The author's abstract of masters thesis

on a theme: “The Investigation of Heat Transfer Processes by means of Numerical Experiments for Heat Units Modernization”

The science expands boundaries of knowledge according to a principle: “A potentia ad actum” – “From possible to real”. In this connection in front of the modern researcher there are more and more challenges, deriving of solutions for which methods of a classical calculus it is impossible.

The formulated mathematical model of practically any problem is characterized by system of the interconnected differential equations with partial derivatives with impossible analytical solution. It is connected with complicated geometry of investigated plants; simultaneous course and mutual influence of such processes as hydrodynamic laminar and turbulent currents, various aspects of heat and mass transfer, electric and magnetic appearances; a nonunique solution of differential partial equations, etc.

All the processes enumerated above in this or that combination happen in thermal units (industrial furnaces, boiler installations, nuclear reactors, MFD generators, etc.).

Thus, frequently the only means for solution of practically important problems are numerical methods. Pioneers in the field of computing process engineering are such sciences as: computational hydrodynamics and heat exchange which are the base for realization of mathematical modeling transfer processes in engineering units and natural phenomena.

The objective of masters work is to receive a solution of set of the differential equations describing convective heat exchange and diffusion processes in the heat power unit (steam and gas generator) in a two-dimensional cartesian field by means of carrying out of numerical experiment. Also in this work it is planned to define a local modification of film coefficient α at all surfaces of the thermal unit.

The mathematical model of a problem consists of a following set of equations.

The X - projection of momentum equation:

The Y - projection of momentum equation (with respect to mass force or a gravity):

,

where are the components of a viscous stress tensor:

Equation of continuity:

Heat conduction equation in the fluids (the equation of Fourier – Kirhgoff):

Heat conduction equation (the equation of Fourier) for solids:

The equation of connection:

At research of combustion processes the given system is supplemented with three more equations of mass transfer. Under the assumption, that between fuel and an oxidizer we have the irreversible single-stage chemical isothermal reaction:

,

where Г – fuel; О – an oxidizer; ПГ – combustion products; ν_i – stehiometrical factors for investigated area of the diffusion equation for fuel and an oxidizer will look like:

,

where C_г = ρ_г / ρ – relative mass concentration of fuel; C_ок = ρ_ок / ρ – relative mass concentration of an oxidizer; m_г and m_ок – velocities of the fuel and an oxidizer flow of only in the single chemical reaction. For combustion products it is possible to note that – C_пг = ρ_пг / ρ.

Thus, the sum of all relative mass concentration is equal to unit. Hence, relative mass concentration of combustion products is defined from the equation:

The reduced set of equations is supplemented with conditions of a uniqueness which include:

• Geometrical conditions which define the form sizes of area in which investigated process takes part;

• Physical conditions are set heat and physical properties of substance which fills investigated area. Besides they consider distribution of interior sources and sinks of heat in the volume;

• Temporary (initial) conditions contain distribution of required magnitude in investigated area in an initial moment;

• Boundary conditions which define singularities of process on the boundaries of investigated area.

The solution of first three equations (calculation of a flow field) is supposed to be received by means of SIMPLER method. Solutions of heat conduction equations in fluids and solids, and also diffusion equations for fuel and an oxidizer is carried out in known fields of velocities U, V by means of CONDUCT program.

The solution of a problem by means of numerical methods will give the distribution of components of velocity U and V, pressure, temperatures, concentration: C_г, C_ок, C_пг in all investigated area of the thermal unit.