Standart k-ϵ Modeli Temelinde Eksenel Simetrik Sıkıştırılamaz Türbülanslı Akış Isı Transferi için Boyutsuz Ana Denklemlerin Türetilmesi

Abstract

In this work, equations that govern axisymmetric incompressible turbulent flow for heat transfer calculations are derived assuming constant thermo-physical properties and a specific nondimensionalization scheme. Vector algebra is used for expanding vector form of governing equations in cylindrical coordinate system. Emphasis is on the derivatives of unit vectors according to azimuthal direction. Reynolds decomposition is used for separating time averaged terms and Reynolds Stress terms. Standard k-ϵ turbulence model is selected for solving closure problem due to the Reynolds stresses. Organization of the governing equations after model inputs is done explicitly. Also, parameters that constitute nondimensionalization scheme are given. Evaluations of the complete process are given. Two major aims of the work are presenting necessary equations explicitly and revealing some key steps for reorganization of the equations. It is also aimed to present novel illustrations in order to contribute comprehension of the concepts.

Heat and Mass Transfers in a Two-Phase Stratified Turbulent Fluid Flow in a Geothermal Pipe with Chemical Reaction

“…The -ε  turbulence model is used to calculate the turbulent viscosity. Given in (21) is the relationship between turbulent viscosity ( T ν ), turbulent kinetic energy (  ), and dissipation (ε). according to [21] and [22] is given as a vector in (22):…”

“…The following are relevant boundary conditions to the problem under consideration as applied successfully by [13] and [21]. The geothermal pipe's walls and the gas-liquid interface don't have a slip condition.…”

Two-Phase Turbulent Fluid Flow in a Geothermal Pipe with Chemical Reaction

“…According to [19], to derive the Turbulent Kinetic Energy (TKE) the following steps are taken: Firstly, the momentum equations are replaced with the mean and fluctuating velocities; secondly, each equation is multiplied by the fluctuating velocities in their respective directions; thirdly, take time average of the decomposed equations; and lastly, apply the Reynolds decomposition rules. The equations are put together by adding them to form a single equation and this summation forms the turbulent kinetic energy equation.…”

“…With the assumption that there was no slip condition at the walls of the pipe, the following boundary conditions were applied successfully by [9,19]: At r = D + /2;…”