Duct ratio optimization design method for large-bypass-ratio split exhaust turbofan engine

Abstract

The invention discloses a bypass ratio optimization design method for a large-bypass-ratio split exhaust turbofan engine. According to design point flight conditions and engine parameters, parameter cycle analysis is conducted on the large-bypass-ratio split exhaust turbofan engine, the oil consumption rate and the unit thrust expression of the engine are obtained, and the mathematical relation between the bypass ratio and the oil consumption rate is established; the method comprises the following steps: firstly, establishing an expression of an optimal low-pressure turbine temperature ratio corresponding to an optimal bypass ratio through partial derivative solving and formula analysis, and finally, obtaining the optimal bypass ratio corresponding to the minimum oil consumption rate by adjusting the pressure ratio of a gas compressor, so as to improve the fuel efficiency and the overall performance of the large-bypass-ratio turbofan engine in the design stage of the engine. Compared with the prior art, the method has the advantages that the optimal bypass ratio corresponding to the minimum oil consumption rate of the engine design point is obtained through rapid iteration of the bypass ratio of the engine design point, and therefore the design period of the large-bypass-ratio turbofan engine is effectively shortened.

Description

Technical Field

[0001] The present invention relates to a method for optimizing the bypass ratio of a turbofan engine, and in particular to a method for optimizing the bypass ratio of a large-bypass-ratio split-exhaust turbofan engine. Background Art

[0002] With increasing fuel economy and environmental protection requirements on civil aviation routes, the term "green aviation" has garnered widespread attention and become a principle that must be considered in the aviation industry when developing new aircraft. High-bypass-ratio split-exhaust turbofan engines are widely used in large transport and wide-body aircraft because their high bypass ratio significantly improves the thrust-to-fuel efficiency ratio. However, the choice of bypass ratio at different pressure ratios directly affects engine performance and fuel consumption. Therefore, when designing a high-bypass-ratio turbofan engine, the optimal bypass ratio that minimizes the non-installed specific fuel consumption at the design point is determined based on the optimal choice of bypass ratio at different pressure ratios.

[0003] Relevant research has been conducted at home and abroad on the design optimization of high bypass ratio turbofan engines. Li Bin et al. studied the impact of the change in the efficiency of rotating parts on the performance of high bypass ratio turbofan engines and found that the reduction in the efficiency of rotating parts increases the fuel consumption rate of the engine. Among them, the change in the efficiency of the supercharger stage has the least impact on the fuel consumption rate, and the change in the efficiency of the low-pressure turbine has the greatest impact on the fuel consumption rate [Li Bin, Ding Ning. Research on the impact of the change in the efficiency of rotating parts on the performance of high bypass ratio turbofan engines [J]. Military and Civilian Dual-Use Technology and Products, 2016, (2): 188-190.]. Yang Kun et al. conducted a thermodynamic cycle analysis on two types of high bypass ratio separated exhaust turbofan engines and found that when the ratio of the external and internal exhaust velocities is equal to the product of the fan and low-pressure turbine efficiencies, the total efficiency and unit thrust of the engine are the largest and the fuel consumption rate is the lowest [Yang Kun, Tu Qiuye, Shi Yang, et al. Thermodynamic cycle analysis of separated exhaust turbofan engines [J]. Journal of Aerospace Power, 2017, 32(9): 2187-2192.]. Abhijit Guha found through research that the optimal fan pressure ratio depends primarily on the specific thrust and less so on the bypass ratio. He derived two simple explicit formulas for each engine type to determine the optimal fan pressure ratio [Guha, Abhijit. Optimum Fan Pressure Ratio for Bypass Engines with Separate or Mixed Exhaust Streams. Journal of Propulsion and Power, September 2001, Vol. 17, No. 5].

[0004] Existing research has primarily focused on analyzing the relationship between bypass ratio and parameters such as aerodynamic performance, thermal performance, and structural strength. However, a systematic optimization method that can achieve minimum fuel consumption at the design point is lacking. Furthermore, methods for determining the optimal bypass ratio for different pressure ratios also have certain limitations. Therefore, a scientifically sound, engineering-practical design method is urgently needed that can automatically optimize the bypass ratio and achieve minimum fuel consumption while maintaining engine performance. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the existing technology and provide a bypass ratio optimization design method for a large bypass ratio split exhaust turbofan engine. By quickly iterating the bypass ratio of the engine design point, the optimal bypass ratio corresponding to the minimum fuel consumption rate of the engine design point is obtained, thereby shortening the design cycle of the large bypass ratio turbofan engine.

[0006] The present invention specifically adopts the following technical solutions to solve the above problems:

[0007] A method for optimizing the bypass ratio of a high-bypass-ratio split-exhaust turbofan engine comprises the following steps:

[0008] S1. At the design point of the engine, calculate the polytropic efficiency e of the low-pressure turbine according to the following formula: tL =1 when the optimal low-pressure turbine temperature ratio

[0009]

[0010] Where, τ λ is the ratio of the total temperature at the combustion chamber outlet to the free stream ambient temperature, τ m1 and τ m2 are the total temperature ratios of cooling gas mixers 1 and 2, τ tH is the high-pressure turbine total temperature ratio, τ tL is the total temperature ratio of the low-pressure turbine, τ r is the ratio of the free stream total temperature to the static temperature, τ cL is the total temperature ratio of the low-pressure compressor, τ cH is the high pressure compressor total temperature ratio, π r is the ratio of the free stream total pressure to the static pressure, π d is the total pressure ratio of the intake duct, π cL is the total pressure ratio of the low-pressure compressor, π cH is the total pressure ratio of the high-pressure compressor, π b is the total pressure ratio of the combustion chamber, π n is the total pressure ratio of the mainstream nozzle, γ t is the specific heat ratio of the gas, τ f is the fan-to-total temperature ratio, C TOL is the low-pressure rotor shaft power extraction coefficient, ηmPL is the power extraction efficiency of the low-pressure rotor shaft, η mL is the power output efficiency of the low-pressure shaft, V 18 is the exit velocity of the bypass nozzle, V0 is the free stream velocity at the far front of the engine, f is the fuel-air ratio of the main combustion chamber, β is the relative bleed air volume, ε1 and ε2 are the relative cooling air volumes 1 and 2;

[0011] S2. Iteratively solve the optimal low-pressure turbine temperature ratio that minimizes the design point fuel consumption rate. Will obtain Substitute the value of into the right side of the following formula τ tL , and judge the calculated and Is the absolute value of the difference less than or equal to the preset threshold? If so, the current calculated As the final Otherwise, the currently calculated As a new Repeat the above process until the calculated and The absolute value of the difference is less than or equal to the preset threshold.

[0012]

[0013] Where, e tH is the variable efficiency of the high-pressure turbine, π tL is the total pressure ratio of the low-pressure turbine, π tH is the total pressure ratio of the high-pressure turbine;

[0014] S3. The optimal low-pressure turbine temperature ratio that minimizes the design point fuel consumption rate is obtained. Substitute the value of τ into the following formula tL , thereby obtaining the optimal bypass ratio α that minimizes the fuel consumption rate at the design point * :

[0015]

[0016] Preferably, the preset threshold is 0.0001.

[0017] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0018] The present invention conducts a parameter cycle analysis on a high bypass ratio split exhaust turbofan engine based on design point flight conditions (flight altitude H, flight Mach number Ma) and engine parameters (such as component efficiency, pressure ratio, thermodynamic characteristics, etc.), obtains the engine's fuel consumption rate and unit thrust expression, and establishes a mathematical relationship between the bypass ratio (α) and the fuel consumption rate (S). Then, the optimal bypass ratio α is established by taking partial derivatives and formula analysis. *The corresponding optimal low-pressure turbine temperature ratio The expression of can finally be obtained by adjusting the compressor pressure ratio to obtain the optimal bypass ratio corresponding to the minimum fuel consumption rate, so as to improve the fuel efficiency and overall performance of the high bypass ratio turbofan engine during the engine design stage. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A flow chart of an algorithm for implementing a bypass ratio optimization design method for a high bypass ratio split exhaust turbofan engine according to the present invention;

[0020] Figure 2 To illustrate the unit parameter performance of a high bypass ratio turbofan engine;

[0021] Figure 3 The optimal bypass ratio of an example high bypass ratio turbofan engine is shown in FIG. DETAILED DESCRIPTION

[0022] The technical solution of the present invention is described in detail below with reference to the accompanying drawings:

[0023] The expressions of fuel consumption rate and unit thrust of high bypass ratio split exhaust turbofan engine design point are as follows:

[0024]

[0025] Where, S is the fuel consumption rate, f o is the total fuel-air ratio of the engine, f is the fuel-air ratio of the main combustion chamber, β is the relative induction volume, ε1 and ε2 are the relative cooling air volumes 1 and 2, α is the engine bypass ratio, F is the engine thrust, and m0 is the engine inlet air mass flow rate.

[0026]

[0027] Where, subscript 0 represents the engine far front, subscript 9 represents the engine mainstream nozzle outlet cross-section, Table 18 below represents the duct nozzle outlet cross-section, a0 is the engine far front sound speed, M0 is the aircraft flight Mach number, T0 is the engine far front ambient temperature, P0 is the engine far front ambient pressure, V8 is the mainstream nozzle outlet velocity, P8 is the mainstream nozzle outlet static pressure, V 18 is the exit velocity of the duct nozzle, P 18 is the static pressure at the duct nozzle outlet, γ c is the specific heat ratio of air, R c is the gas constant of air, γ t is the specific heat ratio of the gas, R t is the gas constant of the fuel gas.

[0028] When the tail nozzle and the duct nozzle of the separated exhaust turbofan engine are not blocked, P8 = P 18=P0, we can obtain the bypass ratio α that produces the minimum fuel consumption when all other variables remain constant. * When P8=P 18 =P0, the above formula can be used to obtain

[0029]

[0030] From the expression of fuel consumption rate, we can see that the larger (1+α)F / m0 is, the smaller the fuel consumption rate is. Therefore, when the right side of equation (3) is at its maximum value, the corresponding bypass ratio corresponds to the optimal bypass ratio α for minimum fuel consumption rate. * Taking the partial derivative of (3) with respect to α and setting the result to zero, we can obtain

[0031]

[0032] because

[0033]

[0034] Therefore, formula (4) becomes

[0035]

[0036] Also because

[0037]

[0038] Where, τ λ is the ratio of the total temperature at the turbine inlet to the free stream ambient temperature, τ m1 and τ m2 are the total temperature ratios of cooling gas mixers 1 and 2, τ tH is the high-pressure turbine total temperature ratio, τ tL is the total temperature ratio of the low-pressure turbine, τ r is the ratio of the free stream total temperature to the static temperature, P t8 is the total pressure at the nozzle outlet section.

[0039] in

[0040]

[0041] Where, π r is the ratio of the free stream total pressure to the static pressure, π d is the total pressure ratio of the intake duct, π cL is the total pressure ratio of the low-pressure compressor, π cH is the total pressure ratio of the high-pressure compressor, π b is the total pressure ratio of the combustion chamber, π tL is the total pressure ratio of the low-pressure turbine, π tH is the total pressure ratio of the high-pressure turbine, π n is the total pressure ratio of the mainstream nozzle.

[0042] therefore

[0043]

[0044] in

[0045]

[0046] There are and Therefore, formula (9) becomes

[0047]

[0048] Where e tL is the variable efficiency of the low-pressure turbine, e tH The variable efficiency of the high-pressure turbine.

[0049] in

[0050]

[0051] Then

[0052]

[0053] There are

[0054]

[0055] and

[0056]

[0057] Where, τ f is the fan-to-total temperature ratio, C TOL is the low-pressure rotor shaft power extraction coefficient, η mPL is the power extraction efficiency of the low-pressure rotor shaft, η mL is the power output efficiency of the low-pressure shaft.

[0058] Combining equations (6) and (13), we can get

[0059]

[0060] The optimal bypass ratio α can be obtained by formula (16): * The corresponding optimal low-pressure turbine temperature ratio The expression of , replace (V8 / V0) with equation (9) 2 , solve the first τ in the bracket of equation (9) tL , and obtain

[0061]

[0062] in

[0063]

[0064] Because formula (17) The equation itself, in addition to other known values, needs to be solved iteratively. tL = 1, we can obtain and use this value as The initial value of

[0065]

[0066] This initial value can be replaced by τ on the right side of formula (17) tL , get a new value Then the The new value of continues to replace the right side of formula (17) and calculates This process continues until Until the change in the calculation is less than 0.0001. Once found The solution of , we can use formula (20) to solve the optimal bypass ratio α * .

[0067]

[0068] Summarizing the above theoretical derivation process, the technical solution of the present invention can be obtained as follows:

[0069] A bypass ratio optimization design method for a high bypass ratio split exhaust turbofan engine, such as Figure 1 As shown, the following steps are included:

[0070] S1. At the design point of the engine, calculate the polytropic efficiency e of the low-pressure turbine according to the following formula: tL =1 when the optimal low-pressure turbine temperature ratio

[0071]

[0072] Where, τ λ is the ratio of the total temperature at the combustion chamber outlet to the free stream ambient temperature, τ m1 and τ m2 are the total temperature ratios of cooling gas mixers 1 and 2, τ tH is the high-pressure turbine total temperature ratio, τ tL is the total temperature ratio of the low-pressure turbine, τ r is the ratio of the free stream total temperature to the static temperature, τ cL is the total temperature ratio of the low-pressure compressor, τ cH is the high pressure compressor total temperature ratio, πr is the ratio of the free stream total pressure to the static pressure, π d is the total pressure ratio of the intake duct, π cL is the total pressure ratio of the low-pressure compressor, π cH is the total pressure ratio of the high-pressure compressor, π b is the total pressure ratio of the combustion chamber, π n is the total pressure ratio of the mainstream nozzle, γ t is the specific heat ratio of the gas, τ f is the fan-to-total temperature ratio, C TOL is the low-pressure rotor shaft power extraction coefficient, η mPL is the power extraction efficiency of the low-pressure rotor shaft, η mL is the power output efficiency of the low-pressure shaft, V 18 is the exit velocity of the bypass nozzle, V0 is the free stream velocity at the far front of the engine, f is the fuel-air ratio of the main combustion chamber, β is the relative bleed air volume, ε1 and ε2 are the relative cooling air volumes 1 and 2;

[0073] S2. Iteratively solve the optimal low-pressure turbine temperature ratio that minimizes the design point fuel consumption rate. Will obtain Substitute the value of into the right side of the following formula τ tL , and judge the calculated and Is the absolute value of the difference less than or equal to the preset threshold (preferably 0.0001)? If so, the current calculated As the final Otherwise, the currently calculated As a new Repeat the above process until the calculated and The absolute value of the difference is less than or equal to the preset threshold.

[0074]

[0075] Where, e tH is the variable efficiency of the high-pressure turbine, π tL is the total pressure ratio of the low-pressure turbine, π tH is the total pressure ratio of the high-pressure turbine;

[0076] S3. The optimal low-pressure turbine temperature ratio that minimizes the design point fuel consumption rate is obtained. Substitute the value of τ into the following formula tL , thereby obtaining the optimal bypass ratio α that minimizes the fuel consumption rate at the design point * :

[0077]

[0078] In order to verify the effect of the technical solution of the present invention, a certain type of high bypass ratio turbofan engine is taken as an example, and its bypass ratio is optimized using the method of the present invention:

[0079] The design point altitude is H = 12.192 km, Ma = 0.8, and the design input parameters of the example high bypass ratio turbofan engine are shown in Table 1.

[0080] Table 1 Example of high bypass ratio turbofan engine design input parameters

[0081]

[0082]

[0083] The premise for calculating the optimal bypass ratio is that the tail nozzle and the outer bypass nozzle of the separate exhaust turbofan engine are not blocked, that is, P8 = P 18 =P0, so to calculate the fan pressure ratio when the outer duct tail nozzle is critical or subcritical, the following formula can be used for calculation

[0084]

[0085] Where, P t18 is the total pressure at the outlet of the duct nozzle, P0 is the ambient pressure, π r is the ratio of the free stream total pressure to the static pressure, π d Total pressure ratio of the intake duct, π f Fan total pressure ratio, π nf Total pressure ratio of the ducted nozzle.

[0086]

[0087] Where β cr It is the critical pressure ratio when the outlet of the bypass is in the critical state.

[0088] Because when the design point altitude and Mach number have been determined, π r , π d are all constant, and β cr , π nf are all constants, so the fan pressure ratio when the outer duct tail nozzle is critical or subcritical can be calculated as π f ≤1.267. Therefore, this example selects a turbofan engine with a fan pressure ratio of 1.25.

[0089] Figure 2 The remaining two design variables, compressor pressure ratio π, are given c The performance results of the design point when the bypass ratio α changes. The range of values ​​is π cL =4, 20<π c <40,8<α<19.6. Figure 2The critical line in the curve is when the mainstream nozzle is in the critical state. The mainstream nozzle to the left of the critical line is in the subcritical state, at this time P8 = P0. Therefore, in the area to the left of the critical line, the condition P8 = P 18 =P0. Figure 2 It can be seen that for each pressure ratio, there is a 18 =Optimal bypass ratio for minimum non-installed fuel consumption at P0. Figure 3 The relationship between the optimum bypass ratio and the compressor pressure ratio is given.

Claims

1. A method for optimizing the bypass ratio of a high-bypass-ratio split-exhaust turbofan engine, characterized in that: The following steps are involved: S1. At the design point of the engine, calculate the polytropic efficiency e of the low-pressure turbine according to the following formula: tL =1 when the optimal low-pressure turbine temperature ratio Where, τ λ is the ratio of the total temperature at the combustion chamber outlet to the free stream ambient temperature, τ m1 and τ m2 are the total temperature ratios of cooling gas mixers 1 and 2, τ tH is the high-pressure turbine total temperature ratio, τ tL is the total temperature ratio of the low-pressure turbine, τ r is the ratio of the free stream total temperature to the static temperature, τ cL is the total temperature ratio of the low-pressure compressor, τ cH is the high pressure compressor total temperature ratio, π r is the ratio of the free stream total pressure to the static pressure, π d is the total pressure ratio of the intake duct, π cL is the total pressure ratio of the low-pressure compressor, π cH is the total pressure ratio of the high-pressure compressor, π b is the total pressure ratio of the combustion chamber, π n is the total pressure ratio of the mainstream nozzle, γ t is the specific heat ratio of the gas, τ f is the fan-to-total temperature ratio, C TOL is the low-pressure rotor shaft power extraction coefficient, η mPL is the power extraction efficiency of the low-pressure rotor shaft, η mL is the power output efficiency of the low-pressure shaft, V 18 is the exit velocity of the bypass nozzle, V0 is the free stream velocity at the far front of the engine, f is the fuel-air ratio of the main combustion chamber, β is the relative bleed air volume, ε1 and ε2 are the relative cooling air volumes 1 and 2; S2. Iteratively solve the optimal low-pressure turbine temperature ratio that minimizes the design point fuel consumption rate. Will obtain Substitute the value of into the right side of the following formula τ tL , and judge the calculated and Is the absolute value of the difference less than or equal to the preset threshold? If so, the current calculated As the final Otherwise, the currently calculated As a new Repeat the above process until the calculated and The absolute value of the difference is less than or equal to the preset threshold. Where, e tH is the variable efficiency of the high-pressure turbine, π tL is the total pressure ratio of the low-pressure turbine, π tH is the total pressure ratio of the high-pressure turbine; S3. The optimal low-pressure turbine temperature ratio that minimizes the design point fuel consumption rate is obtained. Substitute the value of τ into the following formula tL , thereby obtaining the optimal bypass ratio α that minimizes the fuel consumption rate at the design point * :

2. The bypass ratio optimization design method for a high bypass ratio split exhaust turbofan engine according to claim 1, characterized in that: The preset threshold is 0.0001.

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