E3S Web of Conferences 137, 01027 (2019) https://doi.org/10.1051/e3sconf/201913701027 RDPE 2019

Influence of three surface condensers connection setup on power plant unit performance

Ewa Dobkiewicz-Wieczorek1,* 1 Silesian University of Technology / Valmet Automation, [email protected], Poland

Abstract. This paper presents a comparison of three surface condenser connection setups on the cooling water side. Serial, mixed and parallel connections were considered. The thermodynamic justification for the use of more complex configurations was verified. The analysis was conducted based on the calculated heat balances of verified power units for nominal and not nominal parameters for tested connections. The exhaust steam pressure was calculated using the technical data of the surface condenser and cooling water parameters. Three methods of calculating the heat transfer coefficient based on characteristic numbers, HEI method, and the ASME standard, were used. The most advantageous model was indicated and used in heat balance calculations. The assumptions and simplifications for the calculations are discussed. Examples of the calculation results are presented.

The direction of development and transformation in the Polish power industry are a response to the new European 1 Exhaust steam pressure calculation legal regulations, the aim of which is the environmental protection. As a result, diversification of electricity Condensation turbine exhaust steam pressure was production was provoked, additionally coal-fired units calculated using the heat transfer equations. were forced to apply new solutions. New units are getting Model assumed isobaric heat exchange, no condensate greater, technically and technologically more advanced. subcooling. Calculations were made for steady state. Introduced improvement that increases unit efficiency by Thermodynamic calculations in accordance with IAPWS as much as 0.1 percent are important considering the IF-97 [1]. actual requirements and unit efficiency of 45% net. In the case of great unites, when few surface 1.1 Heat transfer equations: condensers are used, it is essential to verify, which Heat transfer equations are: connection setups on the cooling water side would give = ( ) (1) the highest unit efficiency. = ( ) (2) When research, it is necessary to consider the entire 𝑠𝑠 𝑠𝑠 𝑐𝑐 𝑄𝑄̇ 𝑚𝑚̇ 𝑖𝑖 − 𝑖𝑖 1 steam-condensate cycle to analyze exhaust steam pressure Nomenclature: – heat transfer𝑔𝑔 𝑔𝑔 2rate, 1 – exhausted 𝑄𝑄̇ 𝑚𝑚̇ 𝐶𝐶𝐶𝐶 𝑇𝑇 − 𝑇𝑇 𝜂𝜂𝑐𝑐 changes effect on steam flow and thermodynamic steam flow rate, – exhausted steam enthalpy, 𝑠𝑠 parameters fluctuations. The correct calculation of the – condensate 𝑄𝑄enthal̇ py, – cooling water𝑚𝑚̇ flow rate, 𝑠𝑠 exhausted steam pressure value is one of key steps to water specific𝑖𝑖 heat, inlet cooling water 𝑐𝑐 – 𝑔𝑔 – ensure the calculation’s correctness. This paper presents 𝑖𝑖temperature, outlet𝑚𝑚 ̇cooling water temperature, 𝑔𝑔 – 1 analysis of three exhausted steam pressure calculation 𝐶𝐶𝐶𝐶– condenser efficiency 𝑇𝑇 algorithms, comparison of their complexity and the set of 𝑇𝑇2 𝑐𝑐 the data needed for these calculations. The model of the 1.2𝜂𝜂 Condenser heat load: [2],[4],[5]. surface condenser was based on three methods of calculating the heat transfer coefficient: dimensionless Condenser heat load equation is: equation with characteristic numbers, the HEI method and = (3) the ASME standard. The most advantageous model was =𝑠𝑠 (4) indicated after verification with the data from the site. 𝑄𝑄̇ 𝑈𝑈𝐴𝐴 𝐿𝐿𝐿𝐿𝑇𝑇2−𝐿𝐿𝑇𝑇𝐿𝐿1 Study of three surface condenser connection setups on 𝑇𝑇𝑐𝑐−𝑇𝑇1 Nomenclature: – condenser𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 heat𝑙𝑙𝑙𝑙 load𝑇𝑇𝑠𝑠−𝑇𝑇,2 U – heat transfer the cooling water side aims to help to find the answer on coefficient, – surface tube area, – logarithmic the rationale behind using more complex configurations, mean temperature𝑄𝑄̇ difference, T – condensate 𝑠𝑠 to analyze their advantages and disadvantages, and to give temperature,𝐴𝐴 T – steam temperature𝐿𝐿𝐿𝐿, 𝐿𝐿𝐿𝐿– inlet cooling c advice on which system is the best from the water temperature, – outlet cooling water temperature. s 1 thermodynamics perspective. 𝑇𝑇 𝑇𝑇2

© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). E3S Web of Conferences 137, 01027 (2019) https://doi.org/10.1051/e3sconf/201913701027 RDPE 2019

1.3 Heat transfer coefficient - Characteristic experimental research. The heat transfer coefficient was numbers [2]. computed as follows = (6) Heat transfer coefficient, when characteristic number Nomenclature: – uncorrected heat transfer method used, equation is: 1 𝑤𝑤 𝑚𝑚 𝑐𝑐 coefficients, as a function𝑈𝑈 of tube𝑈𝑈 𝐹𝐹 diameter𝐹𝐹 𝐹𝐹 and cooling = 10 (5) 1 water velocity, 𝑈𝑈 – inlet water temperature correction 1 −3 𝐷𝐷𝑜𝑜𝑜𝑜𝑜𝑜 factor, – tube material and gauge correction factors, Tube-Wall resistance𝑈𝑈 was𝑅𝑅𝑚𝑚 +computed𝑅𝑅𝑡𝑡 +𝑅𝑅𝑠𝑠 +as𝑅𝑅𝑓𝑓 follows: 𝑤𝑤 𝐷𝐷𝑖𝑖 – cleanliness factor𝐹𝐹 . 𝑚𝑚 = (5.1) , , 𝐹𝐹 are read from HEI table. values are based 𝐷𝐷𝑜𝑜𝑜𝑜𝑜𝑜 1 𝑐𝑐 Shellside resistance was computed based on on𝐹𝐹 clean, 1.245 mm tube wall gauge, Admiralty metal 𝑅𝑅𝑚𝑚 𝐷𝐷𝑜𝑜𝑜𝑜𝑜𝑜 𝑙𝑙𝑙𝑙 𝐷𝐷𝑖𝑖 2𝐾𝐾𝑚𝑚 1 𝑤𝑤 𝑚𝑚 1 dimensionless equation for heat transfer when the steam 𝑈𝑈tubes𝐹𝐹 𝐹𝐹with 21.1°C cooling water𝑈𝑈 temperature. condenses on the outside horizontal pipe’s surface. Uncorrected heat transfer coefficient is describing as a

= ( ) (5.2) function of tube diameter and water velocity. 𝑠𝑠 introduces a water temperature correction and 𝑁𝑁𝑁𝑁 𝐾𝐾 −1 . 𝑠𝑠 = 0.725 (5.3) 𝑅𝑅 𝐷𝐷𝑜𝑜𝑜𝑜𝑜𝑜 introduces a tube material and gauge correction. 0 25 𝐹𝐹𝑤𝑤 = 𝑣𝑣 (5.4) 𝑁𝑁𝑁𝑁 3 2𝐶𝐶 2 𝑚𝑚 𝐷𝐷𝑜𝑜𝑜𝑜𝑜𝑜 𝛿𝛿𝑐𝑐 𝑔𝑔 𝑑𝑑𝑑𝑑𝑣𝑣𝑣𝑣𝑣𝑣 1.5𝐹𝐹 Heat transfer coefficient - ASME PTC 12.2 - The difference in condensate and wall temperatures 𝐶𝐶𝑣𝑣 𝐾𝐾𝑡𝑡𝜇𝜇𝑐𝑐𝑑𝑑𝑑𝑑𝑐𝑐𝑐𝑐 codes: [5] depends on the thickness of the condensate layer, therefore𝑑𝑑𝑑𝑑𝑐𝑐𝑐𝑐 on the heat transfer coefficient. It is indicating Heat transfer coefficient, when ASME codes used, that the most appropriate calculation method is the equation is: iterative method, but with satisfactory accuracy, the value = 10 (7)

can be calculated as = [3]. 1 −3 𝐷𝐷𝑜𝑜𝑜𝑜𝑜𝑜 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝑅𝑅𝑚𝑚+𝑅𝑅𝑡𝑡 +𝑅𝑅𝑠𝑠+𝑅𝑅𝑓𝑓 Tube-Wall resistance𝑈𝑈 was computed𝐷𝐷𝑖𝑖 as follows: Physical properties𝑐𝑐 𝑐𝑐 of condensate: , , are determined for surface𝑑𝑑𝑑𝑑 and saturation2 average temperature = (7.1) 𝑐𝑐 𝑡𝑡 𝑐𝑐 𝐷𝐷𝑜𝑜𝑜𝑜𝑜𝑜 1 ( ) 𝛿𝛿 𝐾𝐾 𝜇𝜇 Tubeside resistance was computed as follows: = 𝑚𝑚 𝑜𝑜𝑜𝑜𝑜𝑜 𝐷𝐷𝑖𝑖 2𝐾𝐾𝑚𝑚 𝑅𝑅 𝐷𝐷 𝑙𝑙𝑙𝑙 𝑇𝑇𝑠𝑠+ 𝑇𝑇𝑠𝑠+𝑑𝑑𝑑𝑑𝑐𝑐𝑐𝑐 = ( ) (7.2) Tube𝑓𝑓 side resistance was computed based on 𝑇𝑇 2 𝑁𝑁𝑁𝑁 𝐾𝐾𝑡𝑡 dimensionless equation for forced convection for = 0.0158−1 . . (7.3) 𝑅𝑅𝑡𝑡 𝐷𝐷𝑖𝑖 turbulent flow inside a circular pipe: 0 835 0 426 = (7.4) = ( ) (5.5) 𝑁𝑁𝑁𝑁 𝑉𝑉𝑔𝑔 𝐷𝐷𝑖𝑖𝛿𝛿𝑔𝑔 𝑅𝑅𝑅𝑅 𝑃𝑃𝑃𝑃 𝑁𝑁𝑁𝑁 𝐾𝐾𝑡𝑡 −1 . = 𝜇𝜇𝑔𝑔 (7.5) 𝑡𝑡 . . 𝑅𝑅𝑅𝑅 =𝑅𝑅0.021 𝐷𝐷𝑖𝑖 (5.6) 𝑊𝑊𝑔𝑔 4

𝑃𝑃𝑃𝑃𝑔𝑔 0 25 𝑔𝑔 2 0 8 0 43 𝑉𝑉 = 𝛿𝛿𝑔𝑔 𝑁𝑁 𝜋𝜋 𝐷𝐷 𝑖𝑖 (7.6) 𝑁𝑁𝑁𝑁 = 𝑅𝑅𝑅𝑅 𝑃𝑃𝑃𝑃 𝑔𝑔 (𝑃𝑃𝑃𝑃𝑡𝑡 ) (5.7) 𝜇𝜇 𝐶𝐶𝐶𝐶 𝑉𝑉𝑔𝑔 𝐷𝐷𝑖𝑖𝛿𝛿𝑔𝑔 Shellside resistance for the first iteration was computed as 𝑃𝑃𝑃𝑃 𝐾𝐾 = 𝜇𝜇𝑔𝑔 (5.8) follows: 𝑅𝑅𝑅𝑅 𝑊𝑊𝑔𝑔 4 = (7.7) 2 𝑉𝑉𝑔𝑔 = 𝛿𝛿𝑔𝑔 𝑁𝑁 𝜋𝜋 𝐷𝐷 𝑖𝑖 (5.9) 1 𝐷𝐷𝑜𝑜𝑜𝑜𝑜𝑜 Shellside resistance𝑠𝑠 for the3 next𝑚𝑚 iteration𝑡𝑡 was computed𝑓𝑓 / – calculated for water𝜇𝜇 𝐶𝐶𝐶𝐶 temperature and wall 𝑅𝑅 𝑈𝑈 10 − 𝑅𝑅 − 𝑅𝑅 𝐷𝐷𝑖𝑖 − 𝑅𝑅 𝑃𝑃𝑃𝑃 𝐾𝐾 as follows: temperature = 𝑔𝑔 𝑡𝑡 𝑔𝑔 = ( ) ( ) ( ) (7.8) 𝑃𝑃𝑃𝑃Nomenclature𝑃𝑃𝑃𝑃 : – heat transfer coefficient𝑇𝑇, – tube 1 1 2 ̇0 0 𝑠𝑠0 0 𝑡𝑡 𝑠𝑠 𝑐𝑐𝑐𝑐 𝑄𝑄 3 𝜇𝜇 3 𝐾𝐾 𝛿𝛿 3 inside diameter𝑇𝑇 ,𝑇𝑇 − 𝑑𝑑𝑑𝑑– tube outside diameter, Nomenclature determined𝑠𝑠 𝑠𝑠0 as in point 1.3. 𝑖𝑖 𝑅𝑅 𝑅𝑅 𝑄𝑄̇ 𝜇𝜇 𝐾𝐾𝑠𝑠 𝛿𝛿 – tubewall 𝑈𝑈resistance, – tubeside 𝐷𝐷thermal Index 0 means the value from the previous iteration. 𝑜𝑜𝑜𝑜𝑜𝑜 conductivity, – 𝐷𝐷shellside thermal conductivity, Physical properties of condensate: , , are determined 𝑚𝑚 𝑡𝑡 𝐾𝐾 – tubewall resistance, 𝐾𝐾– tubeside resistance, for condensate film = 0.2 . 𝑠𝑠 – shellside 𝐾𝐾resistance, – fouling resistance, 𝛿𝛿 𝐾𝐾 𝜇𝜇 𝑚𝑚 𝑡𝑡 𝑓𝑓 𝑠𝑠 𝑅𝑅 Nuselt number, Prandl𝑅𝑅 number, Reynolds Condenser technical𝑇𝑇 𝑇𝑇 −data:𝐿𝐿𝐿𝐿 Steel𝐿𝐿𝐿𝐿 1.4401 - 𝑠𝑠 – – 𝑓𝑓 – number𝑅𝑅 , – average cooling𝑅𝑅 water temperature, = 15 was assumed to be used, tube dimension

𝑁𝑁𝑁𝑁 cooling water velocity,𝑃𝑃𝑃𝑃 water 𝑅𝑅𝑅𝑅specific heat, 𝑊𝑊 – 𝑔𝑔 – Ø24x0.7mm, condenser efficiency = 0.99, cleanliness 𝑇𝑇 𝑚𝑚 𝑚𝑚 𝐾𝐾 – enthalpy of exhausted steam vaporization, 𝐾𝐾factor k = 0.95; Calculation was done for two pass 𝑔𝑔 𝑔𝑔 𝑐𝑐 𝑉𝑉 – The difference in 𝐶𝐶𝐶𝐶condensate and wall surface condenser with surface𝜂𝜂 tube area 𝑣𝑣𝑣𝑣𝑣𝑣 𝑐𝑐 temperatures𝑑𝑑𝑑𝑑 , – condensate viscosity, – cooling = 19177𝐹𝐹 , quantity of tubes = 31920. 𝑐𝑐𝑐𝑐 𝑑𝑑𝑑𝑑water viscosity, – cooling water density, 2 𝑐𝑐 𝑔𝑔 𝑠𝑠 – condensate𝜇𝜇 density 𝜇𝜇 𝐴𝐴1.6 Turbine’s𝑚𝑚 isentropic efficiency𝑁𝑁 𝛿𝛿𝑔𝑔 𝑐𝑐 In calculation turbine’s isentropic efficiency was used 1.4𝛿𝛿 Heat transfer coefficient - HEI standard [4] = _ (8) In this case, the calculation of heat transfer coefficient is 𝑖𝑖𝑠𝑠_ 𝐿𝐿𝐿𝐿−𝑖𝑖𝑠𝑠 Nomenclature: 1– inlet LP turbine steam enthalpy, based on design guidelines of Heat Exchange Institute _𝜂𝜂 𝑖𝑖𝑠𝑠 𝐿𝐿𝐿𝐿−𝑖𝑖𝑠𝑠0 – exhaust steam enthalpy, – exhaust steam enthalpy (HEI). The proposed function uses the data from 𝑠𝑠 𝐿𝐿𝐿𝐿 when isentropic 𝑖𝑖flow, – exhaust steam pressure, 𝑖𝑖𝑠𝑠 𝑖𝑖𝑠𝑠0 𝑝𝑝𝑠𝑠

2 E3S Web of Conferences 137, 01027 (2019) https://doi.org/10.1051/e3sconf/201913701027 RDPE 2019

was set as a constant because in external test, small Table 1. Input data for calculations impact of vary this value as a function of load, for main 1 series 1 2 3 4 𝜂𝜂calculation, was verified. load 100% 90% 75% 60% 1.7 Calculation procedure and example 48060 48060 48060 48060 calculation results 𝑡𝑡 𝑔𝑔 18.3 16.8 15.2 16.7 Variables calculation was based on the iterative 𝑚𝑚̇ ℎ algorithm. Calculation procedure is the same for 𝑇𝑇1 ℃ 753240 697910 587350 491770 dimensionless equation with characteristic number (CN) 𝑘𝑘𝑘𝑘 𝑠𝑠 and HEI methods but different for ASME standard. 𝑚𝑚_̇ ℎ 278.7 273.6 280 272.6 Input data: – surface tube area, – quantity of tubes, 𝑠𝑠 𝐿𝐿𝐿𝐿 ℃ – cleanliness factor, – tube inside diameter, 𝑇𝑇 _ 579 526 441 358 𝑠𝑠 – tube𝐴𝐴 outside diameter, 𝑁𝑁 – tubewall thermal 𝑐𝑐 𝑖𝑖 𝑠𝑠 𝐿𝐿𝐿𝐿 𝑘𝑘𝑘𝑘𝑘𝑘 0.82 0.82 0.82 0.82 𝐹𝐹conductivity, – cooling 𝐷𝐷water flow rate, – cooling 𝑝𝑝 𝑜𝑜𝑜𝑜𝑜𝑜 𝑚𝑚 water𝐷𝐷 pressure, inlet cooling𝐾𝐾 water temperature, Nomenclature:1 – cooling water flow rate; – inlet 𝑔𝑔 – 𝑔𝑔 𝜂𝜂 𝑚𝑚̇ 𝑝𝑝 _ – inlet LP turbine steam pressure, _ – inlet LP cooling water temperature; – exhausted steam flow 1 𝑚𝑚̇ 𝑔𝑔 𝑇𝑇1 turbine steam temperature,𝑇𝑇 – exhausted steam flow rate; _ – inlet LP turbine steam temperature; _ – 𝑠𝑠 𝐿𝐿𝐿𝐿 𝑠𝑠 𝐿𝐿𝐿𝐿 𝑠𝑠 rate𝑝𝑝 , – condensate subcooling, – turbine𝑇𝑇 efficiency, inlet LP turbine steam pressure𝑚𝑚̇ , – LP turbine’s 𝑠𝑠 𝑠𝑠 𝐿𝐿𝐿𝐿 𝑠𝑠 𝐿𝐿𝐿𝐿 – condenser efficiency, condenser𝑚𝑚̇ pass number isentropic𝑇𝑇 efficiency 𝑝𝑝 𝑐𝑐 1 1 𝑑𝑑𝑑𝑑 𝜂𝜂 𝜂𝜂 Table 2. Example calculation results 𝜂𝜂𝑐𝑐 Calculation procedure CN, HEI method ASME method series 1 2 3 4 - Initialization parameters - Initialization load 100% 90% 75% 60% , parameters Calculation Calculation _ 4.63 4.09 3.47 3.56 𝑠𝑠 𝑄𝑄- ̇ 𝑈𝑈 based on (2) - = ( _ 𝑝𝑝 ( )), 𝑝𝑝𝑠𝑠 𝑅𝑅𝑅𝑅𝑅𝑅 𝑘𝑘𝑘𝑘𝑘𝑘 CN - based on (3) _ = ( _ , _ ) 2 𝑠𝑠 𝑠𝑠 - 𝑇𝑇 based on (4) - 𝑇𝑇 based𝑓𝑓 𝑇𝑇 on𝑠𝑠𝑠𝑠𝑠𝑠 (8) 𝑝𝑝 4.31 3.77 3.12 3.10 𝑠𝑠 𝐿𝐿𝐿𝐿 𝑠𝑠 𝐿𝐿𝐿𝐿 𝑠𝑠 𝐿𝐿𝐿𝐿 - 𝐿𝐿𝐿𝐿=𝐿𝐿𝐿𝐿( _ ( )), -𝑖𝑖 = 𝑓𝑓( 𝑝𝑝, ) 𝑇𝑇 𝑘𝑘𝑘𝑘𝑘𝑘 𝑠𝑠 𝑠𝑠 𝑝𝑝𝑠𝑠 466641 432688 368136 310295 𝑇𝑇_ = ( _ , _ ) - 𝑖𝑖 based on (1) 𝑠𝑠 𝑠𝑠 𝑠𝑠 𝑠𝑠 𝑠𝑠 𝑝𝑝 𝑓𝑓 𝑝𝑝 𝑠𝑠𝑠𝑠𝑠𝑠 𝑇𝑇 𝑥𝑥 𝑓𝑓 𝑝𝑝 𝑖𝑖 𝑘𝑘𝑘𝑘 - based on (8) - based on (2) 𝑄𝑄̇ 3.45 3.41 3.38 3.45 𝑠𝑠 𝐿𝐿𝐿𝐿 𝑠𝑠 𝐿𝐿𝐿𝐿 𝑠𝑠 𝐿𝐿𝐿𝐿 ̇ -𝑖𝑖 = 𝑓𝑓( 𝑝𝑝, ) 𝑇𝑇 - 𝑄𝑄 based on (4) 𝑘𝑘𝑘𝑘 𝑠𝑠 2 2 - 𝑖𝑖 based on (1) - 𝑇𝑇 based on (3)/ (7) 𝑈𝑈 26.6 24.5 21.7 22.2 𝑠𝑠 𝑠𝑠 𝑠𝑠 𝑚𝑚 𝐾𝐾 - 𝑥𝑥 based𝑓𝑓 𝑝𝑝 on 𝑖𝑖(5) / (6) - 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 based on (3) 2 ℃ HEI Next𝑄𝑄̇ iteration - 𝑈𝑈 based on (4) 𝑇𝑇 𝑈𝑈 - 𝐿𝐿𝐿𝐿=𝐿𝐿𝐿𝐿( _ ( )) 4.88 4.28 3.51 3.41 𝑠𝑠 Next𝑇𝑇 iteration 𝑠𝑠 𝑠𝑠 𝑠𝑠 𝑘𝑘𝑘𝑘𝑘𝑘 𝑝𝑝 𝑓𝑓 𝑝𝑝 𝑠𝑠𝑠𝑠𝑠𝑠 𝑇𝑇 𝑝𝑝 467298 433316 368667 310664 In table 1 input data were presented. In table 2 𝑄𝑄̇ 𝑘𝑘𝑘𝑘 2.59 2.52 2.45 2.52 example calculation results compare with real exhausted 𝑘𝑘𝑘𝑘 2 steam pressure were shown. 𝑈𝑈 𝑚𝑚 𝐾𝐾 26.6 24.5 21.7 22.2 1.8 Discussion of the results and exhaust 𝑇𝑇2 ℃ ASME steam pressure calculation method selection. 3.84 3.38 2.83 2.87 Verifying calculations have been made for data from real 𝑝𝑝𝑠𝑠 𝑘𝑘𝑘𝑘𝑘𝑘 466023 432138 367714 310000 units: 65MW and 460MW. This paper presents results for 𝑘𝑘𝑘𝑘 5.19 5.11 5.02 5.06 ϱ ƉƐ;ŬWĂͿ 𝑄𝑄̇ 𝑘𝑘𝑘𝑘 ,ĞĂƚĂůĂŶĐĞ 2 𝑈𝑈 26.6 24.5 21.7 22.2 ϰ͕ϱ E 𝑚𝑚 𝐾𝐾 ,/ Nomenclature:2 ℃ - reference exhausted steam, - 𝑇𝑇 _ calculated exhausted steam, condenser heat load, - ϰ ^D 𝑠𝑠 𝑅𝑅𝑅𝑅𝑅𝑅 – 𝑠𝑠 heat transfer coefficient𝑝𝑝 , – outlet cooling water𝑝𝑝 ϯ͕ϱ temperature 𝑄𝑄̇ 𝑈𝑈 𝑇𝑇2 ϯ the bigger one. Figure 1 presents calculated exhausted steam pressure compared with reference value. The most Ϯ͕ϱ similar results to the expected value gave HEI method ϭ Ϯ ϯ ϰ although results of characteristic numbers method are also correct. The square root error of exhaust steam pressure Fig. 1. Exhausted steam pressure

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was used to assess the series of results. For calculation Using Stodola-Flügel turbine passage equation based on HEI method it is 0.176kPa, for characteristic calculation for 70% and 40% of nominal load were done. numbers method 0.361kPa, for ASME method 0.704kPa. Calculations input data were: , , and value For second reference unite the best results gave needed to exhausted steam pressure calculation. characteristic numbers and HEI method. Least accurate To compare the results operation𝑡𝑡0 following𝑡𝑡20 𝑁𝑁𝑒𝑒𝑒𝑒 indicators results give ASME method. Although this method largely were calculated: gross unit heat rate and unit efficiency. based on similar equations as characteristic numbers = 3600 (9)

method, significant results difference follows on from 𝑄𝑄̇𝑑𝑑 𝑘𝑘𝑘𝑘 shellside resistance calculation. Reviewing the actual = (10) 𝑞𝑞 𝑁𝑁𝑒𝑒𝑒𝑒 [ 𝑘𝑘𝑘𝑘 ℎ] reference data, it is concluded that the results with the best 𝑁𝑁𝑒𝑒𝑒𝑒 Where = ( ) + ( ) accuracy were obtained using the HEI method. It is also 𝜂𝜂 𝑄𝑄̇𝑑𝑑 Comparing the proposed configurations, the following the simplest method when considering the complexity of 𝑑𝑑 0 0 100 19 20 19 assumptions𝑄𝑄̇ were𝑚𝑚 𝑖𝑖 made:− 𝑖𝑖 equal𝑚𝑚 steam𝑖𝑖 distribution− 𝑖𝑖 to the the calculations.

2 Comparison of three surface condenser connection setups on the cooling water side.

Four condenser connection configurations were tested: I- parallel (Fig.2), II-serial (Fig.3), III- parallel-to-serial Fig. 2. Parallel configuration (Fig.4) and IV- serial-to-parallel (Fig.5). For proposed thermal cycle (Fig.6) nominal load heat balance was calculated. Next heat balance for 70% and 40% of nominal load was computed. Considering steam flow change and thermodynamic parameters fluctuations, the influence of the tested connections on improving the unit efficiency was verified. Fig. 3. Serial configuration 2.1 Calculation procedure [6] The unit shown as a Figure 6 was described by energy and mass balances equations. The coefficients of the system of equations were appointed by the enthalpy value at the determined points. Enthalpy was calculated from the thermodynamics dependence in accordance with IAPWS

IF-97. Exhausted steam pressure was calculating based on Fig. 4. Parallel-to-serial configuration algorithm with HEI heat transfer coefficient. By iterating these three calculation steps, the pressure, temperature, enthalpy and mass flow were computed for the determined points at nominal load. Calculations input data were: – live steam pressure, – live steam temperature, – reheated steam 0 temperature, – electric power𝑝𝑝 and value needed to 0 20 𝑡𝑡exhausted steam pressure calculation𝑡𝑡 presented in first Fig.5. Serial-to-parallel configuration part of this thesis𝑁𝑁𝑒𝑒𝑒𝑒 .

Fig.6. Tested thermal cycle scheme

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LP turbine part, the total surface tube in each 2.2 Result discusion configuration is similar, the amount of cooling water is The results of calculations for 100% and 40% loads are the same and the number of tubes has been chosen so that presented in tables 4.1-4.2. Figures 7.1-7.2 show the gross the cooling water velocity does not exceed 2.6 . unit heat rate for the nominal load when the value of 𝑚𝑚 It was assumed: one pass surface condenser except the cooling water flow (7.1) and surface tube area (7.2) was 𝑠𝑠 parallel configuration where two pass surface condenser changed. The results were compared with the results from was selected; use of steel 1.4401 - = 15 ., tube the initial calculations (marked by x).

dimension Ø 22 x 0.5 mm, condenser efficiency𝑊𝑊 = The best results in thermodynamic terms were 𝑚𝑚 𝑚𝑚 𝐾𝐾 0.99, cleanliness factor = 0.95; 𝐾𝐾 obtained for a serial connection. In this case efficiency 𝑐𝑐 In table 3.1 and 3.2 input data for the calculations 𝜂𝜂were was improved by 0.15% compared to the parallel presented. Following, 𝐹𝐹proposed𝑐𝑐 configurations were connection for nominal load and 0.1% for minimum load. compared after changing parameters: temperature or flow Series-parallel connection was also somewhat more of cooling water, heat exchange surface, temperature of favorable, while other configurations are least beneficial. live and reheated steam, cleanliness factor ƋͺϭϬϬйсĨ;ŵŐͿ ƋͺϭϬϬйсĨ;ƐͿ Tabela 3.1 Input data for the calculations (the same for all tŐсϴϭϬϬϬ tŐсϲϭϮϬϬ ƐΕϰϴϳϬϬ ƐΕϯϵϬϬϬ Ŭ:ͬŬtŚ tŐсϳϮϬϬϬ tŐсϵϬϬϬϬ Ŭ:ͬŬtŚ ƐΕϱϴϱϬϬ configuration) ϲϵϴϬ ϲϵϱϬ

28.5 ~48700 ϲϵϲϬ ϲϵϯϬ 2 0 𝑀𝑀𝑀𝑀𝑀𝑀 600 s 𝑚𝑚 81000 ϲϵϰϬ 𝑝𝑝 𝐴𝐴 ϲϵϭϬ 𝑡𝑡 0 ℃ 𝑔𝑔 ϲϵϮϬ 𝑡𝑡 610/600* 𝑚𝑚̇ - ℎ 0.89 ϲϵϬϬ ϲϴϵϬ 𝑡𝑡20 ℃ 16.0 𝜂𝜂1 ϲϴϴϬ ϲϴϳϬ ℃ Tabela𝑇𝑇1 3.2. Input data for the calculations (different for each / // /// /s / // /// /s ĐŽŶĨŝŐƵƌĂƚŝŽŶ ĐŽŶĨŝŐƵƌĂƚŝŽŶ configuration) Fig. 7.1. Gross unit heat rate Fig. 7.2. Gross unit heat rate configuration I** II** III** IV** tested configuration when tested configuration when

change for nominal load 𝑔𝑔 change for nominal load 16252 16242 13935 20903 𝑚𝑚̇ 𝐴𝐴s 2 Figures 7.1-7.2 show the impact𝑔𝑔 of changing the 𝑠𝑠1 𝑚𝑚 𝑚𝑚̇ 𝐴𝐴 16252 16242 13935 13935 relevant parameters on the gross unit heat rate q. On the 2 one hand, the results show that regardless of the tested 𝐴𝐴𝑠𝑠2 𝑚𝑚 16252 16242 20903 13935 2 parameter, the serial system is the most advantageous. On 𝐴𝐴𝑠𝑠3 𝑚𝑚 19640 25000 16840 25260 the other hand, the charts show the savings this configuration gives. For example, a similar indicator q for 𝑁𝑁1 19640 25000 16840 16840 72000 cooling water flow for serial configuration was obtained𝑡𝑡 for 90000 using a parallel configuration 2 ℎ 𝑁𝑁 19640 25000 25260 16840 𝑡𝑡 (Fig.7.1). This gives ℎa 20% reduction in the amount of *) Temperature3 for 40% load cooling water. Figure 7.2 shows that the same indicator q **) 𝑁𝑁Proposed configuration: I-parallel, II-serial ,III- parallel-to-serial and IV- serial-to-parallel as for the base data series in parallel configuration can be Nomenclature: – live steam pressure, –live steam obtained by reducing the surface tube area by 20% for the temperature, –reheated steam temperature, serial configuration - this can be interpreted as a 0 0 – cooling water𝑝𝑝 flow rate, – inlet 𝑡𝑡cooling water decreasing surface tube area during operation. Similar 20 conclusions were reached when analyzing subsequent temperature, – 𝑡𝑡surface tube area – quantity of tubes 𝑔𝑔 1 results for the previously described parameters changes. 𝑚𝑚̇ – LP turbine’s isentropic efficiency𝑇𝑇 𝐴𝐴𝑠𝑠 𝑁𝑁 𝜂𝜂1 Table 4.1. Calculations results for nominal load configuration I-parallel II-serial III-parallel-to-serial IV-serial-to-parallel m p m p m p m p i 𝑘𝑘𝑘𝑘 𝑘𝑘𝑘𝑘 𝑘𝑘𝑘𝑘 𝑘𝑘𝑘𝑘 0 2416392 28.50𝑀𝑀𝑀𝑀𝑀𝑀 2393172 28.50𝑀𝑀𝑀𝑀𝑀𝑀 2413044 28.50𝑀𝑀𝑀𝑀𝑀𝑀 2406960 28.50𝑀𝑀𝑀𝑀𝑀𝑀 34 496260ℎ 0.00384 492192ℎ 0.00291 495648ℎ 0.00368 494604ℎ 0.00270 44 482724 0.00376 478836 0.00341 482148 0.00362 481176 0.00424 53 432900 0.00350 429552 0.00386 432432 0.00366 431568 0.00398 100 2416392 32.41 2393172 32.41 2413044 32.41 2406960 32.41 Operation indicators 6915 6892 6912 6907 0.521 0.522 0.521 0.521 𝑞𝑞 𝜂𝜂

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Table 4.2. Calculations results for 40% of nominal load configuration I-parallel II-serial III-parallel-to-serial IV-serial-to-parallel m p m p m p m p i 𝑘𝑘𝑘𝑘 𝑘𝑘𝑘𝑘 𝑘𝑘𝑘𝑘 𝑘𝑘𝑘𝑘 0 910116 10.82𝑀𝑀𝑀𝑀𝑀𝑀 903996 10.85𝑀𝑀𝑀𝑀𝑀𝑀 909288 10.82𝑀𝑀𝑀𝑀𝑀𝑀 907560 10.83𝑀𝑀𝑀𝑀𝑀𝑀 34 222300ℎ 0.00260 221796ℎ 0.00228 222264ℎ 0.00255 222120ℎ 0.00220 44 205992 0.00254 204624 0.00244 205848 0.00249 205452 0.00271 53 184248 0.00245 183024 0.00259 184068 0.00252 183744 0.00262 100 910116 12.31 903996 12.34 909288 12.31 907560 12.32 Operation indicators 7433 7416 7431 7427 0.484 0.485 0.484 0.485 𝑞𝑞 𝜂𝜂 pump, which will certainly be higher due to the greater 3 Conclusions drop in water pressure due to the flow in the tubes. Summarizing the researches, it has been proven that This paper presents calculation and verification of which the most advantageous configuration for thermodynamic connection setups of surface condensers on the cooling reasons is the serial configuration. Although this setup has water side is the best from thermodynamics perspective. several important disadvantages that can have a The study was not easy, because the phenomena occurring significant impact on the final result. in the last stage of the turbine and in the condenser are complex and difficult to describe using mathematical References formulas. Therefore, in the first part of work, the focus was on describing and choosing the best method for 1. The International Association for the Properties of calculating the exhausted steam pressure of condensing Water and Steam, Revised Release on the IAPWS turbine. Three calculation methods were compared, Industrial Formulation 1997 for the Thermodynamic results were verified with data from the factual site. Properties of Water and Steam Considering the correctness of the results and the 2. Kostowski E.: Przepływ Ciepła, (2006) complexity of the calculations, the method based on HEI 3. Szlachtin P.N.: Turbiny Parowe, (1953) standard has been identified as the most advantageous 4. HEI Standards for Steam Surface, (2012) method for calculating the turbine exhaust steam pressure. 5. ASME PTC 12.2-2010 Steam Surface Condensers It needs to be highlighted that using this method to Performance Test Codes, (2007) calculate heat transfer coefficient requires only the 6. Łukowicz H.: Podstawy siłowni cieplnych, Wykłady cooling water and condenser technical parameters. There is no need to enter the parameters of exhausted steam what simplifies the calculation. In the next step, four condenser connection configurations were tested. In each case, the serial configuration was the most thermodynamically favourable. For nominal parameters, obtained improvement of unit efficiency was around 0.15%. The use of this configuration can improve unit efficiency or reduce design or operating costs by reducing surface tube area, cooling water quantity, superheated steam temperature. However, for a serial connection, the problem of unequal operation of the LP turbine part attention should be paid to. The design of each parts of the turbine is the same, but when serial configuration is used, the exhausted steam pressure of each part is different, so they do not work at their optimal point. This is a significant problem when assuming the work of the unit mainly with nominal parameters. When serial connection is used, there is also a large dependence of the steam parameters of next LP turbine parts, which is not present for a parallel system. Incorrect assumptions or design calculations may have a greater impact to the operation then in parallel configuration. When choosing a series system, attention should also be paid to the useful power of the condensate

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