Elliptic Concept Research Articles

Some new considerations concerning the Rayleigh‐wave velocity in auxetic materials

AbstractThe Rayleigh wave velocity is examined in isotropic and non‐isotropic auxetic (negative Poisson's ratio) solids. A novel approximation of the Rayleigh wave speed c versus the Poisson's ratio of an isotropic solid is derived using the concept of ellipticity. The Rayleigh wave propagation is investigated also for anisotropic incompressible solids, such as thick composite balanced symmetric cross‐ply laminates, exhibiting through‐the‐thickness negative Poisson's ratio. The results show increased wave speed for auxetic laminate configurations, as well as increased sensitivity of the wave speed in the cross‐ply regions corresponding to NPR values. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Elliptic relaxation second moment closure for the turbulent heat fluxes

This study describes the development of near-wall second moment turbulent heat flux model and its application to various turbulent flows with heat transfer to test the performance of the model. The second moment models for turbulent heat fluxes based on the elliptic concept are proposed and closely linked to the elliptic blending model, which is used for the prediction of Reynolds stresses. The new models satisfy the near-wall balance between viscous diffusion, viscous dissipation and pressure–temperature gradient correlation, and also have the characteristics of approaching their respective conventional high Reynolds number model far away from the wall. On the other hand, the traditional heat flux model using the wall-normal vector expression in the wall-reflection model is tested in the present study with the new unit wall-normal vector formulation that appears in the elliptic blending model. To develop and calibrate the new heat flux models, firstly, the distributions of the mean temperature and the scalar flux in a fully developed non-rotating channel flow are solved by the present models in constant wall temperature difference boundary condition. And then, the fully developed rotating channel and square duct flows with heat transfer and the wall bounded turbulent flows with buoyancy are simulated by the new elliptic concept models to show their applicability to the complex flows. The results of prediction are directly compared to the DNS and the LES to assess the performance of new model predictions and show the reasonable agreement with the DNS and the LES data for all the flow fields adopted in the present study.

Numerical analysis of turbulent flow and heat transfer in a square sectioned U-bend duct by elliptic-blending second moment closure

A second moment turbulence closure using the elliptic-blending equation is introduced to analyze the turbulence and heat transfer in a square sectioned U-bend duct flow. The turbulent heat flux model based on the elliptic concept satisfies the near-wall balance between viscous diffusion, viscous dissipation and temperature-pressure gradient correlation, and also has the characteristics of approaching its respective conventional high Reynolds number model far away from the wall. Also, the traditional GGDH heat flux model is compared with the present elliptic concept-based heat flux model. The turbulent heat flux models are closely linked to the ellipticblending second moment closure which is used for the prediction of Reynolds stresses. The predicted results show their reasonable agreement with experimental data for a square sectioned U-bend duct flow field adopted in the present study.

Ellipticity Conditions of the Shallow Water Balance Equations for Atmospheric Data

Abstract Nonlinear normal mode initialization equations, which provide required balance relations for atmospheric data, are considered in the generalized case of shallow water equations in arbitrary orthogonal coordinates. Using the concept of ellipticity in the sense of Douglis–Nirenberg, the conditions of well posedness of boundary value problems for balance equations are derived in the cases of constrained streamfunction, constrained potential vorticity, and constrained pressure fields.