A similarity model of specific heat loss determined by dimensional analysis

Abstract

This article describes an innovative method for the determination of heat flow (specific heat loss; linear heat flow density) from a one-metre length of a twin pipe directly-buried heat network. Such heat losses are currently described by applying analytical procedures based on the heat transfer theory. It is rather complicated to accurately express the heat loss using such procedures, due to the necessity to determine the individual values of thermal resistance. A simpler method to express heat loss is the balance method, as it requires measuring a temperature gradient ∆t between the starting point of the heat network and the end point of the heat collection. A suitable measuring device must provide high-accuracy measurements of the temperature. In the case of very well insulated distribution pipelines and short pipes, the temperature measurements must be accurate to the hundredths of a degree Celsius. It is impossible to install such devices as fixed equipment on every heat distribution network, due to such networks measuring many kilometres and the cost of the appropriate measuring technology. For the aforesaid reasons, the authors created a mathematical model for specific heat losses based on dimensional analysis. This method facilitates the identification of dimensionless criteria based on the relevant dimensional quantities. Functional correlations between the identified criteria may be identified on the basis of the results of physical or numerical experiments. In this study, a database of the results obtained from physical experiments conducted on two heat networks was used. The output of the similarity model was a function describing the heat flow from a one-meter pipe length that was applicable to various alternatives in relation to the geometrical, physical and boundary conditions. The standard deviation of a difference in the heat losses identified by applying the balance method and using the proposed criterial equation for a twin pipe directly-buried pre-insulated heat network was 0.515 W·m−1.