Finite Wall Thickness Research Articles

Direct Numerical Simulation of Turbulent Spray Combustion in the SpraySyn Burner: Impact of Injector Geometry

Spray combustion is one of the most important applications connected to modern combustion systems. Direct numerical simulations (DNS) of such multiphase flows are complex and computationally very challenging. Ideally, such simulations account for atomization, breakup, dispersion, evaporation, and finally ignition and combustion; phase change, heat and mass transfer should be considered as well. Considering the complexity of all those issues, and to simplify again the problem, virtually all DNS studies published up to now replaced the injector geometry by an approximated, simple configuration, mostly without any walls within the DNS domain. The impact of this simplification step is not completely clear yet. The present work aims at investigating the impact of a realistic injector geometry on flow and flame characteristics in a specific burner (called SpraySyn burner). For this purpose, two cases are directly compared: one DNS takes into account the inner geometry of the injector, including walls of finite thickness; a second one relies on a simplified description, as usually done in the literature. It has been found that considering the details of the geometry has a noticeable impact on the evaporation process and ultimately on the flame structure. This is mostly due to the effect of recirculation zones appearing behind thick injector walls; though quite small, they are sufficient to impact the evolution of the flow and of all connected processes.

Hybrid meso-macroscopic simulation of three-dimensional natural convection combined with conjugate heat transfer

In this study, a hybrid model was developed to analyze the three-dimensional natural convection in a cubic cavity filled with a radiatively non-participating medium and bounded by thermally conductive finite thickness walls. Within this model, fluid flow was simulated by the mesoscopic lattice Boltzmann method. To determine the temperature in the solid and fluid regions, the finite difference technique was applied to solve macroscopic energy equation. Numerical modelling was performed for different Rayleigh numbers, heat diffusivity ratios and Biot numbers. It was found that flow behavior was slightly changed when varying the heat diffusivity ratio. Heat transfer rate at the hot wall was enhanced with an increase in the Biot number. Numerical performance of hybrid lattice Boltzmann model was more than 17 times higher than conventional finite difference technique combined with the vorticity – vector potential formulation.

The ratio of shear to elastic modulus of in-plane loaded masonry

When designing unreinforced masonry buildings, the wall stiffness and, consequently, the masonry elastic and shear modulus E and G are essential parameters. Current codes provide empirical estimates of the masonry elastic modulus and a ratio between the shear and elastic modulus, G/E. This ratio, commonly taken as 0.4, is not based on scientific evidence and there appears to be no consensus concerning its value and influencing parameters, meaning that current code standards might not accurately portray the shear deformations of masonry elements. To give the choice of the G/E ratio a theoretical foundation, this paper presents closed-form expressions for the G/E ratio of running-bond masonry that capture the effects of finite joint thickness, finite wall thickness and orthotropic block properties. Based on the geometry of blocks and joints as well as their elastic parameters, a validation of the developed expression using 3D finite element analyses shows good performance. For modern masonry typologies with hollow clay bricks, a G/E ratio of 0.20–0.25 is obtained. For historical masonry typologies, such as dry stacked or mortared stone masonry, as well as solid clay brick masonry, ratios between 0.30 and 0.40 are computed.

Impact of finite wavy wall thickness on entropy generation and natural convection of nanofluid in cavity partially filled with non-Darcy porous layer

This paper investigates the natural convection inside a partially layered porous cavity with a heated wavy solid wall; the geometry is encountered in compact heat exchangers. Alumina nanoparticles are included in the water to enhance the heat exchange process. The incidental entropy generation is also studied to evaluate the thermodynamic irreversibility. The nanofluid flow is taken as laminar and incompressible while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The Darcy number (Da), porosity of the porous layer ( $$\varepsilon$$ ), number of undulations (N), and the nanoparticles volume fraction ( $$\phi$$ ) are varied to assess the heat transfer and the incidental entropy generation. It is found that the waviness of the solid wall augments the average Nusselt number and minimizes the generation of entropy. The results show for some circumstances that the Nusselt number is augmented by 43.8% when N is raised from 0 (flat solid wall) to 4. It is also found that the porosity of the porous layer is a more crucial parameter than its permeability, where a 37.4% enhancement in the Nusselt number is achieved when the porosity is raised from 0.2 to 0.8.

Wave power extraction from a tubular structure integrated oscillating water column

Integrating wave energy converters with marine structures such as breakwaters, piles, and offshore wind turbines offers benefits in terms of wave power extraction, construction costs, and survivability. In this paper, the integration of an oscillating water column(OWC) into a vertical tubular structure is considered. The OWC chamber is enclosed by the tubular-structure with its submerged side partially open to the sea. As ocean waves propagate through the device, an air turbine installed at the top of the chamber can be driven to extract wave power. An analytical model based on potential flow theory and the eigen-function matching method is developed to solve the wave scattering and radiation problems of the device in finite water depths. Wave excitation volume flux, hydrodynamic coefficients, optimal turbine damping and power capture factor are evaluated. Upon successful validation, the model is applied to investigate the effect of the radius and finite wall thickness of the tubular-structure, the size and position of the opening on wave power extraction. We find that a thinner chamber wall thickness offers benefits to wave power extraction in terms of a broader primary band of power capture factor response, and that a broader and higher capture factor band can be achieved by increasing the height of the vertical opening.

Investigation of waveguide antenna arrays with layered dielectrics

A general methodology for calculating antenna arrays with layered dielectric is considered. To demonstrate the proposed methodology, we consider the solution of the problem of radiation of linear waveguide array. Plane-parallel waveguides have a finite wall thickness. Antenna array scans in E and H planes. This problem is solved using Fredholm integral equations of the second kind. To solve the problem, the entire domain of the electromagnetic field is divided into partial intersecting regions An example of constructing Green’s functions of selected partial regions with allowance for their dielectric filling is considered. The formulation of the boundary-value problem for the antenna array in the form of Fredholm integral equations of the second kind using the technique of dividing the determination domain into partial regions with Green’s functions allows us to solve the following problem: calculations of the antenna array with dielectric plugs in the waveguides and with a dielectric coating over the antenna array. This technique allows optimization of dielectric parameters with the aim of aperture matching of the antenna array. The calculation results of the dependence of the reflection coefficient on the phase shift between waveguides in the H-plane are presented. The calculations are performed for different values of the dielectric constant of the plugs in the waveguides and the dielectric constant of the dielectric layer above the antenna array. The influence of the geometric dimensions of the plugs in the waveguides and the dielectric coating above the array is studied.

Effect of finite wall thickness on entropy generation and natural convection in a nanofluid-filled partially heated square cavity

PurposeThe purpose of this paper is to study the effects of finite wall thickness on the natural convection and entropy generation in a square cavity filled with Al2O3–water nanofluid in the presence of bottom heat source.Design/methodology/approachThe moving isothermal heater was placed on the bottom solid wall. The vertical walls (left and right walls) were fully maintained at low temperatures. The rest of the bottom solid wall along with the top horizontal wall was kept adiabatic. The boundaries of the domain are assumed to be impermeable; the fluid within the cavity is a water-based nanofluid having Al2O3 nanoparticles. The Boussinesq approximation is applicable. The dimensionless governing equations subject to the selected boundary conditions are solved using the finite difference method. The current proposed numerical method is proven excellent through comparisons with the existing experimental and numerical published studies.FindingsNumerical results were demonstrated graphically in several forms including streamlines, isotherms and local entropy generation, as well as the local and average Nusselt numbers. The results reveal that the thermal conductivity and thickness of the solid wall are important control parameters for optimization of heat transfer and Bejan number within the partially heated square cavity.Originality/valueAccording to the past research studies mentioned above and to the best of the authors’ knowledge, the gap regarding the problem with entropy generation analysis and natural convection in partially heated square cavity has yet to be filled. Because of this, this study aims to investigate the entropy generation analysis as well as the natural convection in nanofluid-filled square cavity which was heated partially. A square cavity with an isothermal heater located on the bottom solid horizontal wall of the cavity and partly cold sidewalls are essential problems in thermal processing applications. Hence, the authors believe that this present work will be a valuable contribution in improving the thermal performance.

HEAT FLUX JUMP METHOD AS A POSSIBILITY OF CONTACTLESS MEASUREMENT OF LOCAL HEAT TRANSFER COEFFICIENTS

This article deals with the derivation of the temperature response of the finite thickness wall, which is heated by heat flow, as a possibility to measure the local values of the heat transfer coefficient with a very high spatial resolution. In addition to its own experimental measurement technique, it is also possible to use this derivation to describe the gradual heating of the wall while using the temperature oscillation (TOIRT) method for the heat transfer measurement. The system of the partial differential equations and the boundary and initial conditions is solved by a transformation into Laplace’s space, where the task is easier to solve. At the end of the article, the results of the analytical solution are compared with a numerical solution of this problem.

Conjugate natural heat transfer scrutiny in differentially heated cavity partitioned with a conducting solid using the lattice Boltzmann method

In the present paper, we numerically investigated the two-dimensional conjugate heat transfer problems in a unitary computational domain containing both the solid and fluid regions. The physical problem configuration consists of two adiabatic horizontal walls of finite thickness and two vertical walls; the left one is maintained at hot temperature Th and the right one is maintained at cold temperature Tc. The lattice Boltzmann method (LBM) based on the BGK model has been used to simulate laminar natural convection in the partitioned air-filled cavity with a heat-conducting solid. In the interface boundaries of the heat-conducting solid, the continuity of temperature and heat transfer is considered. A series of numerical simulation is carried out over a wide range of the Rayleigh number (Ra = 103–106), the thermal conductivity ratio kr and the solid partition thickness (δ = 1–95℅) and its horizontal position. The results show that the partition reduces the heat transfer rate in the cavity. For a centered partition (Xs = 0.5), the average Nusselt number decreases almost linearly with partition thickness for δ ≤ 0.45; however, it increases for δ ≥ 0.45 due to the confinement in the thin fluid regions. For Ra = 105, the heat transfer rate decreases with the partition position until a critical value close to 0.325 and rises slightly until Xs = 0.5. The critical position value decreases with the Ra number increase and it is close to 0.2 for Ra = 106 where Nu = 3.766. The heat transfer rate is enhanced with the increase in thermal conductivity. Correlations of the average Nusselt numbers are obtained as a function of Rayleigh number.

The effects of exothermic catalytic reactions upon combined transport of heat and mass in porous microreactors

Microreactors for chemical synthesis and combustion have already attracted significant attention. Exothermic catalytic activity features heavily in these devices and thus advective-diffusive transport is of key importance in their analyses. Yet, thermal modelling of the heat generated by catalytic reactions on the internal surfaces of porous microreactors has remained as an important unresolved issue. To address this, the diffusion of heat of catalytic reactions into three phases including fluid, porous solid and solid walls is investigated by extending an existing interface model of porous media under local thermal non-equilibrium. This is applied to a microchannel fully filled with a porous material, subject to a heat flux generated by a catalytic layer coated on the porous-wall boundary. The finite wall thickness and viscous dissipation of the flow kinetic energy are considered, and a two-dimensional analytical model is developed, examining the combined heat and mass transfer and thermodynamic irreversibilities of the system. The analytical solution is validated against the existing theoretical studies on simpler configurations as well as a computational model of the microreactor in the limit of very large porosity. In keeping with the recent findings, the wall thickness is shown to strongly influence the heat and mass transport within the system. This remains unchanged when the symmetricity of the microchannel is broken through placing walls of unequal thicknesses, while deviation from local thermal equilibrium is significantly intensified in this case. Importantly, the Nusselt number is shown to have a singular point, which remains fixed under various conditions.

A lattice Boltzmann analysis of the conjugate natural convection in a square enclosure with a circular cylinder

In this paper, an improved lattice Boltzmann model that incorporates the effect of heat capacity is adopted to simulate the conjugate natural convection in a square enclosure with a circular cylinder, and the square cavity considered is bounded by four finite thickness and conductive walls. Influences of Rayleigh number, wall thermophysical properties, and wall thickness on streamlines, isotherms and Nusselt number are analyzed. It is found that the heat transfer rate obtained for different wall thicknesses is usually smaller than that for the zero wall thickness, while this difference is not apparent for a larger thermal conductivity ration. Additionally, the study also shown that the increase of the outer wall thickness tends to decrease the heat transfer rate. The effects of the geometric parameter, including aspect ratio and vertical cylinder location, on heat transfer are also studied.

Conjugate heat transfer in a duct using nanofluid by two-phase Eulerian–Lagrangian method: Effect of non-uniform heating

The underlying physics behind the effect of non-uniform heating on the heat transfer characteristics for flow of Al2O3-water nanofluid through a duct having finite wall thickness subjected to sinusoidal heat flux has been numerically investigated in this study. The nanofluid is modelled as a single fluid with two phases using the Eulerian-Lagrangian formulation. The concomitant implications of thermal conductivity ratio of solid to fluid, outer tube diameter to inner tube diameter ratio, amplitude of sinusoidal heat flux and volume fraction of nanoparticles on the thermal attributes have been explored and quantified by local and average Nusselt number. The results elucidate a close resemblance between the nature of the variation of local Nusselt number and the applied heat flux, particularly at the intermediate region of the channel. The results also reveal a damping effect on the conjugate heat transfer due to the increase in conducting wall thickness, irrespective of the volume fraction of nanofluid. The confluence of various key parameters on the variation of the magnitudes of the crests and troughs of local Nusselt number are analyzed and this variation proves to be a prime factor in determining the variation of average Nusselt number. Furthermore, the average Nusselt number decreases with amplitude of heat flux. The rate of heat transfer for flow of base fluid through a duct having finite wall thickness is always lower in case of non-uniform heating. However, the use of nanofluid as the heat transfer medium can compensate the decrement in heat transfer due to non-uniform heating.

The features of the use of the waveguide radiators in smart antenna systems

The features of the use of finite waveguide antenna arrays in the structure of modern smart antenna systems are considered. The paper deals with the problem of diffraction of an electromagnetic wave on a finite waveguide antenna array scanning in the E-plane. Antenna array consists of five radiating elements. The open ends of the waveguides are surrounded by a metal screen. The resonator coupling region was chosen as matching elements. The solution of the problem is carried out by the integral equation method on the basis of the selection of overlapping regions. The problem reduces to solving the Fredholm integral equation of the second kind. An array of infinitely thin plates and that of waveguides with a finite wall thickness are considered. The main regularities for choosing the optimal geometric dimensions of the antenna array are established. Studies were carried out for arrays with a number of elements from five to fifteen. The analysis of edge effects in the final antenna array is carried out. It is shown that the introduction of a resonator region into a five-element lattice makes it possible to expand the sector of the radiation angles and avoid the effect of blinding. It is shown that this statement is valid not only for five-element lattices, but also for arrays with a large number of radiating elements. The radiation patterns are calculated. The coefficients of mutual coupling in an array with five elements are investigated. General recommendations for choosing optimal sizes of the resonator coupling region of radiators are considered.

Influences of tube wall on the heat transfer and flow instability of various supercritical pressure fluids in a vertical tube

The subcritical steam generators in the current high temperature gas-cooled reactor pebble-bed module, HTR-PM, in China can be replaced by supercritical steam generators to better coordinate the reactors and the supercritical steam turbine unit to improve the thermal efficiency with no fluid phase change at supercritical pressures. This study then numerically analyzes the heat transfer and flow instabilities of supercritical pressure fluid flow in a vertical tube with zero or finite-thickness walls. The wall thickness has negligible effect on the heat transfer at supercritical pressure water at steady state. However, for transient calculations, the flow rate oscillates intensely beyond a critical heat flux with the zero-thickness wall, while the flows in tubes with finite-thickness walls are very different. The wall properties including density, specific heat and thermal conductivity are varied to analyze why the oscillations are suppressed by the finite-thickness wall. The flow and heat transfer characteristics and the heat stored in the wall compared with the total power are presented during the heating process at various moments. The flow instabilities are also analyzed for water at various pressures and CO2 to analyze the effects of the fluid properties.

A new modelling method for superalloy heating in resistance furnace using FLUENT

The simulation of heating process of superalloys is of great significance to predict the temperature distribution and equilibration time of workpiece. In this paper, a new method was proposed to simulate the heating process of superalloy billet in resistance furnace for all strategies of thermal schemes using commercial CFD software FLUENT. In the model, numerical analysis of natural convection and surface thermal radiation in a chamber electric furnace having heat-conducting solid walls of finite thickness with a heat source located in the side and top walls of the furnace in conditions of convective heat exchange with environment has been carried out, and such conjugate heat transfer process was solved by FLUENT solver. Furthermore, a PID methods was proposed to control the energy source of the resistance wires based on FLUENT UDF, in order to regulate the furnace temperature according thermal scheme. This model was validated through temperature measurement experiment in a small chamber resistance furnace. Compared with the measured data, the model was adequate for predicting the temperature profile and equilibration time of superalloy.

Rectangular Waveguide Cross-Guide Couplers: Accurate Model for Full-Band Operation

In this letter, a precise model for accommodating the cross-guide couplers is proposed and validated. This includes accurate formulas for the polarizabilities of cross slots as well as the effect of finite wall thickness on the coupling level. The proposed model shows a leading performance compared with previously published models in the literature showing a maximum error of 2.5%. The experimental validation shows an excellent agreement with the simulated results.

Characterization of the lid-driven cavity magnetohydrodynamic flow at finite magnetic Reynolds numbers using far-field magnetic boundary conditions

The lid-driven cavity (LDC) flow is a canonic hydrodynamic problem. Here, a 3D LDC flow of electrically conducting, incompressible fluid is studied numerically in the presence of a strong magnetic field, which is applied parallel to the lid plane and perpendicular to the direction of the lid motion. The cavity has electrically conducting walls of finite thickness and an infinitely thin moving lid. The problem is characterized by three dimensionless parameters: the Reynolds number (Re), the Hartmann number (Ha), and the magnetic Reynolds number (Rem). The primary research focus is on the effect of Rem, which was changed in the study from Rem ≪ 1 to the maximal Rem = 2000 at which dynamo action may be expected, while Ha = 100 and Re = 2000. The computational approach is based on the utilization of far-field magnetic boundary conditions by solving the full magnetohydrodynamic (MHD) flow problem at finite Rem for a multi-material domain composed of the inner conducting liquid, conducting walls, and sufficiently large insulating outer domain called “vacuum” (the induced magnetic field vanishes at the vacuum boundaries) using a fractional-step method. The computed results show many interesting features with regard to the effect of Rem on the MHD boundary layer and the bulk flow, generation of a magnetic field and its penetration into vacuum, energy balance, tendency of the magnetic field to become frozen in the fluid and associated magnetic flux expulsion, transition to unsteady flows, and self-excitation of the magnetic field and the associated dynamo-type action at high Rem.

Unsteady Conjugate Natural Convective Heat Transfer and Entropy Generation in a Porous Semicircular Cavity

The problem of unsteady conjugate natural convection and entropy generation within a semicircular porous cavity bounded by solid wall of finite thickness and conductivity has been investigated numerically. The governing partial differential equations with the corresponding initial and boundary conditions have been solved by the finite difference method using the dimensionless stream function, vorticity, and temperature formulation. Numerical results for the isolines of the stream function, temperature, and the local entropy generation due to heat transfer and fluid friction as well as the average Nusselt and Bejan numbers, and the average total entropy generation and fluid flow rate have been analyzed for different values of the Rayleigh number, Darcy number, thermal conductivity ratio, and the dimensionless time. It has been found that low values of the temperature difference reflect the entropy generation, mainly in the upper corners of the cavity, while for high Rayleigh numbers, the entropy generation occurs also along the internal solid–porous interface. A growth of the thermal conductivity ratio leads to an increase in the average Bejan number and the average entropy generation due to a reduction of the heat loss inside the heat-conducting solid wall.

Mixed convection with entropy generation of nanofluid in a lid-driven cavity under the effects of a heat-conducting solid wall and vertical temperature gradient

Mixed convection combined with entropy generation of an alumina–water nanofluid in a lid-driven cavity with a bottom solid wall of finite thickness and conductivity has been examined numerically. Governing equations formulated in dimensionless stream function and vorticity variables on the basis of a single-phase nanofluid model under the effect of Brownian diffusion have been solved by finite difference method of the second-order accuracy. The effects of Richardson number (Ri = 0.01–10.0), thermal conductivity ratio (1.0 ≤ K ≤ 20.0), solid wall thickness (0.1 ≤ δ ≤ 0.3) and nanoparticles volume fraction (0 ≤ ϕ ≤ 0.05) on streamlines, isotherms and isentropic lines as well as average Nusselt number at solid–fluid interface and rate of fluid flow have been analyzed. It has been found that an increase in nanoparticles volume fraction leads to the heat transfer enhancement and reduction of the average Bejan number.

Longwave Stability of Two Liquid Layers Coating Both Sides of a Thick Wall in the Absence of Gravity

A system of two coupled nonlinear equations was calculated to describe the thermocapillary evolution of the free surface deformations of two liquid layers coating both sides of a wall of finite thickness and thermal conductivity in the absence of gravity. The equations were obtained under the small wavenumber approximation. A temperature gradient appears perpendicular to the liquid-wall-liquid system due to the temperature difference between the atmospheres outside the free surfaces of both fluid layers. The linear growth rate of the system was investigated with respect to a variety of parameters. Under some conditions, two stationary modes and one oscillatory mode between them were found. The second stationary mode was concluded to be always stable. It was also found that under different conditions only stationary convection is possible. These results depended on the relative thickness of the two fluid films. It is of interest to know if the coupled free surface perturbations presented a nonlinear sinuous or varicose mode. Thus, a two-dimensional numerical analysis was performed to find out which conditions lead to the sinuous or to the varicose mode of instability.