Simplification of Hydraulic Line Dynamics by Use of Infinite Products

Fig. 1 Shower zones on the ecliptic plane associated with known short-period comets. The dots are in approximate scale to the suggested shower zone size. For illustrative purposes, representations of Earth and Mars orbits are also shown.while at the descending node V = (TT -co). Calculated times of the next comet-ecliptic plane intersections are also presented in Table 1 together with the comet period. From these data it is rather straightforward to apply definition (3) of the proposed meteoroid stream model and generate danger time intervals during which short-period comet shower zones are active. Hazard EvaluationBecause the flux in the shower zone is only vaguely known, it is recommended that, for any mission analysis, the mission trajectory first be checked to see if it will intersect any known active shower zone. If it will, then change of the trajectory should be considered. The probability that it will may be approximated by the ratio of the average total area of the active shower zones compared to the total ecliptic plane area under consideration. This probability is, for example, only 1.07% for the 55 shower zones on the ecliptic plane inside the orbit of Mars.An alternative solution is to adopt a maximum flux for the shower zone, compute the passage time through the zone, and then determine the spacecraft hazard using conventional analysis methods. In this way, stream danger zone effects on the spacecraft can be considered along with the effects of sporadic cometary and asteroidal meteoroid environments. This approach may, however, result in increasing the spacecraft's flux exposure (flux-area-time-product) to levels making design difficult. For example, if the relative maximum flux encountered in a condensation is 10 3 times the sporadic nearEarth flux, then a spacecraft would receive in 525 min the same flux exposure it would receive in one year of operation in the meteoroid environment near Earth.

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“…The terminating volume is 0.6 in. 3 . Three gases are considered: 1) a mixture of 50% N 2 and 50%_He, 2) 100% He, and 3) 100% N 2 .…”

Section: Test Data Verificationmentioning

confidence: 95%

“…The total terminating volume is 4.1 in. 3 . These tests were run using a purging He flow rate sufficient to create a steady-state pressure loss of 5.8 psi.…”

Section: Test Data Verificationmentioning

confidence: 95%

Pneumatic sensing-line nonlinear model.

Harris

Rose

1969

Journal of Spacecraft and Rockets

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“…According to Oldenburger and Goodson, 27 the approximate model of the hyperbolic function was derived as follows …”

Section: Comparison With Approximate Computation Of Distributed Parammentioning

confidence: 99%

Pulsating characteristic of the hydraulic hybrid vehicle system with pipeline effect

Chen

Liu

Jiang

et al. 2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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The configuration and working principle of hydraulic hybrid vehicle (HHV) based on the hydraulic transformer (HT) were described to extend its energy-regenerated potential. The approximate algorithm of basic elements for pipeline distributed parameter model was summarized to simplify the pipeline model calculation, and the various basic elements of this method were proven to be used in the practical application by comparison with the experimentally validated Zhao and Hullender model. The pressure pulsation characteristics between the HT and accumulator of the HHV by considering Zhao model, Hullender model, and original pipeline approximate model was analyzed to optimize the system structure design by the method of the mathematical model, which mainly includes the series accumulator and parallel accumulator, respectively. The simulation result shows that the series accumulator was better than the parallel accumulator in terms of pulsation damping of hydraulic transformer with considering the pipeline effect. The test-rig result shows that the theoretical analysis of the pulsation between the HT and accumulator with pipeline was very close to the measurement data of the experiment in the curve trend, where the theoretical analysis results of pulsation characteristic for HHV were appropriate and reasonable.

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“…Oldenburger and Goodson [34] in their analysis of the dynamics of hydraulic lines replaced the transcendental functions representing the transfer functions by the infinite products of linear factors and their approximations.…”

Section: Abbott Gibson and Mccaig [1] And Mccaig And Gibsonmentioning

confidence: 99%

Resonance in Pressurized Piping Systems

Chaudhry¹

1970

J. Hydr. Div.

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A new approach, based on the transfer matrix method used in the theory of vibrations, is presented to analyze the steady-oscillatory flows, and to determine the resonating characteristics of piping systems. By linearizing the friction loss term, considering the system as distributed and assuming the discharge and pressure head fluctuations as sinusoidal, field matrices for a simple pipeline and for a parallel system are derived.A numerical technique is presented to determine the field matrix for a pipe having variable characteristics along its length. Point matrices for orifices, and for oscillating valves are obtained by linearizing the gate equation. Point matrices for the junction of the main and a branch having various boundary conditions, e.g., dead end, reservoir, orifice, oscillating valve, are also derived.A numerical procedure is outlined for computing the resonant frequencies of piping systems. Expressions are developed to determine the frequency response of systems having periodic forcing functions, such as fluctuating pressure head; fluctuating discharge; and oscillating valve.A number of systems commonly used in waterpower development and water supply schemes are analyzed. The results obtained by the method presented herein are in close agreement with those obtained experimentally by earlier investigators; or determined by using the method of characteristics, impedance theory, or energy concepts.

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Simplification of Hydraulic Line Dynamics by Use of Infinite Products

Cited by 45 publications

References 0 publications

Pneumatic sensing-line nonlinear model.

Pneumatic sensing-line nonlinear model.

Pulsating characteristic of the hydraulic hybrid vehicle system with pipeline effect

Resonance in Pressurized Piping Systems

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