Lumped Parameter Description of Thermoviscous Acoustics in Tubes with Equilateral Triangular Cross-Sections

2019 ◽  
Vol 105 (6) ◽  
pp. 1283-1285
Author(s):  
René Christensen
Keyword(s):  
Boundary Layer ◽  
Transmission Line ◽  
Cross Section ◽  
Cross Sections ◽  
Circular Cross Section ◽  
Lumped Parameter Model ◽  
Entire Cross Section ◽  
Lumped Parameter ◽  
Viscous Loss ◽  
Lumped Parameters

An accurate acoustic model of a tube in the millimeter or sub-millimeter size should include the losses that occur due to viscosity and thermal conduction, collectively termed thermoviscous losses. These losses are prominent in a boundary layer near the tube walls. Under the assumption that the boundary layer is thick compared to a characteristic geometry length, such as the radius for a circular cross-section, and fills out the entire cross-section, the tube can be described via a lumped parameter model. The lumped parameters have been known for several decades for a tube with circular cross-section, but the equilateral triangular tube has only been investigated in terms of transmission line parameters. The lumped parameters have here been established for the equilateral triangular tube as a truncated series solution of the transmission line parameters. One result observed is that the lumped parameter model for a triangular tube has 38% more viscous loss than a circular tube for a given area.

Fractional Lumped Parameter Modeling of Transformer Windings under VFTO

2014 ◽  
Vol 494-495 ◽  
pp. 1529-1533
Author(s):  
Gui Shu Liang ◽  
Guang Bo Zhang ◽  
Xin Liu
Keyword(s):  
Transmission Line ◽  
Lumped Parameter Model ◽  
Voltage Distribution ◽  
High Frequencies ◽  
Simulation Process ◽  
Lumped Parameter ◽  
Lumped Parameter Modeling ◽  
Lumped Parameters ◽  
Simulation Results ◽  
Transient Overvoltage

Very fast transient overvoltage (VFTO) is very dangerous for the transformer which is directly connected to gas insulated substations (GIS). At the same time, due to the continuous increasing of operating frequency in the power system, under the high frequencies of the transmission line calculation and simulation process, it is necessary to consider the frequency-dependent properties of the parameter. In order to study the voltage distribution in transformer windings under VFTO, a new Lumped parameter model which takes into account the fractional characteristics is proposed, named fractional lumped parameter model (FLP). The model divides each turn of transformer windings into proper sections, whose parameters are all lumped parameters. Finally it shows the correctness and validity of the model through the comparation of the experiment datas and simulation results.

scholarly journals Asymptotic Behavior of Stable Structures Made of Beams

2021 ◽  
Author(s):  
Georges Griso ◽  
Larysa Khilkova ◽  
Julia Orlik ◽  
Olena Sivak
Keyword(s):  
Asymptotic Behavior ◽  
Cross Section ◽  
Cross Sections ◽  
Linear Elasticity ◽  
Circular Cross Section ◽  
Linear Elasticity Theory ◽  
Linear Elastic ◽  
The Cross ◽  
Small Rotation ◽  
Stable Structures

AbstractIn this paper, we study the asymptotic behavior of an $\varepsilon $ ε -periodic 3D stable structure made of beams of circular cross-section of radius $r$ r when the periodicity parameter $\varepsilon $ ε and the ratio ${r/\varepsilon }$ r / ε simultaneously tend to 0. The analysis is performed within the frame of linear elasticity theory and it is based on the known decomposition of the beam displacements into a beam centerline displacement, a small rotation of the cross-sections and a warping (the deformation of the cross-sections). This decomposition allows to obtain Korn type inequalities. We introduce two unfolding operators, one for the homogenization of the set of beam centerlines and another for the dimension reduction of the beams. The limit homogenized problem is still a linear elastic, second order PDE.

scholarly journals Effect of liquid cooling on PCR performance with the parametric study of cross-section shapes of microchannels

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yousef Alihosseini ◽  
Mohammad Reza Azaddel ◽  
Sahel Moslemi ◽  
Mehdi Mohammadi ◽  
Ali Pormohammad ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Heat Sink ◽  
Evaluation Criteria ◽  
Circular Cross Section ◽  
Microchannel Heat Sink ◽  
Liquid Cooling ◽  
Maximum Heat ◽  
Maximum Heat Transfer

AbstractIn recent years, PCR-based methods as a rapid and high accurate technique in the industry and medical fields have been expanded rapidly. Where we are faced with the COVID-19 pandemic, the necessity of a rapid diagnosis has felt more than ever. In the current interdisciplinary study, we have proposed, developed, and characterized a state-of-the-art liquid cooling design to accelerate the PCR procedure. A numerical simulation approach is utilized to evaluate 15 different cross-sections of the microchannel heat sink and select the best shape to achieve this goal. Also, crucial heat sink parameters are characterized, e.g., heat transfer coefficient, pressure drop, performance evaluation criteria, and fluid flow. The achieved result showed that the circular cross-section is the most efficient shape for the microchannel heat sink, which has a maximum heat transfer enhancement of 25% compared to the square shape at the Reynolds number of 1150. In the next phase of the study, the circular cross-section microchannel is located below the PCR device to evaluate the cooling rate of the PCR. Also, the results demonstrate that it takes 16.5 s to cool saliva samples in the PCR well, which saves up to 157.5 s for the whole amplification procedure compared to the conventional air fans. Another advantage of using the microchannel heat sink is that it takes up a little space compared to other common cooling methods.

Numerical Investigation of Cross-Section on Aluminum A6063 Thin-Walled Structures under Low-Velocity Impact Loading

2014 ◽  
Vol 1019 ◽  
pp. 96-102
Author(s):  
Ali Taherkhani ◽  
Ali Alavi Nia
Keyword(s):  
Energy Absorption ◽  
Cross Section ◽  
Cross Sections ◽  
Peak Load ◽  
Circular Cross Section ◽  
Absorption Capacity ◽  
Energy Absorption Capacity ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Crush Strength

In this study, the energy absorption capacity and crush strength of cylindrical thin-walled structures is investigated using nonlinear Finite Elements code LS-DYNA. For the thin-walled structure, Aluminum A6063 is used and its behaviour is modeled using power-law equation. In order to better investigate the performance of tubes, the simulation was also carried out on structures with other types of cross-sections such as triangle, square, rectangle, and hexagonal, and their results, namely, energy absorption, crush strength, peak load, and the displacement at the end of tubes was compared to each other. It was seen that the circular cross-section has the highest energy absorption capacity and crush strength, while they are the lowest for the triangular cross-section. It was concluded that increasing the number of sides increases the energy absorption capacity and the crush strength. On the other hand, by comparing the results between the square and rectangular cross-sections, it can be found out that eliminating the symmetry of the cross-section decreases the energy absorption capacity and the crush strength. The crush behaviour of the structure was also studied by changing the mass and the velocity of the striker, simultaneously while its total kinetic energy is kept constant. It was seen that the energy absorption of the structure is more sensitive to the striker velocity than its mass.

scholarly journals Particle separation of a modified feed nozzle hydrocyclone under different operating parameters

2021 ◽  
Vol 11 (5) ◽  
pp. 159-170
Author(s):  
Zsolt Hegyes ◽  
Máté Petrik ◽  
L. Gábor Szepesi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Circular Cross Section ◽  
Particle Separation ◽  
Baffle Plate ◽  
Important Data ◽  
Preliminary Research ◽  
All Speeds ◽  
Plate Solution

During the operation of the hydrocyclone the cut size diameter is the most important data. This is connected to feed rate, which is closely related to the feed cross section. Preliminary research has revealed that square cross-section is more effective than circular cross-section. The research compared 2 types of feed cross sections at 5 different feed rates. One is a standard rectangular cross-section and the other is a square cross-section that narrows with a baffle plate. Preliminary calculations for cut size diameter have shown that better particle separation at all speeds can be achieved with the baffle plate solution. In both types, the increased velocity created decreased cut size diameter. During the simulation, the baffle plate did not cause any abnormalities in the internal pressure and velocity distributions. The simulation revealed that the particles did not behave as previously calculated.

Non-Boussinesq gravity currents and surface waves generated by lock release in a circular-section channel: theoretical and experimental investigation

2019 ◽  
Vol 869 ◽  
pp. 610-633 ◽  
Author(s):  
L. Chiapponi ◽  
M. Ungarish ◽  
D. Petrolo ◽  
V. Di Federico ◽  
S. Longo
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Cross Section ◽  
Cross Sections ◽  
Density Ratio ◽  
Circular Cross Section ◽  
Gravity Currents ◽  
Numerical Code ◽  
Long Distance ◽  
Front Speed

We present a combined theoretical and experimental study of lock-release inertial gravity currents (GCs) propagating in a horizontal channel of circular cross-section with open-top surface in the non-Boussinesq regime. A two-layer shallow-water (SW) model is developed for a generic shape of the cross-section with open top, and then implemented in a finite difference numerical code for the solution in a circular-cross-section channel of the type used in the experiments. The model predicts propagation with (almost) constant speed for a fairly long distance, accompanied by a depression of the ambient free open-top surface behind the front of the current. Sixteen experiments were conducted with a density ratio $r=0.587{-}0.939$ in full-depth and part-depth release conditions, measuring the front speed and the free-surface time series at four cross-sections. The channel was a circular tube 409 cm long, with a radius of 9.5 cm; the lengths of the locks were 52 and 103.5 cm. Density contrast was obtained by adding sodium chloride and dipotassium phosphate to fresh water. The theoretical values of the front speed and of the depression overestimate the experimental values, but they predict correctly their trend for varying parameters and provide reliable insights into the underlying mechanisms. In particular, we demonstrate that the circular cross-section increases the speed of propagation as compared to the standard rectangular cross-section case (for the same initial height and density ratio). The discrepancies between the SW predictions and the present experiments are of the same order of magnitude as those of previously published results for simpler systems (Boussinesq, rectangular). In addition to the depression, which is a wave bound to, and following the front of, the GC, the system also displays two kinds of free-surface waves, namely the initial bump (its amplitude is of the same order as the depression) and some short-length and low-amplitude waves in the tail of the bump. These free waves propagate with a celerity well predicted by the ‘fast’ eigenvalues of the mathematical model. Comparison is provided with the celerity of a solitary wave. It is expected that discrepancies between theory and experiments can be partly attributed to the presence of these waves. The reported insights and SW prediction method can be applied to a variety of cross-sections of practical interest (triangles, trapezoids, etc.).

Numerical Study of Incomplete Stent Apposition Caused by Deploying Undersized Stent in Arteries With Elliptical Cross Sections

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Bo Jiang ◽  
Vikas Thondapu ◽  
Eric K. W. Poon ◽  
Peter Barlis ◽  
Andrew S. H. Ooi
Keyword(s):  
Shear Rate ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Study ◽  
Circular Cross Section ◽  
Blood Stream ◽  
Cfd Simulations ◽  
Elliptical Cross ◽  
Incomplete Stent Apposition ◽  
Computational Fluid Dynamics Cfd

Incomplete stent apposition (ISA) is one of the causes leading to poststent complications, which can be found when an undersized or an underexpanded stent is deployed at lesions. The previous research efforts have focused on ISA in idealized coronary arterial geometry with circular cross section. However, arterial cross section eccentricity plays an important role in both location and severity of ISA. Computational fluid dynamics (CFD) simulations are carried out to systematically study the effects of ISA in arteries with elliptical cross section, as such stents are partially embedded on the minor axis sides of the ellipse and malapposed elsewhere. Overall, ISA leads to high time-averaged wall shear stress (TAWSS) at the proximal end of the stent and low TAWSS at the ISA transition region and the distal end. Shear rate depends on both malapposition distance and blood stream locations, which is found to be significantly higher at the inner stent surface than the outer surface. The proximal high shear rate signifies increasing possibility in platelet activation, when coupled with low TAWSS at the transition and distal regions which may indicate a nidus for in-stent thrombosis.

scholarly journals Computational Study of Zigzag Spacer Design with Elliptical Cross-Section Filaments

2020 ◽  
Vol 307 ◽  
pp. 01047
Author(s):  
Gohar Shoukat ◽  
Farhan Ellahi ◽  
Muhammad Sajid ◽  
Emad Uddin
Keyword(s):  
Mass Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Computational Study ◽  
Flow Direction ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Two Dimensional ◽  
Permeate Flux ◽  
Elliptical Cross

The large energy consumption of membrane desalination process has encouraged researchers to explore different spacer designs using Computational Fluid Dynamics (CFD) for maximizing permeate per unit of energy consumed. In previous studies of zigzag spacer designs, the filaments are modeled as circular cross sections in a two-dimensional geometry under the assumption that the flow is oriented normal to the filaments. In this work, we consider the 45° orientation of the flow towards the three-dimensional zigzag spacer unit, which projects the circular cross section of the filament as elliptical in a simplified two-dimensional domain. OpenFOAM was used to simulate the mass transfer enhancement in a reverse-osmosis desalination unit employing spiral wound membranes lined with zigzag spacer filaments. Properties that impact the concentration polarization and hence permeate flux were analyzed in the domain with elliptical filaments as well as a domain with circular filaments to draw suitable comparisons. The range of variation in characteristic parameters across the domain between the two different configurations is determined. It was concluded that ignoring the elliptical projection of circular filaments to the flow direction, can introduce significant margin of error in the estimation of mass transfer coefficient.

Velocity Field and Energy Dissipation in Viscoplastic Flow in Tubes of Non-Circular Cross-Section

2014 ◽  
Author(s):  
Mario F. Letelier ◽  
Dennis A. Siginer ◽  
Felipe Godoy
Keyword(s):  
Energy Dissipation ◽  
Velocity Field ◽  
Yield Stress ◽  
Cross Section ◽  
Mechanical Energy ◽  
Longitudinal Velocity ◽  
Circular Cross Section ◽  
Viscoplastic Flow ◽  
Entire Cross Section ◽  
Cross Sectional

An analytical method for determining the velocity field, shear stress and energy dissipation in viscoplastic flow in non-circular straight tubes is presented. Bingham’s model of fluid is used for the case of tubes with several cross-sectional contours that can be arbitrarily chosen through a shape factor imposed in the solution for the longitudinal velocity. The analysis is extended to steady flow in tubes in which the cross-section contour exhibits sharp corners. In these cases three flow zones are distinguished: stagnant, non-zero deformation, and plug zones. The method provides the expressions for determining the boundaries and characteristics of those three zones for a wide variety of cross-section shapes. In particular the dynamics of plug-zones for large values of the yield stress and for contours that markedly differ from circumferences is analyzed. Energy dissipation is determined throughout the entire cross-section, so that the effect of shape on mechanical energy loss is assessed in terms of the yield stress and viscosity of the fluid. Some general expressions that help understand energy dissipation mechanisms are derived by using natural coordinates for the velocity field and related variables. These results draw on several recent works from other researchers and the present authors, which have highlighted the significant difficulty of determining the zones of zero deformation in viscoplastic flow when the related solid boundaries are not elementary.

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