Non-uniform Flux Distribution Research Articles

Experimental investigation of non-uniform heating effect on flow and heat transfer of supercritical carbon dioxide :An application to solar parabolic trough collector

In order to reduce the carbon dioxide emission, the supercritical carbon dioxide (sCO2) Brayton cycle is a good choice to convert solar energy into power using solar parabolic trough collectors (PTCs). Because the earth rotation induced non-uniform flux distribution threatens the safe operation of absorber tubes, we investigate the flow and heat transfer of sCO2 in a horizontal tube under non-uniform heating, with the mass fluxes, average heat fluxes and pressures in the ranges of (397∼1244) kg/m2s, (99∼413) kW/m2, and (7.5∼15.7) MPa, respectively. On the contrary to the classical treatment of supercritical fluid (SCF), SCF is treated in a multiphase framework. It is found that, compared with the sCO2 heat transfer in horizontal tubes under uniform heating, the non-uniform heating not only enhances heat transfer, but also increases friction factors. Besides, the non-uniform heating weakens the stratification effect, but the difference of heat transfer between the top and bottom generatrixes cannot be completed eliminated. It is observed that the larger vapor-like-layer thicknesses on tube walls may switch the sCO2 heat transfer from normal heat transfer (NHT) to heat transfer deterioration (HTD). Three heat transfer mechanisms are commented by using the dimensionless numbers regarding the pseudo-boiling in supercritical pressures.

Model-predicted effect of radial flux distribution on oxygen and glucose pericellular concentration in constructs cultured in axisymmetric radial-flow packed-bed bioreactors

Radial flow packed-bed bioreactors (rPBBs) overcome the transport limitations of static and axial-flow perfusion bioreactors and enable development of clinical-scale bioengineered tissues. We developed criteria to design rPBBs with uniform medium radial flux distribution along bioreactor length ensuring uniform construct perfusion. We report a model-based analysis of the effect of non-uniform axial distribution of medium radial flux on pericellular concentration of oxygen and glucose. Albeit pseudo-homogeneous, the model predicts how medium flux, solutes transport and cellular consumption interact and determine the pericellular oxygen and glucose concentrations in the presence of pore transport resistance to design optimal axisymmetric rPBBs and enable control of pericellular environment. Thus, oxygen and glucose supply may match cell requirements as tissue matures. Flow and solute transport in bioreactor empty spaces and construct was described with Navier-Stokes and Darcy-Brinkman equations, and with convection–diffusion and convection–diffusion-reaction equations, respectively. Solute transport in construct accounted for Michaelian cellular consumption and bulk medium-to-cell surface oxygen transport resistance in terms of a transport-equivalent bed of Raschig rings. The effect of relevant dimensionless groups on pericellular and bulk solute concentrations was predicted under typical tissue engineering operation and evaluated against literature data for bone tissue engineering. Axial distribution of medium radial flux influenced the distribution of pericellular solutes concentration, more so at high cell metabolic activity. Increasing medium feed flow rates relieved non-uniform solute concentration distribution and decayed at cell surface for metabolic consumption, also starting from axially non-uniform radial flux distribution. Model predictions were obtained in runtimes compatible with on-line control strategies.

Design, Simulation and Optimization of a Novel Transpired Tubular Solar Air Heater

In this paper, a novel tubular solar air heater is introduced. In this air heater, the hot boundary layer is drawn into the absorber tube and can provide thermal energy at moderate temperatures. Several different cases were simulated and a correlation was proposed to predict the collector’s effectiveness as a function Rayleigh number and Reynolds number. An equation was derived to find the effectiveness of this collector. Finally, a real case was studied with non-uniform solar flux distribution, as well as radiation heat loss. Good agreement was found between the results and those derived by the proposed analytical method. For different suction values, the first-law and the second-law efficiencies were calculated. Based on the exergy analysis, exergy destruction in absorption is the dominant factor that is unavoidable in low-temperature collectors. It was shown that there is an optimum suction value at which the second-law efficiency is maximized. At the optimum point, temperature rise can reach 54 K, which is hardly possible with a flat plate collector. Based on the exergy analysis, the relation between tube wall temperature and air outlet temperature in their dimensionless forms at the optimum working condition was derived, and it was shown that effectiveness at the optimum working condition is around 0.5. This means that the air temperature rise shall be half of the temperature difference between collector wall and the ambient temperatures. A high outlet temperature besides the low cost of construction and maintenance are the main advantages of this air heater. With such a high temperature rise, this type of collector can increase the use of solar energy in domestic applications.

Improving the Uniform Distribution of Water Flux Density in Sprinkler Spray by Adopting Various Installation Methods

In a sprinkler system, the nonuniform water flux distribution resulting from the sprinkler head design, specifically due to the deflector and frame, impedes the primary extinguishing surface cooling effect of the sprinkler. In this study, the effects of the distance between heads, supplying flow rate, head installation direction, and head installation height on the uniformity of the water flux density distribution were investigated. Simulations were conducted using the water flux distribution reproduction method proposed in a previous study. As the distance between heads decreased, water was supplied to the bottom of the head, resulting in the improved uniformity of the water flux distribution. When the flow rate was corrected with the changes in the distance between the heads to maintain the average water flux density supplied to the floor, a uniform water flux distribution was observed even when the distance between heads was relatively large. In the case of head installation direction, the most uniform distribution was observed when the sprinkler heads were installed alternately at angles corresponding to 0° and 135°. As the installation height of the sprinkler heads increased, the difference between the maximum and minimum local water flux densities decreased, leading to a more uniform water flux density distribution.

Numerical investigation of the thermal-hydraulic performance of a novel parabolic trough wavy tubular receiver by using FMWNCT/oil-nanofluid coupled with fins

This study employs a computational fluid dynamics (CFD) approach to assess the performance of a novel wavy profile tube receiver. It integrates rectangular fins and an Oil-based nanofluid, specifically utilizing Thermodyne GG-03 synthetic oil combined with Functionalized Multi-Wall Carbon Tubes (FMWNCT). The synthesis involves rigorous experimental procedures to characterize the thermophysical properties of the oil and nanofluid. Empirical correlations, validated against Bitam et al.'s model [1], guide the numerical analysis. The investigation, utilizing a steady-state κ - ω SST turbulence model with a non-uniform Gaussian thermal flux distribution, explores thermohydraulic performance in fully developed turbulent flow (Reynolds number range: 2 × 104 – 5 × 104). Comparative analysis with Bitam et al.'s work, employing Syltherm 800 oil as a reference, reveals a 25.76% average Nusselt number enhancement with Thermodyne GG-03. Additional improvements are observed: 124.69% with FMWNCT/oil-nanofluid, 137.04% with fins, and 236.54% with combined FMWNCT/oil-nanofluid and fins. These enhancements lead to increased heat transfer coefficients and rates. The friction coefficient rises by less than 60%, mainly attributed to the Nusselt number improvement. At RE = 20000, the Maximum Performance Evaluation Criteria (PEC) is 5.5, signifying significant improvement. Notably, a 300% PEC enhancement is observed compared to Roger and Mayhew's curved tube model [1]. In conclusion, these findings offer valuable insights for efficiently designing wavy tubular receivers in PTR collectors.

Observation of nonvolatile magneto-thermal switching in superconductors

Applying a magnetic field to a solid changes its thermal-transport properties. Although such magneto-thermal-transport phenomena are usually small effects, giant magneto-thermal resistance has recently been observed in spintronic materials and superconductors, opening up new possibilities in thermal management technologies. However, the thermal conductivity conventionally changes only when a magnetic field is applied due to the absence of nonvolatility, which limits potential applications of thermal switching devices. Here, we report the observation of nonvolatile thermal switching that changes the electron thermal conductivity when a magnetic field is applied and retains the value even when the field is turned off. This unconventional magneto-thermal switching arises in commercial Sn-Pb solders and is realized by phase-separated superconducting states and resultant nonuniform magnetic flux distributions. This result confirms the versatility of the observed phenomenon and aids the development of active solid-state thermal management devices.

Production Dynamic Characteristic of Fractured Wells in Multilayer Reservoirs Considering the Effect of Non-Uniform Flux Distribution

Abstract Hydraulic fracturing stimulation, which improves matrix permeability and reduces production costs, has been extensively used in the exploitation of multilayer reservoirs. However, little research on the production dynamic characteristics of vertically fractured wells in stratified reservoirs has been done in the literature. The influence of flux variation along the fracture on the pressure transient behavior has been ignored in these previous works. Therefore, this paper introduces a novel semi-analytical model for fractured wells in multilayer reservoirs, in which the finite difference method is used to characterize fluid flow in the fracture and the Green’s function method is used to characterize fluid flow in the matrix. With the aid of the model, the production dynamic characteristics of fractured wells in multilayer reservoirs can be readily investigated. In addition, based on the assumption of nonuniform flux distribution along the fracture, we successfully recognize four flow regimes occurring in the pressure drop and pressure derivative curves. Following that, the influences of several parameters on the pressure dynamics and layered flux contribution are studied. The calculation results indicate that a larger storability ratio, as well as a larger permeability ratio, can increase the values of the pressure drop and the pressure derivative; the greater the fracture height, the greater the fluid flow into each layer of the fracture. During the production of this model, increasing the fracture conductivity can reduce the pressure drop and pressure derivative, which means lower flow resistance in the fracture.

Study of the pressure transient behavior of directional wells considering the effect of non-uniform flux distribution

During the production, the fluid in the vicinity of the directional well enters the wellbore with different rates, leading to non-uniform flux distribution along the directional well. However, in all existing studies, it is oversimplified to a uniform flux distribution, which can result in inaccurate results for field applications. Therefore, this paper proposes a semi-analytical model of a directional well based on the assumption of non-uniform flux distribution. Specifically, the direction well is discretized into a carefully chosen series of linear sources, such that the complex well trajectory can be captured and the non-uniform flux distribution along the wellbore can be considered to model the three-dimensional flow behavior. By using the finite difference method, we can obtain the numerical solutions of the transient flow within the wellbore. With the aid of Green's function method, we can obtain the analytical solutions of the transient flow from the matrix to the wellbore. The complete flow behavior of a directional well is perfectly represented by coupling the above two types of transient flow. Subsequently, on the basis of the proposed model, we conduct a comprehensive analysis of the pressure transient behavior of a directional well. The computation results show that the flux variation along the direction well has a significant effect on pressure responses. In addition, the directional well in an infinite reservoir may exhibit the following flow regimes: wellbore afterflow, transition flow, inclined radial flow, elliptical flow, horizontal linear flow, and horizontal radial flow. The horizontal linear flow can be observed only if the formation thickness is much smaller than the well length. Furthermore, a dip region that appears on the pressure derivative curve indicates the three-dimensional flow behavior near the wellbore.

Toroidal Nanocrystalline Powder Core With Trapezoidal Cross Section

This paper introduces a toroidal nanocrystalline powder core with a trapezoidal cross section. The non-uniform magnetic flux distribution of toroidal cores with different cross sectional geometries is discussed, the inductance equations are derived, and the geometrical optimisation factor is given in order to retain the highest possible inductance value whilst minimising material usage. A 10-turn coil is wound on the core, with the measured inductance values showing a good match with both FEM and mathematical calculation. The near-field electromagnetic interference (EMI) radiation in close proximity to the inductor is investigated by both FEM and experimental validation, and the toroidal core with a trapezoidal cross section has shown reduced EMI. By adopting a trapezoidal cross section for the toroidal core, a 30 % reduction in material usage and lower EMI are achieved, albeit with a compromise of 14% in inductance.

Study on the convective heat transfer characteristics of supercritical CO2 in mini-channels under unilateral heating conditions for application in a compact solar receiver

The mini-channel in compact solar receiver deliver the high performance in both heat transfer (HT) and pressure resistance. However, the severe variation of thermophysical properties of supercritical CO2 (S-CO2) coupling with the complex nonuniform distribution of solar flux leads to the abnormal flow and heat transfer (FHT) performance of S-CO2 in mini-channels. The present work numerically investigated the detailed FHT of S-CO2 in the horizontal mini-channel with one-side heating. The impacts of buoyancy and flow acceleration on FHT of S-CO2 are demonstrated in detail. The results show that the buoyancy effects can lead to the enhancement on circumferentially average heat transfer performance of S-CO2 while the local deterioration at the top. In contrast, the thermal acceleration effects can worsen the S-CO2 HT. The buoyancy and thermal acceleration effects can be ignored when Ri ≤ 2.7 × 10−3 and Ac ≤ 7.8 × 10−8, respectively. The empirical formula for S-CO2 HT in the mini-channel under single-side heating conditions is developed, with a maximum error of 4.5%.

Detection of Numerical Power Shift Anomalies in Burnup Modeling of a PWR Reactor

This paper presents the detection and interpretation of numerical power density anomalies in the full-core PWR reactor model, developed at the level of RPV. The study shows that in the Monte Carlo neutron transport coupled with burnup modeling, power density anomalies may occur and should be carefully investigated. The power density anomalies originate from the initial core asymmetry due to different designs of top and bottom reflectors and non-uniform initial axial neutron flux distribution. The power density anomalies increase with increasing fuel burnup due to spatial changes in 135Xe concentrations and following power density redistribution along the reactor core. A method for anomaly detection for the semi-symmetric reactor core is proposed.

Structural design challenges and implications for high temperature concentrating solar power receivers

High operating temperatures along with diurnal cycling and high operating stresses bring many material and engineering challenges for concentrated solar power (CSP) receivers. Current design rules in ASME Boiler and Pressure Vessel (B&PV) Code for high temperature structural components were not intended for CSP components. The paper reviews the design rules in several sections of ASME B&PV Code in terms of their applicability in designing high temperature CSP receivers. With some restrictions and modifications, the conditions assumed in the design rules in Section III, Division 5 of ASME B&PV Code are found to closely resemble the loading conditions of CSP receiver, including accounting for the interaction between creep and fatigue damage. The paper applies the proposed design rules to an external tubular receiver design and discusses several lessons learned from the design study. The creep damage accumulation due to high thermal stresses resulting from circumferentially non-uniform flux distribution is found to control the design of CSP receivers. Several mitigation actions to improve the design life of receivers are also discussed.

Analysis and Experimental Investigation of High-Frequency Magnetic Flux Distribution in Mn-Zn Ferrite Cores

This article presents a comprehensive investigation of the high-frequency magnetic flux distributions in manganese-zinc ferrite ring cores. New experimental characteristics are presented and used in the flux modeling. The flux distribution is predicted by a one-dimensional analytical model, a transmission-line model, and finite-element analysis. The models are used to investigate the high-frequency effects, such as skin depth and dimensional resonance. A complete experimental validation is presented. The nonuniform magnetic flux distributions are experimentally validated for two Mn-Zn materials: 3F36 and 3E10. The low permeability 3F36 material performance can be significantly degraded by dimensional resonance. However, the high permeability 3E10 material degrades due to the skin effect. The presented analytical methods show a very good correlation with the measurements.

Effects of Imperfect Assembly and Magnetic Properties on the Three-Pole AMB System

This study is concerned with a three-pole active magnetic bearing (AMB) system with assembly error and non-uniform flux distribution. The assembly error, which is the result of the misalignment of the back-up bearing and the stator of AMB, induces strong nonlinear uncertainty in the AMB dynamics. The non-uniform flux distribution, which is mainly due to non-uniform material properties, manufacturing errors, etc., makes the magnetic force model more complicated. A stable-levitation controller is designed in consideration of the above factors. The controller is designed using the method of feedback linearization and integral sliding mode control (ISMC). Both simulation and experimental results indicate that the rotor can be levitated to the center of the back-up bearing, verifying the effectiveness of the proposed stable-levitation controller.

Inverse Design of Local Solar Flux Distribution for a Solar Methanol Reforming Reactor Based on Shape Optimization

In this work, an inverse design method that couples the multi-physics model for a solar trough thermochemical reactor (SPTR) and shape optimization model is proposed to find out optimal solar flux distribution for maximizing overall reactor performance. The gradient-based segmentation method is applied to convert the continuous solar flux into step-like flux to guide the concentrator system design. Performance comparisons among uniform flux, linear decreasing flux, and the optimized non-linear flux are also conducted to discuss the reliability of SPTR performance improvement. The results show that the optimized non-linear solar flux can improve the methanol conversion, solar thermochemical conversion, and hydrogen yield of SPTR by 2.5, 3.3, and 2.4%, respectively, compared with the uniform flux. This is attributed to the fact that the optimized non-uniform flux distribution enhances the synergy between temperature and reaction fields, and achieves a better match between spatial solar flux supply and local energy demand by reactions. Also, it is shown that the optimized step-like flux, achieved by regressing the optimized non-linear flux, can perfectly maintain SPTR performance and is effective in boosting SPTR performance under different operating conditions.

Quantifying the interacting mechanisms in shape evolution of sessile volatile droplets

Non-uniform distribution of interfacial mass flux across an evaporating droplet will subsequently induce a temperature gradient across the liquid-air interface, and result in thermal Marangoni stress that reforms the flow field inside the droplet. Recent study (Shiri, et al. Phys. Rev. Lett. 2021, Yang, et al. Langmuir 2022) confirmed the role of thermal Marangoni effect on the shape of evaporating single component droplets on completely wetting substrates. Nevertheless, a comprehensive evaluation of the interacting mechanisms is still lacking due to the intrinsic limitation of experimental techniques to decompose the different influence factors. To this end, we formulate a mathematical model to simulate the evaporation of volatile droplets on completely wetting substrates based on the lubrication theory. With this model, we elucidate the interacting physical mechanisms that governs the droplet kinetics during phase change, which includes the capillary effect, the thermal Marangoni effect, the interface motion due to evaporation, as well as the removal of energy barriers by precursor film. A phase diagram is summarized in terms of the Knudsen number and liquid-to-solid Biot number, which quantifies the prevalence of the interacting effects.

A Bi-Layer Dense/Porous Solid Electrolyte Interphase for Enhanced Lithium-Metal Stability

Due to its high theoretical capacity and low electrochemical potential, lithium metal is a highly investigated anode for next-generation high-energy batteries. However, the unstable chemical and topographical heterogeneous surface of lithium gives rise to safety and efficiency concerns that prevent it from being utilized in practical applications. Exposure to electrolyte leads to non-uniform, mixed organic-inorganic solid-electrolyte interphase (SEI) formation, starting a cascading to non-uniform flux distribution, consumption of active materials, and dendrite growth. The SEI is the key feature that will lead to harnessing the capabilities possible with lithium metal.In this work, the formation of a closed-host bi-layer solid electrolyte interphase (SEI) improves the stability of lithium anode. This is successfully realized by forming an interconnected porous LiF-rich artificial SEI in contact with Li metal, and a dense, stable in-situ formed upper layer SEI. The porous layer increases the number of Li/LiF interfaces, which reduces local volume fluctuations and improves Li+ diffusion along these interfaces. Additionally, the tortuous porous structure guides uniform Li+ flux distribution and mechanically suppresses dendrite propagation. The dense upper layer of the SEI accomplishes a closed-host design through reaction with LiNO3 additive and prevents continuous consumption of active materials seen without the additive included in the electrolyte. The duality of a dense top layer with porous bottom layer led to extended cycle life and improved rate performance, evidenced with symmetric cell testing, as well as full cell testing paired with sulfur and LiFePO4 (LFP) cathodes. This work is a good example of a rational design of the SEI, based on comprehensive consideration of various critical factors to improve Li-metal anode stability, and highlights a new pathway to improve cycling and rate performances of Li metal batteries. Figure 1

Thermal Analysis of a Solar Concentrating Collector with Nonuniform Flux Distribution.(Dept.M)

This paper presents a new approach to the thermal analysis of a solar concentrator. The Signal Flow Graph technique is applied to solve the heal Transfer problem in a flat receiver subjected to nonuniform flux distribution. Signal Flow Graph allows in a more easy graphical form to express the essential properties of the analyzed system, and directly obtain any parameter from the graph structural properties. With this method, there is no need of assuming uniform flux distribution over the whole receiver surface as in Hottel-Whillier-Woertz-Bliss approach, A Computer program has been established to obtain the thermal performance under different design and operating conditions using both approaches. In order to verify the theoretical results, an experimental concentrator was built with, one glass cover, flat receiver of 25 cm width and 94 cm length, The receiver is insulated with form plates of 3 cm thickness and fitted with two headers to supply the fresh water uniformly in the length direction. The reflecting surface is formed of unequal mirror segments which are arranged to concentrate most of the falling solar radiation on the upper third of the receiver surface. The set-up is suitably instrumented to measure the temperature at different points and the water mass flow rate through the receiver. The total and beam solar radiation intensities as well as the ambient temperature are also measured during the experimental work. Comparison between the predicted and measured results have shown that the thermal performance as calculated by the Signal Flow Graph is more fitted with the experimental results than that obtained by the HWWB approach. Therefore, the Signal Flow Graph approach is seen to be an easy and precise technique for the thermal analysis of concentrating collectors with nonuniform flux distribution on the receiver surface.

Thermal-fluid-mechanical analysis of tubular solar receiver panels using supercritical CO2 as heat transfer fluid under non-uniform solar flux distribution

The tubular receiver is one of the most attractive options for the directly heated supercritical CO2 (S-CO2) solar receiver, of which tubular panels are the basic modules. Due to the high working pressure and the non-uniform solar flux distribution, the thermal-fluid-mechanical analysis becomes an important research topic for the S-CO2 solar receiver. In this paper, the thermal-fluid-mechanical characteristics of the S-CO2 tubular receiver panel under non-uniform solar flux distribution using S-CO2 as the heat transfer fluid is numerically studied. The effects of solar flux distribution and flow arrangements on the thermal and mechanical performances are discussed with emphasis. The results indicate that: (1) the non-uniform solar flux of the receiver panel will result in the increase in the thermal loss and the thermal stress; (2) adjusting the flow arrangement to match the solar flux distribution can decrease thermal loss and thermal stress; (3) the proposed matching factor can be used as an indicator for the thermal-mechanical performances, and a larger matching factor means a good performance; (4) although the I-type flow arrangement lead to uneven flow allocation with more fluid in middle tubes, it cannot always yield good performances under Gaussian-shaped solar flux distribution, which is greatly depended on the standard deviation of the Gaussian distribution; (5) an ideal flow allocation can be easily determined by the matching factor being set to 1, which provides guidelines for the design and optimization of the tubular solar receiver panel.

Buoyancy effects on convective heat transfer of supercritical CO2 and thermal stress in parabolic trough receivers under non-uniform solar flux distribution

The buoyancy influenced heat transfer characteristics of S-CO2 have been investigated widely in previous studies, but limited to the conditions with constant wall temperature or constant heat flux. The present study numerically investigates the buoyancy effects on the convective heat transfer of S-CO2 and the thermal stress in parabolic trough receivers (PTRs) under the non-uniform solar flux distribution based on a coupled optical-thermal-fluid-mechanical numerical model. The results indicate that the drastic density variation associated with the large temperature gradient of the fluid occurs on the cross-section under the non-uniform solar flux distribution, which further induces the secondary flow. As the secondary flow improves the synergy between the velocity vector and the temperature gradient, the bulk average heat transfer is prominently enhanced due to the buoyancy effect. However, the buoyancy effects on the local heat transfer characteristics are more complex. The buoyancy effect enhances the heat transfer at the bottom but impairs the heat transfer at the top, and the heat transfer enhancement area is expanded along the flow direction. The temperature distribution in the absorber tube wall is greatly flattened due to the buoyancy effect, and the thermal stress is consequently reduced. The buoyancy effects on the thermal and mechanical performances become less significant with the increase in the operating pressure, the inlet velocity and the inlet temperature but with the decrease in DNI. The buoyancy effect in the PTR under non-uniform solar flux distribution can be ignored when Se/Re<0.3, Ri<0.04, Bup<0.002, Buj<80, or Grq/Grth<70.