High-altitude wind direction change model and application to rocket maximum aerodynamic load change characteristic analysis

Abstract

Since the magnitude and vertical shear of high-altitude wind speed remain basically unchanged, the impact of changes in high-altitude wind direction on the maximum aerodynamic load of rockets has not been studied. By constructing a model of high-altitude wind direction changes, taking a certain high-altitude wind as an example, this model ensures that the magnitude and vertical shear of high-altitude wind speed remain basically unchanged at each altitude level, generating 360 sets of high-altitude wind samples with changes in high-altitude wind direction. The study shows that as the high-altitude wind direction angle increases linearly, (1) the maximum aerodynamic load exhibits a periodic change characteristic of decreasing and increasing, with a numerical range of 2885.16 to 3351.97 (Pa·rad), and the difference between the maximum and minimum values ​​is 466.81 (Pa·rad); (2) the qα value increases by 44° to 109°. max The corresponding altitude range is 7.79–7.82 km, with an average of 7.81 km. Other upper-level wind directions increase the angle of qα. max The corresponding altitude range is 9.97 to 10.03 km, with an average of 10.00 km; (3) the upper-level wind direction angle increases by 44° to 109° qα max The corresponding wind speed range is 61.94–62.11 m / s, with an average of 62.04 m / s. Other upper-level wind directions increase with qα. max The corresponding wind speed range is 75.85 to 76.05 (m / s), with an average value of 75.97 (m / s).

Description

Technical Field

[0001] This invention relates to an airborne safety test of high-altitude winds on aerospace, aviation, and other airborne objects, specifically a modeling technique for high-altitude wind direction changes, applied to the maximum aerodynamic load of a certain type of rocket (denoted by the symbol "qα"). max Example analysis of the characteristics of change (hereinafter the same). Background Technology

[0002] qα produced by high-altitude wind max It has a significant impact on the flight safety of aircraft and spacecraft. Currently, considering that the magnitude and vertical shear of high-altitude wind speed remain constant, the effect of changes in high-altitude wind direction on qα is... max The extent of the impact is currently unknown, as no relevant research has been found. The biggest challenge is the lack of a suitable upper-level wind direction variation model. To address this issue, this invention proposes a technique for constructing upper-level wind direction variation models. This model can generate upper-level wind datasets with varying wind speeds and vertical wind shear at all altitude levels, eliminating the significant impact caused by changes in wind speed and vertical wind shear. Taking a certain type of launch vehicle as an example, this model generates upper-level wind datasets with different wind directions, which are then applied to the rocket, and their impact on rocket qα is analyzed. max The influence of numerical value. Summary of the Invention

[0003] The main contents of this invention include the following aspects:

[0004] a) Select any set of upper-level winds as the original data, and obtain the wind speed, wind direction, zonal wind speed, meridional wind speed and vertical wind speed shear at each altitude level. In the process of building the upper-level wind direction change model later, confirm that the magnitude of the upper-level wind speed and the vertical wind speed shear at each altitude level are basically unchanged.

[0005] (b) To ensure that the magnitude and vertical shear of upper-level wind speeds remain essentially constant at each altitude level when upper-level wind direction changes, a constraint relationship was obtained between the changes in wind direction angle and the changes in zonal and meridional wind speeds during the construction of the upper-level wind direction change model. Using this constraint relationship, given the original data on zonal and meridional wind speeds at each altitude level, only the changes in upper-level wind direction angle at each altitude level are needed to obtain the new zonal and meridional wind speed values ​​(while maintaining the same magnitude), thus obtaining new datasets of upper-level zonal and meridional wind speeds at each altitude level. In the example, the array of upper-level wind speed angle changes is set to 0°:1°:359° (the wind direction angle changes at each altitude level, which can be set according to actual needs). Using the upper-level wind direction change model, 360 sets of upper-level wind samples with essentially constant upper-level wind speed magnitude and vertical shear can be obtained.

[0006] c) Using 360 sets of upper-level wind samples obtained from an upper-level wind direction change model, the qα of a certain type of launch vehicle was calculated. max And its corresponding high-altitude wind speed and altitude.

[0007] d) Analyze 360 ​​sets of rocket qα max And the corresponding changes in high-altitude wind speed and altitude. Attached Figure Description

[0008] Figure 1 This is a graph showing the variation of wind speed and direction with altitude for the research object (upper-level wind data can be selected as the research object). The wind speed exhibits a trend of first increasing rapidly with altitude, and then decreasing. Figure 1 (a) The wind speed reaches its maximum at an altitude of 10.5 km, with a range of 0.98–77.00 m / s across the entire altitude range; the wind direction varies significantly at lower altitudes but less so at middle and upper altitudes. Figure 1 (b) Within an altitude of 2 km, the wind direction changes from northeast to northwest, while within 2 to 20 km, the wind direction remains basically unchanged, mainly changing within a small range of about 270°. The wind direction range throughout the entire altitude range is from northeast 8.18° to southwest 257°.

[0009] Figure 2 It is to utilize Figure 1 The graph shows the original upper-level wind data, and after applying an upper-level wind direction change model, 360 sets of zonal wind speed, meridional wind speed, wind speed deviation (wind speed set - original upper-level wind data), and vertical wind shear deviation characteristics were obtained. The horizontal axis in the graph represents the increase in upper-level wind direction angle. Figure 2 (a) shows the variation characteristics of zonal wind speed with increasing altitude and wind direction angle in the upper-level wind dataset. As the upper-level wind direction angle increases, the zonal wind speed across the entire altitude layer generally exhibits a periodic variation characteristic of positive value (westerly wind) → negative value (easterly wind) → positive value (westerly wind). The absolute value of the zonal wind speed generally exhibits a periodic variation characteristic of decreasing → increasing → decreasing → increasing. The zonal wind speed at each altitude layer also exhibits the periodic characteristics of changes in wind direction and the magnitude of changes in the absolute value of wind speed. Figure 2 The zonal wind speed in (a) ranges from -76.80 to 76.80 (m / s). The value of -76.80 (m / s) occurs at an altitude of 10.4 km with a wind direction angle of 182°, while the value of 76.80 (m / s) occurs at an altitude of 10.4 km with a wind direction angle of 2°. In other words, the two extreme values ​​of the zonal wind speed are at the same altitude and the wind direction angles differ by 180°. Figure 2(b) shows the variation characteristics of meridional wind speed with increasing altitude and wind direction angle in the upper-level wind dataset. As the wind direction angle increases, the meridional wind speed across the entire altitude layer generally exhibits a periodic variation characteristic of negative value (north wind) → positive value (south wind), and the absolute value of the meridional wind speed generally exhibits a periodic variation characteristic of increasing → decreasing → increasing → decreasing. The meridional wind speed at each altitude layer also exhibits periodic characteristics of changes in wind direction and changes in the magnitude of the absolute wind speed. Figure 2 (b) shows that the meridional wind speed ranges from -76.80 to 76.80 (m / s). The -76.80 (m / s) value occurs at an altitude of 10.4 km with a wind direction angle increase of 92°, while the 76.80 (m / s) value occurs at an altitude of 10.4 km with a wind direction angle increase of 272°. This means that the two extreme values ​​of the meridional wind speed are at the same altitude and the wind direction angles differ by 180°. Based on the above analysis, it can be seen that the extreme values ​​of both the zonal and meridional wind speeds are at 10.4 km and the wind direction angles differ by 90° from each other. Figure 2 (c) is a characteristic graph of the wind speed deviation obtained by subtracting the original upper-level wind speed from the upper-level wind speed set. This graph shows that the wind speed deviation is very small, ranging from -2.84 × 10⁻⁶. -14 ~-2.84×10 -14 (m / s), whose extreme value is infinitely close to the value 0, it can be determined that the wind speed obtained by the wind direction change model is the same as the original high-altitude wind speed, that is, the wind direction change model ensures that the wind speed remains unchanged. Figure 2 (d) is a characteristic graph of the vertical wind shear deviation obtained by subtracting the original vertical wind shear from the vertical wind shear of the upper-level wind speed data set. It can be clearly seen from this graph that the vertical wind shear deviation is very small, with a value range of -2.13×10. -13 ~2.13×10 -13 (m·s -1 / km), whose extreme value is infinitely close to the value 0, it can be determined that the vertical wind shear obtained by the wind direction change model is the same as the original upper-level wind speed vertical shear, that is, the wind direction change model also ensures the characteristic of the wind speed vertical shear remaining unchanged.

[0010] Figure 3 This describes the variation characteristics of wind direction and wind direction angle at different altitudes (4km, 8km, 12km, 16km) (original data, wind direction angle increases of 100°, 200°, 300°). Figure 3 (a) It can be seen that as the wind direction angle increases, the wind direction angle at each altitude layer exhibits a linear increase with the same slope. The difference in wind direction angle between adjacent samples is 1°. When the wind direction angle reaches 360°, the next wind direction angle is 1°, and then increases linearly again. The characteristics of the increase in different wind direction angles are as follows: Figure 3As shown in (b), the original data represents a 0° increase in wind direction angle. Based on the above analysis, a 100° increase in wind direction angle corresponds to a 100° increase in wind direction at each altitude level in the original data; a 200° increase corresponds to a 100° increase in wind direction at each altitude level in the original data; and a 300° increase corresponds to a 100° increase in wind direction at each altitude level in the original data. Figure 3 (b) It accurately reflects the characteristics of wind direction angle differences between different increases in wind direction angle. For example, the original data, wind direction angle increases of 100°, 200°, and 300° are 334°, 74.00°, 174.00°, and 274.00° at an altitude of 1 km, respectively; wind direction increases of 10 km are 269.00°, 9.00°, 109.00°, and 209.00°; and wind direction increases of 19 km are 257.00°, 357.00°, 97.00°, and 197.00°. It can be seen that at the listed altitude levels, the wind direction deviation between different increases in wind direction angle is consistent with the assumption.

[0011] Figure 4 When the magnitude of the upper-level wind speed and the vertical wind shear remain constant at all altitude levels, and only the upper-level wind direction changes, its qα max ,qα max The deviation and its corresponding height, corresponding height deviation, corresponding wind speed, and corresponding wind speed deviation are shown in the figure. All deviation results in the figure are obtained using the original upper-level wind response results as the baseline data. Figure 4 It can be seen that changes in upper-level wind direction affect qα max It has an impact on both the corresponding wind speed and the corresponding altitude. Figure 4 (a) is qα max The evolution characteristics of qα with increasing upper-level wind direction angle: As the wind direction angle increases at each altitude level, qα... max It exhibits an alternating periodic variation of decreasing and increasing, reaching a local minimum at wind angles of 54° and 270°, corresponding to qα. max The values ​​are 2885.16 (Pa·rad) and 3093.28 (Pa·rad), with a difference of 216° in the upper-level wind direction angle. The local maximum values ​​are reached when the wind direction angle increases by 186° and 334°, corresponding to qα. max The values ​​are 3345.12 (Pa·rad) and 3351.97 (Pa·rad), with a difference of 148° in the upper-level wind direction angle. Figure 4 qα in (a) max The numerical range is 2885.16–3351.97 (Pa·rad), with an average value of 3153.00 (Pa·rad), and the difference between the maximum and minimum values ​​is 466.81 (Pa·rad); based on the original upper-level wind qαmax Based on, qα max Characteristics of deviation variation with increasing upper-level wind direction angle ( Figure 4 (b) and Figure 4 (a) Consistent, it also exhibits periodic variation characteristics, with a numerical range of -353.57 to 113.24 (Pa·rad) and an average value of -85.73 (Pa·rad); qα max The corresponding height and the corresponding height deviation exhibit basically the same characteristics as the upper-level wind direction angle increases. Figure 4 (c) Figure 4 (d)), from Figure 4 (c) It can be clearly seen that qα max The corresponding altitudes are divided into two distinct altitude ranges, with the upper-level wind direction angle increasing by 43° to 44°, qα max The corresponding altitude rapidly decreases from 10.02km to 7.80km, with the high-altitude wind direction angle increasing by 109° to 110°, qα max The corresponding altitude increases rapidly from 7.80 km to 9.99 km; therefore, the upper-level wind direction angle increases from 0° to 43° and from 110° to 359° (qα). max The corresponding altitude range is 9.97–10.03 km, with an average of 10.00 km. The upper-level wind direction angle increases by 44° to 109°. max The corresponding altitude range is 7.79–7.82 km, with an average of 7.81 km, which corresponds to the qα value of the original upper-level wind data. max Compared to the corresponding altitude, the upper-level wind direction angle increases by 44° to 109° (qα). max The corresponding height deviation is a significantly negative value. Figure 4 (d) The numerical range is -2.20 to -2.17 km, with an average value of -2.19 km. Other upper-level wind direction angles increase in value by qα. max The corresponding altitude deviation varies around 0 km, ranging from -0.03 to 0.03 km, with an average value of 0.001 km. The upper-level wind direction angle increases by 43° to 44° with qα. max The corresponding altitude deviation increased directly from 0.02km to -2.19km, and the upper-level wind direction angle increased by 109° to 110° (qα). max The corresponding altitude deviation decreased directly from -2.19km to -0.0002km; qα max The corresponding wind speed and its deviation exhibit basically the same characteristics as the upper-level wind direction angle increases. Figure 4 (e) Figure 4 (f)), similar to Figure 4 (c) and Figure 4 (d), in Figure 4 (e) and Figure 4In (f), the qα of an upper-level wind direction angle increasing by 44° to 109° is different from the qα of an upper-level wind direction angle increasing by 0° to 43° and 110° to 359°. max There are significant differences in the corresponding wind speed or the corresponding wind speed deviation, among which, the upper-level wind direction angle increases by 44° to 109° qα max The corresponding wind speed range is 61.94–62.11 m / s, with an average value of 62.04 m / s. qα max The corresponding wind speed deviation range is -14.03 to -13.87 (m / s), with an average value of -13.94 (m / s); the increase in other upper-level wind direction angles is qα. max The corresponding wind speed range is 75.85–76.05 m / s, with an average value of 75.97 m / s. qα max The corresponding wind speed deviation range is -0.13 to 0.07 (m / s), with an average value of -0.006 (m / s); the upper-level wind direction angle increases by 43° to 44° with qα max The corresponding wind speed drops directly from 76.04 (m / s) to 62.02 (m / s), qα max The corresponding wind speed deviation increases directly from 0.06 (m / s) to -13.95 (m / s), and the upper-level wind direction angle increases by 109° to 110° (qα). max The corresponding wind speed increases directly from 62.00 (m / s) to 75.97 (m / s), qα max The corresponding wind speed deviation decreased directly from -13.97 (m / s) to -0.001 (m / s). Detailed Implementation

[0012] When constructing a model of upper-level wind direction change, it is required that the magnitude of upper-level wind speed and the vertical shear of upper-level wind speed remain constant at each altitude level.

[0013] For a known vertical profile of upper-level wind speeds, the zonal wind speed *u* and the meridional wind speed *v* at each altitude level are known quantities; assuming that the zonal and meridional wind speeds at altitude level *i* are denoted as *u* and *v* respectively. i and v i Then the wind speed V at that altitude level i The expression is:

[0014]

[0015] Wind direction θ i With zonal wind speed u i Meridional wind speed v i The following relationship exists:

[0016]

[0017]

[0018]

[0019] Therefore, it can be seen from the above formula that the zonal wind speed u at altitude level i is... i Meridional wind speed v i Wind speed V i Wind direction θ i All are known quantities; assuming the wind direction change is β, the zonal and meridional wind speeds at this time are denoted as u. ix v ix Then the wind speed V ix The expression is as follows:

[0020]

[0021] Wind direction θ i +β and zonal wind speed u ix Meridional wind speed v ix The following relationship exists:

[0022]

[0023]

[0024]

[0025] Since the wind speed must remain constant during the wind direction change, the following relationship exists from equations (1) and (5):

[0026] V i =V ix (9)

[0027] Expression (6) can be further expressed in the following form:

[0028]

[0029] Similarly, expressions (7) and (8) can be further expressed in the following form:

[0030]

[0031] Substituting equations (2) and (3) into equations (10) and (11) respectively, we obtain the following forms:

[0032]

[0033] Based on expression (9), expressions (13) and (14) can be simplified to the following forms:

[0034] u i cos(β)+v isin(β)=u ix (15)

[0035] v i cos(β)-u i sin(β)=v ix (16)

[0036] In the above formula, u i v i Let be the zonal and meridional wind speeds at altitude i, which are known quantities; expressions (15) and (16) reflect the wind direction change β at altitude i and the new zonal wind speed u at that altitude, under the condition that the magnitude of the high-altitude wind speed and the vertical wind shear remain unchanged. ix New meridian wind speed v ix Therefore, given the wind direction change value β, the new zonal wind speed u at that altitude level can be obtained through expressions (15) and (16). ix New meridian wind speed v ix This is new upper-level wind data obtained from the upper-level wind direction change model, while keeping the wind speed magnitude and vertical wind shear constant at each altitude level.

[0037] In the example, with Figure 1 The research object serves as the raw data for applying the upper-level wind direction change model. Assuming the wind direction change value β is in the range of 0°:1°:359° (in degrees), the model yields 360 sets of upper-level wind samples where the upper-level wind speed magnitude and vertical wind shear remain essentially constant, with only upper-level wind direction changes. The first set of data in the upper-level wind speed set (out of 360 sets) is consistent with the original data, meaning the corresponding maximum aerodynamic load on the rocket (the first value) is also consistent with the original data.

Claims

1. A technique for constructing an upper-level wind direction change model, characterized in that, This model can generate high-altitude wind datasets with different wind directions as needed, while ensuring that the magnitude and vertical shear of high-altitude wind speed remain basically unchanged at each altitude level. This eliminates the significant impact caused by changes in the magnitude and vertical shear of high-altitude wind speed.

2. The upper-level wind direction change model according to claim 1, its characteristic application In-flight safety tests for spacecraft such as launch vehicles.

3. The upper-level wind direction change model according to claim 1 or 2, its characteristic application In-flight safety tests for aircraft and other aircraft.

4. The upper-level wind direction change model according to claim 1, 2 or 3, its characteristic application In-flight safety tests on other high-altitude flying objects.

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