Valve Dynamics Research Articles

Analysis of dynamic nonlinearity of flow control loop through modified relay test probing

Most of the controller tuning methods in process control are based on linear models. Through the development of a detail model of the actuator-pneumatic valve dynamics, we show that even if the static characteristic of the valve is linear (including possible linearity of the flow dependence on the valve opening) the actuator-valve dynamics are strongly nonlinear. Therefore, tuning of the flow loop will be affected by the selection of the operating point and the amplitude of the relay in the relay feedback test (RFT) or modifications of this test. It is shown that Lyapunov linearisation around an equilibrium point fails to provide a local linear model of the system, and modified RFT probing is used for investigation of the system dynamics. The same test is used for the proportional-integral controller tuning in various operating points. It is recommended that the difference in the dynamic response of the loop for different relay amplitudes and operating points should be accounted for by larger stability margins.

Mitral valve dynamics in structural and fluid–structure interaction models

Modelling and simulation of heart valves is a challenging biomechanical problem due to anatomical variability, pulsatile physiological pressure loads and 3D anisotropic material behaviour. Current valvular models based on the finite element method can be divided into: those that do model the interaction between the blood and the valve (fluid–structure interaction or ‘wet’ models) and those that do not (structural models or ‘dry’ models). Here an anatomically sized model of the mitral valve has been used to compare the difference between structural and fluid–structure interaction techniques in two separately simulated scenarios: valve closure and a cardiac cycle. Using fluid–structure interaction, the valve has been modelled separately in a straight tubular volume and in a U-shaped ventricular volume, in order to analyse the difference in the coupled fluid and structural dynamics between the two geometries. The results of the structural and fluid–structure interaction models have shown that the stress distribution in the closure simulation is similar in all the models, but the magnitude and closed configuration differ. In the cardiac cycle simulation significant differences in the valvular dynamics were found between the structural and fluid–structure interaction models due to difference in applied pressure loads. Comparison of the fluid domains of the fluid–structure interaction models have shown that the ventricular geometry generates slower fluid velocity with increased vorticity compared to the tubular geometry. In conclusion, structural heart valve models are suitable for simulation of static configurations (opened or closed valves), but in order to simulate full dynamic behaviour fluid–structure interaction models are required.

Instability of Pressure Relief Valves in Water Pipes

Pressure relief valves in water pipes are known to sometimes chatter when the inlet pressure slightly exceeds the set pressure. While these devices are responsible for numerous fatigue issues in process industries, there is a relatively low number of technical publications covering their performance, especially in heavy fluid applications. The present study is intended as a contribution to the understanding of pressure relief valve dynamics, taking into account fluid-structure interactions. A series of tests were performed with a water relief valve in a test rig. Adjusting the set pressure of the valve to about 30 bars, an upstream pressure varying from 20 bars to 35 bars was imposed, so that the valve opened and the water flow varied from a few m3/h to about 80 m3/h. During the tests, the pipe was equipped upstream and downstream of the valve with static pressure sensors and a flowmeter, the disk lift was measured with a laser displacement sensor, and the spring force was recorded simultaneously. Several fluctuating pressure sensors were also installed in the inlet pipe. Static instability is investigated by comparing the spring force to the hydraulic force. Dynamic instability is observed and it is shown that the resonant behavior of the disk generates an apparent negative pressure drop coefficient at some frequencies. This negative pressure drop coefficient can trigger a dynamic instability in a manner similar to the negative damping effect in leakage-flow vibrations.

Asymptotic State Observers for a Simplified Brass Instrument Model

In this paper, a simplified model of a brass instrument is introduced. It is composed of a valve (including the mechanics of the lips), a jet (coupled with the valve dynamics), and a straight acoustic pipe excited by the jet, radiating in the air, and with frequency independent losses. This model couples an ordinary differential equation (valve) to a partial differential equation (acoustic pipe) through a static nonlinear function (Bernoulli relation on the jet). In fact, the overall system can be described by a ''so-called'' nonlinear neutral state space representation, the state of which being the position and velocity of the valve aperture and the ingoing wave of pressure at the entrance of the pipe. The measured output is the pressure at the open end of the pipe and the control is the mouth pressure. In this paper, methods of control engineering are applied to recover the state from the input and the measured output, assuming that propagation characteristics and player expression parameters are constant: a nonlinear state observer is built.} The robustness to wrong initial conditions and to noise on the measured output are analyzed.

Evaluation of a new Implicit Coupling Algorithm for the Partitioned Fluid-Structure Interaction Simulation of Bileaflet Mechanical Heart Valves

We present a newly developed Fluid-Structure Interaction coupling algorithm to simulate Bileaflet Mechanical Heart Valves dynamics in a partitioned way. The coupling iterations between the flow solver and the leaflet motion solver are accelerated by using the Jacobian with the derivatives of the pressure and viscous moments acting on the leaflets with respect to the leaflet acceleration. This Jacobian is used in the leaflet motion solver when new positions of the leaflets are computed during the coupling iterations. The Jacobian is numerically derived from the flow solver by applying leaflet perturbations. Instead of calculating this Jacobian every time step, the Jacobian is extrapolated from previous time steps and a recalculation of the Jacobian is only done when needed. The efficiency of our new algorithm is subsequently compared to existing algorithms which use fixed relaxation and dynamic Aitken Δ2 relaxation in the coupling iterations when the new positions of the leaflets are computed. Results show that dynamic Aitken Δ2 relaxation outperforms fixed relaxation. Moreover, during the opening phase of the valve, our new algorithm needs fewer subiterations per time step to achieve convergence than the method with Aitken Δ2 relaxation. Thus, our newly developed FSI coupling scheme outperforms the existing coupling schemes.

A time-dependent numerical analysis of flow in a mechanical heart valve: Comparison with experimental results

There is a great need to fabricate heart valves that have similar haemodynamic properties with the natural ones. Towards this goal, we examine the dynamics of fluid flow in a mechanical heart valve with one leaflet. The fluid is incompressible and Newtonian and the leaflet is a neo-Hookean material. The Arbitrary Lagrangian Eulerian method is used to model the fluid-leaflet interaction, and the system of equations is solved using the Finite Element method. The pseudo solid approach along with a set of algebraic equations are used to deform the mesh, while care is taken to avoid remeshing of the domain, at the moment of valve closure. The computational results are compared against the experimental results, and we find an excellent agreement for the time period of valve closure, the time the valve is fully opened, and the value of the maximum valve opening angle. This study indicates that the present model is capable of describing the valve dynamics in physiological geometries.

Structural analysis of the natural aortic valve in dynamics: From unpressurized to physiologically loaded

A novel finite element model of the natural aortic valve was developed implementing anisotropic hyperelastic material properties for the leaflets and aortic tissues, and starting from the unpressurized geometry. Static pressurization of the aortic root, silicone rubber moulds and published data helped to establish the model parameters, while high-speed video recording of the leaflet motion in a left-heart simulator allowed for comparisons with simulations. The model was discretized with brick elements and loaded with time-varying pressure using an explicit commercial solver. The aortic valve model produced a competent valve whose dynamic behavior (geometric orifice area vs. time) closely matched that observed in the experiment. In both cases, the aortic valve took approximately 30 ms to open to an 800 mm 2 orifice and remained completely or more than half open for almost 200 ms, after which it closed within 30–50 ms. The highest values of stress were along the leaflet attachment line and near the commissure during diastole. Von Mises stress in the leaflet belly reached 600–750 kPa from early to mid-diastole. While the model using the unpressurized geometry as initial configuration was specially designed to satisfy the requirements of continuum mechanics for large deformations of hyperelastic materials, it also clearly demonstrated that dry models can be adequate to analyze valve dynamics. Although improvements are still needed, the advanced modeling and validation techniques used herein contribute toward improved and quantified accuracy over earlier simplified models.

Role of Computational Simulations in Heart Valve Dynamics and Design of Valvular Prostheses

Computational simulations are playing an increasingly important role in enhancing our understanding of the normal human physiological function, etiology of diseased states, surgical and interventional planning, and in the design and evaluation of artificial implants. Researchers are taking advantage of computational simulations to speed up the initial design of implantable devices before a prototype is developed and hence able to reduce animal experimentation for the functional evaluation of the devices under development. A review of the reported studies to date relevant to the simulation of the native and prosthetic heart valve dynamics is the subject of the present paper. Potential future directions toward multi-scale simulation studies for our further understanding of the physiology and pathophysiology of heart valve dynamics and valvular implants are also discussed.

Flow Interactions with Cells and Tissues: Cardiovascular Flows and Fluid–Structure Interactions

Interactions between flow and biological cells and tissues are intrinsic to the circulatory, respiratory, digestive and genitourinary systems. In the circulatory system, an understanding of the complex interaction between the arterial wall (a living multi-component organ with anisotropic, nonlinear material properties) and blood (a shear-thinning fluid with 45% by volume consisting of red blood cells, platelets, and white blood cells) is vital to our understanding of the physiology of the human circulation and the etiology and development of arterial diseases, and to the design and development of prosthetic implants and tissue-engineered substitutes. Similarly, an understanding of the complex dynamics of flow past native human heart valves and the effect of that flow on the valvular tissue is necessary to elucidate the etiology of valvular diseases and in the design and development of valve replacements. In this paper we address the influence of biomechanical factors on the arterial circulation. The first part presents our current understanding of the impact of blood flow on the arterial wall at the cellular level and the relationship between flow-induced stresses and the etiology of atherosclerosis. The second part describes recent advances in the application of fluid-structure interaction analysis to arterial flows and the dynamics of heart valves.

On the multiscale modeling of heart valve biomechanics in health and disease

Theoretical models of the human heart valves are useful tools for understanding and characterizing the dynamics of healthy and diseased valves. Enabled by advances in numerical modeling and in a range of disciplines within experimental biomechanics, recent models of the heart valves have become increasingly comprehensive and accurate. In this paper, we first review the fundamentals of native heart valve physiology, composition and mechanics in health and disease. We will then furnish an overview of the development of theoretical and experimental methods in modeling heart valve biomechanics over the past three decades. Next, we will emphasize the necessity of using multiscale modeling approaches in order to provide a comprehensive description of heart valve biomechanics able to capture general heart valve behavior. Finally, we will offer an outlook for the future of valve multiscale modeling, the potential directions for further developments and the challenges involved.

Usage and validation of a fluid structure interaction methodology for the study of different suction valve parameters of a hermetic reciprocating compressor

The dynamics of the flatter valves inside a hermetic reciprocating compressor used in household appliances is the most important factor concerning the gas dynamic behaviour of such a compressor. Hence for a good valve design and for a reliable simulation of the compressor the ability to predict the movement of the valves is indispensable. The present paper describes a methodology which allows the prediction of the valve dynamics. For the validation of the methodology the simulation results of the suction valve dynamics have been compared with experimental data obtained out of measurements with a Laser-Doppler-Vibrometer. Furthermore the method has been used for the variation of some suction valve parameters and their influence onto the overall compressor performance has been shown. The whole methodology has been implemented into a commercial available CFD code (FLUENT) as a user defined function (UDF).

Analytical Coupled Modeling and Model Validation of Hydraulic On/Off Valves

The goal of this paper is to describe a method for modeling high speed on/off valves. This model focuses on the nonlinearities of the electromagnetic, fluidic, and mechanical domains, specifically within solenoid driven poppet style valves. By including these nonlinearities, the model accurately predicts valve transition time for different driving voltages and valve strokes. The model also predicts fluid transients such as pressure ripple. Unique attributes of the model are the inclusion of the effect of eddy currents and fringing while still being fully coupled with the fluid and mechanical domains. A prototype was constructed and used to experimentally validate the model. By developing accurate lumped parameter models, valve dynamics can be applied to hydraulic systems to accurately capture their dynamics.

Dynamic analysis of a nonlinear pressure regulator using bondgraph simulation technique

Abstract The dynamics of a direct pressure regulator valve have been studied through bondgraph simulation technique. The governing equations of the system have been derived from the obtained model. While solving the system equations numerically, various pressure-flow characteristics across the regulator ports and the orifices are taken into consideration. The simulation study identifies some critical parameters, which have significant effect on the transient response of the system. The simulation results are determined using the MATLAB-SIMULINK environment. The main novelty of this work is to present an analytic solution in analyzing a nonlinear complex system with interaction of several energy domains. The other conventional attempts employed before this solution resulted to inaccurate simulation results which can not predict the dynamical response of the system. Numerical results implied to the good accuracy of the bondgraph study, while comparing with experimental results.

Investigation of a nonlinear dynamic hydraulic system model through the energy analysis approach

The dynamics of a pressure regulator valve have been studied using the through Bondgraph simulation technique. This valve consists of several elements that can transmit, transform, store, and consume hydraulic energy. The governing equations of the system have been derived from the dynamic model. In solving system equations numerically, various pressure-flow characteristics across the regulator ports and orifices have been taken into consideration. This simulation study identifies some critical parameters that have significant effects on the transient response of the system. The results have been obtained using the MATLAB-SIMULINK environment. The main advantage of the proposed methodology is its ability to model the nonlinear behavior of the hydraulic resistance of system elements as a function of the fluid flow rate.

Development of a novel passive top–down uniflow scavenged two-stroke GDI engine

The design and performance characteristics of a novel top–down uniflow scavenged gasoline direct-injection two-stroke engine are presented. The novelty of the engine lies in the cylinder head that contains multiple check valves that control scavenging airflow into the cylinder from a supercharged air plenum. When the cylinder pressure drops below the intake plenum pressure during the expansion stroke, air flows into the cylinder through the check valves. During compression the cylinder pressure increases to a level above the intake plenum pressure and the check valves close preventing back-flow into the intake plenum. The engine head design provides asymmetrical intake valve timing without the use of poppet valves and the associated valve-train. In combination with an external Roots-type supercharger that supplies the plenum and exhaust ports at the bottom of the cylinder wall, the novel head provides top–down uniflow air scavenging. Motoring tests indicated that the check valves seal and the peak pressure is governed by the compression ratio. The only drawback observed is that valve closing is delayed as the engine speed increases. In order to investigate the valve dynamics, additional tests were performed in an optically-accessible cold flow test rig that enabled the direct measurement of valve opening and closing time under various conditions.

Fluid–structure interaction methods in biological flows with special emphasis on heart valve dynamics

AbstractThere are numerous examples of fluid–structure interactions (FSIs) within the human body. In all cases, a computer model capable of simulating the phenomenon can aid in the understanding of organ function, failure, and implant design or improvement. In the current paper, two approaches are examined for use in simulating the FSI problem of the dynamics of tissue heart valves. Valve leaflets have nonlinear anisotropic material properties, and undergo complex deformation. Their motion affects—and is affected by—the surrounding blood. This two‐way coupling necessitates a robust algorithm in order to overcome numerical stiffness, convergence challenges, and stability issues. A locally refined Cartesian mesh, sharp interface method has been developed for the fluid flow solution. In the structural domain, the valve leaflet is represented in a Lagrangian fashion and moves based on its experimentally determined material properties. In computing leaflet motion, the anisotropic, nonlinear material properties of the valve leaflet are incorporated using a finite element solver, which calculates the leaflet deformation and stresses based on the stress imparted by the surrounding fluid. Two FSI algorithms have been studied in the context of a sharp‐interface Cartesian grid setting, and each has been validated with benchmark results. The two approaches are compared, and ultimately one is selected as most appropriate for simulating tissue heart valves. In the selected approach, a strongly coupled, partitioned method is used in which subiterations of the fluid and structure solutions are performed at each time step. During the subiterations, the leaflet motion is used as a boundary condition on the fluid, and the fluid stresses act as a boundary condition on the leaflet. In this way, continuity is ensured and two‐way coupling is achieved. The selected approach has overcome the challenges faced by previous simulations reported in the literature, and a robust FSI solution is achieved using physiologic Reynolds numbers, realistic material properties, highly resolved grids, and a dynamic simulation. This approach has the advantage of handling both thin and volumetric embedded objects in a unified fashion, and of treating rigid and deformable structures in the same way, thus allowing a spectrum of potential applications. Copyright © 2009 John Wiley & Sons, Ltd.

Analysis of a mechanical heart valve prosthesis and a native venous valve: Two distinct applications of FSI to biomedical applications

AbstractThis paper reports the application of two commercial codes to the study of distinct cardiovascular problems: dynamics of a mechanical heart valve prosthesis and function of a native venous valve. The choice of code is driven by the characteristics of the problem. The ANSYS‐CFX implicit finite volume code is employed for the mechanical valve where the solution is dominated by the interaction between the local fluid domain and the rigid valve leaflets. The LS‐DYNA explicit dynamics code is used due to the stability of this approach when applied to systems with very flexible structural components such as the leaflets of a venous valve. The mechanical valve dynamics remain consistent for a range of mesh densities and residual criteria but begin to vary once the solution time step is increased above 2E–4 s. Venous valve function after application of a gravitational body load is shown to be dependent on parent vessel elastic modulus, E. The venous valve initially closes to a greater extent with a ‘softer’ parent vessel. Both approaches show promise for further study of these biomedical systems including the cavitation and thrombotic potential of mechanical valves and the local residence of blood constituents in the region of venous valve sinuses. Copyright © 2009 John Wiley & Sons, Ltd.

Computational analysis of ventricular valve–valve interaction: Influence of flow conditions

Apart from dependence on the heart muscle contractility, the pumping efficiency of the heart depends on the functioning of its valves. Valve functionality, expressed as 1 minus the ratio between regurgitant and stroke volume, is the result of the motion of the valve depending on local flow phenomena. In this work, the relation between flow conditions and valve functionality was studied by means of a parameter study of the flow and valve dynamics in a two-dimensional computational model of the left ventricle with two rigid valves. It was found that valve functionality depends strongly on the applied flow conditions as expressed by the Strouhal and the Reynolds numbers. Furthermore, it was found that the regurgitant volume can vary from beat-to-beat resulting in a non-periodic pumping efficiency of the heart. These observations are of importance to future research based on simulations of geometrically more realistic heart valve-ventricle configurations as it may not always be taken for granted that beat-to-beat variations of the pumping efficiency are small.

SIMULATING THE FLUID DYNAMICS OF NATURAL AND PROSTHETIC HEART VALVES USING THE IMMERSED BOUNDARY METHOD

The immersed boundary method is both a general mathematical framework and a particular numerical approach to problems of fluid-structure interaction. In the present work, we describe the application of the immersed boundary method to the simulation of the fluid dynamics of heart valves, including a model of a natural aortic valve and a model of a chorded prosthetic mitral valve. Each valve is mounted in a semi-rigid flow chamber. In the case of the mitral valve, the flow chamber is a circular pipe, and in the case of the aortic valve, the flow chamber is a model of the aortic root. The model valves and flow chambers are immersed in a viscous incompressible fluid, and realistic fluid boundary conditions are prescribed at the upstream and downstream ends of the chambers. To connect the immersed boundary models to the boundaries of the fluid domain, we introduce a novel modification of the standard immersed boundary scheme. In particular, near the outer boundaries of the fluid domain, we modify the construction of the regularized delta function which mediates fluid-structure coupling in the immersed boundary method, whereas in the interior of the fluid domain, we employ a standard four-point delta function which is frequently used with the immersed boundary method. The standard delta function is used wherever possible, and the modified delta function continuously transitions to the standard delta function away from the outer boundaries of the fluid domain. Three-dimensional computational results are presented to demonstrate the capabilities of our immersed boundary approach to simulating the fluid dynamics of heart valves.

Sliding Mode Control of a 2DOF Planar Pneumatic Manipulator

This paper presents a sliding mode controller for a 2DOF planar pneumatic manipulator actuated by pleated pneumatic artificial muscle actuators. It is argued that it is necessary to account for the pressure dynamics of muscles and valves. A relatively detailed system model that includes pressure dynamics is established. Since the model includes actuator dynamics, feedback linearization was necessary to design a sliding mode controller. The feedback linearization and subsequent controller design are presented in detail, and the controller’s performance is evaluated, both in simulation and experimentally. Chattering was found to be quite severe, so the introduction of significant boundary layers was required.