# Archives of Thermodynamics

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### Abstract

Systematic attempts to maximise the efficiency of gas turbine units are achieved, among other possibilities, by increasing the temperature at the inlet to the expansion section. This requires additional technological solutions in advanced systems for cooling the blade rows with air extracted from the compressor section. This paper introduces a new mathematical model describing the expansion process of the working medium in the turbine stage with air film cooling. The model includes temperature and pressure losses caused by the mixing of cooling air in the path of hot exhaust gases. The improvement of the accuracy of the expansion process mathematical description, compared with the currently used models, is achieved by introducing an additional empirical coefficient estimating the distribution of the cooling air along the profile of the turbine blade. The new approach to determine the theoretical power of a cooled turbine stage is also presented. The model is based on the application of three conservation laws: mass, energy and momentum. The advantage of the proposed approach is the inclusion of variable thermodynamic parameters of the cooling medium. The results were compared with the simplified models used in the literature: separate Hartsel expansion, mainstream pressure, weighted-average pressure and fully reversible. The proposed model for expansion and the determination of theoretical power allows for accurate modelling of the performance of a cooled turbine stage under varying conditions.
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### Authors and Affiliations

Paweł Trawiński
1

1. Institute of Heat Engineering, Warsaw University of Technology, Nowowiejska 21/25, 00-665, Warsaw, Poland
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### Abstract

Reliable knowledge of thermo-physical properties of materials is essential for the interpretation of solidification behaviour, forming, heat treatment and joining of metallic systems. It is also a precondition for precise simulation calculations of technological processes. Numerical calculations usually require the knowledge of temperature dependencies of three basic thermo-physical properties: thermal conductivity, heat capacity and density. The objective of this work is to find a correlation that fits the thermal conductivity of selected steel grades as a function of temperature (within the range of 0–800°C) and carbon content (within the range of 0.1–0.6%). The starting point for the analysis are the experimental data on thermal conductivity taken from literature. Using the method of least squares it was possible to fit an equation which allows calculating the thermal conductivity of steel depending on the temperature and carbon content. Two kinds of equations have been analyzed: a linear one (a linear model) and a second degree polynomial (a non-linear model). The thermal conductivity obtained by linear and nonlinear models varies on average from the measured values by 3% and 2.6% respectively.
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### Authors and Affiliations

Rafał Wyczółkowski
1
Dominika Strychalska
1
Vazgen Bagdasaryan
2

1. Czestochowa University of Technology, Department of Production Management, Armii Krajowej 19, 42-200 Czestochowa, Poland
2. Warsaw University of Life Sciences, Institute of Civil Engineering – SGGW, Nowoursynowska 166, 02-787 Warsaw, Poland
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### Abstract

The utilization of solar radiation to obtain high-temperature heat can be realized by multiplying it on the illuminated surface with solar concentrating technologies. High-temperature heat with significant energy potential can be used for many technological purposes, e.g. the production of heat, cold or electricity. The following paper presents the results of the experimental study, on the operation of the parabolic linear absorber in the parabolic concentrator solar system. The parabolic mirror with an aperture of 1 m and a focal length of 0.25 m focuses the simulated radiation onto a tubular absorber with a diameter of 33.7 mm, which is placed in a vacuum tube. The length of the absorber is 1 m. The installation is illuminated by the solar simulator, which allows to carry out tests under constant and repeatable conditions. The simulator consists of 18 metal halide lamps, with a nominal power of 575 W each with a dimming possibility of up to 60%. The paper presents preliminary results of heat absorption by the analysed absorber, temperature increment, collected heat flux, and the pressure drop crucial for the optimization of the absorber geometry.
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### Authors and Affiliations

Bartosz Stanek
1
Łukasz Bartela
1
Daniel Węcel
1
Sebastian Rulik
1

1. Silesian University of Technology, Department of Power Engineering and Turbomachinery, Konarskiego 18, 44-100, Gliwice, Poland
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### Abstract

The highly dynamic and unsteady characteristics of the cavitating flow cause many negative effects such as erosion, noise and vibration. Also, in the real application, it is inevitable to neglect the dissolved air in the water, although it is usually neglected in the previous works to reduce the complexity. The novelty of the present work is analysing the impact of dissolved air on the average/unsteady characteristics of Venturi flow by conducting sets of experimental tests. For this purpose, two different amounts of dissolved air at five pressure levels (i.e. five different sets of cavitation numbers) were considered in the study of cavitating flow inside a Venturi nozzle. The fast Fourier transform analysis of pressure fluctuations proved that the shedding frequency reduces almost by 50% to 66%, depending on the case, with adding the amount of dissolved air. However, the reduction of 14% to 25% is achieved by the vibration transducers. On the other hand, the cavity enlarges as well as bubbly flow is observed in the test chamber at a higher level of dissolved air. Furthermore, it is observed that the re-entrant jet, as the main reason for the cavity detachment, is more effective for the detachment process in cases with a lower level of dissolved air, where the re-entrant jet front penetrates more toward the leading edge.
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### Authors and Affiliations

Emad Hasani Malekshah
1
Włodzimierz Wróblewski
1
Krzysztof Bochon
1
Mirosław Majkut
1
Krzysztof Rusin
1

1. Silesian University of Technology, Department of Power Engineering and Turbomachinery, Konarskiego 18, 44-100 Gliwice, Poland
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### Abstract

In commercially available generation III and III+ PWR (pressurized water reactor) reactors, pressure of steam produced in steam generators varies in a relatively wide range from 5.7 to 7.8 MPa. Therefore, it is important to ask which value of steam pressure should be used for a specific unit, taking into account different location conditions, the size of the power system and conditions of operation with other sources of electricity generation.
The paper analyzes the effect of steam pressure at the outlet of a steam generator on the performance of a PWR nuclear power plant by presenting changes in gross and net power and efficiency of the unit for steam pressures in the range of 6.8 to 7.8 MPa. In order to determine losses in the thermal system of the PWR power plant, in particular those caused by flow resistance and live steam throttling between the steam generator and the turbine inlet, results concerning entropy generation in the thermal system of the power plant have been presented.
A model of a nuclear power plant was developed using the Ebsilon software and validated based on data concerning the Olkiluoto Unit 3 EPR (evolutionary power reactor) power plant. The calculations in the model were done for design conditions and for a constant thermal power of the steam generator. Under nominal conditions of the Olkiluoto Unit 3 EPR power unit, steam pressure is about 7.8 MPa and the steam dryness fraction is 0.997. The analysis indicates that in the assumed range of live steam pressure the gross power output and efficiency increase by 32 MW and 0.735 percentage point, respectively, and the net power output and efficiency increase by 27.8 MW and 0.638 percentage point, respectively.
In the case of all types of commercially available PWR reactors, water pressure in the primary circuit is in the range of 15.5−16.0 MPa. For such pressure, reducing the live steam pressure leads to a reduction in the efficiency of the unit. Although a higher steam pressure increases the efficiency of the system, it is necessary to take into account the limitations resulting from technical and economic criteria as well as operating conditions of the primary circuit, including the necessary DNBR (departure from nucleate boiling ratio) margin. For the above reasons, increasing the live steam pressure above 7.8 MPa (the value used in EPR units that have already been completed) is unjustified, as it is associated with higher costs of the steam generator and the high-pressure part of the turbine.
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### Authors and Affiliations

Rafał Laskowski
1
Adam Smyk
1
Romuald Jurkowski
2
Julien Ancé
3
Marcin Wołowicz
1
Nikołaj Uzunow
1

1. Warsaw University of Technology, Faculty of Power and Aeronautical Engineering, Institute of Heat Engineering, Nowowiejska 21/25, 00-665 Warszawa, Poland
2. Framatome, 1 place Jean Millier, 92400, Courbevoie, Paris, France
3. EDF, 19 rue Pierre Bourdeix, 69007, Lyon, France
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### Abstract

The aim of this work is to examine the impact of the hydrogen blended natural gas on the linepack energy under emergency scenarios of the pipeline operation. Production of hydrogen from renewable energy sources through electrolysis and subsequently injecting it into the natural gas network, gives flexibility in power grid regulation and the energy storage. In this context, knowledge about the hydrogen percentage content, which can safely effect on materials in a long time steel pipeline service during transport of the hydrogen-natural gas mixture, is essential for operators of a transmission network. This paper first reviews the allowable content of hydrogen that can be blended with natural gas in existing pipeline systems, and then investigates the impact on linepack energy with both startup and shutdown of the compressors scenarios. In the latter case, an unsteady gas flow model is used. To avoid spurious oscillations in the solution domain, a flux limiter is applied for the numerical approximation. The GERG-2008 equation of state is used to calculate the physical properties. For the case study, a tree-topological high pressure gas network, which have been inservice for many years, is selected. The outcomes are valuable for pipeline operators to assess the security of supply.
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### Authors and Affiliations

Maciej Witek
1
Ferdinand Uilhoorn
1

1. Warsaw University of Technology, Department of Heating and Gas Systems, Nowowiejska 20, 00-653 Warsaw, Poland
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### Abstract

Thermal augmentation in flat tube of car radiator using different nanofluids has been performed more often, but use of artificial roughness has been seldom done. Artificial roughness in the form of dimple is used in the present research work. Present study shows the impact of dimple shaped roughness and nanofluid (Al2O3/pure water) on the performance of car radiator. The pitch of dimples is kept at 15 mm (constant) for all the studies performed. The Reynolds number of the flow is selected in the turbulent regime ranging from 9350 to 23 000 and the concentration of the nanofluid is taken in the range of 0.1–1%. It has been found that the heat transfer rate has improved significantly in dimpled radiator tube on the expense of pumping power. Furthermore, the heat transfer rate also increases with increase in nanoparticle concentration from 0.1% to 1.0%. The highest heat transfer enhancement of 79% is observed at Reynolds number 9350, while least enhancement of 18% is observed for Reynolds number of 23 000.
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### Authors and Affiliations

Robin Kumar Thapa
1
Vijay Singh Bisht
1
Prabhakar Bhandari
2
Kamal Singh Rawat
3

1. Uttarakhand Technical University, Faculty of Technology, Chakrata Road, Dehradun-248007, Uttarakhand, India
2. K.R. Mangalam University, Mechanical Engineering Department, Sohna Road, Gurgram-122103, Haryana, India
3. MIET, Mechanical Engineering Department, Meerut-250005, Uttar Pradesh, India
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### Abstract

Nitrous oxide is often used in the space industry, as an oxidiser or monopropellant, mostly in self-pressurised configurations. It has potential for growth in use due to the recent rising interest in green propellants. At the same time, modelling the behaviour of a self-pressurising nitrous oxide tank is a challenging task, and few accurate numerical models are currently available. Two-phase flow, heat transfer and rapid changes of mass and temperature in the investigated system all increase the difficulty of accurately predicting this process. To get a get better understanding of the emptying of a self-pressurised nitrous oxide tank, two models were developed: a phase equilibrium model (single node equilibrium), treating the control volume as a single node in equilibrium state, and a phase interface model, featuring a moving interface between parts of the investigated medium. The single node equilibrium model is a variation of equilibrium model previously described in the literature, while the phase interface model involves a novel approach. The results show that the models are able to capture general trends in the main parameters, such as pressure or temperature. The phase interface model predicts nitrous oxide as a liquid, a two-phase mixture, and vapour in the lower part of the tank, which is reflected in the dynamics of changes in pressure and mass flow rate. The models developed for self-pressurisation, while created for predicting nitrous oxide behaviour, could be adapted for other media in conditions near vapour– liquid equilibrium by adding appropriate state equations.
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### Authors and Affiliations

Jakub Szymborski
1
Dariusz Kardaś
1

1. The Szewalski Institute of Fluid Flow Machinery, Polish Academy of Sciences, Fiszera 14, 80-231 Gdansk, Poland

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[1] Król, J., & Ocłoń, P. (2019). Sensitivity analysis of hybrid combined heat and power plant on fuel and CO2 emission allowances price change. Energy Conversion and Management, 196, 127–148.
doi.org/10.1016/j.enconman.2019.05.090

[2] Zhou, Y., Bi, H., & Wang, H. (2023). Influence of the primary components of the high-speed train on fire heat release rate. Archives of Thermodynamics, 44(1), 37–61.
doi.org/10.24425/ather.2023.145876

When citing scientific papers, it is needed to provide a DOI identifier if available.
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• Król and Ocłoń [1] studied a hybrid CHP sensitivity on fuel and CO2 emission allowances price change.
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[3] Ocłoń, P. (2021). Renewable energy utilization using underground energy systems (1st ed.). Springer Nature.
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[4] Ciałkowski, M., & Frąckowiak, A. (2014). Boundary element method in inverse heat conduction problem. In Encyclopedia of Thermal Stresses (pp. 424–433). Springer Netherlands.
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• Ciałkowski and Frąckowiak [4] presented a Boundary element method application for solving inverse heat conduction problems.

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[5] Pourghasemi, B., & Fathi, N. (2023). Validation and verification analyses of turbulent forced convection of Na and NaK in miniature heat sinks. ASME 2023 Verification, Validation, and Uncertainty Quantification Symposium, 17-19 May, Baltimore, USA.
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• Pourghasemi and Fathi [5] validated and verified turbulent forced convection of Na and NaK in miniature heat sinks.
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