Sinusoidal Boundary Research Articles

On finite element method–flux corrected transport stabilization for advection–diffusion problems in a partial differential–algebraic framework

An extension of the finite element method–flux corrected transport stabilization for hyperbolic problems in the context of partial differential–algebraic equations is proposed. Given a local extremum diminishing property of the spatial discretization, the positivity preservation of the one-step θ-scheme when applied to the time integration of the resulting differential–algebraic equation is shown, under a mild restriction on the time step size. As a crucial tool in the analysis, the Drazin inverse and the corresponding Drazin ordinary differential equation are explicitly derived. Numerical results are presented for non-constant and time-dependent boundary conditions in one space dimension and for a two-dimensional advection problem with a sinusoidal inflow boundary condition and the advection proceeding skew to the mesh.

Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition

The aim of the present numerical study is to understand the natural convection flow and heat transfer in an inclined rectangular enclosure with sinusoidal temperature profile on the left wall. The top and bottom walls of the enclosure are kept to be adiabatic. The finite difference method is used to solve the governing equations with a range of inclination angles, aspect ratios and Rayleigh numbers. The results are presented in the form of streamlines, isotherms and Nusselt numbers. The heat transfer increases first then decreases with increasing the inclination of the enclosure for all aspect ratio and Rayleigh number. Increasing the aspect ratio shows a decreasing trend of the heat transfer for all Rayleigh numbers considered. A correlation equation is also introduced for the heat transfer analysis in this study.

Use of heat as tracer to quantify vertical streambed flow in a two‐dimensional flow field

Analytical solutions to the heat transport equation in porous media have been developed in the past to estimate surface water‐groundwater interactions. These solutions, however, are based upon simplifying assumptions that are frequently violated in natural systems. A nonvertical flow field, inherent to most field settings, can violate the one‐dimensional (1‐D) flow assumption and lead to erroneous velocity estimates. In this study, we have developed a 2‐D heat and mass transport finite element‐based numerical model for a stream aquifer cross section experiencing flow‐through. Synthetic multilevel streambed temperature time series were generated with the model using a sinusoidal temperature boundary. The temperature data was used to quantify the vertical flow velocity with a 1‐D analytical solution based on the amplitude decay and phase shift of temperature with depth. Results demonstrate that erroneous vertical components of fluid velocity can be obtained by the 1‐D analytical solution when the true vertical velocity approaches zero and the flow regime becomes almost horizontal. The results also illustrate that the amplitude ratio method performs quite poorly on the gaining side of the stream where the only reliable method is phase shift. On the losing side of the stream, both methods can be employed but a better estimation is obtained from the amplitude ratio method. In general, amplitude ratio and phase shift data should be used in conjunction to maximize the information of the system.

Influence of periodicity of sinusoidal bottom boundary condition on natural convection in porous enclosure

In this paper, natural convective flow within a rectangular enclosure has been investigated numerically. All the walls of the enclosure are adiabatic except the bottom wall, which is partially heated and cooled by sinusoidal temperature profile. Both situations: medium is hydro-dynamically isotropic and anisotropic are considered. The governing equations are written under assumption of Brinkman-extended non-Darcy model, including material derivative, and then solved by numerically using spectral element method (SEM). Main emphasize is given on effect of periodicity parameter (N) on local heat transfer rate (Nux) as well as flow mechanism in the enclosure. The result shows that, as the periodicity is decreased on increasing N, the absolute value of Nux at the bottom left corner point increases in both situations. For odd values of N, the local heat transfer profile is symmetric about the line X=0.5. The entire flow is governed by two type convective cells: (i) rotating clockwise (ii) rotating anticlockwise. Furthermore, increasing of N increases the multiple cellular structures in the form of N+1. The relative impact of media permeability on Nux at (0,0) shows that enhancement of media permeability along Y-direction is much more effective than the same along X-direction. In contrast to isotropic porous media, the effect of the permeability and permeability orientation angle on the flow is complex and often non intuitive. In particular the present analysis shows that, different periodicity of temperature boundary condition has significant effect on the flow mechanism and consequently on the heat transfer rate for both situations.

Numerical Study of Natural Convection in a Two-Dimensional Enclosure with a Sinusoidal Boundary Thermal Condition Utilizing Nanofluid

Nanofluids are considered to offer important advantages over conventional heat transfer fluids. A model is developed to analyze the behavior of nanofluids taking into account the solid fraction χ. The Navier-Stokes equations are solved numerically with Alternating Direct Implicit method (ADI method) for various Grashof numbers 104 and 105; we have an excellent agreement between our numerical code and previously published works. Copper-Water nanofluid is used with Pr = 6.2 and solid volume fraction χ is varied as 0%; 5%; 10%; 15% and 20%. The problem considered is a two-dimensional heat transfer in a square cavity. The vertical walls are differentially heated, the left is maintained at hot con- dition (sinusoidal) when the right one is cold. The horizontal walls are assumed to be insulated, non conducting and impermeable to mass transfer. The nanofluid in the enclosure is Newtonian, incompressible and laminar. The nanopar- ticles are assumed to have a uniform shape and size. Moreover, it is assumed that both the fluid phase and nanoparticles are in thermal equilibrium state and they flow at the same velocity. The thermophysical properties of the nanofluid are assumed to be constant except for the density variation in the buoyancy force, which is based on the Boussinesq approximation. Different correlations are proposed for predicting heat transfer for uniform and sinusoidal boundary thermal conditions.

Influence of Non-Uniform Sinusoidal Periodic Bottom Boundary Condition on Natural Convection in an Isotropic Porous Enclosure

A comprehensive numerical investigation on the natural convection in an isotropic porous enclosure is presented. All the walls of the enclosure are adiabatic except the bottom wall which is partially heated and cooled by sinusoidal temperature profile. The governing equations were written under assumption of Brinkman-extended non-Darcy model, including material derivative, and then solved by numerically using spectral element method (SEM). The heat transfer and fluid flow mechanisms in isotropic case are governed by periodicity parameter (N) Rayleigh Number (Ra), Darcy number (Da), aspect ratio (A), Prandtl number (Pr) and media permeability (K). The main emphasize is given on effect of N on local heat transfer as well as mechanism of heat transfer and fluid flow in enclosure. The results shows that, as the periodicity is decreased on increasing N the absolute value of Nux at the bottom left corner point increases. For odd values of N, the local heat transfer profile is symmetric about the line x=0.5, which is consequence of symmetric boundary condition at the bottom wall of the enclosure. The entire flow is governed by two type convective cells: (i) rotating clockwise (ii) rotating anticlockwise. Furthermore for even values of N cells rotating anticlockwise are dominated and covered the entire domain. In particular the present analysis shows that, different periodicity of temperature boundary condition has the significant effect on the flow mechanism and consequently on the heat transfer rate.

Numerical prediction of turbulent flow structure generated by a synthetic cross‐jet into a turbulent boundary layer

SUMMARYA detailed numerical study using large‐eddy simulation (LES) and unsteady Reynolds‐averaged Navier–Stokes (URANS) was undertaken to investigate physical processes that are engendered in the injection of a circular synthetic (zero‐net mass flux) jet in a zero pressure gradient turbulent boundary layer. A complementary study was carried out and was verified by comparisons with the available experimental data that were obtained at corresponding conditions with the aim of achieving an improved understanding of fluid dynamics of the studied processes. The computations were conducted by OpenFOAM C++, and the physical realism of the incoming turbulent boundary layer was secured by employing random field generation algorithm. The cavity was computed with a sinusoidal transpiration boundary condition on its floor. The results from URANS computation and LES were compared and described qualitatively and quantitatively. There is a particular interest for acquiring the turbulent structures from the present numerical data. The numerical methods can capture vortical structures including a hairpin (primary) vortex and secondary structures. However, the present computations confirmed that URANS and LES are capable of predicting current flow field with a more detailed structure presented by LES data as expected. Copyright © 2011 John Wiley & Sons, Ltd.

Thermal dynamic transfer properties of the opaque envelope: Analytical and numerical tools for the assessment of the response to summer outdoor conditions

The reliable estimation of buildings energy needs for cooling is a crucial issue in the implementation of the EPB Directive 2010/31/EU (formerly 2002/91/EC), especially in central and southern Europe climates. On this purpose one of the main topics is to predict the behavior of the opaque envelope subjected to variable boundary conditions. The EN ISO 13786:2007 technical standard assumes sinusoidal boundary conditions and introduces dynamic thermal characteristics. The aim of this paper is to assess the deviation arising by the use of different approaches for the calculation of the dynamic thermal characteristics of an opaque envelope element under periodic non sinusoidal boundary conditions. The EN ISO 13786 procedure has been firstly applied by decomposing the external forcing temperature by means of the Fast Fourier Transform (FFT) analysis. A comparison with different approaches, such as Finite Difference Methods (FDM) and Transfer Function Methods (TFM), has been carried out. The predictions of the EN ISO 13786 with a sinusoidal forcing temperature (i.e., standard approach) have also been assessed, comparing the results to the ones obtained through the FFT analysis. Furthermore, corrections to the periodic thermal transmittance and to the time shift have been proposed, in order to improve the explicative worth of those parameters.

Hydro-magnetic combined convection in a lid-driven cavity with sinusoidal boundary conditions on both sidewalls

Mixed convection in a square cavity of sinusoidal boundary temperatures at the sidewalls in the presence of magnetic field is investigated numerically. The horizontal walls of the cavity are adiabatic. The governing equations are solved by finite-volume method. The results are obtained for various combinations of amplitude ratio, phase deviation, Richardson number, and Hartmann number. The heat transfer rate increases with the phase deviation up to ϕ = π/2 and then it decreases for further increase in the phase deviation. The heat transfer rate increases on increasing the amplitude ratio. The flow behavior and heat transfer rate inside the cavity are strongly affected by the presence of the magnetic field.

Assessment of mixing problem on the EOF with thermal effects

Abstract A potential of mixing applications on an electroosmotic flow (EOF) with thermal effects is examined. For the thermal conditions, we apply the sinusoidal temperature boundary conditions on the walls. We exemplify two cases: (1) the mixing of laminar flows and (2) Taylor–Aris dispersion model. In the first case, we consider to mix two different samples that flow in parallel along the channel. In addition, by scaling analysis, we qualitatively examined the mixing result. The mixing efficiency is proportional to the temperature difference. Through the Taylor–Aris dispersion model, we found that the temperature gives rise to an increase of the D eff( T) at the low Peclet number where the diffusion and convection effect coexist.

Grid dependence of k–ε model for oscillatory boundary layers

The low Reynolds number k–ε model is used in some commercial hydrodynamic models to determine boundary layer properties. Such models have been found to produce grid-dependent solutions. A reliable engineering estimate of fundamental boundary layer properties is of utmost importance for practicing engineers. Here, the effect of grid spacing in four different versions of the low Reynolds number k–ε model is studied using direct numerical simulation data of a one-dimensional sinusoidal oscillatory boundary layer. A detailed comparison is made for cross-stream velocities, turbulent kinetic energy, bottom shear stress, friction factor and phase difference. For the present data, the limiting value of the distance to the first grid point from the wall is expressed in terms of Stokes layer thickness. It is observed that, in order to predict the boundary layer properties with reasonable accuracy, the first grid point should be placed at a distance of about 0·02 times the Stokes layer thickness from the wall. The results of the present study may be useful for practicing engineers and researchers in their choice of appropriate grid spacing for low Reynolds number k–ε models.

Assessment of near-surface ground temperature profiles for optimal placement of a thermoelectric device

For a thermoelectric device driven by the temperature difference between soil and ambient air, previous analytical work has been performed wherein a sinusoidal surface boundary condition was imposed; the results suggested that optimal placement of the lower terminal of the device should be at a nondimensional depth of x ∗ = 2.28, resulting in a 7% increase in power over placement at a much greater depth. Analysis of temperature data taken in conjunction with operation of a thermoelectric device has shown that the optimal depth for the lower thermal reservoir is much shallower than originally thought ( x ∗ ∼ 1), with increases in performance approaching 70% over that experienced at greater depths. Representative data are presented and interpreted, along with recommendations for future work.

Combined convection in inclined porous lid-driven enclosures with sinusoidal thermal boundary condition on one wall

A numerical study has been performed to obtain combined convection field in an inclined porous lid-driven enclosures heated from one wall with a non-uniformly heater. The lid moves at constant speed and temperature. Darcy-Brinkman-Forchheimer model was adopted to write governing equations and they solved using finite volume method. A detailed parametric study has been presented for different Reynolds numbers (10 ≤ Re ≤ 1000), Grashof numbers (104 ≤ Gr ≤ 105), Darcy numbers (0.01 ≤ Da ≤ 0.1), porosity (0.6 ≤ ε ≤ 0.9) and inclination angle of enclosure (0° ≤ φ ≤ 180°). It is observed that flow field, temperature distribution and heat transfer are affected by inclination angle of the enclosure.

Excitation of surface plasmon polaritons along the sinusoidal boundary of a metamaterial

We present a detailed analysis about the excitation of surface polaritons (SPs) at the sinusoidally corrugated interface between a conventional dielectric medium and a metamaterial (MM) with arbitrary values of dielectric permittivity and magnetic permeability. The strong impact of SPs on the optical response of the interface is demonstrated by numerical examples obtained with a rigorous electromagnetic code. Conditions leading to total absorption of the incident power and to near-field enhancements are explored in new SP regimes provided by the emergence of MMs. In those regimes where waves incident on the surface without corrugation suffer reactive attenuation, we find SP effects very similar to those occurring for metallic gratings, where the introduction of a weak corrugation in an otherwise highly reflecting surface can turn its reflectivity to zero. New SP effects are identified in regimes corresponding to ideally transparent MMs with a negative index of refraction. In these regimes, contrary to the case of metallic gratings, the introduction of a weak corrugation in an otherwise poorly reflecting surface produces high reflectivities in angular regions corresponding to SP excitation. Moreover, maximal absorption of incident waves and maximal intensity of the excited SP do not occur under the same conditions in these regimes. The complex propagation constants of the SPs supported by the corrugated interface are approximately obtained by fitting a phenomenological expression to our numerical results.

A moving boundary problem derived from heat and water transfer processes in frozen and thawed soils and its numerical simulation

The seasonal change in depths of the frozen and thawed soils within their active layer is reduced to a moving boundary problem, which describes the dynamics of the total ice content using an independent mass balance equation and treats the soil frost/thaw depths as moving (sharp) interfaces governed by some Stefan-type moving boundary conditions, and hence simultaneously describes the liquid water and solid ice states as well as the positions of the frost/thaw depths in soil. An adaptive mesh method for the moving boundary problem is adopted to solve the relevant equations and to determine frost/thaw depths, water content and temperature distribution. A series of sensitivity experiments by the numerical model under the periodic sinusoidal upper boundary condition for temperature are conducted to validate the model, and to investigate the effects of the model soil thickness, ground surface temperature, annual amplitude of ground surface temperature and thermal conductivity on frost/thaw depths and soil temperature. The simulated frost/thaw depths by the model with a periodical change of the upper boundary condition have the same period as that of the upper boundary condition, which shows that it can simulate the frost/thaw depths reasonably for a periodical forcing.

Effects of discrete-electrode configuration on traveling-wave electrohydrodynamic pumping

Traveling-wave electrohydrodynamic (EHD) micropumps can be incorporated into the package of an integrated circuit chip to provide active cooling. They can also be used for fluid delivery in microdevices. The pump operates in the presence of a thermal gradient through the fluid layer such that a gradient in electrical conductivity is established allowing ions to be induced. These ions are driven by a traveling electric field. Such a traveling electric field can be realized in practice only via discrete electrodes upon which the required voltages are imposed. The impact of using discrete electrodes to create the traveling wave on the flow rates generated is explored through numerical modeling. The change in performance from an ideal sinusoidal voltage boundary condition is quantified. The model is used to explore the widths of electrodes and the intervening isolation regions that lead to optimized pumping. The influence of the choice of working fluid on the performance of the pump is determined using an analytical model.

Characteristics of turbulent boundary layers over a rough bed under saw-tooth waves and its application to sediment transport

A large number of studies have been done dealing with sinusoidal wave boundary layers in the past. However, ocean waves often have a strong asymmetric shape especially in shallow water, and net of sediment movement occurs. It is envisaged that bottom shear stress and sediment transport behaviors influenced by the effect of asymmetry are different from those in sinusoidal waves. Characteristics of the turbulent boundary layer under breaking waves (saw-tooth) are investigated and described through both laboratory and numerical experiments. A new calculation method for bottom shear stress based on velocity and acceleration terms, theoretical phase difference, φ and the acceleration coefficient, a c expressing the wave skew-ness effect for saw-tooth waves is proposed. The acceleration coefficient was determined empirically from both experimental and baseline k– ω model results. The new calculation has shown better agreement with the experimental data along a wave cycle for all saw-tooth wave cases compared by other existing methods. It was further applied into sediment transport rate calculation induced by skew waves. Sediment transport rate was formulated by using the existing sheet flow sediment transport rate data under skew waves by Watanabe and Sato [Watanabe, A. and Sato, S., 2004. A sheet-flow transport rate formula for asymmetric, forward-leaning waves and currents. Proc. of 29th ICCE, ASCE, pp. 1703–1714.]. Moreover, the characteristics of the net sediment transport were also examined and a good agreement between the proposed method and experimental data has been found.

Experimental investigation on a mechanically pumped two-phase cooling loop with dual-evaporator

This paper describes a well-known space activate thermal control system, two-phase mechanically pumped cooling loop (MPCL) with two evaporators, in ground-based testing. Each evaporator has an outer diameter of 3 mm and a length of 10 m and the total loop of the system is about 40 m. Tests conducted mainly included stable operation tests under sinusoidal temperature boundary condition and unbalanced heat load tests. Experimental data showed that the loop operated stably at about 30 °C variation of the boundary temperature without any temperature overshoot. Meanwhile, the operating temperature could be controlled within ±0.1 °C of the set point temperature with the new design based on TECs. Furthermore, heat load unbalanced between the two evaporators was also successfully demonstrated that the loop has a heat transport capability to deal with the maximal unbalanced heat loads limitation as Top_Load/Bottom_Load = 0 W/160 W or Top_Load/Bottom_Load = 130 W/0 W. When the heat load limitation is reached in one evaporator and a dry-out appears, some heat load employed on the other side such as 10 W will recover it to the set point evaporation temperature. In conclusion, important performance characteristics demonstrated by this MPCL included: (1) operation of the system about 30 m with a mechanical pump; (2) robustness and reliability of an MPCL with multiple evaporators; (3) effectiveness of TECs in controlling the MPCL operating temperature; (4) dealing with a large unbalanced heat load among MPCL evaporators; and (5) easy recovery from the pulse boiling or a dried out state.

Growth/decay of transverse acceleration waves in nonlinear elastic media

A study of transverse acceleration wave phenomena in the context of nonlinear elasticity is carried out. Using singular surface theory, exact amplitude expressions for acceleration waves arising from a sinusoidal boundary condition (BC) are obtained and their temporal evolution and propagation speeds determined. It is shown that amplitude blow up is possible only if the medium ahead is in motion, otherwise a constant amplitude wave occurs. Analytical results are illustrated numerically using simple computational methods/tools. Lastly, erroneous results that were reported in a recently published related study are noted and/or corrected.

Essential role of membrane-attack protein in malarial transmission to mosquito host.

After ingestion of infected blood by a mosquito, malarial parasites are fertilized in the mosquito midgut and develop into motile ookinetes. These ookinetes invade epithelial cells by rupturing the cell membrane and migrate through the cytoplasm toward the basal lamina, on which they develop to oocysts. Here we report that a microneme protein with a membrane-attack complex and perforin (MACPF)-related domain, which we name membrane-attack ookinete protein (MAOP), is produced in the ookinete stage and plays an essential role in midgut invasion by the ookinete. Ookinetes with the MAOP gene disrupted completely lost infectivity to the midgut. After ingestion of blood infected with the disrupted parasite, the midgut epithelium remained intact, making a clear contrast with the damaged midgut epithelium invaded by wild-type ookinetes. Electron microscopic analysis showed that the disruptant ookinetes migrate to the gut epithelium and attach to the cell surface at the apical tip, but are unable to enter the cytoplasm by rupturing the cell membrane. These results indicate that the MAOP molecule acts on the plasma membrane of the host-cell-like mammalian MACPF family proteins that create pores in the membrane of target cells. Another previously identified MACPF-related molecule is produced in the liver-infective sporozoite and has a crucial role in traversing the liver sinusoidal cell boundary. The present finding, thus, suggests that conserved mechanisms for membrane rupture involving MACPF-related proteins are used in different host invasive stages of the malarial parasite, playing a key role in breaching biological barriers of host organs.