Axial Body Forces Research Articles

Optimal flow control of vortex breakdown in a laminar swirling flow

In highly swirling flows, such as hydraulic turbines operating under part-load (PL) conditions, vortex breakdown occurs and performance is impaired. Consequently, it is imperative that mitigation measures are taken. In the present study, a laminar swirling flow with a vortex breakdown at a Reynolds number of 180 is investigated. At the inlet, a swirling velocity profile with a swirl number of 1.095 is set. A stability analysis is conducted to identify unstable modes based on the assumption that vortex breakdown is a global instability. The results indicate that spiral modes with wave number 1 are unstable. An optimal flow control method based on the Adjoint method is then utilized to mitigate vortex breakdown. In the present study, the control method targets vorticity using a minimization algorithm. Control variables include radial and axial body forces. According to the results, the method was effective in mitigating vortex breakdown. A stability analysis conducted during the control process revealed that as the vorticity decreased, the growth-rate of the eigenvalue decreased, indicating that the flow is stabilized.

The role of soluble surfactant in the linear instability of a film coating inside a tube

This study investigates the linear instability of a thin-film coating inside a rigid tube. The flow is assumed to be inertialess and driven by an axial body force (e.g. gravity), an interfacial shearing force, or their combinations. The interface and the bulk of the film are laden with soluble surfactant. The properties of the soluble surfactant, i.e. solubility, sorption kinetics and bulk diffusivity, modulate the interfacial dynamics of the film. The influence of these properties on the linear instability of the film is comprehensively investigated via long-wave approximation analysis and numerical calculation. Two modes, namely the interface mode and the surfactant mode, are identified to dominate the instability. For a quiescent film, it is found that solubility, sorption kinetics and bulk diffusivity act to improve the uniformity of the surface surfactant and mitigate the stabilizing effect of the Marangoni force. For the film driven by the axial body/interfacial shearing force, the results reveal that solubility plays contrasting roles in the interface mode and the surfactant mode. A window with intermediate solubility is detected where the film can be linearly stabilized. Moreover, sorption kinetics is found to destabilize the perturbations with long wavelength whereas it stabilizes the perturbations with finite wavelength. The bulk diffusivity of the surfactant has a non-monotonic influence on the flow instability, and the film can be relatively stable at both strong and weak diffusivity.

Water flow in a cylindrical nanopore with an object

Understanding the physics of water movement through a nanopore with an object is critical for better control of water flow and object translocation. It should help in the design of nanopores as molecular and viral sensors. We evaluated how the external electric field and ion concentrations, pore wall charge density, disk radius and charge density, and ion mobility influence the water flow in a charged cylindrical nanopore using Poisson–Nernst–Planck–Navier–Stokes simulations. We dissected water flow induced by the external electric field (“external” component) from that generated by the field induced by the fixed and mobile charges (“charge” component). The velocity and direction of the axial flow “external” component were controlled directly by the external electric field. The pore wall charges also influenced them indirectly by altering the density and distribution of mobile charges. Higher external concentrations enhanced the axial water flow by lowering its charge component. The ion mobility and disk charge slightly influenced the axial water flow. The axial body forces near the wall drive the axial water flow near the pore wall. If the disk is large, water also flows axially in the opposite direction near the pore center. Local forces near the disk do not control the radial water flow near the disk. The axial body force and water flow near the pore wall do. If an annulus replaces a disk, the axial forces near the pore wall control the radial flow near the annulus and the axial flow within its hole.

Direct material property determination: One‐dimensional formulation utilising full‐field deformation measurements

AbstractA direct approach is described to determine the elastic modulus distribution in a nominally heterogeneous material subject to tensile/compression loading and primarily experiencing deformations in the axial direction. The formulation is developed for uniaxial applications using basic theoretical constructs, resulting in a computational framework that has a matrix form [A] {E} = {R}, where the [A] matrix components are known functions of measured axial strains and axial positions, {R} components are known functions of axial body forces, applied loads and reactions and {E} components are the unknown elastic moduli at discrete locations along the length of the specimen. For a series of one‐dimensional (1D) material property identification procedure with known axial strains at discrete locations and various levels of random noise, results are presented to demonstrate the accuracy and noise sensitivity of the methodology. Finally, experimental measurements for a heterogeneous bone specimen are compared to our 1D model predictions, demonstrating that the predictions are in very good agreement with independent estimates at each load level of interest along the length of the bone specimen.

The quantum character of buckling instabilities in thin rods

Here the buckling of inextensible rods due to axial body forces is mapped to 1D, nonrelativistic, time-independent quantum mechanics. Focusing on the pedagogical case of rods confined to 2D, three simple and physically realizable applications of the mapping are given in detail; the quantum counterparts of these are particle in a box, particle in a delta-function well, and particle in a triangular well. A fourth application examines the buckling counterpart of a quantum many-body problem (in the Hartree approximation). Through a fifth application, given in the form of an exercise, the reader can explore the surprising consequences of adding a second transverse dimension to the rod buckling problem and imposing periodic boundary conditions.

Axisymmetric Body-Force Fields in Elastodynamics of Transversely Isotropic Media

In this paper, a complete elastodynamic solution for axisymmetric problems under axial body-forces in terms of two retarded potential functions in transversely isotropic media is extended to the case of general torsionless axisymmetry. Allowing for both axial and radial distributed internal loads through the use of an extra potential, the new solution retains its completeness via the theory of repeated wave equations. By virtue of its analytical design, the formulation can be reduced to the corresponding elastostatic case by simply suppressing the time-dependence of its potentials as well as the case of isotropy. In the limiting case of the latter material condition, the proposed representation for elastostatic problem degenerates to a recent extension of Love’s potential function.

Analytical Equilibrium Swirling Inflow Conditions for Computational Fluid Dynamics

T HE specification of swirling inflow conditions is an integral and important part of computational fluid dynamics (CFD) of swirling flows, which are complex flows with many practical applications [1], for instance, in turbulent combustion [2]. To specify a swirling velocity profile with a desired swirl number in a traditional CFDanalysis based on aReynolds-averagedNavier–Stokes (RANS) modeling approach is not an easy task, which becomes even more difficult in advanced CFD approaches such as direct numerical simulation (DNS) or large-eddy simulation (LES). DNS or LES of spatially inhomogeneous turbulent flows requires turbulent inflow boundary conditions [3], which may be generated either from an auxiliary simulation, from a proper orthogonal decomposition and linear stochastic estimation [4], from a digital filter reproducing specified statistical data [5], or simply taken as the mean velocity profile with superimposed fluctuations [6], which is essentially a perturbed inflow. With the presence of swirling, inflow conditions are difficult to specify. For RANS-based CFD, an appropriate mean velocity profile is needed. For DNS and LES, apart from the mean velocity profile, information on an appropriate “turbulent” component is needed as well. Pierce and Moin [7] developed a method for generating equilibrium swirling inflow conditions, which represents a logical, idealized starting point for generating swirling velocity profiles. In their method, the swirling inflow is obtained numerically by solving for the flow driven by fictitious axial and azimuthal body forces, where the axial body force represents themean pressure gradient that drives the physical flow. The azimuthal body force is not physically producible and may be thought of as existing only to overcome drag from the walls. This technique was used in LES of a coaxial jet combustor and good agreement with the experimental data was observed [7]. The method can be regarded as an effective and simple means of generating realistic swirling inflow conditions. In this study, efforts have beenmade to derive an analytical formof the equilibrium swirling inflow conditions. The analytical swirling inflow is easy to implement, as it does not require solving for the flow numerically [7]. The particular forms of the analytical equilibrium swirling velocity profiles have been obtained for swirling annular and round jets, which can be directly applied in the specification of swirling inflow conditions for RANS approaches and further explored for the specification of swirling inflow conditions for DNS and LES, regardless of the turbulent component needed in the timedependent simulations. A desired swirl number at the inflow can also be conveniently achieved by adjusting a constant.

Time-harmonic body force loading of a mode-I penny-shaped crack

The present paper is concerned with the problem of determining dynamic SIF of a penny-shaped crack in an infinite elastic medium, which is subjected to the action of time-harmonic axial body forces, placed symmetrically with respect to the crack plane. The solution of the problem is obtained by superposition of the solutions of two simpler problems. The first of these problems is related to the unperturbed (crackless) space under the prescribed axial body forces, while the second problem consists in finding the dynamic SIF of the penny-shaped crack whose faces are directly acted upon by some axial stresses. The form of these axial stresses is determined from the solution of the first problem. Fourier and Hankel transforms have been used to solve the first problem. Next by means of the Hankel transform, the second problem has been reduced to a pair of dual integral equations which have been subsequently transformed into a Fredholm integral equation of the second kind via an auxiliary function. The integral equation has been solved numerically in order to determine the variations of the dynamic stress intensity factor at the rim of the penny-shaped crack for some particular body force loading cases.

Nonlinear analysis of orthotropic beams of solid cross-sections

The paper presents a nonlinear formulation and a finite-differences based numerical solution for the structural behavior of generic orthotropic beams of solid cross-sections. The analysis includes a detailed description of the three-dimensional out-of-plane warping and the solution is achieved by successive iterations while preserving all geometrical nonlinearities. The axial body forces are introduced consistently through the axial differential equilibrium equation. The formulation yields some basic closed-form analytic solutions for homogeneous beams, and the numerical results provide an insight into the coupling effects mechanisms in generic laminated composite beams, including the resulting interlaminar stresses.

WAVE PROPAGATION IN A RESTRICTED TRANSVERSELY ISOTROPIC ELASTIC SOLID WHOSE SLOWNESS SURFACE CONTAINS CONICAL POINTS

By restricting the elastic constants, a model is obtained of a transversely isotropic elastic solid whose slowness surface has two conical points on the symmetry axis as well as a ring of double points in a plane perpendicular to this axis. The radiation problem for this solid is analysed for the axial displacement component caused by a point axial body force.

Static and dynamic axial loading of a partially debonded fiber

The stresses on a partially bonded fiber in a composite material subject to axial loads are derived for both static and dynamic conditions. The static stress intensity is calculated for a fiber which is only partially bonded circumferentially and subject to a constant axial stress gradient, i.e. a uniform axial body force. The same configuration of a single partially bonded fiber is then considered for loading in the form of a dynamic stress gradient in the fiber, and particular attention is given to the stress intensity factor at the edge of the bond when the fiber is subject to a step load. The numerical results show that the dynamic stress always overshoots the static value, and the time taken to achieve the static equilibrium stress can be quite long if the fiber is nearly debonded. This is related to the phenomenon that a very loosely bonded fiber may resonate strongly at a frequency which goes to zero as the size of the bond vanishes.

Experimental and numerical investigation of a propeller with three-dimensional inflow

The goal is to study the three-dimensional (3-D) flow produced by a propeller operating in a 3-D approach flow representative of pusher-prop arrangements on aircraft or underwater vehicles. The research involves both numerical predictions and wind-tunnel experiments. The specific nonuniform inflow studied is generated by a varying mesh screen disk of one large-diameter mesh, one smaller-diameter mesh, and a 30-deg mesh wedge aligned with the tip of the wedge and the centers of the two circular screens matching. This inflow is similar to the wake behind a slender axisymmetric body with a slender planar appendage. The propeller has three blades, and is self-propell ed with respect to the drag of the screen disk. The testing is divided into two main parts. The first deals with propeller performance and the condition needed to reach a self-propelled mode. The second part is the measurement of the mean and turbulent flow downstream of the propeller for two axial locations, x/D - 0.025 and 0.5. The computational work is part of a step-by-step approach to development of a method for analysis of propeller flowfields with three-dimensional inflows of increasing complexity. The fully elliptic, 3-D, Reynolds-averaged, steady-state, primitive-variables Navier-Stokes equations are solved by a Penalty Finite-Element Method. Turbulence modeling is through the integrated turbulence-kinetic-energy (TKE) model. The length scale is algebraically related to the axial velocity profiles. The propeller is modeled as an actuator disk. The mesh disk is modeled as a distribution of axial-body forces, which are related to the local drag. Generally, the agreement achieved between predictions and experiment is considered excellent for a 3-D, turbulent flow of this complexity.

Finite element modeling of acoustic singularities with application to propeller noise

Numerical formulations and results that expand on recent developments in finite element modeling of acoustic volume sources and acoustic dipoles are presented. It is shown that with a suitable structuring of the acoustic field equations it is possible to include monopoles and dipoles within the same analysis framework as has been extensively used for interior duct acoustic and duct inlet radiation problems. This allows the extension of the finite element modeling method to include the noise sources in such applications as propellers enclosed in a duct or in free space with mean flows. The necessary structuring of the acoustic field equations is shown, and example calculations are given for the case of one-dimension al sources and body forces in the presence of mean flow, two-dimensional sources, axial body forces, and transverse body forces in the presence of uniform mean flow. Three-dimensional sources and dipoles are modeled as the Fourier sum of axially symmetric solutions without the necessity of introducing singular elements. It is further demonstrated that distributions of singularities can be readily modeled, and an example is given of the computation of the near- and far-field radiation of a propeller. Comparison of the far-field radiation directivity is made with the Gutin theory.

Numerical simulations of tornado-like vortices. Part 1: Vortex evolution

Abstract An axi-symmetric numerical vortex model suitable for studies of intense atmospheric vortices such as tornadoes and waterspouts is described. The model uses the vorticity- streamfunction form of the equations of motion and unlike earlier models has a stretched grid in the radial direction, providing for economical resolution of both the vortex core and the rotating cloud updraught in which it forms. The model incorporates an axial body force to represent the driving effect of cloud buoyancy, although a simulation is described also in which the latter is modelled directly by including a moisture scheme with latent heat release. In the latter case we have not found parameter values for which a steady flow is attained. The dynamics of vortex evolution conforms broadly with the descriptions given by Leslie (1971) and Smith and Leslie (1978, 1979), an additional feature being that significant intensification occurs following vortex touchdown, before the flow becomes steady. During this phase, a transient feature resembling vortex breakdown develops and then subsides. In contrast with earlier simulations in which the body force is concentrated near the axis, the present calculations demonstrate the possibility of generating a narrow vortex within a broad region of forcing as appears to be the situation in the atmosphere.

Skin Effect in Magneto-Fluid Dynamic Traveling Wave Devices

Electromagnetic propagation through an infinite circular cylindrical traveling wave tube in which a conducting fluid of constant conductivity is moving axially with uniform speed is studied. Asymptotic solutions valid for |αR0|«1 and |αR0»1, where α is the complex separation constant and R0 the tube radius, are obtained and analyzed. Concentrating specifically on the axial body force per unit tube length induced in the fluid, the |αR0|»1 solution indicates, fixing the current sheet input and geometry, that the magnitude of the induced axial force is a marked function of the dimensionless parameter β, equal to the magnetic Reynolds number based on wavespeed and wavelength multiplied by the slip. The body force rises linearly with β for small β, reaches a peak and then, because of the inability of the electromagnetic field to penetrate into the conductor with increasing β (skin effect), falls like β−1/2 for large β. From the practical viewpoint, the results suggest the adjustment of the electrical and fluid mechanical parameters so that operation occurs at that value of β which optimizes the force. It is further indicated, especially for moderate to high β operation, that for efficient utilization and conservation of working fluid mass and electrical energy, injection and acceleration take place in an annulus close to the coils rather than throughout the entire cross section.

Influence of Large Amplitudes on Flexural Vibrations of a Thin Circular Cylindrical Shell

In this paper are derived the equations of nonlinear flexural vibrations for a thin circular cylindrical shell. The assumptions employed in the various steps of derivation are clearly set forth. Axial body force terms which may be of practical importance are included in the equations. Nonlinear periods are obtained for the free vibrations case. Numerical examples are given for a shell with a radius thickness ratio of 100 and two numbers of circumferential waves, 8 and 10. The results are plotted and compared with a previous study on flat plates. In these examples, nonlinear effects are found to be considerably less manifest in cylinders than in corresponding flat plates.