Transmission Line Modeling of Laminar Liquid Wave Propagation in Tapered Tubes

Wiens, Travis; Buhs, Jeremy W. ven der

doi:10.1115/1.4043235

Cited by 3 publications

(5 citation statements)

References 9 publications

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“…where L is the lumped inductance and C is the lumped capacitance [14,23]. For the tapered-wall tube defined in this paper, the dissipation number is…”

Section: We Can Then Apply Open or Closed Boundary Conditions To Obtain The Transmission Matrix In The Formmentioning

confidence: 99%

“…The frequency-domain solution method presented here is computationally faster than existing gridded methods (such as the method of characteristics [13]), as it only calculates pressure and/or flow at the end-points of the tube. It can also be expected to be more accurate than time-domain solutions, such as the transmission line method (TLM), that require an approximation for the frequency-dependent friction terms [13][14][15]. While frequency-domain analytical solutions exist for tubes with tapered and non-tapered geometries [16][17][18], the authors are not aware of any such solution for the case where the wave speed varies.…”

Section: Introductionmentioning

confidence: 99%

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An Analytical Solution for Unsteady Laminar Flow in Tubes with a Tapered Wall Thickness

Wiens

Etminan

2021

Fluids

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Transient fluid flows through tubes are critical in such topics as water hammer, ram pumps and pipeline dynamics. While analytical solutions exist in the literature for simple geometries such as tapered and non-tapered tube diameters, one area that is lacking is the case where the wave speed changes along the length. An example of this is a flexible pipe with a tapered wall thickness. In order to calculate the transient pressure response of such a system, this previously required a computationally expensive gridded method of characteristics (MOC) solution. This paper describes an analytical solution to the dynamic laminar flow of liquid in a tube where the wave speed varies along its length. This frequency-domain solution includes frequency-dependent friction effects. A comparison to a method of characteristics (MOC) solution is used to verify the solution. The paper also discusses some numerical issues and provides an approximate method that can be used for high-frequency calculations where limited numerical precision can cause errors. Finally, a preliminary comparison of the computational performance is presented, in which the new method is an order of magnitude faster to calculate than an MOC solution.

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“…where L is the lumped inductance and C is the lumped capacitance [14,23]. For the tapered-wall tube defined in this paper, the dissipation number is…”

Section: We Can Then Apply Open or Closed Boundary Conditions To Obtain The Transmission Matrix In The Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Analytical Solution for Unsteady Laminar Flow in Tubes with a Tapered Wall Thickness

Wiens

Etminan

2021

Fluids

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“…pipe step contraction) would generate a forward propagating pressure wave. 39 In contrast, a sudden decrease would lead to backpropagation. In order to describe this issue precisely, the viscosity loss coefficient β is introduced as follows 39…”

Section: Integrated Model Of Gmm-fsvmentioning

confidence: 99%

“…The TLM for the block diagram (as shown in Figure 11) can be determined by setting different boundary conditions. Based on the TLM, E ( s ), F ( s ), and G ( s ) in the block diagram are represented by separated transfer functions as follows 39…”

Section: Integrated Model Of Gmm-fsvmentioning

confidence: 99%

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Characteristic investigation of a magnetostrictive fast switching valve for digital hydraulic converter

Chen

Zhu

Zhang

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part I:

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In order to adapt the frequency requirements of fast switching valve applied to the digital hydraulic converter, a 2/2 way fast switching valve driven by giant magnetostrictive material was performed in this article. The finite element simulation of the fast switching valve’s electromagnetic field and flow field was carried out. In addition, the integrated analytical model of giant magnetostrictive material–fast switching valve coupling with enhanced transmission line method was built in MATLAB/Simulink. The displacement and pressure-flowrate characteristics of giant magnetostrictive material–fast switching valve were discussed and validated in the experiments. The results indicated that the nonlinearity magnetization presents a positive relationship with the driving current before it reaches the saturated state, and the hydraulic force at the expected opening is far less than output force caused by magnetostrictive strain. The experimental valve displacements are in good agreement with obtained results from analytical model, which reveals that the analytical model is accurate enough to predict the main performances of the fast switching valve. The maximum valve displacement without supply pressure is up to 68 µm, which attenuates moderately with the growth of supply pressure. The experimental responses of the displacement and the pressure of giant magnetostrictive material–fast switching valve are less than 1 ms. The amplitude of output flowrate is 8.1 L/min at the frequency of 100 Hz when the pressure drop across giant magnetostrictive material–fast switching valve is 6 MPa theoretically. Similarly, the maximum transient flowrate derived from experiments reaches 8.2 L/min at pressure drop across giant magnetostrictive material–fast switching valve of 5.9 MPa, which is basically consistent with that predicted by analytical model. These reveal that the giant magnetostrictive material–fast switching valve can be utilized in the digital hydraulic converter to improve the system’s efficiency.

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Modeling Arbitrarily Shaped Liquid Pipelines Using a Segmented Transmission Line Model

Wiens

2020

Journal of Dynamic Systems, Measurement, and Control

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This paper presents a new method of simulating the dynamic flow and pressure of laminar liquid flow through pipes of arbitrarily changing cross section. This method uses a segmented model based on the previously presented tapered transmission line model (TLM). This new method is computationally efficient and has comparable accuracy to previous methods such as the method of characteristics (MOC), but allow for more flexibility in solution time-step (such as accommodating variable time-step solvers), which is required if the rest of the system model has stiff equations. For the sample geometry presented, the new model calculates the dynamic response an order of magnitude faster than the previous method of characteristics solution, with minimal loss of accuracy.

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Transmission Line Modeling of Laminar Liquid Wave Propagation in Tapered Tubes

Cited by 3 publications

References 9 publications

An Analytical Solution for Unsteady Laminar Flow in Tubes with a Tapered Wall Thickness

An Analytical Solution for Unsteady Laminar Flow in Tubes with a Tapered Wall Thickness

Characteristic investigation of a magnetostrictive fast switching valve for digital hydraulic converter

Modeling Arbitrarily Shaped Liquid Pipelines Using a Segmented Transmission Line Model

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