Extended intrinsic mean spin tensor for turbulence modelling in non-inertial frame of reference

We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in particular, its significance and importance in the approach of the algebraic Reynolds stress modelling, such as in a nonlinear K-ε model. To this end and for illustration of the effect of extended intrinsic spin tensor on turbulence modelling, we examine several recently developed nonlinear K-ε models and compare their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with LES data. Our results and analysis indicate that, only if the deficiencies of these models and the like be well understood and properly corrected, may in the near future, more sophisticated nonlinear K-ε models be developed to better predict complex turbulent flows in a non-inertial frame of reference.

Computation of the stability derivatives via CFD and the sensitivity equations

The method to calculate the aerodynamic stability derivates of aircrafts by using the sensitivity equations is ex- tended to flows with shock waves in this paper. Using the newly developed second-order cell-centered finite volume scheme on the unstructured-grid, the unsteady Euler equations and sensitivity equations are solved simultaneously in a non-inertial frame of reference, so that the aerodynamic stability derivatives can be calculated for aircrafts with complex geometries. Based on the numerical results, behavior of the aerodynamic sensitivity parameters near the shock wave is discussed. Furthermore, the stability derivatives are analyzed for supersonic and hypersonic flows. The numerical results of the stability derivatives are found in good agree- ment with theoretical results for supersonic flows, and variations of the aerodynamic force and moment predicted by the stability derivatives are very close to those obtained by CFD simulation for both supersonic and hypersonic flows.

LEARNERS' CULTURAL FRAME OF REFERENCE

Acquaintance with learners' cultural frame of reference can help second language teachers adjust and extend patterns of communication and create the optimal classroom conditions for acquisition of target language. This paper concentrates on reviewing diverse motivational, cognitive, and communicative styles; exploring their respective common patterns that arc grounded in the Chinese cultural and social and educational context; and examining the implications these three important components have for oral English teachers to work out ways to promote communication.

Spin path integral and quantum mechanics in the rotating frame of reference

We have developed a path integral formalism of the quantum mechanics in the rotating frame of reference, and proposed a path integral description of spin degrees of freedom, which is connected to the Schwinger bosons realization of the angular momenta. We have also given several important examples for the applications in the rotating frames.

Traditional Chinese medicine Qi model

This paper expounds the effect of"Qi"on human body by constructing the model of Qi,classifies the parts according to the category of Yin and Yang on the coordinate frame of 5 models of Yin and Yang,and compares each kind of parts according to the normal image state of human body.with the running direction of integer instead of Qi,the number of Qi in each part is calculated by the method of modern number theory,and the development and changes of human physiology and diseases are explained by"Qi".To explore the Trasitional Chinese Medicine treatment method of"the morbid Qi state of the human body adjusts the qi mode,the direction of qi operation and the intensity of Qi by means of medicinal taste and acupuncture,and returns to the normal state of qi balance mode in the direction of operation".

Computational Studies of Flow through Cross Flow Fans-Effect of Blade Geometry

This present paper describes three dimensional computational analysis of complex internal flow in a cross flow fan. A commercial computational fluid dynamics (CFD) software code CFX was used for the computation. RNG k-ε two equation turbulence model was used to simulate the model with unstructured mesh. Sliding mesh interface was used at the interface between the rotating and stationary domains to capture the unsteady interactions. An accurate assessment of the present investigation is made by comparing various parameters with the available experimental data. Three impeller geometries with different blade angles and radius ratio are used in the present study. Maximum energy transfer through the impeller takes place in the region where the flow follows the blade curvature. Radial velocity is not uniform through blade channels. Some blades work in turbine mode at very low flow coefficients. Static pressure is always negative in and around the impeller region.

Rotation-based finite elements:reference-configuration geometry and motion description

Infinitesimal-rotation finite elements allow creating a linear problem that can be exploited to systematically reduce the number of coordinates and obtain efficient solutions for a wide range of applications,including those governed by nonlinear equations.This paper discusses the limitations of conventional infinitesimal-rotation finite elements(FE)in capturing correctly the initial stress-free reference-configuration geometry,and explains the effect of these limitations on the definition of the inertia used in the motion description.An alternative to conventional infinitesimal-rotation finite elements is a new class of elements that allow developing inertia expressions written explicitly in terms of constant coefficients that define accurately the reference-configuration geometry.It is shown that using a geometrically inconsistent(GI)approach that introduces the infinitesimal-rotation coordinates from the outset to replace the interpolation-polynomial coefficients is the main source of the failure to capture correctly the reference-configuration geometry.On the other hand,by using a geometrically consistent(GC)approach that employs the position gradients of the absolute nodal coordinate formulation(ANCF)to define the infinitesimal-rotation coordinates,the reference-configuration geometry can be preserved.Two simple examples of straight and tapered beams are used to demonstrate the basic differences between the two fundamentally different approaches used to introduce the infinitesimal-rotation coordinates.The analysis presented in this study sheds light on the differences between the incremental co-rotational solution procedure,widely used in computational structural mechanics,and the non-incremental floating frame of reference formulation(FFR),widely used in multibody system(MBS)dynamics.

Applying extended intrinsic mean spin tensor in evolution algorithm for RANS modelling of turbulent rotating channel flow

We present a machine learning based method for RANS modeling in the rotating frame of reference(RFR).The extended intrinsic mean spin tensor(EIMST)is adopted in a novel expansion of the evolution algorithm,named multi-dimensional gene expression programming(MGEP).Based on DNS data,a constrain free model for Reynolds stress is created by considering system rotating.The anisotropy behavior of Reynolds stress is considered in the model,which is then for the first time applied for modeling turbulent flow inside a rotating channel.Compared with the traditional RANS model,the new model can predict the non-symmetric profile of Reynolds stress.Meanwhile,the Taylor-Gortler vortex is captured in our simulations with the new model.It is demonstrated that the application of EIMST in MGEP can be successfully adopted for RANS modeling in the RFR.

Fair and unfair inequality in China

The paper questions the normative value in the Chinese case of standard measures of aggregate income inequality such as the Gini coefficient.Evidence is adduced that people have narrow frames of reference and that they distinguish between income inequalities that they perceive to be fair and those that they perceive to be unfair.It is suggested that value judgements about what is fair or unfair can be guided by people’s own perceptions.People’s perceptions of unfairness can also be important to a government concerned to avoid social instability.The estimation of happiness functions can help to make the relevant distinctions.Examples are given of how fair and unfair inequalities might be identified,using either a criterion of people’s perceptions or one of informed judgements.Unfairness might be more strongly felt in inequalities of economic power than in inequalities of income,although the former can in turn result in inequalities of income.An argument is made for China researchers to extend inequality research and research instruments towards an economics of fairness and unfairness.