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, Estoniaapproach is to model the heat exchanger and look fordiscrepancy between model predictions and what isactually measured, see [10] and [4]. The method usedin this study falls into category a). To make the methodvalid for dynamic operating conditions, empiricalrelations for the mass flow rates are furthermore used.Although district heating systems usually operate inrelatively steady state it can be argued that methodsthat work well to detect diminishing efficiency underdynamic operation should work very well under steadystate condition.DATA USEDThe data used in this study was the same data as wasused in [4]. The data was generated by a simulatorrepresenting an unmixed cross flow heat exchanger.The advantage of using simulated data is that it ispossible to control when and how much fouling willoccur in addition to controlling the inlet temperaturesand the mass flows. The data used had temperaturesfor the hot side in the interval [53, 67] °C and the coldside [12, 27] °C, the mass flow rates for the hot andcold side were in the interval [0.30, 1.45] kg/s.Description of the simulator can be found in [4].FoulingDuring design a heat exchanger is commonly designedto operate under mild fouling by assuming a foulingfactor in the interval 0.0001 to 0.0007. According to [11]and [12] there is usually an induction time before anoticeable amount of fouling has accumulated. In [13] itis shown that the fouling will grow with increased rateduring the fouling period. Figure 1 shows the evolutionof the fouling factor from the time the heat exchangerstarts to accumulate fouling until the simulation isstopped. A dimensionless time is used to make easycomparison between different lengths of data series.allowed to progress to a maximum of R f =0.00033,which corresponds to 25% decrease in the overall heattransfer coefficient.THE DETECTION METHODThe fouling detection is done by estimating the overallheat transfer coefficient, U, by using NTU relations andmonitor the means of U for shift that can be related todiminishing efficiency either because of accumulationof fouling or property changes of the working fluid.NTU method is commonly known and a description of itcan be seen in [1].It is known that effectiveness of a heat exchanger canbe calculated byThe minimum fluid is the fluid that has the minimumvalue of the production of mass flow and specific heat,. Effectiveness for a unmixed cross flow heatexchanger can also be calculated by the followingrelations of the effectiveness to NTU.In normal use, the overall heat transfer is usuallyunknown and it is therefore not possible to calculateNTU directly. It is therefore necessary to estimate NTUfrom the relation between NTU and the effectiveness.The estimation is done by minimizing a score functionwith respect to NTU. The minimizationwas done by using the minimization routine fmincon inMatlab, see [14].The parameter NTU is defined by(1)(2)(3)From Eq. (3) it is easy to derive the formula for U(4)EMPIRICAL RELATIONSFigure 1. Evolution of the fouling factor from the timeThe simulated data sets used in this study include 200sets without fouling and 200 sets with fouling, the datasets are further divided equally between slow and fastfouling. In the fouled cases the data set was withoutfouling for the first 25% and then the fouling factor wasIn the case of heat exchanger under dynamic operationwhere big variations can occur during operation, it ishard to see shift in the overall heat transfer coefficientthat can be related to diminishing efficiency in the heatexchanger. In [15] it is proposed to use empiricalrelations of U to make a heat exchanger model validover a wide range of operating conditions. The heattransfer coefficient can be written as306