CN117494323B - Design method of high-speed waverider with pressure-matched supersonic cooling air film - Google Patents
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Abstract
The invention provides a high-speed waverider design method with a pressure-matched supersonic cooling air film, which comprises the following steps: generating a wave multiplier, giving a supersonic air film arrangement position on the wave multiplier, acquiring supersonic air film spray pipe outlet pressure under a pressure matching condition, determining supersonic air film mass flow rate, supersonic air film Mach number, supersonic air film spray pipe throat height and spray pipe outlet height of the supersonic air film spray pipe, obtaining supersonic air film spray pipe transonic solution, setting Mach number distribution of a supersonic air film spray pipe axis, using the supersonic air film spray pipe transonic solution, spray pipe outlet and Mach number distribution of a supersonic air film spray pipe axis as boundary conditions, determining a spray pipe non-sticking molded line, solving boundary layer displacement thickness, and obtaining a final spray pipe molded line, thereby completing the design of the high-speed wave multiplier with a pressure matching supersonic cooling air film. The invention solves the problem that the surface pressure of the high-speed waverider and the pressure of the supersonic air film are matched with each other.
Description
Technical Field
The invention mainly relates to the technical field of high-speed waverider aircrafts, in particular to a design method of a high-speed waverider with a pressure-matched supersonic cooling air film.
Background
Currently, high-speed wave-taking aircrafts are hot in research in all countries of the world due to the advantages of high flying speed, high speed, difficulty in interception of the 'water-float' flight track and the like. However, high speed flight gives severe aerodynamic heat to the waverider, causing ablation and destruction of the aircraft surface structure, optical window. Taking Mach 6 waverider aircraft as an example, 20km high altitude atmospheric temperature is about 216K, and the turbulent flow Plantain number is 0.9, then the aircraft surface adiabatic temperature is approximately 1720K;100km high air temperature of approximately 195K and laminar flow prandtl 0.7, the aircraft surface insulation temperature is approximately 1340K. The high-speed waverider aircraft is provided with a layer of cooling air film, which is an effective way for improving infrared stealth performance and is the only way for avoiding burning of an optical window.
At present, a supersonic air film of a high-speed wave-taking aircraft is generally arranged in front of an optical window, and a spray pipe is arranged in a wall surface slotting mode, so that the supersonic air film is generated. The supersonic air film for infrared stealth is arranged on the aircraft body, the width of the spray pipe is larger, and the effective cooling area is longer.
The current supersonic velocity air film spray pipe is generally designed based on a one-dimensional spray pipe flow basic theory, and the main design parameters are spray pipe Mach number, air film height, total temperature total pressure and mass flow rate, and the implementation method is as follows:
firstly, determining the supersonic speed air film Mach number and the air film mass flow rate required by the surface cooling length of an aircraft by means of a priori experiment or an empirical curve;
under the condition of total temperature and total pressure of an air source carried by the aircraft, the air film height and throat height of the nozzle outlet are determined along with the air film mass flow rate, and the static temperature and static pressure of the nozzle outlet are determined by an isentropic relation;
setting the length of the spray pipe, setting the Mach number distribution of the axis of the spray pipe, and determining the height of the spray pipe corresponding to the Mach number according to a Mach number and area ratio formula;
and smoothly connecting a series of spray pipe height profile points to obtain a supersonic spray pipe, and arranging the supersonic spray pipe on the surface of the aircraft so as to generate a supersonic air film.
However, current supersonic gas film nozzles suffer from several disadvantages. First of all, the design is theoretically flawed, and the jet flow is not one-dimensional in nature, but at least two-dimensional. In particular, for curved nozzles, the flow is three-dimensional or modified by two-dimensional flow theory in combination with yaw rate. The existing supersonic velocity air film spray pipe is designed by adopting a one-dimensional flow theory, the wall surface of the spray pipe cannot be perfectly wave-cut, in other words, the inner flow passage must have concentrated and converged compression waves, and the problems include: on one hand, the uniformity of the nozzle outlet is very low, the nozzle outlet is mixed with the main flow after being ejected, the heat-resistant performance is reduced, on the other hand, the existence of weak shock waves leads to unequal flow entropy, the static temperature and static pressure of the nozzle outlet are inconsistent with the theoretical results of one-dimensional flow, the air film pressure is difficult to effectively control to be matched with the main flow pressure of an aircraft, the pressure mismatch leads to a wave system structure, the mixing is enhanced, and meanwhile, the optical distortion is increased.
Disclosure of Invention
In the prior art, the supersonic air film cannot be matched with the surface pressure of an aircraft, and the air film and a main stream are mixed and aggravated and flow separated due to the fact that the pressure is not matched, the cooling efficiency is worsened, and the optical distortion is increased. Aiming at the technical problems in the prior art, the invention provides a high-speed waverider design method with a pressure matching supersonic cooling air film.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
on one hand, the invention provides a high-speed waverider design method with a pressure-matched supersonic cooling air film, which comprises the following steps:
generating a waverider, and giving a supersonic air film arrangement position on the waverider;
given the cooling length requirement of the supersonic air film, determining the mass flow rate and Mach number of the supersonic air film;
knowing the surface pressure of the waverider, and determining the outlet pressure of the supersonic velocity air film spray pipe by combining the Mach number of the supersonic velocity air film under the pressure matching condition;
determining the throat height of the supersonic velocity air film spray pipe according to the mass flow rate of the supersonic velocity air film and the outlet pressure of the supersonic velocity air film spray pipe;
determining the nozzle outlet height of the supersonic velocity air film nozzle according to the throat height of the supersonic velocity air film nozzle and the Mach number of the supersonic velocity air film;
solving a parabolic potential function equation for the transonic flow of the throat part of the supersonic gas film spray pipe by adopting a series expansion method to obtain a transonic solution of the supersonic gas film spray pipe;
setting Mach number distribution of the axis of the supersonic air film spray pipe by taking the supersonic air film spray pipe transonic velocity solution and the spray pipe outlet as a starting point and a finishing point respectively;
the supersonic velocity air film spray pipe transonic velocity solution, spray pipe outlet and Mach number distribution of the supersonic velocity air film spray pipe axis are used as boundary conditions, a supersonic velocity air film spray pipe characteristic line grid is constructed, a supersonic velocity flow field in the supersonic velocity air film spray pipe is solved, and then a spray pipe non-sticking line is determined according to a streamline control equation;
solving the displacement thickness of the boundary layer according to the Von Karman momentum integral relation;
performing viscosity correction on the non-sticky molded line of the spray pipe based on the displacement thickness of the boundary layer to obtain a final molded line of the spray pipe;
and connecting a contraction section molded line of the preset supersonic speed air film spray pipe with the spray pipe molded line at the throat to obtain the complete supersonic speed air film spray pipe, and completing the design of the high-speed waverider with the pressure-matched supersonic speed cooling air film.
Compared with the prior art, the invention has the technical effects that at least the following aspects are realized:
(1) The invention solves the problem that the surface pressure of the high-speed wave multiplier and the pressure of the supersonic air film are matched with each other, and the generated supersonic air film is suitable for pressure matching of the high-speed wave multiplier.
(2) The generated supersonic speed air film body is not separated, and the cooling efficiency is high.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to the structures shown in these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for designing a high-speed waverider with a pressure-matched supersonic cooling air film according to an embodiment of the present invention;
FIG. 2 is a Mach-number cloud of flow field cell 1 for 2 different incoming flow Mach numbers, wherein (a) is a Mach-number cloud of flow field cell 1 for an incoming flow Mach number of 3 and an object plane angle of 30 °; (b) Mach number cloud pictures of a 1 st flow field unit with an incoming flow Mach number of 5 and an object plane angle of 30 degrees;
FIG. 3 is a Mach-number cloud of a flow field obtained by solving a swirled eigenvector in one embodiment;
FIG. 4 is a view of a wave multiplier profile generated by an embodiment;
FIG. 5 is a transonic de-schematic diagram of a supersonic nozzle in accordance with an embodiment of the invention;
FIG. 6 is a graph of nozzle axis Mach number distribution in one embodiment;
FIG. 7 is a schematic diagram of a nozzle signature line network and a nozzle non-stick profile in one embodiment;
FIG. 8 is a graph of a high speed wavebody surface temperature profile with a pressure matched supersonic cooling film designed for one embodiment.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, in one embodiment, a method for designing a high-speed wave multiplier with a pressure-matched supersonic cooling air film is provided, including:
generating a waverider, and giving a supersonic air film arrangement position on the waverider;
given the cooling length requirement of the supersonic air film, determining the mass flow rate and Mach number of the supersonic air film;
knowing the surface pressure of the waverider, and determining the outlet pressure of the supersonic velocity air film spray pipe by combining the Mach number of the supersonic velocity air film under the pressure matching condition;
determining the throat height of the supersonic velocity air film spray pipe according to the mass flow rate of the supersonic velocity air film and the outlet pressure of the supersonic velocity air film spray pipe;
determining the nozzle outlet height of the supersonic velocity air film nozzle according to the throat height of the supersonic velocity air film nozzle and the Mach number of the supersonic velocity air film;
solving a parabolic potential function equation for the transonic flow of the throat part of the supersonic gas film spray pipe by adopting a series expansion method to obtain a transonic solution of the supersonic gas film spray pipe;
setting Mach number distribution of the axis of the supersonic air film spray pipe by taking the supersonic air film spray pipe transonic velocity solution and the spray pipe outlet as a starting point and a finishing point respectively;
the supersonic velocity air film spray pipe transonic velocity solution, spray pipe outlet and Mach number distribution of the supersonic velocity air film spray pipe axis are used as boundary conditions, a supersonic velocity air film spray pipe characteristic line grid is constructed, a supersonic velocity flow field in the supersonic velocity air film spray pipe is solved, and then a spray pipe non-sticking line is determined according to a streamline control equation;
solving the displacement thickness of the boundary layer according to the Von Karman momentum integral relation;
performing viscosity correction on the non-sticky molded line of the spray pipe based on the displacement thickness of the boundary layer to obtain a final molded line of the spray pipe;
and connecting a contraction section molded line of the preset supersonic speed air film spray pipe with the spray pipe molded line at the throat to obtain the complete supersonic speed air film spray pipe, and completing the design of the high-speed waverider with the pressure-matched supersonic speed cooling air film.
The type of the waverider is not limited, the design method is not limited, a person skilled in the art can select a proper method to generate the waverider based on the prior art, the method comprises the following steps of, but not limited to, a oscillometric axisymmetric von Karman waverider design method disclosed in Chinese patent application with publication number CN109573092A, a oscillometric axisymmetric von Karman waverider design method fused with a low-speed airfoil disclosed in Chinese patent application with publication number CN109573093A, a variable wall pressure distribution law oscillometric flow field waverider design method disclosed in Chinese patent with publication number CN109598062B, and the like.
Without loss of generality, an embodiment provides a method for designing a waverider, including:
determining the cruising height and cruising Mach number of the high-speed waverider aircraft, and selecting a reference flow field bus, such as a von Karl curve with the minimum resistance characteristic, as an object plane;
solving a 1 st flow field unit by adopting a Taylor-Michael (Taylor-Maccoll) method;
solving a reference flow field by using a 1 st flow field unit and an object plane as boundary conditions through a swirled characteristic line method;
and according to the given waverider trailing edge line, determining the upper and lower surfaces of the waverider through streamline tracking, and generating the waverider.
Wherein the control equation for the 1 st flow field unit is as follows:
；
；
in the middle ofIs the velocity of the vertex ray direction, +.>Is the velocity of the ray normal, +.>Is sound velocity, & lt & gt>Is the angle between the ray emitted from the vertex and the x-axis. No value range exists. The right end of the formula is a known quantity, the left end +.>Also known, the unknown isAnd 2 equations solve 2 unknowns, and solve the ordinary differential equation set through a Dragon-Greek tower method to obtain the 1 st flow field unit. Figure 2 illustrates a 1 st flow field cell mach number cloud of 2 different incoming flow mach numbers in an embodiment wherein (a) is a 1 st flow field cell mach number cloud of 3 for an incoming flow mach number at an object plane angle of 30 °; (b) Mach number cloud for the 1 st flow field unit with incoming flow Mach number of 5 and object plane angle of 30 degrees.
The reference flow field is solved by a method of a rotation characteristic line, and the control equation is as follows:
；
；
；
；
；
where x represents the coordinates of the x-axis, y represents the coordinates of the y-axis,is the flow direction angle +.>Is the mach angle, subscript + denotes the left line feature line, subscript-denotes the right line feature line, and subscript 0 denotes the streamline. />Is the x-axis direction velocity, +.>Is the y-axis direction speed, +.>Is the closing speed->Is Mach number->Density (I)>Is a flow characteristic factor.
And solving the ordinary differential equation set by a second-order Euler method to obtain the reference flow field. As shown in fig. 3, a flow field mach number cloud obtained by solving a swirled characteristic line in one embodiment is shown.
Finally, according to the given waverider trailing edge line, the upper and lower surfaces of the waverider are determined through streamline tracking, and the waverider is generated, as shown in fig. 4, which is a waverider appearance diagram finally obtained by an embodiment.
Under the pressure matching condition, the outlet pressure of the supersonic velocity air film spray pipe is consistent with the surface pressure of the waverider, and according to the relation between the Mach number of the supersonic velocity air film and the isentropic flow, the method comprises the following steps:
；
obtaining the outlet pressure of the supersonic velocity air film spray pipeWherein->Is the specific heat ratio of the gas +.>Is supersonic speed air film Mach number->The total pressure of the air film, namely the total pressure of the air source provided for the supersonic air film spray pipe in the waverider body is a known quantity.
Throat height of supersonic velocity air film spray pipeDetermined by the following formula:
；
in the middle ofIs the specific heat ratio of the gas, +.>Is a gas constant->Is still warm and is filled with->Is the outlet pressure of the supersonic velocity air film spray pipe,is the supersonic gas film mach number.
Nozzle outlet height of supersonic velocity air film nozzleDetermined by the following formula:
；
in the middle ofIs the throat height of the supersonic velocity air film spray pipe, +.>Is the specific heat ratio of the gas, +.>Is the supersonic gas film mach number.
In the design method of the supersonic air film spray pipe provided by the embodiment, the adopted parabolic potential function equation is as follows:
；
in the middle ofIs critical sound velocity of sound velocity line of throat part of supersonic velocity air film spray pipe,/-for>Is the axial velocity of sonic velocity line at the throat of the supersonic velocity air film spray pipe,/->The radial velocity of the sonic velocity line at the throat of the supersonic velocity air film spray pipe is the radial velocity, and x and y respectively represent the x-axis coordinate and the y-axis coordinate on the sonic velocity line at the throat of the supersonic velocity air film spray pipe.
And solving the parabolic potential function equation by adopting a series expansion method for the transonic flow of the throat part of the supersonic gas film spray pipe to obtain a transonic solution of the supersonic gas film spray pipe, as shown in figure 5. Figure 5 is a throat portion of the supersonic velocity air film nozzle,the throat height is the throat height, the broken line is the sonic velocity line, and the sonic velocity line is obtained by solving the transonic velocity solution of the supersonic velocity air film spray pipe, and the Mach number of the sonic velocity line is 1. Upstream (left) of the sonic line is the subsonic region, with Mach numbers less than 1. Downstream (right) of the sonic line is the supersonic region, with Mach numbers greater than 1.
In the design method of the supersonic air film nozzle provided by the embodiment, the supersonic air film nozzle transonic solution and the nozzle outlet are respectively used as a starting point and a finishing point, mach number distribution of the supersonic air film nozzle axis is set, as shown in fig. 6, according to the supersonic air film nozzle transonic solution boundary condition and the supersonic air film nozzle transonic solution boundary condition, namely the supersonic air film nozzle transonic solution and the nozzle outlet are respectively used as the starting point and the finishing point, and position coordinates, mach number and Mach number 1-order derivatives of the starting point and the finishing point are substituted into a B spline curve expression to obtain Mach number distribution of the supersonic air film nozzle axis.
In the design method of the supersonic air film spray pipe provided by the embodiment, the supersonic air film spray pipe transonic solution, the spray pipe outlet and Mach number distribution of the supersonic air film spray pipe axis are used as boundary conditions, a supersonic air film spray pipe characteristic line grid is constructed based on a characteristic line method, a supersonic flow field in the supersonic air film spray pipe is solved, and further a spray pipe non-sticking line is determined according to a streamline control equation, as shown in fig. 7, in the embodiment, a spray pipe characteristic line network and a spray pipe non-sticking line schematic diagram are provided. The characteristic line method is a conventional technical means in the field, a two-dimensional flow hyperbolic equation is solved by adopting the characteristic line method to design the supersonic air film spray pipe, and the supersonic air film spray pipe with a two-dimensional structure has complete internal wave elimination, so that the shock wave is fundamentally eliminated, and the flow field parameters such as pressure, temperature, speed and the like are controllable in distribution. Two eigenvalue equations are given below:
characteristic line method equation 1:
；
characteristic line method equation 2:
；
in the middle ofThickness for loss of momentum>Mach angle->For local Mach number->Is a gasSpecific heat ratio of (c). />Is a flow characteristic factor.
The streamline control equation is:；
in the middle ofIs axial speed, +.>Is the radial velocity.
In the design method of the supersonic velocity air film spray pipe provided by the embodiment, the boundary layer displacement thickness is solved through the following formulas：
；
；
；
In the middle ofIs the thickness of the loss of momentum, +.>Is the boundary layer displacement thickness, +.>Is wall angle->Is boundary layer shape factor>Is a compressible friction coefficient>For local Mach number->Is the specific heat ratio of the gas.
Further, the boundary layer displacement thickness is obtained according to the methodThen, the non-sticking line of the spray pipe is increased in the normal directionIs used for achieving viscosity correction.
It is understood that, a person skilled in the art may use an existing method or use a direct given method to pre-define the designed contraction section profile of the supersonic gas film nozzle according to experience, and the specific design method of the contraction section profile of the supersonic gas film nozzle is not limited in this application.
In a preferred embodiment, a design method of a contraction section profile of a supersonic gas film spray pipe is provided, wherein the coordinates of each point on the contraction section profile of the supersonic gas film spray pipe are [ ]x,y) Determined from the cubic curve, as follows:
；
wherein the method comprises the steps ofIs the inlet height of the supersonic velocity air film jet pipe, < + >>Is the throat height of the supersonic velocity air film spray pipe, +.>Is a given shrink section length.
In a preferred embodiment, a design method of a contraction section profile of a supersonic gas film spray pipe is provided, wherein the coordinates of each point on the contraction section profile of the supersonic gas film spray pipe are [ ]x,y) Determined from the victims curve as follows:
；
wherein the method comprises the steps ofIs the inlet height of the supersonic velocity air film jet pipe, < + >>Is the throat height of the supersonic velocity air film spray pipe, +.>Is a given shrink section length.
In a preferred embodiment, a design method of a contraction section profile of a supersonic gas film spray pipe is provided, wherein the coordinates of each point on the contraction section profile of the supersonic gas film spray pipe are [ ]x,y) Determined from the hyperbola, as follows:
；
wherein the method comprises the steps ofIs the inlet height of the supersonic velocity air film jet pipe, < + >>Is the throat height of the supersonic velocity air film spray pipe, +.>Is given the length of the constriction->Is the relative position of the connecting point of the hyperbola, taking +.>。
The supersonic air film jet pipe designed by the design method of the supersonic air film jet pipe has complete wave elimination, fundamentally eliminates shock waves, has controllable flow field parameter distribution of pressure, temperature, speed and the like, can carry out viscosity correction by depending on a von Karman momentum equation, and is suitable for generating a supersonic air film required by the surface heat reduction stealth of a high-speed wave-taking aircraft.
In order to verify the effectiveness of the above-mentioned design method of the high-speed waverider with the pressure-matching supersonic cooling air film, a simulation example is provided below:
as shown in fig. 8, the high-speed wave multiplier with the pressure-matched supersonic cooling air film designed by the embodiment isolates the high Wen Lailiu of the wave multiplier aircraft and avoids the direct heating of the wave multiplier and the optical window by the high Wen Lailiu. It can be seen that the surface temperature of the wave-taking aircraft downstream of the jet pipe is reduced from 1300K to 400K, and the heat reducing effect is obvious. Also shown in fig. 8 are supersonic film streamlines, and it can be seen that the film uniformly covers downstream along the waverider aircraft wall without flow separation, and thus the effective coverage length is up to the aircraft tail. In this process, although the film-main flow structure is continuously mixed, the film is continuously heated by the main flow, but the cooling effect can still control the temperature below 800K at the tail of the aircraft.
The invention is not a matter of the known technology.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples merely represent a few embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the invention. It should be noted that it would be apparent to those skilled in the art that various modifications and improvements could be made without departing from the spirit of the present application, which would be within the scope of the present application. Accordingly, the scope of protection of the present application is to be determined by the claims appended hereto.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
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| CN116894303A (en) * | 2023-06-06 | 2023-10-17 | 中国人民解放军国防科技大学 | Design method of supersonic nozzle, supersonic nozzle and high temperature supersonic wind tunnel test platform |
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