Performance Time Response Analysis Method for the Unsteady Process of a Ramjet Engine

Abstract

The present invention relates to a performance time response analysis method for an unsteady-state process of a subsonic ramjet engine, comprising the steps of calculating the inlet outlet flow rate, total temperature and total pressure of the subsonic ramjet engine in a steady state; establishing a simulated excitation disk-volume model according to the combustion chamber of the subsonic ramjet engine to obtain the total temperature, total enthalpy, total pressure and outlet flow rate of a simulated outlet of the steady-state combustion chamber model; correcting the simulated outlet total enthalpy and outlet flow rate of the combustion chamber model to obtain the combustion chamber outlet total enthalpy and outlet flow rate considering the volume effect, and combining the simulated volume to obtain an engine unsteady-state thrust variation law and an error diagram of the unsteady-state thrust variation law designed with a non-design point model; the present invention considers the volume effect in the combustion chamber for the performance time response of the engine unsteady-state process, and can more accurately reflect the acceleration and deceleration performance and the influence of unsteady-state processes such as large maneuvers on the performance of the ramjet engine.

Description

Technical Field

[0001] The present invention relates to the field of aeroengines, and particularly to a method for analyzing the time response of the unsteady process of a ramjet engine. Background Art

[0002] A ramjet engine uses the oxygen in the air as an oxidant, and the fuel carried contains little or no oxidant, resulting in a significantly increased specific impulse. Therefore, a missile powered by a ramjet engine has a longer range, a lighter mass, and better maneuverability, and can achieve supersonic cruise flight throughout the whole process, thus being able to greatly improve the penetration ability of the missile. Since the 1980s, almost all countries with the ability to develop missiles have carried out research on ramjet propulsion technology, and various ramjets and their combined engines will become the preferred power devices for tactical missiles, interceptors, and cruise missiles in this century.

[0003] In the unsteady process, with the change of factors such as flight attitude and flight conditions, the parameters in the combustion chamber of the ramjet engine will also change accordingly. If it is possible to quickly obtain the response and specific changes of each parameter within a certain period of time during the unsteady process, it can help designers design and specify a reasonable flight trajectory, and also provide a reference for designing the control law of the ramjet engine. However, for the performance time response of its unsteady process, the volume effect in the combustion chamber needs to be considered. Considering the performance time response characteristics can more accurately reflect its acceleration and deceleration performance and the impact of unsteady processes such as large maneuvers on the performance of the ramjet engine. However, in the prior art, the volume effect is not considered, so there is no method for calculating and reflecting the performance time response of the ramjet engine in the unsteady process. Summary of the Invention

[0004] The purpose of the present invention is to avoid the deficiencies of the prior art and provide a method for analyzing the performance time response of the unsteady process of a scramjet engine that considers the volume effect in the combustion chamber, can quickly judge the unsteady performance parameters of the ramjet engine, is convenient for formulating a reasonable flight trajectory, shortens the iteration cycle, and improves the design efficiency of the flight trajectory.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is: a method for analyzing the performance time response of the unsteady process of a scramjet engine, including the following steps:

[0006] Step 1: Calculate the air flow rate, total temperature, and total pressure at the outlet of the inlet of the scramjet engine under steady state according to the actual flight Mach number Ma and flight altitude H of the scramjet engine and the flow coefficient interpolated on the inlet interpolation characteristic diagram of the flight Mach number Ma and the total pressure recovery coefficient σ.

[0007] Step 2: Establish a simulated shock disk - volume model based on the combustion chamber of the scramjet engine. The simulated shock disk has no volume and is used to simulate the steady - state characteristics of the combustion chamber; the simulated volume V is the same size as the actual combustion chamber volume and is used to simulate the combustion chamber volume.

[0008] Based on the simulated shock disk and the inlet - duct outlet flow rate, total temperature, and total pressure of the scramjet engine under steady - state conditions in Step 1, perform aerodynamic - thermal calculations using steady - state combustion - chamber characteristics to obtain the total temperature T, total enthalpy H, total pressure P, and outlet flow rate W at the simulated outlet of the steady - state combustion - chamber model.

[0009] Step 3: Use Equation (1) and Equation (2) to correct the total enthalpy H and outlet flow rate W at the simulated outlet of the combustion - chamber model in Step (2).

[0010]

[0011]

[0012] In the formula, V is the combustion - chamber simulated volume in Step 2; k is the specific - heat ratio of the gas; R is the universal gas constant; dp / dt is the derivative of the total pressure at the combustion - chamber outlet with respect to time; u is the internal energy of the gas in the combustion chamber, obtained from the total temperature T at the simulated outlet of the steady - state combustion - chamber model, and du / dt is the derivative of the internal energy of the gas in the combustion chamber with respect to time.

[0013] In Equation (2), u is the internal energy of the gas in the combustion chamber. u can be the internal energy of the gas in the combustion chamber before correction or after correction. Whether in explicit format or implicit format, it can be represented by u.

[0014] That is, obtain the total enthalpy H' and outlet flow rate W' at the combustion - chamber outlet considering the volume effect.

[0015] Step 4: Use the obtained total enthalpy H' and outlet flow rate W' at the combustion - chamber outlet considering the volume effect and the simulated volume V, and select a time step to obtain the error graph of the unsteady thrust - change law of the scramjet engine and the unsteady thrust - change law of the scramjet engine designed using the off - design - point model, that is, obtain the characteristic variables of the time - response performance of the scramjet engine.

[0016] Furthermore, Step 3 specifically includes the following steps:

[0017] Step 31: Differentiate the total pressure P at the simulated outlet of the steady - state combustion - chamber model in Step 2 using the implicit Euler format. Then, obtain the total temperature T at the simulated outlet of the steady - state combustion - chamber model based on the total pressure P and total enthalpy H at the simulated outlet of the steady - state combustion - chamber model.

[0018] Calculate the flow rate W' considering the volume effect using Equation (1).

[0019]

[0020] Where dp / dt is the derivative of the total pressure at the combustion chamber outlet with respect to time; dp is the differential of the total pressure; V is the simulated volume, which is the actual combustion chamber volume; T and W are the simulated outlet total temperature and outlet flow rate of the steady-state combustion chamber model in Step 2; R is the universal gas constant.

[0021] Step 32: Try to take the outlet total temperature T', and according to the internal energy conversion formula, obtain Equation (4):

[0022] U' = H - T'·R (4)

[0023] Where U' is the internal energy of the gas in the combustion chamber considering the volume effect; H is the total enthalpy at the simulated outlet of the steady-state combustion chamber model, and R is the universal gas constant.

[0024] Step 33: Differentiate Equation (4), and according to the differential formula of the internal energy of the gas in the combustion chamber, obtain the calculation formula (5) of the total enthalpy H' considering the volume effect:

[0025]

[0026] Where dU' is the differential of the internal energy of the gas in the combustion chamber considering the volume effect; dU' / dt is the derivative of the internal energy of the gas in the combustion chamber with respect to time considering the volume effect; P and W are the total pressure and outlet flow rate at the simulated outlet of the steady-state combustion chamber model; V is the simulated volume, which is the actual combustion chamber volume; R is the universal gas constant.

[0027] Step 34: Calculate the outlet total temperature T' of the combustion chamber considering the volume effect through the simple iteration method until, using the tried outlet total temperature T', according to Equation (4) and Equation (5), the calculated total enthalpy H' considering the volume effect and the actual total enthalpy H' obtained from the relationship between the actual total enthalpy and total temperature at the combustion chamber outlet during the iteration process for the tried outlet total temperature T' 实 are equal; otherwise, continue to continuously iterate and try the outlet total temperature T'. Finally, iteratively obtain the outlet total temperature T', total enthalpy H', and flow rate W' of the combustion chamber considering the volume effect.

[0028] Furthermore, for the solution of Equation (1) and Equation (2) in Step 3, the method of using the implicit Euler format for finite differences for all differential terms is adopted to obtain Equation (3):

[0029]

[0030] Where y iis the current time value; y i-1 is the time value of the previous moment. When calculating at each time step, only the value of the previous time is known, and the current value is unknown. Therefore, the Newton-Raphson iteration is used to solve the formulas (1) and (2); the specific values of W’ and H’ are obtained.

[0031] The beneficial effects of the present invention are as follows: The present invention considers the volume effect in the combustion chamber for the performance time response of the engine's unsteady process. For the performance time response characteristics, it can more accurately reflect its acceleration and deceleration performance and the impact of unsteady processes such as large maneuvers on the performance of the ramjet engine, helping designers and testers quickly determine whether the unsteady performance parameters meet the requirements, formulate a reasonable flight trajectory, shorten the iteration cycle, and improve the design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a schematic diagram of the "shock disk - volume" model;

[0033] Figure 2 is a schematic diagram for calculating the volume effect of the engine combustion chamber;

[0034] Figure 3 is a schematic diagram of the volume effect calculation process;

[0035] Figure 4 is the design result of the performance time response characteristics of the unsteady process. DETAILED DESCRIPTION OF THE INVENTION

[0036] The principles and features of the present invention will be described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0037] To achieve the above object, the present invention provides the following specific implementation manners:

[0038] Example 1: As Figures 1 - 4 shown, a method for analyzing the performance time response characteristics of a scramjet engine's unsteady process includes the following steps:

[0039] (1) According to the actual flight Mach number Ma, flight altitude H of the scramjet engine, and the flow coefficient interpolated on the intake duct interpolation characteristic diagram of the flight Mach number Ma and the total pressure recovery coefficient σ, calculate the intake duct outlet flow rate, total temperature, and total pressure of the scramjet engine under steady state;

[0040] (2) As Figure 1 shown, establish a simulated shock disk - volume model according to the combustion chamber of the scramjet engine. The simulated shock disk has no volume and is used to simulate the steady state characteristics of the combustion chamber; the simulated volume V is the same size as the actual combustion chamber volume and is used to simulate the combustion chamber volume.

[0041] Based on the simulated exciting disk and the inlet flow rate, total temperature, and total pressure at the outlet of the scramjet engine under steady state described in step (1), aerodynamic and thermal calculations are performed using the characteristics of the steady-state combustion chamber to obtain the total temperature T, total enthalpy H, total pressure P, and outlet flow rate W at the simulated outlet of the steady-state combustion chamber model.

[0042] (3) As Figure 2 , Figure 3 shown, the differential of the total pressure P at the simulated outlet of the steady-state combustion chamber model described in step (2) is obtained using the implicit Euler format. Then, based on the total pressure P and total enthalpy H at the simulated outlet of the steady-state combustion chamber model, the total temperature T at the simulated outlet of the steady-state combustion chamber model is obtained.

[0043] The flow rate W' considering the volume effect is calculated by formula (1).

[0044]

[0045] In the formula, dp / dt is the derivative of the total pressure at the combustion chamber outlet with respect to time; dp is the differential of the total pressure; V is the simulated volume, which is the actual combustion chamber volume; T and W are the total temperature and outlet flow rate at the simulated outlet of the steady-state combustion chamber model described in step (2); R is the universal gas constant.

[0046] (4) Try to take the outlet total temperature T'. According to the internal energy conversion formula, formula (4) is obtained:

[0047] U' = H - T'·R (4)

[0048] In the formula, U' is the internal energy of the gas in the combustion chamber considering the volume effect; H is the total enthalpy at the simulated outlet of the steady-state combustion chamber model; R is the universal gas constant.

[0049] (5) Perform differential processing on formula (4). According to the internal energy differential formula conversion, the calculation formula (5) of the total enthalpy H' considering the volume effect is obtained:

[0050]

[0051] In the formula, dU' is the differential of the internal energy of the gas in the combustion chamber considering the volume effect; dU' / dt is the derivative of the internal energy with respect to time considering the volume effect; P and W are the total pressure and outlet flow rate at the simulated outlet of the steady-state combustion chamber model; V is the simulated volume, which is the actual combustion chamber volume; R is the universal gas constant.

[0052] The implicit format for U' in formula (5) is to use the corrected internal energy of the gas in the combustion chamber, so U' is used in formula (5).

[0053] (6) Calculate the total temperature T' at the combustor outlet considering the volume effect by the simple iteration method until the trial total temperature T' at the outlet is used. According to the formulas (4) and (5), calculate the total enthalpy H' considering the volume effect and the actual total enthalpy H' obtained based on the relationship between the actual total enthalpy and total temperature at the combustor outlet during the iteration process for the trial total temperature T' at the outlet. 实 Are equal; otherwise, continue to continuously iterate the trial total temperature T' at the outlet. Eventually, iteratively find the total temperature T', total enthalpy H', and mass flow rate W' at the combustor outlet considering the volume effect.

[0054] For the solution of formulas (1) and (2), use the method of taking the difference for all differential terms in the implicit Euler format to obtain formula (3):

[0055]

[0056] In the formula, y i Is the current time value; y i-1 Is the time value at the previous moment. When calculating at each time step, only the value at the previous time is known, and the current value is unknown. Therefore, use the Newton - Raphson iteration to solve formulas (1) and (2); obtain the specific values of W' and H'.

[0057] (7) Utilize the obtained total enthalpy H' and outlet mass flow rate W' at the combustor outlet considering the volume effect and the simulated volume V, and select the time step to obtain the error graph of the unsteady thrust variation law of the scramjet engine and the unsteady thrust variation law designed by using the off - design point model for the scramjet engine, that is, obtain the characteristic variables of the time response of the performance of the scramjet engine.

[0058] The specific calculation example is as follows:

[0059] The input design points for the unsteady process of the ramjet engine involved in this embodiment include: flight Mach number Ma = 3.5, flight altitude H = 20000 m, inlet mass flow rate Wa = 10.0 kg / s, total pressure recovery coefficient σ = 0.524, mass flow coefficient Total pressure recovery coefficient σ at the design point of the transition section 2des = 0.9, cold - state total pressure recovery coefficient σ of the combustor 3des = 0.93, combustion efficiency η b = 0.92, Mach number Ma at the combustor inlet 3 = 0.1, total temperature T at the outlet 4 = 2000 K, determine the back pressure P at the nozzle outlet according to the flight altitude s0 = 4325.2 Pa.

[0060] The fuel supply rate W of the ramjet engine in this embodimentfb Variation law with time: The fuel supply rate linearly increases from 0.2 kg / s to 0.4 kg / s within 4 s. The calculated time step is 0.05 s.

[0061] As Figure 4 shown, the non-steady performance of the engine is designed using a non-design point model, and the variation law of the thrust is as Figure 4 shown in Case 1. Given the combustion chamber volume V = 1 m3, the variation law of the thrust is as Figure 4 shown in Case 2. The relative error between the two is as Figure 4 shown by the blue line. It can be seen that after considering the volume effect, the time response characteristic of the non-steady process performance lags by 0.4 s, and the relative thrust loss is 1%. That is, the changes in time and thrust of the non-steady performance time response of the scramjet engine are quickly obtained, which is convenient for predicting the non-steady performance of the engine. By using the volume effect model, the influence of the combustion chamber volume can be considered during the calculation of the non-steady performance of the engine, and the prediction result is more accurate.

[0062] The above are only the preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for analyzing the performance time response of the unsteady process of a scramjet engine, characterized in that, it includes the following steps: Step 1: Calculate the inlet duct outlet flow rate, total temperature, and total pressure under steady state of the scramjet engine according to the actual flight Mach number Ma and flight altitude H of the scramjet engine and the flow coefficient interpolated on the inlet duct interpolation characteristic diagram at the flight Mach number Ma and the total pressure recovery coefficient σ Step two: Establish a simulated shock disk - volume model according to the combustion chamber of the scramjet engine. The simulated shock disk has no volume and is used to simulate the steady - state characteristics of the combustion chamber; the simulated volume V is the same size as the actual combustion chamber volume and is used to simulate the combustion chamber volume; Based on the simulated shock disk and the inlet duct outlet flow rate, total temperature, and total pressure under steady - state of the scramjet engine in step one, perform aerodynamic - thermal calculations using the steady - state combustion chamber characteristics to obtain the total temperature T, total enthalpy H, total pressure P, and outlet flow rate W at the simulated outlet of the steady - state combustion chamber model; Step three: Use formula (1) and formula (2) to correct the simulated outlet total enthalpy H and outlet flow rate W of the combustion chamber model in step (2): In the formula, V is the combustion chamber simulated volume in step two; k is the specific heat ratio of the gas; R is the universal gas constant; dp / dt is the derivative of the total pressure at the combustion chamber outlet with respect to time; u is the internal energy of the gas in the combustion chamber, obtained from the total temperature T at the simulated outlet of the steady - state combustion chamber model, and du / dt is the derivative of the internal energy of the gas in the combustion chamber with respect to time; That is, the total enthalpy H' and outlet flow rate W' at the combustion chamber outlet considering the volume effect are obtained; Step four: Utilize the obtained total enthalpy H' and outlet flow rate W' at the combustion chamber outlet considering the volume effect and the simulated volume V, and select a time step to obtain the error graph of the unsteady thrust change law of the scramjet engine and the unsteady thrust change law designed by the off - design point model of the scramjet engine, that is, the characteristic variables of the performance time response of the scramjet engine are obtained.

2. The method for analyzing the performance time response of the unsteady process of a scramjet engine according to claim 1, characterized in that, the specific steps of step three include the following steps: Step 31: Differentiate the total pressure P at the simulated outlet of the steady - state combustion chamber model in step two using the implicit Euler format, and then, obtain the total temperature T at the simulated outlet of the steady - state combustion chamber model according to the total pressure P and total enthalpy H at the simulated outlet of the steady - state combustion chamber model; Calculate the flow rate W' considering the volume effect by formula (1), In the formula, dp / dt is the derivative of the total pressure at the combustion chamber outlet with respect to time; dp is the differential of the total pressure; V is the simulated volume, that is, the actual combustion chamber volume; T and W are the total temperature and outlet flow rate at the simulated outlet of the steady - state combustion chamber model in step two; R is the universal gas constant; Step 32: Try to take the outlet total temperature T', and obtain formula (4) according to the internal energy conversion formula: U' = H - T'·R (4) In the formula, U' is the internal energy of the gas in the combustion chamber considering the volume effect; H is the total enthalpy at the simulated outlet of the steady - state combustion chamber model, and R is the universal gas constant; Step 33: Perform differential processing on formula (4), and convert according to the differential formula of the internal energy of the gas in the combustion chamber, that is, obtain the calculation formula (5) of the total enthalpy H' considering the volume effect: Wherein, dU’ is the differential of the internal energy of the gas in the combustion chamber considering the volume effect; dU’ / dt is the derivative of the internal energy of the gas in the combustion chamber with respect to time considering the volume effect; P and W are the total pressure and outlet flow rate at the simulated outlet of the steady-state combustion chamber model; V is the simulated volume, i.e., the actual combustion chamber volume; R is the universal gas constant; Step 34: Calculate the total temperature T’ at the combustor outlet considering the volume effect by the simple iteration method until, using the trial total temperature T’ at the outlet, the total enthalpy H’ considering the volume effect is calculated according to the formulas (4) and (5), and the actual total enthalpy H’ obtained based on the relationship between the actual total enthalpy and total temperature at the combustor outlet during the iteration process for the trial total temperature T’ at the outlet. 实 They are equal; otherwise, continue to continuously iterate the trial total temperature T’ at the outlet. Eventually, the total temperature T’, total enthalpy H’, and mass flow rate W’ at the combustor outlet considering the volume effect are obtained by iteration.

3. The method for analyzing the performance time response of the unsteady process of a scramjet engine according to claim 1 or 2, characterized in that in step three, for the solution of formula (1) and formula (2), a method of taking the difference of all differential terms using the implicit Euler format is adopted to obtain formula (3): where y i is the current time value; y i-1 is the time value at the previous moment. When calculating at each time step, only the value at the previous time is known, while the current value is unknown. Therefore, the Newton-Raphson iteration is used to solve the formulas (1) and (2); the specific values of W’ and H’ are obtained.

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