scholarly journals Capillary-gravity waves on the interface of two dielectric fluid layers under normal electric fields

2020 ◽  
Vol 73 (3) ◽  
pp. 231-250
Author(s):  
A Doak ◽  
T Gao ◽  
J -M Vanden-Broeck ◽  
J J S Kandola
Keyword(s):  
Electric Fields ◽  
Solitary Waves ◽  
Gravity Waves ◽  
Integral Equation Method ◽  
Travelling Wave ◽  
Boundary Integral ◽  
Dielectric Fluid ◽  
Weakly Nonlinear ◽  
Dielectric Fluids ◽  
Fluid Layers

Summary In this article, we consider capillary-gravity waves propagating on the interface of two dielectric fluids under the influence of normal electric fields. The density of the upper fluid is assumed to be much smaller than the lower one. Linear and weakly nonlinear theories are studied. The connection to the results in other limit configurations is discussed. Fully nonlinear computations for travelling wave solutions are achieved via a boundary integral equation method. Periodic waves, solitary waves and generalised solitary waves are presented. The bifurcation of generalised solitary waves is discussed in detail.

New solutions for periodic interfacial gravity waves

2021 ◽  
Vol 928 ◽  
Author(s):  
X. Guan ◽  
J.-M. Vanden-Broeck ◽  
Z. Wang
Keyword(s):  
Integral Equation ◽  
Excellent Agreement ◽  
Gravity Waves ◽  
Global Bifurcation ◽  
Integral Equation Method ◽  
Finite Depth ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Fourier Expansions ◽  
Wave Profiles

Two-dimensional periodic interfacial gravity waves travelling between two homogeneous fluids of finite depth are considered. A boundary-integral-equation method coupled with Fourier expansions of the unknown functions is used to obtain highly accurate solutions. Our numerical results show excellent agreement with those already obtained by Maklakov & Sharipov using a different scheme (J. Fluid Mech., vol. 856, 2018, pp. 673–708). We explore the global bifurcation mechanism of periodic interfacial waves and find three types of limiting wave profiles. The new families of solutions appear either as isolated branches or as secondary branches bifurcating from the primary branch of solutions.

scholarly journals LIMIT WAVES ON HORIZONTAL SEA FLOOR

1986 ◽  
Vol 1 (20) ◽  
pp. 41
Author(s):  
Chia-Chi Lu ◽  
John D. Wang ◽  
Bernard Le Mehaute
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Boundary Integral Equation ◽  
Gravity Waves ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Wave Crest ◽  
Solution Technique ◽  
Sea Floor ◽  
Surface Gravity Waves

A numerical solution to periodic nonlinear irrotational surface gravity waves on a horizontal sea floor is developed using an iterative Boundary Integral Equation Method (BIEM). This solution technique is subsequently applied to determine the characteristics of limit waves for which the wave crest theoretically ceases to be rounded and become angled with an included angle of 120 degrees.

On the free-surface flow of very steep forced solitary waves

2013 ◽  
Vol 739 ◽  
pp. 1-21 ◽  
Author(s):  
Stephen L. Wade ◽  
Benjamin J. Binder ◽  
Trent W. Mattner ◽  
James P. Denier
Keyword(s):  
Free Surface ◽  
Solitary Waves ◽  
Flow Problem ◽  
Nonlinear Approximation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Boundary Integral ◽  
Weakly Nonlinear ◽  
Nonlinear Solutions

AbstractThe free-surface flow of very steep forced and unforced solitary waves is considered. The forcing is due to a distribution of pressure on the free surface. Four types of forced solution are identified which all approach the Stokes-limiting configuration of an included angle of $12{0}^{\circ } $ and a stagnation point at the wave crests. For each type of forced solution the almost-highest wave does not contain the most energy, nor is it the fastest, similar to what has been observed previously in the unforced case. Nonlinear solutions are obtained by deriving and solving numerically a boundary integral equation. A weakly nonlinear approximation to the flow problem helps with the identification and classification of the forced types of solution, and their stability.

Performance and Durability Validation of Voltage Blocking Technologies to Enable Direct Cooled High-Voltage, High-Power Modules

2021 ◽  
Author(s):  
Ange-Christian Iradukunda ◽  
David Huitink ◽  
Tarek Gebrael ◽  
Nenad Miljkovic
Keyword(s):  
Electric Fields ◽  
High Voltage ◽  
High Power ◽  
Electrical Characterization ◽  
Dielectric Surface ◽  
Surface Coatings ◽  
Dielectric Fluid ◽  
Power Module ◽  
Dielectric Fluids ◽  
And Performance

Abstract Power densification and rising module heat losses cannot be managed by traditional “external-to-case” cooling solutions. This is especially pronounced in high voltage systems, where intervening layers of insulating material between the power devices and cooling solution need to be sufficiently thick to provide adequate voltage isolation. As operating voltages increase, the required thicknesses for these insulating layers become so large that they limit the ability to extract the heat. A direct cooling approach that addresses voltage separation issues represents a unique opportunity to deliver coolant to the hottest regions, while opening up the opportunity for increased scaling of power electronics modules. However technical concerns about long-term performance of coolants and their voltage isolation characteristics coupled with integration challenges impede adoption. Here, the reliability and performance of voltage blocking strategies, namely dielectric fluids and dielectric surface coatings, are examined to advance the feasibility of a direct cooling approach for improved thermal management of high-voltage, high-power module. The breakdown voltage of the dielectric fluid is characterized through relevant temperatures, flow, and electric fields with the ultimate goal of developing design rules for direct integrated cooling schemes. The development and electrical characterization of conformal dielectric surface coatings to provide further protection of the electronics is also undertaken. Results showed the ability for layers of Parylene C to maintain their insulating capacity when subject to E-fields as high as 33.5V/μm.

scholarly journals A Boussinesq-Type Model for Nonlinear Wave-Heaving Cylinder Interaction

Energies ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 469
Author(s):  
Theofanis Karambas ◽  
Eva Loukogeorgaki
Keyword(s):  
Numerical Model ◽  
Nonlinear Wave ◽  
Wave Model ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Floating Body ◽  
Type Model ◽  
Weakly Nonlinear ◽  
Exciting Forces ◽  
Heave Motion

In the present work, a Boussinesq-type numerical model is developed for the simulation of nonlinear wave-heaving cylinder interaction. The wave model is able to describe the propagation of fully dispersive and weakly nonlinear waves over any finite water depth. The wave-cylinder interaction is taken into account by solving simultaneously an elliptic equation that determines the pressure exerted by the fluid on the floating body. The heave motion for the partially immersed floating cylinder under the action of waves is obtained by solving numerically the body’s equation of motion in the z direction based on Newton’s law. The developed model is applied for the case of a fixed and a free-floating circular cylinder under the action of regular waves, as well as for a free-floating cylinder undergoing a forced motion in heave. Results (heave and surge exciting forces, heave motions, and wave elevation) are compared with those obtained using a frequency domain numerical model, which is based on the boundary integral equation method.

scholarly journals Head-on collision of two solitary waves and residual falling jet formation

2009 ◽  
Vol 16 (1) ◽  
pp. 111-122 ◽  
Author(s):  
J. Chambarel ◽  
C. Kharif ◽  
J. Touboul
Keyword(s):  
Residence Time ◽  
Solitary Waves ◽  
Vertical Wall ◽  
Integral Equation Method ◽  
Threshold Value ◽  
Finite Depth ◽  
Boundary Integral ◽  
Jet Formation ◽  
Fully Nonlinear Equations ◽  
Time Calculation

Abstract. The head-on collision of two equal and two unequal steep solitary waves is investigated numerically. The former case is equivalent to the reflection of one solitary wave by a vertical wall when viscosity is neglected. We have performed a series of numerical simulations based on a Boundary Integral Equation Method (BIEM) on finite depth to investigate during the collision the maximum runup, phase shift, wall residence time and acceleration field for arbitrary values of the non-linearity parameter a/h, where a is the amplitude of initial solitary waves and h the constant water depth. The initial solitary waves are calculated numerically from the fully nonlinear equations. The present work extends previous results on the runup and wall residence time calculation to the collision of very steep counter propagating solitary waves. Furthermore, a new phenomenon corresponding to the occurrence of a residual jet is found for wave amplitudes larger than a threshold value.

Nonlinear three-dimensional interfacial flows with a free surface

2007 ◽  
Vol 591 ◽  
pp. 481-494 ◽  
Author(s):  
E. I. PĂRĂU ◽  
J.-M. VANDEN-BROECK ◽  
M. J. COOKER
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Solitary Waves ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Interfacial Flows ◽  
Fully Nonlinear Equations ◽  
Weakly Nonlinear ◽  
Integral Equation Methods ◽  
Superposed Fluids

A configuration consisting of two superposed fluids bounded above by a free surface is considered. Steady three-dimensional potential solutions generated by a moving pressure distribution are computed. The pressure can be applied either on the interface or on the free surface. Solutions of the fully nonlinear equations are calculated by boundary-integral equation methods. The results generalize previous linear and weakly nonlinear results. Fully localized gravity–capillary interfacial solitary waves are also computed, when the free surface is replaced by a rigid lid.

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