RU2699869C1 - Method of determining the sufficiency of cooling oil in a turbojet engine - Google Patents

Abstract

FIELD: aviation.

SUBSTANCE: invention relates to aircraft engineering and can be used in tests of aircraft with turbojet engines to determine the adequacy of oil cooling in design temperature conditions. Proposed method consists in performing flight at selected mode, during flight measuring fuel temperature at fuel-and-oil heat exchanger outlet (FOHE) and oil temperature at engine output, after flight determining parameters of mathematical model, determining fuel temperature at engine inlet under design temperature conditions and initial oil temperature at engine output, then, by successive approximations method, when solving system of differential equations, calculating maximum oil temperature at engine output and comparing it with maximum permissible temperature, if maximum oil temperature at engine outlet does not exceed maximum permissible temperature, conclusion is made on oil cooling sufficiency.

EFFECT: technical result of invention makes it possible to increase reliability of determination of sufficiency of oil cooling in FOHE turbojet engine.

1 cl, 2 dwg

Description

The invention relates to the field of aviation, and in particular to methods for maintaining stable operation of a turbojet engine (turbojet engine).

To ensure reliable operation of the power plant, in particular the turbojet engine, it is necessary to maintain a certain temperature of its elements and systems, including the oil system. Exceeding the temperature may lead to overheating of the turbojet engine. To avoid overheating, a certain amount of heat must be removed through the cooling system.

Cooling systems are divided into two groups: air and liquid. In the first group, engine oil is cooled by atmospheric air in an air-oil heat exchanger (TDC). In the second group, the oil is cooled by fuel (aviation kerosene) in a fuel-oil heat exchanger (hereinafter - TMT), which is usually part of the turbojet engine.

Checking the sufficiency of oil cooling in the turbojet engine is one of the tasks of flight tests. Since the engine should operate normally under any conditions, and the most severe cooling conditions are obtained at high outdoor temperatures and high initial temperatures of working fluids (fuel, oil), cooling is usually calculated and checked not in a standard atmosphere (CA), but in the so-called "calculated atmospheric temperature conditions" (RATU) or in one way or another specially designed calculated temperature conditions (RTU).

As the RATU, the following law of changing the outdoor temperature with height is sometimes applied:

where t _H is the air temperature taken for calculation at a height of H, t _H.CA is the air temperature at a height of H in a standard atmosphere.

In some cases, it is accepted that according to RATU the temperature near the earth is 40 ° C, and then it falls linearly according to some law. Sometimes, on the contrary, an assessment of the performance of certain units is necessary to produce for low air temperatures [1. Vedrov B.C., Taits M.A. Flight tests of aircraft. State Publishing House of the Defense Industry, Moscow, 1951, pp. 28-29.].

, равной 45°С [2. Летные испытания специальных устройств и систем силовых установок самолетов и вертолетов. Под ред. Т.П. Долголенко, М.: Машиностроение, 1984, стр. 100-101.].In other cases, for liquid cooling systems, the RTU can be determined by the temperature of the fuel in the fuel tanks of the aircraft

equal to 45 ° C [2. Flight tests of special devices and systems of power plants of aircraft and helicopters. Ed. T.P. Dolgolenko, Moscow: Engineering, 1984, pp. 100-101.].

принимают равной 120°С. В общем случае

назначают в зависимости от эксплуатационных ограничений работы агрегатов топливной системы и проверки их работы в экстремальных условиях.Design temperature conditions may also be determined by various operational limitations. For example, the temperature of the fuel at the engine inlet, for reasons of thermal stability, should not exceed 120 ° C. To account for this limitation

taken equal to 120 ° C. In general

appoint depending on the operational limitations of the operation of the units of the fuel system and verification of their operation in extreme conditions.

The degree of cooling of the oil is considered satisfactory if, under the design atmospheric conditions, the maximum temperature of the oil at the engine inlet does not exceed the values provided by the operating manual:

, высоты полета Н (измеренной в километрах), температуры наружного воздуха t_H и пересчета максимальной температуры масла, измеренной в фактических условиях летных испытаний, в максимальную температуру масла, соответствующую РАТУ по формулеA known method of determining the sufficiency of oil cooling in terms of RATU, which consists in registering during the flight the maximum temperature of the oil at the engine inlet

, flight altitude N (measured in kilometers), outdoor temperature t _H and recalculation of the maximum oil temperature, measured under actual flight test conditions, to the maximum oil temperature corresponding to the PATH according to the formula

- поправочный коэффициент, зависящий от температуры наружного воздуха и температуры масла, равный 0,3…1,0 [2. стр. 101]. Недостатком этого способа является его ограниченное применение только для турбовинтовых двигателей (ТВД), оборудованных ВМТ.Where

- correction factor, depending on the outdoor temperature and oil temperature, equal to 0.3 ... 1.0 [2. p. 101]. The disadvantage of this method is its limited use only for turboprop engines (TVD) equipped with TDC.

, высоты полета Н (измеренной в километрах), температуры наружного воздуха t_H.B и пересчета температуры масла, измеренной в фактических условиях летных испытаний, в максимальную температуру масла, соответствующую РАТУ, по формуле:The known method [1. p. 448-458.] determining the adequacy of oil cooling in terms of RATU, which consists in registering the temperature of the oil at the engine inlet

, flight altitude N (measured in kilometers), outdoor temperature t _HB and recalculation of the oil temperature, measured under actual flight test conditions, to the maximum oil temperature corresponding to RATU, according to the formula:

where A is a coefficient depending on the type of engine, determined experimentally and having a value of the order of 200;

t _N.RATU - the value of the outdoor temperature, changing according to any given law, for example,

where t _H.CA - standard outdoor temperature at a height of N.

The disadvantage of this method is that it is applicable only to piston engines equipped with TDC.

A known experimental method for determining the sufficiency of oil cooling, in which the temperature characteristics of the oil system of a power plant of an aircraft with an engine equipped with TMT, is determined by refueling fuel tanks with a temperature of 45 ° C or conducting flight tests in climatic conditions where the ambient temperature is not lower than 38 ° C [2. p. 99, 102.]. The degree of oil cooling is considered satisfactory if the oil temperature at the engine exit (inlet at the TMT) for given flight and engine operation modes are within the limits allowed by the operating instructions. The disadvantage of this method is the need for special fuel preparation (heating to 45 ° C) and the search for the specified climatic conditions.

, т.е. получают кривую разогрева. Для проверки достаточности охлаждения находят максимальную температуру масла на кривой разогрева и сравнивают с предельно-допустимой температурой по техническим условиям. Недостатком этого способа является то, что он применим только для поршневых двигателей, оборудованных ВМТ.There is a method based on the preparation of the differential equation of the heat balance between heating the oil in the engine and cooling it in the heat exchanger (in this case, the TDC) [1. p. 459-462.]. As a result of its solution, for a given dependence of the outdoor temperature t _H on the flight altitude (in particular, when setting the change in t _H in the RATU) and given flight and engine operation modes, a functional dependence of the oil temperature change on the flight altitude is obtained

, i.e. get a warming curve. To check the sufficiency of cooling, find the maximum oil temperature on the heating curve and compare with the maximum allowable temperature according to the technical conditions. The disadvantage of this method is that it is applicable only to piston engines equipped with TDC.

Closest to the invention is a method for determining the sufficiency of oil cooling in a turbojet engine [Patent for invention No. 2533597], which consists in flying in the selected mode, during the flight, measure the temperature of the fuel at the engine inlet and the temperature of the oil at the engine outlet, after the flight, determine the average fuel temperature and the maximum oil temperature achieved in the performed mode, determine the fuel temperature at the engine inlet at RTU and the initial oil temperature at the exit one of the engine, after which the method of successive approximations calculates the maximum oil temperature at the engine outlet and compares it with the maximum permissible temperature, if the maximum oil temperature at the engine outlet does not exceed the maximum permissible temperature, conclude that the cooling of the oil is sufficient.

The disadvantage of this method is that it is applicable only to schemes of cooling systems without transferring fuel to the aircraft’s fuel tank, and only in cases where heating occurs quickly enough, the engine goes to steady-state thermal mode and the oil temperature assumes a steady-state maximum value. However, in most cases, cooling systems are used when part of the fuel, having passed the TMT, is transferred to the fuel tank, and the other part enters the combustion chamber of the gas turbine engine (GTE). In this case, the heating process can continue throughout the entire regime with fixing the maximum oil temperature at the end of the mode. [3. Beach M.M. et al., “Lubrication of aircraft gas turbine engines”, Moscow, Mechanical Engineering, 1979, p. 43, 137 ... 139].

The technical result of the invention is to increase the reliability of determining the sufficiency of oil cooling in the TMT of a turbojet engine (turbojet engine).

и выбор начальной температуры масла на входе в ТМТ

, а так же вычисление методом последовательных приближений максимальной температуры масла на входе в ТМТ; отличающийся тем, что в процессе полета осуществляют частичный перепуск топлива, после прохождения им ТМТ, из магистрали подачи топлива в двигатель через перепускной клапан в топливный бак, и измеряют температуру топлива на выходе из ТМТ.The specified technical result is achieved by the fact that in the method for determining the sufficiency of oil cooling in a turbojet engine with ТМТ, including the execution of a flight regime critical for oil overheating, measuring the oil temperature at the inlet of ТМТ during flight, calculating the maximum oil temperature at ТМТ inlet, comparing the calculated maximum temperature of oil at the inlet of TMT at the maximum permissible temperature, determination after flight of the temperature of the fuel at the entrance to TMT at the calculated temperature conditions x

and selection of the initial oil temperature at the inlet of TMT

, as well as the calculation by the method of successive approximations of the maximum oil temperature at the inlet of TMT; characterized in that during the flight, a partial bypass of the fuel is carried out, after passing through the TMT, from the line for supplying fuel to the engine through the bypass valve to the fuel tank, and the temperature of the fuel at the exit of the TMT is measured.

The method may include calculating the maximum temperature of the oil at the inlet of the TMT by the method of successive approximations, based on the solution of a system of differential equations consisting of equations A and B describing a closed system of oil circulation in a gas turbine engine (A) and an open system for transferring fuel to a fuel tank (B) after passing through the fuel TMT such that, after the critical flight condition against overheating oil, selection parameters are determined by a _e, B _e, C _e, R _E, R _E, S _E mathematical process model azogreva oil and fuel such that the mathematical model (the solution of differential equations) corresponds to the experimentally obtained curves for the heating oil and fuel with a certain accuracy:

i = 0, 1, 2, ...,

Where

- соответственно теплоемкость и вязкость масла при температуре

Where

- respectively, the heat capacity and viscosity of the oil at a temperature

- коэффициент теплоотдачи от масла к стенкам трубок ТМТ при температуре

- heat transfer coefficient from oil to the walls of the TMT tubes at a temperature

- соответственно теплоемкость и вязкость топлива при температуре

- respectively, the heat capacity and viscosity of the fuel at a temperature

- коэффициент теплоотдачи от стенок трубок ТМТ к топливу при температуре

- heat transfer coefficient from the walls of the TMT tubes to fuel at a temperature

- соответственно теплоемкость и вязкость масла при температуре

- respectively, the heat capacity and viscosity of the oil at a temperature

- коэффициент теплоотдачи от масла к стенкам трубок ТМТ при температуре

- heat transfer coefficient from oil to the walls of the TMT tubes at a temperature

- соответственно теплоемкость и вязкость топлива при температуре

- respectively, the heat capacity and viscosity of the fuel at a temperature

- коэффициент теплоотдачи от стенок трубок ТМТ к топливу при температуре

- heat transfer coefficient from the walls of the TMT tubes to fuel at a temperature

- параметр математической модели,

- parameter of the mathematical model,

корректировочные коэффициенты до тех пор пока разница вычисленных температур масла в текущем и предыдущем приближениях не станет меньше предопределенной величины погрешности δ.

correction factors until the difference between the calculated oil temperatures in the current and previous approximations becomes less than the predetermined error δ.

The invention is illustrated by drawings, where in FIG. 1 shows a diagram of a gas turbine engine system with partial bypass of fuel; in FIG. 2 is a diagram of the combination of experimental and theoretical data obtained by solving the system of differential equations (A, B) for oil and fuel.

The method allows, according to experimental data obtained under the same conditions, without conducting a new flight experiment to determine the expected maximum oil temperature at a different fuel temperature and conclude that the cooling of the oil is sufficient. The proposed method can be implemented for a cooling system of a turbojet engine with TMT, equipped with a system of partial bypass of fuel into the fuel tank, after passing through it TMT (Fig. 1). In such a cooling system, the heated oil from the engine 1 is pumped out by oil pumps and supplied to the TMT 2 for cooling, then it enters the engine again. The fuel supplied from the fuel tank 3 to the engine, passing TMT and cooling the oil, is partially bypassed through the bypass valve 4 into the fuel tank, the rest enters the combustion chamber. In such a cooling system, it can be assumed that the temperature of the oil at the engine inlet is equal to the temperature of the oil at the outlet of the TMT, the temperature of the oil at the outlet of the engine is equal to the temperature of the oil at the inlet of the TMT. In this system, it is customary to call the temperature of the fuel at the engine inlet the temperature of the fuel at the inlet of the TMT.

The proposed method is as follows.

1. Choose a flight mode (flight altitude and engine operating conditions) at which oil overheating is most possible (the mode is critical in relation to oil overheating), which is known from flight test practice.

и температуру масла на входе в ТМТ

(j=1…n, где n - число замеров). После полета определяют начальную температуру масла

и топлива

максимальную температуру масла

и топлива

достигнутую на выполненном режиме.Perform a flight in the selected mode and periodically measure during the flight, the temperature of the fuel at the exit of TMT

and oil temperature at the inlet of TMT

(j = 1 ... n, where n is the number of measurements). After the flight, the initial oil temperature is determined

and fuel

maximum oil temperature

and fuel

achieved in completed mode.

и

для известных марок масла и топлива определяют методом подбора из известного по опыту диапазона исходные числовые значения параметров математической модели процесса разогрева масла и топлива А_Э, В_Э, С_Э, Р_Э, R_Э, S_Э такие, чтобы погрешность адекватности решения системы дифференциальных уравнений (1) (математической модели) по маслу и топливу Δ_M, Δ_T находилась в пределах границ доверительного интервала с заданной доверительной вероятностью Р_Д=0,952. According to the temperatures obtained

and

for well-known brands of oil and fuel, the initial numerical values of the parameters of the mathematical model of the process of heating the oil and fuel A _E , V _E , C _E , R _E , R _E , S _E such that the accuracy of the solution of the differential equations (1) (mathematical model) for oil and fuel Δ _M , Δ _T was within the boundaries of the confidence interval with a given confidence probability P _D = 0.95

where σ _M , σ _T is the standard deviation of the differences between the measured data for oil and fuel and the corresponding values of the mathematical model

- значения средних величинWhere

- mean values

[four. P.V. Novitsky, I.A. Zograf, "Evaluation of errors of measurement results, 2nd edition, Leningrad, Energomashizdat, 1991, S. 82 ... 86, 211 ... 240"].

численным методом в математической системе «Mathcad». Диапазон, из которого выбираются параметры математической модели, следующий: А_Э=0,65…1,68 град/сек; В_Э=0,006…0,028 сек^-1; С_Э=0,006…0,025 сек^-1; Р_Э=10…30 град/сек; R_Э=0,01…0,03 сек^-1; S_Э=0,1…0,3 сек^-1.The solution of the system of differential equations in the independent variable τ (time) is performed under the initial conditions

numerical method in the mathematical system "Mathcad". The range from which the parameters of the mathematical model are selected is as follows: А _Э = 0.65 ... 1.68 deg / s; In _E = 0.006 ... 0.028 sec ^-1 ; With _E = 0.006 ... 0.025 sec ^-1 ; R _E = 10 ... 30 deg / s; R _e = 0.01 ... 0.03 sec ^-1 ; S _E = 0.1 ... 0.3 sec ^-1 .

. Произвольно выбирают начальную температуру масла на выходе из двигателя

(i=0). В первом приближении принимаем максимальную температуру масла

максимальную температуру топлива

. Начальную температуру масла на выходе из двигателя

рекомендуется выбирать на 10...30 градусов больше

Если, например,

=120°С, то

=140°С.3. Based on the permissible operating conditions (operational limitations of the operation of the fuel system units) determine (assign) the temperature of the fuel at the engine inlet at RTU

. Optionally select the initial oil temperature at the engine outlet

(i = 0). In a first approximation, we take the maximum oil temperature

maximum fuel temperature

. Initial engine oil temperature

it is recommended to choose 10 ... 30 degrees more

If, for example,

= 120 ° C, then

= 140 ° C.

и корректировочные коэффициенты

4. The parameter is calculated

and adjustment factors

5. Next, the maximum oil temperature at the engine outlet is calculated by the method of successive approximations, as follows.

The following complex parameters are calculated:

соответственно теплоемкость и вязкость масла при температуре

Where

respectively heat capacity and viscosity of oil at temperature

- коэффициент теплоотдачи от масла к стенкам трубок ТМТ при температуре

- heat transfer coefficient from oil to the walls of the TMT tubes at a temperature

и

- соответственно теплоемкость и вязкость топлива при температуре

and

- respectively, the heat capacity and viscosity of the fuel at a temperature

- коэффициент теплоотдачи от стенок трубок ТМТ к топливу при температуре

- heat transfer coefficient from the walls of the TMT tubes to fuel at a temperature

и

- соответственно теплоемкость и вязкость масла при температуре

and

- respectively, the heat capacity and viscosity of the oil at a temperature

- коэффициент теплоотдачи от масла к стенкам трубок ТМТ при температуре

- heat transfer coefficient from oil to the walls of the TMT tubes at a temperature

- соответственно теплоемкость и вязкость топлива при температуре

- respectively, the heat capacity and viscosity of the fuel at a temperature

- коэффициент теплоотдачи от стенок трубок ТМТ к топливу при температуре

- heat transfer coefficient from the walls of the TMT tubes to fuel at a temperature

Obtaining, by solving the system of differential equations, the temperature curves for heating the oil at the exit of the engine and fuel in the following approximation (i = i + 1):

Here, the solution of the system of differential equations is performed under the initial conditions:

и максимальную температуру топлива

From the obtained heating curves determine the maximum oil temperature

and maximum fuel temperature

6. Compare the maximum oil temperature calculated in this way with the maximum oil temperature calculated in the previous approximation.

вычисляют температуру масла на входе в ТМТ в следующем приближении, решая систему дифференциальных уравнений (2). Эти действия выполняют до тех пор, пока разница вычисленных температур масла в текущем и предыдущем приближениях не станет меньше заданной величины δ:If the discrepancy is greater than or equal to a predetermined value δ

calculate the temperature of the oil at the entrance to the TMT in the following approximation, solving the system of differential equations (2). These actions are performed until the difference between the calculated oil temperatures in the current and previous approximations becomes less than the specified value δ:

The value of δ should not be greater than the absolute error of the sensor, which can be determined from the passport to the sensor. Usually, the magnitude of the absolute error on the sensors used to measure the temperature of the fuel and oil are in the range of 0.5 ... 2.0.

рекомендуется выбирать на 10…30 градусов больше

Initial engine oil temperature

it is recommended to choose 10 ... 30 degrees more

В случае, если вычисленная температура не превышает предельно допустимой, делают вывод о достаточности охлаждения масла при РТУ.7. The calculated maximum oil temperature is compared with the maximum allowable for technical (operational) conditions

If the calculated temperature does not exceed the maximum allowable, conclude that the cooling of the oil is sufficient during RTU.

Justification of calculation formulas.

In the articles [5. Tsarev V.A. “Theoretical studies of the temperature state of aircraft systems”, Industry Scientific and Technical Journal “Air Fleet Engineering”, Volume LXXVII, No. 3 (662), 2003, pp. 20-26], [6. Tsarev. V.A. “Theoretical studies of the temperature state of gas turbine engine systems during flight tests”, Questions of aviation science and technology. Scientific and technical collection. Issue No. 2-4 (22-24), Moscow, 1994, p. 31-41.] Obtained a system of differential equations describing the temperature state of the working fluids for various schemes of cooling systems. In particular, for the scheme, when part of the fuel passing through the TMT is transferred to the aircraft’s consumable tank, and the other part is sent to the highway leading to the GTE combustion chamber, a system of differential equations of the form

or more generally

where τ is the time, s;

- температура масла на входе в ТМТ (выходе из двигателя), °С;

- oil temperature at the inlet to TMT (engine exit), ° С;

- температура топлива на выходе из ТМТ, °С;

- fuel temperature at the outlet of TMT, ° C;

- емкость масляной системы (количество масла в масляной системе), кг;

- capacity of the oil system (amount of oil in the oil system), kg;

- емкость топливного перепускного контура (количество топлива в перепускном контуре), кг;

- capacity of the fuel bypass circuit (amount of fuel in the bypass circuit), kg;

q is the heat transfer of the engine to oil, kcal / s,

F is the heat transfer area, m ² ;

- массовые расходы соответственно масла и топлива через ТМТ, кг/с;

- mass costs, respectively, of oil and fuel through TMT, kg / s;

- массовый расход топлива в магистрали, ведущую в камеру сгорания двигателя, кг/с;

- mass fuel consumption in the highway leading to the engine combustion chamber, kg / s;

- массовый расход топлива в магистрали перепуска, кг/с;

- mass fuel consumption in the bypass line, kg / s;

- удельная теплоемкость масла, ккал/кг град;

- specific heat of oil, kcal / kg deg;

- удельная теплоемкость топлива, ккал/кг град;

- specific heat of fuel, kcal / kg hail;

- коэффициенты теплоотдачи от масла к стенкам трубок ТМТ и от стенок ТМТ к топливу соответственно, ккал/м² с град;

- heat transfer coefficients from the oil to the walls of the TMT tubes and from the walls of the TMT to the fuel, respectively, kcal / m ² s deg;

A, B, C, P, R, S - parameters (coefficients) of the mathematical model.

This is a system of linear differential equations with constant coefficients and with the right side. To find the change in oil temperature in the calculated temperature conditions, it is necessary to calculate the relative change in the parameters A, B, C, P, R, S obtained at actual temperatures obtained by performing a given engine and flight mode and RTU temperatures.

Heat transfer coefficients are determined from the dependencies:

- значения критериев Нуссельта, характеризующих конвективный теплообмен между средой и поверхностью теплообмена;Where:

- the values of the Nusselt criteria characterizing convective heat transfer between the medium and the heat exchange surface;

- теплопроводность масла и топлива;

- thermal conductivity of oil and fuel;

- наружный (для масла) и внутренний (для топлива) диаметр трубок ТМТ.

- outer (for oil) and inner (for fuel) diameter of TMT tubes.

(по маслу) и

(по топливу) и Рейнольдса (

),From the theory of similarity of thermal processes it is known that the Nusselt criterion is a function of two criteria: Prandtl

(oily) and

(for fuel) and Reynolds (

),

- плотность соответственно масла и топлива,

Where

- the density, respectively, of oil and fuel,

- вязкость соответственно масла и топлива,

- viscosity, respectively, of oil and fuel,

- площадь проходных сечений в ТМТ соответственно для масла и топлива, м²;

- the cross-sectional area in TMT, respectively, for oil and fuel, m ² ;

- объемный расход через ТМТ соответственно масла и топлива,

- volumetric flow rate through TMT, respectively, of oil and fuel,

Volumetric costs can be determined through the pressure drop Δp from the relations:

- диаметр и длина подводящего к ТМТ трубопровода соответственно для масла и топлива.Where

- the diameter and length of the pipeline leading to TMT, respectively, for oil and fuel.

Since in the steady state, at constant revolutions of the engine rotors, the pressure drop Δp is almost constant (the control equipment keeps the pressure constant), only the viscosity and density of the liquid affect the flow rate.

For fuel:

- при ламинарном течении топлива внутри трубок ТМТ,

- with laminar flow of fuel inside the TMT tubes,

- при турбулентном течении топлива внутри трубок.

- with turbulent flow of fuel inside the tubes.

For oil:

- при расположении трубок в шахматном порядке,

- when the tubes are staggered,

- при коридорном расположении трубок в ТМТ.

- with the corridor arrangement of tubes in TMT.

находят с точностью до постоянных, входящих в формулы геометрических параметров, коэффициенты теплоотдачи

[4. Домотенко Н.Т, Кравец А.С и др. «Авиационные силовые установки. Системы и устройства», Москва, Транспорт, 1976, с. 100-109, 220-223.]By known values

find, up to constants included in the formulas of geometric parameters, heat transfer coefficients

[four. Domotenko N.T., Kravets A.S. et al. “Aircraft power plants. Systems and devices ”, Moscow, Transport, 1976, p. 100-109, 220-223.]

We derive the expression for

The Nusselt criterion for the location of the tubes in the TMT in a checkerboard pattern is as follows

Taking into account the coordination of dimensions, we obtain the following expression for

In this way,

- коэффициент, учитывающий все постоянные параметры и константы и равныйWhere

- coefficient taking into account all constant parameters and constants and equal

Similarly, we get

Where

Where

Where

определенные из опыта и учитывающие входящие в формулы постоянные значения и геометрические параметры, примерно равны:Odds

determined from experience and taking into account the constant values and geometric parameters included in the formulas, are approximately equal:

The thermophysical properties of oil and fuel, included in the formulas (viscosity, density, heat capacity, thermal conductivity), depend on temperature. Their numerical values are presented in reference books and industry standards. They can also be calculated using formulas. For example, for the IPM-10 engine oil, the following calculation formulas are applied depending on the oil temperature

, м²/с, для определения вязкости;

, m ² / s, to determine the viscosity;

, для определения плотности;

, to determine the density;

, ккал/кг град, для определения теплоемкости;

, kcal / kg deg, to determine the heat capacity;

, ккал/м с град, для определения теплопроводности.

, kcal / m with hail, for determining thermal conductivity.

For TC-1 fuel, the following formulas are known for the dependence of fuel parameters on fuel temperature

, м²/с, для определения вязкости;

, m ² / s, to determine the viscosity;

, кг/м³, для определения плотности;

kg / m ³ to determine the density;

, ккал/кг град, для определения теплоемкости;

, kcal / kg deg, to determine the heat capacity;

, ккал/м с град, для определения теплопроводности.

, kcal / m with hail, for determining thermal conductivity.

[5. Chertkov Ya.B. “Modern and promising hydrocarbon jet fuels”; Chemistry Publishing House; Moscow, 1968, p. 58, 96-99, 134]

[6. Shishkov I.N., Belov V.B. “Aviation fuels and lubricants and special fluids”; Publishing House "Transport"; Moscow, 1979, p. 130]

[7. Dubovkin N.F. “Handbook of hydrocarbon fuels and their combustion products”; Gosenergoizdat; Moscow. - Leningrad; 1962, p. 66-68, 111-112].

[8. Industry standard. Oils for aircraft gas turbine engines. OST 100148-75.]

Now it is possible to calculate the relative change in the coefficients A, B, C, P, R, S at the actual temperatures obtained during flight tests and the temperatures of the RTU using thermophysical parameters that depend on temperature and are included in the calculation formulas and calculate the maximum oil temperature at the outlet of engine. At the same time, the geometric parameters included in the formulas do not change, and the heat transfer of the engine to oil and fuel consumption with unchanged flight modes and engine control programs change insignificantly and do not significantly affect the relative change.

An example implementation of the method.

1. When performing the specified mode of operation of the engine and flight of the aircraft at a fuel temperature of 69 ° C at the engine inlet, the following data were obtained:

;initial engine oil temperature

;

;initial fuel temperature at the exit of TMT

;

,maximum engine oil temperature

,

maximum fuel temperature at the exit of TMT

=140°С на том же режиме работы двигателя и полета самолета ожидаемую максимальную температуру масла на выходе из двигателя при температуре топлива на входе в двигатель в РТУ

, равной 120°С, и сравнить ее с предельно-допустимой температурой.Used fuel grade TS-1, used oil grade IPM-10. It must be determined at the selected values: δ = 1 ° C and

= 140 ° С at the same engine and airplane flight mode, the expected maximum oil temperature at the engine exit at the fuel temperature at the engine inlet in the RTU

equal to 120 ° C, and compare it with the maximum permissible temperature.

2. According to the obtained data on temperature measurements of oil and fuel, the parameters of the mathematical model are determined from a known range: А _Э = 0.83 deg / s; In _E = 0.018 sec ^-1 ; With _e = 0.0176 sec ^-1 ; P _E = 18 deg / s; R _e = 0.0178 sec ^-1 ; S _e = 0.27 sec ^-1 .

3. Calculate the maximum temperature of oil and fuel in a first approximation (i = 1) by solving the system of differential equations (2).

;

Got:

;

то полученные максимальные значения

подставляют в формулу для определения A_i, B_i, С_i R_i, S_i решают систему дифференциальных уравнений (2) и получают температуру масла во втором приближении (i=2):4. Since

then the maximum values obtained

substitute in the formula for determining A _i , B _i , C _i R _i , S _i solve the system of differential equations (2) and get the oil temperature in the second approximation (i = 2):

In the third approximation (i = 3):

In the fourth approximation (i = 4):

Here, the temperature difference is less than 1 ° C; therefore, the calculated maximum oil temperature at the engine outlet is 174.8 ° C. The maximum allowable temperature of the oil at the outlet of the engine according to the technical conditions is 200 ° C. Therefore, they conclude that oil cooling is sufficient.

The calculated temperature of 174.8 ° C does not exceed the maximum permissible, therefore, they conclude that the oil cooling system is sufficient.

To implement the computational part of the proposed method, a program was developed in the environment of the mathematical system "Mathcad".

Claims (20)

1. A method for determining the sufficiency of oil cooling in a turbojet engine with a fuel-oil heat exchanger (TMT), which includes performing a flight regime critical for oil overheating, measuring the temperature of the oil at the inlet of the TMT during the flight, calculating the maximum oil temperature at the inlet of the TMT, comparing the calculated maximum temperature of the oil at the inlet of the TMT with the maximum permissible temperature, the determination after the flight of the temperature of the fuel at the entrance to the TMT under the calculated temperature conditions

and selection of the initial oil temperature at the inlet of TMT

calculation by the method of successive approximations of the maximum oil temperature at the inlet of the TMT, characterized in that during the flight they partially bypass the fuel, after passing the TMT, from the fuel supply line to the engine through the bypass valve to the fuel tank, and measure the temperature of the fuel at the exit of the TMT . 2. The method according to claim 1, characterized in that the method of successive approximations is based on solving a system of differential equations consisting of equations A and B describing a closed system of oil circulation in a gas turbine engine (A) and an open system for transferring fuel to a fuel tank (B) , after the fuel has passed through TMT, for which, after the flight mode is critical with respect to oil overheating, the parameters A _E , V _E , C _E , _RE , R _E , S _{E of the} mathematical model of the oil and fuel heating process are determined by the selection method, such to mathematically The sky model corresponded to the experimentally obtained heating curves for oil and fuel with a certain accuracy:

i = 0, 1, 2, ..., Where

C _i = B _i K1korr;

S _i = R _i + K3korr, Where

- respectively, the heat capacity and viscosity of the oil at a temperature

- heat transfer coefficient from oil to the walls of the TMT tubes at a temperature

- respectively, the heat capacity and viscosity of the fuel at a temperature

- heat transfer coefficient from the walls of the TMT tubes to fuel at a temperature

- respectively, the heat capacity and viscosity of the oil at a temperature

- heat transfer coefficient from oil to the walls of the TMT tubes at a temperature

- respectively, the heat capacity and viscosity of the fuel at a temperature

- heat transfer coefficient from the walls of the TMT tubes to fuel at a temperature

- parameter of the mathematical model,

correction factors until the difference between the calculated oil temperatures in the current and previous approximations becomes less than a predetermined error δ.

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