Analysis of flow resistance in bundles of power plant condensers

. Shell-side pressure drop is a very important variable in the successful design of the condensers. The prediction of this pressure drop through the horizontal tube banks, with condensation, has long been a problem facing design engineers. Low pressure drop is a requirement in designing condensers for power plants. The paper presents a comparison of the various correlation to determine the pressure drop in the tube bundle. It is an important element for the verification of numerical simulations. Analysis of flow resistance for power plant condenser were made. steady-state porous medium conservation equations of mass, momentum, heat and mass transfer resistance are written in Cartesian coordinate system. Local volume porosity β is defined as ratio of the fluid volume and total volume of the corresponding element. Mass conservation equation for the mixture:


Introduction
A condenser is an important component that affects the efficiency and performance of power plants. Development of advanced numerical methods for shell-side flows in condensers is a critical step in improving current condenser design techniques. The advantage of numerical simulation is that they can provide a more detailed information on fluid flow and heat transfer in the tube bundle. This information may eliminate, in early stages of the design process, the problems related with flow induced vibration and flow distribution and improve overall heat transfer coefficients and increase the unit performance.
Numerical modelling of the power plant condensers play an important role in the design and the diagnosis of this type of heat exchangers [1][2][3][4]. The development of mathematical and physical models should be verified in the way of experiments [5,6]. Due to the significant size of these heat exchangers and an important role in the energy system access to this data is limited.
The shell-side and water-side flows are treated as the steady state and the steam-side flow is assumed to behave as an ideal mixture made up of noncondensable gases and steam only. The steam is taken as saturated. The mixture of noncondensable gases and steam assumed to be perfect gas, although other equations of state could be considered. The two-dimensional steady-state porous medium conservation equations of mass, momentum, heat and mass transfer resistance are written in Cartesian coordinate system. Local volume porosity β is defined as ratio of the fluid volume and total volume of the corresponding element. Mass conservation equation for the mixture: Momentum conservation equations for the mixture: where is the longitudinal coordinate to the flow direction, is the perpendicular coordinate to flow direction, is the velocity in the direction, is the velocity in the direction, is the density, is the pressure, ̇ is the mass flow rate, is the local porosity, is the effective viscosity, is the local flow resistance.
The boundary conditions for the inlet, vent, walls and baffles and plane of symmetry are: • Inlet: The velocity and pressure are specified at inlet boundary.
• Walls: The shell walls and baffles of condenser are assumed to be nonslip, impervious to flow and adiabatic. Thus, the normal velocity components are equal to zero. In the description of the heat exchange in the energy condensers there are three driving forces: the temperature difference, the difference of gas concentrations and a decrease in a vapor pressure associated with a hydraulic flow resistance. Article focuses on the description of the hydraulic flow resistance in a bundle of energy condensers. It compares the several available correlations that can be used to verify the numeric calculations. The flow resistances are one of the components affecting the total pressure drop in tube bundle. The second important element is the establishment of conducting compressible fluid flow. The value of the effective viscosity is assumed in the calculations . The choice of this value also requires optimization as the literature gives different guidelines [7]. The article, however, focuses on the analysis of the flow resistance associated with the flow resistance forces.
where is the resultant speed of the steam. The pressure loss factor can be determined based on the relationship proposed by Rhodesa and Carlucci [9]: where is the tube pitch, is the tube outer diameter and is the coefficient of resistance expressed as: The local porosity in Eq. (5) is defined as follows: where is the number of analysed tubes in a row, is the number of pipes in a row, is the porosity within the tube bundle.
An alternative approach to describe the flow resistance in a bundle of tubes is to use the same as for porous deposits, Darcy's law: The resistance factor is given as: The local porosity in Eq. (13) for hexagonal pitch in bundle is specified as: while for square pitch tubes as: In equations (11) and (12) and respectively are the correction factors that determine the condensation of steam i.e. effects of biphasic mixture on the flow resistance, which are the features of flow direction and the Reynolds number.
Based on experimental work in the Institute of Heat Engineering at Warsaw University of Technology flow resistance coefficients were proposed [11]: • for a hexagonal bundle = 10.69 0.821 300 < < 8000 (20) • for a square bundle = 4 0.951 300 < < 8000 (21) • and from examination [10] for both types of bundle = 7.87 0.88 300 < < 8000 The unit pressure drop was determined as: All above correlations are being used in two-dimensional calculations of energy condensers with isotropy assumption of oppositions of the flow in the bunch.

Analysis of the results
The calculations were carried out for the power plant condenser of the block 50 MW built from brass pipes about the outer diameter of 24 mm, wall thickness of 1 mm and for hexagonal scale of 32 mm. The following parameters were taken: steam pressure at the inlet to the condenser of 7778 Pa, temperature of the cooling water of 25°C, steam speed at the inlet to the condenser of 37.4 m/s and stream of steam of 140 t/h [6]. The cross section of the analysed condenser is described in Fig. 1a with emphasized A-A (hexagonal bunch of the pipes) and B-B (square bunch of the pipes) sections at which drops of the pressure were being analysed. The diameters were selected in a way allowing steam flow in vertical and horizontal direction in the bunch of pipes.
The pressure drops in the sections A-A and B-B were determined based on the numerical simulations with using correlation (9)- (12). Two different effective viscosities were used, which were equalled respectively to 100 and 1000 of the molecular viscosity. An average speed of the steam for section A-A was assumed to be 6 m/s, what corresponded to the individual drops of the pressure of 220 Pa/m for = 100 and of 333 Pa/m for = 1000 (Fig. 1b). For section B-B the individual drops of the pressure for both effective viscosities at the average speed of the steam were equalled to 290 Pa/m. The pressure drops calculated based on the correlations presented in section 2 are shown in Fig. 2 correlations can be observed. A pressure drops between 290-333 Pa/m for an average steam speed of 6 m/s was achieved nearly for all correlations. Only the result from Rhodesa and Carlucci equations shows quite a deviation. The pressure drops described by the correlations are strongly affected by the effective viscosity. The effective viscosity can be optimized in relation to steam balances, what was proposed for example in [10]. As a part of conducted analysis, it can be also stated that the pressure drops for the hexagonal bunches are higher than for the square. These results are also in accordance with the experimental results presented in [12].

Conclusion
In this paper the comparison of the various correlation for the pressure drop in the tube bundle is presented. The pressure drops were analysed for the hexagonal bunch of the pipes as well as for the square. The hexagonal arrangement was also analysed numerically. A good agreement between the results from numerical calculations and empirical correlations for the hexagonal bunch was achieved. It was also shown that the pressure drops for the hexagonal bunch are higher than for square.