A one-dimensional modeling method for scramjet volumetric dynamics

Abstract

This invention discloses a one-dimensional modeling method for scramjet engine volumetric dynamics, comprising the following steps: 1) establishing a mathematical model of the scramjet engine's inlet, combustion chamber, and tail nozzle; 2) establishing mathematical models of the scramjet engine's scramjet shockless mode, scramjet oblique shock mode, and subcombustion mode; and 3) establishing a dynamic model of the scramjet engine based on volumetric dynamics. This invention utilizes volumetric dynamics to establish a one-dimensional scramjet engine model, enabling rapid calculation of changes in combustion chamber axial flow field parameters, meeting the requirements of engine control system design.

Description

Technical Field

[0001] The present invention belongs to the technical field of scramjet engine control, and in particular relates to a one-dimensional modeling method for scramjet engine volumetric dynamics. Background Art

[0002] The foundation and focus of engine control system research lies in the engine model. Research on establishing a mathematical model for scramjet engines began with the concept of supersonic combustion, encompassing modeling of various physical effects in supersonic flow and combustion, as well as modeling of the entire engine. Heiser and Pratt developed a scramjet engine model, the HAP. In combustion chamber calculations, this model assumes ideal chemical equilibrium and uses rational fractions to fit the heat release pattern. This model describes the flow process within the combustion chamber by dividing it into three heat transfer processes: adiabatic compression, isobaric heat release, and expansion heat release, simplifying the analysis process. However, due to the assumption of isobaric combustion, the single-point injection of fuel, and the empirical determination of the heat release start point and flow reattachment point, the model is not accurate enough at high Mach numbers.

[0003] Many domestic researchers have also proposed many one-dimensional models of scramjet engines. Cao Ruifeng from Harbin Institute of Technology analyzed the combustion mode transition boundary of scramjet engines, studied the interaction between the combustion chamber and the isolation section, and established a one-dimensional steady-state mathematical model of the combustion chamber. Existing domestic and foreign literature mainly studies the steady-state model of scramjet engines. There are few studies on the dynamic model of scramjet engines for control system design. The only few literatures study the dynamic real-time model of the engine component level. For example, Liu Minglei and Zhang Haibo from Nanjing University of Aeronautics and Astronautics used the combustion chamber volume effect to establish a real-time model of the scramjet engine component level and conducted closed-loop simulation tests. Although the dynamic model of the scramjet engine component level can describe the dynamic characteristics of the engine, it cannot be used to control the distributed parameters of the scramjet engine. Therefore, it is necessary to establish a one-dimensional dynamic model of the scramjet engine. Summary of the Invention

[0004] Purpose of the Invention: To overcome the shortcomings of the prior art, the present invention provides a one-dimensional volumetric dynamics modeling method for scramjet engines. Based on the operating principles of various scramjet engine components, mathematical models of the scramjet engine's inlet, combustion chamber, and tail nozzle are established, as well as mathematical models of the scramjet engine's shockless mode, scramjet oblique shock mode, and subcombustion mode. Based on these models, a dynamic model of the scramjet engine is established using volumetric dynamics. By using volumetric dynamics to establish a one-dimensional model of the scramjet engine, the present invention can rapidly calculate changes in combustion chamber axial flow field parameters, meeting the requirements of engine control system design.

[0005] Technical Solution: To achieve the above objectives, a one-dimensional modeling method for scramjet engine volumetric dynamics is provided, comprising the following steps:

[0006] Step 1: Based on the working principles of each component of the scramjet engine, a mathematical model of the scramjet engine's inlet, combustion chamber, and tail nozzle is established;

[0007] Step 2: Based on the scramjet combustion field mechanism, mathematical models of the scramjet engine's scramjet shockless mode, scramjet oblique shock mode, and subcombustion mode are established;

[0008] Step 3: Based on the volumetric dynamics principle and the scramjet engine modal model established in step 2, a scramjet engine dynamic model is established.

[0009] Furthermore, the specific steps in step 1 are as follows:

[0010] Step 1-1: Based on the experimental data, the polynomial fitting method is used to give the total temperature distribution along the entire flow direction

[0011]

[0012] Where x is the axial position coordinate of the engine combustion chamber (m), T t (x) is the total temperature at position x, T t2 is the total temperature at the inlet of the isolation section, τ is the total heating ratio, θ is the heat release rate, which is an empirical constant ranging from 1 to 10, χ: dimensionless axial position, x i is the fuel injection point, and x4 is the combustion chamber outlet.

[0013] Step 1-2: Predict the coefficient of friction using the following formula

[0014]

[0015] Where C f : local friction coefficient, k: gas adiabatic index, Re x : local Reynolds number, ρ is the local density, V is the local velocity, x is the local axial position coordinate with the engine inlet as the origin, and μ is the local gas dynamic viscosity, which is calculated by the Sutherland formula

[0016]

[0017] Where μ0 is the viscosity coefficient under standard atmospheric conditions, T s is the Sussinian constant, which is related to the properties of the gas, T c =273.16K, T is the local temperature.

[0018] Step 1-3: Derive the one-dimensional governing equations of the flow field in the scramjet combustion chamber from the basic governing equations of gas dynamics, Mach number Ma, total pressure p t As the one-dimensional coordinate x changes, the relationships are

[0019]

[0020]

[0021] Where, A: combustion chamber cross-sectional area, T t : total temperature; D: hydraulic diameter of combustion chamber;

[0022] Step 1-4: Based on the Mach number and total pressure, other parameters are calculated from the gas dynamics function;

[0023]

[0024]

[0025]

[0026] Where, T: static temperature, P: static pressure, V: velocity, R: molar gas constant.

[0027] Furthermore, the specific steps of step 2 are as follows:

[0028] Step 2-1: Establish the transition boundaries between different combustion modes. The transition boundary between the scramjet-shockless mode and the scramjet-shock mode is as follows: when the minimum Mach number of the combustion chamber is greater than 0.762 times the Mach number of the isolator inlet, the combustion chamber operates in the scramjet-shockless mode; otherwise, the combustion chamber operates in the scramjet-shock mode. The transition boundary between the scramjet-shock mode and the subcombustion mode is as follows: when the minimum Mach number of the combustion chamber is greater than or equal to 1, the combustion chamber operates in the scramjet-shock mode; otherwise, the combustion chamber operates in the subcombustion mode.

[0029] Step 2-2: When the scramjet is in the shock-free mode, the entire flow path is supersonic, and there is no boundary layer separation between the isolator and the combustion chamber. The isolator is considered as a one-dimensional steady Fano flow section, and the combustion chamber is a variable-section heating pipe flow with the engine geometric surface as the flow surface. Solve the ordinary differential equations to obtain the distribution of various aerodynamic parameters of the isolator and the combustion chamber.

[0030] Step 2-3: When the scramjet engine is in the scramjet oblique shock wave mode, the entire flow path is supersonic, and the isolator section and the combustion chamber produce boundary layer separation; the front section of the isolator section is the Fano flow section, and the rear section is the shock compression section; the front section of the combustion chamber is the combustion separation section, and the rear section is the separation and attachment section; the shock compression section of the isolator section and the separation section of the combustion chamber are based on the engine geometric surface minus the separation area as the flow surface, and the Fano flow section of the isolator section and the separation and attachment section of the combustion chamber are based on the engine geometric surface as the flow surface;

[0031] Step 2-4: When the scramjet engine is in the subsonic mode, the high back pressure generated in the combustion chamber will cause a strong shock wave train to appear inside the isolation section. The front section of the isolation section is still the Fano flow section, and the rear section is still the shock wave compression section. The combustion chamber inlet is subsonic, there is no boundary layer separation, and the engine geometric surface is the flow surface.

[0032] Furthermore, the specific steps in step 3 are as follows:

[0033] Step 3-1: Use the combustion chamber inlet as the cavity inlet and the position of the point to be substituted as the cavity outlet. After determining the cavity outlet position, perform volumetric dynamics analysis.

[0034] Step 3-2: Establish a linear ordinary differential equation for the temperature and pressure in the cavity, and obtain the updated equation for the temperature and pressure based on the time step:

[0035]

[0036]

[0037] Where, subscript in: cavity inlet parameter, subscript out: cavity outlet parameter, V C : volume of the cavity, η: combustion efficiency, W: flow rate, W f : Fuel flow, H f : Fuel calorific value, h: Total enthalpy, h C : fuel static enthalpy;

[0038] Step 3-3: Using the steady-state results as the initial values, calculate the total temperature and total pressure using equations (9) and (10), and calculate the Mach number using the flow formula to obtain the static temperature and static pressure;

[0039] Step 3-4: Based on these parameters, the modal modeling method in step (2) is used to solve the problem. At this point, all the parameters of the flow field at time t are obtained, which are used as the initial values ​​at time t+1, and the calculation is repeated until the total temperature and total pressure change rate is 0.

[0040] Beneficial effects: The present invention provides a one-dimensional modeling method for scramjet engine volumetric dynamics. Compared with the prior art, the above technical solution has the following technical effects:

[0041] (1) By analyzing the mechanism of scramjet engines, the present invention reduces the multidimensional flow to a one-dimensional flow along the engine axis. The constructed model can well match the experimental data, thus improving the real-time performance of the model.

[0042] (2) The present invention adopts the volumetric dynamics method to establish a one-dimensional dynamic model of the scramjet engine, which can reflect the dynamic working characteristics of the scramjet engine and meet the requirements of engine control system design. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a schematic diagram of the scramjet engine structure.

[0044] Figure 2 It is a simplified diagram of the volume effect within the combustion chamber.

[0045] Figure 3 It is a flow chart of the present invention.

[0046] Figure 4 This is a comparison chart of the model static pressure output and experimental data.

[0047] Figure 5 This is a comparison chart of the model Mach number output and experimental data.

[0048] Figure 6 This is the tracking diagram of the PI controller thrust over a large range under the flight conditions of H = 27km and Ma = 6.

[0049] Figure 7 This is the graph showing the fuel flow rate change output by the PI controller under the flight conditions of H = 27 km and Ma = 6. DETAILED DESCRIPTION

[0050] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0051] In order to overcome the shortcomings of the prior art, the present invention provides a one-dimensional modeling method for scramjet engine volumetric dynamics, such as Figure 3As shown, based on the operating principles of scramjet engine components, mathematical models of the scramjet engine's inlet, combustion chamber, and tail nozzle are established, as well as mathematical models of the scramjet engine's shockless mode, scramjet oblique shock mode, and subcombustion mode. Based on these models, a dynamic model of the scramjet engine is established using volumetric dynamics. This invention uses volumetric dynamics to establish a one-dimensional model of the scramjet engine, enabling rapid calculation of changes in combustion chamber axial flow field parameters, meeting the requirements of engine control system design.

[0052] A one-dimensional modeling method for scramjet engine volumetric dynamics comprises the following steps:

[0053] Step 1: Based on the working principles of each component of the scramjet engine, a mathematical model of the scramjet engine's inlet, combustion chamber, and tail nozzle is established;

[0054] Step 2: Based on the scramjet combustion field mechanism, mathematical models of the scramjet engine's scramjet shockless mode, scramjet oblique shock mode, and subcombustion mode are established;

[0055] Step 3: Based on the volumetric dynamics principle and the scramjet engine modal model established in step 2, a scramjet engine dynamic model is established.

[0056] In order to facilitate public understanding, the technical solution of the present invention is described in detail below with reference to the accompanying drawings:

[0057] 1. Inlet model

[0058] From the working principle of the scramjet engine, we know that the compression of the airflow in its inlet is mainly completed through three oblique shock waves. Therefore, the basis of the scramjet engine inlet modeling is the oblique shock wave model.

[0059] The shock wave Mach number Ma f , the airflow deflection angle δ, the shock wave angle β can be calculated:

[0060]

[0061] Where,

[0062]

[0063]

[0064] On the basis of obtaining the shock wave angle, the three oblique shock waves in the inlet are solved in sequence by the wave front and wave back formula of the oblique shock wave, and the inlet outlet parameters (i.e., the isolation section inlet parameters) can be calculated from the inlet inlet atmospheric parameters.

[0065] 2. Combustion chamber model

[0066] The one-dimensional model of a scramjet combustion chamber treats the combustion chamber as a one-dimensional pipe and uses one-dimensional gas dynamics equations to describe the flow within the scramjet combustion chamber. Given a variable combustion chamber area, inlet conditions, and fuel addition conditions, the one-dimensional gas dynamics governing equations are solved to obtain the flow parameter distribution along the combustion chamber axis, thereby estimating the scramjet combustion chamber performance parameters.

[0067] Based on the experimental data, the polynomial fitting method is used to give the total temperature distribution along the entire flow direction.

[0068]

[0069] Where x is the axial position coordinate of the engine combustion chamber (m), T t (x) is the total temperature at position x, T t2 is the total temperature at the inlet of the isolation section, τ is the total heating ratio, θ is the heat release rate, which is an empirical constant ranging from 1 to 10, χ: dimensionless axial position, x i is the fuel injection point, and x4 is the combustion chamber outlet.

[0070] The friction coefficient is predicted using the following formula

[0071]

[0072] Where C f : local friction coefficient, k: gas adiabatic index, Re x : local Reynolds number, ρ is the local density, V is the local velocity, x is the local axial position coordinate with the engine inlet as the origin, and μ is the local gas dynamic viscosity, which is calculated by the Sutherland formula

[0073]

[0074] Where μ0 is the viscosity coefficient under standard atmospheric conditions, T s is the Sussinian constant, which is related to the properties of the gas, T c =273.16K, T is the local temperature.

[0075] The one-dimensional control equation of the flow field in the scramjet combustion chamber is derived from the basic control equations of gas dynamics. The Mach number Ma, total pressure p t As the one-dimensional coordinate x changes, the relationships are

[0076]

[0077]

[0078] Where, A: combustion chamber cross-sectional area, T t : total temperature; D: hydraulic diameter of combustion chamber;

[0079] On the basis of the Mach number and total pressure, other parameters are calculated from the gas dynamics function;

[0080]

[0081]

[0082]

[0083] Where, T: static temperature, P: static pressure, V: velocity, R: molar gas constant.

[0084] 3. Nozzle model

[0085] The high-temperature, high-pressure airflow from the combustion chamber expands through the tail nozzle, generating thrust. The thermodynamic process of the gas in the nozzle can be considered as an adiabatic and isentropic flow. According to the flow continuity balance equation of the throat and nozzle outlet cross section:

[0086]

[0087] in,

[0088] The static pressure P6, velocity V6, and flow rate at the tail nozzle outlet can be calculated from formula (7): The total engine thrust is then calculated as:

[0089]

[0090] 4. Scramjet oblique shock wave mode

[0091] First, a model of the interaction between the isolation section and the combustion chamber is established. When boundary layer separation occurs in the combustion chamber, the following relationship exists between the inlet pressure and peak pressure of the separation section of the combustion chamber.

[0092] p3=δp max (34)

[0093] Where, p3 is the pressure at the combustion chamber inlet (isolation section outlet), p max is the peak pressure of the combustion chamber, and δ is the dimensionless similarity criterion number, which can be determined as follows: using the scramjet-shockless mode combustion chamber model, continuously increase the fuel input until the lowest Mach number of the combustion chamber is equal to 0.762 times the Mach number of the isolator inlet, which is the boundary between the scramjet-shockless mode and the scramjet oblique shock mode. Calculate the ratio of the peak pressure of the combustion chamber to the isolator outlet pressure at this time;

[0094] Secondly, the model of the shock wave compression section of the isolation section is established. Based on the calculated isolation section outlet pressure, the isolation section outlet Mach number Ma3 is calculated by the formula, and then other parameters are obtained by the formula:

[0095]

[0096] Where Ma2 is the Mach number at the inlet of the isolation section, p3 is the pressure at the outlet of the isolation section, and p2 is the pressure at the inlet of the isolation section;

[0097] Calculate the length of the shock train in the isolation section again. The empirical relationship for the length of the shock train in a rectangular straight pipe

[0098]

[0099] Where, L s is the shock train length (m), Ma2 is the Mach number at the start of the shock train, and θ2 is the momentum thickness of the boundary layer at the entrance of the isolation section (m)

[0100]

[0101] Re θ is the Reynolds number at the inlet of the isolation section (with the boundary layer momentum thickness θ2 as the characteristic length), D is the equivalent diameter of the inlet of the isolation section (m);

[0102] Then the axial pressure distribution p(x) inside the shock train is calculated by the cubic polynomial

[0103]

[0104] Where χ is the dimensionless axial position, x2 is the shock train entrance position, and x3 is the isolation section exit position;

[0105] Finally, the combustion chamber separation section model can be modeled using the shock wave train internal parameter calculation method, and the axial pressure distribution p(x) of the combustion chamber separation section can be calculated by the quadratic polynomial.

[0106]

[0107] Where, χ: dimensionless axial position, x3 is the combustion chamber inlet position, x max It is the outlet position of the separation section of the combustion chamber, that is, the position of the highest pressure point.

[0108] 5. Subcombustion mode

[0109] First, determine the location of the critical sonic point. For equation (7), when Ma = 1, since the flow field parameters are continuous at the sonic point, ignoring the influence of friction, the following equation must hold:

[0110]

[0111] Where * represents the critical sound speed state.

[0112] The position of the critical sound velocity point can be calculated from the above formula. Taking the first-order derivative of the numerator and denominator with respect to x yields:

[0113]

[0114] Where:

[0115]

[0116]

[0117] Solving this linear equation of two variables can yield two solutions

[0118]

[0119] According to the working principle of scramjet engines, the airflow accelerates from subsonic speed to supersonic speed in the combustion chamber, and the Mach number increases. Therefore, the positive answer should be taken to calculate the Mach number before and after the sonic point.

[0120]

[0121]

[0122] Finally, through formula (23) and formula (24), Ma u As the initial condition, the solution is obtained by integrating forward along the axial direction of the combustion chamber from the critical sonic point, and the distribution of the parameters in the subsonic region of the combustion chamber is calculated in Ma. d The parameter distribution in the supersonic region of the combustor is calculated by integrating backward along the combustion chamber axis from the critical sonic point as the initial condition. The parameter distribution within the isolation section can be calculated using the modeling method of the scramjet oblique shock wave mode isolation section.

[0123] 6. Transcendental shock-free mode

[0124] When a scramjet is in the scramjet shockless mode, the entire flow path experiences supersonic flow, and there is no boundary layer separation between the isolator and the combustion chamber. The aerodynamic parameter distributions of the isolator and combustion chamber can be directly obtained by solving the ordinary differential equations.

[0125] 7. Volumetric dynamics model of scramjet engine

[0126] The scramjet engine dynamic model established in this paper has a combustion chamber structure diagram shown in Figure 1. The combustion chamber inlet is used as the cavity inlet, and the location of the point to be substituted is used as the cavity outlet. After determining the cavity outlet location, volumetric dynamics analysis is performed. A linear ordinary differential equation for the temperature and pressure within the cavity is established, resulting in an update equation for the temperature and pressure based on the time step:

[0127]

[0128]

[0129] Where, subscript in: cavity inlet parameter, subscript out: cavity outlet parameter, V C : volume of the cavity, η: combustion efficiency, W: flow rate, W f : Fuel flow, H f : Fuel calorific value, h: Total enthalpy, h C : Fuel static enthalpy.

[0130] Using the steady-state results as initial values, the total temperature and total pressure are calculated using Equations (25) and (26). The Mach number is calculated using the flow formula, and thus the static temperature and static pressure are obtained. Based on these parameters, the modal modeling method is used to solve the problem. At this point, all the flow field parameters at time t are obtained and used as the initial values ​​at time t+1. The calculation is repeated until the rate of change of the total temperature and total pressure reaches 0.

[0131] To verify the accuracy of the model, the model output was compared with experimental data. Figure 4 and Figure 5 The following figure shows a comparison of the model output and experimental parameters. It can be seen that the model output matches the experimental parameters, effectively capturing the pressure peak during combustion and the pressure rise point in the isolator, with an average error of less than 3%. This comparison of the steady-state model output and experimental parameters demonstrates that the established scramjet mathematical model can be used to simulate the changes in axial flow parameters during scramjet combustion.

[0132] The mathematical model of scramjet engine is used as the controlled object, and the three-point fuel flow wf distributed in the axial direction of the engine combustion chamber is used as the controlled object. i (i=1,2,3) are the control variables, and the engine thrust F is the controlled variable. A digital simulation of thrust command tracking control is performed to verify that the established scramjet engine can be used for the design of control systems.

[0133] Under the atmospheric conditions of 27km altitude and Ma=6, a PI (proportional-integral) controller is designed. The control effect is as follows: Figure 6 and Figure 7 As shown. Figure 6It can be seen that under large-step and small-step acceleration and deceleration control instructions, the established scramjet engine can reflect the working state of the engine and can be used in the design of engine control systems.

[0134] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A one-dimensional modeling method for scramjet engine volumetric dynamics, characterized by: The following steps are involved: Step 1: Based on the working principles of each component of the scramjet engine, a mathematical model of the scramjet engine's inlet, combustion chamber, and tail nozzle is established; Step 2: Based on the scramjet combustion field mechanism, mathematical models of the scramjet engine's scramjet shockless mode, scramjet oblique shock mode, and subcombustion mode are established; Step 3: Based on the volumetric dynamics principle and the scramjet engine modal model established in step 2, a scramjet engine dynamic model is established; The specific steps for establishing the dynamic model of volume dynamics in step 3 are as follows: Step 3-1: Use the combustion chamber inlet as the cavity inlet and the position of the point to be substituted as the cavity outlet. After determining the cavity outlet position, perform volumetric dynamics analysis. Step 3-2: Establish a linear ordinary differential equation for the temperature and pressure in the cavity, and obtain the updated equation for the temperature and pressure based on the time step: Where, subscript in: cavity inlet parameter, subscript out: cavity outlet parameter, V C : volume of the cavity, η: combustion efficiency, W: flow rate, W f : Fuel flow, H f : Fuel calorific value, h: Total enthalpy, h C : fuel static enthalpy; Step 3-3: Using the steady-state results as the initial values, calculate the total temperature and total pressure using equations (1) and (2), and calculate the Mach number using the flow formula to obtain the static temperature and static pressure; Step 3-4: Based on these parameters, the modal modeling method in step (2) is used to solve the problem. At this point, all the parameters of the flow field at time t are obtained, which are used as the initial values ​​at time t+1, and the calculation is repeated until the total temperature and total pressure change rate is 0.

2. The one-dimensional modeling method for scramjet engine volumetric dynamics according to claim 1, characterized in that: The method for establishing a mathematical model of a scramjet combustion chamber in step 1: Step 1-1: Based on the experimental data, the polynomial fitting method is used to give the total temperature distribution along the entire flow direction Where x is the axial position coordinate of the engine combustion chamber, T t (x) is the total temperature at position x, T t2 is the total temperature at the inlet of the isolation section, τ is the total heating ratio; θ is the heat release rate, which is an empirical constant from 1 to 10; χ is the dimensionless axial position, x i is the fuel injection point position, x4 is the combustion chamber outlet position; Step 1-2: Predict the coefficient of friction using the following formula Where C f : local friction coefficient, k: gas adiabatic index, Re x : local Reynolds number, ρ is the local density, V is the local velocity, x is the local axial position coordinate with the engine inlet as the origin, and μ is the local gas dynamic viscosity, which is calculated by the Sutherland formula Where μ0 is the viscosity coefficient under standard atmospheric conditions, T s is the Sussinian constant, which is related to the properties of the gas, T c =273.16K, T is the local temperature; Step 1-3: Derive the one-dimensional governing equations of the flow field in the scramjet combustion chamber from the basic governing equations of gas dynamics, Mach number Ma, total pressure p t As the one-dimensional coordinate x changes, the relationships are Where, A: combustion chamber cross-sectional area, T t : total temperature; D: hydraulic diameter of combustion chamber; Step 1-4: Based on the Mach number and total pressure, other parameters are calculated from the gas dynamics function; Where, P: static pressure, R: molar gas constant.

3. The one-dimensional modeling method for scramjet engine volumetric dynamics according to claim 1, characterized in that: The specific steps of the method for modal modeling of the scramjet engine combustion chamber in step 2 are as follows: Step 2-1: Establish the transition boundaries between different combustion modes. The transition boundary between the scramjet-shockless mode and the scramjet-shock mode is as follows: when the minimum Mach number of the combustion chamber is greater than 0.762 times the Mach number of the isolator inlet, the combustion chamber operates in the scramjet-shockless mode; otherwise, the combustion chamber operates in the scramjet-shock mode. The transition boundary between the scramjet-shock mode and the subcombustion mode is as follows: when the minimum Mach number of the combustion chamber is greater than or equal to 1, the combustion chamber operates in the scramjet-shock mode; otherwise, the combustion chamber operates in the subcombustion mode. Step 2-2: When the scramjet is in the shock-free mode, the entire flow path is supersonic, and there is no boundary layer separation between the isolator and the combustion chamber. The isolator is considered as a one-dimensional steady Fano flow section, and the combustion chamber is a variable-section heating pipe flow with the engine geometric surface as the flow surface. Solve the ordinary differential equations to obtain the distribution of various aerodynamic parameters of the isolator and the combustion chamber. Step 2-3: When the scramjet engine is in the scramjet oblique shock wave mode, the entire flow path is supersonic, and the isolator section and the combustion chamber produce boundary layer separation; the front section of the isolator section is the Fano flow section, and the rear section is the shock compression section; the front section of the combustion chamber is the combustion separation section, and the rear section is the separation and attachment section; the shock compression section of the isolator section and the separation section of the combustion chamber are based on the engine geometric surface minus the separation area as the flow surface, and the Fano flow section of the isolator section and the separation and attachment section of the combustion chamber are based on the engine geometric surface as the flow surface; Step 2-4: When the scramjet engine is in the subsonic mode, the high back pressure generated in the combustion chamber will cause a strong shock wave train to appear inside the isolation section. The front section of the isolation section is still the Fano flow section, and the rear section is still the shock wave compression section. The combustion chamber inlet is subsonic, there is no boundary layer separation, and the engine geometric surface is the flow surface.

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