Search Results (19)

This work studies the influence of a growing boundary layer on the process of supersonic flow around an aerodynamic body. The task is to select and implement in an experiment the parameters of a supersonic flow and to study the flow pattern near the surface of an aerodynamic body at different viscosity values for the incoming flow. Visualization of the shock wave configuration in front of the body and studying the change in the pressure field in the flow region under these conditions is the main goal of this work. The experiment was carried out on an experimental stand created on the basis of a shock tube. The aerodynamic body under study (a semi-cylinder pointed along a circle or an ellipse) was placed in a supersonic nozzle. The model was clamped by lateral transparent walls, which were simultaneously a source of boundary layer growth and the viewing windows for visualizing the flow. For selected modes with Reynolds numbers from 8200 to 45,000, schlieren flow patterns and pressure distribution fields near the surface of the streamlined models and the plate of the growing boundary layer were obtained. The data show a complex, unsteady flow pattern realized near the model which was caused by the viscous-inviscid interaction of the boundary layer with the bow shock wave near the wall. Full article

An approach to estimate the dynamic characteristic of multilayered three-dimensional cubic quasicrystal cylindrical shells, annular plates, and truncated conical shells with different boundary conditions is presented. These investigated structures can be in a vacuum, totally filled with quiescent fluid, and subjected to internal flowing fluid where the fluid is incompressible and inviscid. The velocity potential, Bernoulli’s equation, and the impermeability condition have been applied to the shell–fluid interface to obtain an explicit expression, from which the fluid pressure can be converted into the coupled differential equations in terms of displacement functions. The state-space method is formulated to quasicrystal linear elastic theory to derive the state equations for the three structures along the radial direction. The mixed supported boundary conditions are represented by means of the differential quadrature technique and Fourier series expansions. A global propagator matrix, which connects the field variables at the internal interface to those at the external interface for the whole structure, is further completed by joint coupling matrices to overcome the numerical instabilities. Numerical examples show the correctness of the proposed method and the influence of the semi-vertical angle, different boundary conditions, and the fluid debit on the natural frequencies and mode shapes for various geometries and boundary conditions. Full article

The paper considers the visco-elastic response of the ice cover in a channel under an external load moving with constant speed along the center line. The channel has a rectangular cross-section with a finite depth and width. The fluid in the channel is inviscid and incompressible and its motion is potential. The fluid is covered by a thin sheet of ice frozen to the channel walls. The ice thickness varies linearly symmetrically across the channel, being lowest at the center of the channel and highest at the channel walls. Ice deflections and strains in the ice cover are independent of time in the coordinate system moving with the load. The problem is solved numerically using Fourier transform along the channel and the method of normal modes across the channel. The series coefficients for normal modes are determined by truncation for the resulting infinite systems of linear algebraic equations. The ice deflections and strains in the ice plate are investigated and compared to the case of constant mean ice thickness. It is shown that even a small variation of the ice thickness significantly changes the characteristics of the hydroelastic waves in the channel. Full article

The free transverse vibration of a surface-piercing, vertical cylinder partially submerged in water was studied. The cylinder had an arbitrary non-circular, but symmetric, cross-section in the vibration direction. The water was assumed to be an incompressible and inviscid fluid. The effect of the surface waves of water was neglected in the analysis. The exact solution of velocity potential of water was derived by the method of separation of variables. The unknown coefficients in the solution of the velocity potential were expressed in the form of integral equations, including the dynamic deformation of the beam. Then, the governing differential equation of bending vibration of the cylinder under the hydrodynamic pressure was obtained. The Galerkin method was used to obtain the eigenvalue equation by expanding the wet modes of the cylinder into a series of dry modes. The elliptical cylinders partially submerged in water were taken as the numerical example. The accuracy of the proposed method was evaluated by the convergence studies. As a consequent result, the non-dimensional added virtual mass incremental (NAVMI) factor solutions were compared to the present Galerkin solutions, which can be used as a benchmark test for more sophisticated numerical simulations of computational fluid dynamics. Full article

Equilibrium statistical mechanics predicts that inviscid, two-dimensional, incompressible flow on the sphere eventually reaches a state in which spherical harmonic modes of degrees $n=1$ and $n=2$ hold all the energy. By a separate theory, such flow is static in a reference frame rotating at angular speed $2\Omega /3$ with respect to the inertial frame. The vorticity field in the static frame is an accident of the initial conditions, but, once established, it lasts forever under the stated assumptions. We investigate the possibility of such behavior with a stereographic-coordinate model that conserves energy and enstrophy when the viscosity vanishes. Full article

The linear two-dimensional problem of interaction between an hydroelastic wave propagating along an elastic floating ice plate with built-in vertical rigid plate is studied. The fluid under the ice is inviscid and incompressible. The fluid depth is finite. The deflection of the ice plate is described by the linear theory of thin elastic plates. The flow under the ice is potential. The total velocity potential is decomposed into the potential of the incident wave, even potential caused by the vertical motion of the rigid plate, and an odd potential caused by the rotation of the rigid plate. The vertical mode method is used. The third potential is obtained by solving a mixed boundary-value problem numerically using Chebyshev polynomials. The solution is validated by analysis of its convergence. The first and second potentials, and the corresponding deflections and strains of the ice plate, are obtained analytically. The motions of the rigid plate, as well as deflection and strains in the floating plate, are numerically analyzed. It is shown that the rotation of the rigid plate due to the incident wave is the main factor of increasing strains in the ice plate. Full article

In the current work, the stochastic Burgers’ equation is studied using the Dynamically Orthogonal (DO) method. The DO presents a low-dimensional representation for the stochastic fields. Unlike many other methods, it has a time-dependent property on both the spatial basis and stochastic coefficients, with flexible representation especially in the strongly transient and nonstationary problems. We consider a computational study and application of the DO method and compare it with the Polynomial Chaos (PC) method. For comparison, both the stochastic viscous and inviscid Burgers’ equations are considered. A hybrid approach, combining the DO and PC is proposed in case of deterministic initial conditions to overcome the singularities that occur in the DO method. The results are verified with the stochastic collocation method. Overall, we observe that the DO method has a higher rate of convergence as the number of modes increases. The DO method is found to be more efficient than PC for the same level of accuracy, especially for the case of high-dimensional parametric spaces. The inviscid Burgers’ equation is analyzed to study the shock wave formation when using the DO after suitable handling of the convective term. The results show that the sinusoidal wave shape is distorted and sharpened as the time evolves till the shock wave occurs. Full article

The temporal linear instability of a viscoelastic liquid sheet moving around an inviscid gas in a transverse electrical field is analyzed. The fluid is described by the leaky dielectric model, which is more complex than existing models and enables a characterization of the liquid electrical properties. In addition, the liquid is assumed to be viscoelastic, and the dimensionless dispersion relation of the sinuous and varicose modes between the wavenumber and the temporal growth rate can be derived as a 3 × 3 matrix. According to this relationship, the effects of the liquid properties on the sheet instability are determined. The results suggest that, as the electrical Euler number and the elasticity number increase and the time constant ratio decreases, the sheet becomes more unstable. Finally, an energy budget approach is adopted to investigate the instability mechanism for the sinuous mode. Full article

Viscoelastic liquid sheet of couple-stress type streaming with relative motion into an inviscid gas through porous molium is studied theoretically and quantitatively in this project. To derive the differential equations that describe liquids, gases, and the electric field, we linearized the governing equations of motion and continuity, Maxwell’s equations in quasi-static approximation, and the appropriate boundary conditions at the two interfaces. Then we used the normal mode method. It was demonstrated analytically that the solutions to these differential equations can be found for both symmetric and antisymmetric disturbances, respectively. We could not obtain an explicit form of the growth rates since we could not solve the dispersion relations for both situations because they were obtained in highly complex forms. The Mathematica program is used to solve the dimensionless forms of the dispersion relations numerically using Gaster’s theorem. Various influences on the stability analysis of the considered system have been studied in detail, and it is determined that the system in the presence of a porous material is more unstable than it would be otherwise. In a two-dimensional system, the antisymmetric disturbance case is found to be more unstable than the corresponding symmetric disturbance situation. Some characteristics, such as Wabe number, Ohnesorge number, and electric field, have destabilizing effects, whereas others, such as porosity, medium permeability, viscoelasticity parameter, gas-to-liquid viscosity ratio, and dielachic constants, have stabilizing effects. Finally, it is discovered that the gas-to-liquid velocity ratio plays a dual role in the stability condition depending on whether the gas-to-liquid velocity ratio U ≶ 1. In the past, we have only found evidence of very few previous studies. Full article

The numerical assessment of T-tail flutter requires a nonlinear description of the structural deformations when the unsteady aerodynamic forces comprise terms from lifting surface roll motion. For linear flutter, a linear deformation description of the vertical tail plane (VTP) out-of-plane bending results in a spurious stiffening proportional to the steady lift forces, which is corrected by incorporating second-order deformation terms in the equations of motion. While the effect of these nonlinear deformation components on the stiffness of the VTP out-of-plane bending mode shape is known from the literature, their impact on the aerodynamic coupling terms involved in T-tail flutter has not been studied so far, especially regarding amplitude-dependent characteristics. This term affects numerical results targeting common flutter analysis, as well as the study of amplitude-dependent dynamic aeroelastic stability phenomena, e.g., Limit Cycle Oscillations (LCOs). As LCOs might occur below the linear flutter boundary, fundamental knowledge about the structural and aerodynamic nonlinearities occurring in the dynamical system is essential. This paper gives an insight into the aerodynamic nonlinearities for representative structural deformations usually encountered in T-tail flutter mechanisms using a CFD approach in the time domain. It further outlines the impact of geometrically nonlinear deformations on the aerodynamic nonlinearities. For this, the horizontal tail plane (HTP) is considered in isolated form to exclude aerodynamic interference effects from the studies and subjected to rigid body roll and yaw motion as an approximation to the structural mode shapes. The complexity of the aerodynamics is increased successively from subsonic inviscid flow to transonic viscous flow. At a subsonic Mach number, a distinct aerodynamic nonlinearity in stiffness and damping in the aerodynamic coupling term HTP roll on yaw is shown. Geometric nonlinearities result in an almost entire cancellation of the stiffness nonlinearity and an increase in damping nonlinearity. The viscous forces result in a stiffness offset with respect to the inviscid results, but do not alter the observed nonlinearities, as well as the impact of geometric nonlinearities. At a transonic Mach number, the aerodynamic stiffness nonlinearity is amplified further and the damping nonlinearity is reduced considerably. Here, the geometrically nonlinear motion description reduces the aerodynamic stiffness nonlinearity as well, but does not cancel it. Full article

The hydroelastic response of an elastic thin plate combined with a vertical porous flexible plate floating on a single- or a two-layer fluid is analyzed in the two-dimensional Cartesian coordinate system. The vertical and the horizontal plates are placed in an inverted-L shape and rigidly connected together. The problem is studied with the aid of the method of matched eigenfunction expansions within the framework of linear potential flow theory. The fluid is assumed to be inviscid and incompressible, and the motion is assumed to be irrotational. Time–harmonic incident waves of the traveling mode with a given angular frequency are considered. Then, the least-squares approximation method and the inner product are used to obtain the expansion coefficients of the velocity potentials. Graphical results show the interaction between the water waves and the structure. The effects of several physical parameters, including the length and the complex porous-effect parameter of the vertical plate, on the wave reflection and transmission are discussed. The results show that a vertical plate can effectively eliminate the hydroelastic response of the very large floating structure. The longer a vertical plate is, the more waves are reflected by the vertical plate. With the increase in the porous-effect parameter, the deflection of vertical plate decreases. Besides the effects of the flexural rigidity, the lateral stress, the mooring line angle, the fluid density ratio, and the position of interface on the wave reflection and transmission are discussed. Numerical results show the significant mitigation effect due to the presence of the additional vertical plate. Full article

The periodic flexural-gravity waves propagating along a frozen channel are investigated. The channel has a rectangular cross section. The fluid in the channel is inviscid, incompressible and covered with ice. The ice is modeled by a thin elastic plate whose thickness varies linearly. Two cases have been considered: the ice thickness varies symmetrically across the channel, being the smallest at the center of the channel and the largest at the channel walls; the ice thickness varies from the smallest value at the one wall to the largest value at another wall. The periodic 2D problem is reduced to the problem of the wave profiles across the channel. The solution of the last problem is obtained by the normal mode method of an elastic beam with linear thickness. The behavior of flexural-gravity waves depending on the inclination parameter of the ice thickness has been studied and the results have been compared with those for a constant-thickness plate. Dispersion relations, profiles of flexural-gravity waves across the channel and distributions of strain in the ice cover have been determined. In the asymmetric case, it is shown that for long waves, the most probable plate failure corresponds to transverse strains at the thin edge of the plate, which can lead to detachment of the ice from the corresponding bank. For short waves, the longitudinal stresses within the plate, localized closer to the thick edge, become maximum. This can lead to cracking of the plate in transverse direction. In the symmetric case, the maximum strains are achieved inside the plate—close to the center, but not necessarily in the midpoint. Full article

Layered flows that are commonly observed in stratified turbulence are susceptible to the Taylor–Caulfield Instability. While the modal stability properties of layered shear flows have been examined, the non-modal growth of perturbations has not been investigated. In this work, the tools of Generalized Stability Theory are utilized to study linear transient growth within a finite time interval of two-dimensional perturbations in an inviscid, three-layer constant shear flow under the Boussinesq approximation. It is found that, for low optimization times, small-scale perturbations utilize the Orr mechanism and achieve growth equal to that in the case of an unstratified flow. For larger optimization times, transient growth is much larger compared to growth for an unstratified flow as the Kelvin–Orr waves comprising the continuous spectrum of the dynamical operator and the gravity edge-waves comprising the discrete spectrum interact synergistically. Maximum growth is obtained for perturbations with scales within the region of instability, but significant growth is maintained for modally stable perturbations as well. For perturbations with scales within the unstable region, the unstable normal modes are excited at high amplitude by their bi-orthogonals. For perturbations with modally stable scales, the Orr mechanism is utilized to excite at high amplitude neutral propagating waves resembling the neutral Taylor–Caulfield modes. Full article

The purpose of this paper is to investigate the linear stability analysis for the laminar-turbulent transition region of the high-Reynolds-number instabilities for the boundary layer flow on a rotating disk. This investigation considers axial flow along the surface-normal direction, by studying analytical expressions for the steady solution, laminar, incompressible and inviscid fluid of the boundary layer flow due to a rotating disk in the presence of a uniform injection and suction. Essentially, the physical problem represents flow entrainment into the boundary layer from the axial flow, which is transferred by the spinning disk surface into flow in the azimuthal and radial directions. In addition, through the formation of spiral vortices, the boundary layer instability is visualised which develops along the surface in spiral nature. To this end, this study illustrates that combining axial flow and suction together may act to stabilize the boundary layer flow for inviscid modes. Full article

In this study, the active vibration control of a rectangular plate submerged in water was investigated. Mass dampers were attached to the plate, and the system was modeled via assumed mode. Water is modeled as an inviscid fluid with moving boundaries at fluid–solid interaction surfaces and applied forces on the plate being calculated by Bernoulli equation. The natural frequencies of the plate in vacuum and in water (for partial and fully submerged cases) found from numerical calculations are compared with experimental results to prove the accuracy of the model. Subsequently, for frequency computations, particular frequencies were chosen and active damping was applied for them. To actively control the plate’s vibration by a moving mass with static stable methods, the displacement data of some points were used as input. First, to increase the damping of target mode at low-frequency, the negative acceleration feedback control algorithm in modal-space was applied. Then, the decentralized method was examined. Both methods were successful in suppressing vibration of the submerged rectangular plate. Full article