Thermal Transients in District Heating Systems

Heat fluxes in a district heating pipeline systems need to be controlled on the scale from minutes to an hour to adjust to evolving demand. There are two principal ways to control the heat flux - keep temperature fixed but adjust velocity of the carrier (typically water) or keep the velocity flow steady but then adjust temperature at the heat producing source (heat plant). We study the latter scenario, commonly used for operations in Russia and Nordic countries, and analyze dynamics of the heat front as it propagates through the system. Steady velocity flows in the district heating pipelines are typically turbulent and incompressible. Changes in the heat, on either consumption or production sides, lead to slow transients which last from tens of minutes to hours. We classify relevant physical phenomena in a single pipe, e.g. turbulent spread of the turbulent front. We then explain how to describe dynamics of temperature and heat flux evolution over a network efficiently and illustrate the network solution on a simple example involving one producer and one consumer of heat connected by "hot" and "cold" pipes. We conclude the manuscript motivating future research directions.