A nozzle ablation prediction method based on control mechanism and diffusion contribution degree

Abstract

The application discloses a nozzle ablation prediction method based on control mechanism and diffusion contribution degree, and belongs to the technical field of thermal protection of solid rocket engines. The method obtains nozzle structure parameters, thermal protection material parameters and gas inflow parameters, calculates the Mach number, pressure and temperature of any section of the nozzle based on one-dimensional isentropic flow relationship, respectively calculates the ablation rates under chemical reaction control and diffusion control, calculates Damkohler number by taking the ratio of the two, and determines the ablation control mechanism. Further, the diffusion contribution degree constant is introduced to continuously correct the ablation rate in the transition stage, and finally the predicted ablation rate is output. The method has high calculation efficiency and can improve the prediction accuracy of the nozzle ablation.

Description

Technical Field

[0001] This specification relates to the field of thermal protection technology for solid rocket motors, and more specifically, this application relates to a nozzle ablation prediction method based on control mechanism and diffusion contribution. Background Technology

[0002] During solid rocket motor operation, high-temperature, high-pressure combustion gases containing oxidizing components flow through the nozzle. The thermal protection material on the nozzle wall undergoes thermochemical ablation under the combined effects of aerodynamic heating and chemical composition. The ablation rate directly determines the changes in nozzle throat dimensions and internal profile regression, thus affecting the overall performance of the engine. Therefore, accurately predicting the ablation rate of the nozzle thermal protection material is a crucial step in solid rocket motor design, thermal protection scheme evaluation, and lifespan prediction.

[0003] Nozzle ablation involves two control mechanisms: at low temperatures, the chemical reaction rate at the wall is low, and the ablation rate is controlled by chemical kinetics; at high temperatures, the chemical reaction rate rises rapidly, and the diffusion replenishment capacity of oxidizing components within the boundary layer becomes the limiting factor, thus controlling the ablation rate by diffusion. A transition zone exists between these two mechanisms, where chemical reaction and diffusion jointly constrain the ablation rate. Commonly used ablation prediction methods in engineering fall into two main categories: one is based on fitting empirical formulas to experimental data, which is simple in form but cannot describe the transition of control mechanisms, and the prediction error in the transition zone is generally large; the other is detailed numerical simulation, which has high accuracy but high computational cost, making it difficult to meet the rapid iteration requirements of the design phase. Therefore, a high-accuracy method suitable for rapid prediction in engineering is lacking to address the problems of complex ablation control mechanisms and high computational costs.

[0004] Therefore, there is still a lack of a nozzle ablation prediction method in the existing technology that can take into account the determination of ablation control mechanism, continuous description of transition stage and the need for rapid engineering calculation. Summary of the Invention

[0005] The summary section introduces a series of simplified concepts, which will be further explained in detail in the detailed description section. This summary section is not intended to limit the key and essential technical features of the claimed technical solution, nor is it intended to determine the scope of protection of the claimed technical solution.

[0006] Firstly, this application proposes a nozzle ablation prediction method based on control mechanism and diffusion contribution, including: S1. Obtain the structural parameters and incoming flow parameters of the solid rocket motor nozzle. The nozzle structural parameters include nozzle geometry parameters and thermal protection material performance parameters. The incoming flow parameters include gas composition content, incoming flow pressure and incoming flow temperature. S2. Based on the above nozzle structure parameters and the above incoming flow parameters, calculate the flow characteristics of the gas in the nozzle to obtain the Mach number, pressure and temperature at any cross-sectional position. S3. Based on the above thermal protection material performance parameters and the above flow characteristics, calculate the ablation rate of each oxidizing component under chemical reaction control and diffusion control, respectively. S4. Based on the ablation rate under the control of the above chemical reaction and the ablation rate under the control of the above diffusion, calculate the Damcole number, and determine the control mechanism of the current ablation model based on the Damcole number. S5. Calculate the diffusion contribution constant based on the Damköhler number and the control mechanism described above. S6. Calculate the predicted ablation rate based on the above diffusion contribution constant and the above diffusion-controlled ablation rate. S7. Output the predicted ablation rate to complete the nozzle ablation prediction.

[0007] In one feasible implementation, the above-mentioned nozzle geometry parameters include the nozzle throat diameter, arbitrary cross-sectional diameter, and throat transition radius; the above-mentioned thermal protection material performance parameters include solid wall density, solid element molar amount, and material ablation test correction parameters; and the above-mentioned fuel gas composition content includes oxidizing component content.

[0008] In one feasible implementation, the incoming flow parameters of the gas at any cross-section within the nozzle are calculated based on a one-dimensional isentropic flow relationship, and the Mach number, pressure, and temperature at any cross-section satisfy the following:

[0009] in, For any cross-sectional diameter, The diameter of the nozzle throat. For any cross section, the Mach number is... For the incoming flow pressure, For pressure at any cross section, For the incoming flow temperature, For any cross-sectional temperature, This refers to the specific heat ratio of the fuel gas.

[0010] In one feasible implementation, when At that time, determine The system determines that the gas reaches the speed of sound at the nozzle throat. when At that time, the above Mach number has two solutions, among which Corresponding to the converging section at the front of the Laval nozzle throat, the combustion gas flows at subsonic speeds. Corresponding to the expansion section at the rear end of the Laval nozzle throat, the combustion gas flows at supersonic speeds.

[0011] In one feasible implementation, the oxidizing components in the fuel gas include and One or more of the above-mentioned chemical reactions; the ablation rate under the control of the above chemical reactions is calculated according to the following formula:

[0012] in, The ablation rate under chemical reaction control. Density of the solid wall The amount of oxidizing components participating in the ablation reaction, For the first Partial pressure of the oxidizing component, For the first The reaction order corresponding to the oxidizing component. For the first The reaction kinetic rate of the oxidizing component.

[0013] In one feasible implementation, the above-mentioned first... The reaction kinetic rate of the oxidizing component is calculated according to the Arrhenius equation and satisfies:

[0014] in, For the first The pre-exponential factor of the term response, For the first The temperature index of the reaction, For the first The activation energy of the reaction. The gas constant is... For any cross-section temperature.

[0015] In one feasible implementation, the ablation rate under diffusion control described above is calculated according to the following formula:

[0016] in, The ablation rate under diffusion control. The molar amount of the solid-phase element. The convective heat transfer coefficient is... For the specific heat capacity of the gas at constant pressure, Density of the solid wall and These represent the number of moles of the corresponding oxidizing component per kilogram of fuel gas.

[0017] In one feasible implementation, the above-mentioned convective heat transfer coefficient is calculated according to the Bartz formula and satisfies:

[0018] in, For Prandtl numbers, The gas dynamic viscosity coefficient, The diameter of the nozzle throat. The radius of the transition arc at the throat. This represents the area of ​​the nozzle throat. For the required cross-sectional area, For mass flow rate, This is the temperature correction factor.

[0019] In one feasible implementation, the above temperature correction factor is calculated according to the following formula:

[0020] in, For any cross-sectional temperature, For the incoming flow temperature, The specific heat ratio of the fuel gas. Let be the Mach number for any cross section.

[0021] In one feasible implementation, S4 to S6 above include: calculating the Damcole number according to the following formula:

[0022] when At that time, it was determined that the ablation was in the chemical kinetic control stage; when At that time, it was determined that the ablation was in the diffusion-controlled stage; when When the ablation is within the transition range, it is determined that the ablation is in a transitional stage where chemical kinetics control and diffusion control are combined. The diffusion contribution constant calculated based on the Damköhler number above satisfies:

[0023] in, The diffusion contribution constant, The correction factor is determined by ablation test data of nozzle thermal protection material under different operating conditions; The ablation rate is predicted using the following formula:

[0024] in, To predict the ablation rate; and, when At that time, it was determined that ablation was mainly controlled by chemical reactions. At 0.8, it was determined that ablation was mainly controlled by diffusion. At that time, it was determined that the ablation was in the transitional stage.

[0025] In summary, this invention introduces a diffusion contribution factor η to quantify the dimensionless influence of diffusion on the actual ablation rate during nozzle ablation, enabling the ablation control mechanism to be expressed in a clear parametric form. Compared to methods relying solely on empirical formula fitting, this invention clearly reflects the relationship between chemical reaction control and diffusion control under different operating conditions, with a more explicit physical meaning. This invention utilizes the Damk-Kole number to determine the ablation control mechanism and uses a modified formula to continuously describe the ablation rate in the transition phase, avoiding prediction errors caused by artificial segmentation or abrupt switching between the chemical kinetic control and diffusion control phases in existing methods. Furthermore, the correction coefficient w can be calibrated based on ablation test data of different thermal protection materials, making the method adaptable to different materials and engine operating conditions, thus improving the accuracy of ablation prediction in the transition zone. The calculation process of this invention is mainly based on one-dimensional isentropic flow relationships, Arrhenius reaction kinetics formulas, Bartz convective heat transfer formulas, and algebraic calculations. It eliminates the need for complex coupled numerical models of flow field, heat transfer, and chemical reaction, as well as costly iterative solutions, significantly reducing computational load. This makes it suitable for preliminary design, parameter comparison, and rapid engineering iteration of nozzle thermal protection schemes. This invention employs a unified dimensionless parameter framework to describe the chemical kinetic control stage, the diffusion control stage, and the transition stage where both interact. This allows the ablation rate of the nozzle under different temperatures, cross-sectional locations, and oxidizing components to be calculated within the same model, eliminating the need to switch prediction models for different operating conditions. This facilitates integration with engineering software and practical design applications.

[0026] Other advantages, objectives and features of this application will be apparent in part from the description which follows, and in part from what those skilled in the art will understand through study and practice of this application. Attached Figure Description

[0027] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit this specification. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 A schematic diagram of a nozzle ablation prediction method based on control mechanism and diffusion contribution provided for embodiments of this application; Figure 2 A schematic diagram of the geometry of a nozzle and the materials of its components, provided for an embodiment of this application; Figure 3 A Mach number and pressure curve of an arbitrary cross section is provided for an embodiment of this application; Figure 4 A temperature profile of an arbitrary cross-section of a nozzle is provided as an embodiment of this application; Figure 5 An embodiment of this application provides a nozzle throat at different incoming flow temperatures. Chem curve; Figure 6 An embodiment of this application provides a throat section under different incoming flow temperatures. diff curve graph; Figure 7 This is a curve showing the ablation contribution η of the nozzle throat at different incoming flow temperatures, provided as an embodiment of this application. Detailed Implementation

[0028] The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus. The technical solutions of the embodiments of this application will now be clearly and completely described in conjunction with the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them.

[0029] Please see Figure 1 This is a flowchart illustrating a nozzle ablation prediction method based on control mechanism and diffusion contribution, provided in an embodiment of this application. Specifically, it may include: S1. Obtain the structural parameters and incoming flow parameters of the solid rocket motor nozzle. The nozzle structural parameters include nozzle geometry parameters and thermal protection material performance parameters. The incoming flow parameters include gas composition content, incoming flow pressure and incoming flow temperature. S2. Based on the above nozzle structure parameters and the above incoming flow parameters, calculate the flow characteristics of the gas in the nozzle to obtain the Mach number, pressure and temperature at any cross-sectional position. S3. Based on the above thermal protection material performance parameters and the above flow characteristics, calculate the ablation rate of each oxidizing component under chemical reaction control and diffusion control, respectively. S4. Based on the ablation rate under the control of the above chemical reaction and the ablation rate under the control of the above diffusion, calculate the Damcole number, and determine the control mechanism of the current ablation model based on the Damcole number. S5. Calculate the diffusion contribution constant based on the Damköhler number and the control mechanism described above. S6. Calculate the predicted ablation rate based on the above diffusion contribution constant and the above diffusion-controlled ablation rate. S7. Output the predicted ablation rate to complete the nozzle ablation prediction.

[0030] In one feasible implementation, the above-mentioned nozzle geometry parameters include the nozzle throat diameter, arbitrary cross-sectional diameter, and throat transition radius; the above-mentioned thermal protection material performance parameters include solid wall density, solid element molar amount, and material ablation test correction parameters; and the above-mentioned fuel gas composition content includes oxidizing component content.

[0031] For example, during the operation of a solid rocket motor, the high-temperature, high-pressure gas generated by propellant combustion flows along the nozzle and is accelerated and discharged. The nozzle throat and its surrounding area are prone to thermal ablation due to high flow velocity, drastic pressure and temperature changes, and the combined effects of chemical reactions with oxidizing components such as H₂O, CO₂, OH, O, and O₂, as well as diffusion within the gas boundary layer. Traditional ablation prediction methods often directly employ a single chemical reaction rate model or a single diffusion control model, which fails to reflect the changes in ablation control mechanisms under different temperatures, cross-sectional locations, and oxidizing components. This embodiment first calculates the internal flow characteristics of the nozzle, then establishes chemical reaction-controlled ablation rates and diffusion-controlled ablation rates respectively, and further introduces the Damk-Köhler number and diffusion contribution constant, enabling the predicted ablation rate to adaptively change with the local operating conditions of the nozzle and the reaction-diffusion relationship.

[0032] Specifically, in step S1, the structural parameters and incoming flow parameters of the solid rocket motor nozzle are first obtained. The nozzle structural parameters characterize the nozzle's geometric channel shape and the ablation resistance of the thermal protection material itself. For example, the nozzle throat diameter determines the critical flow state at the throat, the diameter of any cross-section determines the flow area at different axial positions of the nozzle, and the throat transition radius affects the convective heat transfer intensity near the throat. The solid wall density and the molar amount of solid elements are used to convert oxidation consumption into wall material retreat velocity, and the material ablation test correction parameters are used to correct the theoretical model based on actual experimental data. The incoming flow parameters describe the initial state of the gas entering the nozzle, including the content of each oxidizing component in the gas, the incoming flow pressure, and the incoming flow temperature. These parameters collectively determine the chemical oxidation and thermal scouring capabilities of the gas on the nozzle wall.

[0033] In step S2, based on the nozzle geometry and incoming flow parameters obtained in step S1, the flow characteristics of the gas at any cross-sectional position within the nozzle are calculated. Since solid rocket motor nozzles are typically Laval nozzles, the gas gradually accelerates in the convergent section, reaches sonic speed at the throat, and further accelerates to supersonic speed in the expansion section. Therefore, by using the area relationship between the diameter of any cross-section and the throat diameter, combined with a one-dimensional isentropic flow relationship, the Mach number corresponding to that cross-section can be obtained, and the pressure and temperature at that cross-section can be further calculated. This transforms the geometric changes along the nozzle into local thermodynamic and dynamic states, providing cross-sectional input conditions for subsequent ablation rate calculations. Especially near the nozzle throat, where the gas incoming flow parameters change most drastically, this region is often the most sensitive location for ablation; therefore, calculating the flow characteristics of any cross-section can improve the spatial resolution of ablation prediction.

[0034] In step S3, based on the performance parameters of the thermal protection material and the Mach number, pressure, and temperature obtained in step S2, the ablation rates under chemical reaction control and diffusion control are calculated respectively. The ablation rate under chemical reaction control mainly reflects the ability of oxidizing components to react chemically with the solid thermal protection material after reaching the wall surface. Its magnitude is related to the partial pressure of the oxidizing component, the reaction order, the reaction kinetic rate, and the density of the wall material. The reaction kinetic rate can be determined according to the Arrhenius formula, incorporating the influence of temperature on the chemical reaction rate into the model. The ablation rate under diffusion control mainly reflects the ability of oxidizing components to be transported across the boundary layer to the wall surface. Its magnitude is related to the convective heat transfer coefficient of the combustion gas, the specific heat capacity of the combustion gas at constant pressure, the molar amount of solid elements, the wall density, and the molar number of each oxidizing component. Therefore, this invention does not simply use the combustion gas temperature as the sole criterion, but simultaneously considers the local flow state, the concentration of oxidizing components, the heat and mass transfer capacity, and the material properties, making the ablation rate calculation more closely reflect the actual working environment of the nozzle.

[0035] In step S4, the Damcole number is calculated based on the ablation rate under chemical reaction control and the ablation rate under diffusion control. The Damcole number characterizes the relative relationship between the ability of chemical reaction to consume oxidizing gas and the ability of diffusion to replenish oxidizing gas. When the Damcole number is small, it indicates that the chemical reaction consumption rate is less than the diffusion replenishment rate, the supply of oxidizing components near the wall is relatively sufficient, and the ablation process is mainly limited by chemical reaction kinetics. When the Damcole number is large, it indicates that the chemical reaction consumption rate is greater than the diffusion replenishment rate, the supply of oxidizing components near the wall is insufficient, and the ablation process is mainly limited by diffusion mass transfer capacity. When the Damcole number is in the intermediate range, it indicates that both chemical reaction and diffusion replenishment have a significant impact on ablation, and ablation is in a transitional control stage. Through this step, this embodiment can automatically identify the ablation control mechanism based on local operating conditions, rather than manually preset a fixed control mode.

[0036] In step S5, the diffusion contribution constant is calculated based on the Damcole number and the determined control mechanism. This diffusion contribution constant can be understood as the proportion of the diffusion control mechanism's contribution to the actual ablation rate, and its value is typically between 0 and 1. When ablation is mainly controlled by chemical reaction, the diffusion contribution constant approaches 0, indicating that the actual ablation rate is closer to the rate under chemical reaction control; when ablation is mainly controlled by diffusion, the diffusion contribution constant approaches 1, indicating that the actual ablation rate is closer to the rate under diffusion control. When ablation is in the transition stage, the diffusion contribution constant changes continuously according to the Damcole number, thus smoothly characterizing the transition from chemical reaction control to diffusion control. Material ablation test correction parameters can be used to correct this contribution curve, so that the theoretical calculation results can match the measured ablation laws under different thermal protection materials and different engine operating conditions.

[0037] In step S6, the predicted ablation rate is calculated based on the diffusion contribution constant obtained in step S5 and the diffusion-controlled ablation rate obtained in step S3. Since the diffusion-controlled ablation rate can be considered the upper limit of ablation under conditions of restricted oxidizing component transport, and the diffusion contribution constant reflects the degree to which the current ablation process approaches this upper limit, combining the two yields a predicted ablation rate that neither exceeds the diffusion limit nor fails to reflect the limiting effect of the chemical reaction. This approach avoids the problem of excessively high ablation rates that may occur when using a purely chemical reaction model at high temperatures, and also avoids overestimating ablation when using a purely diffusion model at low temperatures or with insufficient reaction kinetics.

[0038] In step S7, the predicted ablation rate is output to complete the nozzle ablation prediction. The output result can be the local ablation rate at any cross-section of the nozzle, or it can be further used to form an ablation rate distribution curve along the nozzle axis to identify high ablation risk locations in the nozzle throat and the areas before and after it.

[0039] In one feasible implementation, the incoming flow parameters of the gas at any cross-section within the nozzle are calculated based on a one-dimensional isentropic flow relationship, and the Mach number, pressure, and temperature at any cross-section satisfy the following:

[0040] in, For any cross-sectional diameter, The diameter of the nozzle throat. For any cross section, the Mach number is... For the incoming flow pressure, For pressure at any cross section, For the incoming flow temperature, For any cross-sectional temperature, This refers to the specific heat ratio of the fuel gas.

[0041] In one feasible implementation, when At that time, determine The system determines that the gas reaches the speed of sound at the nozzle throat. when At that time, the above Mach number has two solutions, among which Corresponding to the converging section at the front of the Laval nozzle throat, the combustion gas flows at subsonic speeds. Corresponding to the expansion section at the rear end of the Laval nozzle throat, the combustion gas flows at supersonic speeds.

[0042] For example, solid rocket motor nozzles are typically Laval nozzles. After the combustion gas enters the nozzle from the combustion chamber, it is gradually accelerated in the convergent section, reaches a critical state at the throat, and then continues to expand and accelerate in the divergent section. Before performing ablation prediction, it is necessary to determine the Mach number, pressure, and temperature of the gas at any cross-section of the nozzle, as these incoming flow parameters directly affect the subsequent chemical reaction rate, the diffusion capacity of oxidizing components, and the intensity of convective heat transfer.

[0043] Specifically, this method approximates the gas flow within the nozzle as a one-dimensional isentropic flow, meaning that the average cross-sectional parameters of the gas flowing along the nozzle axis can be determined by the relationship between the nozzle cross-sectional area and the flow rate. Since the nozzle cross-sectional area is related to its diameter, it can be determined using any cross-sectional diameter. With nozzle throat diameter The ratio of the two values ​​is used to establish the area relationship between the cross section and the throat, and then the Mach number corresponding to the cross section is further calculated. The calculation relationship can be expressed as:

[0044] in, Let the diameter of the nozzle cross section be any. The diameter of the nozzle throat. Let Mach number be the number at any cross-section. This is the specific heat ratio of the gas. Using this formula, the velocity state of the gas at different cross-sectional positions can be determined based on the nozzle geometry, thus indicating whether the gas is in a subsonic, sonic, or supersonic flow state.

[0045] After obtaining the Mach number of any cross-section, the pressure and temperature at that cross-section are further calculated based on the one-dimensional isentropic flow relationship, specifically satisfying:

[0046] in, For the incoming flow pressure, For pressure at any cross section, For the incoming flow temperature, Let be the temperature of any cross-section. From the above relationships, it can be seen that as the gas accelerates within the nozzle, the Mach number gradually increases, and the static pressure and static temperature of the gas gradually decrease; especially in the expansion section, where the gas continues to accelerate from sonic speed to supersonic speed, the decrease in pressure and temperature is even more pronounced.

[0047] When any cross-sectional diameter equal to the diameter of the nozzle throat At this point, the cross-section is the nozzle throat location, which can be determined based on the critical flow relationship. This indicates that the gas reaches sonic speeds at the throat. The nozzle throat is typically the location with the most drastic changes in gas velocity, high heat flux density, and a high risk of ablation. Therefore, accurately determining the critical flow state at the throat is beneficial for subsequent targeted prediction of the throat ablation rate.

[0048] When any cross-sectional diameter Not equal to the diameter of the nozzle throat Since the Laval nozzle may have the same or similar area ratio before and after the throat, the above area-Mach number relationship usually has two different Mach number solutions. The solution corresponds to the converging section at the front end of the nozzle throat, where the gas has not yet reached the speed of sound and is a subsonic flow. The solution corresponds to the expansion section at the rear end of the nozzle throat, where the gas has already passed the throat and continues to expand and accelerate, which is supersonic flow. Therefore, in actual calculations, it is necessary to select the corresponding Mach number solution based on the axial position of the section in the nozzle to avoid confusing the flow states of the convergence and expansion sections.

[0049] like Figure 3 The diagram shows the Mach number and pressure curves for any cross-section of the nozzle in this embodiment of the invention. Clearly, within the Laval nozzle, the gas pressure continuously decreases while the velocity gradually increases. The pressure at the inlet is 10.69 MPa, while at the outlet it drops to atmospheric pressure, approximately 0.1 MPa. The gas's Mach number remains less than 1 in the convergent phase, indicating subsonic flow. It reaches sonic speed at the throat, after which the gas continues to accelerate until it exits the nozzle. In the diverging phase, the gas's Mach number exceeds 1, achieving supersonic flow.

[0050] like Figure 4 The figure shows a temperature curve of an arbitrary cross-section of the nozzle according to an embodiment of the present invention. The inlet flow temperature is 3500K. The high-temperature gas continuously heats the nozzle structure during the flow process, and the heat is continuously transferred to the surrounding structural domain. Therefore, the gas temperature gradually decreases until it drops to about 2400K at the outlet.

[0051] according to Figure 3 and Figure 4It can be observed that the nozzle throat is the narrowest channel, where the incoming gas flow parameters change drastically. At the same time, the high-temperature gas is continuously accelerating, which will cause significant material reduction in the throat. Therefore, it is necessary to focus on studying the ablation situation in this area.

[0052] Through the above embodiments, the method proposed in this invention can link the nozzle geometric parameters with the gas thermodynamic parameters to obtain the Mach number, pressure, and temperature distribution at any cross-section of the nozzle. This distribution not only reflects the flow evolution of the gas within the nozzle from subsonic to sonic and then to supersonic speeds, but also provides a fundamental input for subsequent calculations of chemically controlled ablation rates, diffusion-controlled ablation rates, and the Damcole number. Therefore, this invention enables nozzle ablation prediction to no longer rely on a single inlet parameter, but rather to perform localized calculations based on the actual flow state at different cross-sections, thereby improving the accuracy of ablation prediction for the nozzle throat and its surrounding regions.

[0053] In one feasible implementation, the oxidizing components in the fuel gas include and One or more of the above-mentioned chemical reactions; the ablation rate under the control of the above chemical reactions is calculated according to the following formula:

[0054] in, The ablation rate under chemical reaction control. Density of the solid wall The amount of oxidizing components participating in the ablation reaction, For the first Partial pressure of the oxidizing component, For the first The reaction order corresponding to the oxidizing component. For the first The reaction kinetic rate of the oxidizing component.

[0055] In one feasible implementation, the above-mentioned first... The reaction kinetic rate of the oxidizing component is calculated according to the Arrhenius equation and satisfies:

[0056] in, For the first The pre-exponential factor of the term response, For the first The temperature index of the reaction, For the first The activation energy of the reaction. The gas constant is... For any cross-section temperature.

[0057] In one feasible implementation, the ablation rate under diffusion control described above is calculated according to the following formula:

[0058] in, The ablation rate under diffusion control. The molar amount of the solid-phase element. The convective heat transfer coefficient is... For the specific heat capacity of the gas at constant pressure, Density of the solid wall and These represent the number of moles of the corresponding oxidizing component per kilogram of fuel gas.

[0059] In one feasible implementation, the above-mentioned convective heat transfer coefficient is calculated according to the Bartz formula and satisfies:

[0060] in, For Prandtl numbers, The gas dynamic viscosity coefficient, The diameter of the nozzle throat. The radius of the transition arc at the throat. This represents the area of ​​the nozzle throat. For the required cross-sectional area, For mass flow rate, This is the temperature correction factor.

[0061] In one feasible implementation, the above temperature correction factor is calculated according to the following formula:

[0062] in, For any cross-sectional temperature, For the incoming flow temperature, The specific heat ratio of the fuel gas. Let be the Mach number for any cross section.

[0063] For example, at any cross-section of the nozzle, the ablation of the nozzle's thermal protection material is not solely determined by temperature, but is simultaneously influenced by the chemical reactivity of the oxidizing components with the wall material, and the ability of the oxidizing components to diffuse and replenish the wall material through the combustion gas boundary layer. Therefore, this invention calculates the ablation rate under chemical reaction control and diffusion control, respectively, providing a basis for subsequently determining the ablation control mechanism through the Damköhler number.

[0064] In one feasible implementation, the oxidizing components in the fuel gas may include and One or more of the above components. Under high-temperature combustion gas conditions, these components can undergo oxidation reactions with carbon-based or other solid elements in the nozzle thermal protection material, leading to the consumption of wall material and ablation regression. For the chemical reaction-controlled stage, the arrival of oxidizing components at the wall surface is not a limiting factor; the ablation rate mainly depends on the kinetic ability of each oxidizing component to react with the wall material. Therefore, the ablation rate under chemical reaction control can be expressed as:

[0065] in, The ablation rate under chemical reaction control. Density of the solid wall The amount of oxidizing components participating in the ablation reaction, For the first Partial pressure of the oxidizing component, For the first The reaction order corresponding to the oxidizing component. For the first The reaction kinetic rate of each oxidizing component is given by this formula. This formula shows that the contribution of each oxidizing component to ablation is related to its partial pressure and reaction kinetic rate. A higher partial pressure indicates a higher content of that component in the localized combustion gas, and a stronger ability to participate in the wall oxidation reaction. A higher reaction kinetic rate indicates a faster reaction rate between that component and the wall material. By summing the contributions of each oxidizing component, the total chemical reaction ablation rate in a multi-component combustion gas environment can be obtained.

[0066] The above-mentioned The reaction kinetic rate of the oxidizing component is calculated according to the Arrhenius equation and satisfies:

[0067] in, For the first The pre-exponential factor of the term response, For the first The temperature index of the reaction, For the first The activation energy of the reaction. The gas constant is... Let be the temperature of any cross-section. This formula describes the effect of temperature on the chemical reaction rate. Generally, as the local temperature of the nozzle increases, the exponential term increases, and the reaction kinetic rate increases significantly. Therefore, rapid oxidation and ablation are more likely to occur in high-temperature regions. Different oxidizing components correspond to different pre-exponential factors, temperature exponents, and reaction activation energies, making... The components exhibit different sensitivities to ablation in different temperature ranges, thus reflecting the characteristic that the ablation rate of different components varies with temperature.

[0068] For the diffusion-controlled stage, even with strong wall chemical reactivity, the actual ablation rate may still be limited by the transport capacity of oxidizing components to the wall. When oxidizing components near the wall are rapidly consumed, if the oxidizing components in the main combustion stream cannot promptly cross the boundary layer to replenish the wall, the ablation process will be primarily controlled by diffusion mass transfer. Therefore, this embodiment further calculates the ablation rate under diffusion control:

[0069] in, The ablation rate under diffusion control. The molar amount of the solid-phase element. The convective heat transfer coefficient is... For the specific heat capacity of the gas at constant pressure, Density of the solid wall and These represent the molar number of the corresponding oxidizing component per kilogram of fuel gas. This formula indicates that the diffusion-controlled ablation rate is related to the molar supply of the oxidizing component, the heat and mass transfer capacity of the fuel gas to the wall, and the density of the wall material itself.

[0070] The above convective heat transfer coefficient This parameter characterizes the intensity of heat exchange between the high-temperature combustion gas and the nozzle wall, and in this embodiment, it also serves as a correlation parameter for diffusion mass transfer capability. Stronger convective heat transfer generally indicates more complete exchange of momentum, heat, and components within the boundary layer, and a stronger ability for oxidizing components to replenish the wall. Therefore, in this embodiment, the convective heat transfer coefficient is calculated according to the Bartz formula, satisfying:

[0071] in, For Prandtl numbers, The gas dynamic viscosity coefficient, The diameter of the nozzle throat. The radius of the transition arc at the throat. This represents the area of ​​the nozzle throat. For the required cross-sectional area, For mass flow rate, This is the temperature correction factor. This formula allows for the unified inclusion of nozzle throat dimensions, throat arc transition structure, local cross-sectional area, mass flow rate, and gas physical properties into the heat transfer calculation. Particularly in the area near the nozzle throat, due to its small cross-sectional area, high flow velocity, and concentrated heat flux density, there is typically a large convective heat transfer intensity; therefore, the diffusion-controlled ablation rate in this region requires more focused calculation.

[0072] The above temperature correction factor Calculate according to the following formula:

[0073] in, For any cross-sectional temperature, For the incoming flow temperature, The specific heat ratio of the fuel gas. The Mach number is set to an arbitrary cross-section. This temperature correction coefficient is used to correct for the influence of temperature and Mach number changes on heat transfer intensity during the accelerated expansion of the gas within the nozzle. Because the velocity states of the gas differ in the convergent, throat, and divergent sections of the nozzle, and the local temperature and pressure also change continuously, directly using a fixed heat transfer coefficient would reduce the accuracy of ablation prediction; therefore, the following correction factor is introduced... This allows the convective heat transfer coefficient to be corrected as the local flow state changes, thus more accurately reflecting the thermal environment at any cross-section of the nozzle.

[0074] In summary, this embodiment characterizes the reaction kinetics between the oxidizing component and the thermal protection material using a chemical reaction-controlled ablation rate formula, characterizes the restriction process of oxidizing component transport to the wall using a diffusion-controlled ablation rate formula, and incorporates nozzle geometry, local Mach number, local temperature, fuel gas properties, and mass flow rate into the diffusion control calculation using the Bartz formula and temperature correction coefficient. Thus, subsequent steps can utilize... and The relative magnitudes between them are used to calculate the Damköhler number, which determines whether the current cross-sectional ablation is mainly controlled by chemical reaction, diffusion, or is in a transitional stage where both factors work together. This improves the accuracy and applicability of ablation rate prediction for the nozzle throat and the areas before and after it.

[0075] In one feasible implementation, S4 to S6 above include: calculating the Damcole number according to the following formula:

[0076] when At that time, it was determined that the ablation was in the chemical kinetic control stage; when At that time, it was determined that the ablation was in the diffusion-controlled stage; when When the ablation is within the transition range, it is determined that the ablation is in a transitional stage where chemical kinetics control and diffusion control are combined. The diffusion contribution constant calculated based on the Damköhler number above satisfies:

[0077] in, The diffusion contribution constant, The correction factor is determined by ablation test data of nozzle thermal protection material under different operating conditions; The ablation rate is predicted using the following formula:

[0078] in, To predict the ablation rate; and, when At that time, it was determined that ablation was mainly controlled by chemical reactions. At 0.8, it was determined that ablation was mainly controlled by diffusion. At that time, it was determined that the ablation was in the transitional stage.

[0079] For example, in steps S4 to S6 above, the nozzle ablation control mechanism is determined, and a specific implementation method for predicting the ablation rate is further obtained. Since the ablation of the solid rocket motor nozzle wall is simultaneously affected by the chemical reaction rate and the diffusion supply capacity of oxidizing components, calculating only the ablation rate under chemical reaction control or only the ablation rate under diffusion control is insufficient to accurately reflect the actual ablation process. This embodiment quantifies the relationship between the two control mechanisms by introducing the Damköhler number and the diffusion contribution constant, thereby enabling the ablation prediction results to continuously change with local operating conditions.

[0080] Specifically, in step S4, based on the ablation rate controlled by the chemical reaction... and diffusion-controlled ablation rate Calculate the Damkolle number The formula for its calculation is:

[0081] in, This is used to characterize the relative relationship between the ability of wall chemical reactions to consume oxidizing components and the ability of fuel gas to diffuse into the wall to replenish oxidizing components. The ablation rate under chemical reaction control. The ablation rate under diffusion control. When When the chemical reaction consumes less energy than the diffusion replenishes it, the supply of oxidizing components near the wall is relatively sufficient. At this point, the ablation rate is mainly limited by reaction kinetics, therefore ablation is determined to be in the chemical kinetics-controlled stage. When the chemical reaction consumes more energy than the diffusion replenishes, the oxidizing components cannot be replenished to the wall surface in time. At this point, the ablation rate is mainly limited by the diffusion efficiency, therefore the ablation is determined to be in the diffusion-controlled stage. When the process is in the transition range, it indicates that both chemical reactions and diffusion replenishment have a significant impact on the ablation process. At this point, ablation is in a transitional stage where chemical kinetics control and diffusion control work together.

[0082] In step 55, the diffusion contribution constant is further calculated based on the aforementioned Damköhler number. The formula for its calculation is:

[0083] in, This is the diffusion contribution constant, used to represent the degree of contribution of diffusion control factors to the actual ablation rate; This is a correction factor used to adjust the curve relating the Damcole number to the diffusion contribution. This correction factor can be calibrated using ablation test data of nozzle thermal protection materials under different operating conditions, thus ensuring that the model not only has a theoretical basis but also matches the ablation test results of actual materials. Through this formula, The value of is restricted to between 0 and 1, when When smaller, A value approaching 0 indicates that ablation is more closely controlled by a chemical reaction. When When it is large, A value approaching 1 indicates that ablation is closer to diffusion control; when When it is in the middle range, Follow Continuous variation avoids abrupt switching between chemical reaction control and diffusion control.

[0084] In step S6, the predicted ablation rate is calculated based on the diffusion-controlled ablation rate and the diffusion contribution constant. The calculation formula is as follows:

[0085] in, To predict the ablation rate. Because This indicates that under diffusion-controlled conditions, the oxidizing component can replenish the ablation capacity of the wall surface, while This represents the degree to which the ablation process is close to diffusion control under the current operating conditions. Therefore, multiplying the two values ​​yields a practical prediction that takes into account both chemical reaction limitations and diffusion supply limitations. This approach avoids overestimating ablation by directly using the diffusion rate at low temperatures or when reaction kinetics are weak, and also avoids ignoring the diffusion upper limit by using only the chemical reaction rate under high-temperature, strong reaction conditions, thereby improving the rationality of nozzle ablation prediction.

[0086] This embodiment can also be based on the diffusion contribution constant. The ablation state is determined. When... When diffusion contributes little to the ablation rate, ablation is mainly controlled by chemical reactions, and the actual ablation rate is closer to the value indicated by diffusion. ;when When the diffusion process becomes the main factor limiting the ablation rate, and ablation is primarily controlled by diffusion, the actual ablation rate is closer to... ;when This indicates that both chemical reactions and diffusion mass transfer have a significant impact on the ablation process, and the ablation is in a transitional stage. This method can not only output numerical predictions of the ablation rate but also simultaneously output the corresponding ablation control mechanism, providing a basis for thermal protection design, material selection, and life assessment at different locations in the nozzle throat, convergence section, and divergence section.

[0087] This invention introduces a diffusion contribution factor η to quantify the dimensionless influence of diffusion on the actual ablation rate during nozzle ablation, enabling the ablation control mechanism to be expressed in a clear parametric form. Compared to methods relying solely on empirical formula fitting, this invention clearly reflects the relationship between chemical reaction control and diffusion control under different operating conditions, with a more explicit physical meaning. This invention utilizes the Damk-Kole number to determine the ablation control mechanism and employs a modified formula to continuously describe the ablation rate in the transition phase, avoiding prediction errors caused by artificial segmentation or abrupt switching between the chemical kinetic control and diffusion control phases in existing methods. Furthermore, the correction coefficient w can be calibrated based on ablation test data for different thermal protection materials, making the method adaptable to different materials and engine operating conditions, thus improving the accuracy of ablation prediction in the transition zone. The calculation process of this invention is mainly based on one-dimensional isentropic flow relationships, Arrhenius reaction kinetics formulas, Bartz convective heat transfer formulas, and algebraic calculations. It eliminates the need for complex coupled numerical models of flow field, heat transfer, and chemical reaction, as well as costly iterative solutions, significantly reducing computational load. This makes it suitable for preliminary design, parameter comparison, and rapid engineering iteration of nozzle thermal protection schemes. This invention employs a unified dimensionless parameter framework to describe the chemical kinetic control stage, the diffusion control stage, and the transition stage where both interact. This allows the ablation rate of the nozzle under different temperatures, cross-sectional locations, and oxidizing components to be calculated within the same model, eliminating the need to switch prediction models for different operating conditions. This facilitates integration with engineering software and practical design applications.

[0088] In summary, this invention introduces a diffusion contribution factor η to quantify the dimensionless influence of diffusion on the actual ablation rate during nozzle ablation, enabling the ablation control mechanism to be expressed in a clear parametric form. Compared to methods relying solely on empirical formula fitting, this invention clearly reflects the relationship between chemical reaction control and diffusion control under different operating conditions, with a more explicit physical meaning. This invention utilizes the Damk-Kole number to determine the ablation control mechanism and uses a modified formula to continuously describe the ablation rate in the transition phase, avoiding prediction errors caused by artificial segmentation or abrupt switching between the chemical kinetic control and diffusion control phases in existing methods. Furthermore, the correction coefficient w can be calibrated based on ablation test data of different thermal protection materials, making the method adaptable to different materials and engine operating conditions, thus improving the accuracy of ablation prediction in the transition zone. The calculation process of this invention is mainly based on one-dimensional isentropic flow relationships, Arrhenius reaction kinetics formulas, Bartz convective heat transfer formulas, and algebraic calculations. It eliminates the need for complex coupled numerical models of flow field, heat transfer, and chemical reaction, as well as costly iterative solutions, significantly reducing computational load. This makes it suitable for preliminary design, parameter comparison, and rapid engineering iteration of nozzle thermal protection schemes. This invention employs a unified dimensionless parameter framework to describe the chemical kinetic control stage, the diffusion control stage, and the transition stage where both interact. This allows the ablation rate of the nozzle under different temperatures, cross-sectional locations, and oxidizing components to be calculated within the same model, eliminating the need to switch prediction models for different operating conditions. This facilitates integration with engineering software and practical design applications.

[0089] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for predicting nozzle ablation based on control mechanism and diffusion contribution, characterized in that, include: S1. Obtain the nozzle structure parameters and incoming flow parameters of the solid rocket motor. The nozzle structure parameters include nozzle geometry parameters and thermal protection material performance parameters. The incoming flow parameters include gas composition content, incoming flow pressure, and incoming flow temperature. S2. Based on the nozzle structure parameters and the incoming flow parameters, calculate the flow characteristics of the gas in the nozzle to obtain the Mach number, pressure and temperature at any cross-sectional position; S3. Based on the performance parameters of the thermal protection material and the flow characteristics, calculate the ablation rate of each oxidizing component under chemical reaction control and the ablation rate under diffusion control. S4. Calculate the Damcole number based on the ablation rate under the control of the chemical reaction and the ablation rate under the control of diffusion, and determine the control mechanism of the current ablation model based on the Damcole number. S5. Calculate the diffusion contribution constant based on the Darmquer number and the control mechanism; S6. Calculate the predicted ablation rate based on the diffusion contribution constant and the ablation rate under diffusion control; S7. Output the predicted ablation rate to complete the nozzle ablation prediction.

2. The nozzle ablation prediction method of claim 1, wherein, The nozzle geometry parameters include the nozzle throat diameter, arbitrary cross-sectional diameter, and throat transition radius; the thermal protection material performance parameters include solid wall density, solid element molar amount, and material ablation test correction parameters; and the fuel gas composition content includes the content of oxidizing components.

3. The nozzle ablation prediction method of claim 1, wherein, The incoming flow parameters of the gas at any cross-section inside the nozzle are calculated based on the one-dimensional isentropic flow relationship. The Mach number, pressure, and temperature at any cross-section satisfy the following: wherein, is the arbitrary cross-sectional diameter, is the nozzle throat diameter, is the arbitrary cross-sectional Mach number, is the free stream pressure, is the arbitrary cross-sectional pressure, is the free stream temperature, is the arbitrary cross-sectional temperature, is the gas specific heat ratio.

4. The nozzle ablation prediction method as described in claim 3, characterized in that, When is determined , it is determined that the gas in the throat of the nozzle reaches the speed of sound; When there are two solutions for the Mach number, where corresponding to the converging section of the Laval nozzle throat, the gas is subsonic flow, corresponding to the diverging section of the Laval nozzle throat, the gas is supersonic flow.

5. The nozzle ablation prediction method as described in claim 1, characterized in that, Oxidizing components in the fuel gas include and one or more of The ablation rate controlled by the chemical reaction is calculated according to the following formula: wherein, is the ablation rate under chemical reaction control, is the solid wall density, is the amount of oxidizing component participating in the ablation reaction, is the partial pressure of the oxidizing component, is the reaction order corresponding to the oxidizing component, is the reaction kinetic rate of the oxidizing component.

6. The nozzle ablation prediction method as described in claim 5, characterized in that, The first The reaction kinetic rate of the oxidizing component is calculated according to the Arrhenius equation and satisfies: in, For the first The pre-exponential factor of the term response, For the first The temperature index of the reaction, For the first The activation energy of the reaction. The gas constant is... For any cross-section temperature.

7. The nozzle ablation prediction method as described in claim 1, characterized in that, The diffusion-controlled ablation rate is calculated according to the following formula: in, The ablation rate under diffusion control. The molar amount of the solid-phase element. The convective heat transfer coefficient is... For the specific heat capacity of the gas at constant pressure, Density of the solid wall and These represent the number of moles of the corresponding oxidizing component per kilogram of fuel gas.

8. The nozzle ablation prediction method as described in claim 7, characterized in that, The convective heat transfer coefficient is calculated according to Bartz's formula and satisfies: in, For Prandtl numbers, The gas dynamic viscosity coefficient, The diameter of the nozzle throat. The radius of the transition arc at the throat. This represents the area of ​​the nozzle throat. For the required cross-sectional area, For mass flow rate, This is the temperature correction factor.

9. The nozzle ablation prediction method as described in claim 8, characterized in that, The temperature correction factor is calculated according to the following formula: in, For any cross-sectional temperature, For the incoming flow temperature, The specific heat ratio of the fuel gas. Let be the Mach number for any cross section.

10. The nozzle ablation prediction method as described in claim 1, characterized in that, S4 to S6 include: calculating the Damcole number according to the following formula: when At that time, it was determined that the ablation was in the chemical kinetic control stage; when At that time, it was determined that the ablation was in the diffusion-controlled stage; when When the ablation is within the transition range, it is determined that the ablation is in a transitional stage where chemical kinetics control and diffusion control are combined. The diffusion contribution constant is calculated based on the stated Damköhler number, satisfying the following: in, The diffusion contribution constant, The correction factor is determined by ablation test data of the nozzle thermal protection material under different operating conditions; The ablation rate is predicted using the following formula: in, To predict the ablation rate; and, when At that time, it was determined that ablation was mainly controlled by chemical reactions. At 0.8, it was determined that ablation was mainly controlled by diffusion. At that time, it was determined that the ablation was in the transitional stage.

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