Similarity and weak closing relations for symmetric free turbulence

1979 ◽  
Vol 14 (1) ◽  
pp. 31-37 ◽  
Author(s):  
V. A. Gorodtsov
Keyword(s):  
Closing Relations

Modeling of pressure losses on friction in three-layer laminar flows

2003 ◽  
Vol 3 ◽  
pp. 208-219
Author(s):  
A.M. Ilyasov
Keyword(s):  
Pressure Loss ◽  
Gas Flow ◽  
Mutual Influence ◽  
Fluid Model ◽  
Immiscible Liquid ◽  
Laminar Flows ◽  
Pressure Losses ◽  
Flow Parameters ◽  
Interphase Boundaries ◽  
Closing Relations

In this paper we propose a model for determining the pressure loss due to friction in each phase in a three-layer laminar steady flow of immiscible liquid and gas flow in a flat channel. This model generalizes an analogous problem for a two-layer laminar flow, proposed earlier. The relations obtained in the final form for the pressure loss due to friction in liquids can be used as closing relations for the three-fluid model. These equations take into account the influence of interphase boundaries and are an alternative to the approach used in foreign literature. In this approach, the wall and interphase voltages are approximated by the formulas for a single-phase flow and do not take into account the mutual influence of liquids on the loss of pressure on friction in phases. The distribution of flow parameters in these two models is compared.

scholarly journals Thermal detonation wave in liquid lead – water mixture

2021 ◽  
Vol 2088 (1) ◽  
pp. 012027
Author(s):  
A V Kapustin ◽  
V I Melikhov ◽  
O I Melikhov ◽  
B Saleh ◽  
D V Finoshkina
Keyword(s):  
Heat Transfer ◽  
Shock Wave ◽  
Detonation Wave ◽  
Boundary Conditions ◽  
Internal Structure ◽  
Interfacial Friction ◽  
Liquid Lead ◽  
Water Mixture ◽  
Friction Heat ◽  
Closing Relations

Abstract It was developed the model of thermal detonation in a mixture of continuous liquid lead and dispersed steam/water particles. Stationary equations of mass, impulse and energy conservations laws for multiphase continuum are applied to describe internal structure of thermal detonation wave. They are supplemented by closing relations describing interfacial friction, heat transfer, and fragmentation. Conditions at leading shock wave and at Chapman-Jouguet plane are used as boundary conditions.

System of closing relations of a two-fluid model for the HYDRA-IBRAE/LM/V1 code for calculation of sodium boiling in channels of power equipment

2017 ◽  
Vol 64 (7) ◽  
pp. 504-510 ◽  
Author(s):  
E. V. Usov ◽  
A. A. Butov ◽  
G. A. Dugarov ◽  
I. G. Kudasov ◽  
S. I. Lezhnin ◽  
...  
Keyword(s):  
Fluid Model ◽  
Power Equipment ◽  
Closing Relations ◽  
Two Fluid Model ◽  
Two Fluid

Scaling and forecast of drag reducing additive mechanical degradation along the pipeline

2021 ◽  
pp. 21-31
Author(s):  
Владимир Васильевич Жолобов ◽  
Фёдор Сергеевич Зверев ◽  
Георгий Викторович Несын ◽  
Дмитрий Олегович Лысенко
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Concentration Distribution ◽  
Field Tests ◽  
Full Scale ◽  
Mechanical Degradation ◽  
Actual Problem ◽  
Closing Relations ◽  
Scale Experiment ◽  
Drag Reducing Additive

Введение. Целесообразным является применение стендовых и численных экспериментов с целью определения интегральной гидравлической эффективности присадки при малой добавке высокомолекулярного полимера в трубопроводы большого диаметра. Однако проблема прогнозирования в промышленных условиях неразрывно связана с необходимостью учета деградации присадки. Цель статьи - построение такой математической модели путевой деградации присадки, чтобы ее свободные параметры могли быть идентифицированы на основе как опытно-промышленных, так и стендовых испытаний. Методы. На основе положений теории распространения примесей и тепла в осевых турбулентных потоках сформулирован одномерный вариант математической модели неизотермического течения раствора. С использованием аналогии уравнений распространения тепла и примесей и аналогии в граничных и начальных условиях записано решение для распределения концентрации активной части присадки в виде аналога формулы Шухова для тепловых задач. Результаты. Предложена расчетная процедура для прогнозирования распределения гидравлической эффективности присадки на основе «диффузионного» аналога формулы Шухова с учетом механической деградации. С этой целью разработан алгоритм идентификации входящих параметров. Обсуждение. Определена система соотношений для расчета локальной и интегральной гидравлической эффективности присадки по длине трубопровода. Замыкающие соотношения могут быть получены путем обработки данных опытно-промышленных либо стендовых гидравлических экспериментов. Сформулированы некоторые требования к процедурам проведения и обработки данных экспериментов. Выводы. Прогнозирование гидравлической эффективности присадки целесообразно проводить путем предварительного расчета распределения концентрации активной части полимерной добавки с использованием «диффузионного» аналога формулы Шухова и известных зависимостей гидравлической эффективности от концентрации и других параметров. Introduction. To go before the field tests of drag reducing agents (DRA) in the trunk lines they do laboratory experiments and numerical simulations. A forecasting effort in DRA behavior includes taking account of their degradation. That is why a mathematical model of running degradation where free variables can be determined both in laboratory or full-scale experiment is an actual problem. Methods. One-dimension mathematical model of non-isothermal flow was formulated on the base of corresponding heat and ingredients transfer in the axial turbulent flow. According to correspondence equations as well as boundary conditions of DRA concentration distribution we’ve got a solution in a form of Shukhov’s equation for heat transfer. Results. Forecasting of DRA effectiveness distribution was suggested on the base of “diffusive” analogue of Shukhov’s equation for heat transfer including the degradation effect. Characteristics’ identification procedure was made up. Discussion. Set of correlations was derived for local and cumulative DRA effectiveness along the pipeline while closing relations were evaluated both from laboratory and full-scale experiments. The way of data handling is also suggested. Conclusion. Drag reducing effectiveness forecast should be based on concentration distribution estimation according to “diffusive” analogue of Shukhov’s equation for heat transfer with taking in account of concentration dependence of drag reduction.

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