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, EstoniaTemperature field in the soil around the pipeIn this paper we address the question of how to createa simple yet detailed FEM model for steady state heatloss calculations. The overall heat transfer resistancebetween the DH water and the environment is mainlycomposed of the thermal resistance of the insulationand the thermal resistance of the soil; compared tothese two factors, the thermal resistances of the pipewall and the convective resistance at the surface waterpipeare in practice negligible. The insulation foamalways offers the greatest share in the overallinsulation effect. The contribution of the soil is smalleron small-sized pipes than on large-sized pipes. Theshare is smaller in Insulation Series 2 and 3 [3]. Theheat conductivity coefficient of the soil is the mainparameter affecting the thermal resistance of the soilitself, and its value is often unknown in practice.In thecalculations we chose a value of 1.6 W/(m.K). The soiltemperature influences heat losses from DH pipes. Thesoil layer around the heating pipes slightly warms uparound the pipes. The evaluation of the temperaturefield in the soil is a prerequisite to create a realisticmodel for calculations of heat losses. Finite ElementMethod (FEM) simulations were carried out andtemperature conditions in the soil around a typical DHservice pipe, suitable for low-temperature applicationswere evaluated over a 10-year period.Table 1: Thermal properties of materials.λ [W/(m∙K)] ρ [kg/m³] C p [J/(kg∙K)]λ soil 1.6 ρ soil 1600 C p_soil 2000λ PE 0.43 ρ PE 940 C p_PE 1800Combined heat and moisture transfer is disregarded.The material properties are homogeneous and phasechanges, i.e. freezing and thawing were notconsidered. Table 1 lists the material properties, usedas input values also for the following models; a sketchof the slab-model, where the boundary conditions aredescribed, can be seen in Figure 3.Figure 3: Sketch of the model. Dimensions are in [mm].FEM modelA rectangle representing a semi-infinite soil domain(width: 10–20 m, height: 20–40 m) is the most usedgeometry to model the ground in heat loss calculations[18, 19]. In this paper a finite, circular soil domain wasapplied, instead. Its diameter is 0.5 m and it is equal tothe distance between the surface and the centre of thecasing pipe. Calculations show that the introducedsimplification hardly affects the accuracy of the results.The mesh model and an example of the temperaturefield in a small size twin pipe are shown in Figure 4.λ PUR 0.023λ PEX 0.38ρ PURρ PEX60 C p_PUR 1500938 C p_PEX 550λ Steel 76ρ Steel8930C p_Steel480λ Cu 400 ρ Cu 8930 C p_Cu 385The simulation calculated the soil temperature atvarious x-coordinates from a commercial branch pipe.The selected pipe was the Aluflex twin pipe 16-16/110.Temperatures were set at 55 °C and 25 °C,respectively for the supply pipe and the return pipe.The heat transfer coefficient at the ground surface wasassumed to be 14.6 W/(m2K), including convection andradiation [16]; we set the outdoor air temperatureduring the year according to the harmonic function validfor the Danish climate [17]: M T air 8.0 8.5 sin2 (6) 12 Figure 4: Mesh model of a pre-insulated twin pipeembedded in the ground (top and left). Temperature fieldin Aluflex twin pipe 16-16/110 (bottom-right); temperaturesupply/return/ground: 55/25/8 °C.In [3], where FEM simulations were performed, it isstated that for media pipes size from DN 50 to DN 400,the deviation of the lineal thermal coefficient betweenthe piggy-back laying (arranging the supply pipe belowthe return pipe) and the traditional system (horizontallaying) is less than 1%. The same conclusion can bestated for twin pipes; this is confirmed by calculations84