Dimensionless Geometric Parameters Research Articles

Thermal buckling analysis of functionally graded cylindrical shells

Thermal buckling behavior of cylindrical shell made of functionally graded material (FGM) is studied. The material constituents are composed of ceramic and metal. The material properties across the shell thickness are assumed to be graded according to a simple power law distribution in terms of the volume fraction rule of mixtures. Based on the Donnell shell theory, a system of dimensionless partial differential equations of buckling in terms of displacement components is derived. The method of separation of variables is used to transform the governing equations to ordinary differential equations (ODEs). A shooting method is used to search for the numerical solutions of the differential equations under two types of boundary conditions. Effects of the power law index, the dimensionless geometrical parameters, and the temperature ratio on the critical buckling temperature are discussed in detail.

The Theoretical Analysis of Mass and Energy Flow Through Solar Collector – Chimney System

The goal of the paper was to simplify the designing process for mass and energy flow through solar collector - chimney system. Theoretical analysis allowed to get involved system of three nonlinear analytical equations in dimensionless forms that have been saved. Dimensionless numbers for the problem are well known in the literature on fluid mechanics and thermodynamics: Reynolds, Grashof, Galileo, Biot and Prandtl. In the analyzed equations are also dimensionless geometric parameters expressing the ratios of basic geometrical dimensions of the collector system-chimney: the radius disc collector to the thickness gap, the height and radius of the chimney. In the system of equations, the Reynolds number is treated as the determined number, which is a novelty of the method used.

Study of thermal effectiveness and its relation with NTU in shell and helically coiled tube heat exchangers

In the present study, the effect of operational and geometrical parameters on the thermal effectiveness of shell and helically coiled tube heat exchangers was investigated. Analysis was performed for the steady state. The working fluid of both sides is water, that its viscosity and thermal conductivity were assumed to be dependent on temperature. Based on the results, two correlations have been developed to predict the thermal effectiveness, for wide ranges of mass flow rates ratio, dimensionless geometrical parameters and product of Reynolds numbers. Furthermore, it was found for same values of NTU and Cr, the effectiveness is averagely 12.6% less than the effectiveness of parallel flow heat exchangers and this difference is approximately constant.

Investigation of exergy efficiency in shell and helically coiled tube heat exchangers

This study presents exergy analysis for forced convection heat transfer in shell and helically coiled tube heat exchangers. The effect of operational and geometrical parameters on the exergy efficiency was investigated. Water is selected as the working fluid of both sides. Results show that, the efficiency decreases linearly with the increase of the fluids dimensionless inlet temperature difference. Based on the results, a correlation was developed to predict the efficiency for wide range of mass flow rates ratio (0.1<Rm<4), fluids dimensionless inlet temperature difference (0<RT<0.8), product of Reynolds numbers (3.31E+8<(Rec. Resh)<1.32E+9) and dimensionless geometrical parameters. According to this equation it was found that, the coil which has the maximum number of turns and minimum diameter is more efficient than other coils which have the same length and pitch.

Vibration analysis of rotating pretwisted tapered blades made of functionally graded materials

This paper presents a new structural dynamic model with which vibration characteristics of rotating blades made of functionally graded materials (FGMs) can be investigated. The equations of motion of a rotating pretwisted tapered blade made of FGM are derived using the Rayleigh-Ritz assumed mode method along with the Kane's method. After converting the equations of motion into dimensionless forms, dimensionless natural frequencies are obtained by solving the modal formulation of the dimensionless equations. Various dimensionless geometric parameters like pretwist angle, taper ratios, hub radius ratio and width-to-thickness ratio as well as continuous variation of material properties along the blade thickness are considered to obtain the new structural dynamic model. The accuracy and efficiency of the proposed model are verified through a comparison study first. Then, effects of the volume fraction index, Young's modulus ratio, hub radius ratio, pretwist angle, taper ratios, width-to-thickness ratio and angular speed upon the dimensionless natural frequencies of the FG blade are investigated using the proposed model. In addition, an algebraic condition under which dimensionless natural frequencies can be minimized is obtained.

Parametric investigation on mixing in a micromixer with two-layer crossing channels.

This work presents a parametric investigation on flow and mixing in a chaotic micromixer consisting of two-layer crossing channels proposed by Xia et al. (Lab Chip 5: 748–755, 2005). The flow and mixing performance were numerically analyzed using commercially available software ANSYS CFX-15.0, which solves the Navier–Stokes and mass conservation equations with a diffusion–convection model in a Reynolds number range from 0.2 to 40. A mixing index based on the variance of the mass fraction of the mixture was employed to evaluate the mixing performance of the micromixer. The flow structure in the channel was also investigated to identify the relationship with mixing performance. The mixing performance and pressure-drop were evaluated with two dimensionless geometric parameters, i.e., ratios of the sub-channel width to the main channel width and the channels depth to the main channel width. The results revealed that the mixing index at the exit of the micromixer increases with increase in the channel depth-to-width ratio, but decreases with increase in the sub-channel width to main channel width ratio. And, it was found that the mixing index could be increased up to 0.90 with variations of the geometric parameters at Re = 0.2, and the pressure drop was very sensitive to the geometric parameters.

Numerical analysis of the geometrical and material criteria of acceleration of shear crack to supershear velocity in brittle nanoporous solids

The paper is devoted to the study of dynamic propagation of mode II cracks in porous brittle materials with nanoscale pore size. We compared static (shear strength) and dynamic parameters of crack growth in dry and fluid saturated nanoporous brittle materials at different degrees of confinement. We have shown that pore fluid in nanoporous brittle materials influences mainly the dynamics of crack propagation. This leads in particular to pronounced peculiarities of the dependence of the critical value of dimensionless geometrical parameter of the initial crack (it majorizes the interval of the ratios of length to thickness for the cracks that are capable to accelerate to intersonic velocity) on applied crack normal stress. The results of the study are relevant for understanding the conditions of supershear regime of propagation of mode II cracks as well as for assessment of the ability of mode II cracks in brittle materials (including nanoporous fluid-saturated solids) to develop in supershear regime.

Contact Law and Coefficient of Restitution in Elastoplastic Spheres

A complete contact cycle of an elastoplastic sphere consists of loading and unloading phases. The loading phase may fall into three sequential regimes: elastic, mixed elastic–plastic, and fully plastic. In this paper, we distinguish the transition points among the three regimes via the material hardness and a dimensionless geometric parameter corresponding to the onset of the fully plastic regime. Based on Johnson’s simplified spherical expansion model, together with the well-supported force–indentation relationships in the elastic and fully plastic regimes, we build an analytical approximation for the mixed elastic–plastic regime by enforcing the C1 continuity of a loading force–indentation curve. Unloading responses of the elastoplastic sphere are characterized by an elastic force–indentation relation, which has a Hertzian-type form but takes into account the effects of the strain hardening that occurs in the mixed elastic–plastic regime. We validate the model by comparing with existing quasi-static and impact experiments and show that the model can precisely capture the force–indentation responses. Further validation is performed by employing the proposed compliance model to investigate the coefficient of restitution (COR). We achieve agreement between our numerical results and the experimental data reported in other studies. Particularly, we find that the COR is inversely proportional to the impacting velocity with an exponent equal to 1/6, instead of 1/4 reported by many other models.

Colburn &lt;i&gt;‘j’&lt;/i&gt; Factor and Fanning Friction Factor &lt;i&gt;‘f’&lt;/i&gt; Correlations of Triangular Plain Fin Surface of a Compact Heat Exchanger Using CFD

This paper presents the heat transfer and friction coefficient correlations for triangular plain fin surfaces of plate fin compact heat exchanger. It will be prohibitively expensive and time consuming to fabricate heat exchanger cores and conduct experiments over reasonable ranges of all the geometric variables. In contrast, it is relatively easy and cost effective to carry out a parametric study through numerical simulation and derive acceptable correlations for use in industry. A numerical model has been developed for the triangular plain fin of plate fin heat exchanger. The CFD analysis is carried out using FLUENT 12.1, Colburn factor j and fanning friction factor f are calculated for different Reynolds numbers. These values are compared with the available literature data of j and f factors. The correlations have been expressed in terms of two separate equations over the low and high Re regions along with dimensionless geometric parameters.

Locally and Dynamically Controllable Surface Topography Through the Use of Particle‐Enhanced Soft Composites

A new class of soft composite materials with dynamically tunable and reversible surface topographies is introduced that allows a wide diversity and local positioning of surface features. The particle‐enhanced soft composites are comprised of a soft elastomeric matrix with relatively stiff particles embedded below the surface. Upon application of external stimuli, a surface that is originally smooth and flat (or of other initial topology) transforms to engineered surface topographies. Finite element based micromechanical simulations are used to design and study the hybrid material structures that govern the evolution in surface topographies. Physical prototypes are fabricated using multimaterial 3D‐printing, and then experimentally evaluated to validate the accuracy of our simulations. It is demonstrated that a rich variety in periodic and random surface features including variable waves, crease‐like features, flat apexes, and valleys can be attained by changing different dimensionless geometric parameters (e.g., relative particle size, shapes, spacing, and distributions). Furthermore, these surface features can be locally controlled by positioning of particles and do not rely on instabilities. The material design depends primarily on the geometry of the particles and the arrays, making this approach to on‐demand custom and reversible surface patterning applicable over a wide range of size scales.

Multi-objective and thermodynamic optimisation of a parabolic trough receiver with perforated plate inserts

In this paper, multi-objective and thermodynamic optimisation procedures are used to investigate the performance of a parabolic trough receiver with perforated plate inserts. Three dimensionless perforated plate geometrical parameters considered in the optimisation include the dimensionless orientation angle, the dimensionless plate diameter and the plate spacing per unit meter. The Reynolds number varies in the range 1.02 × 104 ≤ Re ≤ 1.36 × 106 depending on the fluid temperature. The multi-objective optimisation was realised through the combined use of computational fluid dynamics, design of experiments, response surface methodology and the Non-dominated Sorted Genetic Algorithm-II. For thermodynamic optimisation, the entropy generation minimisation method was used to determine configurations with minimum entropy generation rates.

Stretchability of indium tin oxide (ITO) serpentine thin films supported by Kapton substrates

Indium tin oxide (ITO) has been widely used as the electrode material in touch-screen displays and solar cells attributing to its combined high electrical conductivity and optical transparency. Moving forward from wafer based electronics to flexible/stretchable electronics, brittle electronic materials like ITO are significantly hindering the deformability of the integrated systems. To minimize strains in inorganic materials when subjected to stretch, thin metallic and ceramic films can be patterned into serpentine shapes. Although metallic serpentines have received extensive studies, experimental investigations on ceramic serpentines have not been reported. We perform uniaxial tension tests on Kapton-supported ITO serpentine thin films with in situ electrical resistance measurements. It is found that the narrower serpentine ribbons are more stretchable than their wider counterparts. We propose a generic empirical equation to predict the stretchability using three dimensionless geometric parameters. Conclusions reached for Kapton-supported ITO serpentine films are generally applicable to gold, silicon, and other stiff serpentine films bonded to stiff polymer substrates such as Kapton and polyethylene terephthalate.

Performance of High Strength Rock Fall Meshes: Effect of Block Size and Mesh Geometry

In rockfall science, the bullet effect refers to the perforation of a rockfall mesh by a small block traveling at high speed. To date, there is still no comprehensive experimental data set investigating the underlying mecha- nisms of such effect. The bullet effect illustrates the fact that the capacity of a rockfall mesh depends on the size and speed of the impacting block. This paper presents the results of an experimental study on the effect of block size and mesh geometry (aperture and wire diameter) on the mesh performance. The results clearly show that the amount of energy required to perforate the mesh drops as the blocks get smaller. They also suggest that the mesh performance reaches a maximum and reduces to zero when the mesh cannot sustain the static load imposed by very large blocks. The outcome of the first series validates an analytical model for mesh perforation, making it the first simple model capturing the bullet effect. A second series of tests focused on the effect of mesh geometry and it was found that decreasing the mesh aperture by 19 % improves the performance by 50 % while only an extra 30 % could be gained by increasing the wire diameter by 33 %. The outcomes of the second series were used to discuss and redefine a dimensionless geometrical parameter G* and to

Perforated plates for fluid management: Plate geometry effects and flow regimes

Perforated plates are the preferred means of passive management of fluid flow proper and for convective heat transfer applications. The investigation reported here is a synergistic use of numerical simulation and experimentation to provide both in-depth fluid mechanic fundamentals and results for applications. The experimental results validated the choice of the turbulence model. A trio of dimensionless geometrical parameters was varied systematically, as was the Reynolds number to encompass both laminar and turbulent flows. For the laminar flow regime, higher pressure drops were associated with thicker plates and with the staggered-array hole pattern; higher porosities led to lower pressure drops. For the turbulent case, the thinner plate caused higher pressure drops as did the square-array hole pattern; also, the pressure drop was found to depend on the square of the Reynolds number, indicating the dominance of momentum-based losses. These trend reversals are attributable to the differences in separated-flow reattachment patterns for the different plate thicknesses.

A New Approach to Designing the S-Shaped Annular Duct for Industrial Centrifugal Compressor

The authors propose an analytical method for designing the inlet annular duct for an industrial centrifugal compressor using high-order Bezier curves. Using the design of experiments (DOE) theory, the three-level full factorial design was developed for determination of influence of the dimensionless geometric parameters on the output criteria. Numerical research was carried out for determination of pressure loss coefficients and velocity swirl angles using the software system ANSYS CFX. Optimal values of the slope for a wide range of geometric parameters, allowing minimizing losses in the duct, have been found. The study has used modern computational fluid dynamics techniques to develop a generalized technique for future development of efficient variable inlet guide vane systems. Recommendations for design of the s-shaped annular duct for industrial centrifugal compressor have been given.

Thermodynamic analysis of a thermoelectric power generator in relation to geometric configuration device pins

Thermoelectric generators (TEG) are cost effective solid-state devices with low thermal efficiencies. The limitations, due to the operational temperature of the thermoelectric materials, suppress the Carnot efficiency increase of the device. Although thermoelectric generators have considerable advantages over the other renewable energy devices, low convergence efficiency of the device retains thermoelectric devices behind its competitors. In order to keep up with the competition, improvement of device efficiency becomes crucial for the practical applications. The design configuration of the device pin legs, lowering the overall thermal conductance, can improve the device efficiency. Therefore, in the present study, the influence of pin leg geometry on thermal performance of the device is formulated thermodynamically. In this case, the exponential area variation of pin legs is considered and dimensionless geometric parameter ‘a’ is introduced in analysis. The influence of dimensionless geometric parameter on efficiency and power output is demonstrated for different temperature ratios and external load resistance ratios. It is found that increasing dimensionless geometric parameter improves the thermal efficiency of the device; however, the point of maximum efficiency does not coincide with the point of the maximum device output power.

TORSIONAL BUCKLING OF FUNCTIONALLY GRADED CYLINDRICAL SHELLS WITH TEMPERATURE-DEPENDENT PROPERTIES

Based on Hamilton's principle, a new accurate solution methodology is developed to study the torsional bifurcation buckling of functionally graded cylindrical shells in a thermal environment. The effective properties of functionally graded materials (FGMs) are assumed to be functions of the ambient temperature as well as the thickness coordinate of the shell. By applying Donnell's shell theory, the lower-order Hamiltonian canonical equations are established, from which the eigenvalues and eigenvectors are solved as the critical loads and buckling modes of the shell of concern, respectively. The effects of various aspects, including the combined in-plane and transverse boundary conditions, dimensionless geometric parameters, FGM parameters and changing thermal surroundings, are discussed in detail. The results reveal that the in-plane axial edge supports do have a certain influence on the buckling loads. On the other hand, the transverse boundary conditions only affect extremely short shells. With increasing thermal loads, the material volume fraction has a different influence on the critical stresses. It is concluded that the optimized FGM mixtures to withstand thermal torsional buckling are Si3N4/SUS304 and Al2O3/SUS304 among the materials studied in this paper.

Cu surfaces with controlled structures: From intrinsically hydrophilic to apparently superhydrophobic

A series of Cu films with different surface structures were fabricated by an improved electric brush-plating technique. In the absence of surface chemical modification, the Cu films exhibited hydrophobic and even superhydrophobic behaviors due to their three-level hierarchical structures. Based on the classical Wenzel and Cassie models, the effects of two dimensionless geometrical parameters (the aspect ratio and the spacing factor of micro-scale structure) on the wetting behaviors of the Cu films were investigated. It was demonstrated that to obtain the stable Cassie superhydrophobic state, the aspect ratio and the water contact angle on the basal surface should be as large as possible and the spacing factor should be limited within a specific range for given aspect ratio and water contact angle on the basal surface.

Application of ANN and GA for the Prediction and Optimization of Thermal and Flow Characteristics in a Rectangular Channel Fitted with Twisted Tape Vortex Generators

This study reports an application of the hybrid model, including back propagation network and genetic algorithm, for predicting the thermal and flow characteristics in a rectangular channel fitted with multiple twisted tape vortex generators (MT-VG). Dimensionless geometric parameters and Reynolds number were considered as network inputs, and Nusselt number and friction factor were the output variables. The performance of the developed neural networks was found to be superior in comparison with the empirical correlations. In addition, the proposed networks have been considered as two objective functions in order to obtain optimal operation conditions. Since mentioned objectives are conflicting, the multi-objective optimization using genetic algorithm was used for the optimization.

Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer

The paper addresses a contact problem of the theory of elasticity, i.e., the penetration of a circular indenter with a flat base into a soft functionally graded elastic layer. The elastic properties of a functionally graded layer arbitrarily vary with depth, and the foundation is assumed to be elastic, yet much harder than a layer. Approximated analytical solution is constructed, and it is shown that the solutions are asymptotically exact both for large and small values of characteristic dimensionless geometrical parameter of the problem. Numerical examples are analyzed for the cases of monotonic and nonmonotonic variations of elastic properties. Numerical results for the case of homogeneous layer are compared with the results for nondeformable foundation.