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Register a new userFluid-elastic coefficients in single phase cross flow: dimensional analysis, direct and indirect experimental methods
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The importance of fluid-elastic forces in tube bundle vibrations can hardly be over-emphasized, in view of their damaging potential. In the last decades, advanced models for representing fluid-elastic coupling have therefore been developed by the community of the domain. Those models are nowadays embedded in the methodologies that are used on a regular basis by both steam generators providers and operators, in order to prevent the risk of a tube failure with adequate safety margins. From an R&D point of view however, the need still remains for more advanced models of fluid-elastic coupling, in order to fully decipher the physics underlying the observed phenomena. As a consequence, new experimental flow-coupling coefficients are also required to specifically feed and validate those more sophisticated models. Recent experiments performed at CEA-Saclay suggest that the fluid stiffness and damping coefficients depend on further dimensionless parameters beyond the reduced velocity. In this work, the problem of data reduction is first revisited, in the light of dimensional analysis. For single-phase flows, it is underlined that the flow-coupling coefficients depend at least on two dimensionless parameters, namely the Reynolds number $Re$ and the Stokes number $Sk$. Therefore, reducing the experimental data in terms of the compound dimensionless quantity $V_r=Re/Sk$ necessarily leads to impoverish results, hence the data dispersion. In a second step, experimental data are presented using the dimensionless numbers $Re$ and $Sk$. We report experiments, for a 3x5 square tube bundle subjected to water transverse flow. The bundle is rigid, except for the central tube which is mounted on a flexible suspension allowing for translation motions in the lift direction.
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Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In the real-life applications like blood flow, there is often an additional complexity of vorticity being present in the fluid. We present a theory for the dynamics of interaction of fluids and structures. The equations are derived using the variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and unshearable tube with a straight centerline. In the absence of vorticity, our model reduces to previous models considered in the literature, yielding the equations of conservation of fluid momentum, wall momentum and the fluid volume. We show that even when the vorticity is present, but is kept at a constant value, the case of an inextensible, unshearable and straight tube with elastics walls carrying a fluid allows an alternative formulation, reducing to a single compact equation for the back-to-labels map instead of three conservation equations. That single equation shows interesting instability in solutions when the vorticity exceeds a certain threshold. Furthermore, the equation in stable regime can be reduced to Boussinesq-type, KdV and Monge-Amp`ere equations equations in several appropriate limits, namely, the first two in the limit of long time and length scales and the third one in the additional limit of the small cross-sectional area. For the unstable regime, we numerical solutions demonstrate the spontaneous appearance of large oscillations in the cross-sectional area.
The study focuses on the 3D electro-hydrodynamic (EHD) instability for flow between to parallel electrodes with unipolar charge injection with and without cross-flow. Lattice Boltzmann Method (LBM) with two-relaxation time (TRT) model is used to study flow pattern. In the absence of cross-flow, the base-state solution is hydrostatic, and the electric field is one-dimensional. With strong charge injection and high electrical Rayleigh number, the system exhibits electro-convective vortices. Disturbed by different perturbation patterns, such as rolling pattern, square pattern, and hexagon pattern, the flow patterns develop according to the most unstable modes. The growth rate and the unstable modes are examined using dynamic mode decomposition (DMD) of the transient numerical solutions. The interactions between the applied Couette and Poiseuille cross-flows and electroconvective vortices lead to the flow patterns change. When the cross-flow velocity is greater than a threshold value, the spanwise structures are suppressed; however, the cross-flow does not affect the streamwise patterns. The dynamics of the transition is analyzed by DMD. Hysteresis in the 3D to 2D transition is characterized by the non-dimensional parameter Y, a ratio of the coulombic force to viscous term in the momentum equation. The change from 3D to 2D structures enhances the convection marked by a significant increase in the electric Nusselt number.
We report the results of a complete modal and nonmodal linear stability analysis of the electrohydrodynamic flow (EHD) for the problem of electroconvection in the strong injection region. Convective cells are formed by Coulomb force in an insulating liquid residing between two plane electrodes subject to unipolar injection. Besides pure electroconvection, we also consider the case where a cross-flow is present, generated by a streamwise pressure gradient, in the form of a laminar Poiseuille flow. The effect of charge diffusion, often neglected in previous linear stability analyses, is included in the present study and a transient growth analysis, rarely considered in EHD, is carried out. In the case without cross-flow, a non-zero charge diffusion leads to a lower linear stability threshold and thus to a more unstable low. The transient growth, though enhanced by increasing charge diffusion, remains small and hence cannot fully account for the discrepancy of the linear stability threshold between theoretical and experimental results. When a cross-flow is present, increasing the strength of the electric field in the high-$Re$ Poiseuille flow yields a more unstable flow in both modal and nonmodal stability analyses. Even though the energy analysis and the input-output analysis both indicate that the energy growth directly related to the electric field is small, the electric effect enhances the lift-up mechanism. The symmetry of channel flow with respect to the centerline is broken due to the additional electric field acting in the wall-normal direction. As a result, the centers of the streamwise rolls are shifted towards the injector electrode, and the optimal spanwise wavenumber achieving maximum transient energy growth increases with the strength of the electric field.
Minute amount of long chain flexible polymer dissolved in a turbulent flow can drastically change flow properties, such as reducing the drag and enhancing mixing. One fundamental riddle is how these polymer additives interact with the eddies of different spatial scales existing in the turbulent flow and in turn alter the turbulence energy transfer. Here we show how turbulent kinetic energy is transferred through deferent scales in the presence of the polymer additives. In particular, we observed experimentally the emerging of a new scaling range, referred to as the elastic range, where increasing amount of energy is transferred by the elasticity of the polymers. In addition, the existence of the elastic range prescribes the scaling of high-order velocity statistics. Our findings have important implications to many turbulence systems such as turbulence in plasmas or superfluids where interaction between turbulent eddies and other nonlinear physical mechanisms are often involved.
Rod bundle flows are commonplace in nuclear engineering, and are present in light water reactors (LWRs) as well as other more advanced concepts. Inhomogeneities in the bundle cross section can lead to complex flow phenomena, including varying local conditions of turbulence. Despite the decades of numerical and experimental investigations regarding this topic, and the importance of elucidating the physics of the flow field, to date there are few publicly available direct numerical simulations (DNS) of the flow in multiple-pin rod bundles. Thus a multiple-pin DNS study can provide significant value toward reaching a deeper understanding of the flow physics, as well as a reference simulation for development of various reduced-resolution analysis techniques. To this end, DNS of the flow in a square 5x5 rod bundle at Reynolds number of 19,000 has been performed using the highly-parallel spectral element code Nek5000. The geometrical dimensions were representative of typical LWR fuel designs. The DNS was designed using microscales estimated from an advanced Reynolds-Averaged Navier-Stokes (RANS) model. Characteristics of the velocity field, Reynolds stresses, and anisotropy are presented in detail for various regions of the bundle. The turbulent kinetic energy budget is also presented and discussed
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