Abstract:
Abstract: When using the explicit iterative method to solve the temperature of mass concrete with cooling pipes, it is generally considered that the inner and outer surface of metal pipes can be neglected but the temperature difference cannot be neglected when using the plastic pipes. And the plastic pipes are usually regarded as the third boundary condition. For the past researchers, the coefficient of this kind of boundary condition can be got by experiment and inversion, which is yet expensive and may also not be reliable sometimes. To solve the problem, on the base of heat balance condition, a new calculation method is brought forward. It is well known that concrete is a poor conductor of heat, and there is a large temperature difference between the concrete and the cooling water. So, in the shell of a cooling pipe and the concrete near it, it can be assumed that the heat flux is only discharged by cooling water in the pipe and the direction of the temperature gradient is perpendicular to the cooling pipe surface. So, the heat fluxes passing through any circle (take the center pipe as the center of those circles) in the shell of the plastic pipe are equal. Based on these basic principles, the temperature of cooling pipe outer surface can be obtained by the heat flux of the concrete around the pipe, the thermal conductivity, the thickness of the pipe and the temperature of pipe inner surface. When using the conventional iterative method to solve the temperature of the mass concrete with cooling pipes, the iterative method should be used for the unknown water temperature distributions along the cooling pipes. For this new method, the temperature distributions along the inner surface of the pipes is also unknown, so the iterative method should be also used. With this new method, when using the conventional iterative method, the convergence speed is relatively low, or even can not converge. To solve this problem, the iterative algorithm is also improved. When the iteration time is (N-1) and N separately, it is assumed that the corresponding calculated temperature on the outer surface of the cooling pipe is Tn-1 and Tn respectively. And then, when using 0.5(Tn-1+ Tn) as the initial calculation condition for the (N+1)th time, the convergence of the iteration can be easily achieved. The convergence condition of the improved method was proved by mathematical deduction, and the deduction results showed that the convergence could be always reached in different engineering cases. A comparing numerical example was used to comparing the accuracy of the new method and the conventional explicit iterative method. In this comparing numerical example, the calculation results of the finite element method (FEM) considering the pipe as a part of mesh were considered as the theoretical solution. The calculation results showed that in the concrete near adiabatic boundary of the mesh in the comparing example, the temperature difference between the calculation result of conventional explicit iterative method and the theoretical solution was 1.67℃, and the temperature difference between the calculation result of improved method and the theoretical solution was only 0.3℃. So, the improved method can be more accurate than the conventional explicit iterative algorithm. Using these new achievements, the temperature field of a concrete block during construction period was simulated, and the calculation results and testing results were compared. The total number of the iteration times was 15 for the conventional iterative method and only 7 for the improved method in this engineering example. The results show that the calculation value is close to the actual value, and this algorithm has high convergence speed. So this method can be used in engineering projects to prevent mass concrete from cracking.