First-Order Pump Surge Behavior

1978 ◽  
Vol 100 (4) ◽  
pp. 459-466 ◽  
Author(s):  
P. H. Rothe ◽  
P. W. Runstadler
Keyword(s):  
Analytical Model ◽  
Flow Instability ◽  
Lumped Parameter Model ◽  
Piping System ◽  
Unstable Flow ◽  
First Order ◽  
Lumped Parameter ◽  
Quantitative Basis ◽  
Flow Oscillations ◽  
Good Agreement

This paper presents the results of an empirical study undertaken to assess the appropriateness and applicability of a simple, analytical model of pump-piping system flow instability. The analysis is used to describe behavior actually observed in a well defined, simple, pump-piping system. The frequency and amplitude of the flow oscillations observed during pump surge and the range of the pump-piping system characteristic parameters for which unstable flow oscillations occurred are in good agreement with the behavior predicted by the analysis. The results of this work provide a quantitative basis for investigating modifications to the lumped-parameter model in order to make it also appropriate for the analysis of more complex pump or compressor system. Although the analytical model displayed here is not new, a direct comparison of model predictions against similar measurements of first-order pump surge has not been published prior to this work.

Dynamic Model for a Dome-Loaded Pressure Regulator

1997 ◽  
Vol 122 (2) ◽  
pp. 290-297 ◽  
Author(s):  
A. Nabi ◽  
E. Wacholder ◽  
J. Dayan
Keyword(s):  
Physical Model ◽  
Lumped Parameter Model ◽  
Pressure Regulator ◽  
Flow Rates ◽  
First Order ◽  
Runge Kutta Method ◽  
Lumped Parameter ◽  
Wide Range ◽  
Fast Acting ◽  
Good Agreement

A generalized physical model describing dynamic behavior of a fast-acting, dome-loaded, gas pressure regulator was developed. The regulator is designed to respond quickly to command changes, and to operate over a wide range of flow rates and pressures. The analytical lumped-parameter model developed consists of a set of nonlinear, first-order, ordinary differential equations with respect to time, accounting for mass and energy conservation at regulator outlet, command dome and internal feedback compartments. It also accounts for the equation-of-motion for the poppet and the control piston-assembly. The numerical solution, based on a Runge–Kutta method, is amenable to an extensive parametric study of regulator performance, and serves as a useful analytical tool for designing new pressure regulators. Several tests were performed on a fast-acting regulator to verify the physical model. Good agreement between predictions and measurements was obtained. The effect of several parameters, geometrical and operational, on regulator performance was studied. [S0022-0434(00)00402-0]

Dynamic Stability of a Water Brake Dynamometer

1998 ◽  
Vol 120 (1) ◽  
pp. 89-96 ◽  
Author(s):  
R. A. Van den Braembussche ◽  
H. Malys
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Lumped Parameter Model ◽  
Stable Operation ◽  
Pressure Oscillations ◽  
Lumped Parameter ◽  
Flow Oscillations ◽  
Brake Dynamometer ◽  
Low Torque ◽  
Frequency Variations

A lumped parameter model to predict the high frequency pressure oscillations observed in a water brake dynamometer is presented. It explains how the measured low frequency variations of the torque are a consequence of the variation in amplitude of the high frequency flow oscillations. Based on this model, geometrical modifications were defined, aiming to suppress the oscillations while maintaining mechanical integrity of the device. An experimental verification demonstrated the validity of the model and showed a very stable operation of the modified dynamometer even at very low torque.

Lumped Parameter Modeling and Snap-Through Stability Analysis of Planar Hydraulically Amplified Dielectric Elastomer Actuators

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
Amir Hosein Zamanian ◽  
David Y. Son ◽  
Paul S. Krueger ◽  
Edmond Richer
Keyword(s):  
Finite Element ◽  
Analytical Model ◽  
Central Area ◽  
Dielectric Elastomer ◽  
Lumped Parameter Model ◽  
Critical Voltage ◽  
Average Error ◽  
Dielectric Fluid ◽  
Functional Region ◽  
Lumped Parameter

Abstract In this paper, we established an analytical model that avoids extensive numerical computation for the analysis of a hydraulically amplified dielectric elastomer actuator. This actuator comprises a thin elastomer shell filled with an incompressible dielectric fluid coupled with a pair of electrodes placed in the central area. Application of high voltage on the electrodes inflates the actuator due to the induced Maxwell stress that pressurizes the incompressible dielectric fluid. The lumped parameter model predicts the stable functional region and the snap-through instability in the actuator. The model was compared with multi-physics finite element models that considered both linear elastic and nonlinear Mooney–Rivlin materials. The proposed model showed good agreement in the estimation of the actuation strain and the hydrostatic pressure as a function of voltage when compared to the finite element results. The average error in the axial and radial actuation using the proposed analytical model and nonlinear finite element method models was 1.62% and 3.42%, respectively. This shows the model strength in the estimation of the actuator states and the critical voltage to avoid snap-through instability, required in applications such as control algorithms.

scholarly journals Optimization of Lumped Parameter Models to Mitigate Numerical Oscillations in the Transient Responses of Short Transmission Lines

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6534
Author(s):  
Jaimis S. L. Colqui ◽  
Anderson R. J. de Araújo ◽  
Sérgio Kurokawa ◽  
José Pissolato Filho
Keyword(s):  
Power Systems ◽  
Transmission Lines ◽  
Lumped Parameter Model ◽  
Transient Responses ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Spurious Oscillations ◽  
The Time Domain ◽  
Time Transformations ◽  
Good Agreement

The Lumped Parameter Model (LPM) is a known approach to represent overhead transmission lines (TLs), especially when these elements comprehend a few tens of kilometers. LPMs employ a large number of cascaded π-circuits to compute accurately the transient responses. These responses contain numerical spurious oscillations (NSO) characterized by erroneous peaks which distort the transient responses, mainly their peak values. Two modified LPM topologies composed of damping resistances inserted along the longitudinal or transversal branches of the cascaded π-circuits offer significant mitigations in the NSO. In this paper, in an effort to have the maximum mitigation of the NSO and low distortion in the transient responses, two modified topologies with optimized damping resistances are proposed to represent short TLs. Results demonstrate expressive attenuation in the peaks of NSO which reflect good agreement in comparison with the responses computed by the Bergeron’s line model. The mitigation of the NSO is carried out directly in the time domain and it does not require either analog or digital filters.Furthermore, no frequency-to-time transformations are necessary in this procedure. These alternative topologies can be incorporated into any electromagnetic transient program to study switching operations in power systems.

APPROXIMATING THE EFFECT OF VAN DER WAALS FORCE ON THE INSTABILITY OF ELECTROSTATIC NANO-CANTILEVERS

2011 ◽  
Vol 25 (29) ◽  
pp. 3965-3976 ◽  
Author(s):  
ALI KOOCHI ◽  
AMINREZA NOGHREHABADI ◽  
MOHAMADREZA ABADYAN
Keyword(s):  
Van Der Waals ◽  
Convergent Series ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Analytical Results ◽  
Lumped Parameter ◽  
Fringing Field ◽  
Beam Type ◽  
Nano Electromechanical System ◽  
Good Agreement

Beam-type nano-electromechanical system (NEMS) is one of the most components in constructing nano-devices. Herein, a distributed parameter model is used to study the influence of van der Waals (vdW) attraction on the pull-in performance of the cantilever NEMS. Homotopy perturbation method (HPM) is applied to solve the nonlinear governing equation of the actuators in the form of convergent series. Moreover, analytical results are compared with those of numerical method as well as a lumped parameter model. The pull-in voltage and critical cantilever tip deflection of NEMS are determined. Results depict that vdW attraction decreases the pull-in deflection and voltage of the NEMS. On the other hand, the fringing field increases the pull-in deflection while decreases the pull-in voltage of the system. The analytical results have good agreement with numerical results and those available in the literature.

Tuning the Static and Modal Response of Microcantilevers Through Lumped-Parameter Model-Based Design

Aerospace ◽  
2003 ◽  
Author(s):  
Ephrahim Garcia ◽  
Nicolae Lobontiu ◽  
Yoonsu Nam
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Rectangular Cross Section ◽  
Lumped Parameter Model ◽  
Mass Detection ◽  
Force Microscopy ◽  
Lumped Parameter ◽  
Element Simulation ◽  
Three Degree Of Freedom ◽  
Circular Notch

The paper introduces the circular-notch microcantilever design that can be utilized in mass detection and atomic force microscopy (AFM) microsystems. The microcantilever is modeled as a three degree-of-freedom member which is sensitive to bending and torsion. A lumped-parameter model is formulated that gives directly the stiffness closed-form equations and the inertia fractions about the degrees of freedom. It is thus possible to qualify and tune the static and modal responses of this specific microcantilever design in order to match or, on the contrary, to avoid, stiffness and frequency ranges that are of interest by means of only geometry alterations. The microcantilever’s sensitivity to bending and torsion can also be modified by simple manipulation of the defining geometric parameters. The analytical model predictions are confirmed through limit calculations and finite element simulation. The stiffness factors of the circular-notch microcantilever design are compared to the ones of a similar constant rectangular cross-section configuration by means of the analytical model developed herein.

MODELING THE INFLUENCE OF SURFACE EFFECT ON INSTABILITY OF NANO-CANTILEVER IN PRESENCE OF VAN DER WAALS FORCE

2013 ◽  
Vol 13 (04) ◽  
pp. 1250072 ◽  
Author(s):  
ALI KOOCHI ◽  
HOSSEIN HOSSEINI-TOUDESHKY ◽  
HAMID REZA OVESY ◽  
MOHAMADREZA ABADYAN
Keyword(s):  
Surface Energy ◽  
Numerical Solution ◽  
Surface Effect ◽  
Van Der Waals ◽  
Van Der Waals Force ◽  
Lumped Parameter Model ◽  
Lumped Parameter ◽  
Adomian Decomposition ◽  
Vdw Force ◽  
Good Agreement

Surface effect often plays a significant role in the pull-in performance of nano-electromechanical systems (NEMS) but limited works have been conducted for taking this effect into account. Herein, the influence of surface effect has been investigated on instability behavior of cantilever nano-actuator in the presence of van der Waals force (vdW). Three different methods, i.e. an analytical modified Adomian decomposition (MAD), Lumped parameter model (LPM) and numerical solution have been applied to solve the governing equation of the system. The results demonstrate that surface effect reduces the pull-in voltage of the system. Moreover, surface energy causes the cantilever nano-actuator with the assigned parameter to deflect as a softer structure. It is found that while surface effect becomes important for low values of the cantilever nano-actuator thickness, vdW attraction is significant for low initial gap values. Surprisingly, the increase in the initial gap, enhances the contribution of surface effect in pull-in instability of the system while reduces the contribution of vdW attraction. Furthermore, the minimum initial gap and the detachment length of the cantilever nano-actuator that does not stick to the substrate due to vdW force and surface effect has been approximated. A good agreement has been observed between the values of instability parameters predicted via these three methods. Whilst compared to the instability voltage predicted by numerical solution, the pull-in voltage obtained by MAD series and LPM method is overestimated and underestimated, respectively.

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