Variable Cross-section Research Articles

Flow and Heat Transfer Characteristics of the Turbine Blade Variable Cross-Section Internal Cooling Channel with Turning Vane

The gas turbine blades are scoured by high temperature gas sustainedly and long-term in harsh environment. It is of great significance to explore effective cooling methods to lower the turbine blade temperature so as to ensure safe and stable operation of the gas turbine. However, there are few studies on the cooling channel considering the turning vane, variable cross-section characteristics, and rotation effect. In this paper, five kinds of serpentine cooling channel models with variable cross-section properties and different thickness guide vanes are constructed. The effects of different thickness guide vanes on the overall performance of the channel under stationary and rotating conditions are discussed and compared by numerical method. The result shows that when stationary (Re = 10,000–50,000), the turning vane with suitable thickness can increase the Nu/Nu0 by 56.5%. The f/f0 is decreased by 14.2%, and the comprehensive thermal performance is increased by 4.5%. When rotating (Re = 10,000, Ro = 0–0.5), the turning vane with suitable thickness can increase the Nuup/Nu0 and Nuall/Nu0 by 33.0% and 4.0%, respectively. The comprehensive performance of the variable cross-section serpentine channel can be greatly improved by arranging the turning vane structure with appropriate thickness.

The effect of environmental temperature on influence line of concrete beam type bridge

The influence line (IL) contains information induced by a unit force applied at any cross-section of the bridge, and its change can be used for damage identification. However, environmental temperature will also change the bridge IL, thus affect the damage identification effectiveness. In this paper, the main factors affecting the deflection and strain ILs of the concrete beam type bridges are systematically studied considering that temperature affects the structural static characteristics by changing the elastic modulus of concrete material, structural geometry, boundary condition and axial force. Then, based on the analytical formulas of the deflection and strain ILs of the concrete beam type bridge, the iterative calculation formulas describing the relationship between the ILs and the temperature are derived. Finally, the iterative calculation formulas are verified by numerical examples of beams with equal and variable cross-sections, and experiment in Environmental Coupling Test Chamber. The deflection and strain ILs are identified by parking a vehicle at different locations on the bridge progressively in the experiment. The results indicate that the maximum absolute values of the relative change rate (RCR) of the Ils are even up to10%, and the effect of environmental temperature on the IL concrete beam type bridge cannot be ignored. The proposed iterative calculation formulas can effectively consider the effect of environmental temperature, and reduce the maximum absolute values of the RCR of the Ils to be less than 1%. Thus it can be used to calculate the IL of concrete beam type bridges under actual temperature.

Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven

Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven

Energy absorption characteristic and crashworthiness optimization design of VRB-VCS structures under manufacturing constraints

After fully understanding the limitations of traditional variable rolled blank (VRB) and variable cross-sectional (VCS) double-hat shaped beam structures on the energy absorption ability and collision safety optimal design, we propose a variable rolled blank and variable cross-sectional (VRB-VCS) double-hat shaped beam structure with piecewise exponential function. Firstly, the thickness distribution function and the mathematical model of constraint conditions are derived under the constraints of manufacturing rollability. The corresponding finite element (FE) model of the VRB-VCS structure is validated by the dropping hammer impact axial crush experiments, which can predict the crushing process with high fidelity. Secondly, the parametric researches of the energy absorption characteristic of VRB-VCS structure are carried out based on the FE model. The reasonable range of each parameter is obtained by analyzing the influence of the thickness distribution and other key cross-sectional parameters on the energy absorption characteristic and deformation mode of VRB-VCS structure. Finally, the Pareto frontier solutions of the linear and piecewise exponential function VRB-VCS structures are obtained by the multi-objective optimization of the corresponding structures. In comparison to VCS, VRB and linear VRB-VCS structures, the proposed VRB-VCS structure has a higher energy absorption capacity and greater crashworthiness.

Modeling and experimental study on deformation prediction of thin-walled turbine blades during investment casting process

Due to variable cross-sections and a thin-walled structure, gas turbine blades have stringent dimensional, and geometrical tolerance requirements. Single-crystal hollow blades are manufactured using the following investment casting processes: ceramic core preparation, wax injection, ceramic coating, wax removal, metal casting, and finishing. The main causes of the final casting deformation are wax pattern deformation, core deflection, and metal solidification warpage. This paper proposes a numerical simulation method to predict the deformation of the wax pattern, core deflection, and the directional solidification (DS) process of large single-crystal blades. Additionally, it investigates the displacement field and the influence of casting process parameters on dimensional accuracy. Three groups of DS process parameters were selected for experiments, and the deformation prediction was in agreement with the experimental results. The selected blade section deformation is the smallest when the pouring temperature is 1530°C and the withdrawal rate is 5 mm/min. The proposed finite element model is efficient to predict the deformation in all the investment casting processes, providing geometric guidance for the control of the dimensional accuracy of the turbine blade.

Beams With a Varying Cross Section in the Generalized Strain Formulation for Flexure Modeling

Abstract Flexure joints are rapidly gaining ground in precision engineering because of their predictable behavior. However, their range of motion is limited due to a stress limitation and a loss of support stiffness in deformed configurations. The support stiffness can be significantly increased by using leafsprings of which the width and thickness vary over the length of the leafspring. This paper presents formulations for two beam elements with a varying cross section that can be used for the efficient modeling of these types of leafsprings. One of these beam-formulations includes the modeling of the warping due to torsion, which is shown to be essential for accurate modeling. The 90% accuracy in stiffness results and 80% accuracy in stress results, in comparison with results of finite element analyses, are sufficient for the evaluation of concept-designs. Optimizations show that the support stiffness of two typical flexure joints can be increased by a factor of up to 4.0 keeping the same range of motion, by allowing the cross section to vary over the length of the leafspring. In these two flexure joints, 98% of this improvement can already be obtained by only varying the thickness, and keeping a constant width.

Methodology for Designing the Steel Frames of Variable Cross-Section from Rolled I-Beams

Introduction. The article tackles the problem of finding the most efficient in terms of metal consumption I-shaped crosssection for creating a frame of variable section. In this paper from various options of creating the variable in length frame elements the authors study the option of creating the elements from the ordinary I-beams by diagonal slitting followed by welding as one of the most technologically advanced one. To obtain the most efficient in terms of metal consumption cross-section, it is proposed to use a monosymmetric I-beam composed of two different assortment items.Materials and Methods. The review of scientific works related to the topic of designing structures from I-beams allowed the authors to compile a methodology for calculating the optimal section parameters. The implementation of this methodology makes it possible to draw the parameters for finding the most efficient for application cross-sections from the existing assortment of rolled I-beams.Results. The object considered in this study is a frame of a building designed as the braced frame structure from welded single-span frames with elements of variable cross-section (code 828KM). The calculation was made in accordance with the proposed methodology. The results of the calculation show that the use of a monosymmetrical I-beam, composed of two different I-beams, gives opportunity to use the load-bearing capacity of the section to the fullest extent.Discussion and Conclusions. In the result of implementation of the proposed methodology, it became possible to reduce the mass of an I-beam of a variable cross-section compared to the serial one used under similar loads. The result of the study allows us to conclude that the use of frames of variable section formed of I-beams of various cross-sections by diagonal slitting and subsequent welding in the construction of industrial frame buildings is highly perspective.

The evaluation of the seismic performance of tall bridge piers with non-adaptive pushover methods

The number of tall-pier bridges is increasing rapidly in the southwestern region of China, but the seismic behaviors of these special bridges have not been well understood. The present paper evaluates the effectiveness of two multi-mode non-adaptive pushover methods, including the energy-based MPA method and the direct vectorial addition (DVA) based pushover method in predicting the curvature ductility demands of four tall single-column piers. The four tall piers are designed to investigate two parameters including the pier height (60 m or 100 m) and the variation of cross-sections (constant or variable). The effectiveness of each pushover method is evaluated by comparing the curvature ductility demands obtained from pushover analyses with those obtained from incremental dynamic analyses (IDAs), during which both far-field and near-field earthquake records are considered, and the peak ground acceleration (PGA) is employed as the intensity measure of the records. High curvature ductility demands are observed at both bottom and mid-height regions in all tall piers. However, in the piers with variable cross-sections, the demands at the mid-height region are even greater than those at the bottom region. For each tall pier, the location of the maximum curvature ductility demand at the mid-height region is determined based on the parametric study. The comparative evaluations indicate the DVA-based pushover method is capable of predicting the curvature ductility demands at both the mid-height and the bottom regions of the tall piers.

OPTIMIZATION OF THE SHAPE AND DIMENSIONS OF THE CONTINUOUS SECTION OF THE DISCRETE-CONTINUOUS INTER-RESONANCE VIBRATING TABLE

Energy-efficient technologies are an important aspect of the development of mechanical engineering. Therefore, the creation of highly efficient vibration technological equipment is an urgent task. There are discrete-continuous inter-resonance vibration machines that have high values of dynamic amplification of oscillations. Rectangular plates or rods are used as the reactive mass of such vibrating machines. However, the rectangular shape of the plate may not be the optimal shape for achieving maximum energy efficiency. To conduct experimental studies of alternative plates with a variable cross-section to determine the optimal shape of the reactive mass of the vibration machine. Methodology. The selection of alternative options of plates with a variable cross-section, which would satisfy the necessary conditions of fastening and the value of the natural frequency of oscillations, was carried out. Experimental studies were carried out on a sample of an inter-resonance vibrating table. The value of the power supply voltage at which loads of different masses were separated from the working body of the vibrating table for each of the plate samples was compared. Findings (results) and originality (novelty). For the first time, experimental studies of the energy efficiency of inter-resonance vibration machines with plates with a variable cross-section installed as a reactive mass were conducted. It was found that the rhomboid shape of the plate is optimal when using it as a continuous section in a vibration machine with an electromagnetic drive. It was determined that the use of diamond-shaped plates as the reactive mass of the vibrating machine can improve the energy efficiency of the inter-resonance vibrating equipment. For further analysis of plates with a variable cross-section as a reactive mass of an inter-resonance vibration machine, it is necessary to calculate and compare their lumped inertia-stiffness parameters.

SIMULATION OF THE COLD-END TEMPERATURE AND THE OPTIMAL CURRENT OF THERMOELECTRIC COOLER WITH VARIABLE SEMICONDUCTOR CROSS SECTION USING LATTICE BOLTZMANN METHOD

In order to evaluate the effects of variable semiconductor cross section on the cold-end temperature of thermoelectric cooler (TEC), the numerical model of the cold-end temperature field of TEC with variable semiconductor cross section was established using the lattice Boltzmann method (LBM) in this work, Firstly, the Chapman-Enskog expansion method was used to derive the LBM model and build the parameter connection between the continuous equation and the discrete model. Secondly, nine different types of cross section of TECs were designed to calculate cold-end temperature field at different electric current. Finally, it is found that increasing the cross-sectional area of the cold end will decrease the minimum cold-end temperature, but increase the optimal current. While maintaining the same cross-sectional area of the cold end, decreasing the hot-end cross-sectional area has less effect on the minimum cold-end temperature but decreases the optimal current. In order to increase the cooling capacity, the cross-sectional area of the cold end can be appropriately larger. TEC of type 2# with a larger cross section at the cold end reduces the cooling temperature by 15.38 K at the cost of a coefficient of performance reduction of 0.021.

ЕЛЕКТРОМАГНІТНЕ ПОЛЕ БОЧКОПОДІБНОГО ПОЛОГО РЕЗОНАТОРА

In the article is investigates the electromagnetic field of a barrel-shaped hollow resonator. It is significant that in the articles of K.M. Tsibizov developed an approach for determining the fields of waveguide resonator devices with a variable cross section. In this article, this approach is extended to a barrel-shaped hollow resonator. The solution of the Airy equation, which was used by K.M. Tsibizov are approximate solutions obtained through solving an equation that reduces to one of the forms of the hypergeometric equation or the Weber equation. The radial and azimuthal components of the field of a barrel-shaped hollow resonator are the corresponding components of the field of a hollow cylindrical resonator, and the longitudinal component is described by a degenerate hypergeometric function. In this article presents the design of a barrel-shaped waveguide resonator with metal ends and writes expressions for the resonant wavelengths of a barrel-shaped resonator with metal ends for H- and E-oscillations. The resonant wavelengths and resonant frequencies for two barrel-shaped resonators with metal ends are given in accordance with a cylindrical resonator with an equal end radius of the barrel-shaped resonator and equal longitudinal dimensions. The article also presents a waveguide resonator with an open left end and writes down the first five roots of the Airy functions. The consideration of such a resonator aims at demonstrating the generality of the considered approach.The design of a barrel-shaped resonator with open ends, the sections of which are critical, is presented.It is indicated that finding solutions to the equations of functions that describe the longitudinal distribution of the field is a demonstration of the generalization of the approach developed by K.M. Tsibizov, and as examples of the study of resonators of variable cross section: a barrel-shaped waveguide resonator with metal ends, a waveguide resonator with an open left end, and a barrel-shaped resonator with open ends, which are shown in the figures.

Research on laser melting deposition forming process and accuracy of thin-walled hollow bending and torsion structural parts with variable cross-section

Research on laser melting deposition forming process and accuracy of thin-walled hollow bending and torsion structural parts with variable cross-section

Research on bearing capacity of cross-type truss boom with variable cross-section of Crawler cranes

The web crossed truss boom is one of the commonly used truss boom structures of crawler cranes. However, the existing calculations fail to consider the limiting effect of the web members' bending resistance on the chord members, and cannot give full play to the load-bearing capacity of the existing structure. This paper takes the top section of the Crawler crane truss boom as the research object. The single-span truss theoretical model is established according to Timoshenko's elastic stability theory. And the theoretical critical load of the variable cross-section boom is obtained with full consideration of the limitation of the web member's bending resistance on the chord members. The finite element method simulation model is compared and verified. Compared with a large number of simulation experiments and theoretical calculations, it can be concluded that the theoretical calculations in this article are highly consistent with the simulation results, verified the assumptions that the web members' bending resistance help to improve the bending resistance of the chord members, and this will provide certain reference to the engineering designers.

Application of variable-height beams with wooden sub-rafter elements in the roof structures of industrial buildings

The investigation pertains to the coating utilized in single-story industrial buildings. Frame constructions with spans of 24, 30, and 36 meters are examined, employing wood-based elements as rafter structures. The reinforced concrete rafter structures exhibit a pitch of 2-3 meters and are configured in the shape of an I-beam. The truss structures along their length are subdivided into seven sections, featuring variable lengths, flange widths, rib thicknesses, and cross-section heights. Deflection calculations consider the nonlinearity of concrete and reinforcement deformations, adhering to prevailing building codes. The elastic solutions method is employed in conjunction with the finite difference method. The proposed coating designs are distinguished by their ease of manufacturing, transportation, and element installation. The wood-composite rafter structure boasts a lower mass compared to reinforced concrete elements, facilitating installation with a lightweight crane and overall diminishing the coating's weight without compromising its structural integrity. Several beam characteristics for spans of 24, 30, and 36 meters include respective mid-span heights of 1.2 meters, 1.4 meters, and 1.5 meters; volumes of 8.23 cubic meters, 9.25 cubic meters, and 10.6 cubic meters; and weights of 19.8 tons, 22.2 tons, and 25.4 tons. The proposed solution allows for the integration of bending moment and stiffness diagrams for the rafter beam configuration.

К вопросу о принципе наименьшего действия при течении несжимаемой жидкости в осесимметричном канале переменного сечения

A formulation of the principle of least action is proposed as applied to the stationary motion of a non-viscous, non-heat-conducting, incompressible fluid in an axisymmetric channel of variable cross section. As a result of solving the variational problem corresponding to this principle, a connection was found between the components of the velocity vector, which made it possible to determine the shape of the channel in which the implementation of the principle of least action is ensured, and the flow parameters both in the channel itself and in the initial outflow region - the region that forms the flow in some conditional section of the entrance to the channel

Cмешение струй газов различной молекулярной массы с высокоскоростным потоком воздуха при изменении их динамического напора

The results of a computational and experimental study of the distributed transverse injection of hydrogen and methane jets into a high-speed flow are presented. The effect of jets on the flow structure in a rectangular channel of a variable cross section is determined when the dynamic head coefficient changes in the range 1.27-6. It is shown that the mixing efficiency increases with an increase in the dynamic head and, to a lesser extent, with an increase in the molecular weight of the injected gas.

Theoretical and Experimental Studies on Valve-less Piezoelectric Pump with Variable Cross Section Arc-shaped Tubes

Theoretical and Experimental Studies on Valve-less Piezoelectric Pump with Variable Cross Section Arc-shaped Tubes

Sensitivity analysis of thermoacoustic oscillation in cryogenics system based on response surface method

In the practical application of cryogenic systems, the presence of thermoacoustic oscillation can cause a series of adverse consequences such as pressure fluctua-tions, thermal leakage, structural damage, and so on. To ensure stable operation of the system, variable cross-section control pipe fittings are introduced, and re-sponse surface analysis method is used to optimize the parameter design of the control pipe fittings. A series of simulations have been conducted and the response surface method is introduced to conduct variance analysis on the simulation re-sults, and obtain the regression model of the system pressure ratio, then analyze the interaction between parameters. The analysis of variance shows that the cor-relation coefficient and adjustment coefficient are both close to 1.0, the signal to noise ratio is high, and the fitting degree of the regression model is good. The prediction error of the regression model for the pressure ratio is within ?10, and the distribution of the residual meets the random normal distribution, which can predict the system performance within the parameter design range. The interaction between pipe diameter and length has no significant impact on the oscillation state, so in design, priority should be given to the impact of location and pipe diameter. This work will provide the basis for determining the optimal control structure size of oscillation-free piping system.

Numerical Analysis of Flow-Induced Vibration and Noise Generation in a Variable Cross-Section Channel

Numerical Analysis of Flow-Induced Vibration and Noise Generation in a Variable Cross-Section Channel

Уточнение результатов численных расчетов частот поперечных колебаний стержня переменного сечения с упругим закреплением экстраполяционным методом

Thearticle describes a numerical experiment with the results of calculating the natural frequencies of transverse vibrations of a rod of variable cross-section with elastic fixation at one of the ends. The possibility of refining by extrapolation the calculated values of natural frequencies obtained by the method of algebraic polynomials of the fifth degree is analyzed. It is shown that ex-trapolation made it possible to increase the accuracy of calculations by the numerical method by 2-3 orders of magnitude