CN113887156B - Method for correlation of heaven and earth data for transition of hypersonic velocity boundary layer - Google Patents

Method for correlation of heaven and earth data for transition of hypersonic velocity boundary layer Download PDF

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CN113887156B
CN113887156B CN202111479830.3A CN202111479830A CN113887156B CN 113887156 B CN113887156 B CN 113887156B CN 202111479830 A CN202111479830 A CN 202111479830A CN 113887156 B CN113887156 B CN 113887156B
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reynolds number
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CN113887156A (en
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涂国华
李仕博
段茂昌
万兵兵
李晓虎
陈坚强
袁先旭
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Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
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Abstract

The invention discloses a method for correlating transition heaven and earth data of a hypersonic speed boundary layer, which adopts Taylor series expansion to the transition heaven and earth correlation function of the hypersonic speed boundary layer, considers the coupling action among control variables and predicts the transition position of the hypersonic speed boundary layer under the flight condition by using the ground wind tunnel experiment result. The method solves the problems of high requirement on wind tunnel experiments, low transition prediction precision and the like in the prior art.

Description

Method for correlation of heaven and earth data for transition of hypersonic velocity boundary layer
Technical Field
The invention relates to the technical field of aerodynamics, in particular to a method for the data association of transition of a hypersonic speed boundary layer.
Background
At hypersonic velocity, when the reynolds number of the flow is greater than a certain critical value, the boundary layer flow state will transition from laminar flow to turbulent flow. Research shows that the wall friction resistance and the wall heat flow of a turbulent flow boundary layer are generally 3-5 times larger than those of a laminar flow boundary layer under the hypersonic speed condition, so that the accurate prediction of the flight transition position is important for the aerodynamic design and flight control of the hypersonic speed aircraft. However, the conventional relatively general transition prediction method (such as the eN method) greatly depends on the ground wind tunnel experiment and the CFD calculation, and the ground wind tunnel experiment cannot completely simulate the real flight conditions in the sky. Therefore, the heaven and earth data correlation method is provided, the ground wind tunnel experimental data and the CFD data are accurately extrapolated to the real flight conditions, and the method has very important engineering value.
At present, the research on the nature and the ground correlation of the transition of the hypersonic speed boundary layer is still in a starting stage. The BLT method proposed in NASP project in the united states is a method of obtaining aerial data by correcting ground data in consideration of the difference in the sky and the earth of four control variables such as incoming flow noise, that is:
Figure 327893DEST_PATH_IMAGE001
，(1)；
wherein,
Figure 894003DEST_PATH_IMAGE002
representing the transition reynolds number under flight conditions on the fly,
Figure DEST_PATH_IMAGE003
the transition Reynolds number obtained by a ground wind tunnel experiment is a correction coefficient of a certain control variable, and subscripts "noise", "Tw", "k" and "Ts" respectively represent noise, wall temperature ratio, roughness and wind tunnel size. The Yang military soldiers and Liu Zhi Yong in the eleven college of spaceflight propose a world correlation method of transition data based on the formula (patent number: CN 108182312A). The Schmingtao and the plum-stored standard of Beijing university propose a method adopting other control variables for correction, namely:
Figure 992409DEST_PATH_IMAGE004
，(2)；
where f is a correction function. Compared with the previous method of formula (1), the control variables considered by the method are the head blunt Reynolds number, the wall temperature ratio, the Mach number, and the noise, respectively. The method can be well matched with the results of the flight experiment of the HIFIRE-5b in most areas.
However, the effects of different control variables on the transition differences are coupled rather than independent. For example, the wall temperature ratio has a distinct effect on the difference between heaven and earth at different mach numbers. The existing heaven and earth correlation method only considers the influence of a certain control variable on the heaven and earth difference alone, and then calculates the total influence of the control variable on the heaven and earth difference in a simple product mode. Therefore, the ground wind tunnel experiment with only one control variable and different flight conditions on the sky needs to be developed, and the other control variables are required to be completely the same, so that the method has extremely high requirements on the ground wind tunnel experiment. The existing wind tunnel experiment conditions are difficult to meet the requirement, so a transition nature correlation method which reduces the requirement on the wind tunnel experiment and meets the transition prediction precision requirement on engineering needs to be provided.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for associating transition heaven and earth data of a hypersonic velocity boundary layer, and solves the problems of high requirements on wind tunnel experiments, low transition prediction precision and the like in the prior art.
The technical scheme adopted by the invention for solving the problems is as follows:
a method for correlating transition heaven and earth data of a hypersonic speed boundary layer is characterized in that a transition heaven and earth correlation function of the hypersonic speed boundary layer is expanded by adopting Taylor series, the coupling effect among control variables is considered, and the transition position of the hypersonic speed boundary layer under a flight condition is predicted by utilizing a ground wind tunnel experiment result.
As a preferable technical scheme, a transition heaven and earth correlation function of the hypersonic speed boundary layer is expanded by Taylor series, the influence of the individual action of each control variable and the coupling action of each control variable on heaven and earth difference is considered, and the transition position of the hypersonic speed boundary layer under the flight condition is predicted by using the ground wind tunnel experiment result.
As a preferred technical solution, a specific manner of predicting a transition position of a hypersonic velocity boundary layer under a flight condition is: and calculating to obtain the transition Reynolds number of the hypersonic velocity boundary layer under the flight condition.
As a preferable technical scheme, the method comprises the following steps:
s1, obtaining partial derivatives of independent action of each control variable;
s2, obtaining partial derivatives of coupling action of each control variable;
and S3, calculating the transition Reynolds number of the hypersonic velocity boundary layer under the flight condition by using the difference between the ground transition Reynolds number and the heaven and earth control variable.
In a preferred embodiment, in step S1 and/or step S2, the partial derivatives of the independent actions of the control variables and/or the partial derivatives of the coupling actions of the control variables are obtained by using the ground experiment data set.
As a preferable technical solution, in step S3, the difference between the ground transition reynolds number and the heaven and earth control variable is obtained through a ground experiment.
Preferably, the number of the control variables is 5, and the control variables are respectively the reynolds number of the blunt head degree, the wall temperature ratio, the mach number, the incoming flow noise and the attack angle, which are sequentially recorded as
Figure DEST_PATH_IMAGE005
、
Figure 618563DEST_PATH_IMAGE006
、
Figure DEST_PATH_IMAGE007
、
Figure 556082DEST_PATH_IMAGE008
、
Figure DEST_PATH_IMAGE009
The transition probability function of the hypersonic boundary layer is recorded as:
Figure 925883DEST_PATH_IMAGE010
，（3）；
wherein,
Figure 82058DEST_PATH_IMAGE002
represents the transition Reynolds number of the hypersonic boundary layer under the flight condition,
Figure DEST_PATH_IMAGE011
indicating a reynolds number for a surface transition,
Figure 941429DEST_PATH_IMAGE012
representing the transition natural correlation function of the hypersonic boundary layer.
As a preferable technical solution, in step S1, only one control variable is made during the wind tunnel experiment
Figure DEST_PATH_IMAGE013
Changing within a certain range, keeping the other four control variables unchanged to obtain
Figure 550265DEST_PATH_IMAGE014
Different transition Reynolds numbers when varied independently
Figure DEST_PATH_IMAGE015
Plurality to be obtained using Hermite polynomial
Figure 458179DEST_PATH_IMAGE015
Fitting into a curve, and obtaining the curve by derivation
Figure 468860DEST_PATH_IMAGE016
(ii) a Wherein i =1,2,3,4 or 5.
As a preferable technical solution, in step S2, in the wind tunnel experiment, two control variables are set
Figure 249865DEST_PATH_IMAGE013
、
Figure DEST_PATH_IMAGE017
Respectively changing, keeping the other three control variables unchanged, and obtaining multiple groups of transition Reynolds numbers
Figure 345997DEST_PATH_IMAGE015
(ii) a The NURBS method was again used to measure the abscissa as
Figure 57601DEST_PATH_IMAGE013
The ordinate is
Figure 188368DEST_PATH_IMAGE017
Has a function value of
Figure 389542DEST_PATH_IMAGE015
The data matrix is subjected to surface fitting, and then the deviation of the surface is calculated, so that the data matrix can be obtained
Figure 707391DEST_PATH_IMAGE018
(ii) a Then changing the values of i and j, repeating the above process until obtaining multiple groups of any two control variables combined
Figure 222686DEST_PATH_IMAGE018
(ii) a Wherein i =1,2,3,4 or 5, j =1,2,3,4 or 5, i ≠ j.
As a preferable technical solution, in step S3, the reynolds number of the head bluntness, the wall temperature ratio, the mach number, the incoming flow noise, and the attack angle under the ground wind tunnel experiment condition are sequentially and respectively described as
Figure DEST_PATH_IMAGE019
、
Figure 207960DEST_PATH_IMAGE020
、
Figure 330768DEST_PATH_IMAGE021
、
Figure DEST_PATH_IMAGE022
、
Figure 135913DEST_PATH_IMAGE023
To obtain the Reynolds number of ground transition
Figure 189319DEST_PATH_IMAGE003
Then only the Reynolds number of the head bluntness, the wall temperature ratio, the Mach number, the incoming flow noise and the attack angle under the flight condition need to be given and recorded in sequence
Figure DEST_PATH_IMAGE024
、
Figure 825837DEST_PATH_IMAGE025
、
Figure 306497DEST_PATH_IMAGE026
、
Figure DEST_PATH_IMAGE027
、
Figure 864517DEST_PATH_IMAGE028
Obtained by summing the above known parameters
Figure 456036DEST_PATH_IMAGE016
、
Figure DEST_PATH_IMAGE029
Substitution formula
Figure 494530DEST_PATH_IMAGE030
(4) Then, according to the formula (3), the transition Reynolds number of the hypersonic boundary layer under the real flight condition can be obtained
Figure 146091DEST_PATH_IMAGE002
。
Compared with the prior art, the invention has the following beneficial effects:
the method adopts a Taylor series expansion heaven and earth correlation function method, considers the influence of independent change and interaction of each control variable on heaven and earth difference, and predicts the transition position under the flight condition by using the ground wind tunnel experiment result. The invention utilizes the Taylor expansion idea to carry out Taylor expansion on the heaven and earth correlation function, realizes the consideration of the coupling effect among variables and further ensures that the heaven and earth correlation formula is accurate. The invention adopts the Taylor expansion method to carry out Taylor expansion on the heaven and earth correlation function, can consider the influence of the coupling of a plurality of variables on the heaven and earth difference, and has the advantages of more accurate result and the like. The method can be particularly applied to extrapolation of wind tunnel experimental data, and provides a new method for prediction of transition of the hypersonic velocity boundary layer and research of heaven and earth correlation.
Drawings
FIG. 1 is a schematic diagram of the steps of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited to these examples.
Examples
As shown in fig. 1, aiming at the high requirement of the transition nature-to-ground correlation on the wind tunnel experiment, the invention provides a new way for constructing a transition nature-to-ground correlation function based on Taylor expansion, so as to realize accurate extrapolation of wind tunnel experiment data with a plurality of control variables having nature difference. As a preferred solution.
The transition phenomenon of the hypersonic speed boundary layer is related to a plurality of physical quantities, and a ground wind tunnel experiment is difficult to completely simulate a real flight state on the sky, so that certain difference always exists. The method brings difficulty to the prediction of the flight transition position by using a ground wind tunnel experiment. The existing transition heaven and earth correlation method is difficult to consider the influence of the coupling effect of control variables on heaven and earth difference. The method adopts a Taylor series expansion heaven and earth correlation function method, considers the influence of independent change and interaction of each control variable on heaven and earth difference, and predicts the transition position under the flight condition by using the ground wind tunnel experiment result.
The basic principle of the invention is as follows: the influence of the difference of five control variables on the transition heaven and earth correlation is considered, namely the Reynolds numbers of the blunt degree of the head
Figure DEST_PATH_IMAGE031
Wall temperature ratio
Figure 925828DEST_PATH_IMAGE032
Mach number of
Figure DEST_PATH_IMAGE033
Noise of incoming flow
Figure 383354DEST_PATH_IMAGE034
Angle of attack
Figure DEST_PATH_IMAGE035
. For convenience, the above five control variables are used separately
Figure 197727DEST_PATH_IMAGE005
、
Figure 20189DEST_PATH_IMAGE006
、
Figure 97342DEST_PATH_IMAGE007
、
Figure 296242DEST_PATH_IMAGE008
And
Figure 965121DEST_PATH_IMAGE009
and representing, the transition heaven-earth correlation function of the hypersonic velocity boundary layer is recorded as:
Figure 958485DEST_PATH_IMAGE010
，（3）；
wherein,
Figure 712814DEST_PATH_IMAGE002
represents the transition Reynolds number of the hypersonic boundary layer under the flight condition,
Figure 777722DEST_PATH_IMAGE011
indicating a reynolds number for a surface transition,
Figure 301107DEST_PATH_IMAGE012
representing the transition natural correlation function of the hypersonic boundary layer.
Figure 465372DEST_PATH_IMAGE012
Is a self-controlling variable of
Figure 706998DEST_PATH_IMAGE005
、
Figure 247701DEST_PATH_IMAGE006
、
Figure 438642DEST_PATH_IMAGE007
、
Figure 39387DEST_PATH_IMAGE008
And
Figure 502730DEST_PATH_IMAGE009
. According to the Taylor expansion of the multivariate function,
Figure 847123DEST_PATH_IMAGE012
can be unfolded as follows:
Figure 79522DEST_PATH_IMAGE030
(4) obtaining control variable independent action partial derivative by using ground experimental data set
Figure 913485DEST_PATH_IMAGE016
Partial derivative of sum coupling
Figure 864124DEST_PATH_IMAGE029
And the Reynolds number of the ground transition is obtained according to the ground experiment
Figure 746629DEST_PATH_IMAGE011
And difference in space and ground control variables
Figure 99113DEST_PATH_IMAGE036
And the transition Reynolds number under the flight condition can be obtained by combining the formula and extrapolating
Figure 41661DEST_PATH_IMAGE002
。
The method comprises the following specific implementation steps:
and S1, acquiring the influence of independent action of each control variable. In wind tunnel experiments, only one control variable is made
Figure 292645DEST_PATH_IMAGE013
Changing within a certain range, keeping the other four control variables unchanged to obtain
Figure 978842DEST_PATH_IMAGE014
Different transition Reynolds numbers when varied independently
Figure 185832DEST_PATH_IMAGE015
The obtained multiple fit-to-synthesis curves are synthesized by using a Hermite polynomial or other data processing modes, and the curves are derived to obtain
Figure DEST_PATH_IMAGE037
And
Figure 299281DEST_PATH_IMAGE038
. For example, Reynolds number for obtention of head bluntness
Figure 21250DEST_PATH_IMAGE031
Influence of individual action, controlling variable wall temperature ratio
Figure 245558DEST_PATH_IMAGE039
Mach number of
Figure 572634DEST_PATH_IMAGE033
Noise of incoming flow
Figure 591406DEST_PATH_IMAGE034
Angle of attack
Figure 3932DEST_PATH_IMAGE035
Is not changed, is changed
Figure 110560DEST_PATH_IMAGE040
To obtain different transition Reynolds numbers
Figure 292142DEST_PATH_IMAGE015
Fitting into a curve and then obtaining the result
Figure 747394DEST_PATH_IMAGE037
And
Figure 381638DEST_PATH_IMAGE041
. When i is 2,3,4 or 5, the acquisition method is similar to the case.
And S2, acquiring the coupling effect of the control variables. For ease of understanding, only the coupling effect between the two control variables is considered here. In the wind tunnel experiment, the other three control variables are controlled to be unchanged, and two control variables are controlled to be unchanged within a certain range
Figure 947749DEST_PATH_IMAGE013
、
Figure 311734DEST_PATH_IMAGE017
Respectively change
Figure 937887DEST_PATH_IMAGE042
-get one at once
Figure 59427DEST_PATH_IMAGE014
And remain unchanged, order
Figure 429229DEST_PATH_IMAGE017
Varying to obtain a different set of transition Reynolds numbers
Figure 585403DEST_PATH_IMAGE015
(ii) a Then change
Figure 186718DEST_PATH_IMAGE014
Is kept unchanged, and then order
Figure 795554DEST_PATH_IMAGE017
Change to obtain another different set of transition Reynolds numbers
Figure 703467DEST_PATH_IMAGE015
. This is repeated. Then the NURBS method or other data processing method is used to respectively obtain the horizontal and vertical coordinates
Figure 714149DEST_PATH_IMAGE013
、
Figure 744422DEST_PATH_IMAGE017
Function value of
Figure 840554DEST_PATH_IMAGE043
The data matrix is subjected to surface fitting, and then the deviation of the surface is calculated to obtain
Figure 552158DEST_PATH_IMAGE044
. For example, to obtain the wall temperature ratio
Figure 417345DEST_PATH_IMAGE039
Mach number of
Figure 556203DEST_PATH_IMAGE033
Controlling head bluntness Reynolds number under the influence of coupling
Figure 952680DEST_PATH_IMAGE045
Noise of incoming flow
Figure 467975DEST_PATH_IMAGE034
Angle of attack
Figure 187669DEST_PATH_IMAGE035
Make an appointment without change
Figure 497428DEST_PATH_IMAGE006
Taking a constant value, changing
Figure 630469DEST_PATH_IMAGE007
Obtaining a set of transition Reynolds numbers
Figure 683876DEST_PATH_IMAGE046
(ii) a Reissue to order
Figure 523656DEST_PATH_IMAGE006
Take another constant value, change
Figure 4316DEST_PATH_IMAGE007
Another set of transition Reynolds numbers is obtained. Then, the NURBS surface method is used for carrying out surface fitting on the obtained data matrix, and then the obtained data matrix is subjected to surface fitting
Figure 562336DEST_PATH_IMAGE047
、
Figure 966904DEST_PATH_IMAGE007
Obtaining the partial derivatives
Figure 661190DEST_PATH_IMAGE048
. Then changing the values of i and j, repeating the above process until obtaining multiple groups of any two control variables combined
Figure 578331DEST_PATH_IMAGE049
And until obtaining the influence rule data of transition Reynolds number by any two control variables. When i and j are other values, the acquisition method i =2 is similar to the case of j = 3.
S3, the space-to-ground conversion is performed using the equations (3) and (4). After completing S1 and S2, the heaven-earth correlation conversion under different conditions can be performed. Under the experimental condition of utilizing ground wind tunnel
Figure 358068DEST_PATH_IMAGE050
、
Figure 550015DEST_PATH_IMAGE051
、
Figure 364387DEST_PATH_IMAGE052
、
Figure 186849DEST_PATH_IMAGE053
、
Figure 453883DEST_PATH_IMAGE054
To obtain the Reynolds number of ground transition
Figure 652783DEST_PATH_IMAGE003
Then only the flight conditions are given
Figure 400290DEST_PATH_IMAGE055
Obtained by using the above known parameters and S1
Figure 393654DEST_PATH_IMAGE056
、
Figure 147983DEST_PATH_IMAGE041
And obtained in S2
Figure 884995DEST_PATH_IMAGE044
Substituting the formula (4) into the formula (3), and obtaining the transition Reynolds number under the real flight condition
Figure 408380DEST_PATH_IMAGE057
。
The sequence of steps S1 and S2 may be changed or synchronized.
Compared with the existing transition heaven and earth correlation formulas (1) and (2), the method utilizes the Taylor expansion idea to carry out Taylor expansion on the heaven and earth correlation function, realizes the coupling effect among the considered variables, and further ensures the accuracy of the heaven and earth correlation formulas.
The invention adopts the Taylor expansion method to carry out Taylor expansion on the heaven and earth correlation function, can consider the influence of the coupling of a plurality of variables on the heaven and earth difference, and has the advantages of more accurate result and the like. The method can be particularly applied to extrapolation of wind tunnel experimental data, and provides a new method for prediction of transition of the hypersonic velocity boundary layer and research of heaven and earth correlation.
As described above, the present invention can be preferably realized.
All features disclosed in all embodiments in this specification, or all methods or process steps implicitly disclosed, may be combined and/or expanded, or substituted, in any way, except for mutually exclusive features and/or steps.
The foregoing is only a preferred embodiment of the present invention, and the present invention is not limited thereto in any way, and any simple modification, equivalent replacement and improvement made to the above embodiment within the spirit and principle of the present invention still fall within the protection scope of the present invention.

Claims (5)

1. A method for the transition heaven and earth data correlation of a hypersonic speed boundary layer is characterized in that a transition heaven and earth correlation function of the hypersonic speed boundary layer is expanded by adopting Taylor series, the influence of the individual action of each control variable and the coupling action of each control variable on heaven and earth difference is considered, and the transition position of the hypersonic speed boundary layer under the flight condition is predicted by using the ground wind tunnel experiment result;
the specific mode for predicting the transition position of the hypersonic velocity boundary layer under the flight condition is as follows: calculating to obtain a transition Reynolds number of the hypersonic velocity boundary layer under the flight condition;
the method comprises the following steps:
s1, obtaining partial derivatives of independent action of each control variable;
s2, obtaining partial derivatives of coupling action of each control variable;
s3, calculating the transition Reynolds number of the hypersonic velocity boundary layer under the flight condition by using the ground transition Reynolds number and the difference of the heaven and earth control variables;
the number of the control variables is 5, and the control variables are respectively the Reynolds number of the blunt degree of the head, the wall temperature ratio, the Mach number, the incoming flow noise and the attack angle which are sequentially recorded as
Figure 984953DEST_PATH_IMAGE001
、
Figure 678102DEST_PATH_IMAGE002
、
Figure 208441DEST_PATH_IMAGE003
、
Figure 758371DEST_PATH_IMAGE004
、
Figure 374160DEST_PATH_IMAGE005
The transition probability function of the hypersonic boundary layer is recorded as:
Figure 871001DEST_PATH_IMAGE006
，（3）；
wherein,
Figure 318162DEST_PATH_IMAGE007
represents the transition Reynolds number of the hypersonic boundary layer under the flight condition,
Figure 711098DEST_PATH_IMAGE008
indicating a reynolds number for a surface transition,
Figure 592946DEST_PATH_IMAGE009
representing a transition heaven and earth correlation function of the hypersonic velocity boundary layer;
in step S3, the reynolds number, the wall temperature ratio, the mach number, the incoming flow noise, and the attack angle of the head blunt degree under the ground wind tunnel experiment condition are sequentially recorded as
Figure 627898DEST_PATH_IMAGE010
、
Figure 195145DEST_PATH_IMAGE011
、
Figure 758982DEST_PATH_IMAGE012
、
Figure 614942DEST_PATH_IMAGE013
、
Figure 250323DEST_PATH_IMAGE014
To obtain the Reynolds number of ground transition
Figure 344181DEST_PATH_IMAGE008
Then only give flight barThe Reynolds number of the head bluntness, the wall temperature ratio, the Mach number, the incoming flow noise and the attack angle under the part are sequentially recorded as
Figure 610077DEST_PATH_IMAGE015
、
Figure 484492DEST_PATH_IMAGE016
、
Figure 126826DEST_PATH_IMAGE017
、
Figure 340770DEST_PATH_IMAGE018
、
Figure 574305DEST_PATH_IMAGE019
Obtained by summing the above known parameters
Figure 372235DEST_PATH_IMAGE020
、
Figure 552680DEST_PATH_IMAGE021
Substitution formula
Figure 683447DEST_PATH_IMAGE022
(4) Then, according to the formula (3), the transition Reynolds number of the hypersonic boundary layer under the real flight condition can be obtained
Figure 25567DEST_PATH_IMAGE007
；
Wherein,
Figure 77837DEST_PATH_IMAGE020
represents the partial derivative of the independent action of each control variable,
Figure 593132DEST_PATH_IMAGE023
representing the deviation of the coupling of the control variablesA derivative; i =1,2,3,4 or 5, j =1,2,3,4 or 5, i ≠ j.
2. The method as claimed in claim 1, wherein in step S1 and/or step S2, the partial derivatives of independent actions of the control variables and/or the partial derivatives of coupling actions of the control variables are obtained by using a ground experiment data set.
3. The method for the celestial data correlation of the hypersonic boundary layer transition of claim 2, wherein in step S3, the difference between the ground transition reynolds number and the celestial control variable is obtained through a ground experiment.
4. The method for celestial data correlation of transition of hypersonic boundary layer according to claim 3, wherein in step S1, only one control variable is made during wind tunnel experiment
Figure 781667DEST_PATH_IMAGE024
Changing within a certain range, keeping the other four control variables unchanged to obtain
Figure 357005DEST_PATH_IMAGE025
Different transition Reynolds numbers when varied independently
Figure 896571DEST_PATH_IMAGE026
Plurality to be obtained using Hermite polynomial
Figure 153240DEST_PATH_IMAGE026
Fitting into a curve, and obtaining the curve by derivation
Figure 258599DEST_PATH_IMAGE020
(ii) a Wherein i =1,2,3,4 or 5.
5. A method for hyperemia according to claim 4The method for correlating the celestial data of transition of the boundary layer of the sound velocity is characterized in that in step S2, two control variables are made during the wind tunnel experiment
Figure 208101DEST_PATH_IMAGE024
、
Figure 205269DEST_PATH_IMAGE027
Respectively changing, keeping the other three control variables unchanged, and obtaining multiple groups of transition Reynolds numbers
Figure 531208DEST_PATH_IMAGE026
(ii) a The NURBS method was again used to measure the abscissa as
Figure 491074DEST_PATH_IMAGE025
The ordinate is
Figure 345897DEST_PATH_IMAGE027
Has a function value of
Figure 860055DEST_PATH_IMAGE026
The data matrix is subjected to surface fitting, and then the deviation of the surface is calculated, so that the data matrix can be obtained
Figure 520844DEST_PATH_IMAGE028
(ii) a Then changing the values of i and j, repeating the above process until obtaining multiple groups of any two control variables combined
Figure 272899DEST_PATH_IMAGE028
(ii) a Wherein i =1,2,3,4 or 5, j =1,2,3,4 or 5, i ≠ j.
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