DESIGN AND MANUFACTURE OF A SMALL-SCALE GAMMA-TYPE STIRLING ENGINE PROTOTYPE AND ANALYSIS OF EFFICIENCY AND POWER USING FIRST-ORDER DESIGN METHODS

2019 ◽  
Author(s):  
Klünger Arthur Éster Beck ◽  
Jean-Marc Lafay ◽  
Francisco Augusto Aparecido Gomes
Keyword(s):  
Stirling Engine ◽  
Design Methods ◽  
Small Scale ◽  
First Order ◽  
Design And Manufacture

Diffusion Experiments with a Global Discontinuous Galerkin Shallow-Water Model

2009 ◽  
Vol 137 (10) ◽  
pp. 3339-3350 ◽  
Author(s):  
Ramachandran D. Nair
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Water Model ◽  
Order System ◽  
Small Scale ◽  
Shallow Water Model ◽  
First Order ◽  
Advection Diffusion Equation ◽  
Diffusion Scheme ◽  
Cubed Sphere

Abstract A second-order diffusion scheme is developed for the discontinuous Galerkin (DG) global shallow-water model. The shallow-water equations are discretized on the cubed sphere tiled with quadrilateral elements relying on a nonorthogonal curvilinear coordinate system. In the viscous shallow-water model the diffusion terms (viscous fluxes) are approximated with two different approaches: 1) the element-wise localized discretization without considering the interelement contributions and 2) the discretization based on the local discontinuous Galerkin (LDG) method. In the LDG formulation the advection–diffusion equation is solved as a first-order system. All of the curvature terms resulting from the cubed-sphere geometry are incorporated into the first-order system. The effectiveness of each diffusion scheme is studied using the standard shallow-water test cases. The approach of element-wise localized discretization of the diffusion term is easy to implement but found to be less effective, and with relatively high diffusion coefficients, it can adversely affect the solution. The shallow-water tests show that the LDG scheme converges monotonically and that the rate of convergence is dependent on the coefficient of diffusion. Also the LDG scheme successfully eliminates small-scale noise, and the simulated results are smooth and comparable to the reference solution.

Experimental characterization of an innovative low-temperature small-scale Rotary Displacer Stirling Engine

2019 ◽  
Vol 201 ◽  
pp. 112073
Author(s):  
Amirhossein Bagheri ◽  
William C. Mullins ◽  
Phillip R. Foster ◽  
Huseyin Bostanci
Keyword(s):  
Low Temperature ◽  
Stirling Engine ◽  
Small Scale ◽  
Experimental Characterization

Reverberation Intensity Decaying in Range-Dependent Waveguide

2019 ◽  
Vol 27 (03) ◽  
pp. 1950007
Author(s):  
J. R. Wu ◽  
T. F. Gao ◽  
E. C. Shang
Keyword(s):  
Large Scale ◽  
Back Propagation ◽  
Normal Modes ◽  
Small Scale ◽  
Signal Pulse ◽  
First Order ◽  
Orthogonal Property ◽  
Short Signal ◽  
Scale Roughness ◽  
Special Case

In this paper, an analytic range-independent reverberation model based on the first-order perturbation theory is extended to range-dependent waveguide. This model considers the effect of bottom composite roughness: small-scale bottom rough surface provides dominating energy for reverberation, whereas large-scale roughness has the effect of forward and back propagation. For slowly varying bottom and short signal pulse, analytic small-scale roughness backscattering theory is adapted in range-dependent waveguides. A parabolic equation is used to calculate Green functions in range-dependent waveguides, and the orthogonal property of local normal modes is employed to estimate the modal spectrum of PE field. Synthetic tests demonstrate that the proposed reverberation model works well, and it can also predict the reverberation of range-independent waveguide as a special case.

scholarly journals Derivation of Canopy Resistance in Turbulent Flow from First-Order Closure Models

Water ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 1782 ◽  
Author(s):  
Wei-Jie Wang ◽  
Wen-Qi Peng ◽  
Wen-Xin Huai ◽  
Gabriel Katul ◽  
Xiao-Bo Liu ◽  
...  
Keyword(s):  
Friction Factor ◽  
Free Surface Flows ◽  
Hydrodynamic Resistance ◽  
Small Scale ◽  
Length Scale ◽  
Length Scales ◽  
First Order ◽  
Closure Models ◽  
Wide Range ◽  
The Mean

Quantification of roughness effects on free surface flows is unquestionably necessary when describing water and material transport within ecosystems. The conventional hydrodynamic resistance formula empirically shows that the Darcy–Weisbach friction factor f~(r/hw)1/3 describes the energy loss of flowing water caused by small-scale roughness elements characterized by size r (<<hw), where hw is the water depth. When the roughness obstacle size becomes large (but <hw) as may be encountered in flow within canopies covering wetlands or river ecosystem, the f becomes far more complicated. The presence of a canopy introduces additional length scales above and beyond r/hw such as canopy height hv, arrangement density m, frontal element width D, and an adjustment length scale that varies with the canopy drag coefficient Cd. Linking those length scales to the friction factor f frames the scope of this work. By adopting a scaling analysis on the mean momentum equation and closing the turbulent stress with a first-order closure model, the mean velocity profile, its depth-integrated value defining the bulk velocity, as well as f can be determined. The work here showed that f varies with two dimensionless groups that depend on the canopy submergence depth and a canopy length scale. The relation between f and these two length scales was quantified using first-order closure models for a wide range of canopy and depth configurations that span much of the published experiments. Evaluation through experiments suggests that the proposed model can be imminently employed in eco-hydrology or eco-hydraulics when using the De Saint-Venant equations.

scholarly journals A Note on Torsion of Nonlocal Composite Nanobeams

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Luciano Feo ◽  
Rosa Penna
Keyword(s):  
Order Differential Equation ◽  
Scale Effects ◽  
Elastic Equilibrium ◽  
Functionally Graded ◽  
Small Scale ◽  
Cross Sectional ◽  
Graded Materials ◽  
First Order ◽  
Sectional Plane ◽  
Mixed Framework

The ERINGENelastic constitutive relation is used in this paper in order to assess small-scale effects in nanobeams. Structural behavior is studied for functionally graded materials in the cross-sectional plane and torsional loading conditions. The governing boundary value problem has been formulated in a mixed framework. Torsional rotations and equilibrated moments are evaluated by solving a first-order differential equation of elastic equilibrium with boundary conditions of kinematic-type. Benchmarks examples are briefly discussed, enlightening thus effectiveness of the proposed methodology.

Nonlinear Pull-In Instability of Strain Gradient Microplates Made of Functionally Graded Materials

2019 ◽  
Vol 19 (02) ◽  
pp. 1950007 ◽  
Author(s):  
R. Gholami ◽  
R. Ansari ◽  
H. Rouhi
Keyword(s):  
Functionally Graded Materials ◽  
Strain Gradient ◽  
Scale Effects ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Small Scale ◽  
Gradient Theory ◽  
Graded Materials ◽  
First Order ◽  
Size Dependent

In this paper, the size-dependent nonlinear pull-in behavior of rectangular microplates made from functionally graded materials (FGMs) subjected to electrostatic actuation is numerically studied using a novel approach. The small scale effects are taken into account according to Mindlin’s first-order strain gradient theory (SGT). The plate model is formulated based on the first-order shear deformation theory (FSDT) using the virtual work principle. The size-dependent relations are derived in general form, which can be reduced to those based on different elasticity theories, including the modified strain gradient, modified couple stress and classical theories (MSGT, MCST and CT). The solution of the problem is arrived at by employing an efficient matrix-based method called the variational differential quadrature (VDQ). First, the quadratic form of the energy functional including the size effects is obtained. Then, it is discretized by the VDQ method using a set of matrix differential and integral operators. Finally, the achieved discretized nonlinear equations are solved by the pseudo arc-length continuation method. In the numerical results, the effects of material length scale parameters, side length-to-thickness ratio and FGM’s material gradient index on the nonlinear pull-in instability of microplates with different boundary conditions are investigated. A comparison is also made between the predictions by the MSGT, MCST and CT.

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