Large eddy simulations of the turbulent flow between a rotating and a stationary disk

Large eddy simulations of the flow between a rotating and a stationary disk have been performed using a dynamic and a mixed dynamic subgrid-scale model. The simulations were compared to direct numerical simulation results. The mixed dynamic model gave better overall predictions than the dynamic model. Modifications of the near-wall structures caused by the mean flow three-dimensionality were also investigated. Conditional averages near strong stress-producing events led to the same conclusions regarding these modifications as studies of the flow generated by direct numerical simulation, namely a distinct asymmetry of the vortices producing sweeps and ejections.     

Large eddy simulations of the turbulent flow between a rotating and a stationary disk

Large eddy simulations of the flow between a rotating and a stationary disk have been performed using a dynamic and a mixed dynamic subgrid-scale model. The simulations were compared to direct numerical simulation results. The mixed dynamic model gave better overall predictions than the dynamic model. Modifications of the near-wall structures caused by the mean flow three-dimensionality were also investigated. Conditional averages near strong stress-producing events led to the same conclusions regarding these modifications as studies of the flow generated by direct numerical simulation, namely a distinct asymmetry of the vortices producing sweeps and ejections.     

A note on limiting distributions for spacings statistics

Summary Hájek's projection method is used to prove asymptotic normality for a class of spacings statistics.The author thanks Dr. John Petkau for useful discussions.     

Heat transfer and Reynolds' analogy in a turbulent flow with heat release

Zusammenfassung Es wird die Wärmeübertragung von und zu einer voll entwickelten, wärmeabgebenden, turbulenten Strömung in einem Rohr analysiert. Durch die Anwendung der Laplace-Transformation wird die partielle Randwertaufgabe der Temperaturverteilung in einem Rohr von kreisförmigem Querschnitt auf eine gewöhnliche Sturm-Liouvillesche Randwertaufgabe zurückgeführt. Die entsprechenden Eigenwerte und Eigenfunktionen können nun mittels des Ritzschen Verfahrens für verschiedene Werte der Prandtlschen und Reynoldsschen Zahlen berechnet werden.Die Verteilung der Temperatur und des Wärmeflusses entlang der Wand erhält man in Form einer Reihe, deren Glieder diese Eigenwerte und Eigenfunktionen enthalten. Durch Verallgemeinerung des Prandtlschen Wärmequellen-Satzes wird die Reynoldssche Analogie der Wärmeübertragung und der flüssigen Reibung für eine wärmeabgebende turbulente Strömung erweitert.Die genaue asymptotische Wärmefluss und Temperaturverteilung, die man erhält, gestattet eine Abschätzung des Fehlers, den man bei einer Anwendung der Ritzschen Methode und der daraus folgenden Reihenentwicklung erhalten würde. Diese Analyse kann für die wärmeabgebenden turbulenten Strömungen in Atomreaktoren angewendet werden.

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The results presented in this paper were obtained in the course of research sponsored by the Office of Scientific Research of the ARDC, US Air Force under Contract AF 18 (603)-104.     

The heat transfer problem in the wall region of a turbulent boundary layer

The problem of heat transfer in the wall region of a turbulent boundary layer has been investigated. The resonant triad in the theory of hydrodynamic stability was used to obtain the velocity field induced by the coherent structures in the wall region of the turbulent boundary layer, while the small scale turbulence was represented by a simple model. By such a new approach of modeling, the 3-D temperature field is calculated, the mean temperature profile in the wall region and the Nusselt number characterizing the heat flux, which was found to be in good agreement with the experimental observations are obtained. The instantaneous temperature field had streaky structures, thus offering a mechanism for their generation found in numerical simulations. Project supported by the National Natural Science Foundation of China (Grant No. 19132011).     

A note on a characterization of the Poisson and uniform distributions

It is shown that if U, X are independent random variables, X≥0, U is uniformly distributed in (0,1), and X satisfies the equation UX+2∼U+X, then X−2 has the Poisson distribution with the parameter equal one. The above equation also characterizes the uniform distribution if X−2 is a Poisson random variable. Moreover, a multivariate generalization is given. Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994.     

Formulation of wall boundary conditions in turbulent flow computations on unstructured meshes

Features of the formulation and numerical implementation of wall boundary conditions in turbulent flow computations on unstructured meshes are discussed. A method is proposed for implementing weak wall boundary conditions for a finite-volume discretization of the Reynolds-averaged Navier-Stokes equations on unstructured meshes. The capabilities of the approach are demonstrated in several gasdynamic simulations in comparison with the method of near-wall functions. The influence of the near-wall resolution on the accuracy of the computations is analyzed, and the grid dependence of the solution is compared in the case of the near-wall function method and weak boundary conditions.     

A note on positive distributions in Gaussian analysis

We describe positive generalized functional in Gaussian analysis. We focus on the large distribution space (N)^–1. It is shown that a positive distribution is represented by a measure with specific growth of its moments. Equivalently, this statement can be replaced by the integrability condition.Dedicated to Yu. M. Berezanskii on the occasion of his 70th birthdayPublished in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 649–658, May, 1995.     

A short note on convergence near a high order zero

The behaviour of different iteration schemes, when used to find a high order zero, is studied from the point of view of function value reduction. It is found that the ratio between successive function values, for a given scheme, converges to a value for increasing order of the zero.     

A note on the justification of the eddy current model in electrodynamics

The issue of justifying the eddy current approximation of Maxwell's equations is reconsidered in the time‐dependent setting. Convergence of the solution operators is shown in the sense of strong operator limits.     

On the calculation of heat transfer rates in fully turbulent wall flows

A wall function for heat transfer is derived from the heat and mass transfer laws developed by Kader and Yaglom for turbulent wall flows. The wall function is used as a component of a prediction procedure to compute heat transfer rates in boundary layers, pipes, and wall jets. The results are generally in good agreement with the experimental data, but under most conditions the new function gives only a relatively minor improvement over existing functions. However, significant improvement is obtained for very large molecular Prandtl numbers.     

Natural convective boundary-layer flow in a heat generating porous medium with a prescribed wall heat flux

The free convection boundary-layer flow on a vertical surface in a porous medium with local heat generation proportional to (T – T_∞)^p, where T is the local temperature and T_∞ is the ambient temperature, is considered when the surface is thermally insulated. The way in which the flow develops from the leading edge is seen to depend critically on the exponent p. For p ≤ 2 there is a boundary-layer flow for all x > 0, where x measures distance from the leading edge, with the internal heating having a significant effect at large x. For p ≥ 5 there is also a boundary-layer flow to large x but now the internal heating has an increasingly weaker effect as x increases. For 2 < p <  5 the boundary-layer solution breaks down at a finite x, with a singularity developing leading to thermal runaway at a finite distance along the surface.     

Natural convective boundary-layer flow in a heat generating porous medium with a prescribed wall heat flux

The free convection boundary-layer flow on a vertical surface in a porous medium with local heat generation proportional to (T – T_∞)^p, where T is the local temperature and T_∞ is the ambient temperature, is considered when the surface is thermally insulated. The way in which the flow develops from the leading edge is seen to depend critically on the exponent p. For p ≤ 2 there is a boundary-layer flow for all x > 0, where x measures distance from the leading edge, with the internal heating having a significant effect at large x. For p ≥ 5 there is also a boundary-layer flow to large x but now the internal heating has an increasingly weaker effect as x increases. For 2 < p <  5 the boundary-layer solution breaks down at a finite x, with a singularity developing leading to thermal runaway at a finite distance along the surface.     

A note on a generalized network flow model for manufacturing process

Manufacturing network flow （MNF） is a generalized network model that overcomes the limitation of an ordinary network flow in modeling more complicated manufacturing scenarios, in particular the synthesis of different materials into one product and/or the distilling of one type of material into many different products. Though a network simplex method for solving a simplified version of MNF has been outlined in the literature, more research work is still needed to give a complete answer whether some classical duality and optimality results of the classical network flow problem can be extended in MNF. In this paper, we propose an algorithmic method for obtaining an initial basic feasible solution to start the existing network simplex algorithm, and present a network-based approach to checking the dual feasibility conditions. These results are an extension of those of the ordinary network flow problem.     

A note on convergence to mixtures of normal distributions

Double arrays of random variables obtained by normalizing a sequence that is asymptotically close to a martingale difference sequence are considered, and conditions ensuring that the row sums converge in distribution to a mixture of normal distributions are found. The main condition is that the sums of squares in each row converge in probability to a random variable.Research sponsored in part by the Office of Naval Research, Contract # N00014-75-C-0809