基于循环水供暖的室内温度调控分析

Analysis of Indoor Temperature Control Based on Circulating Water Heating

本文研究的是循环水供暖,通过改变进水流量从而改变空间温度分布。对问题的分析首先对房间散热进行分析和计算,即南北墙和窗户的散热,用热源法~([1])对简单热传导问题进行了解析解的求取。当外界温度为0摄氏度,进水温度已知,求空间的动态温度分布。这是一个三维问题,在此模型中将它等效成了一个二维模型,由于此房间中有南北两个暖气片,因此房间中与暖气片等高的空间温度相差不大,将此空间看作恒温体,再通过房间不同高度的热量梯度计算出不同高度的热量,进而求出温度,通过此种方法可求解出整个房间的温度场~([2])。此模型中,由于两个暖气片对称分布,故我们认为同一水平面热量相等,温度相同,即使热量不同,也相差较小,可忽略不计。于是建立了一个只有竖直温度梯度的动态温度分布模型,这是在管流量为定值时的情况。利用二维热传导方程求出空间中某一点的温升关于位置和时间的函数,带入不同时间和位置的值,可得到不同空间的温度,综上,对于此问题最终建立了管流量与室内温度和室外温度的关系。我们通过对于每小时分别计算求解,可得到每小时进水量需要满足的要求,以及通过将24个小时等看作整体,获得总的进水量确定一天累计耗水量最小时的约束条件以及耗水量的最小值。

This article studies the circulating water heating,which changes the spatial temperature distribution by changing the inlet water flow.Firstly analyzes and calculates the heat dissipation of the room,and uses the heat source method[1]to obtain an analytical solution to the simple heat conduction problem.When the outside temperature is 0 degrees Celsius and the inlet water temperature is known,find the dynamic temperature distribution of the space.This method can solve the temperature field of the entire room[2].In this model,due to the symmetrical distribution of the two radiators,we believe that the same level of heat is equal and the temperature is the same.So a dynamic temperature distribution model with only vertical temperature gradient is established,which is the case when the pipe flow is a constant value.Use the two-dimensional heat conduction equation to find the temperature available in different spaces.And the relationship betweenthe tube flow and indoor temperature and outdoor temperature were established.By calculating and solving for each hour separately,we can obtain the requirements that the hourly water inflow needs to meet,and by taking 24 hours as a whole,we can obtain the total water inflow to determine the constraint conditions and the water consumption when the cumulative water consumption in a day is the smallest.