Averaging methods for numerical simulations of flows through heterogeneous porous media

Many natural rock systems contain small patches of different permeability which affect the flow of fluids through them. As these heterogeneities become smaller and more numerous, they become harder to model numerically. We consider how to reduce the computational effort required in simulations by incorporating their effects in the boundary conditions at the edges of each grid block. This is in contrast with current methods which involve often arbitrary changes in the fluid properties. The method is restricted to the case of widely-spaced patches, which simplifies interaction effects. The system then reduces to an array of dipoles, and two averaging methods are proposed for finite grid blocks. Several infinite systems, including vertical and horizontal bands, are also considered as further approximations. There is a great wealth of existing results from different fields which lead to identical mathematical problems and which can be used in these cases. Finally, we consider how to use these techniques when the precise configuration of the grid block is not known, but only its statistical properties. This can lead to results which are very different from the deterministic case.     

Lifting Surface in Subsonic Unsteady Regime

The paper refers to the solution of the integral equation for the acceleration (or pressure) potential for the study of subsonic linearized unsteady flow in view of aeroelastic applications. The case considered is relevant to a trapezoidal wing infinitely thin surface without discontinuities. As is well known [1, 2], the kernel of the integral equation exhibits three singularities, two of which are integrable in elementary form, whereas, for the third one integration in principal part according to Hadamard's rule is necessary. The kernel is therefore reworked in such a way that all the singularities are separated from the regular part, and eventually the discretization is performed in such a way that only the regular part is to be recalculated for each new value of the reduced frequency. Convergence tests, comparison with other methods of solution, and time saving associated with the technique of separation are also shown.Sommario. II lavoro tratta la risoluzione del problema relativo alla equazione integrale nel potenziale di accelerazione (o di pressione) per lo studio di una corrente subsonica linearizzata nonstazionaria, in vista di applicazioni aeroelastiche. Il caso considerato è quello di una superficie alare a pianta trapezoidale in assenza di discontinuità di spessore infinitesimo. Come è noto [1, 2], il nucleo della equazione integrale in parola presenta tre singolarità, due sole delle quali sono integrabili in forma elementare, (o riconducibili ad essa), mentre per la terza è necessario far ricorso alla integrazione in parte principale alla Hadamard. Il nucleo stesso viene quindi rielaborato in modo da isolare tutte le singolarità dalla componente regolare del nucleo; si procede così alla discretizzazione dell' equazione integrale, e, per ogni valore della frequenza ridotta, va ricalcolata solo la parte regolare della matrice risolvente. Vengono poi effettuati tests di convergenza, confronti con altri metodi di soluzione, analisi sui tempi di calcolo e risparmio di tempo di calcolo dovuto alla tecnica di separazione.     

Air-cooled gas-turbine discs: a review of recent research

The flow between corotating compressor or turbine discs and the flow between a turbine disc and an adjacent stationary casing can be respectively modelled by a rotating cavity and by a rotor-stator system. This paper reviews some of the recent experimental and theoretical work on flow and heat transfer in these two classes of rotating-disc systems. Comparisons between the theoretical and measured distributions of velocity, pressure, and Nusselt numbers are made for the rotating cavity with a superimposed radial flow of cooling air. For the rotor-stator system, some recent work on the fluid dynamics is outlined, and particular mention is made of the so-called “ingress problem” and of the use of pre-swirl air to improve the blade-cooling effectiveness.     

Friction factors of finite and infinite square arrays of roughened pins

Friction factors of square arrays of roughened pins in smooth channels have been measured for a range of pin pitch to diameter ratios and roughness heights and for different sizes of array. The influence of the smooth channel has been removed in two ways; by extrapolating the results for a fixed pitch-to-diameter ratio to an infinite number of pins and by calculation from the finite array results. The resultant friction factors are compared with each other and with data obtained by testing single pins in smooth circular channels and transforming by various methods to the fully rough situation.     

End effects for highly elastic-constant viscosity fluids

In the light of a new interpretation, we have studied the end effects for highly elastic-constant viscosity fluids commonly called Boger fluids. In terms of entrance effect only, the presence of primary normal-stress differences in absence of shear-thinning properties results in a decrease of the entrance correction below the Couette (Newtonian) value, whereas the total end correction can be substantially increased by an amount which is strongly dependent on the Weissenberg number or recoverable shear.     

Professor T. C. Papanastasiou's contributions to rheology and computational fluid mechanics

Professor T. C. Papanastasiou's contributions to rheology and computational fluid mechanics are numerous and have a lasting effect. In the short span of a professional career of about 10 years, and in such diverse places as the University of Minnesota, the University of Michigan, and the Aristotle University of Thessaloniki, he developed and implemented new ideas in the fields of rheology and computational fluid mechanics. He dealt with such important topics as: i) modelling of viscoelasticity and viscoplasticity through appropriate constitutive equations; ii) numerical techniques based on the finite element method, streamline integration, inverse of the unknown, and Newton iteration for integral-differential equations; iii) numerical simulation of important polymer processes, such as fiber spinning, film blowing, film casting, extrusion and coextrusion of polymeric liquids; iv) stability analysis of multiple flows; v) three-dimensional computational techniques for generalized Newtonian flows; vi) numerical analysis of viscoplastic flows; vii) solidification problems; viii) outflow boundary conditions, etc.His many contributions include authoring two books in the area of fluid mechanics, one for undergraduate and the other for graduate use. He was a mentor and an advisor to a dozen people, his former students, who have, in their own right, successful careers, some as professors, others as research engineers in major industries. The ideas and foundations of his work are currently pursued and studied by many researchers world-wide, and in this manner it is the most appropriate tribute to him and a guarantee that his name will be remembered for years to come.Dedicated to the memory of Professor Tasos C. Papanastasiou     

Two fluid flow and heat transfer in an inclined channel containing porous and fluid layer

Convective flow and heat transfer in an inclined channel bounded by two rigid plates held at constant different temperatures with one region filled with porous matrix saturated with a viscous fluid and another region with a clear viscous fluid different from the fluid in first region is studied analytically. The coupled nonlinear governing equations are solved using regular perturbation method. It is found that the presence of porous matrix in one of the region reduces the velocity and temperature. Results have been presented for a wide range of governing parameters such as Grashof number, porous parameter, angle of inclination, ratio of heights of the two layers and also the ratio of viscosities.     

流体力学Petrov-Galerkin有限元法研究进展

详细评述了在流体力学分析中Ｐｅｔｒｏｖ－Ｇａｌｅｒｋｉｎ方法（主要是ＳＵＰＧ方法和ＧＬＳ方法）的研究进展，并提出了今后的发展方向和研究重点。     

Liquid–crystalline nematic polymers revisited

A new model for nematic polymers is proposed, based on the probability ψ(u,u,t) for a macromolecule to be oriented along direction u while embedded in a u environment created by its neighbours. The potential of the internal forces is written Φ(u,u) accordingly. The free energy contains a contribution ν Φ + k_BT ln ψ where the brackets mean an average over the probability distribution, while ν is the (uniform) polymer number density. An equation is derived for the time-evolution of the order parameter S = uu − I/3, together with an expression for the stress tensor. These two results offer a generalization of the Doi Model in so far as they include a distortional energy, analogue to the Frank elastic energy for low molecular mass nematics. Extending the Maier–Saupe variational procedure, we specify the way that the internal potential Φ(u,u) must be written for it to favour non-zero values of the order parameter, while giving a penalty to situations with gradients of the order parameter. The result is quite different from the potential proposed a decade ago by Marrucci and Greco (their Φ depends on u only), while it has a clear connection with the so-called Landau-de Gennes (LdG) tensor models, which are based on a free-energy depending on the order parameter and its gradients.     

Unsteady model of drop Marangoni migration in microgravity

The experiments of drop Marangoni migration have been performed by the drop shift facility of short period of 4.5 s, and the drop accelerates gradually to an asymptotic velocity during the free fall. The unsteady and axisymmetric model is developed to study the drop migration for the case of moderate Reynolds numberRe=O(1), and the results are compared with the experimental ones in the present paper. Both numerical and experimental results show that the migration velocity for moderate Reynolds number is several times smaller than that given by the linear YGB theory. The project supported by the National Natural Science Foundation (19789201) and the Ministry of Science and Technology of China (95-Yu-34)