Математические модели высокого уровня в задачах расчета параметров авиационных ГТД

The article describes high-level mathematical models developed to solve special problems arising at later stages of design with regard to calculation of the aircraft gas turbine engine (GTE) under real operating conditions. The use of blade row mathematics models, as well as mathematical models of a higher level, including 2D and 3D description of the working process in the engine units and components, makes it possible to determine parameters and characteristics of the aircraft engine under conditions significantly different from the calculated ones.The paper considers application of mathematical modelling methods (MMM) for solving a wide range of practical problems, such as forcing the engine by injection of water into the flowing part, estimate of the thermal instability effect on the GTE characteristics, simulation of engine start-up and windmill starting condition, etc. It shows that the MMM use, when optimizing the laws of the compressor stator control, as well as supplying cooling air to the hot turbine components in the motor system, can significantly improve the integral traction and economic characteristics of the engine in terms of its gas-dynamic stability, reliability and resource.It ought to bear in mind that blade row mathematical models of the engine are designed to solve purely "motor" problems and do not replace the existing models of various complexity levels used in calculation and design of compressors and turbines, because in “quality” a description of the working processes in these units is inevitably inferior to such specialized models.It is shown that the choice of the mathematical modelling level of an aircraft engine for solving a particular problem arising in its designing and computational study is to a large extent a compromise problem. Despite the significantly higher "resolution" and information ability the motor mathematical models containing 2D and 3D approaches to the calculation of flow in blade machine components have found quite a limited application in practice of computational studies of the aircraft engines and are mainly used in designing the fans, compressors and turbines, as well as in verifying autonomous calculations of these units.В статье описаны математические модели высокого уровня, предназначенные для решения специальных задач, возникающих на более поздних стадиях проектирования и связанных с расчетом авиационного ГТД в реальных условиях эксплуатации. Применение повенцовых математических моделей, а также математических моделей более высокого уровня, включающих 2D и 3D описание рабочего процесса в узлах и элементах двигателя, позволяет определять параметры и характеристики авиационного двигателя в условиях, значительно отличающихся от расчетных.Рассмотрено применения методов математического моделирования (МММ) при решении широкого ряда практических задач, таких как форсирование двигателя впрыском воды в проточную часть, оценка влияния тепловой нестационарности на характеристики ГТД, моделирование режимов запуска и авторотации двигателя и другие. Показано, что применение МММ при оптимизации в системе двигателя законов регулирования направляющих аппаратов компрессора, а также подачи охлаждающего воздуха в горячие элементы турбины может позволить значительно улучшить интегральные тягово-экономические характеристики двигателя с учетом сохранения его газодинамической устойчивости, надежности и ресурса.Следует иметь в виду, что повенцовые математические модели двигателя предназначены для решения чисто «двигательных» задач и не подменяют существующие модели различного уровня сложности, применяемые при расчете и проектировании компрессоров и турбин, так как по «качеству» описания рабочих процессов в этих узлах неизбежно уступают таким специализированным моделям.Показано, что выбор уровня математического моделирования авиационного двигателя для решения той или иной задачи, возникающей при его проектировании и расчетном исследовании, является в значительной степени компромиссной задачей. Несмотря на существенно более высокую «разрешающая способность» и информативность двигательные математические модели, содержащие 2D и 3D подходы к расчету течения в элементах лопаточных машин, нашли достаточно ограниченное применение в практике расчетных исследований авиационных двигателей, а применяются, в основном, при проектировании вентиляторов, компрессоров и турбин, а также поверочных автономных расчетах этих узлов

Ординарные математические модели в задачах расчета параметров авиационных ГТД

The paper presents the analytical review results of the ordinary mathematical models of the operating process used to study aviation GTE parameters and characteristics at all stages of its creation and operation. Considers the mathematical models of the zero and the first level, which are mostly used when solving typical problems in calculating parameters and characteristics of engines.Presents a number of practical problems arising in designing aviation GTE for various applications.The application of mathematical models of the zero-level engine can be quite appropriate when the engine is considered as a component in the aircraft system to estimate its calculated individual flight performance or when modeling the flight cycle of the aircrafts of different purpose.The paper demonstrates that introduction of correction functions into the first-level mathematical models in solving typical problems (influence of the Reynolds number, characteristics deterioration of the units during the overhaul period of engine, as well as influence of the flow inhomogeneity at the inlet because of manufacturing tolerance, etc.) enables providing a sufficient engineering estimate accuracy to reflect a realistic operating process in the engine and its elements.Приведены результаты аналитического обзора ординарных математических моделей рабочего процесса, применяемых для исследования параметров и характеристик авиационных ГТД на всех этапах его создания и эксплуатации. Рассмотрены математические модели нулевого и первого уровня, нашедшие наибольшее применение при решении типовых задач расчета параметров и характеристик двигателей.Показано, что хотя используемые в ММД первого уровня подходы в своем классическом варианте и используют определенные допущения, характерные для одномерного идеализированного подхода (прежде всего, о неизменности характеристик узлов во всем диапазоне эксплуатационных режимов и условий на входе в двигатель), с помощью определенных дополнительных доработок они могут быть использованы и для расчетных оценок параметров и характеристик в реальных условиях работы двигателя.Продемонстрировано, что при использовании математических моделей двигателя первого уровня могут возникать ситуации, когда даже путем введения поправочных функций не удается с достаточной степенью точности отразить реальный рабочий процесс в двигателе и его элементах. В этих случаях следует использовать математические модели двигателя более высокого уровня

Ordinary Mathematical Models in Calculating the Aviation GTE Parameters

The paper presents the analytical review results of the ordinary mathematical models of the operating process used to study aviation GTE parameters and characteristics at all stages of its creation and operation. Considers the mathematical models of the zero and the first level, which are mostly used when solving typical problems in calculating parameters and characteristics of engines.Presents a number of practical problems arising in designing aviation GTE for various applications.The application of mathematical models of the zero-level engine can be quite appropriate when the engine is considered as a component in the aircraft system to estimate its calculated individual flight performance or when modeling the flight cycle of the aircrafts of different purpose.The paper demonstrates that introduction of correction functions into the first-level mathematical models in solving typical problems (influence of the Reynolds number, characteristics deterioration of the units during the overhaul period of engine, as well as influence of the flow inhomogeneity at the inlet because of manufacturing tolerance, etc.) enables providing a sufficient engineering estimate accuracy to reflect a realistic operating process in the engine and its elements

Using Mathematical Modeling Methods for Estimating Entrance Flow Heterogeneity Impact on Aviation GTE Parameters and Performances

The paper considers methodological approaches to the mathematical models (MM) of various levels, dedicated to estimate an impact of the entrance flow heterogeneity on the main parameters and performances of the aviation GTE and it units. By an example of calculation of a twin-shaft turbofan engine in cruiser mode, demonstrates engineering mathematical model capabilities to define the impact of the total pressure field distortion on engine trust and air flow parameters, and also gas dynamic stability margin of the both compressors.It is shown that the presented first level mathematical model allows us to estimate sufficiently the impact of entrance total pressure heterogeneity on the engine parameters. Here reliability of calculations is proved to be true by their comparison with the results, obtained owing to well fulfilled 2D & 3D mathematical models of the engine, which have been repeatedly identified by the results of experiments.It is shown that received results including those on decreasing values of stability margin of both compressors can be used for tentative estimates when choosing a desirable stability margin, providing steady operation of compressors and engine in an entire range of its operating modes. Carrying out a definitive testing calculation using the specialized engine MM of a higher level will not only confirm the results obtained, but also reduce their expected error with regard to the real values reached as a result of tests

The High Level Mathematical Models in Calculating Aircraft Gas Turbine Engine Parameters

The article describes high-level mathematical models developed to solve special problems arising at later stages of design with regard to calculation of the aircraft gas turbine engine (GTE) under real operating conditions. The use of blade row mathematics models, as well as mathematical models of a higher level, including 2D and 3D description of the working process in the engine units and components, makes it possible to determine parameters and characteristics of the aircraft engine under conditions significantly different from the calculated ones.The paper considers application of mathematical modelling methods (MMM) for solving a wide range of practical problems, such as forcing the engine by injection of water into the flowing part, estimate of the thermal instability effect on the GTE characteristics, simulation of engine start-up and windmill starting condition, etc. It shows that the MMM use, when optimizing the laws of the compressor stator control, as well as supplying cooling air to the hot turbine components in the motor system, can significantly improve the integral traction and economic characteristics of the engine in terms of its gas-dynamic stability, reliability and resource.It ought to bear in mind that blade row mathematical models of the engine are designed to solve purely "motor" problems and do not replace the existing models of various complexity levels used in calculation and design of compressors and turbines, because in “quality” a description of the working processes in these units is inevitably inferior to such specialized models.It is shown that the choice of the mathematical modelling level of an aircraft engine for solving a particular problem arising in its designing and computational study is to a large extent a compromise problem. Despite the significantly higher "resolution" and information ability the motor mathematical models containing 2D and 3D approaches to the calculation of flow in blade machine components have found quite a limited application in practice of computational studies of the aircraft engines and are mainly used in designing the fans, compressors and turbines, as well as in verifying autonomous calculations of these units

Analysis of Cruising Fuel Conservation Capabilities of Multi-Mode Engine with the Third Contour

Based on the analysis results from the patent search and review of domestic and foreign publications in variable cycle engines (VCE) was created a classification of the possible schematic diagrams of VCE realizing three-stream engine technologies (the adaptive low pressure compressor (LPC) with air extraction behind stages, FLADE compressor, various feeding types of extraction air to the flowing path of the engine, etc.).To estimate a three-stream engine application as a part of the power-plant (PP) efficiency, was chosen an adaptive LPC technology scheme with the third contour air bypass beyond the critical section of a basic jet nozzle for which a mathematical model (MM) of the PP has been created on the basis of one-dimensional MM of the engine. The MM of the PP included 3D modeling results of the air inlet, the LPC with various air extractions to the third contour, and the jet nozzle taking into account the interaction between the basic stream and the third contour stream.The predicted performance of an air inlet have been used to estimate the changes in a total pressure restoration coefficient and an additional resistance coefficient along «a fluid contour» when air extraction is included in the third contour in several cruiser modes of flight.An integrated characteristic of the LPC has been received at various points and levels of air extraction to the third contour, and parameters of extracted air (depending on the point and amount of air extraction, and also on the fan operating mode) have been calculated. When analyzing the obtained calculation results, the effect of pressure lines displacement to the right (towards the large reduced rates), growth of efficiency values, and also position displacement of its maximum value to the left (towards the descent reduced rates) has been found.To estimate how air extraction of the third contour between the plates of an adjustable supersonic nozzle impacts on its aft deck resistance various parameters of the flowing out air in subsonic cruiser mode of flight have been calculated.As a result of calculations according to the PP MM, under near-the-earth conditions of the subsonic cruiser flight, the effective specific fuel consumption has been reduced by 12,5 %.The results reached allow us to expect significant subsonic effective fuel conservation of the three-stream engine. To prove the calculated results it is further necessary to achieve them under full-scale conditions using the engine-demonstrator.</p