Strength and Service Life of a Steam Turbine Stop and Control Valve Body

The stability of operation of steam turbines depends (along with other factors) on the reliable operation of their steam distribution systems, which are based on stop and control valves. This paper considers the strength of the elements of the K-325-23.5 steam turbine valves, in whose bodies, after 30 thousand hours of operation, cracks came to be observed. Previously determined were the nature of gas-dynamic processes in the flow paths of the valves and the temperature state of the valve body in the main stationary modes of operation. To do this, a combined problem of steam flow and thermal conductivity in stop and control valves was solved in a three-dimensional formulation by the finite element method. Different positions of the valve elements were considered taking into account the filter sieve. The assessment of the thermal stress state of the valve body showed that the maximum stresses in different operating modes do not exceed the yield strength. Therefore, the assessment of the creep of the valve body material is important to determine the valve body damage and service life. Modeling the creep of the stop and control valves of the turbine was performed on the basis of three-dimensional models, using the theory of hardening, with the components of unstable and steady creep strains taken into account. The creep was determined at the maximum power of the turbine for all the stationary operating modes. The maximum calculated values of creep strains are concentrated in the valve body branch pipes before the control valves and in the steam inlet chamber, where in practice fatigue defects are observed. However, even for 300 thousand hours of operation of the turbine (with a conditional maximum power) in stationary modes, creep strains do not exceed admissible values. The damage and service life of the valve bodies were assessed by two methods developed at A. Pidhornyi Institute of Mechanical Engineering Problems of the NAS of Ukraine (2011), and I. Polzunov Scientific and Design Association on Research and Design of Power Equipment. (NPO CKTI) – 1986. The results of assessing the damage and the turbine valve body wear from the effects of cyclic loading and creep of the turbine in stationary modes for 40, 200 and 300 thousand hours show that the thermal conditions of the body in the steam inlet chamber are not violated (without taking into account possible body defects after manufacture). The damage in valve body branch pipes after 300 thousand hours of operation exceeds the admissible value, with account taken of the safety margin. At the same time, the damage from creep in stationary operating modes is about 70% of the total damage. The maximum values of damage are observed in the areas of the body where there are defects during the operation of the turbine steam distribution system. The difference between the results of both methods in relation to their average value is ~20%.

Retrospective Review of a Two-Phase Mechanically Pumped Loop for Spacecraft Thermal Control Systems

The main issues associated with the development of two-phase mechanically pumped loops (2-MPL) for thermal control systems of spacecraft with large heat dissipation were formulated back in the early 80s. They have undeniable advantages over single-phase loops with mechanical pumping and two-phase capillary pumped loops at power more than 6 kW and heat transfer distance more than 10 meters. Intensive research and development of such systems started in the USA together with European, Canadian and Japanese specialists due to plans to build new high-power spacecraft and the Space Station Freedom project. In the 90's, S. P. Korolev Rocket and Space Corporation Energia (Russia) was developing a 2-MPL for the Russian segment of the International Space Station with the capacity of 20...30 kW. For this purpose, leading research organizations of the former Soviet Union were involved. In the last two decades, interest in two-phase heat transfer loops has significantly increased because of high-power stationary communications satellites and autonomous spacecraft for Lunar and Martian missions. The paper presents a retrospective review of worldwide developments of 2-MPLs for thermal control systems of spacecraft with large heat dissipation from the early 80's to the present. The participation of scientists and engineers of the Ukrainian National Aerospace University "KhAI" and the Center of Technical Physics is considered. The main directions of research, development results, and scientific and technical problems on the way to the practical implementation of such system are considered. Despite a large amount of research and development work done, there were no practically implemented projects of spacecraft with the high-power thermal control system until recent days. The first powerful stationary satellite with the 2-MPL was SES-17 satellite on the NEOSAT platform by Thales Alenia Space - France. The satellite was successfully launched into space on October 24, 2021 by onboard Ariane 5 launcher operated by Arianespace from the Europe’s Spaceport in Kourou, French Guiana.

Development of the flow part of reactive type HPC of K-325-23,5 series steam turbine based on the use of modern computer technologies

The results of gas-dynamic design of a new flow part of a reactive type high-pressure cylinder (HPC) of the K-300 series condensing steam turbine are presented. The turbine was developed using a comprehensive methodology implemented in the IPMFlow software package. The methodology includes gas-dynamic calculations of various levels of complexity, as well as methods for analytical construction of the spatial shape of the blade rows based on a limited number of parameterized values. The real thermodynamic properties of water and steam were taken into account in 3D calculations of turbulent flows. At the final stage, 3D end-to-end calculations of the HPC, which consists of 18 stages, were carried out. The technology of parallel computing was applied in the said calculations. It is shown that a significant increase in efficiency and power has been achieved in the developed HPC due to the use of reactive type stages with modern smooth blade profiles and monotonic meridional contours.

Modification of the Redlich-Kwong-Aungier Equation of State to Determine the Degree of Dryness in the CO2 Two-phase Region

The degree of dryness is the most important parameter that determines the state of a real gas and the thermodynamic properties of the working fluid in a two-phase region. This article presents a modified Redlich-Kwong-Aungier equation of state to determine the degree of dryness in the two-phase region of a real gas. Selected as the working fluid under study was CO2. The results were validated using the Span-Wanger equation presented in the mini-REFPROP program, the equation being closest to the experimental data in the CO2 two-phase region. For the proposed method, the initial data are temperature and density, critical properties of the working fluid, its eccentricity coefficient, and molar mass. In the process of its solution, determined are the pressure, which for a two-phase region becomes the pressure of saturated vapor, the volumes of the gas and liquid phases of a two-phase region, the densities of the gas and liquid phases, and the degree of dryness. The saturated vapor pressure was found using the Lee-Kesler and Pitzer method, the results being in good agreement with the experimental data. The volume of the gas phase of a two-phase region is determined by the modified Redlich-Kwong-Aungier equation of state. The paper proposes a correlation equation for the scale correction used in the Redlich-Kwongda-Aungier equation of state for the gas phase of a two-phase region. The volume of the liquid phase was found by the Yamada-Gann method. The volumes of both phases were validated against the basic data, and are in good agreement. The results obtained for the degree of dryness also showed good agreement with the basic values, which ensures the applicability of the proposed method in the entire two-phase region, limited by the temperature range from 220 to 300 K. The results also open up the possibility to develop the method in the triple point region (216.59K-220 K) and in the near-critical region (300 K-304.13 K), as well as to determine, with greater accuracy, the basic CO2 thermodynamic parameters in the two-phase region, such as enthalpy, entropy, viscosity, compressibility coefficient, specific heat capacity and thermal conductivity coefficient for the gas and liquid phases. Due to the simplicity of the form of the equation of state and a small number of empirical coefficients, the obtained technique can be used for practical problems of computational fluid dynamics without spending a lot of computation time.

Vibrations of a Cylindrical Sandwich Shell with a Honeycomb Core Made Using FDM technology

Presented is a model of the dynamic deformation of a three-layer cylindrical shell with a honeycomb core, manufactured by fused deposition modeling (FDM), and skins reinforced with oriented carbon nano-tubes (CNT). A ULTEM 9085 thermoplastic-based honeycomb core is considered. To analyze the stress-strain state of the honeycomb core, a finite element homogenization procedure was used. As a result of this procedure, the dynamic response of the honeycomb core is modeled by a homogeneous orthotropic material, whose mechanical properties correspond to those of the core. The proposed model is based on the high-order theory, extended for the analysis of sandwich structures. The skin displacement projections are expanded along the transverse coordinate up to quadratic terms. The honeycomb core displacement projections are expanded along the transverse coordinate up to cubic terms. To ensure the integrity of the structure, shell displacement continuity conditions at the junction of the layers are used. The investigation of linear vibrations of the shell is carried out using the Rayleigh-Ritz method. For its application, the potential and kinetic energies of the structure are derived. Considered are the natural frequencies and modes of vibrations of a one-side clamped cylindrical sandwich shell. The dependence of the forms and frequencies of vibrations on the honeycomb core thickness and the direction of reinforcement of the shell skins have been investigated. It was found that the eigenforms of a sandwich shell are characterized by a smaller number of waves in the circumferential direction, as well as a much earlier appearance of axisymmetric forms. This means that when analyzing the resonant vibrations of a sandwich shell, it is necessary to take into account axisymmetric shapes. Changing the direction of reinforcement of the skins with CNTs makes it possible to significantly influence the frequencies of the natural vibrations of the shell, which are characterized by a nonzero number of waves in the circumferential direction. It was found that this parameter does not affect the frequencies of the axisymmetric shapes of the shell under consideration.

Experimental and Numerical Analysis of the Shear Properties of Honeycomb Cores Produced Using Additive Technologies

An approach to the experimental and computational study of the shear properties of honeycomb cores (HC) produced using Fused Deposition Modeling (FDM) technology is proposed. The experimental approach is based on a new sample type for testing HCs for shear. This sample contains two HCs and three steel plates. Shear tests are carried out in the TiraTest 2300 universal tensile testing machine. The HCs are made of ULTEM 9085 and PLA with FDM technology, which is implemented in the 3D Fortus 900 system. The tests resulted in obtaining the shear properties of the HCs by averaging the stress-strain curves of five samples. As follows from the analysis of the experimental results, brittle destruction of an HC is observed. Before its destruction, the value of shear deformation for samples made of PLA was 0.0134, and for samples made of ULTEM, 0.0257. The experimental analysis was accompanied by numerical finite element (FE) modeling of shear experiments, taking into account the deformation of the equipment. With the FE modeling of the experiments, to describe the behavior of the samples, it is necessary to take into account the influence, on the measurements of the shear properties, of the equipment and the deformation of each honeycomb cell. The deformation of three plates was taken into account; the elastic properties of the adhesive joint were not taken into account. A computer model of the deformation of the HCs with equipment was built using ANSYS Design Modeler. With FE modeling, only the elastic behavior of the HCs was considered.

Principal Modernization Solutions for a 300 MW Power Unit to be Converted to Operate at Ultra-Supercritical Steam Parameters

This paper analyses the state of power engineering in Ukraine and the main trends in the development of the world market in the field of converting high-capacity powerful power units of thermal power plants into ultra-supercritical (USC) ones. It is shown that the energy sector of Ukraine requires special attention and the introduction of new modern technical solutions. Worldwide trends indicate that the emphasis is now on increasing the steam parameters before a turbine to ultra-supercritical ones. This allows one both to increase the efficiency of power units and to reduce thermal emissions, fighting the global environmental problem of climate warming. The implementation of this approach is proposed taking into account the realities of the Ukrainian economy and the available technical capabilities of the power engineering industry. This paper presents the results of variational computational studies of the thermal scheme of the 300 MW power unit of the K-300-23.5 turbine to be converted into a USC one. The problem was solved under the condition of maximizing the preservation of the thermal scheme, increasing the efficiency of the power unit and minimizing capital investments during the modernization of the turbine. It was chosen to preserve the regeneration system, as well as the medium-pressure (MP) and low-pressure (LP) cylinders. Considered and calculated were variants with the addition to the existing turbine of a USC cylinder and the creation of a new high-pressure cylinder (HPC) with insignificant changes in its overall characteristics. The results of computational studies showed that the most rational variant for modernizing the 300 MW turbine plant is the creation of a new HPC designed for operation at USC steam parameters as well as the addition to the IPC of a new cylinder with the purpose of increasing the reheat steam parameters while preserving the regeneration system.

An Integrated Approach to the Optimization of Plates in Plane Stress State Operated at High Temperatures

Many critical elements of building and machine-building structures during their operation are in difficult operating conditions (high temperature, aggressive environment, etc.). In this case, they can be subject to a double effect: corrosion and material damage. Corrosion leads to a decrease in the cross-section of a structure, resulting in stress increase therein. In turn, damage to the material is accompanied by the appearance of microcracks and voids therein, due to inelastic deformation (creep), leading to a deterioration in its physical properties (for example, the elastic modulus) and a sharp decrease in the stress values at which the structure is destroyed. This article continues the study in the field of the optimal design of structures subject to the aforementioned double effect by the example of the optimization of plates with holes in the plane stress state, exposed to high temperatures (in previous works, the use of this approach was demonstrated in the optimization of the bending elements of rectangular and I-sections). Used as a corrosion equation is the modified Dolinsky mode, which takes into account the (additional) effect of the protective properties of an anticorrosive coating on the corrosion kinetics. Taken as a kinetic equation describing the change in material damage, is Yu. N. Rabotnov’s model, which enables to determine the duration of the incubation period of the beginning of the tangible process of material damage. To study the stress state of a plate, the finite element method is used. With a given contour of the plate, found is the optimal distribution of the thickness of the finite elements into which the given plate is divided. Acting as a constraint of the optimization problem is the parameter of damage to the plate material. The approach proposed in this work can be used to solve similar problems of the optimal design of structures operating under conditions of corrosion and material damage, using both analytical solutions and numerical methods.

The Solution of the Inverse Problem of Identifying the Thermal Conductivity Tensor in Anisotropic Materials

On the basis of A. N. Tikhonov's regularization theory, a technique has been developed for solving inverse heat conduction problems of identifying the thermal conductivity tensor in a two-dimensional domain. Such problems are replaced by problems of identifying the principal heat conductivity coefficients and the orientation angle of the principal axes, with the principal coefficients being approximated by Schoenberg’s cubic splines. As a result, the problem is reduced to determining the unknown coefficients in these approximations and the orientation angle of the principal axes. With known boundary and initial conditions, the temperature in the domain will depend only on these coefficients and the orientation angle. If one expresses it by the Taylor formula for two terms of series and substitutes it into the Tikhonov functional, then the determination of the increments of the coefficients and the increment of the orientation angle can be reduced to solving a system of linear equations with respect to these increments. By choosing a certain regularization parameter as well as some functions for the principal thermal conductivity coefficients and the orientation angle as an initial approximation, one can implement an iterative process for determining these coefficients. After obtaining the vectors of the coefficients and the angle of orientation as a result of the converging iterative process, it is possible to determine the root-mean-square discrepancy between the temperature obtained and the temperature measured as a result of the experiment. It remains to choose the regularization parameter in such a way that this discrepancy is within the root-mean-square discrepancy of the measurement error. When checking the efficiency of using the proposed method, a number of two-dimensional test problems for bodies with known thermal conductivity tensors were solved. The influence of random measurement errors on the error in the identification of the thermal conductivity tensor was analyzed.

Mathematical and Computer Simulation of Hex Head Screws for Implementation on a 3D Printer

In this paper, based on the R-functions theory, methods have been developed and equations have been constructed for the 3D printing of hex-head screws with Bristol, Pentalobe, Polydrive and other types of screw slots. Such screws are used both in personal computers and other high-end equipment. The Bristol slot has four or six radial grooved beams. The advantage of the design of this slot is the correct perpendicular, rather than tangential, vector of force application when the slot is rotated by a tool, which minimizes the risk of stripping out the slot. For this reason, the Bristol slot is used in soft metal screws. Compared to the internal hex, the Bristol slot allows a noticeably higher torque, only slightly higher than that of the Torx slot. This type of slot is used in aviation, high-end telecommunications equipment, cameras, air brakes, agricultural equipment, astronomical equipment, and foreign military equipment. Variations with a pin in the center are found in game consoles to prevent the use of a flat-blade screwdriver as an improvised key. The Pentalobe slot is a five-point slot designed by Apple and used in its products to limit unauthorized disassembly. It was first used in mid 2009 to mount MacBook Pro batteries. Its miniature version was used in the iPhone 4 and later models, in the MacBook Air (available since late 2010 models), and the MacBook Pro with Retina screens. The Polydrive slot is a starlike slot with rounded star points, used in the automotive industry for applications requiring high tightening torque. The Torq-set slot is a cross slot for fasteners requiring high tightening torque. The grooves are slightly offset, not intersecting at one point. Fasteners with this type of slot are used in military aviation, for example, in E-3, P-3, F-16, Airbus, Embraer, and Bombardier Inc. The Phillips Screw Company owns the trademark and manufactures fasteners with this type of slot. The slot design standards are National Aerospace Standard NASM 3781 and NASM 4191 for the ribbed version. The resulting equations for the surfaces of screws were checked during the modeling of the screws before 3D printing. The 3D printing technology allows us to reduce the cost and labor intensity of manufacturing products, including complex slot screws. The analytical recording of designed objects makes it possible to use alphabetic geometric parameters, complex superposition of functions, which, in turn, allows us to quickly change their design elements. The positivity property of the constructed functions at the internal points of an object is very convenient for the implementation of 3D printing.