Unsteady Fluid Forces Research Articles

Research on the mechanism of chlorine corrosion resistance of graphite tailings modified recycled coarse aggregate concrete: Corrosion product transformation and multi-scale mathematical characterization model

This research investigated the impact of substituting sand with graphite tailings (GT) on the chloride ion erosion resistance of recycled aggregate concrete (RAC). The role of GT is to significantly inhibit the penetration of chloride ions into the interior and slow down the corrosion process. However, the durability of graphite tailings recycled aggregate concrete (GTRAC) still depends on the replacement rate of recycled aggregate. At the same time, a multi-scale dynamic model of physical adsorption-chemical binding-free transport and erosion of chloride ions in GTRAC were established based on unsteady viscous fluid force and molecular dynamics.

An application of data-driven modeling for hydroelasticity of an elastically supported semi-circular pipe conveying fluid

PurposeThe paper aims to develop an efficient data-driven modeling approach for the hydroelastic analysis of a semi-circular pipe conveying fluid with elastic end supports. Besides the structural displacement-dependent unsteady fluid force, the steady one related to structural initial configuration and the variable structural parameters (i.e. the variable support stiffness) are considered in the modeling.Design/methodology/approachThe steady fluid force is treated as a pipe preload, and the elastically supported pipe-fluid model is dealt with as a prestressed hydroelastic system with variable parameters. To avoid repeated numerical simulations caused by parameter variation, structural and hydrodynamic reduced-order models (ROMs) instead of conventional computational structural dynamics (CSD) and computational fluid dynamics (CFD) solvers are utilized to produce data for the update of the structural, hydrodynamic and hydroelastic state-space equations. Radial basis function neural network (RBFNN), autoregressive with exogenous input (ARX) model as well as proper orthogonal decomposition (POD) algorithm are applied to modeling these two ROMs, and a hybrid framework is proposed to incorporate them.FindingsThe proposed approach is validated by comparing its predictions with theoretical solutions. When the steady fluid force is absent, the predictions agree well with the “inextensible theory”. The pipe always loses its stability via out-of-plane divergence first, regardless of the support stiffness. However, when steady fluid force is considered, the pipe remains stable throughout as flow speed increases, consistent with the “extensible theory”. These results not only verify the accuracy of the present modeling method but also indicate that the steady fluid force, rather than the extensibility of the pipe, is the leading factor for the differences between the in- and extensible theories.Originality/valueThe steady fluid force and the variable structural parameters are considered in the data-driven modeling of a hydroelastic system. Since there are no special restrictions on structural configuration, steady flow pattern and variable structural parameters, the proposed approach has strong portability and great potential application for other hydroelastic problems.

An analytical frequency response function for fluidelastic instability model of a normal triangular array in cross-flow

A new model based on Theodorsen’s classical theory of aerodynamic instability and the mechanism of flutter is proposed to explain the origin of the time delay, an important parameter for fluidelastic instability prediction, between the tube motion and the non-linear fluidelastic forces. Using this model, a novel time delay function has been theoretically derived with no reliance on unsteady fluid force data, as was the case with earlier models. A stability analysis is carried out based on the new time delay function combined with the experimental static fluid forces for a range of mass damping parameters. The predicted stability threshold is found to compare well with experimental stability data.

Boundary effects on ideal fluid forces and Kelvin's minimum energy theorem

The electrostatic force on a charge above a neutral conductor is generally attractive. Surprisingly, that force becomes repulsive in certain geometries (Levin & Johnson, Am. J. Phys., vol. 79, issue 8, 2011, pp. 843–849), a result that follows from an energy theorem in electrostatics. Based on the analogous minimum energy theorem of Kelvin (Camb. Dublin Math. J., vol. 4, 1849, pp. 107–112), valid in the theory of ideal fluids, we show corresponding effects on steady and unsteady fluid forces in the presence of boundaries. Two main results are presented regarding the unsteady force. First, the added mass is proven to always increase in the presence of boundaries. Second, in a model of a body approaching a boundary, where the unsteady force is typically repulsive (Lamb, Hydrodynamics, 1975, § 137, University Press), we present a geometry where the force can be attractive. As for the steady force, there is one main result: in a model of a Bernoulli suction gripper, for which the steady force is typically attractive, we show that the force becomes repulsive in some geometries. Both the unsteady and steady forces are shown to reverse sign when boundaries approximate flow streamlines, at energy minima predicted by Kelvin's theorem.

Numerical Analysis of Flow Characteristics in Impeller-Guide Vane Hydraulic Coupling Zone of an Axial-Flow Pump as Turbine Device

An axial-flow pump as a turbine (PAT), as compared to the conventional Francis turbine, has the advantages of not being restricted by the terrain and having lower cost to reverse the pump as a turbine for power generation. When an axial-flow pump is reversed as a turbine, the internal flow pattern is more complicated than when in the pump mode, which can cause instability in the whole system and result in degradation of the hydraulic performance and structural vibration. The impeller and guide vane are the core of the axial-flow PAT unit. This research compares the experimental and numerical simulation results in order to verify the energy performance and pressure pulsation signal of the axial-flow PAT. The unsteady flow regime, fluid force, and pressure pulsation characteristics of the impeller-guide vane hydraulic coupling zone are analyzed in detail. The findings demonstrate that both the dominant frequency of the fluid force pulsation signal and the flow field pressure pulsation signal appear at 3 times of the rotation frequency. The blade passing frequency (BPF) of the impeller is the dominant frequency, and other frequency components are also dominated by the harmonic frequency of the BPF. The impeller and guide vane are primarily subject to radial fluid force. Under partial working conditions, the pressure pulsation intensity in the flow field greatly increases, and the pressure pulsation amplitude at the guide vane outlet and impeller outlet appears to be more sensitive to the flow rate change.

Mode interpretation and force prediction surrogate model of flow past twin cylinders via machine learning integrated with high-order dynamic mode decomposition

Understanding and modeling the flow field and force development over time for flow past twin tandem cylinders can promote insight into underlying physical laws and efficient engineering design. In this study, a new surrogate model, based on a convolutional neural network and higher-order dynamic mode decomposition (CNN-HODMD), is proposed to predict the unsteady fluid force time history specifically for twin tandem cylinders. Sampling data are selected from a two-dimensional direct numerical simulation flow solution over twin tandem cylinders at different aspect ratios (AR = 0.3–4), gap spacing (L* = 1–8), and Re = 150. To promote insight into underlying physical mechanisms and better understand the surrogate model, the HODMD analysis is further employed to decompose the flow field at selected typical flow regimes. Results indicate that CNN-HODMD performs well in discovering a suitable low-dimensional linear representation for nonlinear dynamic systems via dimensionality augment and reduction technique. Therefore, the CNN-HODMD surrogate model can efficiently predict the time history of lift force at various AR and L* within 5% error. Moreover, fluid forces, vorticity field, and power spectrum density of twin cylinders are investigated to explore the physical properties. It was found three flow regimes (i.e., overshoot, reattachment, and coshedding) and two wake vortex patterns (i.e., 2S and P). It was found the lift force of the upstream cylinder for AR < 1 is more sensitive to the gap increment, while the result is reversed for the downstream cylinder. It was found that the fluctuating component of the wake of cylinders decreases with increasing AR at L* = 1. Moreover, flow transition was observed at L* = 4.

Unsteady flow simulations in two-stage turbines of a rocket turbopump to estimate blade structural soundness for fatigue

Abstract This study first aims at detailed investigations of three-dimensional unsteady flow field in the reference and optimized rocket turbine stages by performing time-accurate flow simulations based on Transient Blade Row (TBR) method or Time Transformation (TT) method in a commercial software ANSYS CFX. Although TT method is believed to enable relatively low-cost unsteady flow simulation, detailed comparisons between TT method-based and conventional unsteady flow simulations are made before TT method application to Fluid-Structural Interaction (FSI) problem. This study then makes an attempt to conduct structural analyses of the 1st and 2nd stage turbine blades under the influence of unsteady fluid forces caused by rotor-stator interaction predicted by TT method-based flow simulations. The structural analyses are executed by use of MSC Nastran. In this study, two materials are adopted as blade material. After the Fourier-series decomposition of the calculated unsteady pressure distributions, the unsteady pressure information is mapped onto the FEM (Finite Element Method)-modeled turbine blade surface as exciting aerodynamic loading. The frequency response analyses are then performed to calculate alternating stresses of the blade, from which the maximum magnitudes of alternating stress are obtained so as to discuss the rotor blade fatigue life.

Equivalent Theodorsen Function for Fluidelastic Excitation in a Normal Triangular Array

Abstract Fluidelastic instability (FEI) remains the most important mechanism of flow-induced vibrations that can potentially cause large amplitude vibrations and early failure of nuclear steam generator tubes. In the present work, experimental tests are conducted to measure the unsteady and quasi-steady fluid forces acting on a normal triangular tube array of P/D=1.5 subjected to single-phase (water) cross-flow. The quasi-steady forces together with unsteady fluid forces are then used to estimate the time delay between the central tube motion and fluid forces on the tube itself. The time delay effect for the quasi-steady fluidelastic instability model is derived in the frequency domain in the form of an Equivalent Theodorsen Function. The results are compared to the first Equivalent Theodorsen function developed for rotated triangular array by Li and Mureithi [1]. Using the Equivalent Theodorsen Function, a stability analysis is carried out to predict the critical velocity for fluidelastic instability in a normal triangular array subjected to single-phase flow. The predicted stability threshold is consistent with previous published experimental data. The results show that the normal triangular array is more stable than the rotated triangular array.

Vortex Ring Formed by a Butterfly Wing and Dynamic Forces

Butterfly generates unsteady dynamic fluid force with a pair of vortex rings. In order to elucidate the flight mechanism of butterflies, it is necessary not only to clarify the vortex rings formed around the wings but also elucidate the characteristics of the unsteady fluid force generated by the flapping motion. By applying the momentum theory to the vortex rings formed during flapping motion, it is possible to estimate the force generated by flapping motion. In this study, we reconstruct a pair of vortex rings formed by flapping motion based on a small number of visualization results and elucidate dynamic fluid force characteristics. A part of estimation result of Lift estimated by the rough shape vortex rings generated by downstroke and upstroke do not match with the direct measurement result. But not only the peak value of estimation result of Lift is near with the direct measurement result quantitatively but also the value of estimation result between upstroke is a small negative as well as the direct measurement result. Although there is a phase difference between the estimation result and direct measurement result, there is a qualitative and quantitative agreement between estimation results and direct measurement result. From those results, butterfly generate the unsteady dynamic Lift between downstroke, especially at butterfly spread wing maximum (t/T = 0.40). After that, the unsteady dynamic Lift decrease and become 0 at upstroke.

In-Plane Fluidelastic Instability Evaluation of Triangular Array Tube Bundle Using Fluid Force Measured Under Steam–Water Two-Phase Flow Condition

Abstract Recently, tube-to-tube wear indications of triangular tube bundle steam generators (SGs) caused by fluidelastic instability (FEI) in the in-plane direction of U-bend region (in-plane FEI) have been reported. Several experiments were conducted to investigate the characteristics of in-plane FEI by our research groups. In a series of experiments, particular characteristics of in-plane FEI were found. For example, there are the critical velocity difference between the in-plane and the out-of-plane directions, the difference between straight tube bundle tests and U-bend tube bundle tests, etc. To explain these characteristics, unsteady fluid force acting on tubes were measured. The experimental investigation was conducted under high temperature and high-pressure steam–water flow conditions close to the SGs. Stability analyses were conducted using the measured unsteady fluid forces as inputs. First, stability analyses were done to simulate straight tube bundle tests. Analysis results agreed well with experiments and it could explain the effect on critical velocity trend by number of flexible tubes and directions of vibration. Second, U-tube stability analyses were performed by applying unsteady fluid force coefficients for each location of U-bend tube finite element method (FEM) model. From the results, mechanisms of in-plane FEI were understood.

Performance Analysis of Flapping Foil Flow Energy Harvester Mounted on Piezoelectric Transducer using Meshfree Particle Method

Performance of a semi-active flapping foil flow energy harvester, coupled with a piezoelectric transducer has been analyzed in this work. The airfoil is mounted on a spring, damper and piezoelectric transducer arrangement in its translational mode. External excitation is imparted in pitch mode and system is allowed to oscillate in its translational mode as a result of unsteady fluid forces. A piezoelectric transducer is used as an electrical power converter. Flow around moving airfoil surface is solved on a meshfree nodal cloud using Radial Basis Function in Finite Difference Mode (RBF-FD). Fourth order Runge-Kutta Method is used for time marching solution of solid equations. Before the solution of complex Fluid-Structure Interaction problem, a parametric study is proposed to identify the values of kinematic, mechanical and geometric variables which could offer an improved energy harvesting performance. For this purpose, the problem is modelled as a coupled electromechanical system using Lagrange energy equations. Airfoil lift and pitching moment are formulated through Theodorson’s two dimensional thin-plate model and a parametric analysis is conducted to work out the optimized values of pivot location, pitch amplitude, spring stiffness and damping constant. The subsequent computational analysis resulted in an enhanced performance compared to the potential flow model with an efficiency of up to 27% based on total power extraction through the flow. Higher efficiency is obtained when the pitch axis is located aft of mid chord. However, this setting does not correspond to the maximum power output. Interestingly, power is maximized at much lower efficiency values.

Time and frequency domain analyses of fluid force fluctuations in a normal triangular tube array in forced vibrations

Vibrations of tube bundles in heat exchange equipment, such as nuclear steam generators and tube-and-shell type heat exchangers, are often caused by unsteady fluid forces. The study of flow-induced vibration excitation forces on tubes is necessary for understanding the fluid-elastic instability phenomenon. In this paper, a forced vibration method is introduced to investigate unsteady motion-dependent fluid forces in a normal triangular tube array with the pitch ratio of 1.32 that is subjected to water crossflow. Fluid force behaviors of a single flexible central tube and its lift response spectra are investigated in various forced vibration modes. In a seven-tube kernel unit, coupling effects of surrounding tubes on the central tube are also discussed. Results show that the lift force on a flexible vibrating tube mainly depends on the vibration amplitude of tube itself in the lift direction, and is less affected by the degree of freedom, the rotation direction and the main vibration direction of tube vibration. The frequency spectrum of lift responses is dominated by two main frequencies: the vortex alternating frequency and the tube natural frequency. Surrounding flexible tubes increase higher order harmonics of the periodic lift force fluctuations of the central tube. Compared with rear-column tubes, vibrations of the front-column tubes have more significant effects on lift force responses of the tube kernel, which facts causes strong coupling to promote the fluid-elastic instability of tubes.

Studies on High Reliable Turbine Stage Development for Rocket Engine

To improve the launch capability of rocket, rocket engine turbines are required to have high efficiency and high reliability. In reality it is quite difficult to achieve these two goals at the same time. In quest for highly efficient and reliable rocket turbine, the present authors have performed time-accurate calculation using Transient Blade Row (TBR) method of the commercial software ANSYS CFX to investigate unsteady flow behaviors in the two types of turbine stages (so called reference turbine and optimized turbine). This study then attempts to conduct detailed structural analyses of the 1st and 2nd stage turbine blades under the influence of unsteady fluid forces caused by rotor-stator interaction phenomena. Frequency response analysis is performed using the unsteady fluid forces calculated by ANSYS CFX, and the structural analyses are executed by use of MSC Nastran. In the analyses, two materials (Inconel 718 and Ti-6Al-4V) are adopted as blade material.

The Relationship between Flow Field and Unsteady Fluid Forces Acting on a Flat Plate

The Relationship between Flow Field and Unsteady Fluid Forces Acting on a Flat Plate

How do elite artistic swimmers generate fluid forces by hand during sculling motions?

ABSTRACT The purpose of this study was to clarify how elite artistic (synchronised) swimmers generate fluid forces with their hands during two kinds of sculling motions: flat sculling in the back-layout position and support sculling in the vertical position. We used the pressure-distribution measuring method to estimate unsteady fluid forces acting on the hand during sculling motions performed by seven elite artistic swimmers. In addition, we simultaneously analysed sculling motions using three dimensional-direct linear transformation methods. We found that sculling motions continuously generated fluid forces that are large during the stroke phase and small during the transition phase. Lift force was efficiently generated, and a large upward propulsive force was obtained during the stroke phase in both flat and support sculling. During the outside transition from out- to in-sculling, the net vertical load (= gravitational force—buoyant force) was supported by the drag force. In both flat and support sculling, artistic swimmers generated an even fluid force in the upward direction during the in-sculling and out-sculling phases to maintain a stable position.

Nonlinear dynamics of slender inverted flags in uniform steady flows

A nonlinear fluid-elastic continuum model for the dynamics of a slender cantilevered plate subjected to axial flow directed from the free end to the clamped end, also known as the inverted flag problem, is proposed. The extension of elongated body theory to large-amplitude rotations of the plate mid-plane along with Bollay's nonlinear wing theory is employed in order to express the fluid-related forces acting on the plate, while retaining all time-dependent terms in both modelling and numerical simulations; the unsteady fluid forces due to vortex shedding are not included. Euler-Bernoulli beam theory with exact kinematics and inextensibility is employed to derive the nonlinear partial integro-differential equation governing the dynamics of the plate. Discretization in space is carried out via a conventional Galerkin scheme using the linear mode-shapes of a cantilevered beam in vacuum. The pseudo-arclength continuation technique is adapted to construct bifurcation diagrams in terms of the flow velocity, in order to gain insight into the stability and post-critical behaviour of the system. Integration in time is conducted using Gear's backward differentiation formula. The sensitivity of the nonlinear response of the system to different parameters such as the aspect ratio, mass ratio, initial inclination of the flag, and viscous drag coefficient is investigated through extensive numerical simulations. It is shown that for flags of small aspect ratio the undeflected static equilibrium is stable prior to a subcritical pitchfork bifurcation. For flags of sufficiently large aspect ratio, however, the first instability encountered is a supercritical Hopf bifurcation giving rise to flapping motion around the undeflected static equilibrium; increasing the flow velocity further, the flag then displays flapping motions around deflected static equilibria, which later lead to fully-deflected static states at even higher flow velocities. The results exposed in this study help understand the dynamics of the inverted-flag problem in the limit of inviscid flow theory.

An experimental investigation of cavitation surge in draft tube of Francis turbine

Hydro turbines are often used at off-design point to adjust the power output. At off-design condition, a swirl flow occurs downstream of the turbine runner and a cavitation occurs at the vortex core due to the decrease of the pressure. The cavitation in the draft tube can cause a flow instability called draft tube surge. Because the draft tube surge causes the flow rate fluctuation, unsteady fluid forces occurs on the runner, and consequently, the revolution speed of the runner is affected. In the present study, an experimental investigation was carried out. Characteristics of the dynamic fluid forces due to the draft tube surge are examined at first. In addition, the influence of the fluctuation of the revolution speed of the runner on the cavitation surge were examined. The results showed that the cavitation surge caused the hydraulic torque fluctuation on the runner but the fluctuation of the cavity volume were affected by the runner revolution speed.

Turbulent intensity effect on axial-flow-induced cylinder vibration in the presence of a neighboring cylinder

Experimentally investigation is conducted on the turbulent intensity effect on the axial-flow-induced vibration of an elastic cylinder in the presence of a neighboring rigid cylinder. The center-to-center cylinder spacing P∗ (= P/D, where D is the cylinder diameter) is 1.21, 1.36, 1.57 and ∞ (an isolated cylinder). The dimensionless velocity U¯ (=U∞L(mf∕EI)1∕2, where U∞, L, mf, EI, are the free-stream velocity, cylinder length, added mass of fluid per unit length and cylinder flexural rigidity, respectively) is 0.64 ∼ 6.92, and two ranges of incident turbulent intensity Tu are 0.71%–0.80% and 2.30%–2.91%. The cylinder vibration and the flow are simultaneously captured using two laser Doppler vibrometers and a time-resolved particle image velocimetry, respectively. It is found that the level of Tu may have a pronounced effect on the vibration of the elastic cylinder. At high Tu (2.30–2.91%), the vibration amplitude of the elastic cylinder is significantly increased compared with its counterpart at low Tu (0.71–0.80%). Two factors are found to be responsible. Firstly, the instability of the shear layer around the elastic cylinder is amplified through the interaction between the incident flow fluctuation of the high Tu and the unstable shear layer around the vibrating cylinder. As a result, eddies are prone to separation from the cylinder wall, increasing the cylinder-wall pressure fluctuations. Secondly, the eddies are observed to bounce out and then bounce back, thus enhancing unsteady fluid forces.

Study on fluidelastic instability of a tube array subjected to two-phase cross-flow

The fluidelastic instability of a tube array subjected to two-phase cross-flow was investigated by both experimental and theoretical analyses in this paper. Firstly, two series of experiments were designed and carried out to generate the damping and fluidelastic instability data. The experimental measurements of damping ratio, natural frequency of the test tube and the critical velocity of a tube array subjected to two-phase cross-flow were conducted over a homogeneous void fraction range from 0% to 90%. Secondly, a mathematical model of a tube array with unsteady fluid force model was set up, and a computational program to calculate the critical velocity for the fluidelastic instability was written. The effects of void fraction were quantitatively investigated using computer simulation. The results of the theoretical analysis were in good agreement with the experimental data.

Eigenvalue analysis on fluidelastic instability of a rotated triangular tube array considering the effects of two-phase flow

Fluidelastic instability is a key issue in steam generator tube arrays subjected in two-phase flow. Lots of experimental analyses were conducted on fluidelastic instability of a tube array subjected to air-water cross-flow. However, there is seldom theoretical analysis to calculate the critical velocity. Therefore, considering the effect of two-phase flow, the fluidelastic instability of a rotated triangular tube array was studied in this paper. A mathematical model of a tube array with unsteady fluid force model was set up. A program based on the model was written, and an experiment was carried out to verify the correctness of the program. The results of this program were in good agreement with the experimental data. Using this program, the critical velocity of fluid-elastic instability considering the effect of two-phase flow was determined by the eigenvalue analysis. This paper investigated the critical velocities of fluid-elastic instability for void fraction ranging from 0% to 90% with five tube natural frequencies, respectively. The results show that void fraction and tube natural frequency are the key factors in fluidelastic instability, which have an obvious effect on the critical velocity of fluidelastic instability.