Dimensionless Geometric Parameters Research Articles

Mapping low-Reynolds-number microcavity flows using microfluidic screening devices

Low-Reynolds-number flows in cavities, characterized by separating and recirculating flows are increasingly used in microfluidic applications such as mixing and sorting of fluids, cells, or particles. However, there is still a lack of guidelines available for selecting the appropriate or optimized microcavity configuration according to the specific task at hand. In an effort to provide accurate design guidelines, we investigate quantitatively low-Reynolds-number cavity flow phenomena using a microfluidic screening platform featuring rectangular channels lined with cylindrical cavities. Using particle image velocimetry (PIV), supported by computational fluid dynamics (CFD) simulations, we map the entire spectrum of flows that exist in microcavities over a wide range of low-Reynolds numbers (Re = 0.1, 1, and 10) and dimensionless geometric parameters. Comprehensive phase diagrams of the corresponding microcavity flow regimes are summarized, capturing the gradual transition from attached flow to a single vortex and crossing through two- and three-vortex recirculating systems featuring saddle-points. Finally, we provide design insights into maximizing the rotational frequencies of recirculating single-vortex microcavity systems. Overall, our results provide a complete and quantitative framework for selecting cavities in microfluidic-based microcentrifuges and vortex mixers.

A strip cut in a transversely isotropic elastic solid

The three-dimensional problems of a strip cut in a transversely isotropic elastic space, when the isotropy planes are perpendicular to the plane of the cut, are investigated using the asymptotic methods developed by Aleksandrov and his coauthors. Two cases of the location of the strip cut are considered: along the first axis of a Cartesian system of coordinates (Problem A) or along the second axis (Problem B). Assuming that the normal load, applied to the sides of the cut (normal separation friction) can be represented by a Fourier series, one-dimensional integral equations of problems A and B are obtained, the symbols of the kernels of which are independent of the number of the term of the Fourier series. A closed solution of the problem is derived for a special approximation of the kernel symbol. Regular and singular asymptotic methods are also used to solve the integral equations by introducing a dimensionless geometrical parameter, representing the ratio of the period of the applied wavy normal load to the thickness of the cut strip. The normal stress intensity factor on the strip boundary is calculated using the three methods of solving the integral equations indicated.

Plasma Jet for Flight Control

The need for high-speed flight-control devices has surged with recent interest in hypersonic flight. Plasma-based devices offer actuation times that are orders of magnitude smaller than conventional mechanical actuators. The plasma jet, which uses energy deposition to generate a high-speed jet, is evaluated for flight control. The jet is created by pulsing a cavity with energy deposition. The gas expands through a converging nozzle, inducing a jet flow. This research focuses on characterizing the forces generated by a single pulse of the plasma jet, assuming energy is deposited uniformly throughout the cavity and the jet exits to quiescent flow. A one-dimensional analytical model is developed to predict the force and impulse generated by the jet as well as the temporal evolution of the pressure, density, and temperature in the cavity. A relation between the dimensionless energy deposition and the dimensionless impulse is developed and verifiedwith computational results. It is shown that the dimensionless impulse generated by the jet is essentially independent of the dimensionless geometric parameters of the cavity. Additionally, a simplified analysis shows that the force from an array of plasma jets is sufficient to replace a conventional aerodynamic flap.

Torsion of a punch attached to transversely-isotropic half-space with functionally graded coating

The paper focuses on analytical solution for the problem about torsion of a circular punch attached to a transversely-isotropic elastic half-space with functionally-graded coating. The problem is reduced to dual integral equations by using integral transformations technique. The scheme of numerical construction of the kernel transform of the integral equation is developed. Approximations of the kernel transform by analytical expressions of special kind are proposed and explicit solution is derived with these approximations. It is shown that the derived solutions are asymptotically exact at both large and small values of characteristic dimensionless geometrical parameter of the problem. The application of the solution is illustrated by example of a steel substrate with functionally graded yttrium stabilized zirconia coating.

A modified equation for the stress concentration factor in countersunk holes

The present study introduces an accurate and modified equation for the stress concentration factor of a uniaxially loaded isotropic plate with a centered countersunk hole. ANSYS Parametric Design Language (APDL) was used to build a finite element (FE) model for the plate and to run the analysis. The FE modeling strategy was initially verified and then used to solve for the maximum stress concentration factor at the countersunk hole. The effect of the dimensions of the plate and the countersunk hole, which were represented by four governing dimensionless parameters, on the value of the stress concentration factor was examined by performing several runs of the FE code. Factorial and multi parameter fit analyses were conducted on the FE results to formulate a general parametric equation for the maximum stress concentration factor in terms of the four dimensionless geometric parameters. A comparison between the results of the present equation and an older equation has shown a higher accuracy in the maximum stress concentration factor of the present equation especially at high ratios of countersink depth to plate's thickness for very thick plates (thickness equal to or greater than twice the radius of hole). ► 3-D FE model was built to study the stress concentration around countersunk holes. ► Factorial analysis has determined the main geometric parameters of the SCF equation. ► A general equation of the SCF around countersunk holes was formulated and tested. ► The new equation reduced the error in the SCF of deep sinking holes of an older equation.

The action of a strip punch on a transversely isotropic half-space

Three-dimensional contact problems on the action of an absolutely rigid punch, in the form of a strip in plan, on a transversely isotropic elastic half-space, when the isotropy planes are perpendicular to the boundary of the half-space are investigated. In view of the fact that the elastic rigidity of the boundary of the half-space, characterizing the normal displacement under the action of a given concentrated force, depends considerably on the chosen direction on this boundary, two cases of the arrangement of the punch are considered: along the first or second axis of a Cartesian system of coordinates on the body boundary (Problems A and B). The normal displacement of the body boundary under the action of a specified concentrated normal force, after using a double Fourier transformation, is obtained in a form that is free of quadratures, which enables the stiffness of the boundary in different directions to be determined without difficulty, as well as the direction of the extremal stiffness. Assuming that the function, which describes the form of the base of the punch, can be represented by a Fourier series, one-dimensional integral equations of contact Problems A and B, the symbols of the kernels of which are independent of the number of the term of the Fourier series, are obtained. For a special approximation of the symbol of the kernel, a closed solution of the contact problem is derived in terms of Mathieu functions using Rvachev's method, which is a closed solution of the analogous contact problem of the action of a strip punch on an isotropic elastic half-space. To solve the integral equations of contact problems, regular and singular asymptotic methods are used with the introduction of a dimensionless geometrical parameter λ, which represents the ratio of the value of the period of the wavy base of the punch to the thickness of the contact strip. Using the method of orthogonal functions, the integral equations are also reduced to an infinite system of linear algebraic equations, to solve which the reduction method is employed for any values of λ.

Effects of manifold geometries on flow distribution to parallel microchannels

For efficient scale up of microchannel devices, uniform flow distribution to parallel microchannels is very important. In the present work, a dimensionless geometric parameter indicating the optimal manifold configuration is derived through a numerical parametric study and validated by micro particle image velocimetry. It is clearly shown that the flow uniformity is maximized when the dimensionless parameter is about 0.8. This study presents a simple and systematic design methodology for a uniform flow distribution to multiple microchannels operating in parallel.

Stability of Homogeneous Smart Beams based on the First Order Shear Deformation Theory Located on a Continuous Elastic Foundation

1 Abstract—This paper studies stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter and foundation coefficient on the stability of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data. Keywords—Stability, Homogeneous beam- Piezoelectric layer. I. INTRODUCTION HE applications of the smart materials have drawn attention in aerospace engineering, civil engineering, mechanical and even bio-engineering. The analysis of a coupled piezoelectric structure has recently been keenly researched because piezoelectric materials are more extensively used either as actuators or sensors. Examples include the analytical modelling and behaviour of a beam with surface-bonded or embedded piezoelectric sensors and actuators (1-3), and the use of piezoelectric materials in composite laminates and for vibration control (4). The use of finite element method in the analysis of piezoelectric coupled structures has been studied (5-8). Crawley and de Luis (9) developed the analytical model for the static and dynamic response of a beam structure with segmented piezoelectric actuators either bonded or embedded in a laminated composite. LaPeter and Cudney (10) proposed an analytic model for the segmented piezoelectric actuators bonded on a beam or a plate, and found the equivalent forcing functions of the actuators. The piezoelectric bimorph column structures were used as sensing elements. Dobrucki and Pruchnicki (11) presented an analysis theory of an axisymmetric piezoelectric bimorph. They also described a sensing theory for using the axisymmetric piezoelectric bimorph. Chandrashekhara and Bhatia (12) developed a finite element model for the active buckling control of laminated composite plates with surface bonded or embedded piezoelectric sensors that are either continuous or segmented. The dynamic buckling behavior of the laminated plate subjected to a linearly increasing compression load is investigated in their work. Chase and Bhashyam (13) derived optimal design equations to actively stabilize laminated plates loaded in excess of the critical buckling load using a large number of sensors and actuators. To the author's knowledge, there is no analytical solution available in the open literatures for stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation. In the present work, stability of homogeneous beams with piezoelectric layers subjected to axial load that is simply supported at both ends lies on a continuous elastic foundation studied. Appling the Hamilton's principle, the equilibrium equations of beam are derived and solved. The effects of applied voltage, dimensionless geometrical parameter and foundation coefficient on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Propagation of shallow water waves in an open parabolic channel using the WKB perturbation technique

A singular perturbation analysis based on the WKB technique to study the hydrodynamic performance of periodic ocean waves that are incident on an open parabolic channel of constant depth is proposed. We derive a linear model to predict the propagation of the long ocean waves into the channel. In this manner, the spatial distribution for the surface elevation of the ocean waves inside the channel as a function of two dimensionless parameters, namely, a kinematical parameter, κ and a geometrical parameter ε , is governed by a second-order ordinary differential equation. The kinematical parameter κ denotes the ratio of the potential head, due to gravity, to the kinetic head of the ocean waves along the longitudinal axis of the parabolic channel. Meanwhile, ε is a dimensionless geometrical parameter that represents a characteristic ratio of the parabolic channel. Using matching conditions, simple expressions for the reflection and transmission coefficients are obtained.

Geometric stress distribution along the weld toe of the outer brace in two-planar tubular DKT-joints: Parametric study and deriving the SCF design equations

Regarding the research efforts expended so far on the calculation of stress concentration factors (SCFs) in tubular joints, two major shortcomings can be noted: (a) significant effort has been devoted to the study of SCFs in various uni-planar connections. Nevertheless, for multi-planar joints which cover the majority of practical applications, very few investigations have been reported due to the complexity and high cost involved; (b) majority of these research works focused on the study of SCFs at certain positions such as the saddle, crown toe, and crown heel, and they have ignored the hot-spot stress (HSS) at other positions along the weld toe. In the present paper, effects of dimensionless geometrical parameters on the SCF distribution along the weld toe of main (outer) braces in the axially loaded right-angle two-planar tubular DKT-joints are investigated. In order to study the multi-planar effect, SCF distribution in two-planar joints is compared with the distribution in a uni-planar joint having the same geometrical properties. A complete set of SCF database is constructed based on the two-planar DKT-joint Finite element models which are verified against experimental results and the predictions of Lloyd’s Register (LR) equations. The FE models cover a wide range of geometrical parameters. Six new SCF parametric formulae are developed through nonlinear regression analyses for the accurate and reliable fatigue design of two-planar DKT-joints under axial loads. An assessment study of these equations is conducted against the experimental data, the original FEM database and the acceptance criteria recommended by the UK Department of Energy.

Stability of Functionally Graded Beams with Piezoelectric Layers Based on the First Order Shear Deformation Theory

Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter, functionally graded index and piezoelectric thickness on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data. Keywords—StabilityFunctionally graded beamFirst order shear deformation theory -Piezoelectric layer.

Inverse analysis for evaluation of the shear modulus of inhomogeneous media by torsion experiments

The present paper addresses the problem on torsion of a circular indentor with a flat base on a half-space covered by an inhomogeneous coating with shear modulus arbitrarily varying in-depth. Approximate analytical solution of this problem is developed. The obtained formulas allow one to determine the distribution of contact stresses under indentor, as well as the dependence of the torsion moment applied to the indentor from the twisting. It is shown that the approximate formulas are asymptotically exact both at large and small values of characteristic dimensionless geometrical parameter of the problem. Based on the analysis of the derived solution, we suggest evaluation technique for the shear modulus of a functionally-graded coating in the case when it depends on one parameter only. The technique uses the data received in the course of torsion experiments by a series of indentors of various radii.

Surface effects in various bending-based test methods for measuring the elastic property ofnanowires

The size-dependent elastic property of nanowires induced by the surface effect isinvestigated by using the core–shell model. The overall effective elastic moduli ofnanowires with regular polygonal cross-sections are unified into a simple and explicitrelation. It is found that the effect of surface elasticity on the elastic moduli can bewell characterized by two dimensionless material and geometric parameters withclear physical meaning. Finite element simulations demonstrate that the derivedtheoretical relation is applicable for all the vibration, bending, and buckling testmethods for measuring the mechanical properties of nanowires. The analyticalresult is also validated by comparing it with relevant experimental measurements.This study is helpful not only for interpreting various phenomena associatedwith size-dependent mechanical properties of nanowires but also for developingand evaluating test techniques for material characterization at the nanoscale.

Comprehensive Evaluation Analysis and Optimization Methodology of Tool Geometric Parameters for High Speed Cutting

Tool geometric parameters, which are key factors to be considered in tool design, have a direct effect on tool cutting performance. Based on the diversity and complexity of geometric parameters and technological goals, we select cutting force and temperature as initial input conditions to build a comprehensive dimensionless tool geometric parameters evaluation method. According to the multilevel weight relationships between the technological goals and the basic cutting characteristics, the evaluation factors for cutting force and temperature are determined. The comprehensive evaluation method (CEM) is then applied to analyze and optimize the key parameters of a saw milling tool. As shown by the research results, the parameters obtained by the CEM prove that some tool parameters from actual production were reasonable, while others had re-optimized space. The CEM is shown to be effective and feasible. Also, the analysis results have an explicit guiding function for production practice.

An equilibrium penny-shaped crack in an inhomogeneous elastic medium

The problem of a penny-shaped tensile crack in a continuously-inhomogeneous space is considered. The problem reduces to a dual integral equation for which an approximate analytical solution is constructed. It is proved that the approximate solution of the integral equation is asymptotically exact for both small and large values of the dimensionless geometric parameter of the problem. The accuracy of the solution obtained is investigated. Expressions are presented for the stress intensity factor, the energy of the opening of the crack, the displacements of its sides and the normal components of the stress tensor in the neighbourhood of its contour. In the numerical analysis of the solution of the problem, special attention is paid to analysing of the problem when the first derivative of the change in the elastic properties of the material changes sign.

Mixed Convection in a Vertical Heated Channel: Influence of the Aspect Ratio

In mechanical and environmental engineering, mixed convection is a frequently encountered thermal fluid phenomenon which exists in atmospheric environment, urban canopy flows, ocean currents, gas turbines, heat exchangers, and computer chip cooling systems etc... . This paper deals with a numerical investigation of mixed convection in a vertical heated channel. This flow results from the mixing of the up-going fluid along walls of the channel with the one issued from a flat nozzle located in its entry section. The fluid- dynamic and heat-transfer characteristics of vented vertical channels are investigated for constant heat-flux boundary conditions, a Rayleigh number equal to 2.57 10 10 , for two jet Reynolds number Re=3 10 3 and 210 4 and the aspect ratio in the 8-20 range. The system of governing equations is solved with a finite volumes method and an implicit scheme. The obtained results show that the turbulence and the jet-wall interaction activate the heat transfer, as does the drive of ambient air by the jet. For low Reynolds number Re=3 10 3 , the increase of the aspect Ratio enhances the heat transfer of about 3%, however; for Re=2 10 4 , the heat transfer enhancement is of about 12%. The numerical velocity, pressure and temperature fields are post-processed to compute the quantities of engineering interest such as the induced mass flow rate, and average Nusselt number, in terms of Rayleigh, Reynolds numbers and dimensionless geometric parameters are presented. and natural convection was initiated in the 1960's and mainly based on experimental approaches. Natural convection between heated vertical parallel plates is the most frequently used configuration in convection air cooling of electronic equipment. The passive character of cooling by natural convection makes it very attractive for applications in electronic devices. A review of the literature shows that laminar natural convection in vertical channel has been studied by several authors: Elenbaas (1) led the first experimental study which was used in the follow as reference solution. Bodoi and Osterle (2) have obtained the first numerical solution of the natural convection in vertical channel. Their results were in good agreement with those Elenbaas. In order to increase the cooling requirements, researches for methods to improve the heat transfer parameters or to analyze standard configurations to carry out optimal geometrical parameters for a better heat transfer rate

Effective pipe-to-borehole thermal resistance for vertical ground heat exchangers

The effective pipe-to-borehole thermal resistance of a vertical ground heat exchanger is investigated numerically. An analysis is carried out to determine the dimensionless geometrical parameters affecting such resistance. The heat transfer rates between the U-shaped pipes and the borehole are determined numerically and compared with some well-known limiting analytical solutions. A best-fit correlation for the effective pipe-to-borehole thermal resistance is presented in dimensionless form. The results are compared against approximate analytical solutions that represent the U-shaped pipes as a single pipe of equivalent diameter and against experimental data available in the literature. It is found that the available models do not accurately represent the effective pipe-to-borehole thermal resistance.

Passing ability of fresh concrete: A probabilistic approach

In the present paper, it is first reminded that the probability of granular blocking of a suspension crossing a flow contraction increases with the number of particles crossing the obstacles, their volume fraction and the ratio between the diameter of the particles and the contraction gap. It is moreover reminded that this phenomenon can be described using a simple dimensionless geometric parameter as this phenomenon only slightly depends on the rheology of the suspending fluid. An adaptation of this dimensionless parameter to the specific case of concrete is proposed and compared to experimental results. Finally, an application to the prediction of the passing ability of Ordinary Rheology Concrete (ORC) and Self Compacting Concrete (SCC) is proposed and compared to the European technical recommendations.

Correlation equations for optimum design of annular fins with temperature dependent thermal conductivity

Correlation equations for optimum design of annular fins with temperature-dependent thermal conductivity are obtained in the present work. The nonlinear fin equation which is associated with variable thermal conductivity condition is solved by Adomian decomposition method that provides an analytical solution in the form of an infinite power series. The optimum radii ratio of an annular fin which maximizes the heat transfer rate has been found as a function of Biot number and the fin volume for a given thermal conductivity parameter describing the variation of the thermal conductivity. The fin volume is fixed to obtain the dimensionless geometrical parameters of the fin with maximum heat transfer rate. The data from the present solutions is correlated for a suitable range of Biot number and the fin volume. The simple correlation equations presented in this work can assist for thermal design engineers for optimum design of annular fins with temperature-dependent thermal conductivity.

Dynamic buckling of shallow pin-ended arches under a sudden central concentrated load

When a shallow arch is subjected to an in-plane load that is applied suddenly, the arch will oscillate about an equilibrium position due to the kinetic energy imparted to the arch by the sudden load. If the suddenly applied load is sufficient large, the motion of the arch may reach an unstable equilibrium position, leading to dynamic buckling of the arch. This paper presents a study of the dynamic in-plane buckling of a shallow pin-ended circular arch under a central radial load that is applied suddenly with infinite duration. The method of conservation of energy is used to establish the criterion for dynamic buckling of the shallow pin-ended arch and analytical solutions for the lower and upper dynamic buckling loads of the arch under this sudden central load with infinite duration are obtained. It is found that the dynamic buckling loads of a shallow pin-ended arch under a sudden central load with infinite duration are lower than its static buckling loads, and that the dynamic buckling load increases with an increase of a dimensionless arch geometric parameter that is introduced. The effect of static preloading on the dynamic buckling of a shallow pin-ended arch is also investigated. It is found that the pre-applied static load decreases its dynamic buckling loads, but increases the sum of the pre-applied load and the dynamic buckling load.