Wyniki wyszukiwania - BazTech

1

The effects of variable operational parameters on an aero engine labyrinth seals performance

Szymański A., Dykas S., Majkut M., Strozik M.

Transactions of the Institute of Fluid-Flow Machinery

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2018

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nr 140

83--104

EN

The paper presents the accurate assessment of the amount of gas flowing through three types of aero-engine expander sealing. Structures consisting of straight-through labyrinth seals – with one, two and three fins are considered. The study deploys two independent approaches. The first one focuses on the experimental research using high-precision test section with non-rotating labyrinth seals specimen connected to a high capacity vacuum installation. Experimentally tested seals are of actual size (model to engine scale is 1:1). High accuracy hot-wire anemometry probes, and orifice plate are deployed to evaluate the flow indicators accurately, allowing for comparison of different sealing structures. The second approach uses quasi-two-dimensional axissymmetric, steady-state Reynolds averaged Navier Stokes (RANS) computations to simulate the flow field. Various meshes and turbulence models were tested, presenting capabilities as well as limitations of specific computational approaches. The experimental and computational results were compared with literature data, showing a good agreement regarding overall trends, yet underlining some local discrepancies. This paper brings two significant findings. The 2D RANS methods tend to overestimate the leakage when compared with experimental results, and the difference is more significant for advanced arrangements. There is a notable difference between the performance of labyrinth seal with one fin and structure with two and three fins. In some operational areas, one-finned seal performs better than more advanced ones, reducing the leakage more effectively. This feature of one finned seal is not intuitive, as one would expect it to perform worse than a seal with two or three fins.

2

Numerical and experimental investigation of the fan with cycloidal rotor

Dykas S., Majkut M., Smołka K., Strozik M., Chmielniak T., Staśko T.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 2

447--454

EN

In this paper, the investigation of the cycloidal rotor fan (CRF) was presented. A CRF with four blades of the NACA0012 profile was used for the analysis. The CFD calculations were carried out by means of Ansys CFX commercial software. The experimental tests were done using velocity field measurement with the LDA technique. Numerical results were compared with experimental measurement in terms of velocity values. The CRF performance characteristic was prepared on the basis of experimental and numerical results.

3

Assessment of the capability of available methods of flow field numerical modelling on the example of air flow through a channel with a circular bump

Dykas S., Majkut M., Smołka K., Strozik M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2017

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Vol. 21, No 3

185--294

EN

This paper is an attempt at a systematic approach to the flow field analysis in the case of air flowing through a straight channel with a circular bump. The results of the authors’ own experimental measurements are compared to those obtained by means of both an in-house and a commercial CFD code. Apart from the RANS method, which is commonly used in engineering applications, a decision was made to use the URANS and LES methods, which are available both in the in-house academic code and in the commercial program. The comparison between the calculation results is performed using what is referred to as the numerical Schlieren image, which for the RANS calculations is compared to the Schlieren image obtained from experimental testing.

4

The performance of a steam-gas power unit of a velox-type cycle

Smołka K., Dykas S.

Journal of Power Technologies

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2017

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Vol. 97, nr 5

343--348

EN

For many years, the Institute of Power Engineering and Turbomachinery of the Silesian University of Technology has been using a Velox-type small-capacity gas-steam power unit for teaching and research purposes. The Velox-type gas-steam cycle is characterized by a much higher ratio of power obtained from the steam turbine and the gas turbine, respectively, compared to classical gas-steam cycles which are now in use worldwide. This paper presents a thermodynamic analysis of the Veloxtype gas-steam cycle as a small capacity combined heat and power plant (CHP). The systems are modelled in the EBSILO Nr Professional. The advantages and drawbacks of the Velox-type cycle compared to the classical one are presented.

5

The assessment of the calculation method for determining characteristics of one straight ﬁn labyrinth sea

Szymański A., Dykas S., Majkut M., Strozik M.

Transactions of the Institute of Fluid-Flow Machinery

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2016

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nr 134

89--107

EN

The method for the selection of a calculation scheme for the evaluation of the ﬂow behaviour of labyrinth seal with one straight ﬁn, against smooth wall, was presented. Experimental results were obtained from measurement data carried out on the in house, vacuum test section. The advantage of the test rig is a circular shape of the labyrinth specimen, providing similar shape to conﬁguration operated in practise. In computational ﬂuid dynamics study diﬀerent types of mesh resolution were tested, with variable volume discretization in the area of a labyrinth ﬁn tip. Moreover, a wide range of turbulence models basing on k-ε and k-ω, exploiting the (Reynolds Average Navier Stokes) scheme, for the ﬂow pattern evaluation, were examined. All obtained results were compared with literature data, covering research conducted on similar conﬁgurations. The presented study shows challenges as well as the possibilities of calculation simpliﬁcation and compares results obtained by means of simulations and experiment. The proposed method is characterised by excellent agreement of computational results with experiment data.

6

Condensation wave identification in moist air transonic flows through nozzles

Dykas S., Smołka K., Majkut M., Strozik M.

Transactions of the Institute of Fluid-Flow Machinery

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2016

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nr 131

67--77

EN

This paper identifies the location of water vapour spontaneous condensation during air expansion in convergent-divergent nozzles. The comprehensive analysis proposed herein includes an analytical solution together with experimental and numerical investigations. Numerical calculations are performed using an in-house computational fluid dynamics code based on the solution of Reynolds averaged Navier-Stokes equations supplemented with additional partial differential equations modelling the condensation process of water vapour contained in atmospheric air. Experiments were carried out using an in-house facility adapted for measurements of atmospheric air transonic flows.

7

Ocena niestacjonarnego pola przepływowego w uszczelnieniu labiryntowym przy użyciu metod numerycznej mechaniki płynów

Szymański A., Dykas S.

Modelowanie Inżynierskie

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2016

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T. 28, nr 59

76--85

PL

W artykule przedstawiono analizę numeryczną niestacjonarnego pola przepływowego w modelu turbinowego uszczelnienia labiryntowego w rzeczywistych warunkach pracy dla dwóch różnych struktur uszczelnienia labiryntowego z okładziną o strukturze plastra miodu oraz ze ścianą gładką. Oprócz strat przecieku, obszar ten jest szczególnie istotny z uwagi na zjawisko generacji hałasu szerokopasmowego powstałego w wyniku turbulentnych zjawisk przepływowych. Wyniki przedstawiono jako wielkości akustyczne w funkcji częstotliwości. Pozwoliło to na określenie częstotliwości głównych, przy których zaistniały ich szczytowe wartości. Dodatkowo porównano zmianę bezwymiarowej wartości przecieku w czasie. Wyniki obliczeń wskazały wpływ zastosowanej struktury uszczelnienia na tłumienie fluktuacji ciśnienia oraz wartości przecieku przy różnych prędkościach obrotowych wirnika.

EN

This work aims to perform detailed time-dependent flow analysis of gas turbine stage model equipped with tip labyrinth seal against honeycomb or smooth land, in order to identify the noise generated aerodynamically. Two different sealing structures were investigated – honeycomb structure and smooth land. The main scopes of this investigation were evaluation of unsteady flow field behaviour, indication regions were the vorticity and broadband noise is generated. Also an impact of the sealing structure on the flow behind the rotor was checked. To evaluate results, acoustic pressure – p’ and Sound Pressure Level (SPL) values were used. Discharge coefficient, as a measure of non-dimensional leakage has also been inquired and compared. The results shown an influence of honeycomb structure, and rotational velocity of rotor on pressure fluctuations and noise damping.

8

Efekt odparowania fazy ciekłej na fali uderzeniowej w przepływach okołodźwiękowych powietrza wilgotnego z kondensacją pary wodnej

Szymański A., Dykas S., Majkut M.

Modelowanie Inżynierskie

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2015

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T. 26, nr 57

54--62

PL

W pracy przeprowadzono analizę numeryczną przepływu transonicznego powietrza atmosferycznego, które ze swojej natury zawsze zawiera pewną ilość pary wodnej, w dyszach de Lavala. Do obliczeń wybrano dyszę de Lavala o dużej prędkości ekspansji i połówkową dyszę zbieżno-rozbieżną o znacznie mniejszej prędkości ekspansji. Obliczenia przeprowadzono za pomocą własnego kodu CFD, w którym zamodelowano powstawanie fazy ciekłej w wyniku kondesacji spontanicznej pary wodnej zawartej w powietrzu wilgotnym. W obliczeniach przepływu okołodźwiękowego uwzględniono również obecność prostopadłej fali uderzeniowej w części naddźwiękowej dyszy w celu analizy efektu odparowani fazy ciekłej.

EN

This paper presents a numerical analysis of the atmospheric air transonic flow through de Laval nozzles. By nature, atmospheric air always contains a certain amount of water vapour. The calculations were made using a Laval nozzle with a high expansion rate and a convergent-divergent (CD) “half-nozzle”, referred to as a transonic diffuser, with a much slower expansion rate. The calculations were performed using an in-house CFD code. The computational model made it possible to simulate the formation of the liquid phase due to spontaneous condensation of water vapour contained in moist air. The transonic flow calculations also take account of the presence of a normal shock wave in the nozzle supersonic part to analyse the effect of the liquid phase evaporation.

9

Economic evaluation of A-USC power plant with CO2 capture unit

Stępczyńska-Drygas K., Dykas S., Łukowicz H., Czaja D.

Journal of Power Technologies

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2015

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Vol. 95, spec.

75--83

EN

Achieving CO2 emission control while keeping electricity prices competitive is one of the most important economic and technical challenges. The strategy for lowering the CO2 emission from the coal-based power plants includes first of all raising electricity generation efficiency. Currently, steam temperatures in ultra-supercritical (USC) power plants are limited to approximately 627ºC by the use of the most advanced commercially available ferritic steels. To go to higher temperatures, high-nickel alloys must be used. The nickel alloys are at an advanced stage of development and are expected to be available to support construction of a demonstration plant in Europe in 2021. For pulverized coal (PC) plants the development means progressing to advanced ultra-supercritical (A-USC) steam conditions - 35MPa/700/720ºC. It turned out that the concept consists in gradually raising the live steam temperature and pressure can become economically unjustified. Cost-effectiveness of new investments can be provided only by a significant increase in the efficiency of electricity generation. In the paper the economic evaluation of 900 MW PC unit is presented. The main aim is to compare the cost of electricity generation in USC (28MPa/600/620ºC) and A-USC (35MPa/700/720ºC) power unit. The variants with CO2 capture installation by chemical absorption MEA are considered. Compared to a USC design, the capital cost of the A-USC PC plant will be higher, but the operating cost will be lower. Because of the higher efficiency of the A-USC plant, the differential in operating cost increases as fuel price increases and CO2 cost charges are included.

10

Analiza termodynamiczna ultra-nadkrytycznego bloku węglowego z turbiną pomocniczą

Stępczyńska-Drygas K., Dykas S.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

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2014

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z. 86 [290], nr 1

79--86

PL

Konieczność zmniejszenia emisji gazów cieplarnianych oraz poprawy ekonomiki wytwarzania energii elektrycznej spowodowały znaczny postęp w dziedzinie bloków węglowych. Nowe perspektywy otwiera generacja bloków na zaawansowane parametry ultra-nadkrytyczne pary o temperaturze 700°C/720°C. Znaczne zwiększenie temperatury pary, zwłaszcza wtórnie przegranej, pogłębia problem różnicy temperatur w podgrzewaczach regeneracyjnych zarówno wysoko jak i niskoprężnych, co skutkuje wzrostem strumieni generowanej entropii oraz problemami materiałowymi. Rozwiązaniem może być wprowadzenie do obiegu dodatkowej upustowo-przeciwprężnej turbiny pomocniczej. Obieg turbiny pomocniczej jest prostym obiegiem bez przegrzewu wtórnego. Skutkuje to tym, że ma on niższą sprawność w porównaniu do obiegu głównego. Zmniejsza się zysk z zastosowania przegrzewu międzystopniowego, gdyż znaczny strumień pary, który jest kierowany do turbiny pomocniczej nie zostaje przegrzany ponownie. Zysk wynikający z minimalizacji generacji entropii w podgrzewaczach regeneracyjnych powinien zatem zrekompensować straty wynikające ze znacznego zmniejszenia strumienia przegrzewanej pary. W artykule przedstawiono analizę termodynamiczną obiegu prostego oraz koncepcyjnego bloku węglowego na zaawansowane ultra-nadkrytyczne parametry pary o mocy 900 MW z upustowo-przeciwprężną turbiną pomocniczą.

EN

The necessity of the reduction of greenhouse gases emissions and improving the economics of electricity generation resulted in significant progress in the development of the coal-fired power plants. New perspectives gives the generation of power plants for advanced ultra-supercritical (A-USC) steam parameters of temperature of 700°C/720°C. A significant increase of the steam temperature, especially reheated, increases the problem of the temperature differences in the high and low-pressure feed water heaters. This results in the increase of generated entropy and material problems. The solution can be introducing into the steam cycle an auxiliary extraction-backpressure turbine (AT). The AT cycle is a simple cycle without steam reheating. As the result it has lower efficiency in comparison with the main cycle. The use of the AT leads to the reduction of profit resulting from the reheating of steam, because the mass flow of steam transmitted to the boiler reheater is reduced. The benefit resulting from the decrease of the entropy generation in the feed water heaters should then exceed the loss related with the reduction of the steam mass flow, which is reheated in the boiler. In the paper the thermodynamic analysis of the simple cycle and the conceptual 900 MW power plant with the auxiliary extraction-backpressure turbine is presented.

11

Numerical analysis of a tip labyrinth seal of high rotating rotor

Szymański A., Dykas S., Wróblewski W., Rulik S.

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2014

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nr 146

153--163

EN

Labyrinth seal constantly is a prime turbine sealing solution because of low price, low maintenance, minimal rub particulate contamination and high temperature capability. This work aims to perform detailed CFD investigation of high speed rotating labyrinth seal. There have been found an impact of rotational velocity and pressure ratio on discharge characteristics of the rotor. Discharge characteristics were calculated for variety of pressure ratios. Moreover influence of rotor roughness was shown in each case. Performed inquiry results were shown as relative mass flow rate in function of mentioned parameters. From variety of configurations, an optimal seal configuration – providing the lowest leakage can be found.

12

Experimental and numerical study on condensation in transonic steam flow

Majkut M., Dykas S., Strozik M., Smołka K.

Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka

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2014

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nr 145

89--90

EN

The present paper describes an experimental and numerical study of steam condensing flow in a linear cascade of turbine stator blades. The experimental research was performed on the facility of a small scale steam power plant located at Silesian University of Technology in Gliwice. The test rig of the facility allows us to perform the tests of steam transonic flows for the conditions corresponding to these which prevail in the low-pressure (LP) condensing steam turbine stages. The experimental data of steam condensing flow through the blade-to-blade stator channel were compared with numerical results obtained using the in-house CFD numerical code TraCoFlow. Obtained results confirmed a good quality of the performed experiment and numerical calculations.

13

Modelowanie numeryczne strat w stopniu turbinowym

Dykas S., Machalica D., Szymański A.

Modelowanie Inżynierskie

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2014

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T. 20, nr 51

15--22

PL

Artykuł przedstawia analizę pracy stopnia turbiny gazowej silnika lotniczego pod względem generowania strat przepływowych. W celu ilościowego opisu strat przyjęto energetyczny, entropowy współczynnik oraz dodatkowo współczynnik strat ciśnienia. Rozkłady współczynników strat zostały przedstawione wzdłuż wysokości kanału łopatkowego. Wszystkie te współczynniki zostały określone na podstawie danych z niestacjonarnego pola przepływu i zostały przeanalizowane dla różnego wzajemnego położenia łopatek wirnikowych i kierowniczych. Do obliczeń przepływowych wykorzystano komercyjne oprogramowanie Ansys CFX. Analizy przedstawione w pracy zostały wykonane z wykorzystaniem metody URANS oraz dwóch różnych modeli turbulencji. Pierwszym z nich jest model Shear Stress Transport (SST), drugim należący do grupy modeli hybrydowych Scale-Adaptive Simulation (SAS).

EN

In this article an investigation of the flow losses in an aircraft gas turbine stage has been made. To measure the values of losses three parameters have been used; pressure loss coefficient, energy loss coefficient and entropy generation coefficient. The distribution of parameters has been shown as a function of relative height of the stage. All coefficients were calculated from transient flow analysis done by means of CFD methods for five different mutual positions of rotor and stator blades. For these analyses a commercial Ansys CFX software has been used. The numerical tests have been calculated using URANS calculating method with two different turbulence models. Shear Stress Transport (SST) model and hybrid Scale-Adaptive Simulation (SAS) model.

14

Application of hybrid CFD/CAA technique for modeling pressure fluctuations in transonic flows

Dykas S., Wróblewski W., Rulik S.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2013

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Vol. 17, No 3-4

145--154

EN

Solving AeroAcoustics (CAA) problems by means of the Direct Numerical Simulation (DNS) or even the Large Eddy Simulation (LES) for a large computational domain is very time consuming and cannot be applied widely for engineering purposes. In this paper in-house CFD and CAA codes are presented. The in-house CFD code is based on the LES approach whereas the CAA code is an acoustic postprocessor solving non-linearized Euler equations for fluctuating (acoustic) variables. These codes are used to solve the pressure waves generated aerodynamically by a flow over a rectangular cavity and by the vortex street behind a turbine blade. The obtained results are discussed with respect to the application of the presented numerical techniques to pressure waves modeling in steam turbine stages.

15

Research on steam condensing flows in nozzles with shock wave

Dykas S., Majkut M., Smołka K., Strozik M.

Journal of Power Technologies

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2013

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Vol. 93, nr 5

288--294

EN

The paper presents experimental and numerical results of steam transonic flows in Laval nozzles. The geometries of half arc nozzles were used in testing. Subject to investigation was the behavior of shock waves in the wet steam region. Due to high back pressure the shock wave was created in the divergent part of the nozzle, and interaction with the nozzle walls caused instability in the flow. The experimental results were compared with numerical calculations of steam condensing transonic flow.

16

Operation of conceptual A-USC power unit integrated with CO2 capture installation at part load

Stępczyńska-Drygas K., Bochon K., Dykas S., Łukowicz H., Wróblewski W.

Journal of Power Technologies

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2013

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Vol. 93, nr 5

383--393

EN

Nowadays, the main aim of the development of coal-fired power industry concentrates on improving the efficiency of electricity generation and on reducing the CO2 emission. Modern power systems require from the power units ability to flexible work at part loads with high efficiency. The paper presents the conceptual 900 MWcoal-fired power unit. Unit operates with advanced ultra-supercritical (A-USC) steam parameters 35MPa/700ºC and net efficiency of 49%. Improvement of the efficiency results in significant reduction of CO2 emission. Further reduction of emission requires integration of coal-fired power plants with CO2 capture installation. Newly built power plant offers a possibility of fully optimized integration to reduce the efficiency loss, which is related with post-combustion capture process. The CO2 capture by wet chemical absorption MEA can be characterized with three indicators: the demand for heat, electric power to drive auxiliary equipment and cooling. In order to calculate these indicators the capture process was modeled in Aspen Plus. Calculated indicators for nominal and part load operation were used to model integrated power unit in Ebsilon Professional 10.0. The characteristics of operation of power unit integrated with CO2 capture installation were determined.

17

Numerical modeling of CO2 separation process

Remiorz L., Rulik S., Dykas S.

Archives of Thermodynamics

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2013

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Vol. 34, no. 1

41--53

EN

Paper presents the results of numerical modelling of a rectangular tube filled with a mixture of air and CO2 by means of the induced standing wave. Assumed frequency inducing the acoustic waves corresponds to the frequency of the thermoacoustic engine. In order to reduce the computational time the engine has been replaced by the mechanical system consisting of a piston. This paper includes the results of model studies of an acoustic tube filled with a mixture of air and CO2 in which a standing wave was induced.

18

Calculation of a 900 MW conceptual 700/720ºC coal-fired power unit with an auxiliary extraction-backpressure turbine

Stępczyńska K., Kowalczyk Ł., Dykas S., Elsner W.

Journal of Power Technologies

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2012

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Vol. 92, nr 4

266--273

EN

This paper presents the calculations for different configurations of a 900 MW power unit for advanced 700/720°C ultra-supercritical steam parameters with a single and double steam reheat. The use of such high parameters, especially the reheated steam temperature, involves thermodynamic and material problems related to high temperature differences in the feed water heaters. In relation to this, a concept of the modification of the feed water heaters system by using an auxiliary extraction-backpressure turbine fed with steam from the cold reheat steam line is presented. The steam from the bleeds and the turbine outlet is directed to regenerative heaters fed in the classical system from the intermediate pressure turbine, which reduces the temperature differences in these exchangers and simplifies the main turbine IP part structure.

19

Obliczenia ultra-nadkrytycznego bloku węglowego o mocy 900 MW z odzyskiem ciepła ze spalin

Stępczyńska K., Łukowicz H., Dykas S., Czaja D.

Archiwum Energetyki

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2012

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T. 42, nr 2

155--164

EN

Improving the efficiency of electricity generation is the main way to reduce fossil fuels consumption and carbon dioxide emission. Development of technology of coal-fired power units 50 plus for advanced ultra-supercritical steam parameters gives new opportunities. However, exceeding the unit net efficiency barrier of 50% except the increasing steam parameters requires also the modifications of the power unit cycle configuration. In the paper is presented conception of 900 MW power unit for ultra-supercritical steam parameters of 700/720°C with waste heat recovery from the boiler exhaust gases. The calculations were carried out for the hard coal fired unit and lignite fired unit. In the case of hard coal fired power unit due to the low exhaust flue gas temperature (110°C) the use of waste heat recovery system offers slight improving of the boiler efficiency and the efficiency of electricity generation. Significant potential exists in the case of the lignite fired units, where the exhaust loss from the boiler is much higher (exhaust gas temperature 170°C). In the paper is presented thermodynamic analysis of two variants of the waste heat recovery in the steam cycle. In the first variant the heat of the boiler exhaust flue gases from the air heater outlet is used to heat up the water in the low pressure feed water system. In the second considered variant the part of the boiler exhaust flue gases is taken before the air heater and its used to heat up the water in the high pressure feed water heaters system.

PL

Poprawa sprawności wytwarzania energii elektrycznej jest podstawą redukcji zużycia paliw kopalnych oraz ograniczenia emisji dwutlenku węgla. Rozwój technologii bloków węglowych 50 plus na zaawansowane parametry ultra-nadkrytyczne pary otwiera nowe perspektywy. Przekroczenie bariery 50% sprawności netto bloku poza zwiększeniem parametrów pary wymaga również modyfikacji struktury samego obiegu. W artykule przedstawiono koncepcję bloku węglowego 900 MW na zaawansowane ultra-nadkrytyczne parametry pary 700/720°C z odzyskiem ciepła ze spalin wylotowych. Obliczenia przeprowadzono dla bloku opalanego węglem kamiennym oraz węglem brunatnym. W przypadku węgla kamiennego ze względu na niską temperaturę spalin wylotowych (110°C) zastosowanie odzysku ciepła odpadowego daje niewielkie zyski dla poprawy sprawności energetycznej kotła oraz sprawności wytwarzania energii elektrycznej. Znaczny potencjał istnieje natomiast w przypadku bloków opalanych węglem brunatnym, gdzie strata wylotowa z kotła jest większa (temperatura spalin 170°C). Przedstawiono analizę termodynamiczną dwóch wariantów wykorzystania ciepła odpadowego w obiegu. Pierwszy zakłada wykorzystanie ciepła spalin wylotowych zza kotłowego podgrzewacza powietrza w układzie regeneracji niskoprężnej, drugi pobranie części spalin sprzed kotłowego podgrzewacza powietrza.

20

Models for water steam condensing flows

Wróblewski W., Dykas S., Chmielniak T.

Archives of Thermodynamics

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2012

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Vol. 33, no. 1

67-86

EN

Abstract The paper presents a description of selected models dedicated to steam condensing flow modelling. The models are implemented into an in-house computational fluid dynamics code that has been successfully applied to wet steam flow calculation for many years now. All models use the same condensation model that has been validated against the majority of available experimental data. The state equations for vapour and liquid water, the physical model as well as the numerical techniques of solution to flow governing equations have been presented. For the single-fluid model, the Reynolds-averaged Navier-Stokes equations for vapour/liquid mixture are solved, whereas the two-fluid model solves separate flow governing equations for the compressible, viscous and turbulent vapour phase and for the compressible and inviscid liquid phase. All described models have been compared with relation to the flow through the Laval nozzle.