CN111723537B - Method, device, equipment and storage medium for measuring molecular flow thermal adaptation coefficient - Google Patents

Method, device, equipment and storage medium for measuring molecular flow thermal adaptation coefficient Download PDF

Info

Publication number
CN111723537B
CN111723537B CN202010558870.6A CN202010558870A CN111723537B CN 111723537 B CN111723537 B CN 111723537B CN 202010558870 A CN202010558870 A CN 202010558870A CN 111723537 B CN111723537 B CN 111723537B
Authority
CN
China
Prior art keywords
adaptation coefficient
thermal adaptation
molecular flow
measuring
incidence angle
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010558870.6A
Other languages
Chinese (zh)
Other versions
CN111723537A (en
Inventor
姜利祥
李涛
商圣飞
焦子龙
郑慧奇
唐振宇
向树红
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Spacecraft Environment Engineering
Original Assignee
Beijing Institute of Spacecraft Environment Engineering
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Spacecraft Environment Engineering filed Critical Beijing Institute of Spacecraft Environment Engineering
Priority to CN202010558870.6A priority Critical patent/CN111723537B/en
Publication of CN111723537A publication Critical patent/CN111723537A/en
Application granted granted Critical
Publication of CN111723537B publication Critical patent/CN111723537B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • G06F30/28Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • G06F30/25Design optimisation, verification or simulation using particle-based methods
    • GPHYSICS
    • G16INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16CCOMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
    • G16C10/00Computational theoretical chemistry, i.e. ICT specially adapted for theoretical aspects of quantum chemistry, molecular mechanics, molecular dynamics or the like
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00Details relating to the application field
    • G06F2113/08Fluids
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/08Thermal analysis or thermal optimisation
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14Force analysis or force optimisation, e.g. static or dynamic forces
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02TCLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Computing Systems (AREA)
  • General Physics & Mathematics (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Fluid Mechanics (AREA)
  • Algebra (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Physics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • General Health & Medical Sciences (AREA)
  • Spectroscopy & Molecular Physics (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Aerodynamic Tests, Hydrodynamic Tests, Wind Tunnels, And Water Tanks (AREA)

Abstract

The application discloses a method, a device, equipment and a storage medium for measuring a molecular flow thermal adaptation coefficient, wherein the method comprises the steps of firstly measuring a pressure value of incoming flow atmosphere with a preset incidence angle to a measurement plane based on a three-wire torsional pendulum micro-thrust measurement system, secondly calculating the molecular flow thermal adaptation coefficient corresponding to the preset incidence angle by utilizing a Max Wei Fanshe model based on the pressure value, then constructing a reference curve between the preset incidence angle and the thermal adaptation coefficient, and determining the molecular flow thermal adaptation coefficient corresponding to the incidence angle based on the incidence angle formed by the incoming flow of the atmosphere relative to a structural surface element of an aircraft and the reference curve in the flight process of the aircraft. The aerodynamic force calculation precision of the aircraft with the complex appearance is effectively improved.

Description

Method, device, equipment and storage medium for measuring molecular flow thermal adaptation coefficient
Technical Field
The invention relates to the aerodynamic and thermal technical field of ultra-low rail lean gas and aircraft action, in particular to a method, a device, equipment and a storage medium for measuring a molecular flow thermal adaptation coefficient.
Background
Lean gas dynamics has important application background in the aerospace field. The atmosphere in LEO orbits and near space is very thin and cannot sustain normal human life activities, but it is sufficient to have a significant impact on high-speed flying spacecraft in orbit. The impact of atoms moving at high speed on the spacecraft can increase aerodynamic resistance, so that the orbit of the spacecraft is lowered, even crashed, and the service life of the spacecraft is shortened.
Because of the lean effect, the conventional continuous medium assumption is not true, so the N-S equation for continuous flow processing is no longer applicable, resulting in the fact that the aerodynamic, thermal effects of lean gas on the wall cannot be calculated using the N-S equation. Early students often calculated aerodynamic drag experienced by an aircraft using drag coefficients. However, the drag coefficient is a macroscopic parameter, which currently has a reference value of the drag coefficient only for regular standard shapes such as planes, spheres, columns, etc., but the drag coefficient obviously cannot meet the requirements for complex aircraft shapes.
A direct monte carlo (DSMC) method of calculating a lean gas has been proposed later, which describes the movement of the lean gas at a molecular level, so that it becomes possible to calculate a lean gas flow of a complex shape. Reflection models for the action of the lean gas with the wall surface include specular reflection, diffuse reflection models with incomplete energy adaptation (DRIA), object plane reflection models (CLL), maxwell Wei Bi plane reflection models (Maxwell), and the like. Specular reflection means that the particles and the wall surface do not exchange energy and are directly specularly reflected. Diffuse reflection refers to the complete thermal adaptation of the incident molecules to the surface of the material, with the probability of the molecular velocity direction being the same in all directions. The incomplete energy adaptive diffuse reflection model (DRIA) refers to the fact that the probability of random distribution of the velocity direction of reflected molecules is the same, but the thermal adaptation degree with the surface of the material is variable. The object plane reflection model (CLL) provides distribution functions for normal and tangential components of the reflected molecular velocity, and the main parameters of the distribution functions are normal energy adaptation coefficient and tangential energy adaptation coefficient. The Maxwell model Wei Bi surface reflection (Maxwell) is a superposition of specular and diffuse reflection, and it is assumed that alpha particles adapt to wall temperature and diffuse reflection, and 1-alpha particles are specular reflection.
It is easy to see that specular and diffuse reflection are both extreme reflection models and do not describe well the action of molecules with walls. While the object plane reflection model (CLL) is physically more realistic, it contains both tangential and normal adaptation parameters, and the two parameters have a certain coupling, so that the parameters are difficult to determine, and thus the object plane reflection model (CLL) is difficult to be practically applied. While the Maxwell model Wei Bi is the most widely used model with relatively good effect, the parameter α in the Maxwell model Wei Bi is a key parameter for limiting the calculation accuracy.
The adaptation coefficients in the Maxwell Wei Bi plane reflection model (Maxwell) are affected by many aspects of material properties, roughness, incoming gas properties, velocity, etc., and there has been no data reference available. Researchers either take experimental parameters, such as 0.5, 0.9, to study, or take the two extreme conditions directly, taking 0 and 1 directly to give the envelope. It can be seen that the measurement of aerodynamic resistance is difficult for a Maxwell model (Maxwell) of Maxwell Wei Bi surface by a direct Monte Carlo simulation method for thin gas flow with a complicated profile due to the limitation of the parameter α.
Disclosure of Invention
In view of the foregoing drawbacks or shortcomings of the prior art, it is desirable to provide a method, apparatus, device, and storage medium for measuring a thermal adaptation coefficient of a molecular stream. The thermal adaptation coefficient corresponding to the aircraft when the aircraft receives the incoming air flow is effectively obtained by constructing a curve between the incidence angle and the molecular flow thermal adaptation coefficient.
In order to achieve the above purpose, the invention adopts the following technical scheme:
in a first aspect, the present invention provides a method for determining a thermal adaptation coefficient of a molecular flow, which is characterized by comprising:
measuring the pressure value of an atmospheric incoming flow pair measuring plane with a preset incident angle based on a three-wire torsion pendulum micro-thrust measuring system;
calculating a molecular flow thermal adaptation coefficient corresponding to the preset incidence angle by using a Maxwell Wei Fanshe model based on the pressure value;
constructing a reference curve between the preset incidence angle and the thermal adaptation coefficient;
during the flight of an aircraft, a molecular flow thermal adaptation coefficient corresponding to an incident angle formed by an atmospheric inflow relative to a structural surface element of the aircraft is determined based on the incident angle and the reference curve.
In one embodiment, determining a molecular flow thermal adaptation coefficient corresponding to an incident angle of an incoming atmospheric flow with respect to a structural bin of the aircraft based on the incident angle and the reference curve comprises:
a plurality of structural elements divided into which the exterior of the aircraft is acquired,
determining the angle of incidence of the incoming atmospheric flow with respect to each of said structural elements;
and searching a molecular flow thermal adaptation coefficient corresponding to the incidence angle in the reference curve by utilizing the incidence angle, wherein the first axis direction of the reference curve represents the angle value of the incidence angle, and the second axis direction represents the molecular flow thermal adaptation coefficient.
In one embodiment, the step of calculating the molecular flow thermal adaptation coefficient corresponding to the preset angle of incidence using a maxwell Wei Fanshe model based on the pressure value includes:
obtaining a pressure statistic calculation formula of the lean gas to the wall surface based on a Maxwell Wei Fanshe model;
and calculating a molecular flow thermal adaptation coefficient corresponding to the preset incidence angle based on the pressure value and the pressure statistic calculation formula.
In one embodiment, the step of calculating the pressure value on the measurement plane based on aerodynamic forces of the incoming atmosphere comprises:
the step of measuring the pressure value of the incoming flow atmosphere at a preset incidence angle to a measurement plane based on the three-wire torsional pendulum micro-thrust measurement system comprises the following steps of:
measuring aerodynamic force of incoming flow atmosphere at a preset incidence angle to a measurement plane by using a three-wire torsion pendulum micro-thrust measuring system;
a pressure value on the measurement plane is calculated based on the aerodynamic force of the measurement plane.
In one embodiment, the three-wire torsional pendulum micro thrust measurement system comprises a thrust measuring plate, a thrust transmission rod, a laser and a reflecting mirror;
the step of measuring aerodynamic force of incoming flow atmosphere at a preset incidence angle to a measurement plane by using the three-wire torsional pendulum micro-thrust measuring system comprises the following steps of:
emitting incoming air to the measuring plane along a preset angle, pushing the thrust measuring plate to rotate so as to drive the reflecting mirror to rotate, and enabling the reflecting light position of the laser to move by the rotation of the reflecting mirror;
and calculating the aerodynamic force of the incoming air supplied to the thrust measuring plate based on the displacement of the reflected light.
In one embodiment, the step of measuring aerodynamic force of the incoming atmosphere at a preset angle of incidence to the measurement plane using the three-wire torsional pendulum micro-thrust measurement system further comprises:
and adjusting the angle between the thrust measuring plate and the thrust transmission rod to measure aerodynamic force at different preset incidence angles.
The invention provides a measuring device for a molecular flow thermal adaptation coefficient, which is characterized by comprising a pressure measuring module for measuring a plane, a pressure calculation expression acquisition module, a reference curve construction module, a processing module and a thermal adaptation coefficient acquisition module;
the pressure measurement module of the measurement plane is used for measuring the pressure value of the incoming flow atmosphere with a preset incidence angle on the measurement plane based on the three-wire torsional pendulum micro-thrust measurement system;
the molecular flow thermal adaptation coefficient calculation module is used for calculating a molecular flow thermal adaptation coefficient corresponding to the preset incidence angle by using a Maxwell Wei Fanshe model based on the pressure value;
the reference curve construction module is used for constructing a reference curve between the preset incidence angle and the thermal adaptation coefficient;
and the thermal adaptation coefficient acquisition module is used for determining a molecular flow thermal adaptation coefficient corresponding to the incidence angle based on the incidence angle formed by the atmospheric incoming flow relative to the structural surface element of the aircraft and the reference curve in the flight process of the aircraft.
In one embodiment, the thermal adaptation coefficient acquisition module comprises:
a structural-surface-element acquisition subunit for acquiring a plurality of structural-surface elements divided into by the exterior of the aircraft,
an incidence angle determination subunit for determining an incidence angle formed by the incoming atmospheric flow with respect to each of the structural bins;
and the searching subunit is used for searching the molecular flow thermal adaptation coefficient corresponding to the incidence angle in the reference curve by utilizing the incidence angle, wherein the first axis direction of the reference curve represents the angle value of the incidence angle, and the second axis direction represents the molecular flow thermal adaptation coefficient.
In one embodiment, the molecular flow thermal adaptation coefficient calculation module comprises a pressure statistic calculation formula acquisition unit and a molecular flow thermal adaptation coefficient calculation unit;
the pressure statistic calculation formula acquisition unit is used for acquiring a pressure statistic calculation formula of the lean gas to the wall surface based on a Maxwell Wei Fanshe model;
and the pressure calculation expression acquisition unit is used for calculating a molecular flow thermal adaptation coefficient corresponding to the preset incidence angle based on the pressure value and the pressure statistics calculation formula.
In one embodiment, the measurement plane pressure measurement module includes a measurement plane aerodynamic force measurement unit and a measurement plane pressure calculation unit;
the aerodynamic force measuring unit of the measuring plane is used for measuring aerodynamic force of incoming flow atmosphere with a preset incidence angle to the measuring plane by using a three-wire torsional pendulum micro-thrust measuring system;
and the pressure calculation unit is used for calculating the pressure value on the measurement plane based on the aerodynamic force of the measurement plane.
In a third aspect, the invention provides a computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the method described above when executing the computer program.
In a fourth aspect, the invention provides a computer readable storage medium having stored thereon a computer program, characterized in that the computer program, when executed by a processor, implements the method described above.
Compared with the prior art, the invention has the beneficial effects that:
according to the technical scheme, firstly, the pressure value of incoming flow atmosphere with a preset incidence angle to a measurement plane is measured based on a three-wire torsional pendulum micro-thrust measurement system, secondly, a molecular flow thermal adaptation coefficient corresponding to the preset incidence angle is calculated by utilizing a Max Wei Fanshe model based on the pressure value, then a reference curve between the preset incidence angle and the thermal adaptation coefficient is constructed, and in the flight process of an aircraft, the molecular flow thermal adaptation coefficient corresponding to the incidence angle is determined based on the incidence angle formed by the incoming flow of the atmosphere relative to a structural element of the aircraft and the reference curve. According to the embodiment of the application, the molecular flow thermal adaptation coefficient of the air inflow to the aircraft is determined through the pre-constructed reference curve, so that the aerodynamic resistance of the air inflow to the aircraft is calculated, and the calculation efficiency of the aerodynamic resistance of the air inflow to the aircraft is effectively improved. In the molecular flow thermal adaptation coefficient calculation process corresponding to the set incidence angle, the ultra-low rail atmospheric resistance is very small, and how to measure the micro thrust is a technical difficulty, while the three-wire torsion pendulum micro thrust measurement system can measure the micro thrust very accurately, so that the technical difficulty is well solved.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the detailed description of non-limiting embodiments, made with reference to the following drawings, in which:
FIG. 1 is a flow chart of a method for determining a thermal adaptation coefficient of a molecular flow according to an embodiment of the present invention;
FIG. 2 is a flow chart illustrating the steps of measuring the pressure value on the measuring plane according to the embodiment of the present invention;
FIG. 3 is a flowchart illustrating a step of calculating a thermal adaptation coefficient of a molecular flow according to a preset incident angle in an embodiment of the present invention;
FIG. 4 is a flow chart illustrating the steps of obtaining the thermal adaptation coefficients of molecular flows with different incident angles according to an embodiment of the present invention;
FIG. 5 is a block diagram illustrating an exemplary configuration of a device for measuring a thermal adaptation coefficient of a molecular flow according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a computer device suitable for implementing embodiments of the present invention;
fig. 7 is a schematic structural diagram of a three-wire torsional pendulum micro thrust measuring system according to an embodiment of the present invention.
In the figure: 1-thrust measuring plate, 2-thrust transmission rod, 3-laser, 4-reflector and 5-scale.
Detailed Description
The present application is described in further detail below with reference to the drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be noted that, for convenience of description, only the portions related to the invention are shown in the drawings.
It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
As mentioned in the background art, the Maxwell Wei Bi surface reflection model (Maxwell) is the most widely used model and has better effect at present, but the parameter α in the Maxwell Wei Bi surface reflection model (Maxwell) becomes a key parameter for limiting the calculation accuracy. The adaptation coefficients in the Maxwell Wei Bi plane reflection model (Maxwell) are affected by many aspects of material properties, roughness, incoming gas properties, velocity, etc., and there has been no data reference available. Researchers either take experimental parameters, such as 0.5, 0.9, to study, or take the two extreme conditions directly, taking 0 and 1 directly to give the envelope. It can be seen that, due to the limitation of the parameter α, the determination of aerodynamic resistance is difficult and the accuracy is low when the flow of thin gas with a complicated shape is performed by using the simulation method of direct monte carlo on the Maxwell model Wei Bi surface.
Therefore, how to provide a method for obtaining a suitable thermal adaptation coefficient so that the accuracy is higher when the ultra-low orbit aircraft with a complex shape is subjected to the calculation of the resistance of the lean gas by adopting the direct Monte Carlo simulation method is the improvement direction of the application.
The basic concept of the invention is to construct a reference curve of angle-thermal adaptation coefficients based on pressure values measured by a three-wire torsional pendulum micro-thrust measuring system and pressure calculation expressions obtained based on a Maxwellian Wei Fanshe model, and obtain the thermal adaptation coefficients of different angles from the reference curves of the angle-thermal adaptation coefficients under different incidence angles. Based on the above conception, the invention provides a method, a device, equipment and a storage medium for measuring a thermal adaptation coefficient of a molecular flow, in particular to a technical scheme for measuring a thermal adaptation coefficient parameter in a Maxwell model (Maxwell) Wei Bi surface reflection model in a Monte Carlo (MC) or direct Monte Carlo (DSMC) calculation method of the action of a molecular layer on a thin gas and a wall surface.
Referring to fig. 1, fig. 1 shows a flow chart of a method for determining a thermal adaptation coefficient of a molecular flow according to an embodiment of the present application. As shown in fig. 1, the method includes:
in step 10, measuring the pressure value of the atmospheric incoming flow at a preset incidence angle to a measurement plane based on a three-wire torsional pendulum micro-thrust measuring system;
in step 20, calculating a molecular flow thermal adaptation coefficient corresponding to the preset incident angle by using a max Wei Fanshe model based on the pressure value;
in step 30, a reference curve between the preset incident angle and the thermal adaptation coefficient is constructed;
in step 40, during the flight of the aircraft, a coefficient of thermal adaptation of the molecular flow corresponding to the angle of incidence is determined based on the angle of incidence formed by the incoming flow of the atmosphere with respect to the structural elements of the aircraft and the reference curve.
In the above steps it is necessary to know that the measuring plane is provided in a laboratory, and that the incoming air is generated by means of high-speed jet devices, such as rocket engines, jet pipes, etc. The preset angle of incidence refers to the angle between the incoming atmosphere and the normal of the measuring plane.
The macroscopic aerodynamic integral equation is for Maxwell, a Maxwell model Wei Bi plane reflection, which is a superposition of specular and diffuse reflection, assuming that particles with alpha are diffusely reflected by adapting to wall temperature, and particles with 1-alpha are specularly reflected.
Based on a laboratory, a measured pressure value is obtained, then a macroscopic aerodynamic integration equation is used for obtaining an expression of the pressure in a wall reflection model (Maxwell), and a parameter alpha, namely a thermal adaptation coefficient, is obtained according to the equivalent relation of the pressure value and the pressure in the wall reflection model (Maxwell).
Referring to fig. 2, fig. 2 shows a schematic flow chart of step 10, the step 10 comprising:
step 101, measuring aerodynamic force of incoming flow atmosphere with a preset incidence angle to a measurement plane by using a three-wire torsional pendulum micro-thrust measuring system;
step 102, calculating a pressure value on the measurement plane based on the aerodynamic force of the measurement plane.
Fig. 6 shows a specific structure of the three-wire torsional pendulum micro thrust measurement system. As shown in fig. 6, the three-wire torsional pendulum micro thrust measuring system comprises a thrust measuring plate 1, a thrust transmission rod 2, a laser 3 and a reflecting mirror 4. The measuring plane is formed on a thrust measuring plate 1 of the three-wire torsional pendulum micro thrust measuring system, the thrust measuring plate 1 is used for receiving aerodynamic force of incoming flow, a thrust transmission rod is used for connecting the thrust measuring plate 1 and a torsional pendulum main body at a certain installation angle, the laser 3 is used for providing incident light, and the reflector 4 is used for reflecting the incident light.
The following describes the process of measuring aerodynamic force of an incoming air at a preset angle of incidence at a preset speed on a measurement plane by combining with a specific structure of the three-wire torsional pendulum micro-thrust measurement system.
Transmitting incoming air to the thrust measuring plate 1 along a preset angle to push the thrust measuring plate 1 to rotate, so that the reflecting mirror 4 is driven to rotate through the thrust transmission rod 2, and the reflecting mirror rotates to enable the reflected light position of the laser 3 to move;
and calculating the aerodynamic force of the incoming air supplied to the thrust measuring plate 1 based on the displacement of the reflected light. The displacement of the reflected light can be measured by the scale 5, the reflected light is reflected to the scale 5, and the displacement is obtained through the reading change of the scale 5.
Specifically, firstly, the three-wire torsional pendulum micro-thrust measuring system is used for measuring the aerodynamic force F born by the measuring plane when the incoming air at the preset speed is sprayed to the measuring plane at the preset incidence angle theta.
The pressure p of the measuring plane on the thrust measuring plate is obtained according to the formula (1):
wherein A is the area of the thrust plate.
The preset incident angle theta is set, and the area A of the thrust measuring plate is measured in advance, so that the pressure p of the incoming air to the measuring plane at the preset speed can be obtained.
Preferably, the step of measuring aerodynamic force of incoming air at a preset incident angle to a measurement plane by using the three-wire torsional pendulum micro-thrust measurement system further comprises: and adjusting an angle beta between the thrust measuring plate and the thrust transmission rod to measure aerodynamic force at different preset incidence angles.
Referring to fig. 3, fig. 3 shows a schematic flow chart of step 20. The step 20 includes:
step 201, obtaining a pressure statistic calculation formula of the lean gas to the wall surface based on a Maxwell Wei Fanshe model;
step 202, calculating a molecular flow thermal adaptation coefficient corresponding to the preset incidence angle based on the pressure value and the pressure statistic calculation formula.
In the step, a pressure statistic calculation formula of the pressure generated by direct collision gas, diffuse reflection gas and specular reflection gas on the wall surface is respectively deduced based on a Maxwell Wei Fanshe model; and acquiring the pressure calculation expression based on a pressure statistic calculation formula of the pressure generated by the direct collision gas, the diffuse reflection gas and the specular reflection gas on the wall surface.
For the high-speed incoming flow of the rarefied atmosphere, the incoming flow is very rarefied, so that the gas cannot generate the viscous effect under the condition of continuous flow, and a particle statistics method Monte Carlo (MC) method is adopted for simulating the gas, namely, the gas is regarded as mutually independent small particles. In addition, the temperature of the gas is far higher than the condensation temperature of the gas, and the effect of cold adsorption on the wall surface can not be generated. Therefore, in the current theoretical process, the statistical calculation formula of the pressure of the direct collision of the lean gas against the wall surface is:
wherein U, v and w are respectively corresponding to the sub-speeds of X, Y, Z in three directions, ρ is the density of the incoming gas, U is the normal speed,for the molecular velocity ratio, α is the adaptation coefficient in Maxwell model (Maxwell), whose value is between 0 and 1, erf () is the error function, and R is the gas constant.
erf () is an error function whose expression is:
according to the definition of the Maxwell model, particles with alpha adapt to wall temperature and diffuse reflection, and particles with 1-alpha reflect specularly. The diffuse reflection part has Maxwell distribution of the speed of reflection of incoming particles, the speed of thermal movement, and the size of the diffuse reflection part is adapted to the wall temperature T w Its average velocity v r Can be expressed as:
where v is the component velocity in any direction.
Wherein the distribution function f (v) is:
and similarly, the diffuse reflection pressure p can be obtained according to pressure integral re1 The method comprises the following steps:
wherein T is the local gas molecular temperature, the specularly reflected fraction p re2 Positive pressure expressions follow as if it were normal, since their flow is opposite.
The pressure p of the final plate is:
p=p in +αp re1 +(1-α)p re2 (7)
from the formulas (1) to (7)
In step 20, the formula (8) and the formula (1) are combined, so that:
the adaptation coefficient α can be obtained according to equation (9).
The aerodynamic force of the incoming flow atmosphere with each preset incident angle to the measurement plane is measured through the three-wire torsional pendulum micro-thrust measurement system, so that different relation curves of preset angles and thermal adaptation coefficients can be established, and the thermal adaptation coefficients corresponding to different incident angles can be obtained through measurement.
Specifically, step 30 of constructing a reference curve between the preset incident angle and the thermal adaptation coefficient includes:
based on a three-wire torsion pendulum micro-thrust measuring system, measuring aerodynamic force of incoming flow atmosphere with a preset incidence angle to a thrust measuring plate;
calculating a pressure value on the thrust measuring plate based on aerodynamic force of the measuring plane;
calculating a molecular flow thermal adaptation coefficient corresponding to the preset incidence angle by using a Maxwell Wei Fanshe model based on the pressure value;
changing the preset incidence angle, and returning to the step of measuring aerodynamic force of incoming flow atmosphere at the preset incidence angle to a thrust measuring plate based on the three-wire torsion pendulum micro thrust measuring system;
and obtaining a molecular flow thermal adaptation coefficient corresponding to each preset incident angle.
Referring to fig. 4, fig. 4 shows a schematic flow chart of step 40. Determining a molecular flow thermal adaptation coefficient corresponding to an incident angle of an incoming flow of the atmosphere relative to a structural bin of the aircraft based on the incident angle and the reference curve comprises:
step 401, obtaining a plurality of structural elements divided into by the exterior of the aircraft,
step 402, determining an incident angle formed by the incoming atmospheric flow relative to each of the structural surface elements;
and step 403, searching a molecular flow thermal adaptation coefficient corresponding to the incidence angle in the reference curve by utilizing the incidence angle, wherein the first axis direction of the reference curve represents the angle value of the incidence angle, and the second axis direction represents the molecular flow thermal adaptation coefficient.
It should be noted that, the first axis direction and the second axis direction refer to directions of coordinate axes where the curves are located, and may specifically include, but not limited to, an X axis and a Y axis.
In the application link, the included angle between the front part of the aircraft and the incoming flow of the atmosphere can be determined according to the shape of the aircraft in the flight process. For example, the front of an aircraft is bullet-shaped, the bullet surface of which may be divided into a plurality of structural elements, also referred to as grid elements, and the angle of the incoming atmospheric flow with respect to each structural element is referred to as the angle of incidence. Through the determined multiple structural surface elements of the outer surface of the aircraft, the corresponding included angles of each structural surface element are respectively determined, and the corresponding incident angles of the aircraft in different shapes can be obtained. The pre-constructed curve is then used to determine the thermal adaptation coefficient corresponding to the angle of incidence.
Assuming that the incident angle corresponding to the vertex of the aircraft is 0 degrees, the incident angle of a certain point on the side is 80 degrees, and the thermal adaptation coefficient corresponding to 0 degrees and the thermal adaptation coefficient corresponding to 80 degrees can be obtained according to a pre-established reference curve of the preset incident angle and the thermal adaptation coefficient.
The values of the thermal adaptation coefficients of different angles can be obtained through the mode, so that the thermal adaptation coefficients of the incoming flow blown to different positions of the aircraft are known, aerodynamic forces of different positions of the aircraft can be calculated, and then aerodynamic forces on small surface elements corresponding to the positions are added up to be aerodynamic forces received by the aircraft.
Referring to fig. 5, fig. 5 shows a device for measuring a thermal adaptation coefficient of a molecular flow according to an embodiment of the present application. The device comprises a pressure measuring module 501 for measuring a plane, a molecular flow thermal adaptation coefficient calculating module 502, a reference curve constructing module 503 and a thermal adaptation coefficient obtaining module 504;
the pressure measurement module 501 of the measurement plane is used for measuring the pressure value of the incoming flow atmosphere with a preset incidence angle to the measurement plane based on the three-wire torsional pendulum micro-thrust measurement system;
the molecular flow thermal adaptation coefficient calculation module 502 is configured to calculate a molecular flow thermal adaptation coefficient corresponding to the preset incident angle using a maxwell Wei Fanshe model based on the pressure value;
a reference curve construction module 503, configured to construct a reference curve between the preset incident angle and the thermal adaptation coefficient;
the thermal adaptation coefficient obtaining module 504 determines, during the flight of the aircraft, a molecular flow thermal adaptation coefficient corresponding to an incident angle formed by an incoming air flow relative to a structural element of the aircraft based on the incident angle and the reference curve.
Optionally, the thermal adaptation coefficient acquisition module 504 includes a structural bin acquisition subunit, an incident angle determination subunit, and a lookup subunit;
a structural-bin acquisition subunit configured to acquire a plurality of structural bins into which an exterior of the aircraft is divided;
an incidence angle determination subunit for determining an incidence angle formed by the incoming atmospheric flow with respect to each of the structural bins;
and the searching subunit is used for searching the molecular flow thermal adaptation coefficient corresponding to the incidence angle in the reference curve by utilizing the incidence angle, wherein the first axis direction of the reference curve represents the angle value of the incidence angle, and the second axis direction represents the molecular flow thermal adaptation coefficient.
Alternatively, the molecular flow thermal adaptation coefficient calculation module 502 includes a pressure statistic calculation formula acquisition unit and a molecular flow thermal adaptation coefficient calculation unit;
the pressure statistic calculation formula acquisition unit is used for acquiring a pressure statistic calculation formula of the lean gas to the wall surface based on a Maxwell Wei Fanshe model;
and the pressure calculation expression acquisition unit is used for calculating a molecular flow thermal adaptation coefficient corresponding to the preset incidence angle based on the pressure value and the pressure statistics calculation formula.
Optionally, the reference curve construction module 503 includes a aerodynamic force measurement unit, a pressure value calculation unit, a repetitive processing unit, and a molecular flow thermal adaptation coefficient;
the aerodynamic force measuring unit is used for measuring aerodynamic force of incoming flow atmosphere at a preset incidence angle to the thrust measuring plate based on the three-wire torsional pendulum micro thrust measuring system;
a pressure value calculation unit for calculating a pressure value on the thrust measuring plate based on aerodynamic force of the measuring plane;
a molecular flow thermal adaptation coefficient calculation unit that calculates a molecular flow thermal adaptation coefficient corresponding to the preset incident angle using a maxwell Wei Fanshe model based on the pressure value;
the repeated processing unit is used for changing the preset incidence angle and returning to the step of measuring aerodynamic force of incoming flow atmosphere at the preset incidence angle to the thrust measuring plate based on the three-wire torsional pendulum micro thrust measuring system;
the molecular flow thermal adaptation coefficient obtaining unit obtains a molecular flow thermal adaptation coefficient corresponding to each preset incident angle.
Optionally, the three-wire torsional pendulum micro thrust measurement system comprises a thrust measuring plate, a thrust transmission rod, a laser and a reflecting mirror;
the aerodynamic force measuring unit of the measuring plane comprises:
the aerodynamic force measuring subunit is used for emitting incoming air onto the measuring plane along a preset angle, pushing the thrust measuring plate to rotate so as to drive the reflecting mirror to rotate, and the reflecting mirror rotates so that the reflected light position of the laser moves;
and the aerodynamic force calculating subunit is used for calculating the aerodynamic force of the incoming air supplied to the thrust measuring plate based on the displacement of the reflected light.
Optionally, the aerodynamic force measurement unit of the measurement plane further comprises:
and the angle adjusting subunit is used for adjusting the angle between the thrust measuring plate and the thrust transmission rod so as to measure aerodynamic force under different preset incidence angles.
Fig. 5 is a schematic structural diagram of a computer device according to an embodiment of the present invention. As shown in fig. 5, a schematic diagram of a computer system 600 suitable for use in implementing a terminal device or server of an embodiment of the present application is shown.
As shown in fig. 5, the computer system 600 includes a Central Processing Unit (CPU) 601, which can perform various appropriate actions and processes according to a program stored in a Read Only Memory (ROM) 602 or a program loaded from a storage section 608 into a Random Access Memory (RAM) 603. In the RAM 603, various programs and data required for the operation of the system 600 are also stored. The CPU 601, ROM 602, and RAM 603 are connected to each other through a bus 604. An input/output (I/O) interface 606 is also connected to bus 604.
The following components are connected to the I/O interface 605: an input portion 606 including a keyboard, mouse, etc.; an output portion 607 including a Cathode Ray Tube (CRT), a Liquid Crystal Display (LCD), and the like, a speaker, and the like; a storage section 608 including a hard disk and the like; and a communication section 609 including a network interface card such as a LAN card, a modem, or the like. The communication section 609 performs communication processing via a network such as the internet. The drive 610 is also connected to the I/O interface 606 as needed. Removable media 611 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, or the like is installed as needed on drive 610 so that a computer program read therefrom is installed as needed into storage section 608.
In particular, the process described above with reference to fig. 5 may be implemented as a computer software program according to embodiments of the present disclosure. For example, embodiments of the present disclosure include a computer program product comprising a computer program tangibly embodied on a machine-readable medium, the computer program comprising program code for performing the aircraft stand allocation method of a plurality of aircraft as described above. In such an embodiment, the computer program may be downloaded and installed from a network through the communication portion 609, and/or installed from the removable medium 611.
The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
The units or modules described in the embodiments of the present application may be implemented by software, or may be implemented by hardware. The described units or modules may also be provided in a processor. The names of these units or modules do not in some way constitute a limitation of the unit or module itself.
As another aspect, the present application also provides a computer-readable storage medium, which may be a computer-readable storage medium contained in the foregoing apparatus in the foregoing embodiment; or may be a computer-readable storage medium, alone, that is not assembled into a device. The computer readable storage medium stores one or more programs for use by one or more processors in performing the aircraft stand allocation methods described herein for a plurality of aircraft.
The foregoing description is only of the preferred embodiments of the present application and is presented as a description of the principles of the technology being utilized. It will be appreciated by persons skilled in the art that the scope of the invention referred to in this application is not limited to the specific combinations of features described above, but it is intended to cover other embodiments in which any combination of features described above or equivalents thereof is possible without departing from the spirit of the invention. Such as the above-described features and technical features having similar functions (but not limited to) disclosed in the present application are replaced with each other.

Claims (8)

1. A method for determining a thermal adaptation coefficient of a molecular flow, comprising:
measuring the pressure value of an atmospheric incoming flow pair measuring plane with a preset incident angle based on a three-wire torsion pendulum micro-thrust measuring system;
calculating a molecular flow thermal adaptation coefficient corresponding to the preset incident angle using a maxwell Wei Fanshe model based on the pressure value includes:
obtaining a pressure statistic calculation formula of the lean gas to the wall surface based on a Maxwell Wei Fanshe model;
calculating a molecular flow thermal adaptation coefficient corresponding to the preset incidence angle based on the pressure value and the pressure statistic calculation formula;
constructing a reference curve between the preset incidence angle and the thermal adaptation coefficient comprises:
based on a three-wire torsion pendulum micro-thrust measuring system, measuring aerodynamic force of incoming flow atmosphere with a preset incidence angle to a thrust measuring plate;
calculating a pressure value on the thrust measuring plate based on aerodynamic force of the measuring plane;
calculating a molecular flow thermal adaptation coefficient corresponding to the preset incidence angle by using a Maxwell Wei Fanshe model based on the pressure value;
changing the preset incidence angle, and returning to the step of measuring aerodynamic force of incoming flow atmosphere at the preset incidence angle to a thrust measuring plate based on the three-wire torsion pendulum micro thrust measuring system;
obtaining a molecular flow thermal adaptation coefficient corresponding to each preset incident angle;
during the flight of an aircraft, a molecular flow thermal adaptation coefficient corresponding to an incident angle formed by an atmospheric inflow relative to a structural surface element of the aircraft is determined based on the incident angle and the reference curve.
2. The method of determining a molecular flow thermal adaptation coefficient according to claim 1, wherein determining a molecular flow thermal adaptation coefficient corresponding to an incident angle formed by an atmospheric inflow with respect to a structural element of the aircraft based on the incident angle and the reference curve comprises:
a plurality of structural elements divided into which the exterior of the aircraft is acquired,
determining the angle of incidence of the incoming atmospheric flow with respect to each of said structural elements;
and searching a molecular flow thermal adaptation coefficient corresponding to the incidence angle in the reference curve by utilizing the incidence angle, wherein the first axis direction of the reference curve represents the angle value of the incidence angle, and the second axis direction represents the molecular flow thermal adaptation coefficient.
3. The method for determining a thermal adaptation coefficient of a molecular flow according to claim 1, wherein the three-wire torsional pendulum micro-thrust measurement system comprises a thrust measuring plate, a thrust transmission rod, a laser and a reflecting mirror, and the measuring the aerodynamic force of the incoming air at a preset incident angle to the thrust measuring plate based on the three-wire torsional pendulum micro-thrust measurement system comprises:
emitting incoming air to the measuring plane along a preset angle, pushing the thrust measuring plate to rotate so as to drive the reflecting mirror to rotate, and enabling the reflecting light position of the laser to move by the rotation of the reflecting mirror;
and calculating the aerodynamic force of the incoming air supplied to the thrust measuring plate based on the displacement of the reflected light.
4. The method for determining a thermal adaptation coefficient of a molecular flow according to claim 3, wherein the changing the preset incident angle comprises:
and adjusting the angle between the thrust measuring plate and the thrust transmission rod to measure aerodynamic force at different preset incidence angles.
5. The measuring device for the molecular flow thermal adaptation coefficient is characterized by comprising a pressure measuring module for measuring a plane, a molecular flow thermal adaptation coefficient calculating module, a reference curve constructing module and a thermal adaptation coefficient obtaining module;
the pressure measurement module of the measurement plane is used for measuring the pressure value of the incoming flow atmosphere with a preset incidence angle on the measurement plane based on the three-wire torsional pendulum micro-thrust measurement system;
the molecular flow thermal adaptation coefficient calculation module is used for calculating a molecular flow thermal adaptation coefficient corresponding to the preset incidence angle by using a Maxwell Wei Fanshe model based on the pressure value;
the molecular flow thermal adaptation coefficient calculation module comprises a pressure statistic calculation formula acquisition unit and a molecular flow thermal adaptation coefficient calculation unit;
the pressure statistic calculation formula acquisition unit is used for acquiring a pressure statistic calculation formula of the lean gas to the wall surface based on a Maxwell Wei Fanshe model;
a pressure calculation expression obtaining unit, configured to calculate a molecular flow thermal adaptation coefficient corresponding to the preset incident angle based on the pressure value and the pressure statistics calculation formula;
the reference curve construction module is used for constructing a reference curve between the preset incidence angle and the thermal adaptation coefficient;
the reference curve construction module comprises a aerodynamic force measurement unit, a pressure value calculation unit, a repeated processing unit and a molecular flow thermal adaptation coefficient;
the aerodynamic force measuring unit is used for measuring aerodynamic force of incoming flow atmosphere at a preset incidence angle to the thrust measuring plate based on the three-wire torsional pendulum micro thrust measuring system;
a pressure value calculation unit for calculating a pressure value on the thrust measuring plate based on aerodynamic force of the measuring plane;
a molecular flow thermal adaptation coefficient calculation unit that calculates a molecular flow thermal adaptation coefficient corresponding to the preset incident angle using a maxwell Wei Fanshe model based on the pressure value;
the repeated processing unit is used for changing the preset incidence angle and returning to the step of measuring aerodynamic force of incoming flow atmosphere at the preset incidence angle to the thrust measuring plate based on the three-wire torsional pendulum micro thrust measuring system;
the molecular flow thermal adaptation coefficient obtaining unit obtains a molecular flow thermal adaptation coefficient corresponding to each preset incident angle;
and the thermal adaptation coefficient acquisition module is used for determining a molecular flow thermal adaptation coefficient corresponding to the incidence angle based on the incidence angle formed by the atmospheric incoming flow relative to the structural surface element of the aircraft and the reference curve in the flight process of the aircraft.
6. The apparatus for measuring a thermal adaptation coefficient of a molecular flow according to claim 5, wherein the thermal adaptation coefficient acquisition module comprises:
a structural-surface-element acquisition subunit for acquiring a plurality of structural-surface elements divided into by the exterior of the aircraft,
an incidence angle determination subunit for determining an incidence angle formed by the incoming atmospheric flow with respect to each of the structural bins;
and the searching subunit is used for searching the molecular flow thermal adaptation coefficient corresponding to the incidence angle in the reference curve by utilizing the incidence angle, wherein the first axis direction of the reference curve represents the angle value of the incidence angle, and the second axis direction represents the molecular flow thermal adaptation coefficient.
7. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the method of any of claims 1-4 when executing the computer program.
8. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the method of any of claims 1-4.
CN202010558870.6A 2020-06-18 2020-06-18 Method, device, equipment and storage medium for measuring molecular flow thermal adaptation coefficient Active CN111723537B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010558870.6A CN111723537B (en) 2020-06-18 2020-06-18 Method, device, equipment and storage medium for measuring molecular flow thermal adaptation coefficient

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010558870.6A CN111723537B (en) 2020-06-18 2020-06-18 Method, device, equipment and storage medium for measuring molecular flow thermal adaptation coefficient

Publications (2)

Publication Number Publication Date
CN111723537A CN111723537A (en) 2020-09-29
CN111723537B true CN111723537B (en) 2024-02-13

Family

ID=72567418

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010558870.6A Active CN111723537B (en) 2020-06-18 2020-06-18 Method, device, equipment and storage medium for measuring molecular flow thermal adaptation coefficient

Country Status (1)

Country Link
CN (1) CN111723537B (en)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
RU2460982C1 (en) * 2011-03-28 2012-09-10 Открытое акционерное общество "ОКБ Сухого" Method of determining aerodynamic characteristics of aircraft
CN110046473A (en) * 2019-05-27 2019-07-23 中国空气动力研究与发展中心高速空气动力研究所 A kind of aircraft atmospheric parameter calculation method, device and computer equipment
CN110851957A (en) * 2019-10-15 2020-02-28 南京航空航天大学 Atmospheric data sensing system resolving method based on deep learning

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2944623B1 (en) * 2009-04-21 2011-06-10 Airbus France METHOD AND TOOL FOR SIMULATING THE AERODYNAMIC BEHAVIOR OF AN AIRCRAFT IN FLIGHT IN THE NEIGHBORHOOD

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
RU2460982C1 (en) * 2011-03-28 2012-09-10 Открытое акционерное общество "ОКБ Сухого" Method of determining aerodynamic characteristics of aircraft
CN110046473A (en) * 2019-05-27 2019-07-23 中国空气动力研究与发展中心高速空气动力研究所 A kind of aircraft atmospheric parameter calculation method, device and computer equipment
CN110851957A (en) * 2019-10-15 2020-02-28 南京航空航天大学 Atmospheric data sensing system resolving method based on deep learning

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
天宫飞行器低轨控空气动力特性一体化建模与计算研究;李志辉;吴俊林;彭傲平;唐歌实;;载人航天(02);全文 *
超低轨航天器气动设计与计算方法探讨;胡凌云;张立华;程晓丽;靳旭红;丁延卫;;航天器工程(01);全文 *

Also Published As

Publication number Publication date
CN111723537A (en) 2020-09-29

Similar Documents

Publication Publication Date Title
McNamara et al. Approximate modeling of unsteady aerodynamics for hypersonic aeroelasticity
CN111595549B (en) Method, device, equipment and storage medium for measuring ultralow rail resistance coefficient
He et al. Simulation of rocket plume and lunar dust using DSMC method
Milosavljević et al. The cluster-merger shock in 1E 0657–56: faster than a speeding bullet?
Lovejoy et al. Reinterpreting aircraft measurements in anisotropic scaling turbulence
CN115349054A (en) System and method for rapid wind flow measurement in complex terrain by lidar
CN105975677B (en) A kind of method for quick predicting of complex appearance low orbit spacecraft aerodynamic characteristic
CN109740288A (en) A method of the aero-optical effect of simulation High Speed Flow Field culminant star optical transport
Soria-Salinas et al. Wind retrieval from temperature measurements from the rover environmental monitoring Station/Mars science laboratory
CN111723537B (en) Method, device, equipment and storage medium for measuring molecular flow thermal adaptation coefficient
Burt et al. A low diffusion particle method for simulating compressible inviscid flows
Strelnitski et al. H2O masers and supersonic turbulence
Cheremisin et al. Photophoretic interaction of aerosol particles and its effect on coagulation in rarefied gas medium
Jin et al. Monte Carlo simulation for aerodynamic coefficients of satellites in Low-Earth Orbit
Melville Dynamic aeroelastic simulation of complex configurations using overset grid systems
Gupta et al. Flow evolution and unsteady spectra of dynamic stall at transitional Reynolds numbers
Starshak et al. Computer-graphics-based optical tracking for hypersonic free-flight experiments
Santos Gas-surface interaction effect on round leading edge aerothermodynamics
Chen et al. The summary on atmospheric disturbance problems in the motion imaging of high resolution earth observation system
Wei et al. Method of image quality assessment based on human visual system and structural similarity
Kryuchkov et al. Investigation of dynamic motion processes of modernized uav using mathematical model of numerical simulation
Myint et al. AERODYNAMIC CHARACTERISTICS OF AN AIRCRAFT WITH A COMPLEX SHAPE TAKING INTO ACCOUNT THE POTENTIAL OF MOLECULAR FLOWINTERACTION WITH A SURFACE
Margha et al. Dynamic Transition of Unsteady Supersonic Flow From Mach to Regular Reflection Over a Moving Wedge
Liu Aerodynamic Characteristics of Supersonic Thin Airfoil and Wing
Han et al. Comparison of methods for curvature estimation from volume fractions

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant