Mathematical modeling of unsteady heat processes in countercurrent heat exchangers

The countercurrent heat exchangers, usually are widely used in power engineering, metallurgy, chemical industry and other industries. For the design, management of heat exchangers in transient conditions, it is necessary to know sufficiently accurate mathematical models of non-stationary thermophysical processes flowing in them. The paper deals with a mathematical model of one-dimensional unsteady heat fluxes, consisting of the equations of heat transfer, hydrodynamics and state. The issues of assumptions and accounting for various physical factors, including phase transitions that determine the specific kind of mathematical model, are discussed. The resulting mathematical model allows for countercurrent heat exchangers to simulate the temperature, taking into account not only the transitional and phase transformations in refrigerants, but also taking into account the spatial distribution of the physical parameters of the flow. For the numerical solution of differential equations "rectangle" scheme was used same for both environments. The error of approximations of such a scheme has a second order. The resulting system of algebraic equations was modernized, since in this scheme the coefficients must be calculated through an unknown temperature, and the heat transfer must be determined through an unknown temperature of the countercurrent coolant. A new scheme was obtained for explicitly calculating the temperature of the coolant. The results of numerical calculations for a counter-flow heat exchanger are given. For this device, the air does not change its phase state, but the oxygen change. In such conditions, the density and flow rate are significantly variable along the length of the apparatus, respectively, and the heat transfer coefficient between oxygen and air cannot be considered constant along the length of the flow. For calculations, large pressures in the flows were taken p₁ = 5 • 10⁶Pa, p₂ = 2,4 • 10⁶Pa. The length of the heat exchange surface was taken 9 m, the interaction area of the flows F = 1100 m² . The flow temperatures at the initial moment of time were set as T₁ (0, x) = 315K, T₂ (0, x) = 90K. The data given correspond to a typical industrial shell-and-tube heat exchanger. The influence of the constant and piecewise constant heat transfer coefficient k along the length of the flow, on the heat exchanger's operation was investigated. According to the results, it follows that the heat transfer coefficient, its distribution, significantly affects the heat exchange process. The resulting mathematical model and its finite-difference representation allow physically-based numerical simulation of one-dimensional unsteady heat fluxes in countercurrent heat exchangers. This model allows to take into account the distribution of physical parameters along the length of the streams, such as density, speed, heat capacity and heat transfer between the streams, and allows to simulate the flows of counterflow refrigerants with phase transitions.

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