КОМПРЕССОРНЫЙ ПРОФИЛЬ С4: АВТОМАТИЗАЦИЯ ПРОЕКТИРОВАНИЯ

The paper presents the results of designing a compressor blade profile of type C4 using CAD, which implements the method of nonlinear transformation. Girst transformation was used by the authors. All calculations and graphical representations were made in the computer algebra system Mathcad. For the calculation and graphical representation the centreline is approximated with three nonlinear segments in the form of second order Bezier curve. After determining the first and last point of the second order Bezier curve, the coordinates of the middle point on the intersection of tangential lines that start at the first and last point of the curve are determined. After the approximation of three sections with second order Bezier curves the integral function of the blade back (convex side of the contour) of the profile C4 considering the leading and trailing edges are made as arcs. According to the analytical formulas, the geometric parameters of the curved profile were calculated, which are necessary for calculating the strength of the compressor blade.В работе представлены результаты проектирования компрессорного профиля типа С4 с использованием системы автоматизированного проектирования (САПР). В САПР реализован метод нелинейных преобразований Гирста. Все вычисления и графические построения выполнены в интегрированном математическом пакте MathCAD. Для вычислений и построений средняя линия профиля аппроксимируется кривой Безье 2-го порядка с углами наклона касательных в начальной и конечной точках этой кривой, определяемых углом поворота потока в решетке профилей в соответствии с расчетом проточной части компрессора. В работе определены координаты точек сопряжения окружностей входной и выходной кромок с выпуклой и вогнутой частями профиля (спинка и корытце профиля). Спинка и корытце симметричного исходного профиля аппроксимируются дугами окружностей входной и выходной кромок и тремя кривыми Bezier 2-го порядка. После аппроксимации обводов исходного профиля было получено интегральное уравнение исходного симметричного компрессорного профиля типа С4. Аналитическое описание обводов профиля и средней линии дало возможность осуществить нелинейные преобразования Гирста и получить сначала уравнение изогнутого профиля, затем построить одиночный профиль типа С4, потом записать уравнение решетки профилей с заданным углом установки профиля в решетке и соответствующим шагом и построить графический образ компрессорной решетки. В исходной системе координат рассчитаны геометрические параметры симметричного компрессорного профиля, необходимые для прочностных расчетов

Моделирование решетки профилей транспортного газотурбинного двигателя

In the development of gas turbine engines (GTE) it is necessary to simulate the flow section of blade machines (turbines, compressors). At the same time, it is rational to use previously designed profiles and set of profiles with high aerodynamic and efficient performance. This is due to the fact that the process of creating profiles of a nozzle and moving blades set requires the participation of a large team and considerable labor and time costs. Many sets were created for the graphic-analytical design method, which leads to an increase in the development time and a decrease in the universality in terms of the use of programming languages and digital technologies. The article presents the design scheme of the nozzle profile sets of type С8626, the main fragments of the mathematical model of the sets, the results of the design of the original profile С8626 and the sets, comparison of the geometric parameters of the source and built profiles. The contours of the initial profile are approximated by second-order Bezier curves, and the leading and trailing edges are circular arcs. The coordinates of the points of conjugation of the circles of the leading and trailing edges with convex (suction side) and concave (pressure side) profile surfaces are determined. After approximation of the contours of the initial profile, an integral system of equations of the original C8626 turbine profile was obtained. The proposed mathematical model can be considered as independent, it can be a subsystem (software module) of CAD, to represent the shearer of the electronic atlas of profiles and etc.При разработке газотурбинных двигателей необходимо моделировать проточную часть лопаточных машин (турбины, компрессора). При этом рационально использовать ранее спроектированные профили и решетки профилей. Это связано с тем, что процесс создания профилей сопловых и рабочих решеток требует участия большого коллектива и значительных трудовых и временных затрат. Многие решетки создавались для графоаналитического метода проектирования, что приводит к увеличению сроков разработки, снижению универсальности в плане применения языков программирования и цифровых технологий. В статье представлены расчетная схема решетки сопловых профилей типа С8626, основные фрагменты математической модели решетки, а также результаты проектирования и сравнения геометрических параметров исходного и построенного профилей. Обводы исходного профиля аппроксимированы кривыми Безье 2-го порядка, а входная и выходная кромки - дугами окружностей. Определены координаты точек сопряжения окружностей входной и выходной кромок с выпуклой (спинка) и вогнутой (корытце) поверхностями профиля. После аппроксимации обводов исходного профиля была получена интегральная система уравнений исходного турбинного профиля типа С8626. Предлагаемая математическая модель может рассматриваться как самостоятельная или как подсистема (программный модуль) САПР, представлять страницу электронного атласа профилей и т.д

ϒ production in p–Pb collisions at √sNN=8.16 TeV

ϒ production in p–Pb interactions is studied at the centre-of-mass energy per nucleon–nucleon collision √sNN = 8.16 TeV with the ALICE detector at the CERN LHC. The measurement is performed reconstructing bottomonium resonances via their dimuon decay channel, in the centre-of-mass rapidity intervals 2.03 < ycms < 3.53 and −4.46 < ycms < −2.96, down to zero transverse momentum. In this work, results on the ϒ(1S) production cross section as a function of rapidity and transverse momentum are presented. The corresponding nuclear modification factor shows a suppression of the ϒ(1S) yields with respect to pp collisions, both at forward and backward rapidity. This suppression is stronger in the low transverse momentum region and shows no significant dependence on the centrality of the interactions. Furthermore, the ϒ(2S) nuclear modification factor is evaluated, suggesting a suppression similar to that of the ϒ(1S). A first measurement of the ϒ(3S) has also been performed. Finally, results are compared with previous ALICE measurements in p–Pb collisions at √sNN = 5.02 TeV and with theoretical calculations.publishedVersio

(Anti-)deuteron production in pp collisions at 1as=13TeV

The study of (anti-)deuteron production in pp collisions has proven to be a powerful tool to investigate the formation mechanism of loosely bound states in high-energy hadronic collisions. In this paper the production of (anti-)deuterons is studied as a function of the charged particle multiplicity in inelastic pp collisions at s=13 TeV using the ALICE experiment. Thanks to the large number of accumulated minimum bias events, it has been possible to measure (anti-)deuteron production in pp collisions up to the same charged particle multiplicity (d Nch/ d \u3b7 3c 26) as measured in p\u2013Pb collisions at similar centre-of-mass energies. Within the uncertainties, the deuteron yield in pp collisions resembles the one in p\u2013Pb interactions, suggesting a common formation mechanism behind the production of light nuclei in hadronic interactions. In this context the measurements are compared with the expectations of coalescence and statistical hadronisation models (SHM)

Multiplicity dependence of inclusive J/psi production at midrapidity in pp collisions at root s=13 TeV

Measurements of the inclusive J/psi yield as a function of charged-particle pseudorapidity density dN(ch)/d eta in pp collisions at root s = 13 TeV with ALICE at the LHC are reported. The J/psi meson yield is measured at midrapidity (vertical bar y vertical bar <0.9) in the dielectron channel, for events selected based on the charged-particle multiplicity at midrapidity (vertical bar eta vertical bar <1) and at forward rapidity (-3.7 <eta <-1.7 and 2.8 <eta <5.1); both observables are normalized to their corresponding averages in minimum bias events. The increase of the normalized J/psi yield with normalized dN(ch)/d eta is significantly stronger than linear and dependent on the transverse momentum. The data are compared to theoretical predictions, which describe the observed trends well, albeit not always quantitatively. (C) 2020 European Organization for Nuclear Research. Published by Elsevier B.V.Peer reviewe

Elliptic flow of charged particles at midrapidity relative to the spectator plane in Pb–Pb and Xe–Xe collisions

Measurements of the elliptic flow coefficient relative to the collision plane defined by the spectator neutrons v2{ SP} in collisions of Pb ions at center-of-mass energy per nucleon–nucleon pair √ 2.76 TeV and Xe ions at √ sNN = sNN =5.44 TeV are reported. The results are presented for charged particles produced at midrapidity as a function of centrality and transverse momentum for the 5–70% and 0.2–6 GeV/c ranges, respectively. The ratio between v2{ SP} and the elliptic flow coefficient relative to the participant plane v2{4}, estimated using four-particle correlations, deviates by up to 20% from unity depending on centrality. This observation differs strongly from the magnitude of the corresponding eccentricity ratios predicted by the TRENTo and the elliptic power models of initial state fluctuations that are tuned to describe the participant plane anisotropies. The differences can be interpreted as a decorrelation of the neutron spectator plane and the reaction plane because of fragmentation of the remnants from the colliding nuclei, which points to an incompleteness of current models describing the initial state fluctuations. A significant transverse momentum dependence of the ratio v2{ SP}/v2{4} is observed in all but the most central collisions, which may help to understand whether momentum anisotropies at low and intermediate transverse momentum have a common origin in initial state f luctuations. The ratios of v2{ SP} and v2{4} to the corresponding initial state eccentricities for Xe–Xe and Pb–Pb collisions at similar initial entropy density show a difference of (7.0 ±0.9)%with an additional variation of +1.8% when including RHIC data in the TRENTo parameter extraction. These observations provide new experimental constraints for viscous effects in the hydrodynamic modeling of the expanding quark–gluon plasma produced in heavy-ion collisions at the LHC

First measurement of Ωc0 production in pp collisions at s=13 TeV

The inclusive production of the charm–strange baryon 0 c is measured for the first time via its hadronic √ decay into −π+ at midrapidity (|y| &lt;0.5) in proton–proton (pp) collisions at the centre-of-mass energy s =13 TeV with the ALICE detector at the LHC. The transverse momentum (pT) differential cross section multiplied by the branching ratio is presented in the interval 2 &lt; pT &lt; 12 GeV/c. The pT dependence of the 0 c-baryon production relative to the prompt D0-meson and to the prompt 0 c-baryon production is compared to various models that take different hadronisation mechanisms into consideration. In the measured pT interval, the ratio of the pT-integrated cross sections of 0 c and prompt + c baryons multiplied by the −π+ branching ratio is found to be larger by a factor of about 20 with a significance of about 4σ when compared to e+e− collisions

КОМПРЕССОРНЫЙ ПРОФИЛЬ С4: АВТОМАТИЗАЦИЯ ПРОЕКТИРОВАНИЯ

The paper presents the results of designing a compressor blade profile of type C4 using CAD, which implements the method of nonlinear transformation. Girst transformation was used by the authors. All calculations and graphical representations were made in the computer algebra system Mathcad. For the calculation and graphical representation the centreline is approximated with three nonlinear segments in the form of second order Bezier curve. After determining the first and last point of the second order Bezier curve, the coordinates of the middle point on the intersection of tangential lines that start at the first and last point of the curve are determined. After the approximation of three sections with second order Bezier curves the integral function of the blade back (convex side of the contour) of the profile C4 considering the leading and trailing edges are made as arcs. According to the analytical formulas, the geometric parameters of the curved profile were calculated, which are necessary for calculating the strength of the compressor blade.В работе представлены результаты проектирования компрессорного профиля типа С4 с использованием системы автоматизированного проектирования (САПР). В САПР реализован метод нелинейных преобразований Гирста. Все вычисления и графические построения выполнены в интегрированном математическом пакте MathCAD. Для вычислений и построений средняя линия профиля аппроксимируется кривой Безье 2-го порядка с углами наклона касательных в начальной и конечной точках этой кривой, определяемых углом поворота потока в решетке профилей в соответствии с расчетом проточной части компрессора. В работе определены координаты точек сопряжения окружностей входной и выходной кромок с выпуклой и вогнутой частями профиля (спинка и корытце профиля). Спинка и корытце симметричного исходного профиля аппроксимируются дугами окружностей входной и выходной кромок и тремя кривыми Bezier 2-го порядка. После аппроксимации обводов исходного профиля было получено интегральное уравнение исходного симметричного компрессорного профиля типа С4. Аналитическое описание обводов профиля и средней линии дало возможность осуществить нелинейные преобразования Гирста и получить сначала уравнение изогнутого профиля, затем построить одиночный профиль типа С4, потом записать уравнение решетки профилей с заданным углом установки профиля в решетке и соответствующим шагом и построить графический образ компрессорной решетки. В исходной системе координат рассчитаны геометрические параметры симметричного компрессорного профиля, необходимые для прочностных расчетов

CAD System for Automatic Design of C1 Compressor Profile

A system for computer-aided design (CAD) for the construction of a C1 compressor profile (CAD_C1) in the integrated Mathcad package is developed. Results of the design of a symmetric initial C1 profile and a curved C1-based profile CAD-C1 are presented. CAD-C1 is constructed according to a modular principle, i.e., it constitutes a complex of information-bound computational software modules. The principal advantage of such a structure of the system is that each module is solved as an individual complete problem and, independently of the other modules, may be altered in the course of development and improvement of the system. Independent connection (complementation) of other modules and systems is also possible. Designs of two variants of curved profiles with identical (practically maximal) turning angle of the flow is implemented in corresponding software modules, using a method of growing thickness of the profile along the normal to the center line of the profile and a method based on nonlinear Hearst transformations. The geometric characteristics of the different design variants are calculated, statistical estimation of the correlation indices of the approximation results is performed, graphical construction of the variant profiles is realized, and the geometric parameters of the profiles are varied along the length of the profile chord. CAD_System C1 may be considered as an autonomous system and as a subsystem. © 2019, Springer Science+Business Media, LLC, part of Springer Nature