12th International Symposium on District Heating and Cooling

The <strong>12th</strong> <strong>International</strong> <strong>Symposium</strong> on District Heating and Cooling,September 5 th to September 7 th , 2010, Tallinn, Estoniaapplications. Low-temperature district heating systemsare defined as networks where fluids at a temperaturebelow 50 °C are used, while a medium-temperaturedistrict heating system is defined as using fluids attemperatures not higher than 70 °C [11, 12].Steady-state heat losses from pre-insulated buriedpipes are generally treated by use of the followingequation [10], which is valid for each pipe-i:where Uij is the heat transfer coefficient between pipe-iand pipe-j, Tj is the temperature of the water in pipe-jand T0 is the temperature of the ground. In case of twoburied pipes, which is the most common application inthe DH sector, the heat losses can be calculated asfollows, respectively for the supply pipe and the returnpipe, where T1 is the supply temperature and T2 is thereturn temperature.(1)Supply pipe: (2)Return pipe: (3)Equations (2) and (3) show how the heat transfer fromeach pipe can be seen as linear superimposition of twoheat fluxes, the first one describing the heat transferbetween the pipe and the ground, the second onerepresenting the heat transfer between the supply pipeand the return pipe. The equations can also bere-arranged in the following way:thermal coefficient, which is function of the temperaturein this case. U-values are dependent both ontemperature and time. If the time-dependency due tothe ageing of the foam can be restrained by introducingeffective diffusion barriers, that is not true for theintrinsic dependency on temperature. It is practice toevaluate the steady state heat loss applying a thermalconductivity value that corresponds to a hypothesizedmean temperature of the insulation. Nevertheless weneed models based, for example, on the finite elementmethod (FEM) when complex geometries or a highdegree of detail are requested.Temperature dependant thermal conductivity ofPUR insulation foamIn this paragraph the authors want to explain anddemonstrate the importance of taking into account thetemperature-dependency of the thermal conductivity ofthe insulation (lambda-value). The temperaturegradient in the insulation foam in the radial direction isoften higher then 10 °C/cm, meaning that the thermalconductivity of the material locally varies remarkably. Inthe example shown Figure 2, it varies more than 10%of the prescribed mean value. This affects themagnitude of the heat transfer. Considering a life cycleassessment of a DH system, the main impact to theenvironment is represented by heat losses [13]. Thethermal conductivity of the insulation material inpre-insulated DH pipes is usually stated at atemperature of 50 °C. The lambda-coefficients werechosen according to the available data at the end of2009; the lambda-value at 50 °C for straight pipes,axial continuous production was set to 0.024 W/(mK)and for flexible pipes to 0.023 W/(mK). Since April 2010new results are available [14]. It is preferable to have amodel that takes into account the temperaturedependencyof the thermal conductivity of theinsulation foam. The calculations in this paper use thefollowing expression, if not differently stated. It derivesfrom experimental data [15]:λ(T) = 0.0196734 + 8.0747308 . 10-5.T [W/(mK)] (1)Supply pipe: (4)Return pipe: (5)Equations (4) and (5) show how the heat transfer fromeach pipe can be calculated by use of only one linearFigure 2: Thermal conductivity in the insulation, horizontalcross-section of the pipe. Pipe: Aluflex 16-16/110,temperatures supply/return/ground 55/25/8 °C.83