CN115048752A - Design method for supersonic-speed-crossing wind tunnel semi-flexible wall spray pipe - Google Patents
Design method for supersonic-speed-crossing wind tunnel semi-flexible wall spray pipe Download PDFInfo
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Abstract
A design method for a semi-flexible wall spray pipe across a supersonic wind tunnel belongs to the technical field of aerodynamic wind tunnel design. Firstly, determining a nozzle molded surface and a throat block molded surface of an initial Mach number; assuming the slope of the turning point of the non-adhesive profile, calculating the profile of the non-adhesive spray pipe, and enabling the coordinate, the slope and the curvature of the turning point of the non-adhesive profile superposed with the boundary layer to be consistent with the coordinate, the slope and the curvature of the turning point of the wall surface of the throat block; determining the required height of the throat, translating the throat block along the tangent direction of the turning point, keeping the coordinate of the turning point unchanged, and compensating the elongation required by translation of the throat block by the length of the flexible plate. The spray pipe molded surface at the downstream of the turning point is realized by the residual flexible plate and the outlet end plate of the fixed molded surface, and the constraint conditions of the length of the flexible plate and the height of the spray pipe outlet are met. The semi-flexible wall spray pipe is developed for solving the problems that the semi-flexible wall spray pipe can not only ensure the continuous slope and curvature of each part of a molded surface like a fully flexible wall spray pipe, but also ensure that the molded surface of a throat block is suitable for different Mach numbers, and can ensure that the flow field quality is consistent with that of the fully flexible wall spray pipe.
Description
Technical Field
The invention relates to a design method of a wind tunnel semi-flexible wall spray pipe, and belongs to the technical field of aerodynamic wind tunnel design.
Background
At present, the mainstream supersonic wind tunnel generally adopts a flexible-wall spray pipe to replace a fixed-block spray pipe. The flexible-wall spray pipe has the advantages of wide Mach number adjusting range, small Mach number interval, large number of molded surfaces, high Mach number precision, high spray pipe molded surface replacing efficiency and capability of optimizing the flow field quality through the adjusting molded surfaces. Because the mach number wave intensity in the initial expansion zone of the nozzle is low, the flow in the zone conforms to the radial flow characteristics, the influence of the small change of the profile on the flow characteristics is negligible, in other words, the profile of the initial expansion zone does not need to be simulated particularly accurately, so that the profile of the throat zone can be replaced by a rigid throat block. The nozzle form of the combination of the flexible plate and the throat block is a semi-flexible wall nozzle.
Compared with a full-flexible-wall spray pipe, the semi-flexible-wall spray pipe basically inherits the advantages of the flexible-wall spray pipe, reduces the number of supporting mechanisms, saves construction cost, improves system reliability and reduces operation and maintenance cost. However, the semi-flexible wall nozzle has more constraint conditions and great design difficulty. The main design difficulty of the semi-flexible wall nozzle is to ensure that the slope and curvature of each part of the molded surface are continuous like a fully flexible wall nozzle, and to ensure that the molded surface of the throat block is suitable for different Mach numbers.
Therefore, a new design method of a wind tunnel semi-flexible wall nozzle is needed to solve the above technical problems.
Disclosure of Invention
The present invention has been developed to solve the problems of a semi-flexible wall nozzle that not only can ensure continuous slope and curvature at each position of the profile, but also can ensure that the throat block profile is suitable for different mach numbers, and can ensure that the flow field quality is consistent with that of a fully flexible wall nozzle, and a brief summary of the present invention is provided below to provide a basic understanding of some aspects of the present invention. It should be understood that this summary is not an exhaustive overview of the invention. It is not intended to determine the key or important part of the present invention, nor is it intended to limit the scope of the present invention.
The technical scheme of the invention is as follows:
a design method for a semi-flexible wall spray pipe across a supersonic wind tunnel comprises the following steps:
step 1: setting basic geometric parameters of the nozzle, and designing a throat block profile;
given a target value for the spout outlet height and the spout width (i.e., the parallel wall spacing); determining the length of a flexible plate of the spray pipe by referring to the length of a molded surface of the full-flexible-wall spray pipe with the maximum Mach number after the turning point; and taking the minimum Mach number as the design Mach number of the throat block, namely taking the profile of the initial expansion zone of the Mach number as the design profile of the throat block.
Selecting a power coefficient n of an initial expansion polynomial curve of the non-adhesive surface, and substituting the power coefficient n into a formula (1) to obtain the initial expansion curve of the non-adhesive surface:
In the formula, h t The throat part with non-adhesive surface has half height and coordinates of (0, h) t ），x a The horizontal coordinate of the turning point A of the non-adhesive molded surface is shown, and theta a is a turning angle, namely the inclination angle of the molded surface at the turning point A of the non-adhesive molded surface to the axis of the spray pipe; assuming that the flow at the inflection point A of the non-viscous profile is radial spring flow, the coordinate (x) of the inflection point A of the non-viscous profile is a ，y a ) The flow conservation relation of the one-dimensional pipe is given, and the expression is as the formula (2):
Wherein γ is the specific heat ratio of air, γ =1.4, M a Local Mach number of turning point;
the boundary layer displacement thickness from the throat to the turning point is approximately expressed by a 3 rd order polynomial:
In the formula
Is the horizontal coordinate of the turning point of the non-adhesive molded surface,
the displacement thickness of the boundary layer at the turning point A of the non-adhesive profile is calculated by a Tucker method.
And (3) superposing the displacement thickness of the non-adhesive surface layer and the boundary layer of the spray pipe according to the following formula to obtain coordinates (X, Y) of the spray pipe surface along the way:
Wherein x and y are coordinates of a non-adhesive surface,
the inclination angle of the non-adhesive profile.
And 2, step: determining coordinates (X) of the center of rotation D of the throat Block D ,Y D ）；
The central point of the nozzle outlet section is the origin (0, 0) of the coordinate system, and the coordinate of the rotation center D of the nozzle throat block is (X) D ,Y D ) The coordinate of the turning point P of the throat block is (X) P ,Y P ) The profile inclination angle of the turning point P point of the throat block is
；
The centre of rotation being located in the vicinity of the nozzle outlet and the distance Y from the centre of rotation to the axis of the nozzle D Is the height Y of the nozzle outlet out 1.5-2 times of the total weight of the composition; the included angle between the connecting line of the rotating center D and the turning point P of the throat block and the tangent line of the turning point P of the throat block
The calculation formula of (a) is as follows:
Thereby calculating the distance PD between the rotation center D and the turning point P of the throat block and the X of the rotation center D The following were used:
And step 3: rotating the throat block, and determining the coordinate and the curvature radius of the rotated throat block in a nozzle coordinate system;
rotating the throat block anticlockwise around a rotation center under the Mach number of the design point in the step 1, wherein the throat block anticlockwise around the rotation center is the direction for reducing the size of the throat; the coordinate (X) of the new throat is obtained after rotation t ,Y t ) And radius of curvature at the throat Rt; radius of curvature R at throat t Height Y of throat t The ratio is greater than 10 and the throat blocks maintain a contracted profile at all times.
And 4, step 4: designing the displacement thickness of the non-adhesive profile and the boundary layer in the throat block area to ensure that the coordinates of the spray pipe profile obtained by superposing the non-adhesive profile and the boundary layer in the turning point P of the throat block tend to be consistent;
the power coefficient n =3 of the initial expansion polynomial curve given the inviscid profile; taking the displacement thickness of the throat boundary layer of the designed profile as the displacement thickness of the boundary layer at the current throat
The initial value of (A) is obtained by the formula (eight) to obtain the half height of the throat without the adhesive surface
；
Wherein W is the width of the nozzle;
initial value of inclination angle for given inviscid profile turning point A
Initial value of
Is less than
Calculating the coordinate of the turning point A of the non-adhesive surface as (X) by the formula nine and the formula ten A ,Y A ）；
Calculating displacement thickness of boundary layer of T and non-adhesive profile turning point A at throat by characteristic line method and Tucker boundary layer correction method
And
the coordinates of the turning point P of the throat block are obtained by calculation (
,
）：
Checking and calculating the coordinate (X) of turning point P of throat block P ,Y P ) And (a)
,
) Whether the two are consistent; if the non-adhesive surface is inconsistent, adjusting the inclination angle of the non-adhesive surface turning point
Repeating the step 4, and performing iterative calculation until the two are consistent; boundary layer displacement thickness at throat in the process
And gradually converge.
And 5: calculating the molded surface of the flexible plate to ensure that the coordinates of the flexible plate and the throat block at the turning point P of the throat block are consistent;
given outlet height of non-sticking profile
Calculating according to formula thirteen to obtain outlet Mach number
An initial value of (1);
Calculating the coordinate of a non-adhesive surface of the flexible plate, the height of the outlet of the spray pipe and the displacement thickness of the surface layer of the outlet by a characteristic line method and a Tucker surface layer correction method; and (4) adopting the outlet height of the new non-adhesive molded surface as an initial value to carry out iterative calculation until the deviation between the target height of the outlet of the spray pipe and the calculated value of the outlet height of the spray pipe is reduced to be within 0.1 mm.
Fitting the displacement thickness of the boundary layer from the throat to the outlet by using a cubic curve and a straight line, and then solving the displacement thickness and the slope of the boundary layer of the turning point A of the non-adhesive profile; if the boundary layer thickness at the inflection point A of the non-adhesive profile and the boundary layer displacement thickness in the step 4 are not equal
If not, according to the displacement thickness of the boundary layer of the new turning point, returning to the step 4 to recalculate the coordinate of the turning point P of the throat block (
,
) Up to the coordinate (X) of the turning point P of the laryngeal block P ,Y P ) And (a)
,
) Substantially identical.
Step 6: the throat block rotates around the turning point P of the throat block, and the slopes of the throat block and the flexible plate at the turning point P of the throat block are consistent;
calculating the slope and inclination angle of the flexible plate at the turning point P according to the following formula
；
Comparing the slopes of the two sides of the turning point of the wall, i.e. the slope of the downstream end point of the throat section and the slope of the upstream end point of the flexible wallThere is a deviation within 0.05 °; the slope deviation is compensated by the rotation of the throat block around the turning point of the wall surface, in order to compensate the change of the throat height, the throat block translates along the direction of the inclination angle of the flexible plate at the turning point P of the throat block, the translation amount keeps the throat height unchanged, the displacement amount is compensated by the length of the flexible plate, and the coordinates (X, Y) on the throat block after the rotation and the translation (the: (the) coordinates
) Calculated as follows:
In the formula (I), the compound is shown in the specification,
is the distance between the point on the throat block and the turning point P of the throat block,
is the inclination angle of the line connecting the point on the throat block and the turning point P of the throat block.
And 7: calculating and correcting the height of the outlet of the spray pipe;
superposing the displacement thickness of the non-adhesive profile and the boundary layer to calculate the coordinates of the flexible plate of the spray pipe along the way, the outlet height of the adhesive profile and the length of the flexible plate required by the adhesive profile;
the total length of the flexible wall is determined in step 1, and a part of flexible plate is remained by deducting the extension amount of the translation of the compensation throat block and the length of the flexible plate required by the downstream profile of the turning point P of the throat block, and the part of flexible plate exists in an inclined straight line form, has an inclined angle consistent with the inclination of the outlet of the viscous profile and extends to the actual outlet of the spray pipe;
if the calculated value of the height of the outlet of the spray pipe has deviation from the target height of the outlet of the spray pipe, the height of the outlet of the non-adhesive profile in the step 5 is modified by adopting a dichotomy
And (4) recalculating the steps 5-7 until the deviation between the calculated value of the height of the outlet of the spray pipe and the target height of the outlet of the spray pipe is reduced to be within 0.1 mm.
And 8: designing a throat block upstream curve aiming at each Mach number, wherein the upstream curve is composed of piecewise polynomial curves with continuous curvatures, and a combination of curves for 5 times and straight lines is adopted, wherein the curves for 5 times can ensure that the coordinates, the slope and the curvatures at the connecting points are continuous, and the curvatures of the straight lines at the connecting points are zero; because the lengths of the section of molded lines are different, in order to compensate the length difference of the molded lines, a sliding groove mechanism form is adopted at the inlet of the spray pipe; the sliding groove rotates around the inlet of the spray pipe, and the flexible plate stretches and retracts in the sliding groove when the Mach number is changed; the flexible plate molded lines in the sliding grooves are straight lines.
The invention has the following beneficial effects:
1. the method adopts twice rotation of the throat block and once translation of the throat block to enable the throat block to be matched with theoretical profiles of various design Mach numbers, adopts self-adaptive iterative computation to generate a flexible plate profile, and is suitable for design of a semi-flexible wall spray pipe;
2. the design method of the semi-flexible wall spray pipe has the advantages of wide Mach number range, excellent uniformity of a spray pipe flow field, adjustable proportional size of the spray pipe and the like;
3. the invention is easy to realize, has high production efficiency of the spray pipe molded surface, can generate a large amount of molded surfaces in a short time, and has good development prospect.
Drawings
FIG. 1 is a schematic diagram of a design scheme of a design method of a cross-supersonic wind tunnel semi-flexible wall nozzle, wherein A is a non-adhesive profile turning point, D is a rotation center, P is a throat block turning point, h t Is half height of throat part with non-adhesive surface,
the height of the outlet of the non-adhesive profile surface;
FIG. 2 is a design flow chart of a design method of a cross-supersonic wind tunnel semi-flexible wall nozzle;
FIG. 3 is a graph of a flexible plate profile of a design method of a semi-flexible wall nozzle spanning a supersonic wind tunnel.
Detailed Description
In order that the objects, aspects and advantages of the invention will become more apparent, the invention will be described by way of example only, and in connection with the accompanying drawings. It is to be understood that such description is merely illustrative and not intended to limit the scope of the present invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.
The connection mentioned in the present invention is divided into a fixed connection and a detachable connection, the fixed connection (i.e. the non-detachable connection) includes but is not limited to a folding connection, a rivet connection, an adhesive connection, a welding connection, and other conventional fixed connection methods, the detachable connection includes but is not limited to a screw connection, a snap connection, a pin connection, a hinge connection, and other conventional detachment methods, when the specific connection method is not clearly defined, the function can be realized by always finding at least one connection method from the existing connection methods by default, and a person skilled in the art can select the connection method according to needs. For example: the fixed connection selects welding connection, and the detachable connection selects hinge connection.
The first embodiment is as follows: the embodiment is described with reference to fig. 1 to fig. 3, and the method for designing the transonic wind tunnel semi-flexible wall nozzle in the embodiment is implemented by taking a 0.6 m continuous transonic wind tunnel (FL-61) as an example, according to the following steps:
step 1: the profile of the throat block is designed given the basic geometrical parameters of the nozzle.
(1) The basic geometric parameters of the semi-flexible wall nozzle are given.
The design Mach numbers of the FL-61 wind tunnel semi-flexible wall nozzle are 1.15, 1.2, 1.3, 1.4, 1.5 and 1.6. The height of the outlet of the spray pipe is 600mm, namely the height of the inlet of the test section. The width of the nozzle is 600 mm. The molded line length from the turning point to the nozzle outlet can refer to the molded line length of the full-flexible-wall nozzle downstream of the turning point M =1.6, and the length of 900mm meets the requirement of M = 1.6.
(2) And (4) designing the Mach number of the given throat block and designing the molded surface of the throat block.
In order to obtain a shorter throat block, the profile of the design mach number M =1.15 before the turning point is selected as the throat block profile. Selecting a power coefficient n =3 of an initial expansion polynomial curve of the non-adhesive surface, and substituting the power coefficient n =3 into the following formula to obtain the initial expansion curve of the non-adhesive surface:
In the formula, ht is half height of throat with no adhesive surface, x a Is the abscissa of the turning point, and is,
the turning angle is the inclined angle of the turning point type facing the axis of the spray pipe; assuming that the flow at the turning point is radial spring flow, x a 、y a Given the conservation of flow in one-dimensional pipe, the expression is as follows:
Wherein γ is the specific heat ratio of air, γ =1.4, M a Local Mach number of turning point;
the boundary layer displacement thickness from the throat to the turning point is approximately expressed by a 3 rd order polynomial:
In the formula
Is the horizontal coordinate of the turning point of the non-adhesive molded surface,
is the boundary layer displacement thickness at the turning point A of the non-adhesive profile calculated by a Tucker method,
is the boundary layer displacement thickness between the throat and the turning point, and is a function of the abscissa x.
And (3) superposing the displacement thickness of the non-adhesive surface layer and the boundary layer of the spray pipe according to the following formula to obtain coordinates (X, Y) of the spray pipe surface along the way:
Wherein x and y are coordinates of a non-adhesive surface,
the inclination angle of the non-adhesive profile.
Thereby obtaining the profile coordinate of the throat block, wherein the axial distance between the throat and the turning point of the throat block is 231mm,
=0.947°，
=0°， 
=20.99，
=6537.617mm，dX=0.0mm，dY=0.0mm。
step 2: determining coordinates (X) of the center of rotation D of the throat Block D ,Y D ）；
Center of the nozzle outlet cross-sectionThe point is the origin (0, 0) of the coordinate system, and the coordinate of the rotation center D of the nozzle throat block is (X) D ,Y D ) The coordinate of the turning point P of the throat block is (X) P ,Y P ) The profile inclination angle of the turning point P point of the throat block is
；
The centre of rotation being located in the vicinity of the nozzle outlet and the distance Y from the centre of rotation to the axis of the nozzle D Is the height Y of the nozzle outlet out 1.5-2 times of the total weight of the composition; the included angle between the connecting line of the rotating center D and the turning point P of the throat block and the tangent line of the turning point P of the throat block
The calculation formula of (a) is as follows:
Thereby calculating the distance PD between the rotation center D and the turning point P of the throat block and the X of the rotation center D The following were used:
Rotation center coordinate of FL-61 wind tunnel semi-flexible wall nozzle
=525mm，
=509.795mm, 621.5mm from the throat cross-section.
And step 3: rotating the throat block, and determining the coordinate and the curvature radius of the rotated throat block in a nozzle coordinate system;
under each design Mach number in the step 1, rotating the throat block anticlockwise around a rotation center, wherein the direction of reducing the size of the throat is anticlockwise around the rotation center; the coordinate (X) of the new throat is obtained after rotation t ,Y t ) And radius of curvature at the throat Rt; radius of curvature R at throat t Height Y of throat t The ratio is greater than 10 and the throat blocks maintain a contracted profile at all times.
And obtaining other design Mach numbers and initial expansion curves.
M=1.2，
，
，
=5630.807mm。
M=1.3，
，
=15.9，
=4411.12mm。
M=1.4，
，
=13.94，
=3702.096mm。
M=1.5，
，
=12.85，
=3233.001mm。
M=1.6，
，
=12.27，
=2900.246mm。
And 4, step 4: designing the displacement thickness of the non-adhesive profile and the boundary layer in the throat block area to ensure that the coordinate of the spray pipe profile obtained by superposing the non-adhesive profile and the boundary layer and the coordinate of the throat block profile at the turning point P of the throat block tend to be consistent;
the power coefficient n =3 of the initial expansion polynomial curve given the inviscid profile; taking the displacement thickness of the throat boundary layer of the designed profile as the displacement thickness of the boundary layer at the current throat
The initial value of (A) is obtained by the formula (eight) to obtain the half height of the throat without the adhesive surface
；
Wherein W is the width of the nozzle;
initial value of inclination angle for given inviscid profile turning point A
Initial value of
Is less than
Calculating the coordinate of the turning point A of the non-adhesive surface as (X) by the formula nine and the formula ten A ,Y A ）；
Calculating displacement thickness of boundary layer of T and non-adhesive profile turning point A at throat by characteristic line method and Tucker boundary layer correction method
And
the coordinates of the turning point P of the throat block are obtained by calculation (
,
）：
Checking and calculating the coordinate (X) of turning point P of throat block P ,Y P ) And (a)
,
) Whether the two are consistent; if the non-adhesive surface is inconsistent, adjusting the inclination angle of the non-adhesive surface turning point
Repeating the step 4, and performing iterative computation until the two are consistent; boundary layer displacement thickness at throat in the process
And gradually converge.
And 5: calculating the molded surface of the flexible plate to ensure that the coordinates of the flexible plate and the throat block at the turning point P of the throat block are consistent;
given outlet height of non-sticking profile
Calculating according to a formula thirteen to obtain an outlet Mach number
An initial value of (1);
Calculating the coordinate of a non-adhesive surface of the flexible plate, the height of the outlet of the spray pipe and the displacement thickness of the surface layer of the outlet by a characteristic line method and a Tucker surface layer correction method; and (4) adopting the outlet height of the new non-adhesive molded surface as an initial value to carry out iterative calculation until the deviation between the target height of the outlet of the spray pipe and the calculated value of the outlet height of the spray pipe is reduced to be within 0.1 mm.
Fitting the displacement thickness of the boundary layer from the throat to the outlet by using a cubic curve and a straight line, and then solving the displacement thickness and the slope of the boundary layer of the turning point A of the non-adhesive profile; if the displacement thickness of the boundary layer at the turning point A of the non-adhesive profile and the displacement thickness of the boundary layer in the step 4 are the same
Inconsistency, according to newThe displacement thickness of the boundary layer of the turning point returns to the step 4 to recalculate the coordinate of the turning point P of the throat block (
,
) Up to the coordinate (X) of the turning point P of the laryngeal block P ,Y P ) And (a)
,
) Substantially identical.
Calculating the coordinates of the profile of the spray pipe, the T of the throat, the turning point A of the non-adhesive profile and the displacement thickness of the boundary layer at the outlet of the spray pipe by a characteristic line method and a Tucker boundary layer correction method:
(1) the characteristic line method comprises the following calculation steps:
1) and calculating flow field parameters of the initial expansion section and the turning point. In the initial expansion section, a series of left extension characteristic lines are emitted from an inlet boundary condition (transonic velocity resolution right extension characteristic line at the throat), the characteristic lines are reflected in the form of right extension characteristic lines after meeting the profile curve of the initial expansion section, and are reflected in the form of left extension characteristic lines after meeting the central line of the nozzle, and the steps are repeated until the left extension characteristic lines reach the turning point. The flow field parameters in this region are solved using the following equations.
The included angle between the flow direction of the flow field of the spray pipe and the axial line is defined as the airflow angle
The included angle between the tangent of the characteristic line and the flow direction is defined as a Mach number angle, and the included angle satisfies the following formula:
mach angle formula:
Facing the flow direction, the left side characteristic line is called a left-extending characteristic line, and the right side characteristic line is called a right-extending characteristic line. The planter-meier angle is a function of mach angle, satisfying the following equation:
Assuming the presence of a left extension eigenfunction in the nozzle
And a right extension eigenfunction
The right-extension eigenfunction is expressed as the Plantt-Meier anglevAngle of air flow
One-half of the sum of the values,
(ii) a The left-extension eigenfunction is expressed as half the difference between the prandtl-meier angle and the air flow angle,
；
the right stretching characteristic line satisfies the following relation:
The left extension characteristic line satisfies the following relational expression:
Therefore, the temperature of the molten metal is controlled,
The aerodynamic parameters in the non-stick profile region of the nozzle tube satisfy the following equations:
compatibility equations:
Namely, it is
Formula (5.8)
Flow field parameters at turning points need to be given by interpolation calculation, and the turning points are found by linear regression
The value is obtained.
2) And calculating flow field parameters of partial wave eliminating areas and characteristic points. The known condition being the turning point
And
boundary conditions of the feature points:
and
a total of 4 known conditions, assuming a polynomial function
A, b, c and
4 unknowns in total, and simultaneously solving to obtain
Expression of (2) and abscissa of feature point
. Then, a left extension characteristic line is sent out from a part of nodes on the right extension characteristic line where the turning points are located to the molded surface of the semi-evanescent wave zone, flow field parameters except for a vertical coordinate y of the molded surface are solved by using formulas (1) to (8), and the solution of the vertical coordinate y can be obtained by using linear interpolation, and is as follows:
And (3) solving the flow field parameters in the semi-anechoic region by using the formulas (1) to (8).
3) And calculating flow field parameters in the complete wave elimination region. And the left extension characteristic lines emitted from all nodes on the right extension characteristic lines in front of the characteristic points are projected onto the molded surface and do not reflect the right extension characteristic lines. Boundary conditions are satisfied on the profile
And
and calculating all flow field parameters on the molded surface by using the formulas (1) - (9).
(2) And (3) calculating the displacement thickness distribution of the boundary layer:
1) displacement thickness of boundary layer at throat
The boundary layer displacement thickness at the throat is calculated by the following empirical formula.
In the formula h t Is half height of throat without adhesive surface, T 0 Is the total temperature of the gas to be heated,
is the radius of curvature at the throat,
is based on a reference temperature T am The kinematic viscosity coefficient of (a).
2) Boundary layer displacement thickness of spray pipe along way
The boundary layer displacement thickness of the nozzle along the way is calculated by a Tucker method.
The principle of calculating the boundary layer displacement thickness by the Tucker method is as follows:
the integral of momentum equation for shock-free, steady, compressible viscous flow is given by:
Conversion to the following form:
In the formula (I), the compound is shown in the specification,
and f is the ratio of the boundary layer momentum thickness to the boundary layer thickness
G is the ratio of displacement thickness of the boundary layer to the thickness of the boundary layer
H is the ratio of g to f
。
Assuming that the velocity profile within the boundary layer is exponentially distributed, the following equation is:
Then use the boundary layer thickness
Displacement thickness of boundary layer
Boundary layer momentum thickness
Is substituted by the expression of the formula f, g to obtain
For large reynolds number ranges, the velocity type parameter N =7 is chosen as the standard value. Tucker gives the relation that
Coefficient of friction
Is expressed as follows
In the formula
Thus, therefore, it is
Substituting the expressions of the parameters g, f and N into the momentum integral equation to obtain a new expression of the momentum equation as follows
In the formula (I), the compound is shown in the specification,
In order to take account of wave system and boundary layer interference correction, displacement boundary layer thickness is adopted
The modification is made, and for the parapressure gradient, the expression of the integral decomposition of the momentum equation over the integration interval (a, b) is as follows:
In the formula (I), the compound is shown in the specification,
Coordinate Xa of known point a, Mach number Ma and displacement thickness of boundary layer
And the coordinates Xb and the Mach number Mb of the point b are calculated to obtain the boundary layer displacement thickness of the point b
. The boundary layer displacement thickness of each point on the spray pipe along the way is obtained through calculation by the formula.
3) Boundary layer displacement thickness polynomial fitting
The slope and curvature of the boundary layer thickness curve are continuous, and the boundary layer displacement thickness from the throat to the turning point is approximately represented by a 3 rd order polynomial:
In the formula
Is the horizontal coordinate of the turning point of the non-adhesive molded surface,
is calculated by a Tucker method at the turning point A of the non-adhesive molded surfaceBoundary layer displacement thickness.
The boundary layer displacement thickness between the turning point and the outlet of the spray pipe is basically in a linear growth rule, and the boundary layer displacement thickness from the turning point to the outlet of the spray pipe is expressed by a linear relation:
4) Translation of displacement thickness of boundary layer of parallel wall
The thickness of the displacement of the boundary layer of the parallel walls is converted to the profile wall by the following formula.
Where w is one-half the parallel wall spacing and Y (x) is one-half the height of the nozzle cross-section.
The new outlet height of the non-adhesive molded surface is adopted as an initial value to carry out iterative calculation until the deviation between the target height of the outlet of the spray pipe and the calculated value of the outlet height of the spray pipe is reduced to be within 0.1mm, and the method comprises the following steps:
assuming no-stick profile exit height of the nozzle
，
The target value of the half height of the outlet of the spray pipe is obtained. Calculating the throat height of the inviscid surface according to the one-dimensional pipe flow theory
The following formula:
Specific heat ratio in the formula
。
And calculating the displacement thickness distribution of the non-adhesive surface and the adhesive surface layer of the spray pipe of the first wheel by using the height of the non-adhesive throat as an initial value according to a characteristic line method and a Tucker adhesive surface layer correction method. And (3) superposing the displacement thickness of the non-adhesive surface layer and the boundary layer of the spray pipe according to the following formula to obtain coordinates (X, Y) of the spray pipe surface along the way:
Wherein x and y are coordinates of a non-adhesive surface,
the inclination angle of the non-adhesive profile. From this, the calculated height of the nozzle outlet is given by:
Because the calculated value of the height of the outlet of the spray pipe has deviation from the target height of the outlet of the spray pipe, the target height of the outlet of the spray pipe and the displacement thickness of the boundary layer are required to reversely solve the outlet height of the non-adhesive surface,
And recalculating the throat height of the non-adhesive profile and the profile of the spray pipe by using the outlet height of the non-adhesive profile, and obtaining the calculated value of the outlet height of the spray pipe again. The above process is iterated repeatedly until the difference between the calculated nozzle outlet height and the target nozzle outlet height is reached.
Step 6: the throat block rotates around the turning point P of the throat block, and the slopes of the throat block and the flexible plate at the turning point P of the throat block are consistent;
calculating the slope and inclination angle of the flexible plate at the turning point P of the throat block according to the following formula
；
Comparing the slopes of two sides of the wall surface turning point, namely the slope of the downstream end point of the throat section and the slope of the upstream end point of the flexible wall, wherein the slopes of the two sides have deviation within 0.05 degrees; the slope deviation is compensated by the rotation of the throat block around the turning point of the wall surface, in order to compensate the change of the throat height, the throat block translates along the direction of the inclination angle of the flexible plate at the turning point P of the throat block, the translation amount keeps the throat height unchanged, the displacement amount is compensated by the length of the flexible plate, and the coordinates (X, Y) on the throat block after the rotation and the translation (the: (the) coordinates
) Calculated as follows:
In the formula (I), the compound is shown in the specification,
is the distance between the point on the throat block and the turning point P of the throat block,
is the inclination angle of the line connecting the point on the throat block and the turning point P of the throat block.
In conclusion, the Mach number profile and the slope of the throat block at the turning point are consistent by rotating the throat block around the turning point, and the following can be obtained: m =1.2 of the total weight of the composition,
=1.278°，
=0.00513°。
M=1.3，
=2.132°，
=-0.00265°。
M=1.4，
=3.057°，
=-0.00361°。
M=1.5，
=4.047°，
=-0.0132°。
M=1.6，
=5.077°，
=-0.0184°。
in conclusion, the throat height is ensured to be matched with the design Mach number by translating the throat block, and the following can be obtained:
M=1.2，
=5630.807mm，dX=0.6534mm，dY=0.0108mm。
M=1.3，
=4411.12mm，dX=0.403mm，dY=0.015mm。
M=1.4，
=3702.096mm，dX=0.4602mm，dY=0.0245mm。
M=1.5，
=3233.001mm，dX=1.4685mm，dY=0.1032mm。
M=1.6，
=2900.246mm，dX=1.8315mm，dY=0.1613mm。
and 7: calculating and correcting the height of the outlet of the spray pipe;
superposing the displacement thickness of the non-adhesive profile and the boundary layer to calculate the coordinates of the flexible plate of the spray pipe along the way, the outlet height of the adhesive profile and the length of the flexible plate required by the adhesive profile;
the total length of the flexible wall is determined in step 1, and a part of flexible plate is remained by deducting the extension amount of the translation of the compensation throat block and the length of the flexible plate required by the downstream profile of the turning point P of the throat block, and the part of flexible plate exists in an inclined straight line form, has an inclined angle consistent with the inclination of the outlet of the viscous profile and extends to the actual outlet of the spray pipe;
if the calculated value of the height of the outlet of the spray pipe deviates from the target value of the height of the outlet of the spray pipe, the height of the outlet of the non-sticky profile in the step 5 is modified by adopting a dichotomy
And (4) recalculating the steps 5 to 7 until the deviation between the calculated value of the height of the outlet of the spray pipe and the target height of the outlet of the spray pipe is reduced to be within 0.1mm, and in conclusion, generating a flexible plate profile curve in a self-adaptive manner according to the height of the outlet of the spray pipe and the length of the flexible plate, as shown in fig. 3.
And 8: designing a throat block upstream curve aiming at each Mach number, wherein the upstream curve is composed of piecewise polynomial curves with continuous curvatures, and a combination of curves for 5 times and straight lines is adopted, wherein the curves for 5 times can ensure that the coordinates, the slope and the curvatures at the connecting points are continuous, and the curvatures of the straight lines at the connecting points are zero; because the lengths of the section of molded lines are different, in order to compensate the length difference of the molded lines, a sliding groove mechanism form is adopted at the inlet of the spray pipe; the sliding groove rotates around the inlet of the spray pipe, and the flexible plate stretches and retracts in the sliding groove when the Mach number is changed; the flexible plate molded lines in the sliding grooves are straight lines.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless it is specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
In the description of the present invention, it is to be understood that the orientation or positional relationship indicated by the orientation words such as "front, rear, upper, lower, left, right", "lateral, vertical, horizontal" and "top, bottom", etc. are usually based on the orientation or positional relationship shown in the drawings, and are only for convenience of description and simplicity of description, and in the case of not making a reverse description, these orientation words do not indicate and imply that the device or element being referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore, should not be considered as limiting the scope of the present invention; the terms "inner and outer" refer to the inner and outer relative to the profile of the respective component itself.
Spatially relative terms, such as "above … …," "above … …," "above … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial relationship to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device in the figures is turned over, devices described as "above" or "on" other devices or configurations would then be oriented "below" or "under" the other devices or configurations. Thus, the exemplary term "above … …" can include both an orientation of "above … …" and "below … …". The device may be otherwise variously oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
It should be noted that the terms "first," "second," and the like in the description and claims of this application and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the application described herein are capable of operation in sequences other than those illustrated or described herein.
It should be noted that, in the above embodiments, as long as the technical solutions can be aligned and combined without contradiction, those skilled in the art can exhaust all possibilities according to the mathematical knowledge of the alignment and combination, and therefore, the present invention does not describe the technical solutions after alignment and combination one by one, but it should be understood that the technical solutions after alignment and combination have been disclosed by the present invention.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. A design method for a semi-flexible wall spray pipe of a cross supersonic wind tunnel is characterized by comprising the following steps:
step 1: setting basic geometric parameters of the nozzle, and designing a throat block profile;
and 2, step: determining coordinates (X) of the center of rotation D of the throat Block D ,Y D ）；
And step 3: rotating the throat block, and determining the coordinate and the curvature radius of the rotated throat block in a nozzle coordinate system;
and 4, step 4: designing the displacement thickness of the non-adhesive profile and the boundary layer in the throat block area to ensure that the coordinate of the spray pipe profile obtained by superposing the non-adhesive profile and the boundary layer and the coordinate of the throat block profile at the turning point P of the throat block tend to be consistent;
and 5: calculating the molded surface of the flexible plate to ensure that the coordinates of the flexible plate and the throat block at the turning point P of the throat block are consistent;
step 6: the throat block rotates around the turning point P of the throat block, and the slopes of the throat block and the flexible plate at the turning point P of the throat block are consistent;
and 7: calculating and correcting the height of the outlet of the spray pipe;
and 8: designing a throat block upstream curve aiming at each Mach number, wherein the upstream curve is composed of piecewise polynomial curves with continuous curvatures, and a combination of curves for 5 times and straight lines is adopted, wherein the curves for 5 times can ensure that the coordinates, the slope and the curvatures at the connecting points are continuous, and the curvatures of the straight lines at the connecting points are zero; because the lengths of the molded lines are not consistent, a sliding groove mechanism is adopted at the inlet of the spray pipe for compensating the length difference of the molded lines; the sliding chute rotates around the inlet of the spray pipe, and the flexible plate stretches in the sliding chute when the Mach number is changed; the flexible plate molded lines in the sliding grooves are straight lines.
2. The method for designing the semi-flexible wall nozzle spanning the supersonic wind tunnel according to claim 1, wherein the method comprises the following steps: the step 1 comprises the following steps:
setting a target value of the height of the outlet of the spray pipe and the width of the spray pipe; determining the length of a flexible plate of the spray pipe by referring to the length of a molded surface of the full-flexible-wall spray pipe with the maximum Mach number after the turning point; taking the minimum Mach number as the design Mach number of the throat block, namely taking the profile of the initial expansion area of the Mach number as the design profile of the throat block;
selecting a power coefficient n of an initial expansion polynomial curve of the non-adhesive surface, and substituting the power coefficient n into a formula (1) to obtain the initial expansion curve of the non-adhesive surface:
In the formula, h t The throat part with non-adhesive surface has half height and coordinates of (0, h) t ），x a The horizontal coordinate of the turning point A of the non-adhesive molded surface is shown, and theta a is a turning angle, namely the inclination angle of the molded surface at the turning point A of the non-adhesive molded surface to the axis of the spray pipe; assuming that the flow at the inflection point A of the non-viscous profile is radial spring flow, the coordinate (x) of the inflection point A of the non-viscous profile is a ，y a ) The flow conservation relation of the one-dimensional pipe is given, and the expression is as the formula (2):
Wherein γ is the specific heat ratio of air, γ =1.4, M a Local Mach number of turning point;
the boundary layer displacement thickness from the throat to the turning point is approximately expressed by a 3 rd order polynomial:
In the formula (I), the compound is shown in the specification,
is the boundary layer displacement thickness at the turning point A of the non-adhesive profile calculated by a Tucker method,
is the boundary layer displacement thickness between the throat and the turning point and is a function of the abscissa x;
superposing the displacement thickness of the non-adhesive surface and the boundary layer of the spray pipe according to a formula (4) to obtain the coordinates (X, Y) of the spray pipe surface along the way:
Wherein x and y are coordinates of the non-adhesive surface,
the inclination angle of the non-adhesive profile.
3. The method for designing the semi-flexible wall nozzle spanning the supersonic wind tunnel according to claim 2, wherein the method comprises the following steps: the step 2 comprises the following steps:
the central point of the nozzle outlet section is the origin (0, 0) of the coordinate system, and the coordinate of the rotation center D of the nozzle throat block is (X) D ,Y D ) The coordinate of the turning point P of the throat block is (X) P ,Y P ) The profile inclination angle of the turning point P point of the throat block is
；
The centre of rotation being located in the vicinity of the nozzle outlet and the distance Y from the centre of rotation to the axis of the nozzle D Is the height Y of the nozzle outlet out 1.5-2 times of the total weight of the composition; the included angle between the connecting line of the rotating center D and the turning point P of the throat block and the tangent line of the turning point P of the throat block
The calculation formula of (a) is as follows:
Thereby calculating the distance PD between the rotation center D and the turning point P of the throat block and the X of the rotation center D The following were used:
4. The method for designing the semi-flexible wall nozzle of the transonic wind tunnel according to claim 3, wherein the method comprises the following steps: the step 3 comprises the following steps:
rotating the throat block anticlockwise around a rotation center under the Mach number of the design point in the step 1, wherein the throat block anticlockwise around the rotation center is the direction for reducing the size of the throat; the coordinate (X) of the new throat is obtained after rotation t ,Y t ) And radius of curvature at the throat Rt; radius of curvature R at throat t Height Y of throat t The ratio is greater than 10 and the throat blocks maintain a contracted profile at all times.
5. The method for designing the semi-flexible wall nozzle spanning the supersonic wind tunnel according to claim 4, wherein the method comprises the following steps: the step 4 comprises the following steps:
the power coefficient n =3 of the initial expansion polynomial curve given the inviscid profile; taking the displacement thickness of the throat boundary layer of the designed profile as the displacement thickness of the boundary layer at the current throat
The initial value of (2) is obtained by the formula (8) to obtain the throat half height without adhesive surface
；
Wherein W is the width of the nozzle;
initial value of inclination angle for given inviscid profile turning point A
Initial value of
Is less than
Calculating the coordinate of the turning point A of the non-adhesive surface as (X) by the formula (9) and the formula (10) A ,Y A ）；
Calculating displacement thickness of boundary layer of T and non-adhesive profile turning point A at throat by using characteristic line method and Tucker boundary layer correction method
And
from this, the coordinates of the turning point P of the throat block are calculated (
,
）：
Checking and calculating the coordinate (X) of turning point P of throat block P ,Y P ) And (a)
,
) Whether the two are consistent; if the non-adhesive surface is inconsistent, adjusting the inclination angle of the non-adhesive surface turning point
Repeating the steps4, iteratively calculating until the two are consistent; boundary layer displacement thickness at throat in the process
And gradually converge.
6. The method for designing the semi-flexible wall nozzle spanning the supersonic wind tunnel according to claim 5, wherein the method comprises the following steps: the step 5 comprises the following steps:
given outlet height of non-sticking profile
Calculating according to formula thirteen to obtain outlet Mach number
An initial value of (1);
Calculating the coordinate of a non-adhesive surface of the flexible plate, the height of the outlet of the spray pipe and the displacement thickness of the surface layer of the outlet by a characteristic line method and a Tucker surface layer correction method; adopting the outlet height of the new non-adhesive molded surface as an initial value to carry out iterative calculation until the deviation between the target height of the outlet of the spray pipe and the calculated value of the outlet height of the spray pipe is reduced to be within 0.1 mm;
fitting the boundary layer displacement thickness from the throat to the outlet by using a cubic curve and a straight line, and then solving the boundary layer displacement thickness and the slope of the turning point A of the non-adhesive profile; if the boundary layer thickness at the inflection point A of the non-adhesive profile and the boundary layer displacement thickness in the step 4 are not equal
If not, according to the displacement thickness of the boundary layer of the new turning point, returning to the step 4 to recalculate the coordinate of the turning point P of the throat block (
,
) Up to the coordinate (X) of the turning point P of the laryngeal block P ,Y P ) And (a)
,
) Substantially identical.
7. The method for designing the semi-flexible wall nozzle of the transonic wind tunnel according to claim 6, wherein: the step 6 comprises the following steps:
calculating the slope and inclination angle of the flexible plate at the turning point P of the throat block according to the following formula
；
Comparing the slopes of two sides of the wall turning point, namely the slope of the downstream end point of the throat section and the slope of the upstream end point of the flexible wall, wherein the slopes of the two sides have a deviation within 0.05 degrees; the slope deviation is compensated by the rotation of the throat block around the wall surface turning point, in order to compensate the change of the throat height, the throat block is translated along the direction of the slope angle of the flexible plate at the turning point P of the throat block, the translation amount keeps the throat height unchanged, the displacement amount is compensated by the length of the flexible plate, and the coordinates (X, Y) on the throat block are compensated by the coordinates after the rotation and the translation
Calculated as follows:
In the formula (I), the compound is shown in the specification,
is the distance between the point on the throat block and the turning point P of the throat block,
is the inclination angle of the line connecting the point on the throat block and the turning point P of the throat block.
8. The method for designing the semi-flexible wall nozzle spanning the supersonic wind tunnel according to claim 7, wherein the method comprises the following steps: the step 7 comprises the following steps:
superposing the displacement thickness of the non-adhesive profile and the boundary layer to calculate the coordinates of the spray pipe flexible plate along the way, the outlet height of the adhesive profile and the length of the flexible plate required by the adhesive profile;
the total length of the flexible wall is determined in step 1, and a part of flexible plate is remained by deducting the extension amount of the translation of the compensation throat block and the length of the flexible plate required by the downstream profile of the turning point P of the throat block, and the part of flexible plate exists in an inclined straight line form, has an inclined angle consistent with the inclination of the outlet of the viscous profile and extends to the actual outlet of the spray pipe;
if the calculated value of the height of the outlet of the spray pipe deviates from the target height of the outlet of the spray pipe, the height of the outlet of the non-sticky profile in the step 5 is modified by adopting a dichotomy
Recalculating the step 5 to the step 7 until the deviation between the calculated value of the height of the outlet of the spray pipe and the target height of the outlet of the spray pipe is reduced to be within 0.1 mm.
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