CN108446419B - Supersonic velocity boundary layer characteristic thickness estimation method - Google Patents

Supersonic velocity boundary layer characteristic thickness estimation method Download PDF

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CN108446419B
CN108446419B CN201810043267.7A CN201810043267A CN108446419B CN 108446419 B CN108446419 B CN 108446419B CN 201810043267 A CN201810043267 A CN 201810043267A CN 108446419 B CN108446419 B CN 108446419B
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黄章峰
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Abstract

The invention discloses a method for estimating the characteristic thickness of a supersonic boundary layer, which comprises the following steps: arrangement evaluation points of target positions in the normal direction on the wall surface: the evaluation points are distributed inside and outside the boundary layer, and the distribution positions of the evaluation points are determined according to the equivalent thickness of the grids in the normal direction; interpolating the position of the evaluation point by using the flow field data on the grid nodes near the evaluation point to obtain a flow field in the normal direction of the target position on the wall surface, and projecting the flow field to an orthogonal patch coordinate system; establishing a functional relation between the comprehensive judgment characteristic quantity and the wall surface distance at the evaluation point; and determining characteristic points through a judgment criterion, and estimating the characteristic thickness of the boundary layer according to the distance between the characteristic points and the wall surface. Under the conditions of complex geometry and incoming flow, the method can quickly and accurately estimate the characteristic thickness of the boundary layer for the numerical calculation result of the supersonic flow with the Mach number of 3-20.

Description

Supersonic velocity boundary layer characteristic thickness estimation method
Technical Field
The invention relates to the field of numerical calculation of supersonic aircrafts, in particular to a supersonic boundary layer characteristic thickness estimation method.
Background
Aerospace technology is related to national economy and safety, wherein one of the challenging aerodynamic problems in high-speed flight technology is prediction of the transition position of a boundary layer. Because the friction coefficient and the heat transfer coefficient of the turbulent flow are far larger than those of the laminar flow, whether the boundary layer is twisted and where the boundary layer is twisted directly influence the friction resistance, the thermal protection, the flow separation position and the like of the aircraft. If the transition position can be predicted accurately and the occurrence of the transition is delayed, the lift-drag ratio can be improved, the fuel consumption is reduced, a basis is provided for the thermal protection design, and the performance of the aircraft is greatly improved. The prediction of transition of the boundary layer is one of the prerequisites of accurately predicting the resistance and heat flow of the supersonic aircraft, and is also one of the bottlenecks of the aerodynamic development and the thermal protection design of the novel aerospace aircraft. And the identification of the boundary layer characteristic parameters is the premise of accurate prediction of the boundary layer transition position.
However, the boundary layer characteristic thickness identification technology established based on the classical theory and the traditional method has many problems in the boundary layer characteristic parameter identification of the supersonic complex three-dimensional boundary layer, which are mainly shown in the following aspects:
for complex three-dimensional flow, it cannot be guaranteed that computational grids in a boundary layer are perpendicular to a wall surface, and the definition of the characteristic thickness of the boundary layer is based on flow direction velocity distribution in the normal direction of the wall surface, so that a complex three-dimensional flow field needs to be projected to the normal direction of the wall surface by adopting a numerical interpolation method. Since the velocity profile in the boundary layer varies greatly, enough evaluation points are arranged in the boundary layer to detect the variation trend of the flow velocity, the density and the like, so that the flow field variation trend in the boundary layer is analyzed and the feature thickness is estimated. Therefore, automatically and reasonably arranging the evaluation point on the wall surface normal line directly affects the accuracy of positioning.
For the supersonic complex three-dimensional flow field, the velocity profile of the wall surface in the normal direction is complex. The boundary layer thickness boundary is judged according to the ratio of the local speed to the flow direction speed outside the boundary layer by the traditional theoretical method, however, because the flow outside the supersonic boundary layer is the flow after shock wave, the flow direction speed outside the boundary layer does not approach a constant but decreases along with the increase of the normal direction, and at the moment, the boundary layer thickness judgment method defined by the traditional theory is adopted to cause failure.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a supersonic velocity boundary layer characteristic thickness estimation method, which can quickly and accurately estimate the boundary layer characteristic thickness for a supersonic velocity flow numerical calculation result with the Mach number of 3-20 under the conditions of complex geometry and incoming flow.
The purpose of the invention is realized by the following technical scheme.
A supersonic velocity boundary layer characteristic thickness estimation method comprises the following steps:
s1, arranging evaluation points in the normal direction of the target position on the wall surface: the evaluation points are distributed inside and outside the boundary layer, and the distribution positions of the evaluation points are determined according to the equivalent thickness of the grids in the normal direction;
s2, interpolating at the evaluation point position by using the flow field data on the grid nodes near the evaluation point to obtain a flow field of a target position on the wall surface in the normal direction, and projecting the flow field data to an orthogonal patch coordinate system;
s3, establishing a functional relation between the comprehensive judgment characteristic quantity and the wall surface distance on the evaluation point;
and S4, determining a characteristic point through the judgment criterion, and estimating the characteristic thickness of the boundary layer according to the distance between the characteristic point and the wall surface.
In step S1, a projection algorithm is used to calculate the equivalent thickness of the normal direction grid, so as to determine the distribution position of the evaluation point:
setting the unit normal direction of the target position on the wall surface as
Figure GDA0003307437120000021
The target position is taken as a first evaluation point, which is marked as A0The next point is A1The other points are denoted as Ai(ii) a From the known evaluation point AiTo the next evaluation point Ai+1Is represented by a vector
Figure GDA0003307437120000022
Point AiTo point Ai+1Is recorded as
Figure GDA0003307437120000023
Distance evaluation point AiThe nearest mesh node is denoted as Bi，BiVectors to other grid nodes within the same grid are noted as
Figure GDA0003307437120000024
Wherein j is 1, … 7; vector
Figure GDA0003307437120000025
In the unit normal direction
Figure GDA0003307437120000026
Is projected as
Figure GDA0003307437120000027
Vector
Figure GDA0003307437120000028
In the unit normal direction
Figure GDA0003307437120000029
Is at an included angle of
Figure GDA00033074371200000210
Ranging from 0 to pi, where an angle of 0 represents a vector
Figure GDA00033074371200000211
In the unit normal direction
Figure GDA00033074371200000212
Are in the same direction, and the included angle is pi/2 to represent a vector
Figure GDA00033074371200000213
In the unit normal direction
Figure GDA00033074371200000214
Is perpendicular to the direction of the vector, and the included angle is pi to represent the vector
Figure GDA00033074371200000215
In the unit normal direction
Figure GDA00033074371200000216
In opposite directions; then point AiTo point Ai+1Distance d ofiWith BiDetermining the equivalent thickness of the grid according to the formula di＝a×piJCalculation of which take J such that
Figure GDA00033074371200000217
Is the minimum value, and a is the evaluation point distance weighting coefficient.
In step S2, interpolation is performed at the evaluation point position to obtain a flow field in the normal direction of the target position on the wall surface, and the flow field is projected to the orthogonal patch coordinate system:
get the unit normal direction of the wall target position
Figure GDA0003307437120000031
For the interior of a wallIn the direction of
Figure GDA0003307437120000032
Velocity at evaluation point farthest from wall surface
Figure GDA0003307437120000033
In a manner that
Figure GDA0003307437120000034
Projecting on a plane in the normal direction, unitizing the obtained projection velocity vector to obtain the direction of flow
Figure GDA0003307437120000035
In the direction normal to the wall
Figure GDA0003307437120000036
And the direction of flow
Figure GDA0003307437120000037
The vertical direction being the spanwise direction
Figure GDA0003307437120000038
Wherein the flow direction, the normal direction in the wall surface and the spreading direction meet the right-hand rule; an orthogonal body coordinate system is formed by the flow direction, the normal direction in the wall surface and the spreading direction;
the velocity vector of the rectangular coordinate system
Figure GDA0003307437120000039
Decomposing the velocity vector into the flow direction, the normal direction in the wall surface and the spreading direction to obtain the velocity vector under the orthogonal body-attached coordinate system after the normal is broken off
Figure GDA00033074371200000310
In step S3, a functional relationship between the comprehensive determination feature quantity at the evaluation point and the wall surface distance is established:
the following integrated decision functions were defined for quantitative analysis at the evaluation points:
Figure GDA00033074371200000311
wherein eta isiIs evaluation point AiCoordinates in the normal direction in the wall, uiξIs the velocity in the flow direction, rho, in a coordinate system of a patchiIs the density at the evaluation point, and b, c, d are the exponential weighting values of the terms.
Prediction process of boundary layer characteristic thickness in step S4:
firstly, all evaluation points AiF (η) of (C)i) Comparing to obtain f (eta)i) Point of maximum value of (A)mTaking Am-2、Am-1、Am、Am+1、Am+2Total of 5 points fit f (η)i) In AmA continuous function s (eta) near the point, s' (eta) is obtained by deriving s (eta), and the eta value at the maximum position of s (eta) is taken as deltarAs boundary layer reference scale, i.e. deltar＝η|s′(η)＝0；
Note delta99For nominal boundary layer thickness, take δ99＝AδrWherein A (M) is a boundary layer nominal thickness scaling factor that is a function of Mach number M;
note deltadFor the displacement of boundary layer, take deltad＝BδrWherein B (M) is a boundary layer displacement thickness scaling factor that is a function of Mach number M;
let θ be the boundary layer momentum displacement thickness, then take θ ═ C δrWhere C (M) is a boundary layer momentum displacement thickness scaling factor, which is a function of Mach number M.
Compared with the prior art, the technical scheme of the invention has the following beneficial effects:
(1) the invention improves the prediction precision of the boundary layer thickness by a reasonable evaluation point arrangement method and high-precision interpolation.
(2) The method can solve the problem that the boundary layer thickness defined by the traditional theory is invalid by constructing a reasonable judgment criterion and coping with the situation that the far-field incoming flow speed is not easy to define under the conditions of complex geometric shapes and incoming flows. High judgment precision is achieved within the range of 3-20 Ma.
(3) The invention can realize the quick automatic batch processing of the computer program through the definite point distribution, interpolation and judgment method, reduces the condition that the data is often required to be led out for manual judgment in the past, and greatly improves the calculation efficiency and precision.
(4) The decision function is based on local flow field data, multi-point block parallel computation can be achieved, and computing efficiency is improved.
Drawings
FIG. 1 is an overall flow chart of a supersonic boundary layer characteristic thickness estimation method;
FIG. 2 is a flow chart for determining the distribution positions of evaluation points;
FIG. 3 is a schematic illustration of determining a next evaluation point location in a two-dimensional flow field;
FIG. 4 is a schematic illustration of determining a next evaluation point location in a three-dimensional flow field;
fig. 5 is a diagram showing an example of application of the comprehensive decision function.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The method for estimating the characteristic thickness of the supersonic velocity boundary layer, disclosed by the invention, comprises the following steps of:
s1, reasonably arranging evaluation points in the normal direction of the target position on the wall surface, wherein the evaluation points are distributed inside and outside the boundary layer, and the evaluation points in the boundary layer are distributed more densely so as to really distinguish the change of physical quantities such as speed, density and the like in the boundary layer. The distribution position of the evaluation points, namely the distance between the evaluation points is determined according to the equivalent thickness of the grids in the normal direction, and the estimation is carried out according to the equivalent thickness of the grid closest to the evaluation points.
In step S1, for different grid shapes and their different position relationships with the normal direction, the projected algorithm is used to calculate the equivalent thickness of the normal direction grid, so as to determine the distribution position of the evaluation point, as shown in fig. 2.
If the evaluation points in the boundary layer are arranged too little or the distance is not reasonable, so that key features of the boundary layer are lost, the blind arrangement of too many evaluation points can greatly increase the calculation amount and reduce the efficiency, and even the calculation cannot be carried out. The characteristic can realize the arrangement method of the evaluation points on the normal line matched with the height of the grid, thereby reasonably evaluating the speed profile change in the boundary layer.
Setting the unit normal direction of the target position on the wall surface as
Figure GDA0003307437120000051
The target position is taken as a first evaluation point, which is marked as A0The next point is A1The other points are denoted as Ai. From the known evaluation point AiTo the next evaluation point Ai+1Is represented by a vector
Figure GDA0003307437120000052
Point AiTo point Ai+1Is recorded as
Figure GDA0003307437120000053
Distance evaluation point AiThe nearest mesh node is denoted as Bi，BiVectors to other grid nodes within the same grid are noted as
Figure GDA0003307437120000054
Where j is 1, … 7. Vector
Figure GDA0003307437120000055
In the unit normal direction
Figure GDA0003307437120000056
Is projected as
Figure GDA0003307437120000057
Vector
Figure GDA0003307437120000058
In the unit normal direction
Figure GDA0003307437120000059
Is at an included angle of
Figure GDA00033074371200000510
Ranging from 0 to pi, where an angle of 0 represents a vector
Figure GDA00033074371200000511
In the unit normal direction
Figure GDA00033074371200000512
Are in the same direction, and the included angle is pi/2 to represent a vector
Figure GDA00033074371200000513
In the unit normal direction
Figure GDA00033074371200000514
Is perpendicular to the direction of the vector, and the included angle is pi to represent the vector
Figure GDA00033074371200000515
In the unit normal direction
Figure GDA00033074371200000516
In the opposite direction. Then point AiTo point Ai+1Distance d ofiWith BiDetermining the equivalent thickness of the grid according to the formula di＝a×piJCalculation of which take J such that
Figure GDA00033074371200000517
Is the minimum value, and a is the evaluation point distance weighting coefficient. Taking a two-dimensional flow field as an example, FIG. 3, where βi1I.e. the minimum angle of the grid to the vector direction, so that the height P will be projectedi1Multiplying by a as the equivalent thickness of the grid. The projection of the three-dimensional flow field is similar, as in fig. 4.
And S2, interpolating at the position of the evaluation point by using the flow field data on the grid nodes near the evaluation point to obtain the flow field of the target position on the wall surface in the normal direction, and projecting the flow field to the orthogonal patch coordinate system.
Since the evaluation point in the wall surface normal direction is not on the grid node, there is no direct numerical calculation data, and therefore, interpolation at the evaluation point using the data of the existing grid point is required.
Get the unit normal direction of the wall target position
Figure GDA00033074371200000518
Is the normal direction in the wall surface
Figure GDA00033074371200000519
Velocity at evaluation point farthest from wall surface
Figure GDA00033074371200000520
In a manner that
Figure GDA00033074371200000521
Projecting on a plane in the normal direction, unitizing the obtained projection velocity vector to obtain the direction of flow
Figure GDA00033074371200000522
In the direction normal to the wall
Figure GDA00033074371200000523
And the direction of flow
Figure GDA00033074371200000524
The vertical direction being the spanwise direction
Figure GDA00033074371200000525
The flow direction, the normal direction in the wall surface and the spreading direction meet the right-hand rule, and the flow direction, the normal direction in the wall surface and the spreading direction form an orthogonal sticker coordinate system.
The velocity vector of the rectangular coordinate system
Figure GDA0003307437120000061
Decomposing the velocity vector into the flow direction, the normal direction in the wall surface and the spreading direction to obtain the velocity vector under the orthogonal body-attached coordinate system after the normal is broken off
Figure GDA0003307437120000062
And S3, establishing a functional relation between the comprehensive judgment characteristic quantity and the wall surface distance on the evaluation point.
In step S3, a comprehensive decision function is used to establish a relationship with the boundary distance, not just the flow velocity. As shown in fig. 5, the incoming flow velocity and the boundary layer thickness are not easily and directly determined by the distribution of the velocity u in the wall surface normal direction, the position with a large velocity gradient can be obtained by calculating du/dy, and the position of the maximum value and the corresponding boundary layer characteristic thickness can be quickly and accurately obtained by determining the function u × du/dy.
The following integrated decision functions were defined for quantitative analysis at the evaluation points:
Figure GDA0003307437120000063
wherein eta isiIs evaluation point AiCoordinates in the normal direction in the wall, uiξIs the velocity in the flow direction, rho, in a coordinate system of a patchiIs the density at the evaluation point, and b, c, d are the exponential weighting values of the terms.
And S4, determining a characteristic point through the judgment criterion, and estimating the characteristic thickness of the boundary layer according to the distance between the characteristic point and the wall surface.
And predicting parameters such as the characteristic thickness of the boundary layer by using the maximum value point of the comprehensive judgment function in the step S3.
Firstly, all evaluation points AiF (η) of (C)i) Comparing to obtain f (eta)i) Point of maximum value of (A)mTaking Am-2、Am-1、Am、Am+1、Am+2Total of 5 points fit f (η)i) In AmA continuous function s (eta) near the point, s' (eta) is obtained by deriving s (eta), and the eta value at the maximum position of s (eta) is taken as deltarAs a boundary layer reference scale (i.e. boundary layer characteristic thickness), i.e. deltar＝η|s′(η)＝0。
Note delta99For nominal boundary layer thickness, take δ99＝AδrWherein A: (M) is a conversion factor of the nominal thickness of the boundary layer, is a function of Mach number M, can be obtained by engineering fitting of a large number of samples in advance, and has good universality because A (M) is close to a constant in the range of M being 3-20.
Note deltadFor the displacement of boundary layer, take deltad＝BδrAnd B (M) is a conversion factor of the displacement thickness of the boundary layer, is a function of the Mach number M, and can be obtained by performing engineering fitting on a large number of samples in advance.
Let θ be the boundary layer momentum displacement thickness, then take θ ═ C δrWherein C (M) is a conversion factor of the momentum displacement thickness of the boundary layer, is a function of the Mach number M, and can be obtained by performing engineering fitting on a large number of samples in advance.
Example 1:
s1, the evaluation point distance weighting coefficient is 0.9.
S2, a three-dimensional 3-degree polynomial interpolation may be applied to the evaluation points: based on the flow field information of 64 grid points near the point, the result is independent of the interpolation sequence of three directions
S3, determining the flow field characteristics of the evaluation point in the normal direction by adopting the weighting mode of the combined characteristic quantity of the following formula
Figure GDA0003307437120000071
S4, estimating the nominal thickness delta of the boundary layer with A being 1.3-1.5 in the Mach number M being 3-2099。
While the present invention has been described in terms of its functions and operations with reference to the accompanying drawings, it is to be understood that the invention is not limited to the precise functions and operations described above, and that the above-described embodiments are illustrative rather than restrictive, and that various changes and modifications may be effected therein by one skilled in the art without departing from the scope or spirit of the invention as defined by the appended claims.

Claims (3)

1. A supersonic velocity boundary layer characteristic thickness estimation method is characterized by comprising the following steps:
s1, arranging evaluation points in the normal direction of the target position on the wall surface: the evaluation points are distributed inside and outside the boundary layer, and the distribution positions of the evaluation points are determined according to the equivalent thickness of the grids in the normal direction;
s2, interpolating at the evaluation point position by using the flow field data on the grid nodes near the evaluation point to obtain a flow field of a target position on the wall surface in the normal direction, and projecting the flow field data to an orthogonal patch coordinate system;
s3, establishing a functional relation between the comprehensive judgment characteristic quantity and the wall surface distance on the evaluation point;
the following integrated decision functions were defined for quantitative analysis at the evaluation points:
Figure FDA0003307437110000011
wherein eta isiIs evaluation point AiCoordinates in the normal direction in the wall, uiξIs the velocity in the flow direction, rho, in a coordinate system of a patchiIs the density at the evaluation point, and b, c, d are the exponential weighting values of the terms;
s4, determining characteristic points through a judgment criterion, and estimating the characteristic thickness of the boundary layer according to the distance between the characteristic points and the wall surface;
the prediction process of the boundary layer characteristic thickness comprises the following steps:
firstly, all evaluation points AiF (η) of (C)i) Comparing to obtain f (eta)i) Point of maximum value of (A)mTaking Am-2、Am-1、Am、Am+1、Am+2Total of 5 points fit f (η)i) In AmA continuous function s (eta) near the point, s' (eta) is obtained by deriving s (eta), and the eta value at the maximum position of s (eta) is taken as deltarAs boundary layer reference scale, i.e. deltar＝η|s′(η)＝0；
Note delta99For nominal boundary layer thickness, take δ99＝AδrWherein A (M) is a boundaryA layer nominal thickness scaling factor that is a function of the Mach number M;
note deltadFor the displacement of boundary layer, take deltad＝BδrWherein B (M) is a boundary layer displacement thickness scaling factor that is a function of Mach number M;
let θ be the boundary layer momentum displacement thickness, then take θ ═ C δrWhere C (M) is a boundary layer momentum displacement thickness scaling factor, which is a function of Mach number M.
2. The method for estimating the characteristic thickness of the supersonic boundary layer according to claim 1, wherein the step S1 is implemented by calculating the equivalent thickness of the normal direction grid by using a projection algorithm, so as to determine the distribution position of the evaluation points:
setting the unit normal direction of the target position on the wall surface as
Figure FDA0003307437110000021
The target position is taken as a first evaluation point, which is marked as A0The next point is A1The other points are denoted as Ai(ii) a From the known evaluation point AiTo the next evaluation point Ai+1Is represented by a vector
Figure FDA0003307437110000022
Point AiTo point Ai+1Is recorded as
Figure FDA0003307437110000023
Distance evaluation point AiThe nearest mesh node is denoted as Bi，BiVectors to other grid nodes within the same grid are noted as
Figure FDA0003307437110000024
Wherein j is 1, … 7; vector
Figure FDA0003307437110000025
In the unit normal direction
Figure FDA0003307437110000026
Is projected as
Figure FDA0003307437110000027
Vector
Figure FDA0003307437110000028
In the unit normal direction
Figure FDA0003307437110000029
Is at an included angle of
Figure FDA00033074371100000210
Ranging from 0 to pi, where an angle of 0 represents a vector
Figure FDA00033074371100000211
In the unit normal direction
Figure FDA00033074371100000212
Are in the same direction, and the included angle is pi/2 to represent a vector
Figure FDA00033074371100000213
In the unit normal direction
Figure FDA00033074371100000214
Is perpendicular to the direction of the vector, and the included angle is pi to represent the vector
Figure FDA00033074371100000215
In the unit normal direction
Figure FDA00033074371100000216
In opposite directions; then point AiTo point Ai+1Distance d ofiWith BiDetermining the equivalent thickness of the grid according to the formula di＝a×piJCalculation of which take J such that
Figure FDA00033074371100000217
Is the minimum value, and a is the evaluation point distance weighting coefficient.
3. The method for estimating the characteristic thickness of the supersonic boundary layer according to claim 1, wherein in step S2, interpolation is performed at the position of the estimated point to obtain a flow field in a direction normal to the target position on the wall surface, and the flow field is projected under an orthogonal patch coordinate system:
get the unit normal direction of the wall target position
Figure FDA00033074371100000218
Is the normal direction in the wall surface
Figure FDA00033074371100000219
Velocity at evaluation point farthest from wall surface
Figure FDA00033074371100000220
In a manner that
Figure FDA00033074371100000221
Projecting on a plane in the normal direction, unitizing the obtained projection velocity vector to obtain the direction of flow
Figure FDA00033074371100000222
In the direction normal to the wall
Figure FDA00033074371100000223
And the direction of flow
Figure FDA00033074371100000224
The vertical direction being the spanwise direction
Figure FDA00033074371100000225
Wherein the flow direction, the normal direction in the wall surface and the spreading direction meet the right-hand rule; the flow direction,An orthogonal patch coordinate system is formed in the normal direction and the spreading direction in the wall surface;
the velocity vector of the rectangular coordinate system
Figure FDA00033074371100000226
Decomposing the velocity vector into the flow direction, the normal direction in the wall surface and the spreading direction to obtain the velocity vector under the orthogonal body-attached coordinate system after the normal is broken off
Figure FDA00033074371100000227
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