Comparison Of Power Plant Steam Condenser Heat Transfer Models For On-LineCondition Monitoring
Jussi Saari, Juha Kaikko, Esa Vakkilainen, Samuli Savolainen
Reference: ATE 5021
To appear in: Applied Thermal Engineering
Received Date: 23 August 2012
Revised Date: 31 July 2013
Accepted Date: 1 September 2013
Please cite this article as: J. Saari, J. Kaikko, E. Vakkilainen, S. Savolainen, Comparison Of PowerPlant Steam Condenser Heat Transfer Models For On-Line Condition Monitoring, Applied ThermalEngineering (2013), doi: 10.1016/j.applthermaleng.2013.09.005.
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COMPARISON OF POWER PLANT STEAM CONDENSER HEAT TRANSFER MODELS FOR ON-LINE CONDITION MONITORING
Jussi Saari a,*, Juha Kaikko a, Esa Vakkilainen a, Samuli Savolainen b
a Lappeenranta University of Technology, P.O. Box 20, FI-53851 Lappeenranta
b Fortum Power and Heat Oy, P.O. Box 100, FI-00048 FORTUM
* Corresponding author, Tel. +358 294 462 111; fax: +358 5 411 7201, E-mail address: email@example.com
In this paper heat transfer models for large power plant condenser were examined. The goal was to develop a model capable of predicting not only the condenser pressure but the overall heat transfer coefficient. Such a model can be used for condenser condition monitoring. The results of a two-dimensional (2-D) condenser heat transfer model and single-point, zero-dimensional (0-D) model are presented together with the results from Heat Exchanger Institute (HEI) standards curves. Both 0-D and 2-D models can account for the effects of steam-side pressure drop and in a simplified manner also some effects of tube bundle geometry. For all models an experimental correction as a function of cooling water temperature was implemented to improve their accuracy. The results are presented in comparison with the measured plant data for three different tube bundle geometries, with and without the experimental correction factor. The 2-D model proved to be the most consistently accurate of the models both without the correction, and at varying steam and coolant flow with the correction applied. The results indicate significant local variation of pressure drop related effects, which the 0-D model failed to accurately predict particularly in cases of close temperature approach. In predicting the heat transfer coefficient the HEI model was the least accurate, significantly overestimating the impact of coolant flow rate change, and failing to match the measurements even with a correction applied.
Keywords: Heat exchanger; Condenser; Steam surface condenser; Fouling
A area [m2] B width [m] C experimental correction factor for condensation heat transfer coefficient: C=hadjusted/ hcorrelation [-] Cf friction factor [-] cp specific heat in isobaric process [J kg-1 K-1] d diameter [m] f friction factor (Darcy) [-] Fx correction term for U in HEI standards[-] G mass velocity [kg s-1 m-2] g gravitational acceleration [m s-2] h 1. heat transfer coefficient [W m-2 K-1] 2. specific enthalpy [kJ kg-1] hfg latent heat of condensation [kJ kg-1] imax number of calculation segments in tube axis direction [-] jmax number of tube rows in steam flow direction [-]k thermal conductivity [W m-1 K-1] L length [m] m fluid mass flow rate [kg s-1] N number of tubes [-] n index of calculation elements [-] NTU Number of Transfer Units (dimensionless conductance) [-] Nu Nusselt number [-]
P tube pitch [m] p pressure [Pa] Pr Prandtl number [-] R thermal resistance [K W-1] Re Reynolds number [-] R thermal resistance per surface area [m2 K W-1] s tube wall thickness [m] T temperature [C] w velocity [m s-1] x steam quality [-] U overall heat transfer coefficient [W m-2 K-1]
Greek symbols p pressure drop [Pa] heat exchanger effectiveness [-] heat transfer rate [W] dynamic viscosity [Pa s] density [kg m-3]
Subscripts C cumulative c cold (sea water) side cl clean gr gravity h hot (steam) side i 1. tube inside
2. calculation element index in tube axis direction in inlet j calculation element index in tube row direction L liquid phase o tube outside out outlet s tube surface sh 1. shell
2. shear T transverse to steam flow direction tb tube TOT total TRU true value (according to measurements) V vapour phase
This paper concerns the development of a heat transfer model for seawater condensers of a large steam power plant, providing a reasonable compromise between computational time and accuracy of the results. The model should provide results fast enough to be used as a part of an on-line condition monitoring system, while also accurate enough for determining foulant layer development inside the seawater tubes, as well as showing likely changes in condenser performance if the plant operating parameters are slightly varied.
Predicting the heat transfer in a large condenser is challenging. Depending on the required accuracy and maximum acceptable computation time, different approaches are possible. The fastest but least accurate option are correlations
provided by Heat Exchanger Institute (HEI) or British Electrotechnical and Allied Manufacturers Association (BEAMA), giving the overall heat transfer coefficient U as a function of cooling water flow and inlet temperature, and various tabulated correction factors . While simple, this method fails to account for several phenomena affecting heat transfer and is unlikely to yield accurate results for heat transfer coefficients, though condenser pressure prediction is satisfactory. A calculation based on an average U determined from heat transfer coefficients at average flow conditions was also considered questionable given the vast local variations in flow conditions in a large condenser.
At the other extreme, detailed 2-D and 3-D numerical models have been developed to model the behaviour of both large power plant condensers and laboratory-scale test equipment. Al-Sanea et al. used a single-phase 2-D model . Later Al-Sanea et al. and Bush et al.  implemented two-phase 2-D models. A quasi-3-D method was used to model power station condensers by Zhang et al. , and laboratory-scale test condenser by Zhang and Bokil . Malin used a 3-D model  to model a marine condenser. Ramon and Gonzalez developed a 3-D model of a church window type condenser , and Prieto et al. compared the results of similar model to both HEI correlations and a 2-D simplification of the 3-D model . Hu and Zhang developed improvements to turbulence  and inundation  modelling for numerical condenser simulations. Zeng et al.  developed 3-D models of three power plant condenser configurations, and compared the results to HEI correlations. While the 3-D models are likely the most accurate option in the absence of extensive proprietary data available to condenser manufacturers, the difficulties of modelling two-phase flow, phase change and interaction of the two phases will still produce significant uncertainties in the results. For on-line condition monitoring purposes or a use as a component module of a larger power plant model, the computational complexity of such numerical models would also be excessive.
The approaches studied in this paper are a 2-D model based on a geometrical simplification broadly similar to that presented by Prieto et al. in  calculating the condenser as a heat exchanger network of smaller condensers, and a 0-D model based on an average U calculated at average flow conditions. The possibility of an even simpler implementation was investigated by comparing these results to calculation with an average U obtained from the HEI standards for steam surface condensers. All three methods were implemented for three separate condenser types, one of which is similar to the church window type analyzed by Prieto et al. All condensers considered are of two-pass configuration with seawater in horizontal tubes.
The 2-D method described in this paper differs from that of Prieto et al. mainly in the treatment of condensation heat transfer, and in the inclusion of an experimental parameter to fit the model to measured performance. In  the vapour phase heat transfer coefficient was determined according to Taborek  and the phase change and heat and mass transfer were modelled according to film theory by Colburn and Hougen , corrected by Ackermanns factor according to . The condensate film heat transfer coefficient was obtained from Nusselts correlation for single horizontal tube without vapour shear, originally presented in , and modified by a shear correction from .
In this work it was assumed that given the simplification of actual flow patterns into 2-D or 0-D models and the difficulties of modelling condensate behaviour and the possible formation and effects of inert gas pockets in the tube bundle, a purely theoretical model could not achieve sufficient accuracy. An experimental correction factor C was introduced to fit the model results to measurements by adjusting the condensation heat transfer coefficient obtained from heat transfer correlations (i.e. C = hadjusted/hcorrelation). The unadjusted hcorrelation is based on correlations of Nusselt number Nu for gravity- and shear-dominated cases. With an experimental correction applied to account for the uncertainties in condensation modelling, it appeared unlikely that the more elaborate approach of  would be advantageous over the simpler method presented here.
The sensitivity of the developed 2-D and 0-D models and HEI standards curves to changes in steam and coolant flow rates is investigated and compared to measurement data for three different condenser types to the extent that available data allowed. Results are studied both with and without the experimental correction factor in order to also obtain information on the relative usefulness of the models for predicting condenser performance if data for fitting the correction factor is not available.
2 THE STUDIED CONDENSERS AND THEIR 2-D SIMPLIFICATIONS
Three tube bundle configurations were studied. Labelled A, B, and C, these are shown in Fig. 1, with the simplified geometries to illustrate the treatment of steam flow in the models. The simplification resulted from assuming steam to enter the tube bank perpendicularly, and estimating the average number of rows jmax that the steam would flow across in the bundle. Each tube bundle has two water-side passes, splitting the shown tube bundles to top and bottom passes in A and left and right-side passes in B and C.
Figure 1. Studied tube bundle configurations. The green area in the top figures represents the actual tube bundle configuration viewed in tube axis direction, the lower figures the 2-D model simplification.
In the 2-D model the steam flow is assumed to be in perfect cross flow across the tubes, with parallel directions for vapour and liquid phase flows. In geometries A and C the number of tubes NT transverse to the steam flow was estimated to remain relatively constant so that there would be NTOT/jmax tubes in each row. The geometry B represents the church window type in which the cross-sectional area for steam flow reduces more clearly after each row. The tube bank is estimated to narrow steadily until finally NT,jmax = 0.30NT,1.
The tube arrangement in each condenser is equilateral triangular. The main physical characteristics as well as typical operating conditions are described in Table 1. All condensers are used in large condensing power plants with seawater cooling. The plants operate at base load, with the seawater flow rate switched between a lower value during winter and higher in summer. The condensers are equipped with an on-line cleaning system continuously rotating cleaning balls through the tubes.
Table 1. Main specifications and typical base-load operating conditions of the studied condenser types. A B C Number of tubes per pass [-] 5225 6500 8800 Tube material SMO steel Titanium Titanium Tube thermal conductivity [W/mK] 14 21 21 Tube outer diameter [mm] 28.0 24.0 22.0 Tube pitch [mm] 35.0 32.5 27.5 Tube wall thickness [mm] 0.8 0.5 0.5 Tube length [m] 8.89 8.97 9.27 Shell width [m] 6.7 6.7 6.7 Cooling water mass flow rate [kg/s] 4800 or 6200 4500 or 5900 4400 or 5800 Cooling water temperature [C] 0-20 0-20 0-20 Steam mass flow rate [kg/s] 105 105 105 Steam pressure at inlet [mbar] 25-60 20-55 20-55
3 MODEL DESCRIPTION
In the model the heat transfer in a condenser is determined by four separate thermal resistances. Presented for a unit area, these are the tube outside condensation resistance Ro, tube wall conduction resistance Rw, tube inside convection
resistance Ri, and tube inside fouling thermal resistance Rtf. The last term represents the net effect caused by the foulant layer, including changes in convective heat transfer due to surface changes. The effects of tube-side flow maldistribution, heat conduction in tube axis direction, tube outside fouling, inert gases in steam, leakages, and heat losses to the environment were considered negligible and not considered in the model.
If the model is used to find condenser pressure ph,in at a given cooling water mass flow rate cm and inlet temperature Tc,in and steam mass flow rate hm , a value for Rtf must be assumed. If the condenser pressure is known, Rtf can be determined using the model. Rtf or ph,in is found in all models by adjusting the unknown parameter to such a value that the calculated heat transfer rate matches the actual, as described in Algorithm 1 in Appendix A. The pressure ph,in is steam pressure immediately above the tube bundle; it is assumed that two velocity heads, based on velocity determined at unobstructed free flow area of the shell above the tube bundle, Ash = LtbBsh, are lost as the steam flow accelerates, decelerates and turns into the tube bank. The actual heat transfer rate can be determined from the cold-side measurements or estimated from the hot side.
To determine the fouling resistance the algorithm accounts for all discrepancies between calculated and measured results by adjusting the Rtf. A sufficiently accurate modelling of biofouling was considered impossible and the available data is in...