물, 증기, 얼음의 압력과 온도에 대한 정밀계산 : CFD를 위한 공식

이장창(Jang-Chang Lee),Meng-Sing Liou 대한기계학회 2009 대한기계학회 춘추학술대회 Vol.2009 No.11

An accurate approach is proposed for calculating the thermodynamic properties of water in three states: liquid, steam and ice, and the transitional states among them. The formulation is expressed in terms of quantities that are naturally used in Computational Fluid Dynamics (CFD), namely the specific volume (υ) and specific internal energy (υ), through the use of Gibbs free energy. The Gibbs free energy formula proposed by IAPWS, formulated as a function of pressure and temperature, is used as a basis in our calculations. The Jacobian matrix resulting from the transformation between sets of variables (p, T) and (υ, u) are derived for each phase; the Newton-Raphson method is used to iteratively solve the nonlinear equations. Numerical calculations have been carried out for the entire phase diagram covering all three phases. The numerical results are compared with the original data of IAPWS and the associated errors are analyzed. It is confirmed that the pressure and temperature are accurately calculated, with largest relative error on the order of 10?? in the ice phase. Hence, other thermodynamic properties are also obtained within the same level of accuracy. The method proposed in this paper for calculating pressure and temperature, variables needed in CFD, is reliable and can be applied to the numerical simulation of multiphase flows, including phase changes.

Ar의 녹는점에 관한 분자동역학적 고찰

정재동(Jae Dong Chung) 대한설비공학회 2007 설비공학 논문집 Vol.19 No.12

As a starting point of investigating what molecular dynamic simulations can reveal about the nature of atomic level of heating and cooling process, argon described by the LJ potential is considered. Stepwise heating and cooling of constant rates are simulated in the NPT (constant number, pressure and temperature) ensemble. Hysteresis is found due to the superheating and supercooling. Drastic change of volume and energy is involved with phase change, but the melting point can not be obtained by simply observing the changes of these quantities. Since liquid and solid phases can co-exist at the same temperature, Gibbs free energy should be calculated to find the temperature where the Gibbs free energy of liquid is equal to that of the solid since the equilibrium state is the state of minimum Gibbs free energy. The obtained melting temperature, T = 0.685, is close to that of the experiment with only 2% error.

Evaluation method of iodine re-evolution from an in-containment water pool after a loss of coolant accident, Part I: pH estimation of a solution with various chemicals

Kim, T.H.,Jeong, J.H. Pergamon Press ; Elsevier Science Ltd 2016 Annals of nuclear energy Vol.87 No.2

Radioactive iodine, which is released into the atmosphere of the containment building, is absorbed into the containment spray water and dissolved to be ionized. This iodine-rich water is then transported to the in-containment refueling water storage tank (IRWST) in APR1400 nuclear power plants. When the pH of the water is below 7, the dissolved iodine converts to molecular iodine and re-evolves from the water and returns to the atmosphere. A series of studies have been conducted in order to evaluate the iodine re-evolution from the IRWST. This study consists of two parts: the pH evaluation method and the evaluation of the iodine re-evolution. This paper presents the first part, i.e. the pH evaluation method. The equilibrium concentrations of various chemicals in a solution are determined at the minimum Gibbs' free energy. This method is useful for complex reactant problems rather than equilibrium constants method because the latter method requires numerous equilibrium constants and there might be missing equilibrium constants associated with the solution. The calculated pH values of solutions are compared with the experimental measurements in order to validate this method and the thermodynamic data of the chemicals incorporated into the program. The estimated values for solutions are in good agreement with the experimental measurements within a difference of less than 3.3%.

Accurate calculation of the pressure and temperature of water, steam, and ice: Formulation for CFD

이장창,Meng-Sing Liou 대한기계학회 2010 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.24 No.11

An accurate approach is proposed for calculating the thermodynamic properties of water in three states: liquid, steam and ice, and the transitional states among them. The formulation is expressed in terms of quantities that are naturally used in Computational Fluid Dynamics (CFD), namely the specific volume ( v ) and specific internal energy ( u ), through the use of Gibbs free energy. The Gibbs free energy formula proposed by IAPWS, formulated as a function of pressure and temperature, is used as a basis in our calculations. The Jacobian matrix resulting from the transformation between sets of variables ( p,T ) and (v,u ) are derived for each phase; the Newton-Raphson method is used to iteratively solve the nonlinear equations. Numerical calculations have been carried out for the entire phase diagram covering all three phases. The numerical results are compared with the original data of IAPWS and the associated errors are analyzed. It is confirmed that the pressure and temperature are accurately calculated, with largest relative error on the order of 10−7 in the ice phase. Hence, other thermodynamic properties are also obtained within the same level of accuracy. The method proposed in this paper for calculating pressure and temperature, variables needed in CFD, is reliable and can be applied to the numerical simulation of multiphase flows, including phase changes.

The Prediction of pH by Gibbs Free Energy Minimization in The Sump Solution Under LOCA Condition of PWR

윤형주 한국원자력학회 2013 Nuclear Engineering and Technology Vol.45 No.1

It is required that the pH of the sump solution should be above 7.0 to retain iodine in a liquid phase and be within the material compatibility constraints under LOCA condition of PWR. The pH of the sump solution can be determined by conventional chemical equilibrium constants or by the minimization of Gibbs free energy. The latter method developed as a computer code called SOLGASMIX-PV is more convenient than the former since various chemical components can be easily treated under LOCA conditions. In this study, SOLGASMIX-PV code was modified to accommodate the acidic and basic materials produced by radiolysis reactions and to calculate the pH of the sump solution. When the computed pH was compared with measured by the ORNL experiment to verify the reliability of the modified code, the error between two values was within 0.3 pH. Finally,two cases of calculation were performed for the SKN 3&4 and UCN 1&2. As results, pH of the sump solution for the SKN 3&4was between 7.02 and 7.45, and for the UCN 1&2 plant between 8.07 and 9.41. Furthermore, it was found that the radiolysis reactions have insignificant effects on pH because the relative concentrations of HCl, HNO3, and Cs are very low.

THE PREDICTION OF pH BY GIBBS FREE ENERGY MINIMIZATION IN THE SUMP SOLUTION UNDER LOCA CONDITION OF PWR

Yoon, Hyoungju Korean Nuclear Society 2013 Nuclear Engineering and Technology Vol.45 No.1

It is required that the pH of the sump solution should be above 7.0 to retain iodine in a liquid phase and be within the material compatibility constraints under LOCA condition of PWR. The pH of the sump solution can be determined by conventional chemical equilibrium constants or by the minimization of Gibbs free energy. The latter method developed as a computer code called SOLGASMIX-PV is more convenient than the former since various chemical components can be easily treated under LOCA conditions. In this study, SOLGASMIX-PV code was modified to accommodate the acidic and basic materials produced by radiolysis reactions and to calculate the pH of the sump solution. When the computed pH was compared with measured by the ORNL experiment to verify the reliability of the modified code, the error between two values was within 0.3 pH. Finally, two cases of calculation were performed for the SKN 3&4 and UCN 1&2. As results, pH of the sump solution for the SKN 3&4 was between 7.02 and 7.45, and for the UCN 1&2 plant between 8.07 and 9.41. Furthermore, it was found that the radiolysis reactions have insignificant effects on pH because the relative concentrations of HCl, $HNO_3$, and Cs are very low.

Equilibrium Crystal Shape of BaZrO3 and Space Charge Formation in the (011) Surface by Using Ab-Initio Thermodynamics

김지수,김영철 한국물리학회 2017 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.70 No.1

We investigated the equilibrium crystal shape of BaZrO3 and the space charge formation in an O-terminated (011) surface by using ab-initio thermodynamics. Twenty-two low-indexed (001), (011), and (111) surfaces were calculated to analyze their surface Gibbs-free energy under the stable condition of BaZrO3. Based on the Gibbs-Wulff theorem, the equilibrium crystal shape of BaZrO3 changed from cubic to decaoctahedral with decreasing Ba chemical potential. The dominant facets of BaZrO3 were {001} and {011}, which were well consistent with experimental observations. The space charge formation in the (011) surface was evaluated using the space-charge model. We found that the (011) surface was even more resistive than the (001) surface.

지구 핵에 수산화물의 존재에 관한 연구

김영호 ( Young Ho Kim ),도재기 ( Jae Ki Do ),황길찬 ( Gil Chan Hwang ) 한국광물학회 2008 광물과 암석 (J.Miner.Soc.Korea) Vol.21 No.4

외핵은 대부분 철로 이루어져 있으나 외핵의 밀도를 10% 정도 줄일 수 있는 희석 원소가 존재해야 한다. 외핵에서 존재할 가능성이 있는 가벼운 희석원소가 수소와 산소라는 가정 하에, 고압 하에서 수소의 열역학적 안정성을 적철석(Fe2O3)+수소(H2)→괴타이트(FeOOH) +철(Fe) 반응관계식을 이용하여 계산하였다. 열역학적 해석 결과, 상온 및 상압에서 이러한 화학반응의 깁스자유에너지는 12.62kJ/mol로 계산되었다. 상온에서 압력이 증가함에 따라 깁스자유에너지 값은 감소하여 0.068GPa에서`0 kJ/mol`을 나타내었다. 압력이 증가함에 따라 깁스자유에너지 값은 일정한 비율로 점차적으로 감소하여 200GPa에서는 -208.26kJ/mol을 나타내었다. 이러한 열역학적 분석 결과로 볼 때 고압 하에서 수소와 철산화물이 반응하여 철원소와 철 수산화물을 생성하는 환원반응이 선호되며, 수소와 산소가 철수산화물의 형태로 원시지구 핵 내에 존재하게 되었을 가능성을 배제할 수 없다. Earth outer core is composed of iron mainly with some diluent elements, which account for the observed ca. 10% density deficit compared to the pure iron. Among candidates as the light diluents, hydrogen and oxygen were selected, and the thermodynamic stability of the following reaction was calculated; hematite+hydrogen→goethite+iron. At ambient conditions, Gibb`s free energy of this reaction is 12.62kJ/mol. On increasing pressure at room temperature, it decreases to zero at 0.068GPa. This energy decreases at constant rate down to 200GPa, which shows -208.26 kJ/mol at that pressure. From these results, this chemical reaction prefers the reduction environment forming the iron element and iron oxyhydroxide, so possible presence of iron oxyhydroxide with iron at proto-core can not be ruled out.

Thermodynamic conditions for formation of single phase in Bi-superconductor thin films

Park, No-Bong,Park, Yong-Pil,Kim, Jeong-Ho Elsevier 2003 CURRENT APPLIED PHYSICS Vol.3 No.6

<P><B>Abstract</B></P><P>High quality BSCCO thin films have been fabricated by means of an ion beam sputtering at various substrate temperatures, <I>T</I><SUB>sub</SUB>, and ozone gas pressures, <I>p</I>O<SUB>3</SUB>. The correlation diagrams of the BSCCO phases appearing against <I>T</I><SUB>sub</SUB> and <I>p</I>O<SUB>3</SUB> have been established in the 2212 and 2223 compositional films. In spite of 2212 compositional sputtering, Bi2201 and Bi2223 phases as well as Bi2212 have emerged as stable phases depending on <I>T</I><SUB>sub</SUB> and <I>p</I>O<SUB>3</SUB>. From these results, the thermodynamic evaluations of Δ<I>H</I> and Δ<I>S</I>, which are related with Gibbs’ free energy change for single Bi2212 or Bi2223 phase have been performed.</P>

Structural Analysis of ZnO Nanowires Synthesized by Using a Low-temperature Hydro-thermal Method

이상효,이준석,WonBae Ko,강태성,홍진표,SeungNam Cha 한국물리학회 2012 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.60 No.10

Structural properties of vertically aligned ZnO nanowires (NWs) prepared with hydrothermal synthesis at various temperatures and different precursor concentrations are systematically described. The ZnO NWs are synthesized via an aqueous solution method with zinc nitrate (Zn(NO<SUB>3</SUB>)<SUB>2</SUB>∙6H<SUB>2</SUB>O) hexahydrate and hexamethylenetetramine (HMT) on ZnO seed layers. The growth speed and shape of ZnO NWs are particularly determined, depending on various mole concentrations. The structural analysis of the ZnO NWs is performed using X-ray diffraction, scanning electron microscopy and tunneling electron microscopy. Finally, the correlation of structural results with growth conditions, such as mole concentration and growth temperature of chemical precursors is discussed, based on Gibbs free energy.