A method for predicting thrust of a single expansion nozzle in a test condition

Abstract

The application discloses a method for predicting the thrust of a single-side expansion nozzle in a test state. First, at least three groups of performance data of the single-side expansion nozzle are obtained through simulation or test, and the data includes total pressure, total temperature, back pressure, flow rate and thrust coefficient of the nozzle. Second, the total pressure and the total temperature in each group of simulation or test are ensured to be the same, and if the total pressure and the total temperature are not the same, the total pressure and the total temperature are converted into the same total pressure and total temperature by using a formula. Then, a y=Ae ‑Bx +C function is introduced to establish a continuous relationship between the converted nozzle thrust and the back pressure, and the data at any point in the sample range is known. Only the relationship between the thrust coefficient and the pressure ratio is considered, and the influence of the specific heat ratio is ignored, so that the thrust coefficient is considered to be equal as long as the pressure ratio of the nozzle is the same. The nozzle thrust in the test state may be affected by the high-altitude cabin structure, and the application provides correction relationship formulas of different factors, so that the full-flow field thrust prediction of the nozzle can be more accurately constructed.

Description

Technical Field

[0001] This invention relates to a method for predicting the thrust of a unilateral expansion nozzle under experimental conditions, belonging to the field of unilateral expansion nozzle technology. Background Technology

[0002] Horizontal takeoff and landing, reusable hypersonic vehicles suitable for near-space flight have become a cutting-edge research hotspot in the 21st-century aerospace field. As the main thrust-generating component of hypersonic vehicles, the exhaust system is crucial to the overall performance of the vehicle. When the Mach number exceeds 6, the thrust provided by the exhaust nozzle accounts for approximately 70% of the total thrust generated by the engine.

[0003] Hypersonic vehicle nozzles differ from traditional axisymmetric configurations. They must not only meet the high expansion ratio required for high Mach number flight but also be integrated with the vehicle's design. Single-sided expansion nozzles balance these two requirements, offering inherent advantages. Single-sided expansion nozzles have a wide operating range, potentially encompassing everything from severe overexpansion to severe underexpansion. The development of single-sided expansion nozzles is heavily reliant on testing. Nozzle testing is conducted on high-altitude test platforms, requiring multiple sets of tests and incurring significant costs. Developing nozzle thrust prediction methods can greatly reduce costs and shorten the development cycle.

[0004] The nozzle thrust coefficient is one of the most important performance parameters in nozzle performance evaluation and also the most complex indirect test parameter in high-altitude nozzle simulation tests. Accurately measuring thrust and correcting simulation biases are crucial aspects of high-altitude simulation test technology research. The nozzle thrust measured directly on the test bench is affected by objective test conditions and may deviate from the "true" thrust of the nozzle. Therefore, it is necessary to study in detail the specific factors affecting the force on the nozzle and understand the magnitude of each factor's influence on the thrust coefficient to facilitate correction of the test measurement results. Only then can a thrust measurement value consistent with the actual working conditions of the nozzle be obtained, thereby increasing the accuracy of nozzle thrust prediction. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the thrust of a single-sided expanding nozzle under test conditions. By establishing a fixed functional relationship between nozzle thrust and back pressure, a rapid prediction capability for nozzle thrust is constructed. Furthermore, by combining the corrected relationship of multiple thrust influencing factors on a high-altitude test platform, the prediction results can be made more accurate.

[0006] The technical solution adopted in this invention is a method for predicting the thrust of a unilateral expansion nozzle under experimental conditions, comprising the following steps:

[0007] Step 1: Obtain a set of performance data for a unilateral expansion nozzle through simulation or experimentation. This set of data includes the nozzle's total pressure P*, total temperature T*, and back pressure P. bFlow rate m g Flow coefficient C m Axial thrust F x Axial thrust coefficient C fx The formulas used to solve for nozzle performance parameters include:

[0008]

[0009] In the formula, m s For the ideal flow rate of the nozzle; A8 is the nozzle throat area; F is the nozzle internal thrust; subscript i represents the nozzle inlet parameter, and subscript out represents the nozzle outlet parameter; R x V is the horizontal component of the integral of the nozzle wall pressure; e,s To improve spray management, the exit speed needs to be considered; C p It is a specific heat at constant pressure;

[0010] Step 2: Process the obtained data to ensure that the total temperature and total pressure are the same for each operating condition. If they are different, a conversion is required. The conversion formula is: F x1 =m g1 V e1,s C fx In the formula m g1 P b1 F x1 For the converted flow rate, back pressure, and axial thrust, P1 * and T1 * The unified total pressure and total temperature are consistent with the total pressure and total temperature in the data to be predicted.

[0011] Step 3, change y = Ae -Bx The +C function introduces the relationship between the converted nozzle thrust and back pressure, and solves the coefficients A, B, and C through nonlinear fitting to establish a continuous relationship between the two.

[0012] Step 4: Given the total pressure and back pressure, the pressure drop ratio can be calculated. The ideal exit velocity of the nozzle can be obtained from the pressure drop ratio. Based on the established relationship between nozzle thrust and back pressure, the relationship between pressure drop ratio and thrust coefficient can be further obtained. The thrust coefficient is treated as a single-valued function of pressure drop ratio, and a function correction method is used to predict the nozzle thrust.

[0013] Step 1 requires obtaining at least three sets of data through simulation or experimentation. These data should ideally encompass a relatively complete nozzle state, ranging from under-expansion to over-expansion. For nozzles in an over-expansion state, the pressure drop ratio should not be too low. For single-sided expansion nozzles, the upper expansion surface should be in an RSS state, and the lower lip plate in an FSS state.

[0014] Step 4 involves finding the corresponding thrust coefficient from the pressure ratio in the data to be predicted, and then correcting the final output predicted thrust using a function. The correction function is as follows:

[0015] When the nozzle penetration length is flush with the exhaust diffuser inlet, i.e., S=0:

[0016] ΔC fe =(2.4966E-04)C fx

[0017] Define conformity For small-diameter exhaust diffusers, based on the variation law of the influence of exhaust diffuser diameter on nozzle thrust coefficient, the following correction formula can be given. Since large diameter has almost no effect on nozzle thrust performance, correction is only applied to small-diameter exhaust diffusers:

[0018] The impact of small-diameter exhaust diffusers on nozzle performance:

[0019] ΔC fd =(3.1519E-04)C fx

[0020] The thrust coefficient decrease rate is relatively consistent for single-channel ramjet nozzles of different sizes, and the thrust coefficient decrease is also relatively uniform for dual-channel nozzles. However, the influence of model scaling differs slightly between the two. Therefore, the impact of model size on the thrust coefficient can be differentiated between single-channel and dual-channel nozzles, and correction relationships can be given separately, with the specific correction amount ΔC. fc They are respectively:

[0021] Single channel:

[0022] ΔC fc = -0.00362ln(x-0.03051)

[0023] Dual-channel:

[0024] ΔC fc = -0.00192ln(x-0.03797)

[0025] x is the scaled-down size, x < 1.

[0026] Regarding the influence of secondary flow rate on the thrust coefficient of the test nozzle, the maximum difference in thrust coefficient caused by secondary flow rate less than 40% of the mainstream flow rate is 0.04%, and the following relationship is given:

[0027] ΔC fs =0.0004C fx (0.0001~0.0004)

[0028] When the nozzle is fully immersed in the exhaust diffuser, the ejector effect becomes more pronounced, and the airflow velocity changes more drastically within the diffuser. At this point, the nozzle thrust coefficient measured at points inside the high-altitude chamber is approximately 0.17% lower than that measured at points inside the diffuser. Since the outer wall of the nozzle is entirely within the diffuser at this stage, the pressure values ​​measured at points within the diffuser are more accurate. Therefore, when conducting tests with the nozzle fully immersed in the diffuser, it is best to place the pressure measuring points within the diffuser to ensure more precise measurement results. When placing the measuring point within the drainage area, When the measuring point is placed inside the high-altitude chamber, the following correction formula can be used:

[0029]

[0030] f1 = 0.17%.

[0031] The beneficial effects of this invention compared with the prior art are as follows: The method for predicting the thrust of a single-sided expansion nozzle under test conditions provided by this invention can greatly save test costs, quickly predict nozzle thrust, and shorten the nozzle design cycle. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of a single-sided expansion nozzle under test conditions.

[0033] Figure 2 This represents the predicted range for nozzle pressure ratio.

[0034] Figure 3 This is a flowchart for predicting thrust in a single-sided expansion nozzle.

[0035] Figure 4 This is a fitting curve of nozzle thrust versus back pressure under the same total temperature and total pressure, representing a specific example of the invention.

[0036] Figure 5 The predicted thrust coefficient curve of nozzle 1 in a specific example of the present invention is compared with that of the test point.

[0037] Figure 6 This is a fitting curve of nozzle thrust versus back pressure under the same total temperature and total pressure, representing a specific example of the invention, nozzle 2.

[0038] Figure 7 The predicted thrust coefficient curve of nozzle 2 in a specific example of the present invention is compared with that of the test point.

[0039] Explanation of reference numerals in the attached figures: Figure 1 1. Single-sided expansion nozzle, 2. High-altitude chamber, 3. Exhaust diffuser. Figure 2 4. Lower lip plate RSS status, 5. Prediction region, 6. Over-dilation status, 7. Under-dilation status. Figure 5 This is a graph showing the relationship between thrust coefficient and drop pressure ratio. The solid cubes represent experimentally measured data. Figures 6-7 The significance of China Figure 4 and Figure 5 Same. Detailed Implementation

[0040] The present invention will now be described in detail with reference to the accompanying drawings and specific examples.

[0041] Example 1:

[0042] Four sets of pressure ratios were measured in the exhaust-expansion test of nozzle 1, ranging from 10 to 70. The pressure ratio data of 10, 30, and 50 were selected as samples to predict the state with a pressure ratio of 70.

[0043] Table 1. Raw data for nozzle 1

[0044] 70 7355 514725.4 69.98 352.77 302.22 0.5730 0.94234 50 7218 360761.9 49.98 237.86 301.9 0.3854 0.9661 30 9235 276981.9 29.99 171.88 301.2 0.2955 0.9483 10 13193 132496.9 10.04 63.45 301.08 0.1431 0.82074

[0045] The total pressure of the three sets of data in the sample is different. By transforming the formula in step 2, the data of the sample are converted to the same total temperature and total pressure.

[0046] Table 2 Sample data after nozzle 1 conversion

[0047] 70 7355 514725.4 69.98 352.77 302.22 0.57303 0.94234 50 10298 514725.4 49.98 339.64 302.22 0.5495 0.9661 30 17162 514725.4 29.99 319.55 302.22 0.5482 0.9483 10 51253 514725.4 10.04 246.61 302.22 0.5549 0.82074

[0048] Then, the thrust-back pressure relationship curve was fitted using the same total temperature and pressure conditions. The fitting result is as follows: Figure 4 The fitted curve is as follows:

[0049]

[0050] Figure 5 It can be seen that the predicted thrust coefficient and the predicted thrust coefficient curve are quite similar. Substituting the desired back pressure value, the predicted thrust is 348.9484 N, and the predicted thrust coefficient is 0.9321. Since the back pressure measuring point is located inside the high-altitude chamber, the secondary flow rate of the nozzle accounts for 20% of the mainstream flow, therefore the calculation yields:

[0051]

[0052] ΔC fs =0.0004C fx =0.00037

[0053]

[0054] After correction, the predicted thrust was calculated to be 349.7346 N, while the experimental thrust was 352.77 N, with a difference of only 0.86% between the predicted and experimental values.

[0055] Example 2

[0056] Five sets of pressure ratios were measured for nozzle 2 during the experiment, ranging from 2.82 to 10. The pressure ratio data of 2.82, 6, 8 and 10 were selected as samples to predict the state with a pressure ratio of 4.

[0057] Table 3 Original test data for nozzle 2

[0058]

[0059]

[0060] Since the nozzle in this experiment uses atmospheric air intake, the total pressure of the nozzle is relatively constant. Therefore, it is no longer necessary to convert the total pressure and total temperature. The data in Table 3 can be directly subjected to curve fitting, and the fitting results are as follows: Figure 6 The fitted curve is as follows:

[0061]

[0062] Figure 7 It can be seen that the thrust coefficient curve at the test point is in good agreement with the predicted thrust coefficient curve. Substituting the back pressure value to be predicted, the predicted thrust is 48.9872 N, while the thrust value obtained from the experiment is 47.5025 N, with a difference of only 3.03%. Since the exhaust diffuser was not used in this experiment, no further correction is required.

[0063] The parts of this invention not described in detail are techniques known to those skilled in the art.

Claims

1. A method for predicting the thrust of a unilateral expansion nozzle under experimental conditions, characterized in that, Includes the following steps, Step 1: Obtain a set of performance data for a single-sided expansion nozzle through simulation or experimentation; Step 2: Process the obtained data to ensure that the total temperature and total pressure are the same for each operating condition. If they are different, conversion is required. Step 3, The function introduces the relationship between the axial thrust and back pressure of the nozzle after the transformation, and solves the coefficients A, B, and C by nonlinear fitting to establish the continuous relationship between the two. Step 4: Given the total pressure and back pressure, calculate the pressure drop ratio. Obtain the ideal exit velocity of the nozzle from the pressure drop ratio. Based on the established relationship between the axial thrust and back pressure of the nozzle, further obtain the relationship between the pressure drop ratio and the thrust coefficient. Use the method of treating the thrust coefficient as a single-valued function of the pressure drop ratio and supplementing it with function correction to predict the nozzle thrust. In step 4, when the nozzle penetration length is flush with the exhaust diffuser inlet, that is... When the correction function is: ； In step 4, the following is defined: For small-diameter exhaust diffusers, a correction is applied using the following function: ； In step 4, the influence of model size on the thrust coefficient is differentiated between single-channel and dual-channel models, and correction relationships are given for each. The specific correction amounts are as follows. They are respectively: Single channel: ； Dual-channel: ； x is the scaled-down size. .

2. The method for predicting the thrust of a unilateral expansion nozzle under experimental conditions according to claim 1, characterized in that, Step 1 requires obtaining at least three sets of data through simulation or experimentation. These data include nozzle states ranging from under-expansion to over-expansion. A single-sided expansion nozzle in an over-expansion state is at least in the upper expansion surface RSS state and the lower lip plate FSS state.

3. The method for predicting the thrust of a unilateral expansion nozzle under experimental conditions according to claim 1, characterized in that, The performance data includes the total pressure of the nozzle. Total temperature Back pressure ,flow Flow coefficient Axial thrust Axial thrust coefficient .

4. The method for predicting the thrust of a unilateral expansion nozzle under experimental conditions according to claim 1, characterized in that, In step 4, regarding the impact of secondary flow rate on the thrust coefficient of the test nozzle, the maximum difference in impact of secondary flow rate (less than 40% of the mainstream flow rate) on the nozzle thrust coefficient is 0.04%, and the correction function is: 。 5. The method for predicting the thrust of a unilateral expansion nozzle under experimental conditions according to claim 1, characterized in that, In step 4, when the nozzle is fully inserted into the diffuser for the test, the pressure measuring point is placed inside the diffuser. When placing the measuring point within the drainage area, When the measuring point is placed inside the high-altitude cabin, the correction function is: 。

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