Fluid-solid Interaction Model for Hydraulic Reciprocating O-ring Seals

Elastohydrodynamic lubrication characteristics of hydraulic reciprocating seals have significant effects on sealing and tribology performances of hydraulic actuators, especially in high parameter hydraulic systems. Only elastic deformations of hydraulic reciprocating seals were discussed, and hydrodynamic effects were neglected in many studies. The physical process of the fluid-solid interaction effect did not be clearly presented in the existing fluid-solid interaction models for hydraulic reciprocating O-ring seals, and few of these models had been simultaneously validated through experiments. By exploring the physical process of the fluid-solid interaction effect of the hydraulic reciprocating O-ring seal, a numerical fluid-solid interaction model consisting of fluid lubrication, contact mechanics, asperity contact and elastic deformation analyses is constructed with an iterative procedure. With the SRV friction and wear tester, the experiments are performed to investigate the elastohydrodynamic lubrication characteristics of the O-ring seal. The regularity of the friction coefficient varying with the speed of reciprocating motion is obtained in the mixed lubrication condition. The experimental result is used to validate the fluid-solid interaction model. Based on the model, The elastohydrodynamic lubrication characteristics of the hydraulic reciprocating O-ring seal are presented respectively in the dry friction, mixed lubrication and full film lubrication conditions, including of the contact pressure, film thickness, friction coefficient, liquid film pressure and viscous shear stress in the sealing zone. The proposed numerical fluid-solid interaction model can be effectively used to analyze the operation characteristics of the hydraulic reciprocating O-ring seal, and can also be widely used to study other hydraulic reciprocating seals.

Fluid-solid interaction of resistance loss of flexible hose in deep ocean mining

The resistance loss of transportation was studied and the influences of buoyancy layout,mineral content and elastic modulus of flexible hose were investigated based on three-dimensional finite element model of fluid-solid interaction by MSC.MARC/MENTAT software.The numerical results show that the resistance losses increase with the increase of mineral content Cv and velocity of internal fluid v and decrease with the increase of elastic modulus E of flexible hose.The buoyancy layout and the velocity of internal fluid have greater impacts on the resistance losses than the elastic modulus of flexible hose.In order to reduce the resistance losses and improve the efficiency of the deep-ocean mining,Cv and v must be restricted in a suitable range (e.g.10%-25% and 2.5-4 m/s).Effective buoyancy layout (such as Scheme C and D) should be adopted and the suitable material of moderate E should be used for the flexible hose in deep-ocean mining.

Fractional four-step finite element method for analysis of thermally coupled fluid-solid interaction problems

An integrated fluid-thermal-structural analysis approach is presented. In this approach, the heat conduction in a solid is coupled with the heat convection in the viscous flow of the fluid resulting in the thermal stress in the solid. The fractional four-step finite element method and the streamline upwind Petrov-Galerkin （SUPG） method are used to analyze the viscous thermal flow in the fluid. Analyses of the heat transfer and the thermal stress in the solid axe performed by the Galerkin method. The second-order semi- implicit Crank-Nicolson scheme is used for the time integration. The resulting nonlinear equations are lineaxized to improve the computational efficiency. The integrated analysis method uses a three-node triangular element with equal-order interpolation functions for the fluid velocity components, the pressure, the temperature, and the solid displacements to simplify the overall finite element formulation. The main advantage of the present method is to consistently couple the heat transfer along the fluid-solid interface. Results of several tested problems show effectiveness of the present finite element method, which provides insight into the integrated fluid-thermal-structural interaction phenomena.

Fluid-solid interaction analysis of torque converters

In order to extend the service life of torque converters, it is essential to predict the pressure condition and improve its weak areas. According to computational fluid dynamics and structural statics, a model of torque converter is constructed using software ANSYS. Then, a fluid-solid interaction(FSI) analysis method is proposed to obtain its stress distribution, in which the fluid pressure is applied to the coupling surface to calculate the interaction between fluid and solid. The results show that the fluid pressure at the inlet of the impeller is maximum and decreases along the flow direction, the pressure at the inlet of the turbine blade is minimum and the outlet pressure is the largest, increasing along the flow direction gradually;the pressure distribution of the impeller is concentrated mainly at the corner, especially between the inner ring and the impeller blades;the pressure of the turbine is concentrated mainly on the connection between turbine and the outer edge of the blade.

Simulation on Dynamic Bending Features of Fabric Based on Fluid-Solid Interaction Technique

This paper is devoted to the two-dimensional nonlinear modeling of the fluid-solid interaction (FSI) between fabric and air flow, which is based on the Automatic Incremental Dynamic Nonlinear Analysis (AIDNA)-FSI program in order to study the dynamic bending features of fabrics in a specific air flow filed. The computational fluid dynamics (CFD) model for flow and the finite element model (FEM) for fabric was set up to constitute an FSI model in which the geometric nonlinear behavior and the dynamic stress-strain variation of the relatively soft fabric material were taken into account. Several FSI cases with different time-dependent wind load and the model frequency analysis for fabric were carried out. The dynamic response of fabric and the distribution of fluid variables were investigated. The results of numerical simulation and experiments fit quite well. Hence, this work contributes to the research of modeling the dynamic bending behavior of fabrics in air field.

Comparison of base-isolated liquid storage tank models under bi-directional earthquakes

Seismic response of ground supported baseisolated liquid storage tanks are evaluated under bi-directional earthquakes. The base-isolated liquid storage tanks are modeled using mechanical analogs with two and three lumped masses (Model 1 and Model 2). Two types of isolation systems, such as sliding system and elastomeric system, are considered for the present study. The isolation systems are modeled using Wen’s equation for hysteretic isolation systems. Response of base-isolated liquid storage tanks, evaluated through two different modeling approaches, is compared. Both the models predict similar sloshing displacement. The effect of interaction between the mutually perpendicular seismic responses of the isolator is investigated for both the models. It is observed that interaction affects the peak seismic response of the base-isolated liquid storage tanks significantly, under the bi-directional earthquake components.

A High-Accuracy Curve Boundary Recognition Method Based on the Lattice Boltzmann Method and Immersed Moving Boundary Method

Applying numerical simulation technology to investigate fluid-solid interaction involving complex curved bound-aries is vital in aircraft design,ocean,and construction engineering.However,current methods such as Lattice Boltzmann(LBM)and the immersion boundary method based on solid ratio(IMB)have limitations in identifying custom curved boundaries.Meanwhile,IBM based on velocity correction(IBM-VC)suffers from inaccuracies and numerical instability.Therefore,this study introduces a high-accuracy curve boundary recognition method(IMB-CB),which identifies boundary nodes by moving the search box,and corrects the weighting function in LBM by calculating the solid ratio of the boundary nodes,achieving accurate recognition of custom curve boundaries.In addition,curve boundary image and dot methods are utilized to verify IMB-CB.The findings revealed that IMB-CB can accurately identify the boundary,showing an error of less than 1.8%with 500 lattices.Also,the flow in the custom curve boundary and aerodynamic characteristics of the NACA0012 airfoil are calculated and compared to IBM-VC.Results showed that IMB-CB yields lower lift and drag coefficient errors than IBM-VC,with a 1.45%drag coefficient error.In addition,the characteristic curve of IMB-CB is very stable,whereas that of IBM-VC is not.For the moving boundary problem,LBM-IMB-CB with discrete element method(DEM)is capable of accurately simulating the physical phenomena of multi-moving particle flow in complex curved pipelines.This research proposes a new curve boundary recognition method,which can significantly promote the stability and accuracy of fluid-solid interaction simulations and thus has huge applications in engineering.

Reduced-order modeling and vibration transfer analysis of a fluid-delivering branch pipeline that consider fluid–solid interactions

The efficient dynamic modeling and vibration transfer analysis of a fluid-delivering branch pipeline(FDBP)are essential for analyzing vibration coupling effects and implementing vibration reduction optimization.Therefore,this study proposes a reduced-order dynamic modeling method suitable for FDBPs and then analyzes the vibration transfer characteristics.For the modeling method,the finite element method and absorbing transfer matrix method(ATMM)are integrated,considering the fluid–structure coupling effect and fluid disturbances.The dual-domain dynamic substructure method is developed to perform the reduced-order modeling of FDBP,and ATMM is adopted to reduce the matrix order when solving fluid disturbances.Furthermore,the modeling method is validated by experiments on an H-shaped branch pipeline.Finally,transient and steady-state vibration transfer analyses of FDBP are performed,and the effects of branch locations on natural characteristics and vibration transfer behavior are analyzed.Results show that transient vibration transfer represents the transfer and conversion of the kinematic,strain,and damping energies,while steady-state vibration transfer characteristics are related to the vibration mode.In addition,multiple-order mode exchanges are triggered when branch locations vary in frequency-shift regions,and the mode-exchange regions are also the transformation ones for vibration transfer patterns.

FLUID-SOLID COUPLING MATHEMATICAL MODEL OF CONTAMINANT TRANSPORT IN UNSATURATED ZONE AND ITS ASYMPTOTICAL SOLUTION

The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport, a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid_solid interaction mechanics theory. The asymptotical solutions to the nonlinear coupling mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of pore pressure, pore water velocity and contaminant concentration in unsaturated zone has been presented under the conditions of with coupling and without coupling gas phase. An example problem was used to provide a quantitative verification and validation of the model. The asymptotical solution was compared with Faust model solution. The comparison results show reasonable agreement between asymptotical solution and Faust solution, and the gas effect and media deformation has a large impact on the contaminant transport. The theoretical basis is provided for forecasting contaminant transport and the determination of the relationship among pressure_saturation_permeability in laboratory.

Feasibility of monitoring a mine fan by using interaction of vibrator system

The impeller of turbo machinery is a typical nonlinear multi-oscillator system.The vibration of each module is coupling, including fluid-solid coupling of the blade.The subject of our investigation was a KDF-5 mine fan for which we analyzed air vibration signals and axial vibration signals by using correlation dimension analysis under five variable working conditions.The results indicate that their correlation dimension curves show a uniform trend.That is to say, the characteristics of the variation signals of the integral structure are correlated and mutually embodied.It proves that it is possible to monitor the working state of a mine fan by coupling the vibration signals and air vibration signals for these are more sensitive in representing the status of the impeller system.

Simulation of dynamic fluid-solid interactions with an improved direct-forcing immersed boundary method

Dynamic fluid-solid interactions are widely found in chemical engineering, such as in particle-laden flows, which usually contain complex moving boundaries. The immersed boundary method （IBM） is a convenient approach to handle fluid-solid interactions with complex geometries. In this work, Uhlmann＇s direct-forcing IBM is improved and implemented on a supercomputer with CPU-GPU hybrid architec- ture. The direct-forcing IBM is modified as follows： the Poisson＇s equation for pressure is solved before evaluation of the body force, and the force is only distributed to the Cartesian grids inside the immersed boundary. A multidirect forcing scheme is used to evaluate the body force. These modifications result in a divergence-free flow field in the fluid domain and the no-slip boundary condition at the immersed boundary simultaneously. This method is implemented in an explicit finite-difference fractional-step scheme, and validated by 2D simulations of lid-driven cavity flow, Couette flow between two concentric cylinders and flow over a circular cylinder. Finally, the method is used to simulate the sedimentation of two circular particles in a channel. The results agree very well with previous experimental and numerical data, and are more accurate than the conventional direct-forcing method, especially in the vicinity of a moving boundary.

ADirect-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems

In this paper,we develop a direct-forcing immersed boundary projection method for simulating the dynamics in thermal fluid-solid interaction problems.The underlying idea of the method is that we treat the solid as made of fluid and introduce two virtual forcing terms.First,a virtual fluid force distributed only on the solid region is appended to the momentum equation to make the region behave like a real solid body and satisfy the prescribed velocity.Second,a virtual heat source located inside the solid region near the boundary is added to the energy transport equation to impose the thermal boundary condition on the solid boundary.We take the implicit second-order backward differentiation to discretize the time variable and employ the Choi-Moin projection scheme to split the coupled system.As for spatial discretization,second-order centered differences over a staggered Cartesian grid are used on the entire domain.The advantages of this method are its conceptual simplicity and ease of implementation.Numerical experiments are performed to demonstrate the high performance of the proposed method.Convergence tests show that the spatial convergence rates of all unknowns seem to be super-linear in the 1-norm and 2-norm while less than linear in the maximum norm.

Fluid-solid coupling numerical simulation of micro-disturbance grouting treatment for excessive deformation of shield tunnel

Micro-disturbance grouting is a recovery technique to reduce the excessive deformation of operational shield tunnels in urban areas.The grout mass behaves as a fluid in the ground before hardening to form a grout–soil mixture,which highlights the necessity of using fluid–solid coupling method in the simulation of grouting process.Within a discrete element modeling environment,this paper proposes a novel fluid-solid coupling method based on the pore density flow calculation.To demonstrate the effectiveness of this method,it is applied to numerical simulation of micro-disturbance grouting process for treatment of large transverse deformation of a shield tunnel in Shanghai Metro,China.The simulation results reveal the mechanism of recovering tunnel convergence by micro-disturbance grouting in terms of compaction and fracture of soil,energy analysis during grouting,and mechanical response of soil-tunnel interaction system.Furthermore,the influence of the three main grouting parameters(i.e.,grouting pressure,grouting distance,and grouting height)on tunnel deformation recovery efficiency is evaluated through parametric analysis.In order to efficiently recover large transverse deformation of shield tunnel in Shanghai Metro,it is suggested that the grouting pressure should be about 0.55 MPa,the grouting height should be in the range of 6.2–7.0 m,and the grouting distance should be in the range of 3.0–3.6 m.The results provide a valuable reference for grouting treatment projects of over-deformed shield tunnel in soft soil areas.

基于FSI系统的(u_i,p)格式大型渡槽动力分析

槽体固体以位移为基本未知量,槽内水体以流场压力p为基本未知量,用能量变分原理推导了流固耦合(FSI)系流有限元分析的(ui,p)格式,给出流固耦合系统的动力特性方程,并基于FSI系统的(ui,p)格式建立渡槽槽体-水体-槽墩-基础-地基系统的力学模型,采用非对称模态提取法求解了渡槽的动力特性,并用隐式-显式积分算法计算了强震作用下大型渡槽的动力响应。计算结果表明,基于(ui,p)格式的流固耦合系统有限元分析的格式,考虑到槽体与水体的相互作用,简化了计算模型,提高了计算精度,同时也得出不同过水量下槽体结构动力特性和动力响应的变化规律等结论。

BIFURCATIONS OF A CANTILEVERED PIPE CONVEYING STEADY FLUID WITH A TERMINAL NOZZLE

This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin method. The static stability is studied by the Routh criteria. The method of averaging is employed to investigate the stability of the periodic motions. A Runge-Kutta scheme is used to examine the analytical results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one makes the periodic motions of the system lose the stability by doubling-period bifurcation.

Fluid-solid strong-interaction model of mechanical seals in reactor coolant pumps

The studies on the mechanisms and performances of the mechanical seals in reactor coolant pumps are very important for the safe operations of the pressurized water reactor power plants. Based on the hydrostatic mechanical seal in reactor coolant pumps, an analytical fluid-solid strong-interaction model is proposed in this paper. According to the design features and operafional principles of the seal, an analytical method to calculate the mechanical deformation of the seal assembly is developed based on the ring deformation theory. A strong-interaction algorithm combining the analysis of the mechanical deformation of the seal assembly and flow field between the seal faceplates is utilized, in which the three kinds of equations including the fluid domain, solid domain and coupling action are constituted in the same equations set and all the variables are solved simul- taneously. So the analytical fluid-solid strong-interaction model used for the seal is built. Moreover, the model is verified by the experimental results. Based on the model, the design parameters of the seal are studied. Two different conditions of the general case and fixed seal leakage rate are discussed respectively, and the regularities that the seal behaviors are affected by the parameters of the holding screws on the clamp rings and seal faceplates are obtained. The research results can provide a theoretical basis for performance analysis, design and assemblage of the seal. Compared to the numerical methods, the proposed model has the unique advantages of high efficiency, convenience and easy application of constraints.

Seismic behavior of variable frequency pendulum isolator

Earthquake performance of a flexible one-story building isolated with a variable frequency pendulum isolator （VFPI） under near-fault and far-field ground motions is investigated. The frictional forces mobilized at the interface of the VFPI are assumed to be velocity dependent. The interaction between frictional forces of the VFPI in two horizontal directions is duly considered and coupled differential equations of motion of the isolated system in the incremental form are solved iteratively. The response of the system with bi-directional interaction is compared with those without interaction. In addition, the effects of velocity dependence on the response of the isolated system are also investigated. Moreover, a parametric study is carried out to critically examine the influence of important parameters on bi-directional interaction effects of the frictional forces of the VFPI. These parameters are： the superstructure time period, frequency variation factor （FVF） and friction coefficient of the VFPI. From the above investigations, it is observed that the dependence of the friction coefficient on relative velocity of the system does not have a noticeable effect on the peak response of the system isolated with VFPI, and that the bi-directional interaction of frictional forces of the VFPI is important and if neglected, isolator displacements will be underestimated and the superstructure acceleration and base shear will be overestimated.

INSTABILITY AND CHAOS IN A PIPE CONVEYING FLUID WITH ADDED MASS AT FREE END

This paper shows the mechanism of instability and chaos in acantilevered pipe conveying steady fluid. The pipe underconsideration has added mass or a nozzle at the free end. TheGalerkin method is used to transform the original system into a setof ordinary differential equations and the standard methods ofanalysis of the discrete system are introduced to deal with theinstability. With either the nozzle parameter or the flow velocityincreasing, a route to chaos can be observed very clearly: the pipeundergoing buckling (pitchfork bifurcation), flutter (Hopfbifurcation), doubling periodic motion (pitchfork bifurcation) andchaotic motion occurring finally.

CO-DIMENSION 2 BIFURCATIONS AND CHAOS IN CANTILEVERED PIPE CONVEYING TIME VARYING FLUID WITH THREE-TO-ONE INTERNAL RESONANCES

The nonlinear behavior of a cantilevered fluid conveying pipe subjected to principal parametric and internal resonances is investigated in this paper.The flow velocity is divided into constant and sinusoidal parts.The velocity value of the constant part is so adjusted such that the system exhibits 3:1 internal resonances for the first two modes.The method of multiple scales is employed to obtain the response of the system and a set of four first-order nonlinear ordinary- differential equations for governing the amplitude of the response.The eigenvalues of the Jacobian matrix are used to assess the stability of the equilibrium solutions with varying parameters.The co- dimension 2 derived from the double-zero eigenvalues is analyzed in detail.The results show that the response amplitude may undergo saddle-node,pitchfork,Hopf,homoclinic loop and period- doubling bifurcations depending on the frequency and amplitude of the sinusoidal flow.When the frequency of the sinusoidal flow equals exactly half of the first-mode frequency,the system has a route to chaos by period-doubling bifurcation and then returns to a periodic motion as the amplitude of the sinusoidal flow increases.