Propagation Of Sinusoidal Waves Research Articles

MHD peristaltic two-phase Williamson fluid flow, heat and mass transfer through a ureteral tube with microliths: Electromagnetic therapy simulation

The ureter typically experiences a frequency of one to five peristaltic contractions per minute. However, it is important to note that these contractions can be disrupted by various physical and mechanical irritants. Ionic contents in the urine make it electrically conducting and responsive to electromagnetic body forces. MHD can be deployed in bio magnetic therapy to control or mitigate symptoms associated with peristaltic pumping in the urinary system. This article therefore focuses on the hydromagnetic effects on flow patterns of urine with debris (monoliths). The mechanism of urine flow is largely coordinated by the kidneys. The flow inside the ureter is interrupted by microliths, which are generated by the sedimentation of excretory products. To simulate this, a two-phase formulation is adopted, comprising the electromagnetic urological viscous fluid phase and the particulate phase for solid grains. The peristaltic propulsion of two-phase liquid in the ureter is simulated as a sinusoidal wave propagation of incompressible non-Newtonian fluid. The Williamson viscoelastic model is deployed for the rheology. Heat transfer is also included with Soret thermo-diffusion and viscous heating effects. Long wave and low Reynolds number approximations are employed based on lubrication theory. The mass, momentum, energy and concentration conservation equations with associated boundary conditions are rendered non-dimensional via appropriate scaling transformations. A numerical solution is achieved via BVP4C MATLAB quadrature. Graphical visualizations of the velocity, temperature and concentration (solid grains) are given for the influence of suspension parameter ( ζ ), Hartmann number (M), Prandtl number (Pr), Weissenburg number (We), particle volume fraction (C), Eckert number (Ec), Soret number (Sr), Schmidt number (Sc). The novelty of the present work is therefore the simultaneous consideration of a generalized two-phase model, wall slip, non-Newtonian characteristics, cross diffusion, viscous dissipation, mass diffusion, magnetic body force and curvature effects in peristaltic urological transport, which has not been undertaken previously. The detailed simulations reveal that the flow velocity is reduced due to the presence of solid particles and the channel curvature, in comparison to the flow in an unobstructed channel devoid of solid particles. Enhancing the hydrodynamic slip parameter speeds up the movement of particles and fluid near the channel walls, boosts wall skin friction, raises pressure difference in the pumping area, and amplifies bolus magnitudes.The rise in peristaltic pumping results in a reduction in solid particle concentration, which is significant phenomena.This theoretical approach may aid in treating conditions such as Urinary Tract Infections (UTIs). The computations effectively demonstrate that significant manipulation of urological pumping characteristics can be achieved with an electromagnetic field. Some new features of two-phase ureteral dynamics are highlighted as relevant to magnetic therapy techniques, which may be beneficial to clinicians.

Investigation of pressure wave propagation and attenuation characteristics in managed pressure drilling by fast switching throttle valve

Pressure waves possess many significant applications in the oil and gas drilling engineering field, such as mud pulse telemetry (MPT) and measurement while drilling (MWD). The focus of this research is to study the pressure wave propagation and attenuation characteristics of wellbore liquid-phase flow in managed pressure drilling (MPD) by fast switching throttle valve (FSTV). First, a mathematical model of transient pressure wave propagation along the wellbore in both upstream and downstream directions is proposed in MPD by FSTV based on the one-dimensional transient flow theory. The model considering the frictional shear effect between the pipe walls is solved by utilizing the method of characteristics. Meanwhile, boundary conditions at the drill string inlet and annulus outlet, at the throttle valve, at the junction of drill bit, and at the reducer are adequately taken into account according to the actual situation of fluid flow. Second, a laboratory experiment of excited pressure waves in a vertical wellbore is conducted to measure the variation of the pressure fluctuation with different pump rates by FSTV. Comparing with the measurement result, the calculation result is discovered that the overall change is consistent, where the maximum absolute relative error at the peak of the pressure wave is only 4.5%. Finally, it further analyzes influential factors affecting the propagation and attenuation behaviors of wellbore pressure waves in liquid-phase flow based on the model. The results indicate that pressure waveforms present sinusoidal wave propagation, and pump rates, pressure wave speed, excitation time, fluid type, mud density, fluid viscosity, and borehole size exert varying degrees of influence on downhole pressure fluctuations. The proposed model achieves accurate quantitative interpretation and analysis of downhole pressure wave in MPD by FSTV, which has important significance for the realization of safe and efficient drilling.

Water level response in wells to dynamic shaking in confined unconsolidated sediments: A laboratory study

This paper focuses on laboratory experiments designed to investigate the influence of dynamic shaking on water level fluctuations in boreholes completed in unconsolidated sediments. A large flume filled with natural sandy sediments was subjected to horizontal dynamic loading at different frequencies (0.5–15 Hz) and accelerations (0.1 g, 0.15 g, 0.25 g and 0.5 g), generated by a shaking table. Thus, the change in characteristics of the water and saturated sediments were investigated, i.e. how water levels and hydraulic properties change with time, are of significant interest. A range of different of water level changes following oscillating pore pressure for hydrostatic and hydrodynamic (flowing) conditions were observed: oscillation, step-rise, step-rise with oscillation, and step-drop with oscillation, similar to those observed in the field after earthquakes. We found that water level declines occur when the imposed frequency is less than 2 Hz, while the magnitude of acceleration shows weak correlation with the water level change when it is less than 0.5 g. Sinusoidal wave propagation reduces hydraulic conductivity first sharply, stabilizes, and is then followed by a constant value with a slight increase. Heterogeneous consolidation, mechanical resonance, compaction, dilation, and re-packing of the grain structure may constitute physically plausible mechanisms for water level fluctuations and hydraulic parameter adjustment. Laboratory experiments can therefore provide an insight and a quantitative process-oriented approach to better understand groundwater level response to seismic waves.

Nearshore coastal flow processes using weighted-averaged equations

This work uses the weighted residual method to simulate non-hydrostatic flows in ocean and coastal areas in a vertically-averaged framework. A Vertically-Averaged and Moment equations set is developed. The system is solved through a hybrid finite volume-finite difference numerical scheme to tackle the hyperbolic and elliptic parts of the equations. Data of seven challenging tests are used to evaluate the model ability to reproduce non-linearity, dispersion, wave breaking, bore propagation, sheet flow and wave reflection. The tests comprise propagation of sinusoidal waves over a submerged bar; convergence of the numerical scheme; solitary wave transformation over a dry reef flat, a wet reef flat and an exposed reef crest; collision of two solitary waves; and solitary wave reflection on a vertical wall under non-breaking and breaking conditions. The results highlight the accuracy of the model without prescribing any treatment for wave breaking. The conjunction of long and short waves with wave shoaling, run-up and receding flows is accurately reproduced. The model is considered an alternative tool to Boussinesq-type models to solve non-linear flows in the nearshore region, with the advantage of having an automatic mimic of wave breaking due to the field variables used to produce the weighted residual depth-averaged equations.

Description of the Fields of Vibration in 2D Latticed Structures with Triangular (Hexagonal) Cells

This article deals with the problem of describing the fields of vibration in string lattices with triangular (centered hexagonal) cells. The problems of this kind have not been adequately studied despite the fact that the required models find application in the dynamic analysis of various machines and structures as well as in crystallography and materials science. Equations of motion are provided. Problems of propagation of sinusoidal waves and induced oscillations under a random broadband force action are considered.

Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects

BackgroundIn last few decades, a new class of working materials which comprises from two solid materials dispersed in a continuous phase liquid was established and deeply scrutinized. These materials are called hybrid nanomaterials. This research article aims to investigate entropy optimization in hybrid nanomaterial flow through a rotating peristaltic channel walls. Flow behavior is analyzed between the channels which is caused by propagation of sinusoidal waves. Viscosity of fluid is considered variable instead of constant characteristics. Fluid saturates through porous attributes of channel walls. Nonliear radiative flux and convective condition are considered. Slip conditions are imposed at the boundary of walls. MethodsBuilt-in-Shooting technique is employed to obtain the numerical outcomes for the considered flow problem. ResultsImpacts of sundry variables on the entropy, temperature and velocity are scrutinized through different graphs. Numerical result presents that the axial velocity escalates with the inclusion of hybrid nanomaterial. The temperature of fluid enhances through higher estimations of hybrid nanoparticles. ConclusionsHere the flow behavior is discussed between the channels which are caused by propagation of sinusoidal waves with speed c. Entropy generation rate is minimum for variable viscosity and maximum for hybrid nanoparticles. Hybrid nanoparticles increase the temperature of fluid. Bejan number presents the similar impact for variable viscosity and thermal slip parameters. Temperature field decays through higher values of Brinkman number.

A dynamic homogenization model for long-wavelength wave propagation in corrugated sandwich plates

In the present work, a new dynamic homogenization model is developed to investigate the long-wavelength wave propagation in a corrugated sandwich plate. With the harmonic motion assumption and using a shifting operator, the governing equations of the plate are firstly represented in a state-space form. Then, a dynamic homogenization model is developed via the two-scale homogenization method. Based on this model and considering the propagation of sinusoidal waves, the dispersion relations and corresponding wave modes can be easily obtained. In order to validate the developed homogenization model, the obtained dispersion relations are compared with those predicted by the spectral element method. It is found that the present method gives accurate results in low frequency range. Furthermore, the effects of some geometric and material parameters on the dispersion relations for the corrugated sandwich plate are also discussed. The developed homogenization model is expected to be helpful in the prediction and control of dynamic responses of corrugated or even lattice sandwich structures.

Depth‐integrated nonhydrostatic free‐surface flow modeling using weighted‐averaged equations

SummaryIn this study, a depth‐integrated nonhydrostatic flow model is developed using the method of weighted residuals. Using a unit weighting function, depth‐integrated Reynolds‐averaged Navier‐Stokes equations are obtained. Prescribing polynomial variations for the field variables in the vertical direction, a set of perturbation parameters remains undetermined. The model is closed generating a set of weighted‐averaged equations using a suitable weighting function. The resulting depth‐integrated nonhydrostatic model is solved with a semi‐implicit finite‐volume finite‐difference scheme. The explicit part of the model is a Godunov‐type finite‐volume scheme that uses the Harten‐Lax‐van Leer‐contact wave approximate Riemann solver to determine the nonhydrostatic depth‐averaged velocity field. The implicit part of the model is solved using a Newton‐Raphson algorithm to incorporate the effects of the pressure field in the solution. The model is applied with good results to a set of problems of coastal and river engineering, including steady flow over fixed bedforms, solitary wave propagation, solitary wave run‐up, linear frequency dispersion, propagation of sinusoidal waves over a submerged bar, and dam‐break flood waves.

Depth-Averaged Non-Hydrostatic Hydrodynamic Model Using a New Multithreading Parallel Computing Method

Compared to the hydrostatic hydrodynamic model, the non-hydrostatic hydrodynamic model can accurately simulate flows that feature vertical accelerations. The model’s low computational efficiency severely restricts its wider application. This paper proposes a non-hydrostatic hydrodynamic model based on a multithreading parallel computing method. The horizontal momentum equation is obtained by integrating the Navier–Stokes equations from the bottom to the free surface. The vertical momentum equation is approximated by the Keller-box scheme. A two-step method is used to solve the model equations. A parallel strategy based on block decomposition computation is utilized. The original computational domain is subdivided into two subdomains that are physically connected via a virtual boundary technique. Two sub-threads are created and tasked with the computation of the two subdomains. The producer–consumer model and the thread lock technique are used to achieve synchronous communication between sub-threads. The validity of the model was verified by solitary wave propagation experiments over a flat bottom and slope, followed by two sinusoidal wave propagation experiments over submerged breakwater. The parallel computing method proposed here was found to effectively enhance computational efficiency and save 20%–40% computation time compared to serial computing. The parallel acceleration rate and acceleration efficiency are approximately 1.45% and 72%, respectively. The parallel computing method makes a contribution to the popularization of non-hydrostatic models.

Peristaltic flow of Burgers’ fluid with compliant walls and heat transfer

A theoretical analysis is presented to investigate the peristaltic flow and heat transfer characteristics of Burgers’ fluid. Burgers’ fluid falls under the category of non-Newtonian fluids and is the subclass of rate type fluids which is used to describe the motion of the earth’s mantle. The channel is governed by the propagation of sinusoidal waves that help the walls contract and relax. Moreover, the walls of the channel are of compliant nature. Both the walls are at different temperatures. Mathematical formulation is first developed and then solved by using the long wavelength assumption i.e. the wavelength of the peristaltic wave is large in comparison to the mean half-width of the channel. The results of velocity, temperature and heat transfer coefficient at the upper wall are constructed and analyzed.

Three dimensional peristaltic flow of Williamson fluid in a rectangular duct

In present article, three dimensional peristaltic flow of a Williamson fluid model in rectangular channel has been discussed. The flow is unsteady and caused by propagation of sinusoidal waves due to peristaltic pumping. The equations of motion are derived for constitutive relation of Williamson model and are finally simplified under restrictions of low Reynolds number and long wavelength. The highly nonlinear and nonhomogeneous partial differential equations are solved by using homotopy perturbation method with combination of eigen function expansion method. The expression for pressure rise is found numerically. The final calculations for velocity, pressure gradient, pressure rise and stream functions are narrated graphically.

A Study of Creeping Sinusoidal Flow of Bio-Rheological Fluids through a Two-Dimensional High Permeability Medium Channel

The creeping sinusoidal flow of non-Newtonian couple stress fluids in a two-dimensional porous medium channel with deformable walls, is investigated as a model of peristaltic physiological gastric transport. A mathematical model is developed which is also applicable to hemodynamics of diseased arteries. The assumptions of long wavelength and low Reynolds number approximation are employed for creeping (viscous-dominated) flow. Solutions for axial velocity, volumetric flow rate, pressure gradient and stream function are obtained. The influence of couple stress rheological parameter and permeability parameter on velocity profile, pressure gradient and stream lines patterns are computed with the aid of Mathematica Software. Keywords: Sinusoidal wave propagation, Couple stress fluid, Porous channel, Stream lines, Cerebral diseased hemodynamics, Gastric flow. Read more →

SU‐D‐220‐05: Dynamic Ultrasound Evaluation of Radiation‐Induced Vocal Cord Injury in Head and Neck Cancer Patients

Purpose: Curative radiation for oral cavity, oropharyngeal, hypopharyngeal and nasopharyngeal cancers can injure the vocal cords which can adversely affect speech and quality of life. Vocal cords are difficult to image with conventional MRI, CT or ultrasound. Currently, no imaging technique is available in the clinic to visualize and evaluate such injury. The purpose of this study is to develop a dynamic ultrasound technology to quantify radiation‐induced vocal cord injury. Methods: Eight healthy volunteers and five post‐radiation patients were enrolled under IRB approval. Each participant was scanned using a clinical ultrasound scanner (Sonix Touch) with a 14‐MHz linear array transducer. The ultrasound probe was placed in the transverse plane approximately parallel to the vocal foldˈs mucosal wave propagation. Each participant was asked to phonate the vowel sound “a” and sustain the phonation for 5 seconds while 315 dynamic (consecutive) ultrasound images of the vocal fold were recorded. Vocal cord vibration patterns were obtained through these consecutive images. Vibration frequency and 2‐D dimensions were computed to measure vocal cord performance. Results: The vocal cords were clearly visualized using dynamic ultrasound in all participants. Vocal cord vibration patterns of the healthy volunteers revealed smooth sinusoidal wave propagation. In contrast, the patterns of post‐radiation vocal cords presented irregular wave propagation. M‐mode videos parallel and vertical to vocal cord vibration direction were generated. The vocal cord vibration pattern was most disrupted in the patient with clinically‐identifiedvocal cord injury. Aliased frequency estimated from M‐mode video could be used to distinguish damaged vocal cord injury from normal vocal cord. Conclusions: In the effort to develop a noninvasive imaging technique for evaluating vocal cord injury post radiotherapy, we identified dynamic ultrasound as a promising tool. Ultrasound is safe, simple, and cost‐effective. This study demonstrated its feasibility in imaging the vocal cords and quantifying the vocal cord condition.Part of this research is supported by Susan Komen Grant (KG101373).

Peristaltic transport of a generalized Burgers’ fluid: Application to the movement of chyme in small intestine

The present investigation deals with the peristaltic transport of generalized Burgers’ fluid with fractional element model in a channel. The analysis is carried out under long wavelength and low Reynolds number assumptions. An efficient mathematical tool, namely, Adomian decomposition method, is used to obtain the analytical approximate solutions of the fractional differential equation. The channel is governed by the propagation of sinusoidal waves that help the walls contract and relax but not expand beyond the natural boundary. The expressions of axial velocity, volume flow rate and pressure gradient are obtained. The effects of the fractional parameters and the material constants are discussed on pressure difference and the friction force across one wavelength. The comparative studies for various models of viscoelastic fluids such as fractional generalized Burgers’ model, generalized Burgers’ model, fractional Burgers’ model and Burgers’ model are performed. It is inferred that the movement of viscoelastic chyme with generalized Burgers’ model through the small intestine is favorable in comparison to the movement of viscoelastic chyme with fractional generalized Burgers’ model.

Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel

The paper presents the transportation of viscoelastic fluid with fractional Maxwell model by peristalsis through a channel under long wavelength and low Reynolds number approximations. The propagation of wall of channel is taken as sinusoidal wave propagation (contraction and relaxation). Homotopy perturbation method (HPM) and Adomian decomposition method (ADM) are used to obtain the analytical approximate solutions of the problem. The expressions of axial velocity, volume flow rate and pressure gradient are obtained. The effects of fractional parameters ( α ) , relaxation time ( λ 1 ) and amplitude ( ϕ ) on the pressure difference and friction force across one wavelength are calculated numerically for different particular cases and depicted through graphs.

Hybrid finite-volume finite-difference scheme for the solution of Boussinesq equations

A hybrid scheme composed of finite-volume and finite-difference methods is introduced for the solution of the Boussinesq equations. While the finite-volume method with a Riemann solver is applied to the conservative part of the equations, the higher-order Boussinesq terms are discretized using the finite-difference scheme. Fourth-order accuracy in space for the finite-volume solution is achieved using the MUSCL-TVD scheme. Within this, four limiters have been tested, of which van-Leer limiter is found to be the most suitable. The Adams-Basforth third-order predictor and Adams-Moulton fourth-order corrector methods are used to obtain fourth-order accuracy in time. A recently introduced surface gradient technique is employed for the treatment of the bottom slope. A new model HYWAVE, based on this hybrid solution, has been applied to a number of wave propagation examples, most of which are taken from previous studies. Examples include sinusoidal waves and bi-chromatic wave propagation in deep water, sinusoidal wave propagation in shallow water and sinusoidal wave propagation from deep to shallow water demonstrating the linear shoaling properties of the model. Finally, sinusoidal wave propagation over a bar is simulated. The results are in good agreement with the theoretical expectations and published experimental results. Copyright © 2005 John Wiley & Sons, Ltd.

Group velocity and reflection phenomena in numerical approximations of hyperbolic equations

Recent analyses of spurious phenomena near interfaces and boundaries of numerical approximations of hyperbolic equations have produced a host of interesting, concrete results which are reviewed in this paper. What characterizes these analyses is that they rely on tools of mathematical physics, in particular in the systematic use of Fourier transforms and the concept of sinusoidal wave propagation. This leads to a description of numerical inaccuracy in terms of dispersion, and a description of spurious numerical solutions in terms of wave packets and group velocities. It is in providing the mathematics needed to describe spurious reflection at numerical boundaries and at interfaces in mesh refinement that the most applied results of this theory are obtained.

Longitudinal pulse propagation characteristics in striated muscle.

The real part of the complex Young's modulus of whole frog sartorius muscle in the resting state was derived from step pulse propagation data in the frequency range 1.0-10 000 Hz. The derivation was based on Fourier integral analysis of the shapes of the propagated pulses to obtain velocities and attenuation coefficients for various harmonic frequencies. The results were consistent with previous sinusoidal wave propagation studies in the higher-frequency range. The general frequency response of the muscle was analogous to the "standard linear solid" model. The relaxation time spectrum derived from the modulus-frequency function showed similar spectral contents to spectra obtained with other methods. The advantages and limitations of the pulse method are discussed.

Effective Dynamic Properties of a Fiber-Reinforced Material and the Propagation of Sinusoidal Waves

A theoretical study is presented on the propagation of a plane sinusoidal wave through a material that is reinforced with parallel fibers in one direction. The wave propagates in a direction normal to the fibers, and both fiber and matrix are made of linear elastic materials. An integral formulation for the scattered-wave solution of an isolated fiber is used to study the multiple scattering in an infinite slab of the composite material. The transmitted and reflected waves from the composite and from a homogeneous slab are shown to be similar. By matching the two sets of results, formulas expressed in terms of the isolated-fiber solution are derived for the wave speed, the effective density, and the modulus of the composite. In general, the effective density and modulus so defined are complex numbers and depend on the wave frequency. This fact indicates the possible existence of dissipation and dispersion in the composite under dynamic loadings. A series solution is presented for a composite containing circular fibers, and approximate closed form results are obtained for the limiting case of very long wavelength. As expected, the material does not exhibit dispersion and dissipation at this limit.

Propagation of Sinusoidal Small-Amplitude Waves in a Deformed Viscoelastic Solid. I

The propagation of a sinusoidal wave of small amplitude in an initially isotropic viscoelastic solid, which is subjected to a static pure homogeneous deformation, is discussed. The secular equation for a plane wave propagating an arbitrary direction with respect to the principal directions of the static deformation is derived. The complex slownesses corresponding to propagation along the principal axes of the static strain are found. Relations are obtained between these and the principal stresses associated with the static deformation, which generalize earlier formulas obtained by Ericksen for elastic materials.