flow region. The streamwise velocities were reasonably close to ideal fluid flow calculations, with large streamwise surface velocity fluctuations, in the non-aerated flow region. Overall, the study demonstrated the application of optical techniques to prototype spillway flows, provided that some careful validation was undertaken.

Ideal planar fluid flow over a submerged obstacle: Review and extension

A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height; perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour. doi:10.1017/S1446181121000341

On the Semi-Analytical Solutions in Hydrodynamics of Ideal Fluid Flows Governed by Large-Scale Coherent Structures of Spiral-Type

We have presented here a clearly formulated algorithm or semi-analytical solving procedure for obtaining or tracing approximate hydrodynamical fields of flows (and thus, videlicet, their trajectories) for ideal incompressible fluids governed by external large-scale coherent structures of spiral-type, which can be recognized as special invariant at symmetry reduction. Examples of such structures are widely presented in nature in “wind-water-coastline” interactions during a long-time period. Our suggested mathematical approach has obvious practical meaning as tracing process of formation of the paths or trajectories for material flows of fallout descending near ocean coastlines which are forming its geometry or bottom surface of the ocean. In our presentation, we explore (as first approximation) the case of non-stationary flows of Euler equations for incompressible fluids, which should conserve the Bernoulli-function as being invariant for the aforementioned system. The current research assumes approximated solution (with numerical findings), which stems from presenting the Euler equations in a special form with a partial type of approximated components of vortex field in a fluid. Conditions and restrictions for the existence of the 2D and 3D non-stationary solutions of the aforementioned type have been formulated as well.

Optimization approach to suppression of vibrations: For axially moving webs in a fluid flow

A web (continuum) traveling in a flow of ideal fluid between two fixed supports with a constant velocity and performing transverse vibrations is considered by modeling the web as an isotropic type elastic panel. The fluid flow is considered as a potential flow. The web transverse vibration process is analyzed taking into account both material elasticity and the fluid-structure interaction between the traveling material and the surrounding flowing fluid. It is supposed that the actuator system is used for suppression of occurring transverse vibrations. An optimization approach based on the modern control theory and calculus of variations is proposed for determining the optimal suppressive actions at a given time interval. The quality of suppression vibration process is evaluated by means of the functional depending on displacements and velocities at the terminal time. The example (carried out in an analytical way) illustrating all basic stages of finding of optimal vibration suppression is presented.

A metamaterial-free fluid-flow cloak.

The model of ideal fluid flow around a cylindrical obstacle exhibits a long-established physical picture, where originally straight streamlines are deflected over the whole space by the obstacle. Inspired by transformation optics and metamaterials, recent theories have proposed the concept of fluid cloaking, which is able to recover the straight streamlines, as if the obstacle did not exist. However, such a cloak, similar to all previous transformation-optics-based devices, relies on complex metamaterials with inhomogeneous parameters and is difficult to implement. Here we deploy the theory of scattering cancellation and report on the experimental realization of a fluid-flow cloak without metamaterials. This cloak is realized by engineering the geometry of the fluid channel, which effectively cancels the dipole-like scattering of the obstacle. The cloaking effect is demonstrated through the direct observation of recovered straight streamlines in the fluid flow. Our work sheds new light on conventional fluid control and may find application in microfluidic devices.

Effect of water depth on Kelvin–Helmholtz instability in a shallow water flow

It is well known that the interface between two regions of an incompressible ideal fluid flow moving in a relative motion is necessarily destabilized, regardless of the velocity difference’s strength. This phenomenon is the so-called Kelvin–Helmholtz instability. However, a large number of works demonstrated a surprising result that the instability is suppressed for shallow water flows; the interface is stabilized if the Froude number, defined by the velocity difference’s ratio to the gravity wave’s speed, is sufficiently large. In a limited way, these authors used the shallow water equations without the higher-order effect of the dispersive terms. Thus, this investigation aims at examining these higher-order dispersive effects to analyze the interface stability problem of tangential-velocity discontinuity in shallow water flows. In particular, we use the Green–Naghdi equations to introduce the dispersive terms related to the depth and the depth-averaged horizontal velocities of the fluid. We show that the interface stability depends on the Froude number (i.e., the velocity difference’s strength) and the water depth. A critical value of the Froude number to stabilize the interface is smaller than the case of no dispersive terms, and the flow in a deeper region is more stable than in a shallower one. We also consider the distribution of kinetic and potential energy to clarify a feature characteristic of a large class of instabilities in shallow water flow. The instability of flows is caused by the decrease in the kinetic energy during the perturbation of waves. This phenomenon is known as negative energy modes and plays a vital role in applying the model to industrial equipment. A conclusion is that the equipartition of energies occurs if and only if the velocity difference is zero and the water depth is shallow enough to ignore the dispersive terms.

Вызванные скорости вне струи идеального движителя

Object and purpose of research. The paper is devoted to the analysis of induced flow velocities outside the ideal propeller jet. The purpose is to widen capabilities of estimations. Materials and methods. Analysis of data on this issue has shown that complicated and quite labor-consuming methods are used for these purposes. It is attempted to devise a calculation scheme based on direct determination of induced velocities from discrete sinks simulating the ideal propeller. For this purpose an algorithm and software is developed for PC implementation. Testing of the computer program allowed us to define conditions ensuring the accuracy of calculations, it confirmed practically full agreement with the data obtained by other authors and possibility for widening the range of its application. Main results. Systematic calculations of induced velocities outside the ideal propeller jet were done allowing us to determine the flow velocity at any point of a wide area for engineering purposes. Conclusion. Longitudinal and radial component velocities induced by ideal propeller outside its jet were calculated based on directly assessed influence of the system of sinks distributed over the propeller disk on the ideal fluid flow. The algorithm for calculations was developed, the software was written and tested. Systematic calculations of induced velocities were done, which could be used for practical estimations.