Effect of non-condensable gas on heat transfer in steam turbine condenser and modelling of ejector pump system by controlling the gas extraction rate through extraction tubes

Energy Conversion and Management 126 (2016) 228–246

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Effect of non-condensable gas on heat transfer in steam turbine condenser and modelling of ejector pump system by controlling the gas extraction rate through extraction tubes Dušan Strušnik a,⇑, Marjan Golob b, Jurij Avsec a a b

University of Maribor, Faculty of Energy Technology, Hocˇevarjev trg 1, SI-8270 Krško, Slovenia University of Maribor, Faculty of Electrical Engineering and Computer Science, Smetanova ulica 17, SI-2000 Maribor, Slovenia

a r t i c l e

i n f o

Article history: Received 1 June 2016 Received in revised form 20 July 2016 Accepted 31 July 2016

Keywords: Condenser Ejector Fuzzy logic Non-condensable gas Operating principle Pumped gas

a b s t r a c t The paper describes the impact of non-condensable gas (NCG) on heat transfer in a steam turbine condenser (STC) and modelling of the steam ejector pump system (SEPS) by controlling the gas extraction rate through extraction tubes. The ideal connection points for the NCG extraction from the STC are identified by analysing the impact of the NCG on the heat transfer and measuring the existing system at a thermal power plant in Slovenia. A simulation model is designed using the Matlab software and Simulink, Neural Net Work, Fuzzy Logic and Curve Fitting Toolboxes, to control gas extraction rate through extraction tubes of the gas pumped from the STC, thus optimising the operation of the steam ejector pump system (SEPS). The gas extraction rate from the STC is controlled in the extraction tubes by pumping only the NCG to the maximum extent. The SEPS is optimised by selecting a Laval nozzle of appropriate size to reduce the steam for the operation of the SEPS, whereby the amount of the extracted NCG is maintained. As the SEPS motive steam is produced in a boiler, the consumption of coal for the production of the SEPS motive steam is reduced as well as the greenhouse gas environmental pollution. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction A STC is an important subset of a condensing steam turbine. Its main purpose is to maintain the prescribed vacuum condition of around 0.01 MPa by evacuating exhaust gases from the steam turbine. Exhaust gases are multiphase gases, comprising a condensable gas (CG) and a NCG. The CG includes dry and wet vapour. Water vapour is removed from the STC through its condensation and by pumping the condensate into the boiler feeding system. NCG is evacuated by means of a SEPS. If no NCG evacuation takes place from the STC, the condensation area in the STC would be filled with the NCG and the condensation process would stop. Fig. 1 shows the principle of exhaust gas evacuation from the STC by means of the SEPS [1,2]. It is evident from Fig. 1 that cooling water from a nearby river is used for the CG condensation. The condensate is collected at the bottom of the STC and pumped into the boiler feeding system using the condensate pump, while the NCG phase is pumped into the

⇑ Corresponding author. E-mail address: [email protected] (D. Strušnik). http://dx.doi.org/10.1016/j.enconman.2016.07.082 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

atmosphere through the connection tube and using the SEPS. The connection element is installed in the upper part of the STC. SEPS are devices designed to use the pressure energy of a working fluid for the transport of another working fluid, whereby no mechanical work is supplied or recovered. SEPS can be operated with incompressible fluids (liquids), and in this application they are normally referred to as jet pumps or educators. They are used as vacuum compressors or vacuum pumps in order to produce vacuum in steam turbine systems, in refrigeration systems, for bulk material transport etc. The actual efficiency is low, ranging from 0.1 to 0.35 [1,2]. The process is non-reversible due to mixing of two flows. Some other authors also analysed the SEPS in the following papers [3–7]. Water vapour from the turbine steam extraction 1, previously expanded in the steam turbine, thus emitting part of its energy, is used for the operation of the SEPS. The quality of water vapour, travelling to steam extraction 1 of the steam turbine is regulated with pressure amounting to approx. 0.9 MPa and temperature to approx. 570 K. In our case, a SEPS is a two-stage flow-type compressor of a primary and secondary stage [1,2]. In the primary stage, i.e. the condensation stage, the pumped gas from the STC is compressed at a pressure of approximately 0.01 MPa. A mixture of the pumped gas from the STC and motive steam from the primary

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229

Nomenclature Abbreviations ANN artificial neural network ANFIS adaptive neural fuzzy inference system B, C article Cl close CG condensable gas FLC fuzzy logic controller F-Cl fast close F-Op fast open HP high pressure LP low pressure MAE mean absolute error MP middle pressure MSE mean square error NCG non-condensable gas Op open R2 correlation coefficient RMSE root mean square error SCADA supervisory control and data acquisition SEPS steam ejector pump system STC steam turbine condenser Parameters A surface, m2 Ai inner tube cross-section, m2 AL narrowest Laval nozzle cross section area, m2 At tube surface area, m2 A2 inlet diffuser cross sectional area, m2 c mixture molar density, kmol/m3 cpc cooling water specific conductivity, J/(kg K) steam speed at the exit from the Laval nozzle, m/s c1 c2 inlet diffuser mixed gas speed, m/s D molecular diffusivity, (MPa m2)/s DCG-NCG diffusion of condense gas in binary mixture, condense gas in non-condensable gas, (MPa m2)/s DCG-NCG,Tex diffusion of condensable gas in non-condensable gas at Tex, (MPa m2)/s DCG-NCG,T2 diffusion of condensable gas in non-condensable gas at T2, (MPa m2)/s DNCG-CG diffusion of non-condensable gas in a binary mixture of condensable gas in non-condensable gas (MPa m2)/s D(pex,Tex) experimental value of diffusivity of component at pex and Tex, (MPa m2)/s D(p2,T2) diffusivity of a component at p2 and T2, (MPa m2)/s tube inner diameter, m Di Do tube outer diameter, m dTNCG temperature difference of condensate boundary layer due to non-condensable gas layer, K dqQNCG-loss heat loss difference due to the non-condensable gas layer around the tube, W dnNCG differential of non-condensable gas quantity, kmol g gravitational acceleration, m/s2 h gas enthalpy, kJ/kg h0 specific enthalpy of motive steam, kJ/kg h1 specific enthalpy of steam Laval nozzle expansion, kJ/ kg h1s specific enthalpy of steam isentropic Laval nozzle expansion, kJ/kg h3 diffuser outlet mixed gas specific enthalpy, kJ/kg isentropic specific enthalpy of diffuser outlet mixed h30 gas, kJ/kg h4 specific enthalpy of the pumped gas, kJ/kg k heat transfer through a tube, W/(m2 K)

mNCG


! NCG;z nNCG/A p pNCG-z pNCG-1 pac pex pAir pH2O ps px, p1 p0 p2 p3 p4 pCG(298 K) pCG(313 K) qQt qPgen qmi qmt qmnon-out qm0 qm4 R R0 Rm Rmix2 rNCG-o ri ro Tac Tex Tm Tmean Tmix2 Tov Ts Tp-1 T0 T2 Vi

v2

ai ao

Dhco DTAir DTc

share of non-condensable gas in pumped-out mixture, % condensable gas molar flux density at a distance of z, kmol/(m2 s) amount of non-condensable gas per surface area unit, kmol/m2 pressure, MPa partial pressure of non-condensable gas at a distance along the z axis, MPa partial pressure of non-condensable gas on the condensate layer surface, MPa actual pressure, MPa experimental pressure, MPa partial air pressure, MPa partial steam pressure, MPa saturation water vapour pressure, MPa pressure in the mixing section, MPa inlet motive steam pressure, MPa diffuser inlet mixed gas pressure, MPa exhaust ejector mixed gas pressure, MPa pumped gas pressure, MPa saturation water vapour pressure at a temperature of 298 K, MPa saturation water vapour pressure at a temperature of 313 K, MPa heat transfer difference of STC tube generated power in the case of SEPS motive steam expansion in the turbine, kW mass flow of working fluid cross individual turbine component, kg/s amount of cooling water through a tube of the STC, kg/ s mass flow of the pumped non-condensable gas from the STC, kg/s motive steam mass flow through the Laval nozzle, kg/s pumped gas mass flow, kg/s gas constant, kJ/(kg K) motive steam gas constant, kJ/(kg K) universal gas constant, kJ/(kmol K) gas constant of the gas mixture in the mixing section, kJ/(kg K) outer radius of non-condensable gas layer around tube, m tube inner radius, m tube outer radius, m actual temperature, K experimental temperature, K temperature of the mixture, K average temperature of extracted gases, K diffuser inlet mixed gas temperature, K temperature of tube outer wall, where the steam condenses, K water vapour saturation temperature, K temperature of extracted gas of tube-i, K inlet motive steam temperature, K corrected temperature of the binary mixture, K valve position of tube -i, % inlet diffuser specific volume of the mixed gas, m3/kg heat transfer coefficient on tube inner side, W/(m2 K) heat transfer coefficient on tube outer side, W/(m2 K) water vapour steam condensation enthalpy, kJ/kg driving air temperature difference, K inlet-outlet cooling water temperature difference of the STC, K

230

DTH2O DTln DT1 DT2 Dhi Dz wCG kNCG kc kco kh

lc lco Uc

qc qco

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driving water vapour temperature difference, K logarithmic mean temperature difference between steam and cooling water in the STC (K), temperature difference between steam and cooling water on the outlet side of the STC, K temperature difference between steam and cooling water on the outlet side of the STC, K difference of specific enthalpy of working fluid of individual component, kJ/kg difference of distance in the direction of z axis from boundary condensation surface, mm molar fraction difference of condensable gas, kmol heat conductivity of non-condensable gas, W/(m K) heat conductivity of cooling water, W/(m K) heat conductivity of condensate layer, W/(m K) heat conductivity of tube, W/(m K) dynamic viscosity of cooling water, MPa s dynamic viscosity of condensate layer, MPa s volume flow of cooling water through tube, m3/s cooling water density, kg/m3 condensate density, kg/m3

ejector stage is led to the primary cooler. Most of the CG is condensed here and returned to the condenser through a special barometer loop. The mixture remaining in the primary cooler after the condensation is pumped at the steam pressure of the secondary (atmospheric) stage and compressed to the pressure slightly higher than the atmospheric pressure, then led, together with the motive steam from the second stage, to the secondary cooler. The CG is also condensed in this cooler. The condensate passes through the condensate pot to the STC and the residual NCG to the atmosphere. Analysis of the NCG impact on condensation process and STC heat transfer has been studied by many authors [8–11]. The results show that the presence of even a small amount of NCG in steam substantially reduces the STC heat transfer. Artificial neural networks (ANN) can be used as an alternative to analytical modelling approach. ANN is a model of a complex system, where a large number of equal elements react to signals in relation to one another. These are mathematical models, imitating the structure and functionalities of biological neural networks [12]. The essential property of an ANN is that it is capable of finding itself correlative dependence or regression between the input and output values. When the ANN is created, it works in situations not encountered during the creation process, which means that it can resolve the tasks, where the solution does not exist, in the form of a sequence of steps, such as in computer algorithms; nevertheless, there is a risk of unpredictable performance [13–17]. Fuzzy logic controller (FLC) is based on expert knowledge expressed in terms of rules and can thus be employed to predict the behaviour of many uncertain systems. The FLC advantage is that it does not require knowledge of the underlying physical models as a precondition for its application. The FLC design is relatively simple and is based on criteria correlation of input-output variables [13]. The correlation between the inputs-outputs is described with If-then rules, allowing the implementation of complex nonlinear system in the manner in which people think [13]. The FLC functioning and design are described in more detail by the authors of the following papers [18–23]. Neural networks can learn from data. Opposite, FLC cannot learn, but they are easy to understand. To improve the modelling approach, hybrid intelligent systems that increase the capability of learning and adapting automatically have been used by researchers for many different purposes in a variety of engineering systems. Among the many neural network system, one of the most used and powerful is the Adaptive neural fuzzy inference system

Subscripts d id i, j M M2 Nu n o Pr Re S t z

gd gLaval-is ,0 ,mix2

and Superscripts turbine component number turbine component iteration iterations Mach number Mach number in the mixing section Nusselt number number of learning data sets output value Prandl number Reynold number pattern target value axis diffuser isentropic efficiency Laval nozzle isentropic efficiency motive steam specific heat ratio specific heat ratio of the gas mixture in the mixing section

(ANFIS). ANFIS shows very good learning and prediction capabilities, which makes it an efficient tool to deal with encountered uncertainties in any system. It was used by researchers in various engineering systems [24–27]. The objective of this investigation is to establish FLC and ANN based model for simulation the operation of the SEPS, serving to extract the NCG from the STC. The simulation model of the control of the amount of the pumped gases through the extraction tubes was designed by means ANN, FLC, Curve Fitting Toolbox, and xsteam toolbox. The simulation model works so that the dimension of the Laval cross-section of the Laval nozzle of the primary and secondary stage of the SEPS changes until the required and actual amount of the pumped gases become equal. The FLC calculation unit is intended to control the open positions of control valves, by means of input signals, i.e. temperatures of the pumped gas through extraction tubes. Nonlinear ANN computes temperature and pressure of water vapour used for the SEPS’s drive by means of 3 input data items, i.e. temperature, pressure and water vapour mass flow, entering the steam turbine, The ANN was designed by using real process data from the thermal power plant. 2. Analysis of the NCG impact on condensation process and STC heat transfer The analysis of the NCG impact on condensation and the STC heat transfer comprises two parts. In the first part, the NCG impact on the condensation process of the isolated tube in the STC was analysed, where diffusivity of CG through the layer of NCG and CG binary mixture was examined. In the second part, the NCG impact on heat transfer through the isolated pipe was analysed. Using the results of the analyses and the measurements performed of the existing system, a temperature profile of the STC was developed, from which ideal connections points were identified for extraction of NCG from the STC. The measurements of the existing system were obtained from the supervisory control and data acquisition system (SCADA) [28] at a thermal power plant in Slovenia in the 2013/2014 heating season. 2.1. Analysis of NCG impact on isolated tube condensation process in the STC In the condensation process, the temperature driving force transports exhaust gases from a steam turbine to the cooled

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231

Fig. 1. Principle of the steam turbine exhaust gas evacuation from the STC by means of the SEPS.

Fig. 2. Condensation of a steam turbine exhaust gases in a water-cooled STC.

surfaces of the STC, where NCG cannot condensate. As a consequence, a layer of NCG is formed around the cooled surfaces, thus reducing the heat transfer [9–11]. It is essential to continuously remove NCG from the turbine condenser; otherwise, the STC becomes saturated with NCG and the water vapour condensation process stops. Fig. 2 shows the condensation of exhaust gases from a steam turbine in a water-cooled STC, namely water vapour condensation in the presence of NCG and condensation of pure water vapour [29]. The temperature profile (top r.h. diagram in Fig. 2) shows that during the condensation of water vapour or CG in the presence

of NCG, the condensate temperature drops from 298 K to 283 K. As a result, the temperature driving force DTAir between the condensate and cooling water is halved and the quantity of condensate is reduced by the same amount. This means that for the condensation of the same quantity of water vapour, in the presence of NCG, the amount of cooling water increases. The condensate becomes undercooled and as such it is pumped into the boiler feedwater system. This results in losses due to increased cooling water quantity, losses due to reheating of the undercooled condensate and losses due to a lower output of the steam turbine. The steam turbine output is lower because the NCG increases pressure in the

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STC and water vapour in the steam turbine in unable to expand to the prescribed pressure level in the STC. This results in a lower output of the process [29]. The effect of NCG on water vapour condensation is described by Fick’s law of constitutive diffusion of a substance [29]. Molecular diffusion in a binary mixture is a consequence of uncontrolled movement of molecules [30–32]. Transmission of substances results from the changing of positions of molecules in a space rather than from collisions between the molecules. Collisions between the molecules provide a basis for the transfer of heat, energy and momentum, but they decelerate the transfer of substance. Molecular diffusion is more intense in gases than in liquids and solids. The intensity of the phenomena of transfer in the flow of fluids and gases is also affected by turbulence [30]. The bases of a turbulent transfer are temporal fluctuation of speed in individual places, resulting in eddy currents within fluids. When there is a temperature gradient in the current of fluids, thermal energy is also transferred in the same way with the swirling currents. Fick’s law states that a substance is diffused relative to a current of mixture in the direction of a decrease in concentration. The index of Fick’s molecular diffusion of compound DCG-NCG, defines diffusion of CG into a binary mixture of CG and NCG [30,33,34]. Diffusivity DNCG-CG is defined by diffusion of NCG into a binary mixture of CG and NCG. Similarly, diffusion in a binary mixture was computed by the authors in the following papers [35–37]. Table 1 shows the experimentally obtained values of molecular diffusivity in various binary gas mixtures and at various temperatures [30]. Experimentally obtained values of molecular diffusivity apply only to selected temperature and pressure conditions. The remaining values are calculated using equation [30]:

Dðp2;T2Þ ¼ Dðpex;TexÞ 

 7 pex T ac 4  pac T ex

ð1Þ

where D(p2,T2) is diffusivity of a component at actual pressure pac and actual temperature Tac in the STC, D(pex,Tex) is experimental value of diffusivity of a component at pressure pex and temperature Tex, pex/pac is the pressure ratio between the actual and experimental value in the STC and Tac/Tex is the temperature ratio between the experimental and actual value in the STC.


! To calculate the molar flux density of the component N CG;z , Stefan’s law of density of molar flux, one-sided diffusion and one-dimensional geometric conditions in the direction of z axis (Fig. 2), computed by means of [30]:




! c  DCGNCG DwCG NCG;z ¼   1  wCG Dz

ð2Þ




! where NCG;z is molar flux density of CG at a distance along z axis (Fig. 2), c is molar density of a mixture, DCG-NCG is diffusivity of CG into a binary mixture of CG and NCG, DwCG is molar fraction difference of CG and Dz difference of distance in the direction of z axis from the boundary condensation surface (Fig. 2). In our case, the tables or manuals for water vapour are used to read for given conditions the values of pressure of water vapour saturation at a temperature of 313 K, which is

Table 1 Fick’s molecular diffusivities in binary gas mixtures [30]. System

Temperature, Tex (K)

Molecular diffusivity, D (MPa m2)/s

Air-CO2 Air-H2O Air-H2O Air-Benzene CO-N2

276.2 289.1 313 298.2 273.0

1.42  106 2.82  106 2.92  106 0.96  106 1.77  106

p = pCG(313 K) = 7.375  103 MPa at a temperature of 298 K, which is p = pCG(298 K) = 3.166  103 MPa. In the absence of NCG, the molar flux density of CG is 3  104 kmol/(m2 s) [30]. In Table 1 of binary system molar diffusivity a reading is taken for water vapour-air, namely DCG-NCG = 2.92  106 (MPa m2)/s at a temperature of 313 K, which means the water vapour diffusivity or CG into air or NCG. Using Eq. (1), the above value is corrected by the temperature difference T2 = ((313 K + 298 K)/2) = 305.5 K (corrected temperature of the binary mixture) to obtain the calculation of actual value of diffusivity of CG into NCG:

 DCGNCG;T2 ¼ DCGNCG;Tex

T2 T ex

74

¼ 2:92  106 

 7 305; 5 4 313

¼ 2:8  106 ðMPa  m2 Þ=s

ð3Þ

where DCG-NCG,T2 is diffusivity of CG into NCG at a temperature of T2, DCG-NCG,Tex is diffusivity of CG into NCG at a temperature of Tex from Table 1, Tex is temperature of a binary gas mixture for air-H2O pair from Table 1 and T2 is the corrected temperature of the binary mixture. Given that in our case the condensation is one-sided onedimensional diffusion in the direction of the z axis, the equation of the Stefan’s law (Eq. (2)) is used to compute the density of the NCG flux and transformed, taking into account the boundary conditions and integration, into the equation [30]:




! DCGNCG p NCG;z ¼  ln NCGz Rm  T m pNCG1

ð4Þ

where Rm is the universal gas constant, Tm is temperature of the mixture, pNCG-1 is partial NCG pressure on the surface of the condensate layer and pNCG-z is partial pressure of the NCG at a distance along the z axis (Fig. 2). Partial pressure of NCG as a function of the z coordinate z (Fig. 2) is described by equation [30]:

pNCGz ¼ pNCG1  exp

!


! NCG;z  Rm  T c DCGNCG

ð5Þ

In assessing the total amount of NCG per unit of surface nNCG/A, we derive from the gas equation in its differential form and the integration is used for solving it [30]:

Z 0

1

pNCGz ðzÞdz ¼

Rm  T c A

Z

nNCG

dnNCG ;

ð6Þ

0

where A is surface and dnNCG is differential of the NCG amount. By taking into account the pressure distribution the amount of NCG per unit of surface is calculated [30]:

nNCG 1 ¼ Rm  T c A

Z 0

1

pNCGz ðzÞdz ¼

pNCG1 Rm  T c

Z




! N CG;z Rm T c

1

exp

DCGNCG

! ðzÞdz

0

ð7Þ Eqs. (6) and (7) are used to compute the trend of the partial pressure of NCG and the change of the total amount of NCG per unit of surface nNCG/A, at different temperatures of the condensate boundary layer as a function of the distance along z axis (Fig. 2). Table 2 shows the data used in the calculations. Fig. 3 shows the trend of NCG partial pressure as a function of the distance from the surface of the condensate layer at different temperatures of the boundary layer. It is evident from the Fig. 2 that the partial pressure of the NCG increases while the temperature of the condensate boundary layer decreases. In our case, the highest partial pressure of the NCG amounts to 6.148  103 MPa at a temperature of the condensate boundary layer of 283 K and decreases exponentially. At a temperature of 298 K, the partial pressure of the NCG on the condensate boundary layer amounts to 4.209  103 MPa and decreases to the temperature of the

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D. Strušnik et al. / Energy Conversion and Management 126 (2016) 228–246 Table 2 Data on water vapour condensation on the condensate boundary layer at different temperatures [30]. Condensate temperature (K)

Steam saturation pressure p = ps (MPa)

Temperature of mixture, Tm (K)

Diffusivity, DCG-NCG (MPa m2)/s

Partial air pressure, pNCG-1 (MPa)

Flux density,


! N CG;z (kmol/(m2 s))

313 311 308 303 298 293 288

7.375  103 6.674  103 5.622  103 4.241  103 3.166  103 2.337  103 1.704  103 1.227  103

313 312 310.5 308 305.5 303 300.5 298

2.92  106 2.9  106 2.88  106 2.84  106 2.8  106 2.76  106 2.72  106 2.68  106

0 0.701  103 1.753  103 3.134  103 4.209  103 5.038  103 5.671  103 6.148  103

3  104 2,8  104 2.4  104 1,9  104 1,5  104 1,1  104 0,7  104 0,4  104

NCG Partial Pressure (MPa)

x 10

As it is impossible to carry out the pumping of the NCG precisely at the above indicated points, the suction pipe of the SEPS is connected to the coolest points of the STC.

-3

6

Condensate Layer Temperature 283 K Condensate Layer Temperature 288 K Condensate Layer Temperature 293 K Condensate Layer Temperature 298 K Condensate Layer Temperature 303 K Condensate Layer Temperature 308 K Condensate Layer Temperature 311 K

5 4

2.2. Analysis of the effect of the NCG on the heat transfer through the isolated tube of the STC

3 2 1 0 0

15

10

5

20

25

30

35

40

Distance From The Condensate Layer Surface (millimetres) Fig. 3. Ratio between the partial pressure of the NCG and the distance from the surface of the condensate layer at different temperatures of the condensate boundary layer.

Quantity Of The NCG Per Unit Area (kmol/m2)

2.5

x 10

-3

CG 13%, NCG 87% At 283 K CG 23%, NCG 77% At 288 K CG 37%, NCG 63% At 293 K CG 50%, NCG 50% At 298 K CG 63%, NCG 37% At 303 K CG 80%, NCG 20% At 308 K CG 93%, NCG 7% At 311 K CG 100% At 313 K

2 1.5

k¼

1 0.5 0

The condensation heat in the STC is released into the environment by means of cooling water flowing on the inner side of the tube. The tubes in the STC are integrated into tube bundles. The number of tubes in a tube bundle depends on the amount of the exhaust steam from the steam turbine, the design and the tube material. In our case, losses will be analysed in more detail, occurring when heat passes through an isolated tube of the STC. The losses occurring when heat passes through the isolated tube result from the heat resistance of the tube and the NCG layer around it. The tube heat resistance depends on the tube material, which is closely linked to the tube price. A layer of NCG around the tube considerably reduces the heat transfer as it acts as an insulator. The impact of NCG on heat transfer through a tube was described in more detail by the authors in the following papers: [10,11,38– 41]. The heat transfer through the isolated STC tube is calculated using the equation:

0

5

10

15

20

25

30

35

40

45

50

Distance From The Condensate Layer Surface (millimetres) Fig. 4. Amount of the NCG per unit of surface at different concentrations of the mixture and temperatures of the condensate boundary layer.

condensate boundary layer of 313 K, where no NCG is present on the boundary layer. Fig. 4 shows the concentration of the NCG per unit of surface nNCG/A computed by means of Eq. (7). Fig. 4 shows that the concentration of the NCG decreases as a function of the distance of the condensate boundary layer, whereby the decrease is the slowest when the share of the NCG in a binary mixture is the largest. In this case, the transfer of heat of the binary mixture is the lowest, as the concentration of the NCG is the highest close to the condensate boundary layer that prevents diffusion of the CG into the NCG layer. As the distance from the boundary layer of the condensate layer increases, the amount of the NCG per unit of surface decreases exponentially and after several millimetres it becomes equal to the pressure in the STC. At the points where a phase transformation takes place of the physical state of the CG (condensation), the concentration and the partial pressure of the NCG are the highest. The above points are the most appropriate connecting points for pumping the NCG from the STC.

ro ai ri

1 þ kro  ln rro þ rNCG0  ln rNCGo þ a1o kNCG ro h

ð8Þ

i

where k is heat transfer through the tube, ro is outer tube radius, ai is heat transfer coefficient on the inner side of the tube, ri is inner tube radius, kh is conductivity of the tube, rNCG-o is outer radius of the NCG layer around the tube, kNCG is heat conductivity of the NCG and ao is heat transfer coefficient on the external side of the tube. The following values were used in the calculations: heat conductivity of the tube, brass kh = 120 W/(m K) and heat conductivity of NCG, kNCG = 0.0265 W/(m K). The heat transfer coefficient on the inner side of the tube ao is computed using the Dittus-Boelter equation [10,11,38]:

ao ¼

¼

kc  Nu kc  0; 023  Re0;8  Pr0;4 ¼ Di Di /c 0;8  0;4 D  q i c A kc  0; 023  i l  cpkc clc c

Di

ð9Þ

where kc is heat conductivity of cooling water, Di is inner tube diameter, Uc is volume flow of cooling water through the tube, Nu is the Nusselt number, Re is the Reynolds number, Pr is the Prandtl number, Ai is inner tube cross-section, qc is cooling water density, lc is dynamic viscosity of cooling water, cpc is specific conductivity of cooling water. The following values were used in the calculations: heat conductivity of cooling water kc = 0.598 W/(m K), volume flow of cooling water through the tube Uc = 5.444  103 m3/s, inner tube cross-section Ai = 3.4618  104 m2, cooling water density

D. Strušnik et al. / Energy Conversion and Management 126 (2016) 228–246

qc = 998 kg/m3, dynamic viscosity of cooling water lc = 1.003  109 MPas and specific conductivity of cooling water cpc = 4182 J/(kg K) [38]. The heat transfer coefficient on the external side of the isolated tube ao in condensation of water vapour saturation, where a condensation layer film is obtained, is calculated by means of:

ao ¼ 0; 728 

g  Dhco  q2co  k3co Do  lco  ðT s  T ov

!0;25 ð10Þ

where Do is outer tube diameter, lco is dynamic viscosity of condensate layer, Ts is water vapour saturation temperature, Tov is tube outer wall temperature, where water vapour condensates, g is gravitational acceleration, Dhco is water vapour condensation enthalpy, qco is condensate density and kco is condensate layer heat conductivity. The following values were used in the calculations: gravitational acceleration g = 9.81 m/s2, water vapour condensation enthalpy Dhco = 2.38  106 J/kg, condensate density qco = 992 kg/ m3, condensate layer heat conductivity kco = 0.627 W/(m K), condensate layer dynamic viscosity lco = 0.6531  109 MPas, water vapour saturation temperature Ts = 312.5 K and tube outer wall temperature where water vapour condensates Tov = 311 K. The heat transfer of the isolated tube of the STC is calculated using:

qQ t ¼ k  At  DT ln ¼ k  At 

" # DT 1  DT 2 ln DDTT 12

¼ qmt  cpc  DT c

ð11Þ

where qQt is heat transfer difference of the STC tube, At is tube surface, DTln is logarithmic mean temperature difference between water vapour and cooling water in the STC, DT1 is temperature difference between water vapour and cooling water on the outlet side of the STC, DT2 is temperature difference between water vapour and cooling water on the inlet side of the STC, qmt is amount of cooling water through the STC tube, cpc is specific heat of cooling water, DTc is inlet-outlet temperature difference of the cooling water of the STC. The following values were used in the calculations: logarithmic temperature difference of the STC DTln = 12.65 K and amount of cooling water through the STC tube qmt = 0.054463 kg/s. The temperature difference of the condensate boundary layer due to the NCG layer around the isolated tube is calculated by means of [38]:

dT NCG ¼ 

difference due to the NCG layer around the tube and kNCG is heat conductivity of the NCG. The STC heat power of the existing system in a thermal power plant in Slovenia is taken into consideration in the analysis, amounting to 2.38  107 W, where 10 kg/s of CG condenses on average from the steam turbine. The cooling water flow rate from the cooling tube bundle of the STC is 258.7 kg/s. The cooling water temperature at the inlet of the STC is 285 K and 307 K at the outlet. The STC tube bundle comprises 4750 tubes. The tube inner diameter is 0.021 m and the tube outer diameter 0.023 m, whereby the tube length is 6.4 m. The analysis results show that even a small layer of NCG around the STC tube considerably reduces the heat transfer. Fig. 5 shows thermal transmittance and heat transfer when the NCG layer around the STC tube changes. Fig. 5 shows that the isolated tube of the STC has the highest thermal transmission when the thickness of the NCG around the tube is the smallest. By increasing the thickness of the NCG layer around the tube, heat transmission and heat passing through the tube are reduced as the NCG layer around the tube acts as an insulator. If the NCG layer around the tube is 0.6  106 m, the heat transfer through the tube is reduced by 60% and by 82% if the NCG layer is 2  106 m. The NCG layer around the tube reduces water vapour diffusion to the cooled surface and lowers the temperature of the condensate boundary layer. Fig. 6 shows the temperature of the air layer and condensate boundary layer when the thickness of the NCG layer around the STC tube increases. Fig. 6 shows that the condensate boundary layer temperature is the highest when there is no NCG layer around the STC tube and it amounts to 313 K. As the thickness of the NCG layer around the

313.02 313

Temperature (K)

234

NCG Temperature (K) Condensate Bundary Layer Temperature (K)

312.98 312.96 312.94 312.92 312.9 312.88 0

dqQ NCGloss 2  p  kNCG  r NCGo

0.2

0.4

0.6

0.8

1

1.2

5000

2

1.8 x 10

Fig. 6. Temperature of the air layer and of the condensate boundary layer when the thickness of the NCG layer around the STC tube increases.

900

Heat Through The Tube (W)

Tube Heat Transfer (W/m2K)

800 4000

Heat Transfer (W/m2K)

Heat Through The Tube (W)

1.6

Thickness Of The NCG Layer Araund The Tube (metres)

where dTNCG is temperature difference of the condensate boundary layer due to the NCG layer around the tube, dqQNCG-loss is heat loss

3000

2000

700 600 500 400 300 200

1000

100 0

1.4

-6

ð12Þ

0

0.5

1

1.5

Thickness Of The NCG Layer x 10-6 Araund The Tube (meters)

2

0

0

0.5

1

1.5

2

Thickness Of The NCG Layer x 10-6 Araund The Tube (meters)

Fig. 5. Thermal transmittance and heat transfer in case of increase of the thickness of the NCG layer around the STC tube.

D. Strušnik et al. / Energy Conversion and Management 126 (2016) 228–246

tube increases, the temperature of the condensate boundary layer decreases. When the thickness of the NCG layer is 2  106 m, the temperature of the boundary layer is reduced by 0.125 K to 312.875 K. The temperature variation of the air layer around the tube is negligible. The overall losses resulting from the heat transfer through the STC tube are the losses arising from the thermal resistance of the tube material and the losses arising from the NCG layer around the tube. They are shown in Fig. 7. The largest share of the losses of the STC is caused by the NCG layer around the tube, namely 90% of the total losses arising from the transfer of heat of the STC. The remaining losses are the losses caused by the thermal resistance of the material and cannot be avoided. The losses may be reduced by choosing a more appropriate tube material, which is linked to the costs. Any excessive losses arising from the NCG layer around the tube are avoided by preventing the atmospheric air from entering the STC and by pumping the NCG from the STC in a more reliable manner. The calculation shows that when the total amount of NCG around the tube is 2.195  104 m3, the thermal power of the STC is reduced by 20%. If the overall amount of the NCG around the tube is 8.78  104 m3, the thermal power of the STC is reduced by 50%. If, however, the total amount of the NCG around the tube is 2.195  103 m3, the thermal power of the STC is reduced by as much as 74%. The NCG pumping from the STC has to be ensured even before the above gas reaches the tubular cooling surfaces. The NCG concentration is the highest on the coldest places of the STC. The coldest places of the STC were identified by means of an

16 14

Loss (W/K)

12 10 Totall Loss (W/K) Losses Due To NCG Layer Araund Tube (W/K) Losses Due To Thermal Resistance (W/K)

8 6 4 2 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2 -6

x 10

Thickness Of The NCG Layer Araund The Tube (metres) Fig. 7. STC losses when the thickness of the NCG layer around the tube increases.

235

analysis of the temperature profile of the existing STC in a thermal power plant in Slovenia, shown in Fig. 8. The circles numbered from 1 to 3 in Fig. 8 show the ideal connecting points for the NCG pumping. Some other authors analysed various systems using a temperature profile [42–45]. The connecting points 1, 2 and 3 are located so as to create a complete circle of connections used for gas pumping. Each connecting point has 3 connections. Two connections are on the external side of the cooling tube bundle and one is in the central part of the cooling tube bundle. Fig. 9 shows a schematic diagram of the control of the quantity of pumped gases through the extraction tubes. The connecting locations interconnect the extraction tubes for STC gas pumping. The extraction tubes are fitted with 3 control valves to control the amount of the pumped gas depending on the temperature of the pumped gas. The amount of the pumped gas increases through the extraction tubes, where the pumped gases are cooler and decreases, at the same time, through the extraction tubes, where the pumped gases are warmer. As a result, pumping of a larger amount of NCG is ensured and of a smaller amount of CG, given that the NCG concentration is the highest on the colder places. This way, the total amount of the pumped gases from the STC can be reduced, the SEPS operates more efficiently and consumes less energy for its operation. 3. Simulation model of the control of the amount of pumped gases through extraction tubes The simulation model of the control of the amount of the pumped gases through the extraction tubes was designed by means of the Matlab software and a set of tools provided by the above software: Simulink, ANN, FLC, Curve Fitting Toolbox, and x-steam toolbox. The simulation model comprises the following auxiliary simulations models: nonlinear ANN unit, x-steam calculation unit, SEPS calculation unit, FLC calculation unit and pumped gas calculator. The simulation model works so that the dimension of the Laval cross-section of the Laval nozzle of the primary and secondary stage of the SEPS changes until the required and actual amount of the pumped gases become equal. The required amount of pumped gases is calculated using the functional equation as a function of the average temperature of the pumped gases, developed by means of the results of the existing system analyses. The actual amount of the pumped gases is comprised of the gases pumped by the SEPS from the STC depending on the dimension of the Laval cross-section. When both amounts of the pumped

Fig. 8. Temperature profile of the STC and ideal connecting locations for NCG pumping.

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Fig. 9. Control of the amount of the pumped gases through extraction tubes.

Fig. 10. Algorithm of the simulation model of the control of the amount of the pumped gases through extraction tubes.

gases are equal, the simulation model displays the results of the Laval nozzle diameter of the primary and secondary stage of the SEPS, the amount of the pumped gases, the quality and quantity of the water vapour passing through the Laval nozzles. Fig. 10 shows the simulation model algorithm. 3.1. Auxiliary simulation model: nonlinear ANN unit Nonlinear ANN unit (Fig. 10) is a nonlinear ANN system, which, by means of 3 input data items, i.e. temperature, pressure and water vapour mass flow, entering the steam turbine, computes 2 output data items, i.e. temperature and pressure of water vapour used for the SEPS’s drive. The ANN was designed by using real process data of the 2013/2014 heating season from the SCADA system [28] in a thermal power plant in Slovenia. SCADA contains more than 850 groups of data concerning the district heating system,

constantly recorded on an hourly basis 365 days a year. Some other authors used in their research the SCADA system [46–50]. Three groups of input data were used in the creation of the nonlinear ANN unit, expressed in the [3  4793] matrix form and 2 groups of output data, expressed in the [2  4793] matrix form. As a result, each group contains 4793 data items. The nonlinear ANN unit algorithm structure comprises an input layer, two hidden layers and an output layer. The input layer contains 3 neurons, the first hidden layer contains 35 neurons, the second hidden layer 5 neurons and the output layer 2 neurons. The nonlinear ANN unit algorithm structure (Fig. 10) was selected through validation and it has minimum errors between the results provided by the nonlinear ANN algorithm structure and the real process results. The X-steam calculation unit is not to be specifically introduced. Its role is to calculate the enthalpy and entropy values of water vapour used as the SEPS motion steam.

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3.2. Auxiliary simulation model: SEPS calculation unit

Table 3 The geometrical data of the existing SEPS [2].

Once the thermodynamic properties of water vapour used for the SEPS operation are known, the SEPS calculation units compute the mass flow of water vapour used for the SEPS operation, water vapour speed in the narrowest Laval diameter, speed of water vapour from the Laval nozzle and quantity of removed NCG from the STC [2]. The calculations recorded in the primary and secondary calculation units are based on the thermodynamic transformation of the SEPS shown in Fig. 11. Several other authors described the thermodynamic transformation of the SEPS in a similar way [3,51,52]. The motive steam enters the ejector at point 0 and flows through the Laval nozzle, where the steam expands at supersonic speed. In the mixing section x, the expanded motive steam pumps gases from the STC 4, where they mix with each other from point 1 to point 2. The mixture of gases enters a diffuser section, where kinetic energy of gas transforms into pressure energy and at point 3, the gases exit at a higher pressure and a lower speed. The analysis is based on the facts of conservation of momentum, mass and energy balances in each part of the ejector (Laval nozzle, mixing and diffuser sections) [1,2]. The following facts are taken into consideration in the calculation: there is no heat transfer in the transformations in the Laval nozzle, the motive steam expands in the Laval nozzle from the initial state of p0 up to pressure in mixing section, px (Fig. 11), we assume that pressure px in the mixing section equals the gas pumping pressure p4 (Fig. 11), the gases in the mixing section mix with each other, potential energy is negligibly low and is not taken into consideration and outlet speed from the diffuser is extremely low and is therefore neglected [2]. The motive steam mass flow through the Laval nozzle is calculated using the equation [2,52]:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u  ,,0 þ1 u 0 1 AL  p0 t,0 2 qm0 ¼ pffiffiffiffiffi    gLavalis R0 ,0 þ 1 T0

ð13Þ

where qm0 is motive steam mass flow through the Laval nozzle, AL is narrowest Laval nozzle cross section area, p0 is inlet motive steam pressure, T0 is inlet motive steam temperature, ,0 is motive steam specific heat ratio, R0 is motive steam gas constant and gLaval-is. is Laval nozzle isentropic efficiency. The Laval nozzle isentropic efficiency is defined as [2,53–55]:

gLavalis ¼

h0  h1  0; 97 h0  h1s

ð14Þ

where h0 is specific enthalpy of motive steam, h1 is specific enthalpy of steam Laval nozzle expansion and h1s specific enthalpy of steam

Parameter

Primary ejector

Secondary ejector

Narrowest Laval nozzle diameter (m) Laval nozzle outlet diameter (m) Diffuser inlet diameter (m) Final diameter of a diffuser (m) Diffuser expansion angle (°) Nozzle efficiency (%) Diffuser efficiently (%)

0.0098 0.0396 0.0496 0.1025 10 0.97 0.75

0.0121 0.0264 0.0323 0.0872 10 0.97 0.75

isentropic Laval nozzle expansion. Steam speed at the exit from the Laval nozzle is calculated as [2,53–55]:

c1 ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  gLavalis  ðh0  h1s Þ

ð15Þ

where c1 is steam speed at the exit from the Laval nozzle. The motive steam expanded in the Laval nozzle and gases pumped from the STC are mixed in the mixing section. The thermodynamic analysis is described by means of the mass, momentum and energy balance equations [1,2]. Mass balance equation [2,53–55]:

qm0 þ qm4 ¼

A2  c 2

v2

ð16Þ

where qm4 is pumped gas mass flow, A2 is inlet diffuser cross sectional area, c2 is inlet diffuser mixed gas speed and v2 is inlet diffuser specific volume of the mixed gas. Geometrical data of the existing SEPS is indicated in Table 3. Momentum balance equation [2,53–55]:

qm0  c1 þ p4  A2 ¼ ðqm0 þ qm4 Þ  c2 þ p2  A2

ð17Þ

where p4 is pumped gas pressure and p2 is diffuser inlet mixed gas pressure. Energy balance equation [2]:

  c2 qm0  h0 þ qm4  h4 ¼ ðqm0 þ qm4 Þ  h2 þ 2 2

ð18Þ

where h4 is specific enthalpy of the pumped gas. Pressure in the mixing section px = p1 = p4 is taken into consideration in the calculation. The diffuser conditions are calculated using the energy balance equation [2,53–55]:

h2 þ

c32 ¼ h3 2

ð19Þ

where h3 is diffuser outlet mixed gas specific enthalpy. By introducing isentropic efficiency of a diffuser we obtain [2,53–55]:

Fig. 11. Thermodynamic transformation of the SEPS [2].

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D. Strušnik et al. / Energy Conversion and Management 126 (2016) 228–246

h30  h2 ¼ gd  ðh3  h2 Þ

ð20Þ

where h30 is isentropic specific enthalpy of diffuser outlet mixed gas and gd is diffuser isentropic efficiency. Gas pumped mass flow qm4 is calculated using a derived equation where thermodynamic properties of the mixed gas are taken into consideration, Mach number in the mixing section and geometrical properties of the diffuser. The Mach number in the mixing section is calculated [2,53,54]:

c2 M 2 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ,mix2  Rmix2  T mix2

h

qm0  c1

p2  ,mix2 

M 22

i

ð22Þ

þ 1  p4

1  ,mix2 p3 ,mix2 g  M22  ½,mix2  1 ¼1  d 2 p2

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n h ioffi 2 1 B2  4  h4 qm20  h0  C  ,,mix21  A2  p2  1 þ ,mix2  M 2 2

ð23Þ

qm0  c1 p  p2 þ 4 p2  A2  ,mix2 p2  ,mix2

ð24Þ

By inserting Eq. (23) into Eq. (21) we obtain [2]: 1  ,mix2   p3 ,mix2 g  ð,mix2  1Þ qm0  c1 þ p4  A2  d  1 1¼0 2  ,mix2 p2 p2  A2

ð27Þ Part B in Eq. (27) is calculated [2]:

B ¼ qm0  ðh0 þ h4 Þ

If p3 is known, Eq. (24) is solved, and p2 is obtained and then M2 is calculated from Eq. (23). It is necessary to determine c2, T2 and qm4. Taking into account Eq. (16), the energy Eq. (18) can be written as follows [2]:

qmnonout ¼ qm4  0:75

The FLC calculation unit is intended to control, by means of input signals, i.e. temperatures of the pumped gas through extraction tubes or connection points 1, 2 and 3, the open positions of control valves. Any extraction tube or connection point has its own control valve, Fig. 9. FLC calculation unit has 3 input signals, 3 output signals and comprises 8 correction rules, specifying the

F-Cl Cl

1

Op F-Op

Ok

Valve 1 Position 0.5

0 20

30

40

50

T1 Connecting 2 1 Low Sucked Gas Temperature

High

Ok

0.5

0 20

30

40

T2 Ok

Connecting 3 1 Low Sucked Gas Temperature

50

High

1.If is T1 (Low) and T2 is (Ok) and T3 is (Ok) then is V1 (F-Op),V2 is (Cl) and V3 is (Cl) 2.If is T1 (High) and T2 is (Ok) iand T3 is (Ok) then is V1 (F-Cl), V2 is (Op) and V3 is (Op) 3.If is T1 (Ok) and T2 is (Low) and T3 is (Ok) then is V1 (Cl), V2 is (F-Op) and V3 is (Cl) 4.If is T1 (Ok) and T2 is (High) and T3 is (Ok) then is V1 (Op), V2 is (F-Cl) and V3 is (Op) 5.If is T1 (Ok) and T2 is (Ok) and T3 is (Low) then is V1 (Cl), V2 is (Cl) and V3 is (F-Op) 6.If is T1 (Ok) and T2 is (Ok) and T3 is (High) then is V1 (Op), V2 is (Op) and V3 is (F-Cl) 7.If is T1 (Low) and T2 is (Low) and T3 is (High) then is V1 (F-Op), V2 is (F-Op) and V3 is (F-Cl) 8.If is T1 (High) and T2 is (High) and T3 is (Low) then is V1 (F-Cl) and V2 is (F-Cl) and V3 is (F-Op)

Rules

0.5

0 0

20

40

60

80

100

V1 1

F-Cl Cl

Op F-Op

Ok

Valve 2 Position

0.5

0 0

1

20

F-Cl Cl

40

60

V2 Ok

80

100

Op F-Op Valve 3 Position

0.5

0

0 10

ð30Þ

where qmnon-out is mass flow of the pumped non-condensable gas from the STC.

High

Ok

ð29Þ

The pumped gas mass (qm4) is a two-phase mixture comprising condensable steam and non-condensable gas. The analyses of the existing SEPS [1] showed that the ratio of the pumped two-phase mixture is 1:4 on average. The mass flow of the non-condensable gas is calculated using the equation [2]:

0.5

10

ð28Þ

3.3. Auxiliary simulation model: FLC calculation unit

ð25Þ

10

mix2

2  h4

C ¼ qm0  c1 þ p4  A2  p2  A2

where p3 is pressure of exhaust ejector mixed gas. If the inlet diffuser cross-section area A2 is known, it is possible to express M2 as a function of p2 from Eq. (22) to obtain [2]:

Low Connecting 1 1 Sucked Gas Temperature

qm4 ¼

B 

Part C in Eq. (27) is calculated [2]:

Eqs. (19)–(21) are used to obtain the equation [2]:

M 22 ¼

From Eq. (26) we express c2 and insert it into Eq. (17) to obtain a quadratic equation for the calculation of the mass flow rate of pumped gas from STC, whose solution is [2]:

ð21Þ

where M2 is Mach number in the mixing section, ,mix2 is specific heat ratio of the gas mixture in the mixing section, Rmix2 is gas constant of the gas mixture in the mixing section and Tmix2 is diffuser inlet mixed gas temperature. Using Eqs. (16), (17) and (21) the necessary diameter A2 is expressed and calculated [2,53]:

A2 ¼

 p2 ,mix2  R  Tmix2 c22 þ Rmix2  T mix2 ,mix2  1 2  ,mix2 ,mix2 2 ð26Þ þ  M2 ¼ A2  c2  p2 ,mix2  1 2

qm0  h0 þ qm4  h4 ¼ A2  c2 

20

30

40

50

0

T3

20

40

60

V3 Fig. 12. Architecture of FLC calculation unit valve positions of extraction tubes.

80

100

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D. Strušnik et al. / Energy Conversion and Management 126 (2016) 228–246

correlation of input-output signals. The FLC calculation unit architecture is shown in Fig. 12. The input signals are marked Low, Ok and High and designate the temperature of the pumped gases. The output signal designations are: F-Cl fast closure, Cl closure, Ok, Op opening and F-Op fast opening. 3.4. Auxiliary simulation model: pumped out gas calculator The auxiliary model of the pumped out gas calculator computes mean temperatures of pumped out gases and the required amount of pumped out gases. The FLC calculation unit computes the mean value of the pumped out gases using the equation:

T mean ¼

Pn i¼1 T pi  V i Pn i¼1 V i

ð31Þ

where Tmean is mean temperature of the pumped out gases, Tp1 is temperature of the pumped out gas of the tube and Vi is the position of the valve of the tube. Using the results of the mean temperatures of the pumped out gases and the equation, generated with the Matlab Curve Fitting tool, the auxiliary model computes the share of the NCG in the pumped out mixture. The equation for the calculation of the share of NCG is made on the basis of the analyses of the pumped out gas of the existing system and by means of the Sum of Sine model of stage 2:

mNCG ¼ 99:44  sinð0:01493  T mean þ 22:67Þ

and pressure of steam admitted to the turbine) and two set of output data (motive steam temperature and pressure). Each piece of input data of the ANN has a precisely defined output data item. The neuron weights are defined in the ANN design so that the final sum of the results of all neurons provides a result with the minimum possible errors between the input output data. Several learning algorithms are available to obtain the relationships between the inputs and the outputs. The most widely used algorithm is the feed-forward back-propagation learning Levenberg-Marquardt algorithm [60,61]. Furthermore, these equations were used by some earlier researchers [62–66]. The mean square error (MSE) is defined as

MSE ¼

n 1X ðtj  oj Þ2 n j¼1

and the root mean square error (RMSE) is defined as follows

"

n X RMSE ¼ ð1=nÞ ½t j  oj 2

4. Validation of simulation model The simulation model validation is carried out by testing different ANN architectures and verifying the pressure dynamics in the STC, provided by the simulation model and real process results. The ANNs architectures are designed by testing the model with the best correspondence between the ANNs results and the real process data [28]. The real process data of the 2013/2014 heating season in a matrix form [5  4793] was used in the ANN design [28]. Three sets of input data were used (mass flow, temperature

ð34Þ

In addition, the correlation coefficient (R2), mean absolute error (MAE) and mean absolute percentage error (MAPE) are respectively defined as

"Pn

ð32Þ

where mNCG is the share of NCG in the pumped out mixture. The results of Eq. (32) are shown in Fig. 13. The analysis of the measurements of the existing system shows that in order to maintain the pressure of 0.01 MPa and temperature of 312 K in the STC, it is necessary to pump from the STC 0.043 kg/s of NCG. The auxiliary simulation model computes the required amount of the pumped out gases as a function of the temperature of the pumped out gases according to the diagram shown in Fig. 13. Some other authors also analysed the conditions in the ejector by means of modelling [56–59].

#1=2

j¼1

R2 ¼ 1 

þ 0:823  sinð0:3484  T mean  55:99Þ

ð33Þ

MAE ¼

2 j¼1 ðt j  oj Þ Pn 2 j¼1 ðoj Þ

# ð35Þ

n 1X jtj  oj j n j¼1

ð36Þ

where t is the target value, o is the output value, and n is the number of learning data sets. Input and output layers are normalized in the (1, 1) or (0, 1) range. In addition, the correlation coefficient ranges between 0 and 1. A very good fit yields an R2 value of 1, whereas a poor fit results in a value near 0 [11]. The ANNs testing results of different architectures feed-forward back-propagation learning Levenberg-Marquardt algorithms are indicated in Table 4. Table 4 shows that the winning nonlinear ANN structure used in the nonlinear ANN unit has the 35-5 architecture (in bold), as this architecture has the lowest errors. The architecture of the winning ANN structure was presented in detail in chapter 3 and shown in Fig. 10. The process of design and regression of the winning nonlinear ANN structure, used in the nonlinear ANN unit, is shown in Fig. 14. It is evident from Fig. 14 that the creation of the nonlinear ANN structure, used in the nonlinear ANN unit, was carried out in 700 epochs. The best validation performance in terms of MSE is

Proportion Of NCG In The Sucked Out Gas (%)

95 90 85 80

75 70 285

290

295

300

305

310

Mean Temperature Of The Sucked Out Gas K Fig. 13. Results of Eq. (32).

315

320

325

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D. Strušnik et al. / Energy Conversion and Management 126 (2016) 228–246

Table 4 The ANNs testing results of learning with the Levenberg-Marquardt algorithm. Hidden neurons

Hidden layers

Epochs

Data set size

MSE

RMSE

R2

MAE

10-8-5 60-10 35-5 10-5 9-3 120 80 40

3 2 2 2 2 1 1 1

700 700 700 700 700 700 700 700

4793 4793 4793 4793 4793 4793 4793 4793

43.7962 50.1995 41.0635 45.7717 55.2172 52.2107 52.5508 45.6821

6.6178 7.0852 6.4081 6.7655 7.4308 7.2257 7.2492 6.7588

0.9999 0.9999 0.9999 0.9999 0.9999 0.9998 0.9998 0.9999

3.0765 3.2408 2.8508 3.1879 3.6369 2.8141 2.7487 3.0329

Validation: R 2=0.99992

10

10

10

1.8

600

Y= T Fit Data

500 400 300 200 100

200 400 Target

1.7

600

Output ~= 1*Target + 0.18

Train Validation Test Best

Training: R =0.99998

600

1.6

1.5

0

50

100

150

600

400 300 200 100

200 400 Target

400 300 200 100

200 400 Target

700 Epochs

600

2

Y= T Fit Data

500

Y= T Fit Data

500

2

Test: R =0.99995

Output ~= 1*Target + 0.14

Mean Squared Error (MSE)

10

1.9

Output ~= 1*Target + 0.16

10

Output ~= 1*Target + 0.13

2

Best Validation Performance is 41.063 at epoch 54

All: R =0.99995 600

Y= T Fit Data

500 400 300 200 100

600

200 400 Target

600

Temperature (K)

Fig. 14. End regression design procedure of the winning ANN nonlinear structure, using the auxiliary simulation model of the nonlinear ANN unit.

640 620 600 580 Real Proces Motive Steam Temperature ANN Results Motive Steam Temperature

560

Pressure (MPa)

540 0.93 0.92 0.91 0.9

Real Proces Motive Steam Pressure ANN Results Motive Steam Pressure

0.89 0

500

1000

1500

2500

2000

3000

3500

4000

4500

5000

Time (minutes) Fig. 15. Comparison of results of the nonlinear ANN structure, employed in the auxiliary simulation model of the nonlinear ANN unit and the real process.

41.063 at epoch 54. Regression R2 is 0.99995. Fig. 15 shows a comparison of the results provided by the winning nonlinear ANN structure, employed in the nonlinear ANN unit and the real process results. Moreover, the pressure dynamics in the real process STC was verified, top diagram in Fig. 16, and the pressure dynamics in the STC, provided by the simulation model, bottom diagram Fig. 16.

The mean values of the analysed period show that between the real process data and the results provided by both simulations models the differences of the pressure in the STC are minimal. The mean value of the pressure of the analysed period in the real process STC amounts to 9.321  103 MPa and the mean value of pressure in the STC, provided by the simulation model to 9.291  103 MPa. The pressure difference is 3  105 MPa, which

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D. Strušnik et al. / Energy Conversion and Management 126 (2016) 228–246

Pressure (MPa)

0.014

Real Proces Pressure In The STC, Mean Value 0.009321 MPa

0.012 0.01 0.008

Pressure (MPa)

0.014 Simulation Model Results Pressure In The STC, Mean Value 0.009291 MPa 0.012 0.01 0.008 500

1000

1500

2000

2500

3000

Time (minutes)

Temperature (K)

Fig. 16. Verification of pressure dynamics in the STC.

308

Pipe 1

Pipe 2

Valve 1

Valve 2

Pipe 3

305 302 299

Valve Position (%)

296 90

Valve 3

80 70 60 50 40 30 20

0

500

1000

1500

2000

2500

3000

Time (seconds) Fig. 17. Temperatures and positions of control valves on extraction tubes.

is negligible. The above facts confirm the quality of the simulation model. 5. Simulation model results The results of the simulation model show the control of the pumped amount of gases from the STC with the intention of pumping a larger amount of NCG and consequently, streamlining the SEPS operation. The pumping of a larger amount of NCG is ensured through the control of the pumped out amount of gas through the tubes. The amount of the pumped out gases through the tubes is controlled so that the amount of the pumped out gases is increased in the tube with a lower temperature of the pumped out gases and decreased in the tube with a higher temperature of the pumped out gases. The concentration of NCG is the highest on colder surfaces, as indicated in chapter 2.3. By installing additional connection points and controlling the amount of the pumped out gases through the tubes, additional cold points are obtained where the concentration of NCG is the highest due to low temperatures. These sites are ideal for NCG pumping. The simulation model input data includes simulated temperatures of pumped out gases through the extraction tubes in the 296.5 K to 308 K range. Fig. 17 shows the model input data and the control valve positions on the extraction tubes. The positions of valves in Fig. 17 are the results of the auxiliary simulation model of the FLC calculation unit, computed as a function of the temperature of the evacuated gases. By means of the

temperatures and the positions of the control valves on extraction tube, the above auxiliary simulation model also computes the mean temperature of the removed gases from the STC and the required extraction amount. The simulation model results are shown in Fig. 18. Point 1 in Figs. 18, 19, 21 and 22 represents the pumping conditions of the existing SEPS in a thermal power plant in Slovenia and point 2 the pumping conditions, where the extracted quantity is controlled in the extraction tubes. It is evident from Fig. 18 that the minimal required quantity of extracted gases from the STC is 0.0445 kg/s at the mean temperature of extracted gases amounting to 299 K. The above temperature of extracted gases may be achieved by controlling the gas extraction rate through the extraction tubes. By means of the results of the required quantity of extracted gases and the results of the actual quantity of extracted gases the simulation model corrects the dimension of the Laval nozzle in the Laval cross-section until the required quantity and the actual quantity of the extracted gases are equal. The simulation model computes the actual quantity of the extracted gases as a function the quality of water vapour used for the operation of the SEPS, and the dimension of the Laval nozzle in the Laval cross-section. The results of the dimensions of the nozzle in the Laval cross-section of the primary and secondary ejector stage in various water vapour qualities used for the operation of the SEPS, are shown in Fig. 19. The required dimensions of the Laval nozzle in the Laval crosssections are reduced depending on the required and actual extraction quantity and vice versa. The quality of water vapour used for

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D. Strušnik et al. / Energy Conversion and Management 126 (2016) 228–246 308

Temperature (K)

Pumped Gas Out Total Temperature

305 302 299

Mass Flow (kg/s)

296 0.06 Pumped Gas Out Request Quantity

0.055 1

0.05 2

0.045 0.04

0

500

1000

1500

2000

2500

3000

Time (seconds) Fig. 18. Overall temperature and required amount of gas extraction.

Secondary Ejector Laval Diameter (metre)

Primary Ejector Laval Diameter (metre)

-3

11

x 10

Motive Steam 0.9 MPa 553 K Motive Steam 1.1 MPa 593 K Motive Steam 1.3 MPa 613 K Motive Steam 1.5 MPa 643 K

10 1 9

2

8 7 Motive Steam 0.9 MPa 553 K Motive Steam 1.1 MPa 593 K Motive Steam 1.3 MPa 613 K Motive Steam 1.5 MPa 643 K

0.013 0.012 1 2

0.011 0.01 0.009 0

500

1000

1500

2000

2500

3000

Time (seconds) Fig. 19. Results of the model of the Laval cross-sections of the Laval nozzle of the primary and secondary ejector stages in various water vapour qualities.

the operation of the SEPS also has a large impact on the dimension of the Laval nozzle in the Laval cross-section. In the case of water vapour of better quality, a smaller Laval cross-section of the Laval nozzle is needed and vice versa. Fig. 20 shows the amounts of extracted gases in cases of motive steam of different qualities for the primary and secondary ejector stage. In Fig. 20, the blue curve shows the total amount of extracted gases pumped by the secondary ejector stage and the red1 curve, however, the total amount of extracted gases pumped by the primary ejector stage, whereas the green curve shows the amount of NCG fed into the secondary ejector stage 2 and the violet curve the amount of CG fed into the secondary ejector stage. Fig. 21 shows the results of the SEPS motive steam consumption model and the power that would be obtained in the case of expansion of the above indicated amount of water vapour in the steam turbine. The generated power in the case of SEPS motive steam expansion in the turbine is calculated [67]:

qP gen ¼

d X qmi  Dhi ;

ð37Þ

id ¼1

where qPgen is generated power in the case of SEPS motive steam expansion in the turbine, id is the iteration of individual component of the turbine, d is the number of individual components of the tur1 For interpretation of color in ‘Fig. 20’, the reader is referred to the web version of this article.

bine, qmi is the mass flow of working fluid cross individual turbine component and D hi is the difference of specific enthalpy of the working fluid of individual component. It is evident from the results in Fig. 21 that the SEPS motive steam consumption is the highest at the poorest steam quality due to the fact that in this case the nozzle dimension in the Laval cross-section is the largest. The SEPS motive steam consumption is the lowest when the steam quality is the best, due to the fact that in this case the dimension of the nozzle in the Laval crosssection is the smallest. Moreover, the results were analysed of the simulation model of the generated power in the case of expansion of the amount of steam used for the operation of the SEPS from the quality of steam entering the steam turbine (9.2 MPa and 793 K) to the quality of steam used for the operation of the SEPS. Fig. 22 shows the results of the simulation model. Fig. 22 shows that additional steam turbine power produced in the case of expansion of the amount of steam used for the operation of the SEPS is the largest in the expansion of water vapour in the steam turbine up to the quality of 0.9 MPa and 553 K and the lowest in expansion of water vapour in the steam turbine up to the quality of 1.5 MPa and 643 K. The results of the model of average values of the generated steam turbine power from Figs. 21 and 22 are shown in Table 5, where Power-1 is the average value of power generated by the steam turbine during the expansion of the water vapour quantity used for the operation of the SEPS, from the

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D. Strušnik et al. / Energy Conversion and Management 126 (2016) 228–246 0.06

0.06

Motive Steam Quality 0.9 MPa 553 K

0.04 0.03

Secondary Ejector Total Gas Sucked Out Primary Ejector Total Gas Sucked Out NCG Sucked Into The Secondary Ejector CG Sucked Into The Secondary Ejector

0.02

0.04

0.02 0.01

0 0.06

0 0.06

Motive Steam Quantity 1.3 MPa 613 K

Secondary Ejector Total Gas Sucked Out Primary Ejector Total Gas Sucked Out NCG Sucked Into The Secondary Ejector CG Sucked Into The Secondary Ejector

0.03

0.01

Motive Steam Quality 1.5 MPa 643 K

0.05

Mass Flow (kg/s)

0.05

Mass Flow (kg/s)

Motive Steam Quality 1.1 MPa 593 K

0.05

Mass Flow (kg/s)

Mass Flow (kg/s)

0.05

0.04 Secondary Ejector Total Gas Sucked Out

0.03

Primary Ejector Total Gas Sucked Out

0.02

NCG Sucked Into The Secondary Ejector

0.04 0.03

Secondary Ejector Total Gas Sucked Out Primary Ejector Total Gas Sucked Out NCG Sucked Into The Secondary Ejector CG Sucked Into The Secondary Ejector

0.02

CG Sucked Into The Secondary Ejector

0.01 0

0.01

0

500

1000

1500

2000

2500

0

3000

0

500

1000

Time (seconds)

1500

2000

2500

3000

Time (seconds)

Steam Turbine Power (kW) Mass Flow (kg/s)

Fig. 20. Amounts of extracted gases in cases of motive steam of different qualities for the ejector primary and secondary stage.

Motive Steam Consumption 0.9 MPa 553 K Motive Steam Consumption 1.1 MPa 593 K Motive Steam Consumption 1.3 MPa 613 K Motive Steam Consumption 1.5 MPa 643 K

0.26 0.24

1

0.22 2

0.2 0.18 280 260

Motive Steam Quality 0.9 MPa 553 K Motive Steam Quality 1.1 MPa 593 K Motive Steam Quality 1.3 MPa 613 K Motive Steam Quality 1.5 MPa 643 K

1

240 220 2

200 180 500

1000

1500

2000

2500

3000

Time (seconds) Fig. 21. Results of the SEPS motive steam consumption model and generated power in the case of expansion of the indicated amount of steam in the steam turbine.

Table 5 Results of the model of average values of the generated power of the steam turbine in Figs. 21 and 22.

Fig. 22. Results of the model of the generated power of steam turbine in the case of expansion of the amount of steam to the quality of steam used for the operation of the SEPS.

water vapour quality entering the steam turbine to the quality of the outlet steam from the steam turbine and Power-2 is the average value of power generated by the steam turbine during the expansion of the amount of water vapour used for the operation

Pressure (MPa)

Temperature (K)

Consume (kg/s)

Power-1 (kW)

Power-2 (kW)

Difference (kW)

0.9 1.1 1.3 1.5

553 593 613 643

0.2240 0.2045 0.1918 0.1845

234.80 214.31 200.97 193.31

87.344 65.28 54.93 42.06

147.46 149.03 146.04 151.25

of the SEPS, from the quality of steam entering the steam turbine to the quality of steam used for the operation of the SEPS. The results of the simulation model of average values show that in the case of expansion of the average amount of steam of 0.224 kg/s, used for the operation of the SEPS of the quality of 0.9 MPa and 553 K, the steam turbine would additionally generate 234.8 kW of power. In the case of expansion of the above amount of water vapour in the steam turbine only up to the quality of steam used for the operation of the SEPS, the steam turbine would

D. Strušnik et al. / Energy Conversion and Management 126 (2016) 228–246 650 0.9

Motive Steam Temperature

Steam Pressure In The Laval Diameter 600

0.8

Pressure (MPa)

Pressure (MPa) Temperature (K)

244

550 Motive Steam Pressure 1.4 1.2

0.6 0.5

1 0.4 Steam Density In The Laval Diametre

1300

3.6

1200

3.4 3.2

Speed (m/s)

Density (kg/m3)

0.7

3 2.8 2.6

1100 1000

800

2.4

700

2.2

600

2

500 0

50

100

150

200

250

300

Steam Velocity From The Primary Ejector Nozzle Steam Velocity From The Secondary Ejector Nozzle Steam Velocity In The Laval Diameter

900

0

50

100

150

200

250

300

Time (seconds)

Time (seconds)

Fig. 23. Conditions of steam that expands in the Laval nozzle.

additionally generate 87.34 kW. The difference in power amounts to 147.46 kW. In the case of expansion of the average amount of steam of 0.1845 kg/s, used for the operation of the SEPS of the quality of 1.5 MPa and 643 K, the steam turbine would additionally generate 193.31 kW of power. In the case of expansion of the above amount of steam in the steam turbine only up to the quality of steam used for the operation of the SEPS, the steam turbine would additionally generate 42.06 kW of power. The difference in power amounts to 151.25 kW. By changing the quality of steam used for the operation of the SEPS the condition of the steam expanded in the Laval nozzle also changes. Fig. 23 shows the condition of steam expanded in the Laval nozzle at the Laval cross-section of 0.0074 m of the primary stage, at the Laval cross-section of 0,009 m of the ejector secondary stage and sinusoidal oscillation of quality of steam used for the operation of the SEPS. The results of the model show that as regards the selection of an appropriate nozzle and quality of steam for the operation of the SEPS there are no substantial differences in terms of the improved performance. An essential difference as regards the performance is expressed so that for the operation of the SEPS, the steam is used that has previously lost part of its internal energy or has expanded in the steam turbine up to the quality of steam envisaged to be used for the operation of the SEPS. Therefore, the Laval nozzles are selected of the Laval cross-section, corresponding to the available steam quality and the required extracted amount. The efficiency of the operation of the SEPS is also ensured through the extraction of as cold as possible gases, as NCG is larger in such gases and thereby the total required extraction is lowered. The measurements and analyses of the SEPS show that when the quality of the motive steam for the operation of the SEPS is 0.9 MPa, 553 K and the pressure in the STC is 10,000 Pa, the average amount of gases extracted from the STC amounts to 0.057 kg/s, containing 75% of NCG and 25% of CG. As a result, 0.043 kg/s of NCG is extracted on average from the STC and 0.014 of CG. The results under points 1 and 2 in Fig. 18 also provide similar quantities of extracted gases. Point 1 represents the extracted amount of steam of the existing system in a district heating installation in Slovenia and point 2, however, the extracted amount of

steam by controlling the amount of extracted gases through the tubes. By using additional connection points and controlling the extracted amount of gases through extraction tubes, almost only NCG is extracted from the STC. The results of the simulation model show that in this case, the SEPS can operate with two Laval nozzles of a smaller geometrical cross-section. In the primary ejector stage, the Laval nozzle may be reduced from the initial Laval crosssection of 0.01 m to 0.0094 m and in the secondary ejector stage, from 0.013 m of the Laval cross-section to 0.0117 m, points 1 and 2 in Fig. 19. As a result of smaller dimensions of the Laval nozzles, the consumption of the SEPS motive steam is reduced. The average consumption of steam for the operation of the existing SEPS is 0.264 kg/s and the average consumption of steam for the operation of the SEPS with the control of the extracted amount of steam through the extraction tubes is 0.212 kg/s, points 1 and 2 in Fig. 21. Therefore, the average savings regarding the steam consumption amount to 0.052 kg/s. The above indicated amount of steam can be used for other purposes. If the amount of steam saved expands in the steam turbine, the turbine would additionally generate 53 kW of power. If the additionally generated power is multiplied by the steam turbine operating hours, i.e. 7200 h/year, the additionally generated electricity amounts to 381600 kWh.

6. Conclusion This paper presents a simulation model that streamlines the operation of the SEPS, serving to extract the NCG from the STC. The operation of the SEPS is streamlined by adequately dimensioning the Laval cross-section of two Laval nozzles in the primary and secondary ejector stage. The SEPS consumes less motive steam if the dimensions of the Laval nozzles are properly selected. The streamlining of the SEPS is based on a well thought-out selection of the quality of the steam used by the SEPS for its operation, a well thought-out selection of points of connection through which the NCG are pumped out of the STC and by controlling the amount of pumped out gases through the points of connection or extraction tubes. A well thought-out selection of the motive steam for the operation of the SEPS is based on the fact that the steam has

D. Strušnik et al. / Energy Conversion and Management 126 (2016) 228–246

previously expanded in the steam turbine to the quality of steam needed for the operation of the SEPS. The well though-out selection of the connecting locations is based on the analysis of the impact of NCG on the transfer of STC heat and the temperature analysis of the STC in the existing system of the district heating plant in Slovenia. The control of the amount of gases extracted through the extraction tubes facilitates the pumping of almost only NCG from the STC, thus reducing the total amount that has to be pumped out from the SEPS in order to maintain the required pressure in the STC. By carrying out the above measures and choosing the appropriate dimension of the Laval cross-section of the Laval nozzle the consumption of the motive steam for the operation of the SEPS is reduced and the efficiency of the operation of the SEPS improved.

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