Non-uniform Boundary Conditions Research Articles

Application of 2-D GDQ Method to Analysis a Thick FG Rotating Disk with Arbitrarily Variable Thickness and Non-Uniform Boundary Conditions

Application of 2-D GDQ Method to Analysis a Thick FG Rotating Disk with Arbitrarily Variable Thickness and Non-Uniform Boundary Conditions

Comparative numerical analysis between butt and lap joints of Mg alloy friction stir welding with considering tilted tool effect

Magnesium (Mg) alloy, as an important lightweight structural metal, can be effectively joined by the friction stir welding (FSW) method. Understanding FSW temperature and material flow coupling process in butt and lap welding configurations has important theoretical significance. In this study, the tilted tool induced incomplete contact distance is calculated by process parameters and slip rate, and the deflection of the contact interface is related to the tool torque. The non-uniform boundary conditions are considered. The numerical model is proposed and experimentally validated by using the measured temperatures and thermo-mechanically affected zone (TMAZ) profiles. The comparative numerical analysis between butt and lap welding with three levels of process parameters is further conducted. The peak temperature and material flow velocity along the specified circumferences in FSBW are more than 10 K and 4 mm/s higher than these in FSLW, respectively. When the rotation rate increases from 600 rpm to 800 rpm, the peak temperature and material flow velocity along the specified circumferences increase about 20 K and 9 mm/s, respectively. When the welding speed decreases from 150 mm/min to 30 mm/min, the temperature and material flow velocity fluctuations along the specified circumference decreases about 25 K and 14 mm/s, respectively.

Application of von-Karman model for laminated composite singly curved shells with non-uniform boundary conditions

The industrial applications of singly curved shells significantly increased in modern engineering structures and several of those have non-uniform boundary conditions. A detailed relative performance study for the non-uniformly restricted shells can popularize their use further among practicing engineers. The literature review confirms that there is dearth of research studies in this area. This paper aims to fill up that void. A finite element code of C0 continuity combining von-Karman strains, first order shear deformation theory and eight noded curved elements is proposed. Wide variety of shell problems are solved for different boundary conditions, laminations, radii of curvatures, thickness, and plan dimensions. Relative nondimensional deflections and fundamental frequencies are studied for varying boundaries. It is concluded that although the performances of shells are comparable for different boundaries, the shells with CCCC edges offer better performances. These shells should have longer span along the arch direction, a symmetric 16°/-16°/-16°/16° laminate, side/thickness = 100, and radius of curvature/plan = 0.75 to achieve minimum deflection and maximum fundamental frequency.

Microscale Thermal–Structural Modeling for Carbon Fibers Subjected to a Hypersonic Boundary Layer

With regard to the thermal protection system, the thermal–structural responses of modern ablative materials are of primary importance in many aspects, including material selection and sizing. Due to the intricate nature of their porous structure and complicated thermal conditions they are subjected to, ablative materials may exhibit unexpected behavior, which can potentially lead to material failure. In this study, two solvers—a direct simulation Monte Carlo solver and a finite-volume-based material response solver—are coupled together to predict the microscale thermal–structural performance of a thermal protection system material like phenolic impregnated carbon ablator. In this approach, individual fibers are modeled at the microscale, which provides valuable knowledge of porous media behavior. Nonuniform boundary conditions, including the heat flux and external force, are captured by the direct simulation Monte Carlo solver, and the detailed thermal and structural performance of the fiber is captured by the material response solver. The results show that individual fibers do not fail based on the temperature gradient and applied aerodynamic forces. However, it is shown that the attachment points of the fibers are the most vulnerable. This vulnerability can potentially lead to a breakdown of the binders, which would separate fibers and cause material failure.

The effect of non-uniform inlet boundary conditions on the performance of the multiphase pump

Multiphase pump is an important equipment for oil and gas transportation. The gas-liquid distribution pattern at the inlet of a multiphase pump is crucial to its performance. We propose through an experiment that slug flow and annular flow are the main forms of gas-liquid distribution at the inlet of multiphase pumps. The effects of different flow patterns on the performance of multiphase pumps were investigated through numerical simulations and experimental tests. The results show that the multiphase pump is best adapted to the homogeneous bubble model, followed by the elastic flow and poorly by the annular flow. The energy conversion characteristic of annular flow is poor, and the higher the GVF is, the more obvious this characteristic is. The pressure distribution in the outlet region of the guide vane of the slug flow model is the most inhomogeneous, thus creating a larger vortex scale. The decrease in pressurization of the annular flow is most obvious with increasing GVF. At 30 % GVF, it decreased by 43 kPa compared to the uniform bubble flow model. The different flow patterns have a large effect on the impeller performance, but the distribution of the gas-liquid two-phase at the guide vane outlet tends to stabilize. The significance of this study is to further understand the performance of the first stage impeller of multiphase pumps under special working conditions, and then provide reference for the overall design of multistage pumps to broaden the scope of multiphase pump applications.

Thermal analysis for laminated plates with arbitrary supports under non-uniform temperature boundary conditions

This paper aims to investigate thermal behaviors of composite laminated plates with different supports under non-uniform temperature boundary conditions. The thermo-elastic solutions of temperature, displacements, and stresses for the laminated plate with arbitrary layer numbers and thickness are obtained based on the three-dimensional theory of thermoelasticity. By applying the Fourier law of heat conduction and the thermoelastic equations, the state-space equations are established by employing the temperature, heat flux, displacements, and stresses as state variables without the hypothesis of displacement form. The differential quadrature method is introduced to discretize the in-plane state variables. On the basis of the continuities of state variables at the interfaces in the laminated plate, the relationships of temperature, heat flux, displacements, and stresses between the top and bottom surfaces can be derived. By simultaneously considering temperature and mechanical boundary conditions applied to the surfaces of the laminated plate, the initial state variables for temperature, displacements, and stresses can be determined uniquely. The errors in the temperature, displacements and stresses resulting from the differential quadrature method can be eliminated by incrementally augmenting the number of sampling points in the convergence study. The accuracy of the present method is thoroughly verified by comparing the current results with both the finite element solutions and the findings reported in previous literature. Finally, the influences of surface temperature, length-to-thickness ratios, material properties, layer numbers, and support types for the distributions of the temperature field, displacements, and stresses in the laminated plate are discussed in detail.

Free Convection in a Square Ternary Hybrid Nanoliquid Chamber with Linearly Heating Adjacent Walls.

In this study, mathematical modeling of the energy transfer and flow characteristics of ternary nanoliquid in a square enclosure is performed. In the cavity considered, the left and bottom borders are warmed uniformly or non-uniformly when the rest of the borders are cooled. The robust finite element method with quads and triangles as elements is used to work out the control equations of the problem. The current study is validated against previously published works, and good agreement is shown. The isolines are investigated for various Rayleigh numbers at uniform and non-uniform thermal boundary conditions. The impact of ternary hybrid nanofluids on the mean Nusselt number at hot borders is explored in dependence on the Rayleigh number and nanoparticle concentration. A comparative study of different fluids for the mean Nusselt number at heated borders is also conducted and analyzed with appropriate graphs and tables. It has been shown that ternary nanofluids can be more effective compared to mono- and hybrid nanofluids, with a more essential growth of the energy transport rate with nanoadditives concentration.

Evaluating soil water movement and soil water content uniformity under sprinkler irrigation with different soil texture and irrigation uniformity using numerical simulation

Water movement and its distribution uniformity in the soil are essential for the design of sprinkler irrigation systems. They are both crucial factors influencing nutrient migration and the productivity of crops. In this study, a new numerical simulation method was proposed to investigate the soil water movement in sprinkler irrigation under nonuniform infiltration boundary conditions using COMSOL software. Besides, two soil tank experiments were conducted to test the reliability of the simulation model. Finally, the model was applied to evaluate the effects of sprinkler irrigation uniformity, soil texture, and initial soil water content on soil wetting patterns and soil water content uniformity. The results showed that the COMSOL-2D predictions of the vertical wetting fronts were in good agreement with the experimental data. The soil texture and initial soil water content influenced the soil wetting pattern and the risks of surface runoff and deep percolation in sprinkler irrigation systems. When the water application rate was 11.35 mm h−1 with an irrigation duration of 10 h, it was easy to cause surface runoff in silty clay loam while deep percolation in loamy sand. Additionally, when the initial soil water content is high, it should be better to avoid irrigation or cut down the irrigation duration to prevent percolation. The water within the soil was more uniformly distributed than that applied through a sprinkler irrigation system. The uniformity coefficient of soil water content distribution (CUs) increased from 87.75 % to 95.56 %, as the uniformity coefficient of sprinkler irrigation (CU) increased from 40.74 % to 82.41 %. Although a higher initial soil water content brought a higher soil CUs value, it also led to a higher risk of percolation. The experimental and simulation results indicated that the COMSOL-2D model could be used to accurately simulate soil water movement in sprinkler irrigation and determine the suitable operation mode of low-pressure sprinklers.

Finite Difference Method for Solving the Two-Dimensional Laplace Equation in Curvilinear Coordinates

Abstract This paper presents a numerical method for solving the two-dimensional Laplace equation in curvilinear coordinates using a finite difference scheme. Laplace equation is a differential equation used to describe various physical phenomena studied within different branches of engineering. The two-dimensional Laplace equation has analytic solutions only for simple shaped domains and simple boundary conditions (first and second kind). Even so, the results are usually complicated to interpret and use. The present paper proposes a method to solve the equation for domains bounded by complex inner and outer curves. The boundary curves are defined by a set of points from which the equations of curves are approximated by using Fourier series. The domain is generated by blending the two curves using a blending function. The results are a set of continuous parametric equations which are defining the domain in angle and radius variables. Following a method presented in the literature, the Laplace equation is transformed from Cartesian coordinates to curvilinear coordinates, as the Fourier series is easily differentiable. Next, the new Laplace equation is approximated using the finite difference method and a MATLAB code is developed to solve the system of linear equations using successive over-relaxation method (SOR). The presented method is used to simulate steady two-dimensional heat conduction in a polygonal shape domain, with uniform and non-uniform Dirichlet boundary conditions. Results are analyzed in order to determine the model’s precision, speed and convergence criteria.

Displacements and stresses around a circular tunnel in an elastic medium with pseudo-static horizontal earthquake body forces

This manuscript presents an analytical solution based on the complex variable approach for computing displacements and stresses around a single circular tunnel in a linear elastic medium in the presence of pseudo-static horizontal earthquake body forces. The solution has been obtained with the imposition of uniform as well as non-uniform radial displacement boundary conditions along the tunnel’s periphery taking the ground volume loss (GVL) as a governing input parameter. The non-uniform radial displacements’ boundary condition along the tunnel periphery has been modelled by using the Gaussian distribution function. The effects of the distribution of the tunnel’s peripheral displacements, Poisson’s ratio of the continuum and the depth to radius of the tunnel on the results have been examined. Necessary validation exercise, in the presence of horizontal earthquake acceleration, has also been carried out by comparing the obtained results with that computed on the basis of the finite element method. The results were also compared with that reported in literature. It was observed that with an increase in the pseudo static acceleration, there is (i) a significant increase in the horizontal displacements, (ii) a generation of non-symmetric displacement and stress pattern, (iii) an increase in the shear stresses, and (iv) the development of high deviatoric stress zones around the tunnel periphery.

Effect of inlet gas and liquid velocity profiles on one-group interfacial area transport equation in a vertical large rectangular channel

Bubbly flows appear in many heat and mass transfer equipment. The interfacial area concentration is a critical parameter in determining the performance of the heat and mass transfer systems. The one-dimensional one-group interfacial area transport equation (IATE) was developed based on area-averaged bubbly flow data collected under uniform inlet flow boundary conditions. The applicability of the IATE to the flow systems with non-uniform inlet flow boundary conditions was not comprehensively examined. This study investigated the effect of inlet liquid and gas velocity profiles on measured interfacial area concentration changes along the flow direction. The data used in this study were collected for vertical upward air-water two-phase flow in a rectangular channel with a gap length of 10 mm and width of 200 mm. The test conditions were the superficial gas velocity ranging from 0.0870 to 0.288 m/s and the superficial liquid velocity ranging from 0.515 to 2.53 m/s. The interfacial area concentrations with uniform and non-uniform inlet flow boundary conditions measured in a large vertical rectangular channel were compared under the same area-averaged flow rate conditions. Then, the predictive capability of the IATE to the bubbly flow test data with uniform and non-uniform inlet flow boundary conditions was assessed. Some non-uniform inlet flow boundary conditions, including channel-center peaking of liquid flow (CPF), channel-center peaking of gas flow (CPG), single-side-wall peaking of liquid flow (SPF), and single-side-wall peaking of gas flow (SPG), significantly affected the interfacial area concentration changes along the axial location at relatively high superficial gas or liquid velocity conditions. The IATE's predictive capability deteriorated for several non-uniform inlet flow boundary conditions, including double-side-wall peaking of gas flow (DPG) and single-side-wall peaking of liquid flow (SPF), specifically at relatively high superficial liquid velocity conditions. The maximum percentage error of the interfacial area concentration prediction by the IATE for these non-uniform inlet flow boundary conditions reached 75%.

Development of a deployable Synthetic Aperture Radar antenna for a nanosatellite conceptual design

For a real-time maritime surveillance application in the extended territorial waters of New Zealand, this work aims to develop a viable concept design for a deployable Synthetic Aperture Radar (SAR) antenna to fit in a CubeSat design space. To trade off a large antenna aperture, which is essential to enhance SAR performance, and a high packaging efficiency, potentially ≤ 12U, a 4 m x 0.3 m reflectarray with a stiff-and-flexible and novel passive deployable system is selected as the most promising solution for this application. A High Strain Composite (HSC) structure with a shallow “tape-measure” inspired shape is presented to support the SAR reflectarray and compactly stow it through a rollable deployment system. The release of the elastic energy stored in the coiled structure will enable the deployment, and the structural stiffness will be provided by a boundary condition that maintains the naturally curved cross-section during stowage. With this design constraint, the transition zone (ploy region) that develops between the stowed and deployed state may significantly impact the stowage capabilities. The elastic behaviour of the structure will be analytically studied in terms of the change of curvatures and bending stiffness as they dominate the deformed shape in the coiling process. Existing analytical models that predict the ploy regions are considered to estimate the natural ploy length and the equivalent coil diameter. Finite Element (FE) models are developed to compare the analytical models and explore the stress field generated within the ploy region when the length of this region is forced to be shorter than the natural ploy length. FE model observations and data are also used to improve the analytical model that describes the deformed shape by imposing non-uniform boundary conditions on the curvatures’ field distribution within the ploy region.

Reduced order modelling using parameterized non-uniform boundary conditions in room acoustic simulations.

Quick simulations for iterative evaluations of multi-design variables and boundary conditions are essential to find the optimal acoustic conditions in building design. We propose to use the reduced basis method (RBM) for realistic room acoustic scenarios where the surfaces have inhomogeneous acoustic properties, which enables quick evaluations of changing absorption materials for different surfaces in room acoustic simulations. The RBM has shown its benefit to speed up room acoustic simulations by 3 orders of magnitude for uniform boundary conditions. This study investigates the RBM with two main focuses: (1) various source positions in diverse geometries, e.g., square, rectangular, L-shaped, and disproportionate room, (2) two-dimensional and three-dimensional (3D) inhomogeneous surface absorption by parameterizing numerous acoustic parameters of surfaces, e.g., the thickness of a porous material, cavity depth, switching between a frequency independent (e.g., hard surface) and frequency dependent boundary condition. Results of numerical experiments show speedups of more than 2 orders of magnitude compared to a high fidelity numerical solver in a 3D case where reverberation time varies within one just noticeable difference in all the frequency octave bands.

Ginzburg Landau Model for Nanofluid Convection in the Presence of Time Periodic Plate Modulation

Here we study thermal modulation effect on nanofluid convection and discuss heat and mass transfer in the layer. The non-uniform time periodic boundary conditions of the system are considered. A weak non-linear stability analysis has been performed and obtained heat and mass transfer coefficients as a function of the system parameters. The Ginzburg Landau model was employed to derive nanofluid convective amplitude at different stages of flow disturbances and modulation. Slow variations of time scale shows that thermal modulation impact on transport phenomenon for the case of out phase modulation (OPM) and (lower boundary modulation) LBM. Also the effect of IPM (in-phase modulation) is observed low effect on Nu and which are similar to un-modulation case. It is also justified that LBM restuls are similar to gravity modulation results. It is found that thermal modulation and concentration Rayleigh numbers are either stabilize or destabilize the system. Further, GL model shows better results on regulation of transport process

Analysis on the Effects of Different Receiver Structures and Porous Parameters on the Volumetric Effects and Heat Transfer Performance of Porous Volumetric Solar Receiver

The volumetric solar receiver is an important heat transfer component of the concentrated solar power (CSP) system. Moreover, in order to improve the absorption of concentrated solar radiation, the porous media are widely used in volumetric solar receiver. In recent years, many studies were concerned with the effects of porosity, pore number density and size, Reynolds number, and Darcy number on heat and flow performance in volumetric solar receiver. However, there are few studies on the effects of structure type and geometric parameters on the volumetric effects and the radiation characteristics of a porous volumetric solar receiver with nonuniform heat flux boundary condition. In this contribution, in order to analyze the effects of structures on the volumetric effects and heat transfer performance, we design six types of porous volumetric receiver structures, whereas the volume of different structures keeps consistent. Then, we apply the local non-thermal-equilibrium model and also consider the effect of structure shape on the concentrating solar radiation transport characteristic. Furthermore, we apply the Gaussian distribution model (GDM) to simulate the actual nonuniform heat flux boundary condition. The result shows that drum-type structure (RT-III) has the best heat transfer performance among the six structures; e.g., the outlet average temperature of fluid is up to 851 K when the pore size and porosity of porous media are 2 mm and 0.7, respectively, which is 41 K increased than the scaled cone-type structure. In addition, the pore diameter has less influence on the outlet temperature of fluid, but it has greater influence on the pressure drop. The contribution can provide a reference for this type of solar receiver design and reconstruction.

Hermite radial basis-differential quadrature solution for nonlinear buckling problem of non-uniform continuity boundaries of delaminated cylindrical shells

The progression in developing the composite material led to raise the delamination problem in different structural elements, the continuity paths of the within-thickness delamination problem usually were assumed as uniform to make the governing equations and the solution easier. This paper introduces a treatment of the buckling problem of the delaminated cylindrical shells of composite material with non-uniform delamination boundary using Hermite polynomial as a radial basis in differential quadrature method. The governing differential equations for internally delaminated cylindrical shell subjected to uniformly distributed compression load are obtained considering the variational principle. The non-dimensional analysis is carried out to get the simplest form of the governing differential equation. Both of continuity conditions at non-uniform delamination paths and boundary conditions for hinged and fixed supports are considered, and discretized using the differential quadrature method. The obtained critical buckling load at different thicknesses is verified with both of the exact solution and the solution obtained from generalized differential quadrature that used Lagrange interpolated polynomial as a test function. The results show that the Hermit radial basis differential quadrature is efficient, rapid and simple for treating the non-uniform continuity boundaries.

Influence of non-uniform thermal boundary on flow and heat transfer characteristics in rectangular channel

In this paper, the flow behavior and heat transfer characteristic in a rectangular channel are numerically investigated. The non-uniform thermal boundary condition is arranged along the streamwise direction at the bottom of the rectangular channel. Furthermore, based on the flow field parameters obtained with numerical simulation, the dynamic modal decomposition (DMD) is carried out for viscous layer, buffer layer, and logarithmic region, respectively. The numerical results show that the hot bands of non-uniform thermal boundary affect the interaction of the velocity streaks along the streamwise direction, which reduces the vorticity of the buffer layer and the fluctuation of the velocity gradient vector. In the terms of entropy analysis, it can be found that the hot bands of non-uniform thermal boundary play a similar role of “riblets” and block the self-sustainment of the turbulent coherent structures. Moreover, the results of DMD manifest that the hot bands of non-uniform thermal boundary can improve the stability of viscous layer and buffer layer. The development of turbulent boundary layer is delayed by affecting the fluid characteristics in buffer layer. Compared to the channel without non-uniform thermal boundary condition, the maximum drag reduction rate of 8.35% can be achieved in considered cases, while a reduction in heat transfer performance of 2.74% occurs. In addition, the comprehensive performance coefficient increases slightly to 1.0013.

A series of multi-domain matched interface and boundary algorithms for dynamic and static responses of annular sectorial plates

A series of multi-domain matched interface and boundary (MDMIB) algorithms are proposed to analyze the free vibration and bending of annular sectorial thin plates. Through an in-depth understanding of the matched interface and boundary (MIB) method, six types of MDMIB algorithms are developed herein by using various domain decomposition techniques for handling bi-directional crossing interfaces due to non-homogeneous elastic foundations and discontinuous loads, which cannot be treated by the conventional MIB method. The rationale of the MDMIB method is to divide the entire computational domain into multiple subdomains that can be connected by using the interconnecting conditions between crossing interfaces and mesh lines. Annular sectorial plates, having non-uniform boundary conditions, partially supported elastic foundations, and patch loads, are all considered. Numerous examples are chosen to examine the computational performance of the MDMIB algorithms. For verification, the present results are checked against existing and finite element solutions. It is shown that the proposed MDMIB algorithms are highly effective to deal with the bi-directional interface problems.

Thermal analysis for clamped laminated beams with non-uniform temperature boundary conditions

The focus of this study is thermal responses of a clamped composite laminated beam with arbitrary layer numbers under non-uniform temperature boundary conditions. Analytical solutions of temperature, stresses, and displacements are derived based on the theory of thermoelasticity. The temperature distribution in the laminated beam is divided into two parts. The first part is constructed to satisfy the inhomogeneous temperature boundary conditions, while the second part is obtained on the basis of the Fourier law of heat conduction and the temperature environment. On the other hand, the unit pulse function and the Dirac delta function are introduced to translate the clamped support into the simply support with an unknown horizontal stress. According to the continuities at the interface and the state space method, the relationships of displacements and stresses between the top and bottom surfaces of the laminated beam are derived. Finally, the unknown coefficients of displacements and stresses are determined by the mechanical boundary conditions. It can be observed from the numerical results that this method has excellent convergence performance. The accuracy of this method is verified by comparing with the results of the finite element method. Furthermore, the effects of surface temperature, material properties, length-to-thickness ratio and layer numbers on the distributions of temperature, displacements and stresses in the laminated beam are in depth investigated.

Mass transfer from a sheared spherical rigid capsule

Solute mass transfer from a spherical fluid-filled rigid capsule subjected to shear flow is studied numerically, while considering unsteady, continuous, and nonuniform boundary conditions on its surface. Here, the capsule acts as a reservoir with its initially encapsulated solute concentration decaying over time. This scenario differs from the classical case study of either constant concentration or constant mass flux at the surface of the particle. The flow and the concentration field are computed using fully three-dimensional lattice Boltzmann simulations, where the fluid-structure two-way coupling is achieved by the immersed boundary method. The effects of the flow and the boundary conditions on mass transfer efficacy are quantified by the Sherwood number (the dimensionless mass transfer coefficient), which is found to increase due to the combined effects of forced convection and the rotation of the capsule. Having continuity of both the concentration and the mass flux on the capsule significantly decreases the Sherwood number as compared to the case with constant and uniform boundary condition. All the obtained results can be applied to heat transfer in the case of cooling an initially hot spherical particle, for which the concentration must be replaced by the temperature and the Sherwood number by the Nusselt number.