Abstracts

Mathematical Modelling

Use of Reynolds equations in modeling of turbulent flows (more precisely, of energocontaining structure of such flows) has resulted in creation of a plenty of models, i.e. statistical models for of one-point moments (such as usual, central and mixed moments) that have been constructed by unconditional averaging of "instant" differential equations of hydrodynamics (such as Navier - Stokes equations ) according to Reynolds method. Nevertheless, in spite of tremendous experience in modeling the universal model for various types of flows have not been worked out. Moreover, it fails to construct and exact enough (even at essential "lengthening" of Freedman-Keller chain) model of some specifically taken turbulent shear flow with an opportunity of adequate calculations of all set of "average" and "pulsating" characteristics. To the basic lacks of such models must be assumed the impossibility of detailed description of the turbulent flow connected to an intermittency of dynamic fields. Now there are models of new generation which is taking into account the intermittency effect and which are intensively developing. The basic advantage of such models is the opportunity of more detailed description of turbulent flows by means of conditional averages, i.e. conditional one-point statistical moments of dynamic fields of each of intermittenting mediums of flow. However attempts, undertaken in this direction, has been resulted in significant complication of modeling and gave a lot of questions of theoretical character, including questions of closing of the equations for conditional average. Moreover, these equations contain complete average and again the Reynolds equations are necessary for their definition. As a consequence, models of such type can not to increase the efficiency and accuracy of calculations of turbulence characteristics.
The convincing acknowledgement to aforesaid is "Collective testing of turbulence models" the results of which is in organizers's opinion of these rounds as "unfavourable". Most of submitted models to testing are analogue of the "k-e" model, i.e. in essence it were models constructed on basis of the averaging by Reynolds method. Thereupon it is natural to assume the method of Reynolds contains some defect are hampering to constructing of more effective and exact models of turbulent flows.
In given work the analysis of known methods of modeling of energy-containing (large-scale) structure of inhomogeneous turbulent flows have been carried out, the problem of constructing models based on Reynolds equations has been opened and illustrated that the method of reception of such equations (the method of Reynolds) contains defect of fundamental character. It is marked the defect found out here are hampering the progress of increasing of quality of mathematical models of turbulent flows and that the problem may be solved by use of a new method of modeling [1] with taking into account effect of an intermittency of various dynamic fields of considered turbulent flow.
The results of the carried out analysis and conclusions made at it are illustrated on an example of constructing model (according to the method [1]) of the turbulent wall boundary layer in conditions of an intermittency. At this have been indicated the excellent accordance of conditional averages (for each of intermittenting mediums) and complete averages of the statistical characteristics, including "average" and "pulsating", with experimental data, available in the literature.

1 Nuzhnov Yu.V. Conditional Averaging of the Navier-Stokes Equations and a New Approach to Modelling Intermittent Turbulent Flows//J. Fluid Dynamics. 1997. Vol..32, No.4. P.489-494.

Note. Abstracts are published in author's edition

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