Flux Gradient Research Articles

Lattice Boltzmann method for simulation of solid–liquid conjugate boiling heat transfer surface with mixed wettability structures

Based on the one-component multiphase lattice Boltzmann method, a novel solid–liquid conjugate boiling heat transfer pseudo-potential lattice Boltzmann (LB) model is tentatively proposed in this paper. By respectively introducing the physical property parameters of solids and liquids into the relaxation time τT of the temperature distribution equation, different energy transfer rates in solid, liquid, and vapor regions can be successfully predicted. After verifying the accuracy, stability, and reasonability of this model, the bubble detaching behavior and boiling heat transfer performance on the rectangular cavity structure are analyzed through setting different contact angles of the cavity surface and plane heating surface. The results show that the hydrophobic cavity surface can initialize bubble nucleation earlier and obviously increase the bubble detaching frequency because of its gas-bounding character, while the hydrophilic plane heating surface can restrict the expansion of bubbles and delay the appearance of film boiling. Moreover, for uniform wettability surfaces, the bubble detaching period varies in the quadratic equation with the surface contact angle due to the interaction of surface tension and buoyancy, and there is a minimum detaching period. While for the mixed wettability surfaces, the bubble detaching period also has a minimum value with the decrease in the contact angle the cavity surface, but the average bubble detaching diameter basically does not change with the cavity surface contact angle; moreover, the cavity surface contact angle corresponding to the minimum detaching period also increases with the increase in the plane heating surface contact angle. In addition, for the boiling heat transfer surface with cavity structure, the maximum heat flux and temperature gradient occur on the cavity surface, and the local heat flux of the hydrophobic cavity surface is higher than that of the hydrophilic cavity surface. This work will provide useful help for the further development of the conjugate boiling heat transfer LB model and clarify the mechanism of enhanced boiling heat transfer on a mixed wettability surface.

Effects of non-Fourier bioheat transfer on bone drilling temperature in orthopedic surgery: Theoretical and in vitro experimental investigation.

The mechanical drilling process is a typical step in treating bone fractures to fix broken parts with screws and plates. Drilling generates a significant amount of heat and elevates the temperature of the bone, which can cause thermal osteonecrosis and damage to the surrounding bone tissue and nerves. Thermal inertia between heat flux and temperature gradient in nonhomogeneous interior structural medium-like biological tissues is arguable. Therefore, this paper proposes an analytical model of heat propagation in bone drilling for orthopedic surgery based on the hyperbolic Pennes bioheat transfer equation (HPBTE). Drilling experiments in bovine cortical bone samples were also carried out using an infrared thermography approach to confirm the proposed analytical model. Around the drilled hole surface, thermal necrosis is spread out from 1 to 10 mm. Increased feed rate reduces necrosis penetration distance and increases intense bone necrosis. The HPBTE includes thermal relaxation time effect and internal convective function of tissue perfusion rate. As these factors are not considered in the parabolic heat transfer equation (PHTE), the results show that the HPBTE is more accurate in predicting temperature and thermal osteonecrosis than the PHTE. As a result, proposed analytical model is a handy tool for calculating temperature to avoid thermal damage while improving process efficiency. Furthermore, it has the capability of controlling the manual or robotic drilling procedure for minimally invasive operations.

Surfzone bedform migration and sediment flux implications to large scale morphologic evolution

Field observations of small scale seabed morphology were obtained over 4 weeks at two locations separated 66 m along a cross-shore transect during the 2014 MEGAPEX Experiment conducted as part of the longer term Sand Engine mega-nourishment project along the North Sea Coast of The Netherlands. The seafloor was continuously covered by dynamic bedforms with amplitudes ranging 0.02–0.40 m and wavelengths ranging 0.20–2.5 m. Ripple migration rates were up to 3.6 m/h, dependent on the energy of the waves and currents. Under the assumption of bedload dominant transport, cross-shore and alongshore sediment volume flux by ripples was estimated from observations at the spatially separated imaging locations. The average and maximum ripple sediment volume flux was found to be 0.22 and 1.7 m3/m/day, respectively, with larger fluxes during spring flood tides and storm wave conditions. The daily averaged fluxes were usually oriented about 30° north of shore-normal, moving in the same direction as a nearby transverse sandbar migration direction. Estimated gradients in the sediment flux within the surfzone were computed from bed level change measurements of the inner surfzone including a larger scale transverse sandbar measured from subsequent jetski surveys. We find that the estimated gradients in surfzone sediment flux are conceivably driven by small variations in the sediment flux driven by sand ripple migration, supported by our observations of ripple driven sediment flux at the two ripple imaging stations. A simple conceptual model is presented that shows how small scale bedforms may contribute to the growth and decay of larger scale bathymetric features, such as sandbars. Results suggest that sediment flux by small scale sand ripples and megaripples could significantly contribute to larger scale morphologic development in the surfzone.

Thermal lagging effect on heat transport within living biological tissues

Thermal lagging effect on heat transport within living biological tissues is explored in the context of different relaxation mechanisms. The governing equations of temperature rooted the delay effect between heat flux and temperature gradient, as well as non-equilibrium effect between blood vessel and peripheral tissues, are constructed separately via the classic dual-phase lag model (DPL) and generalized dual-phase lag model (GDPL). An analytical procedure based on the Laplace transform technique and its limit theorem is then proposed. The expressions and effective values of phase lags rooted different effect have been derived and further estimated. On this basis, the temperature response of a biological tissue with its boundary exposed to a pulse heat flux is analyzed. The detailed parametric study has been conducted to explore the dependence of these phase lags on tissue structures and their effect on heat transport properties. The results highlight the contributions of the delay effect and non-equilibrium effect in temperature prediction and state that the delay effect is dominated for a larger tissue size. Meanwhile a significant difference has also been observed with the boundary conditions that obey different thermal conduction mechanism.

A robust, interpolation‐free and monotone finite volume scheme for diffusion equations on arbitrary quadrilateral meshes

AbstractA novel monotone finite volume (FV) scheme on arbitrary quadrilateral meshes, such as extremely distorted meshes with concave, twisted, or even negative volume cells, is proposed to solve diffusion equations with discontinuous tensor coefficients. The first advantage of our scheme is that no auxiliary unknown is needed thus the efficiency and accuracy are improved. The second advantage is that the convex decomposition of the conormal vector relies only on the locations of cell centers and reduces geometric restrictions on cell shapes to preserve positivity. The difficulties of constructing discrete normal fluxes across the material interface are overcome by introducing primary unknowns on the opposite side of the interface into the discrete stencil with some virtual adjustments on their positions, based on the continuity of normal flux and tangent gradients. Numerical tests demonstrate that our new scheme is second‐order accurate, unconditionally monotone, and comparisons with some existing methods in terms of efficiency and accuracy are also given.

Energy Harvester Based on an Eccentric Pendulum and Wiegand Wires.

This study proposed an energy harvester that combines an eccentric pendulum with Wiegand wires to harvest the kinetic energy of a rotating plate. The energy harvester converts the kinetic energy into electrical energy to power sensors mounted on the rotating plate or wheel. The kinetic model is derived from the Euler–Lagrange equation. The eccentric pendulum generates a swing motion from the direction variation of the centrifugal force and the gravitational force. The magnetic circuit is designed such that, during the swing motion, an alternating magnetic field is formed to induce the output voltage of the Wiegand wire. COMSOL software was used to simulate magnetic flux density and optimize the geometric parameters of magnets. Response surface methodology was used to formulate the output voltage model. Magnetic flux density affects output voltage dramatically. However, the output voltage is not sensitive to the gradient of magnetic flux density. The experimental results indicate that when the Wiegand wire is 14.2 mm from the magnet, the generation power is 0.118–1.15 mW, in a speed range of 240–540 rpm. When the Wiegand wire is 7.0 mm from the magnet, the generation power is 0.741–1.06 mW, in a speed range of 480–660 rpm.

An efficient meshfree computational approach to the analyze of thermoelastic waves of functionally graded materials in a two-dimensional space

In this paper, a meshless local radial point interpolation method (RPIM) is proposed for the thermoelastic analysis of functionally graded materials (FGMs) under thermal shocks. The properties of such materials are temperature-dependent varying and change gradually through thickness based on the Mori–Tanaka scheme and the volume fraction power law distribution (Appendix A). The characterization and visualization of the FGMs under a prescribed temperature gradient or heat flux are then detailed. The proposed method does not need any background cell-based integration and is thus very suitable to deal with complex geometries and scattered data. Moreover, the shape functions of this method possess the properties of the Kronecker delta, wherein the essential boundary conditions can be analytically satisfied. The numerical results are fully discussed and validated by the corresponding outcomes of the moving least squares (MLS) method, demonstrating the high capability and efficiency of RPIM proposed here in simulating the dynamic thermoelastic analysis of FGMs.

Carbon dioxide measurements above a wheat crop. II CO2 flux density and the effects of diffuse radiation

The relationships between the daytime CO2 flux density above a wheat crop and both solar irradiance and evapotranspiration are investigatedusing physical and biophysical measurements made in 1971 in Australia. Well-established flux‒gradient relations are used to estimate the hourly CO2flux density using the measured CO2 concentration at heights of 1 m and 2 m above the crop.Principal component regression identifies four key environmental variables (diffuse and beam shortwave irradiance, leaf-area index, humidity deficit) whose variations together explain almost 80% of the variations in the hourly CO2 flux. For the diffuse ratio Sd/Sg ≈ 0.9 (generally overcast skies), where Sd and Sg are the observed diffuse and global broadband shortwave irradiances (wavelength range 285 nm to 2800 nm), respectively, both light-use and water-use efficiencies are found to be around double those for Sd/Sg ≈ 0.1 (sunny skies). For a given value of Sg this doubling in the water-use efficiency is primarily due to the sensitivity of the CO2 flux to the diffuse ratio.Profile measurements of narrowband (350 to 950 nm) irradiance within the canopy confirm that the increase in light-use efficiency is primarily due to the greater interception of radiation in the canopy under an increased diffuse ratio, up to 15 percent in overcast conditions.

Calibration of Large Photonis Fission Chambers in Standard Neutron Fields of the BR1 Reactor

Small fission chambers manufactured by Photonis, Reuter-Stokes, CEA, and Centronic are routinely calibrated in standard neutron fields of the BR1 reactor at SCK CEN in Mol, Belgium. Two irradiation fields are available: fast spectrum in the MARK3 convertor and thermal spectrum in the Empty Cavity. In this work, for the first time the calibration procedure of larger fission chambers (Photonis CFUL01 and CFUM21 type) with the deposit length exceeding the length of the convertor is presented. Spatial energy correction factors taking into account the neutron flux shape beyond the convertor and radial gradient of the neutron flux were calculated with MCNP and experimentally validated. The combination of calibration (i.e., effective mass measurement) in fast and thermal irradiation fields allows for determination of the purity of ²³⁸U deposit. This is demonstrated on three CFUL01-type fission chambers with purity between 99.8% and 99.998%.

Study of shock wave/boundary layer interaction from the perspective of nonequilibrium effects

Shock wave/boundary layer interaction (SWBLI) is a widespread phenomenon in supersonic flows and has received extensive attention. The boundary layer is generated due to viscous stress, which is a kind of macroscopic manifestation of molecular nonequilibrium motion, namely, nonequilibrium effects. In this paper, an investigation is conducted on SWBLI from the perspective of nonequilibrium effects. A method is proposed for studying nonequilibrium effects based on the Navier–Stokes (NS) equations and the Reynolds-averaged NS (RANS) equations. The SWBLI at Mach 2 and Mach 6 is concerned. The results show that nonequilibrium effects associated with the incident shock wave are weaker than that in the boundary layer for a Mach 2 incoming flow. Neither the separation shock wave nor the incident shock wave has an obvious interaction with nonequilibrium effects in the boundary layer. However, the nonequilibrium effects of the incident shock wave are stronger for a Mach 6 incoming flow, and it has an obvious interaction with the nonequilibrium effect in the boundary layer. We also discuss the relation between nonequilibrium effects and energy conversion in the boundary layer. The analysis reveals that changes in the gradients of total energy-related nonequilibrium effects contribute to the change in total energy by influencing the gradient of the heat flux and the power of viscous stress. Thus, this work provides the flow characteristics of boundary layer separation and energy conversion mechanism of SWBLI from the perspective of nonequilibrium effects, as well as the interaction of nonequilibrium effects between the shock wave and boundary layer.

Space-fractional heat transfer analysis of hybrid nanofluid along a permeable plate considering inclined magnetic field

In this study, the Caputo space-fractional derivatives of energy equation are used to model the heat transfer of hybrid nanofluid flow along a plate. The plate is considered permeable and affected by an inclined magnetic field. We use the space-fractional derivative of Fourier’s law to communicate between the nonlocal temperature gradient and heat flux. The hybrid nanofluid is formed by dispersing graphene oxide and silver nanoparticles in water. The new fractional integro-differential boundary layer equations are reduced to ordinary nonlinear equations utilizing suitable normalizations and solved via a novel semi-analytical approach, namely the optimized collocation method. The results reveal that the increment of the order of space-fractional derivatives and the magnetic inclination angle increase the Nusselt number. Also, an increase in the order of space-fractional derivatives leads to a thicker thermal boundary layer thickness resulting in a higher temperature. It is also found that the temperature of the fluid rises by changing the working fluid from pure water to single nanofluid and hybrid nanofluid, respectively. What is more, the proposed semi-analytical method will be beneficial to future research in fractional boundary layer problems.

Non-Abelian Braiding in Spin Superconductors Utilizing the Aharonov-Casher Effect.

Spin superconductor (SSC) is an exciton condensate state where the spin-triplet exciton superfluidity is charge neutral while spin 2(ℏ/2). In analogy to the Majorana zero mode (MZM) in topological superconductors, the interplay between SSC and band topology will also give rise to a specific kind of topological bound state obeying non-Abelian braiding statistics. Remarkably, the non-Abelian geometric phase here originates from the Aharonov-Casher effect of the "half-charge" other than the Aharonov-Bohm effect. Such topological bound state of SSC is bound with the vortex of electric flux gradient and can be experimentally more distinct than the MZM for being electrically charged. This theoretical proposal provides a new avenue investigating the non-Abelian braiding physics without the assistance of MZM and charge superconductor.

Influence of polymers on flow and heat transfer due to peristaltic waves: a molecular approach

This work aims to have an insight into the effects of polymers on flow and heat transfer due to peristaltic waves. Oldroyd-B model, based on kinetic theory, is considered to study the relation between the molecular structure of the polymers and the rheological properties. The main advantage of using this model is the inclusion of information based on molecular structure. Such inclusion in stress tensor incorporates the effects of stretching and orientation of the molecules. Some significant applications polymer-peristalsis can be found in tissue engineering, intake of food, and medicines. Approximations of long-wavelength and low Reynolds number are used to investigate the main features of the problem. Pressure gradient, velocity, temperature, trapped bolus, drag coefficient, and heat flux at the wall are studied numerically. The analysis is based on the change in important parameters like polymer concentration, relaxation time, Weissenberg number, and Brinkman number. Results show that by increasing polymer concentration parameter, Weissenberg number, and relaxation time parameter, the negative pressure gradient in the flow geometry increases. By increasing the polymer concentration parameter and time relaxation parameter, the velocity and temperature profiles increase. An increase in polymer concentration increases the size of the trapped bolus. Drag parameter at the wall decreases while heat flux increases when polymer concentration and Weissenberg number are increased.

Comparison of calculation methods for lead cooled fast reactor reactivity effects

This study analyzes three different reactivity feedback coefficients of the Advanced Lead-cooled Fast Reactor Demonstrator (ALFRED) reactor. During the evaluations, the central difference Direct Perturbation Method (DPM) and the Linear Perturbation Theory (LPT) were applied to determine the feedback coefficients and their uncertainties due to cross-section data. The continuous energy SERPENT Monte Carlo code, the multigroup TSUNAMI-3D sequence of the SCALE program package, and PARTISN discrete ordinate neutron transport code coupled with SEnTRi developed by the authors was applied, and the properties of these fundamentally different calculations are presented. In order to validate the methodologies, lead void coefficient calculations were performed for the Comet critical assembly, which confirmed that a good agreement could be reached between the different methods and measurement results. Besides the high-level transport approximation, the calculations indicated that the appropriate spatial resolution has outstanding importance in describing the high flux gradient.

Evaluating benthic flux measurements from a gradient flux system

AbstractMultiple methods exist to measure the benthic flux of dissolved oxygen (DO), but many are limited by short deployments and provide only a snapshot of the processes occurring at the sediment–water interface. The gradient flux (GF) method measures near bed gradients of DO and estimates the eddy diffusivity from existing turbulence closure methods to solve for the benthic flux. This study compares measurements at a seagrass, reef, and sand environment with measurements from two other methods, eddy covariance and benthic chambers, to highlight the strengths, weaknesses, and uncertainty of measurements being made. The results show three major areas of primary importance when using the GF method: (1) a sufficient DO gradient is critical to use this method and is limited by the DO sensor precision and gradient variability; (2) it is important to use similar methods when comparing across sites or time, as many of the methods showed good agreement but were often biased larger or smaller based on the method; and (3) in complex bottom types, estimates of the length scale and placement of the DO sensors can lead to large sources of error. Careful consideration of these potential errors is needed when using the GF method, but when properly addressed, this method showed high agreement with the other methods and may prove a useful tool for measuring long‐term benthic fluxes of DO or other chemical sensors or constituents of interest that are incompatible with other methods.

Stellar activity correction using PCA decomposition of shells

Context.Stellar activity and instrumental signals are the main limitations to the detection of Earth-like planets using the radial-velocity (RV) technique. Recent studies show that the key to mitigating those perturbing effects might reside in analysing the spectra themselves, rather than the RV time series and a few activity proxies.Aims.The goal of this paper is to demonstrate that we can reach further improvement in RV precision by performing a principal component analysis (PCA) decomposition of the shell time series, with the shell as the projection of a spectrum onto the space-normalised flux versus flux gradient.Methods.By performing a PCA decomposition of shell time series, it is possible to obtain a basis of first-order spectral variations that are not related to Keplerian motion. The time coefficients associated with this basis can then be used to correct for non-Dopplerian signatures in RVs.Results.We applied this new method on the YARARA post-processed spectra time series of HD 10700 (τCeti) and HD 128621 (αCen B). On HD 10700, we demonstrate, thanks to planetary signal injections, that this new approach can successfully disentangle real Dopplerian signals from instrumental systematics. The application of this new methodology on HD 128621 shows that the strong stellar activity signal seen at the stellar rotational period and one-year aliases becomes insignificant in a periodogram analysis. The RV root mean square on the 5-yr data is reduced from 2.44 m s−1down to 1.73 m s−1. This new approach allows us to strongly mitigate stellar activity, however, noise injections tests indicate that rather high signal-to-noise ratio (S/N > 250) is required to correct for the observed activity signal on HD 128621.

Sampling molecular gas in the Helix planetary nebula: Variation in HNC/HCN with UV flux

Context. Observations of molecular clouds, prestellar cores, and protoplanetary disks have established that the HNC/HCN ratio may be a potent diagnostic of molecular gas physical conditions. The processes that govern the relative abundances of these molecules nevertheless remain poorly understood. Aims. We seek to exploit the wide range of UV irradiation strengths within the ∼pc diameter Helix planetary nebula to explore the potential role of UV radiation in driving HNC/HCN. Methods. We performed IRAM 30 m and APEX 12 m radio line observations across six positions within the Helix Nebula, making use of radiative transfer and photodissociation modeling codes to interpret the results for line intensities and line ratios in terms of the molecular gas properties. Results. We have obtained the first detections of the plasma-embedded Helix molecular knots (globules) in HCN, HNC, HCO+, and other trace molecules. Analysis of the HNC/HCN integrated line intensity ratio reveals an increase with radial distance from the Helix central star. In the context of molecular line ratios of other planetary nebulae from the literature, the HNC/HCN ratio appears to be anticorrelated with UV emission over four orders of magnitude in incident flux. Models of the photodissociation regions within the Helix using the RADEX and Meudon codes reveal strong constraints on the column density (1.5–2.5 × 1012 cm−2) of the molecular gas, as well as pressure and temperature. Analysis of the molecular ion HCO+ across the Helix indicates that X-ray irradiation is likely driving HCO+ production in the outer regions of planetary nebulae, where photodissociation is limited but cold gas and ionized molecules are abundant. Conclusions. Although the observational results clearly indicate that UV irradiation is important in determining the HNC/HCN ratio, our photodissociation region modeling indicates that the UV flux gradient alone cannot reproduce the observed variation in HNC/HCN across the Helix Nebula. Instead, HNC/HCN appears to be dependent on both UV irradiation and gas pressure and density.

Failure analysis of waste heat boiler tubing caused by a high local heat flux

In a process gas synthesis for ammonia production, steam precursors are produced in a shell and tube heat exchanger (HE), called a waste heat boiler (WHB), because it uses heat from a gaseous produced in the reformer. The process gas flows in the tube, and a saturated water-steam mixture is on the outer shell side. In many cases, the waste heat boiler fails because of corrosion, erosion, and a combination of both. In this present work, a new failure mechanism of WHB tube is reported. The tube failed due to excessive oxidation wastage and had black products on the water-steam side. The oxide product was magnetite, intact on the surface, and the water-steam flow eroded some. The microstructure of the failed tube was composed of pearlite and ferrite without observed degradation. A computational model based on computational fluid dynamics revealed flow recirculation attributed to sudden enlargement at the end of the ferrule.This created high heat flux at some distance from the ferrule end; consequently, the tube excessively oxidized because of the high heat flux and temperature gradient across the tube thickness. This study provides a basis for developing HE designs and exploring the damage mechanism of shell and tube heat exchangers.

Propagation Prediction of Body Waves in Fluid-Saturated Soils with Flow-Independent Viscosity

A systematic study of wave theory in thermoviscoelastic soil is essential for engineering applications such as geophysical exploration. In the present work, the influences of flow-independent viscosity of the soil skeleton and the thermal effect on elastic waves are considered, and the propagation behaviors of body waves in thermoviscoelastic saturated soil are investigated. Firstly, the thermoviscoelastic dynamic coupling model of saturated soil were established by employing the Biot model, the generalized thermoelastic theory, and the Kelvin–Voigt linear viscoelastic model. Secondly, the dispersion equations of body waves in thermoviscoelastic saturated soil were theoretically derived with structural symmetry considered. Finally, the variations of wave velocity and the attenuation coefficient of the body waves with the thermophysical parameters are discussed. The results revealed that the enhancement of the relaxation time of soil caused an increase of wave velocity and the attenuation coefficient of P1, P2, and S waves, and a decrease of the wave velocity and attenuation coefficient of the thermal wave. Different ranges of the permeability coefficient and frequency have different effects on the P1, P2, and S waves. The variation of thermal conductivity and the phase-lags of heat flux and temperature gradient only affect the thermal wave.

Investigation and Validation of Unstructured Mesh Methodologies for Modeling Experimental Reactors

This paper summarizes a methodology developed at École Polytechnique Fédérale de Lausanne for the neutronic modeling of the CROCUS experimental reactor and proposes solutions to the challenges one may face while modeling a research reactor with a complex geometry. Indeed, the double-lattice configuration of CROCUS makes it difficult to use codes for neutron diffusion and transport relying on a structured mesh description. For this reason, and based on the available in-house competences, we decided to make use of the neutronic capabilities of the GeN-Foam multiphysics solver, which takes advantage of general finite volume methodologies on unstructured meshes to provide sufficient flexibility for the study of unconventional reactor designs. In this work, GeN-Foam is used to build a first SP3 model of CROCUS based on an unstructured mesh to have an explicit modeling of the double lattice and the water gap between the two lattices. Form functions are then used to reconstruct the intra-pin fission rates for validation against measured distributions. We also discuss the limitations of the SP3 approximation of neutron transport in regions with steep neutron flux gradients and the planned future developments.