Non-dimensional Geometric Parameters Research Articles

Thermal Divergence of Supersonic Functionally Graded Plates

This paper presents the thermal divergence analysis of supersonic plates made of functionally graded materials. The governing equations are based on the first-order shear deformation theory. The effects of steady aerodynamic pressure loadings in conjunction with elevated temperature are evaluated. It is assumed that the plate is subjected to uniform and linear temperature distributions across the thickness. The material properties of the functionally graded plates are assumed to follow power law distribution in the thickness direction. The Galerkin method is employed to transform the resulting partial differential equations into ordinary differential equations. The solutions for the complex eigenvalue problem are obtained through the standard eigenvalue algorithm. The variation of non-dimensional aerodynamic pressure and geometric parameters such as plate aspect ratio and relative thickness, as well as gradient index on critical temperature and divergence boundaries are examined for uniform and linear temperature distributions.

Experimental study of velocity fields in rectangular shallow reservoirs

Velocity fields in rectangular shallow reservoirs with different length-to-width and expansion ratios were investigated in an experimental study, to evaluate the effect of geometry on the flow field. A wide range of combinations of these two non-dimensional geometric parameters were tested at constant hydraulic conditions. Ultrasound velocity profilers were used to measure the horizontal velocity components across the entire reservoir surface, allowing for the visualization of streamlines and of the instantaneous and average velocities. Five different types of flow patterns were identified, depending on the values of the length-to-width ratio and expansion ratio of the reservoir. Asymmetrical flow patterns were found to develop for certain combinations of these geometric parameters despite the perfect reservoir symmetry. A critical comparison of these new experimental results with those of other works is provided.

Geometrical effect on SCF distribution in uni-planar tubular DKT-joints under axial loads

Despite the frequent use of DKT-joints in offshore structures, no parametric equation is available for determining the distribution of stress concentration factors (SCFs) along the brace-to-chord intersection of this type of tubular joints. In the present paper, the effect of non-dimensional geometrical parameters and brace-to-chord inclination angle on the distribution of SCFs and DKT-/KT-joint SCF ratios (SRs) along the weld toe of tubular DKT-joints under the balanced axial loads is studied. Thereafter, a parametric equation is proposed for predicting the distribution of SCFs along the 360° spatial curve of the weld toe. The proposed equation satisfies the acceptance criteria recommended by the UK Department of Energy (DoE), and consequently can reliably be used for design purposes.

On Dominant Oscillation Frequency of a Simplified Fluidic Oscillator

In the present study, we investigate a self-excited oscillatory phenomenon of a two-dimensional confined jet with a rectangular-cross-section cylinder as a downstream target. More specifically, in order to reveal the effects of a kinematic parameter the Reynolds number Re and various geometric parameters upon the jet-oscillation frequency fD, we conduct experiments at Re < 5000 in water and in air by an ultrasonic velocity profiler and a hot-wire anemometer, respectively. As a result, we specify the effects of Re and four non-dimensional geometric parameters upon fD, which is non-dimensionalised as the Strouhal number St. As the four geometric parameters, we consider (1) the streamwise target size, (2) the channel breath, (3) the cross-streamwise target size and (4) the target distance in non-dimensional forms with a length scale of the jet's breadth. It is found that the Re effect is negligible. This guarantees a wide-range workability as flowmeters. All the results can be summarised in an empirical formula describing the relation of St with the four geometric parameters.

On Dominant Oscillation Frequency of a Simplified Fluidic Oscillator

In the present study, we investigate a self-excited oscillatory phenomenon of a two-dimensional confined jet with a rectangular-cross-section cylinder as a downstream target. More specifically, in order to reveal the effects of a kinematic parameter the Reynolds number Re and various geometric parameters upon the jet-oscillation frequency fD, we conduct experiments at Re Re and four non-dimensional geometric parameters upon fD, which is non-dimensionalised as the Strouhal number St. As the four geometric parameters, we consider (1) the streamwise target size, (2) the channel breath, (3) the cross-streamwise target size and (4) the target distance in non-dimensional forms with a length scale of the jet's breadth. It is found that the Re effect is negligible. This guarantees a wide-range workability as flowmeters. All the results can be summarised in an empirical formula describing the relation of St with the four geometric parameters.

Experimental Study on SNCF of Welded CHS-CFSHS T-Joints under Axial Loading

The initiation position can be predicted by studying on strain concentration factors (SNCF) and SNCF distributions. This paper concerns an experimental investigation of SNCF of welded T-joints composed of circular hollow section (CHS) braces and concrete-filled square hollow section (CFSHS) chords under axial loading on the braces with two load cases of tension and compression. Static experiments were performed on eight test specimens designed for considering different non-dimensional geometric parameters and C50 grade concrete. Compared with joints made of CHS-SHS, the experimental results indicate that the CHS-CFSHS T-joints have lower strain concentration factors which may increase fatigue strength. The position of the maximum SNCF is usually located at 00 or 900 of the intersection line between a CHS brace and a CFSHS chord.

Optimization of reactive mufflers

A new approach to optimization of reactive mufflers, which is based on use of muffler prototype with nondimensional geometrical parameters and integral criterion of acoustic performance of mufflers, is proposed. Implementation of the approach using the example of chamber mufflers is considered.

Vibration of bilayered cylindrical shells with layers of different materials

In this analysis, a comparative study for natural frequencies of two-layered cylindrical shells was presented with one layer composed of functionally graded material and the other layer of isotropic material. Love’s thin shell theory was exploited for the strain-displacement and curvature-displacement relationships. For governing frequency equations, the Rayleigh-Ritz method was utilized to minimize the Lagrangian functional in the form of an eigenvalue problem. Frequency spectra were computed for long, short, thick, and thin cylindrical shells by varying the nondimensional geometrical parameters, length-to-radius and thickness-to-radius ratios for a simply supported end condition. Influence of different configurations of cylindrical shells on the shell frequencies was studied. For validity, the results obtained were compared with some results of isotropic and single-layered functionally graded cylindrical shells from the literature.

Variability of Energy Dissipation and Shear Rate with Geometry in Unbaffled Surface Aerator

The dissipation rate of turbulent kinetic energy () and shear rate (γ) are the key process parameters for mixing in surface aerators. At constant dynamic variables (rotational speed), both  and γ are greatly affected by the geometric parameters (impeller diameter, cross-sectional area of the tank, liquid height, rotor blade length and immersion height). By doing numerical computation by VISIMIX ®, present work analyzes the effect of non-dimensional (which is non-dimensionalized through rotor diameter) geometric parameters on e and g. With an increase in liquid height, there is an increase in the case of energy dissipation and shear rate values. In the case of tank area and blade length, it is vice versa. Energy dissipation and shear rate are not affected by the variation in immersion height of the impeller.

Variability of Energy Dissipation and Shear Rate with Geometry in Unbaffled Surface Aerator

mixing in surface aerators. At constant dynamic variables (rotational speed), both  and γ are greatly affected by the geometric parameters (impeller diameter, cross-sectional area of the tank, liquid height, rotor blade length and immersion height). By doing numerical computation by VISIMIX ®, present work analyzes the effect of non-dimensional (which is non-dimensionalized through rotor diameter) geometric parameters on e and g. With an increase in liquid height, there is an increase in the case of energy dissipation and shear rate values. In the case of tank area and blade length, it is vice versa. Energy dissipation and shear rate are not affected by the variation in immersion height of the impeller. © 2009 BCREC UNDIP. All rights reserved [Received: 17 October 2009, Revised: 12 December 2009, Accepted: 20 December 2009] [How to Cite : B. Kumar. (2009). Variability of Energy Dissipation and Shear Rate with Geometry in Unbaffled Surface Aerator. Bulletin of Chemical Reaction Engineering and Catalysis , 4(2): 55-60. doi:10.9767/bcrec.4.2.7110.55-60 ] [ How to Link/ DOI : http://dx.doi.org/10.9767/bcrec.4.2.7110.55-60 || or local: http://ejournal.undip.ac.id/index.php/bcrec/article/view/7110 ]

Analysis of the Wicking and Thin-Film Evaporation Characteristics of Microstructures

The topology and geometry of microstructures play a crucial role in determining their heat transfer performance in passive cooling devices such as heat pipes. It is therefore important to characterize microstructures based on their wicking performance, the thermal conduction resistance of the liquid filling the microstructure, and the thin-film characteristics of the liquid meniscus. In the present study, the free-surface shapes of the static liquid meniscus in common microstructures are modeled using SURFACE EVOLVER for zero Bond number. Four well-defined topologies, viz., surfaces with parallel rectangular ribs, horizontal parallel cylinders, vertically aligned cylinders, and spheres (the latter two in both square and hexagonal packing arrangements), are considered. Nondimensional capillary pressure, average distance of the liquid free-surface from solid walls (a measure of the conduction resistance of the liquid), total exposed area, and thin-film area are computed. These performance parameters are presented as functions of the nondimensional geometrical parameters characterizing the microstructures, the volume of the liquid filling the structure, and the contact angle between the liquid and solid. Based on these performance parameters, hexagonally-packed spheres on a surface are identified to be the most efficient microstructure geometry for wicking and thin-film evaporation. The solid-liquid contact angle and the nondimensional liquid volume that yield the best performance are also identified. The optimum liquid level in the wick pore that yields the highest capillary pressure and heat transfer is obtained by analyzing the variation in capillary pressure and heat transfer with liquid level and using an effective thermal resistance model for the wick.

Natural convection in tilted rectangular enclosures with a vertically situated hot plate inside

A numerical study of laminar natural convection in tilted rectangular enclosures that contain a vertically situated hot plate is performed. The plate is very thin and isothermal on both lateral ends, and it acts as a heat source within the medium. Three surfaces of the rectangular enclosure are insulated while one lateral surface is cold. Navier–Stokes equations, continuity equation and the energy equation, along with the Boussinesq approximation, are expressed in the form of vorticity-transport equations. All the pertinent equations are solved using the finite volume method with SIMPLE algorithm. The Rayleigh numbers and the tilt angle of the enclosure are ranged from 10 5 to 10 7 and from 0° to 90°, respectively. The aspect ratios of the rectangular enclosures that are considered in this study are A = 1 and A = 2. The isotherms and streamlines are produced for various Rayleigh numbers and geometrical conditions, and steady-state Nusselt numbers are computed. The steady-state plate-surface-averaged Nusselt numbers are computed for each case as a function of Rayleigh number and other non-dimensional geometrical parameters and a correlation useful for practical problems was derived.

Elastic buckling of hexagonal chiral cell honeycombs

The paper describes a combined analytical, numerical and experimental analysis on the compressive strength of hexagonal chiral honeycombs due to elastic buckling of the unit cells under flatwise compressive loading. Hexagonal chiral honeycombs are cellular structures composed noncentresymmetric unit cells, with an in-plane negative Poisson’s ratio (NPR) with a value of −1. Cylinders connected by tangent ligaments at 60° degrees compose the unit cells. Approximated analytical models are proposed for the purpose of initial design assuming the main contribution to the elastic collapse stress being given by the nodes, and considering also the superposition of the critical elastic loads of each component of the unit cell. The models are expressed in terms of nondimensional geometric unit cell parameters (ligament to cylinder radius aspect ratio and relative density), and core material properties. Finite element calculations using shell and brick elements are also performed on unit cell models with periodic boundary conditions using linear bifurcation buckling analysis. The analytical and numerical results are compared with the outcome of a series of experimental flatwise compressive tests carried out on chiral honeycomb samples manufactured using rapid prototyping technique in PA sintered powder and ABS plastics. The comparison shows good convergence between the sets of results, and highlights the specific deformation mechanisms of the hexagonal chiral honeycomb cell.

Stability of Electrohydrodynamic Induction Pumping of Liquid Film in Vertical Annular Configuration

Instability of electrohydrodynamic (EHD) induction pumps can manifest itself in a sudden drop/jump in pump output. The instability can also result in alternating/bidirectional flow. To understand and avoid this erratic behavior of the pump operation, a nondimensional stability analysis of EHD induction pumping of liquid film in a vertical annular configuration in the presence of an external load (i.e., pressure gradient and gravitational force) for repulsion mode is carried out. A general nondimensional stability criterion is presented, indicating that the stability of the pump depends on the nondimensional geometric parameters of the pump as well as the nondimensional electric properties of the liquid film. A stability map based on dimensionless electric conductivity and liquid-film thickness is presented. The effect of the dimensionless angular velocity on the nondimensional interfacial velocity under the influence of a pressure gradient and gravitational force is investigated. It is also shown that the erratic behavior of the unstable pump can be eliminated by a proper selection of geometric and liquid-film parameters, as well as the traveling electric-wave frequency.

Non-dimensional analysis for effective design of semi-active electrorheological damping control systems

This paper presents a non-dimensional analysis for effective design of semi-active electro- rheological (ER) damping control systems. The non-dimensional equations consist of the Bingham number, the non-dimensional damping force, the dynamic range and the non-dimensional geometric parameter. After showing the effectiveness of the proposed analysis scheme through a comparative examination of predictions and measured values of the non-dimensional damping force, sequential steps for the ER damper design have been developed. A flow mode type ER damper, considering control performance of a semi-active quarter-car system, has been designed on the basis of the proposed non-dimensional design steps. To assess the effectiveness of the proposed non-dimensional design methodology, the field-dependent damping forces of an ER damper have been experimentally evaluated and compared with those obtained from the non-dimensional analysis.

Dynamic stress concentrations for an axially loaded strut at discontinuities due to an elliptical hole or double circular notches

Numerical modeling, simulation, and analysis of axial struts with geometrical discontinuities subjected to dynamic loading conditions is the focus of this paper. Understanding how geometrical discontinuities influence the stress distribution within a structural member is critical for design applications. Furthermore, understanding how axial struts perform under dynamic loading conditions is critical in the design of automobiles, airplanes, and a large number of potentially dynamically loaded structures. A large amount of research investigating static loading conditions of struts with geometrical discontinuities has been conducted. With the development of finite element (FE) codes, numerical dynamic analyses can be completed much easier and at much lower costs than would occur for experimental methods.In this research, FE simulations were conducted on struts with centrally located elliptical discontinuities. A good correlation was found between the results from these simulations and experiments conducted using the photolaserelastic technique. Based on these correlations, models of struts with circular notches located at the sides of the strut were simulated under the same loading condition. The stress distributions of the models were studied to determine the maximum stress state for each geometric configuration. This information was used to determine the dynamic stress concentration factor for each configuration.Three-dimensional surface plots were constructed illustrating how the numerically determined dynamic stress concentration factor varies with strut and discontinuity geometry. Design equations are presented that relate the dynamic stress concentration factor to non-dimensional geometric parameters. These equations are a useful tool for engineers involved in automotive and aerospace component design.

Bearing capacity of strip footings with horizontal confinement

For a strip footing under axial loading, the bearing capacity is influenced by the presence of rigid walls confining the foundation soil. This problem is investigated within the framework of the theory of yield design, considering both a perfectly rough and a frictionless contact condition at the interfaces with the walls in the case of a purely cohesive soil. Upper bounds for the correction factor to be applied to the classical value of the bearing capacity are determined, as functions of the non-dimensional geometric parameter of the problem, through the kinematic approach, implementing virtual velocity fields inspired from the solution to the problem of inverted extrusion. In the perfectly rough case, it appears that the new upper bound is a significant improvement of those already available. A very simple relationship is established, which derives the upper bound for the frictionless walls from the upper bound for the rough walls. A general conclusion of the analysis is that, for the values of the geometric parameter that are likely to be encountered in practice, the increase in the bearing capacity due to the presence of the rigid walls remains very small. To cite this article: J. Salençon, C. R. Mecanique 331 (2003).

On the kinematic design of the 5R planar, symmetric manipulator

A complete kinematic characterization of the 5R planar, symmetric manipulator, intended as a design aid, is proposed in this paper. The characterization scheme relies on the configuration of the Cartesian workspace plots (CWP), the Cartesian workspace singularity plots (CWSP), the joint workspace plots (JWP) and the joint workspace singularity plots (JWSP). These plots are given in terms of two nondimensional geometric parameters, λ and μ, that represent the lengths of the manipulator links; these parameters can be used to investigate the relationships between the link lengths of the manipulator and the underlying workspace and singularity distribution. The plots can be regarded as an atlas of the workspace and singularity distribution that should find applications in analysis and design.

Stress concentration in cone–cylinder intersection

The finite element method and shell theory were employed to investigate cone–cylinder shell intersections. The developed special-purpose computer program Sais (stress analysis in intersecting shells) was used for elastic stress analysis of branch connections. A comparison of calculated results with experimental data is presented. A parametric study of non-radial models of the cone–cylinder shell intersection subjected to internal pressure loading was performed. The intersections of thin and middle thickness shells were analysed. The results are presented in graphical form. Non-dimensional geometric and angular parameters are considered to analyse the effects of changing these parameters on stress ratios in the shell intersection.

Parametric Study of Simplex Fuel Nozzle Internal Flow and Performance

A numerical study is presented of the effects of changes in simplex nozzle geometry on its performance. A computational model based on the arbitrary-Lagrangian-Eulerian method with an adaptive grid-generation scheme is used. Three nondimensional geometric parameters are studied: the length-to-diameter ratio of the swirl chamber L s /D s and orifice l o /d o and the swirl-chamber-diameter-to-exit-orifice-diameter ratio D s /d o , The variations in the atomizer performance, caused by the changes in the geometric parameters, are presented in terms of the film thickness at the exit of the orifice, the spray cone angle, and the discharge coefficient. Results indicate that these geometric parameters have a significant effect on the internal flow and performance of simplex nozzles. With a constant mass flow through the nozzle over the range of parameters considered, an increase in L s /D s produces an increase in the film thickness at the orifice exit, a decrease in the spray cone half-angle, and a slight decrease followed by an increase in the discharge coefficient. Conversely, increasing l o /d o decreases film thickness, spray cone angle, and discharge coefficient. An increase in D s /d o results in a decrease in film thickness and discharge coefficient and a decrease in spray cone angle.