Shock response of a system of two submerged co-axial cylindrical shells coupled by the inter-shell fluid

The shock response of a submerged system consisting of two co-axial cylindrical shells coupled with the fluid filling the inter-shell space is considered. The shock–structure interaction is modeled using a semi-analytical methodology based on the use of the classical apparatus of mathematical physics. Both the fluid and structural dynamics of the interaction is addressed, with special attention paid to the interplay between the two. It is demonstrated that the wave effects due to multiple reflections of the pressure waves travelling in the inter-shell fluid to a large degree determine the structural dynamics of the system, but have a more pronounced effect on the outer shell than on the inner one. It is also established that the effect of changing the thickness of the outer shell on the stress–strain state of the inner shell is incomparably more pronounced than vice versa. The investigation culminates with the results of a parametric study of the overall peak stress in the system, an example of utilizing the approach developed based on the introduced model and aiming at facilitating structural optimization of industrial systems at the pre-design stage in the context of shock resistance.     

Transient radiation by a submerged fluid-filled cylindrical shell

The radiation by a submerged fluid-filled cylindrical shell in response to a transient external pressure pulse is considered, and a semi-analytical model based on the Reissner–Mindlin shell theory is employed to simulate the interaction numerically. Two types of radiated waves that have been previously seen in experimental images for a submerged evacuated cylindrical shell are observed in both the external and internal fluids, the symmetric Lamb waves S₀ and the antisymmetric Lamb (or pseudo-Rayleigh) waves A₀. The third type of radiated waves is also observed that has not been explicitly imaged either experimentally or numerically for a submerged evacuated cylindrical shell, and it is demonstrated that these waves are the Scholte–Stoneley waves A. The effect that the complex structure of the radiated field has on the wave phenomena in the internal fluid is analyzed for shells of several different thicknesses, and the results of this analysis are summarized in the form of diagrams suitable for the use at the pre-design stage.     

Resonance-like phenomena in a submerged cylindrical shell subjected to two consecutive shock waves: The effect of the inner fluid

A submerged fluid-filled cylindrical shell subjected to a sequence of two shock waves originated at the same source is considered. It is demonstrated that, unlike in the case of a submerged evacuated shell, there exists a certain critical range of the values of the delay between the incident wavefronts where both the peak compressive and the peak tensile stress observed in the structure are significantly (60% or more) higher than the respective stresses in the same system subjected to a single-front loading. It is further demonstrated that the highest and the lowest hydrodynamic pressure attained in the system is also dramatically affected for certain values of the delay between the incident wavefronts, with the maximum double-front pressure being more than 30% higher than its single-front counterpart. The practical relevance of the findings is discussed in the context of the pre-design analysis of industrial systems subjected to shock loading.     

On the possibility of shock-induced cavitation in submerged cylindrical shell systems

A circular cylindrical shell loaded by one or two fluids and responding to an external shock wave is analyzed in the context of the possible inception of shock-induced cavitation. Several scenarios of fluid contact are considered including a submerged evacuated shell and a submerged fluid-filled shell for three different combinations of the parameters of the internal and external fluids. A semi-analytical shell-shock interaction model is employed in order to predict the regions of the fluids where cavitation is likely to occur, and the respective cavitation development is hypothesized about. The most interesting and practically important finding is that when fluid is present both inside and outside the shell, there exist conditions when cavitation is expected to occur in both the internal and external fluid, resulting in a particularly complex and violent structural re-loading occurring upon the collapse of the respective cavitation regions. The inception of cavitation in the internal fluid alone and in the external fluid alone is also possible. The findings are summarized in a manner that is suitable for use at the pre-design stage as a guide for preliminary assessment of the possibility of shock-induced cavitation in fluid-interacting industrial systems.     

Numerical investigation of the interaction of a vortex dipole with a deformable plate

Energy harvesting from coherent fluid structures is a current research topic due to its application in the design of small self-powered sensors for underwater applications. The impact of a vortex dipole with a deformable cantilevered plate at the plate tip is herein studied numerically using a strongly coupled staggered fluid–structure interaction algorithm. Three dipole Reynolds numbers, Re=500, 1500, and 3000, are investigated for constant plate properties. As the dipole approaches the plate, positive vorticity is produced on the impact face, while negative vorticity is generated at the tip of the plate. Upon impact, the dipole splits into two, and two secondary dipoles are formed. The circulation and, therefore, the trajectories of these dipoles depend on both the Reynolds number and the elasticity of the plate, and these secondary dipoles may return for subsequent impacts. While the maximum deflection of the plate does not depend significantly on Reynolds number, the plate response due to subsequent impacts of secondary dipoles does vary with Reynolds number. These results elucidate the strong interdependency between plate deformation and vortex dynamics, as well as the effect of Reynolds number on both.     

DES evaluation of near-wake characteristics in a shallow flow

Three-dimensional numerical modeling using Detached Eddy Simulation (DES) based on unsteady Reynolds-Averaged Navier–Stokes (RANS) with the k–ω SST (Shear-Stress Transport) turbulence model has been carried out to evaluate the characteristics of a shallow wake flow. The shallow wake is generated by inserting a sharp-edged bluff body in the open channel flow. A horseshoe vortex is captured in front of the body, which stretches downstream and envelops the vortices that form part of the shear layers. The mean and instantaneous flow field characteristics in the wake are examined and compared at different downstream locations to evaluate the three-dimensional features in the flow. Streamwise positive directed velocity is observed in the wake centerline at horizontal planes close to the bed. Flow features hitherto not captured in experimental studies can be identified in sections parallel to the bed and body. A typical signature of three-dimensionality, upward ejection of fluid elements from the bed towards the free surface, is also observed in the wake.     

Performance of a shock tube facility for impact response of structures

This paper presents a numerical approach to compute the performance of a double diaphragm shock tube facility for structural response investigations. To assess the influence of different sources of dissipation, including partial diaphragm opening and shock tube vibration, numerical simulations are carried out using several different finite element models of increasing complexity to compute shock tube performance. The numerical model accounting for tearing and partial opening of the diaphragms is the one that best reproduces the results of the experiment, thus indicating that the diaphragm non-ideal opening process is the most relevant cause of losses. Both the numerical and the experimental results agree in predicting shock tube efficiency in terms of intensity of the reflected shock of about 50–60% with respect to ideal, one-dimensional conditions.     

环形激波聚焦流场特性的数值研究

针对环形激波聚焦过程产生的高温、高压特性,采用间断有限元方法模拟了环形激波在同轴圆柱形激波管内的聚焦流场特性。计算结果表明,采用间断有限元方法能够有效地捕捉激波聚焦过程形成的二次激波、涡环、三波交点和球面双马赫反射等主要流动特征。此外,通过改变环形管道内外半径对聚焦流场进行模拟发现,环形管道外径对中心轴线上聚焦峰值压力的大小和位置影响较小,环形管道内径对中心轴线上聚焦峰值压力的大小和位置影响较大。计算结果可以为工程应用提供一定的理论指导。     

Galloping instability and control of a rigid pendulum in a flowing soap film

A pendulum suspended in a fast flowing soap film may show sustained oscillations. The conditions necessary for self-excited motion to occur are outlined: a flow velocity above a threshold value along with geometrical constraints. The role of vortex shedding is discussed, and the observed instability is shown to be well-described by the galloping instability. Experimental results are supported by numerical simulations. Furthermore, we observe that the instability may be suppressed by attaching a long enough filament to the rear of the pendulum.     

Vibrations and stability of a periodically supported rectangular plate immersed in axial flow

Vibrations and stability of a thin rectangular plate, infinitely long and wide, periodically supported in both directions (so that it is composed by an infinite number of supported rectangular plates with slope continuity at the edges) and immersed in axial liquid flow on its upper side is studied theoretically. The flow is bounded by a rigid wall and the model is based on potential flow theory. The Galerkin method is applied to determine the expression of the flow perturbation potential. Then the Rayleigh–Ritz method is used to discretize the system. The stability of the coupled system is analyzed by solving the eigenvalue problem as a function of the flow velocity; divergence instability is detected. The convergence analysis is presented to determine the accuracy of the computed eigenfrequencies and stability limits. Finally, the effects of the plate aspect ratio and of the channel height ratio on the critical velocity giving divergence instability and vibration frequencies are investigated.     

Modal characteristics of a flexible cylinder in turbulent axial flow from numerical simulations

In this paper the vibration behavior of a flexible cylinder subjected to an axial flow is investigated numerically. Therefore a methodology is constructed, which relies entirely on fluid–structure interaction calculations. Consequently, no force coefficients are necessary for the numerical simulations. Two different cases are studied. The first case is a brass cylinder vibrating in an axial water flow. This calculation is compared to experiments in literature and the results agree well. The second case is a hollow steel tube, subjected to liquid lead–bismuth flow. Different flow boundary conditions are tested on this case. Each type of boundary conditions leads to a different confinement and results in different eigenfrequencies and modal damping ratios. Wherever appropriate, a comparison has been made with an existing theory. Generally, this linear theory and the simulations in this paper agree well on the frequency of a mode. With respect to damping, the agreement is highly dependent on the correlation used for the normal friction coefficients in the linear theory.     

A Lagrangian approach for the coupled simulation of fixed net structures in a Eulerian fluid model

A Lagrangian approach for the coupled numerical simulation of fixed net structures and fluid flow is derived. The model is based on solving the Reynolds-averaged Navier–Stokes equations in a Eulerian fluid domain. The equations include disturbances to account for the presence of the net. For this purpose, forces on the net are calculated using a screen force model and are distributed on Lagrangian points to represent the geometry of the net. In comparison to previous approaches based on porous media representations, the new model includes a more physical derivation and simplifies the necessary numerical procedure. Hence, it is also suitable for arbitrary geometries and large scale simulations. An extensive validation section provides insight into the performance of the new model. It includes the simulation of steady currents through single and multiple fixed net panels and cages, and wave propagation through a net panel. Different solidities, inflow velocities and angles of attack are considered. The comparison of loads on and velocity reductions behind the net with available measurements indicates superior performance of the proposed model over existing approaches for a wide range of applications.     

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

Simulation of self-coordination in a row of beating flexible flaplets for micro-swimmer applications: Model and experiment study

In this study, we present a model that simulates hydrodynamic self-coordination in a row of flexible flaplets. We control the flaplets in order that their tips follow a fixed-amplitude oscillatory motion profile. When brought together at a low Reynolds-number environment, the flaplets interact with each other in the form of bending deflections at their tips, which causes the frequency of the individual oscillations to vary until a coordinated steady state is reached. The model design steps are experimentally verified and the coordination results of both the experiment and the model are compared. The model’s internal states are then analysed for a better understanding of the synchronization collective effect. The coordination of the flaplets is found to settle in the direction of propulsion forces ascent. The stability of the resulted synchronization and propulsion forces are examined over long periods. The model is meant to be simplified and mostly linear so that it can be utilized for state forecasting in a real-time control application of a swimmer robot. Finally, we experimentally study the propulsion performance of five beating flaplets that follow prescribed oscillation profiles forming a metachronal wave. The flow results show that the flaplets, that beat in coordination, are efficient at generating a uni-directional steady-streaming transport of the fluid at their surface.     

Active vortex-induced vibration control of a circular cylinder at low Reynolds numbers using an adaptive fuzzy sliding mode controller

An adaptive fuzzy sliding mode control (AFSMC) scheme is applied to actively suppress the two-dimensional vortex-induced vibrations (VIV) of an elastically mounted circular cylinder, free to move in in-line and cross-flow directions. Laminar flow regime at Re=90, low non-dimensional mass with equal natural frequencies in both directions, and zero structural damping coefficients, are considered. The natural oscillator frequency is matched with the vortex shedding frequency of a stationary cylinder at Re=100. The strongly coupled unsteady fluid/cylinder interactions are captured by implementing the moving mesh technology through integration of an in-house developed User Define Function (UDF) into the main code of the commercial CFD solver Fluent. The AFSMC approach comprises of a fuzzy system designed to mimic an ideal sliding-mode controller, and a robust controller intended to compensate for the difference between the fuzzy controller and the ideal one. The fuzzy system parameters as well as the uncertainty bound of the robust controller are adaptively tuned online. A collaborative simulation scheme is realized by coupling the control model implemented in Matlab/Simulink to the plant model constructed in Fluent, aiming at determination of the transverse control force required for complete suppression of the cylinder streamwise and cross-flow oscillations. The simulation results demonstrate the high performance and effectiveness of the adopted control algorithm in attenuating the 2D-VIV of the elastic cylinder over a certain flow velocity range. Also, the enhanced transient performance of the AFSM control strategy in comparison with a conventional PID control law is demonstrated. Furthermore, the effect of control action on the time evolution of vortex shedding from the cylinder is discussed. In particular, it is observed that the coalesced vortices in the far wake region of the uncontrolled cylinder, featuring the C(2S)-type vortex shedding characteristic mode, are ultimately forced to switch to the classical von Kármán vortex street of 2S-type mode, displaying wake vortices of moderately weaker strengths very similar to those of the stationary cylinder. Lastly, robustness of AFSMC is verified against relatively large structural uncertainties as well as with respect to a moderate deviation in the uniform inlet flow velocity.     

A theoretical computational model of a plate in hypersonic flow

A theoretical model of an elastic panel in hypersonic flow is derived to be used for design and analysis. The nonlinear von Kármán plate equations are coupled with 1st order Piston Theory and linearized at the nonlinear steady-state deformation due to static pressure differential and thermal loads. Eigenvalue analysis is applied to determine the system’s stability, natural frequencies and mode shapes. Numerically time marching the equations provides transient response prediction which can be used to estimate limit cycle oscillation amplitude, frequency and time to onset. The model’s predictive capability is assessed by comparison to an experiment conducted at a free stream flow of Mach 6. Good agreement is shown between the theoretical and experimental natural frequencies and mode shapes of the fluid–structure system. Stability analysis is performed using linear and nonlinear methods to plot stability, flutter and buckling zones on a free stream static pressure vs temperature differential plane.     

Application of the VOF method to the sloshing of a fluid in a partially filled cylindrical container

In a previous work we solved numerically the steady-state motion of an ideal fluid that fills a moving cylindrical container with partitions, and were able to compute the equivalent moments of inertia. Here we extend this work in two steps. First we introduce time dependence and then free surfaces, and are able to compute the transient motion of the fluid not filling the container. The main body of the work has to do with the treatment of free surfaces. Our approach is an extention to three dimensions of the volume of fluid method of Hirt and Nichols. The solution algorithm is outlined, and two examples that demonstrate its capability are presented.