CN114112286A - Hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method - Google Patents

Hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method Download PDF

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CN114112286A
CN114112286A CN202111451269.8A CN202111451269A CN114112286A CN 114112286 A CN114112286 A CN 114112286A CN 202111451269 A CN202111451269 A CN 202111451269A CN 114112286 A CN114112286 A CN 114112286A
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fitting
throat section
profile
nozzle
boundary layer
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CN114112286B (en
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李震乾
杨彦广
梁杰
石义雷
陈爱国
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Ultra High Speed Aerodynamics Institute China Aerodynamics Research and Development Center
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Ultra High Speed Aerodynamics Institute China Aerodynamics Research and Development Center
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M9/00—Aerodynamic testing; Arrangements in or on wind tunnels
    • G01M9/02—Wind tunnels
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention relates to the technical field of wind tunnel nozzles, in particular to a hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method. The method comprises the steps of designing a fitting reference spray pipe according to a typical running state of a fitting throat section, enabling an inlet radius, a contracted section length, an expanded section length and an outlet radius of the fitting reference spray pipe to be the same as those of an original spray pipe through processing, obtaining a displacement thickness of a reference boundary layer through calculation processing, further obtaining a reverse derivation non-adhesive profile through reverse derivation, fitting on the reverse derivation non-adhesive profile to obtain a non-adhesive profile of the fitting throat section, adding the displacement thickness of the boundary layer at a corresponding position to obtain a physical profile of an expanded part of the fitting throat section, and combining the expanded part and the contracted part of the physical profile of the fitting throat section to obtain a complete physical profile of the fitting throat section. The method can fully consider the influence of the operation Mach number, the total temperature, the total pressure and the displacement thickness of the boundary layer caused by the change of a test medium of the fitting throat section, ensure the accuracy of the fitting throat and realize the fitting of the throat sections with different requirements.

Description

Hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method
Technical Field
The invention relates to the technical field of wind tunnel nozzles, in particular to a hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method.
Background
In order to change the Mach number of the spray pipe in the prior art, the throat section (comprising the contraction section of the spray pipe and the partial expansion section connected with the throat part) can be replaced on the basis of the axial symmetric profile spray pipe of the existing hypersonic wind tunnel, and the expansion section is shared, so that the engineering quantity can be greatly reduced, and the equipment construction cost is saved.
At present, the throat fitting design of the axisymmetric profile nozzle of the hypersonic wind tunnel is to form an L-shaped non-adhesive profile of the original nozzle (the nozzle of the throat section to be replaced)2The design of the non-adhesive molded surface of the fitting section is firstly carried out, and then the displacement thickness of the same coordinate point of the original spray pipe is added to form the physical molded surface of the fitting section. The method has the disadvantages that only Mach number change of the fitting throat section and an original nozzle can be considered, and boundary layer thickness change caused by differences of total temperature, total pressure, test medium change, different running typical states and the like cannot be considered, so that the method is not beneficial to accurate fitting of the throat section and can cause larger deviation under certain conditions. Along with the development of aerodynamics, the requirements of throat section fitting with unchanged nozzle Mach number, total operating temperature, total pressure and change of gas medium also appear, and the requirements cannot be realized by adopting the original design method.
Disclosure of Invention
Technical problem to be solved
The invention aims to provide a hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method, which can realize accurate fitting of a required throat section according to requirements and solve the problems in the prior art.
(II) technical scheme
In order to achieve the above object, in a first aspect, the present invention provides a hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method, including the following steps:
(1) designing to obtain a fitting reference spray pipe by adopting a design method which is the same as that of the original spray pipe and taking the operation Mach number, the total temperature, the total pressure, the gas medium, the inlet radius and the outlet radius of the fitting throat section as design input conditions;
(2) processing the fitted reference nozzle using the following relationship:
xN＝xN*xE/xNE
yN＝yN*yE/yNE
keeping the inlet radius, the contraction section length and the outlet radius of the fitting reference nozzle consistent with the original nozzle;
calculating boundary layer displacement thickness delta of the fitting reference nozzle by adopting the following relational expressionNAnd (3) processing:
δ＝δN*yE/yNE
obtaining the displacement thickness delta of the reference boundary layer;
wherein: x is the number ofNTo fit the X-coordinate, y, of a reference nozzleNTo fit the Y coordinate, x, of the reference nozzleEExpanded length of primary nozzle, xNETo fit the length of the expanded section of the reference nozzle, yEIs the outlet radius of the original nozzle, yNEFitting the outlet radius of the reference nozzle;
(3) in the physical profile L of the original spray pipe1The displacement thickness delta of the reference boundary layer is subtracted to form a reversely derived non-adhesive profile L3；
(4) In said backward development of the inviscid profile L3The design of the non-adhesive profile of the fitting throat section is completed, the displacement thickness delta of the reference boundary layer at the corresponding position is added on the non-adhesive profile of the expansion part of the fitting throat section to form the physical profile L of the fitting throat section4The expansion part of (1);
(5) designing and obtaining the physical profile L of the fitting throat section according to requirements4A constricted portion of (a);
(6) the fitted throat section physical profile L obtained in the steps (4) and (5) is subjected to4And the fitted throat section physical profile L4Are combined to obtain the physical profile L of the fitting throat section4。
Optionally, the fitting reference nozzle is designed by a characteristic line method.
Optionally, the boundary layer displacement thickness of the fitting reference nozzle is obtained by the following method:
and obtaining the value of the boundary layer shape factor H and the value of the momentum thickness theta by solving an axisymmetric Von-Karman momentum equation:
Figure BDA0003386116170000031
in the formula: x is the number ofNTo fit the X-coordinate, y, of a reference nozzleNTo fit the Y coordinate of the reference nozzle, MeDesign Mach number, C for fitting reference nozzlefIs coefficient of friction, θfThe gas flow deflection angle is shown, and gamma is the specific heat ratio of gas;
solving the boundary layer displacement thickness delta by adopting a momentum thickness weighting methodNThe weighting formula of the momentum thickness weighting method is as follows:
Figure BDA0003386116170000032
wherein H is the boundary layer shape factor, δNAnd k is the boundary layer displacement thickness, k is a weighting coefficient, and theta is the momentum thickness obtained through prediction.
Optionally, the value range of the weighting coefficient k is between 0 and 1, verification is performed by adopting a numerical simulation method, and determination is performed by an iteration method.
Optionally, the fitting of the inviscid profile design of the throat section in step (4) comprises the following steps:
(41) deriving inviscid profile L in the reverse direction3The above assumes a fitting point;
(42) and (3) adopting a cubic curve equation to complete the design of the fitting throat inviscid profile:
y＝a0+a1x+a2x2+a3x3
in the formula a0，a1，a2，a3Is the undetermined coefficient;
the boundary conditions of the above cubic curve equation are as follows:
x＝0：y＝y*；
Figure BDA0003386116170000041
x＝xat：y＝yat；
Figure BDA0003386116170000042
substituting the boundary conditions into an equation to obtain undetermined coefficients, and substituting the undetermined coefficients into a formula to obtain the following fitting equation of the non-adhesive surface of the fitting throat section:
Figure BDA0003386116170000043
in the formula: y is the throat radius of the fitting throat section; y isatDeriving a fitted point radius of the unbonded surface in a reverse direction; x is the number ofatDeriving axial coordinates of the fitting point of the non-adhesive surface in a reverse direction; thetaatThe dip angle of the fit point inviscid curve of the inviscid profile is reversely deduced, wherein X is the X coordinate of the fit throat section, and Y is the Y coordinate of the fit throat section;
(43) and (3) verifying the flow field quality of the non-adhesive line by adopting a characteristic line method without considering the viscosity influence, finishing the design if the flow field index meets the design requirement, and adjusting the position of a fitting point until the flow field index meets the requirement if the flow field index does not meet the requirement.
Optionally, the fitted throat section physical profile L in step (5)4The contraction part of the flow is obtained by the following Witoszynski empirical formula of ideal incompressible axial symmetric flow:
Figure BDA0003386116170000044
wherein Y is the throat radius of the fitting throat section, YLIs the inlet radius, XLFor the length of the constriction, XL＝2YLX is the X coordinate of the fitting throat section and Y is the Y coordinate of the fitting throat section.
(III) advantageous effects
The technical scheme of the invention has the following advantages: the invention provides a hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method, which is characterized in that a fitting reference nozzle is designed according to a typical running state of the fitting throat section, the inlet radius, the contraction section length, the expansion section length and the outlet radius of the fitting reference nozzle are made to be the same as those of an original nozzle through processing, the displacement thickness of a reference boundary layer is obtained through calculation processing, then backward derivation non-adhesive profiles are obtained through backward derivation, non-adhesive profiles of the fitting throat section are obtained through fitting on the backward derivation non-adhesive profiles, the displacement thickness of the boundary layer is added at the corresponding position to obtain a physical profile of an expansion part of the fitting throat section, and the expansion part and the contraction part of the physical profile of the fitting throat section are combined to obtain a complete physical profile of the fitting throat section. The method can fully consider the influence of the operation Mach number, the total temperature, the total pressure and the displacement thickness of the boundary layer caused by the change of a test medium of the fitting throat section, ensure the accuracy of the fitting throat and realize the fitting of the throat sections with different requirements.
Drawings
The drawings of the present invention are provided for illustrative purposes only, and the proportion and the number of the components in the drawings do not necessarily correspond to those of an actual product.
FIG. 1 is a schematic representation of a fitted throat section profile according to an embodiment of the present invention;
fig. 2 is a partially enlarged schematic view of fig. 1.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
The design method of the hypersonic wind tunnel axisymmetric profile nozzle fitting throat section provided by the embodiment of the invention comprises the following steps:
(1) and designing by adopting the same design method as the original spray pipe and taking the operation Mach number, the total temperature, the total pressure, the gas medium, the inlet radius and the outlet radius of the fitting throat section as design input conditions to obtain the fitting reference spray pipe. It should be noted that the original nozzle is a hypersonic wind tunnel axisymmetric profile nozzle of the throat section to be replaced, and the design thereof generally adopts MOC/BL method calculation, i.e. characteristic line method/boundary layer correction, which are mature prior art, and are not described in detail in the present application.
(2) Processing the fitted reference nozzle using the following relationship:
xN＝xN*xE/xNE
yN＝yN*yE/yNE
and keeping the inlet radius, the contraction section length and the outlet radius of the fitting reference nozzle consistent with the original nozzle.
Calculating boundary layer displacement thickness delta of the fitting reference nozzle by adopting the following relational expressionNAnd (3) processing:
δ＝δN*yE/yNE
obtaining the displacement thickness delta of the reference boundary layer;
wherein: x is the number ofNTo fit the X-coordinate, y, of a reference nozzleNTo fit the Y coordinate, x, of the reference nozzleEExpanded length of primary nozzle, xNETo fit the length of the expanded section of the reference nozzle, yEIs the outlet radius of the original nozzle, yNETo fit the exit radius of the reference nozzle.
In one embodiment, the boundary layer displacement thickness δ of the fitted reference nozzleNThe method comprises the following steps:
and obtaining the value of the boundary layer shape factor H and the value of the momentum thickness theta by solving an axisymmetric Von-Karman momentum equation:
Figure BDA0003386116170000061
in the formula: x is the number ofNTo fit the X-coordinate, y, of a reference nozzleNTo fit the Y coordinate of the reference nozzle, MeDesign Mach number, C for fitting reference nozzlefIs coefficient of friction, θfThe gas flow deflection angle is shown, and gamma is the specific heat ratio of gas;
solving the boundary layer displacement thickness delta by adopting a momentum thickness weighting methodNThe weighting formula of the momentum thickness weighting method is as follows:
Figure BDA0003386116170000071
wherein H is the boundary layer shape factor, δNAnd k is the boundary layer displacement thickness, k is a weighting coefficient, and theta is the momentum thickness obtained through prediction.
Optionally, the value range of the weighting coefficient k is between 0 and 1, verification is performed by adopting a numerical simulation method, and determination is performed by an iteration method. It should be noted that, the verification is performed by using a numerical simulation method, and the determination by using an iterative method may all be performed by using the prior art, which is not described herein again.
(3) In the physical profile L of the original spray pipe1The displacement thickness delta of the reference boundary layer is subtracted to form a reversely derived non-adhesive profile L3。
(4) In said backward development of the inviscid profile L3The design of the non-adhesive profile of the fitting throat section is completed, the displacement thickness delta of the reference boundary layer at the corresponding position is added on the non-adhesive profile of the expansion part of the fitting throat section to form the physical profile L of the fitting throat section4The expansion part of (2).
The non-adhesive profile design of the fitting throat section in the step (4) can be carried out by adopting the following method, comprising the following steps:
(41) deriving inviscid profile L in the reverse direction3The above assumes a fitting point;
(42) and (3) adopting a cubic curve equation to complete the design of the fitting throat inviscid profile:
y＝a0+a1x+a2x2+a3x3
in the formula a0，a1，a2，a3Is the undetermined coefficient;
the boundary conditions of the above cubic curve equation are as follows:
x＝0：y＝y*；
Figure BDA0003386116170000072
x＝xat：y＝yat；
Figure BDA0003386116170000073
substituting the boundary conditions into an equation to obtain undetermined coefficients, and substituting the undetermined coefficients into a formula to obtain the following fitting equation of the non-adhesive surface of the fitting throat section:
Figure BDA0003386116170000081
in the formula: y is the throat radius of the fitting throat section; y isatDeriving a fitted point radius of the unbonded surface in a reverse direction; x is the number ofatDeriving axial coordinates of the fitting point of the non-adhesive surface in a reverse direction; thetaatIn order to reversely deduce the inclination angle of the fitting point inviscid curve of the inviscid surface, X is the X coordinate of the fitting throat section, and Y is the Y coordinate of the fitting throat section.
On the basis, the displacement thickness delta of the reference boundary layer at the corresponding position is added to the non-adhesive profile of the expansion part of the fitting throat section, namely the fitting formula of the expansion part of the physical profile L4 of the fitting throat section is as follows:
Figure BDA0003386116170000082
(43) and (3) verifying the flow field quality of the non-adhesive line by adopting a characteristic line method without considering the viscosity influence, finishing the design if the flow field index meets the design requirement, and adjusting the position of a fitting point until the flow field index meets the requirement if the flow field index does not meet the requirement. It should be noted that, the flow field quality of the unbonded line is verified by using the characteristic line method and the fitting point position is adjusted according to the verification result, which is not described herein again.
(5) Designing to obtain a physical profile L of a fitting throat section according to requirements4The constriction of (a). It should be noted that the physical profile that can be required can be designed by using the existing design method, for example, the physical profile can be obtained by using the following empirical formula calculation of the ideal incompressible axial symmetric flow:
Figure BDA0003386116170000091
wherein Y is the throat radius of the fitting throat section, YLIs the inlet radius, XLFor the length of the constriction, XL＝2YLX is the X coordinate of the fitting throat section and Y is the Y coordinate of the fitting throat section.
In addition, it should be noted that, although the inlet size of the constricted portion of the fitting throat section is generally the same as the inlet size of the constricted portion of the original nozzle, the problem of profile butt joint is not involved in the replacement, and therefore, if there is a special need, the inlet size of the constricted portion of the fitting throat section may not be the same as the inlet size of the constricted portion of the original nozzle, and the implementation method can be implemented by using the prior art, and is not described herein again.
(6) Fitting the physical profile L of the throat section obtained in the steps (4) and (5)4And fitting throat section physical profile L4The contraction parts are combined together to obtain a fitted throat section physical profile L4. Referring to FIGS. 1 and 2, a fitting throat section physical profile obtained by the design method of the present application is schematically shown, in which L1Is the physical molded surface of the original spray pipe,L2is a non-adhesive molded surface of the original spray pipe, L3For deriving the non-adhesive profile in the reverse direction, L4Fitting the physical profile of the throat section.
The method comprises the steps of designing a fitting reference spray pipe according to a typical running state of a fitting throat section, enabling an inlet radius, a contracted section length, an expanded section length and an outlet radius of the fitting reference spray pipe to be the same as those of an original spray pipe through processing, obtaining a displacement thickness of a reference boundary layer through calculation processing, further obtaining a reverse derivation non-adhesive profile through reverse derivation, fitting on the reverse derivation non-adhesive profile to obtain a non-adhesive profile of the fitting throat section, adding the displacement thickness of the boundary layer at a corresponding position to obtain a physical profile of an expanded part of the fitting throat section, and combining the expanded part and the contracted part of the physical profile of the fitting throat section to obtain a complete physical profile of the fitting throat section. The method can fully consider the influence of the operation Mach number, the total temperature, the total pressure and the displacement thickness of the boundary layer caused by the change of a test medium of the fitting throat section, ensure the accuracy of the fitting throat and realize the fitting of the throat sections with different requirements.
It is worth to be noted that the X coordinate and the Y coordinate of the original nozzle, the fitting reference nozzle and the fitting throat section in the present application all adopt the coordinate system commonly adopted in the field of nozzle design, that is, the axial direction of the nozzle is the X axis, the direction perpendicular to the X axis at the throat is the Y axis, and the intersection point of the X axis and the Y axis is the origin of coordinates.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: each embodiment does not include only one independent technical solution, and in the case of no conflict between the solutions, the technical features mentioned in the respective embodiments can be combined in any way to form other embodiments which can be understood by those skilled in the art.
Furthermore, modifications may be made to the technical solutions described in the foregoing embodiments, or equivalents may be substituted for some of the technical features thereof, without departing from the scope of the present invention, and the essence of the corresponding technical solutions does not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (6)

1. A hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method is characterized by comprising the following steps:
(1) designing to obtain a fitting reference spray pipe by adopting a design method which is the same as that of the original spray pipe and taking the operation Mach number, the total temperature, the total pressure, the gas medium, the inlet radius and the outlet radius of the fitting throat section as design input conditions;
(2) processing the fitted reference nozzle using the following relationship:
xN＝xN*xE/xNE
yN＝yN*yE/yNE
keeping the inlet radius, the contraction section length and the outlet radius of the fitting reference nozzle consistent with the original nozzle;
calculating boundary layer displacement thickness delta of the fitting reference nozzle by adopting the following relational expressionNAnd (3) processing:
δ＝δN*yE/yNE
obtaining the displacement thickness delta of the reference boundary layer;
wherein: x is the number ofNTo fit the X-coordinate, y, of a reference nozzleNTo fit the Y coordinate, x, of the reference nozzleEExpanded length of primary nozzle, xNETo fit the length of the expanded section of the reference nozzle, yEIs the outlet radius of the original nozzle, yNEFitting the outlet radius of the reference nozzle;
(3) in the physical profile L of the original spray pipe1The displacement thickness delta of the reference boundary layer is subtracted to form a reversely derived non-adhesive profile L3；
(4) In said backward development of the inviscid profile L3The design of the non-adhesive profile of the fitting throat section is completed, the displacement thickness delta of the reference boundary layer at the corresponding position is added on the non-adhesive profile of the expansion part of the fitting throat section to form the physical profile L of the fitting throat section4The expansion part of (1);
(5) designed according to requirementsObtaining the physical profile L of the fitting throat section4A constricted portion of (a);
(6) the fitted throat section physical profile L obtained in the steps (4) and (5) is subjected to4And the fitted throat section physical profile L4Are combined to obtain the physical profile L of the fitting throat section4。
2. The hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method according to claim 1, characterized in that: and designing by adopting a characteristic line method to obtain the fitting reference spray pipe.
3. The hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method according to claim 2, characterized in that: the boundary layer displacement thickness of the fitting reference nozzle is obtained by the following method:
and obtaining the value of the boundary layer shape factor H and the value of the momentum thickness theta by solving an axisymmetric Von-Karman momentum equation:
Figure FDA0003386116160000021
in the formula: x is the number ofNTo fit the X-coordinate, y, of a reference nozzleNTo fit the Y coordinate of the reference nozzle, MeDesign Mach number, C for fitting reference nozzlefIs coefficient of friction, θfThe gas flow deflection angle is shown, and gamma is the specific heat ratio of gas;
solving the boundary layer displacement thickness delta by adopting a momentum thickness weighting methodNThe weighting formula of the momentum thickness weighting method is as follows:
Figure FDA0003386116160000022
wherein H is the boundary layer shape factor, δNAnd k is the boundary layer displacement thickness, k is a weighting coefficient, and theta is the momentum thickness obtained through prediction.
4. The hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method according to claim 3, characterized in that: the value range of the weighting coefficient k is between 0 and 1, the verification is carried out by adopting a numerical simulation method, and the determination is carried out by adopting an iteration method.
5. The hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method according to claim 1, characterized in that: the design of the non-adhesive profile of the fitting throat section in the step (4) comprises the following steps:
(41) deriving inviscid profile L in the reverse direction3The above assumes a fitting point;
(42) and (3) adopting a cubic curve equation to complete the design of the fitting throat inviscid profile:
y＝a0+a1x+a2x2+a3x3
in the formula a0，a1，a2，a3Is the undetermined coefficient;
the boundary conditions of the above cubic curve equation are as follows:
x＝0：y＝y*；
Figure FDA0003386116160000031
x＝xat：y＝yat；
Figure FDA0003386116160000032
substituting the boundary conditions into an equation to obtain undetermined coefficients, and substituting the undetermined coefficients into a formula to obtain the following fitting equation of the non-adhesive surface of the fitting throat section:
Figure FDA0003386116160000033
in the formula: y is the throat radius of the fitting throat section; y isatDeriving a fitted point radius of the unbonded surface in a reverse direction; x is the number ofatDeriving axial coordinates of the fitting point of the non-adhesive surface in a reverse direction; thetaatThe dip angle of the fit point inviscid curve of the inviscid profile is reversely deduced, wherein X is the X coordinate of the fit throat section, and Y is the Y coordinate of the fit throat section;
(43) and (3) verifying the flow field quality of the non-adhesive line by adopting a characteristic line method without considering the viscosity influence, finishing the design if the flow field index meets the design requirement, and adjusting the position of a fitting point until the flow field index meets the requirement if the flow field index does not meet the requirement.
6. The hypersonic wind tunnel axisymmetric profile nozzle fitting throat section design method according to claim 1, characterized in that: the fitted throat section physical profile L in the step (5)4The contraction part of the flow is obtained by the following Witoszynski empirical formula of ideal incompressible axial symmetric flow:
Figure FDA0003386116160000041
wherein, y*To fit the throat radius, Y, of the throat sectionLIs the inlet radius, XLFor the length of the constriction, XL＝2YLX is the X coordinate of the fitting throat section and Y is the Y coordinate of the fitting throat section.
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CN115048752A (en) * 2022-08-16 2022-09-13 中国航空工业集团公司沈阳空气动力研究所 Design method for supersonic-speed-crossing wind tunnel semi-flexible wall spray pipe
CN115046722A (en) * 2022-08-16 2022-09-13 中国航空工业集团公司沈阳空气动力研究所 Method for calibrating mach number of cross-supersonic-velocity wind tunnel nozzle
CN117007274A (en) * 2023-10-07 2023-11-07 中国空气动力研究与发展中心设备设计与测试技术研究所 Subsonic wind tunnel loop mass flow measurement method

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