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, EstoniaWhere i is constant, ii is temperature dependent and iiiis mass flow dependent. In this study only mass flowdependency was considered, since it has been shownby previously by [15] that the temperature dependencycan be neglected. The relation for the heat transfercoefficient can therefore be written as(5)The effect of the empirical relations can be seen inFigure 2. It can clearly be seen that including theempirical relations really helps to reduce the variationsin the overall heat transfer coefficient.By assuming that Eq. (6) applies to both the hot andthe cold side and neglecting the thermal resistance inthe separating metal, the overall heat transfercoefficient, U, can be written as(6)where y is the exponent of the Reynolds number. In [1]it is recommended to use y=0.8 for turbulent flow,which is expected in a heat exchanger.It can be practical to normalize U with a referencemass flow.The overall heat transfer coefficient according to thereference mass flow and is similarlyAfter inserting Eq. (7) and (8) into Eq. (4) to make itmass flow dependent and normalizing, the estimatedoverall heat transfer coefficient will become(8)(7)Figure 2. The figure shows the evolution of the number oftransfer units and the overall heat transfer coefficient withand without the empirical relations.To detect fouling a CuSum chart is used, see [16]. TheCuSum chart was chosen since it is known to beeffective to detect shift in mean values. When usingCuSum charts it is necessary to define two CuSumparameters, a decision limit to prevent false detectionand a reference value for deviations. Detection is madewhen the cumulative sum of deviations goes over thedecision limit.It can be seen in Figure 3 that the method is veryconsistent in detecting diminishing efficiency. Figure 4shows the detection if no empirical relations are used.The overall heat transfer coefficient in Eq. (9) is thevariable that is used to detect the fouling in the heatexchanger.(9)RESULTSAs mentioned above the method was applied to thesame data set as was used in [4].Measurement errors were added to the inlet and outlettemperatures as well as the mass flows to make themeasurements more realistic. Measurement errors of0.2 °C were assumed on the temperatures and 1–2%measurement errors to the mass flows.Figure 3. The CuSum chart quickly detects the shift in theoverall heat transfer coefficient.307