CN109815549B - Design method of single-pair supersonic flow direction vortex generating device - Google Patents
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Abstract
The invention discloses a design method of a single-pair supersonic flow direction vortex generating device. The method comprises the steps of specifying the arc radius of an upper wall surface, dividing a vortex generation section into a plurality of infinitesimal sections with equal deflection angles, gradually solving a streamline equation from the end point of the lower wall surface of a transition section to the downstream by solving an ultrasonic arc outer flow field to obtain an initial lower wall surface molded line, and then superposing the displacement thickness of a local boundary layer to the initial lower wall surface molded line to obtain a final lower wall surface molded line; and then, determining an equivalent expansion angle, and designing the molded lines of the upper wall surface and the lower wall surface of the test window. The design method utilizes the streamline of the supersonic circular arc outer flow field to construct the vortex generation section, avoids unnecessary background wave systems generated in the vortex generation section, and can realize the control of the strength and the scale of the supersonic flow direction vortex only by changing the curvature radius of the vortex generation section. The design method of the test device is feasible for carrying out experimental research on the characteristics of supersonic flow direction vortex in the scramjet engine and the interference mechanism between the supersonic flow direction vortex and downstream shock wave strings.
Description
Technical Field
The invention relates to the field of pneumatic experiments of scramjet engines, in particular to a design method for generating supersonic vortices.
Background
Supersonic flow vortices are a common flow phenomenon, especially in high mach number inlet ducts, and flow vortices are the main flow characteristic inside them. The generation of the supersonic flow vortex is mainly related to the separation flow formed by coherent induction of a shock wave/boundary layer, and because of the requirement of practical engineering design, the shock wave/boundary layer interference in the air inlet channel is generally strong, the supersonic flow vortex is difficult to avoid as an accessory. The existence of the flow direction vortex is like a double-edge sword, and for combustion, the mixing of airflow and fuel oil can be enhanced by means of the flow direction vortex, so that the combustion efficiency is improved; however, for the inlet, the existence of the flow vortex may be more "bad than good" mainly because the low total pressure air is gathered in the flow vortex, and the air is most sensitive to the backpressure gradient and is a short plate with the backpressure resistance capability of the whole inlet cross section, once the high backpressure formed by the downstream combustion is applied to the vortices, the shock wave cluster is likely to be promoted to overflow the inlet pipeline, the non-starting phenomenon of the inlet is induced, and the flight safety is damaged. Therefore, it is important to study the supersonic flow direction vortex in the pipe.
For the necessity of research, how to simulate supersonic flow direction vortex in the experiment is the basic condition for carrying out the related research. However, the existing theory and test method are based on a vortex generator, which can actually and effectively generate a flowing vortex, but while generating the flowing vortex, an oblique shock wave generated by a vortex generator slope and an expansion fan at the tail are introduced, and the existence of the oblique shock wave and the expansion fan can form reflection in a pipeline, when the oblique shock wave and the expansion fan are incident into a supersonic flowing vortex, irreversible influence is caused on the characteristics of development, evolution, breakage and the like of the flowing vortex, so that if the flowing characteristic of the supersonic flowing vortex in the pipeline and the coupling interference problem of the supersonic flowing vortex and downstream shock wave series flow need to be simply researched, the vortex generator scheme is not suitable.
Therefore, how to design the supersonic flow direction vortex in the pipeline by a pneumatic design method and avoid the interference of background wave systems such as other oblique shock waves, expansion waves and the like is a key problem which needs to be solved urgently at present.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for designing a single-pair supersonic flow direction vortex generating device without a background wave system, which can generate a fully developed single-pair supersonic flow direction vortex without a background wave system, and has good versatility.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a design method of a single pair of supersonic flow direction vortex generating devices comprises a Laval nozzle, a transition section, a vortex generating section and a test window which are connected in sequence; the design of the vortex generation section comprises the following steps:
(1) calculating to obtain the total deflection angle theta of the vortex generation section through a Prandtl-Meyer relational expression according to the Mach number of the outlet of the Laval nozzle and the Mach number requirement of the test window;
(2) averagely dividing the total deflection angle theta of the vortex generation section into n parts of deflection angles delta theta, wherein each part of deflection angle delta theta corresponds to an arc infinitesimal section;
(3) setting the curvature radius of the upper wall surface of the vortex generation section as R;
(4) the first right-going expansion wave L in the vortex generation section1Starting point A1Establishing a rectangular coordinate system for an origin, wherein two coordinate axes of the rectangular coordinate system are an x axis and a y axis, and the outlet airflow direction of the vortex generation section is taken as the positive x axis;
(5) calculating to obtain a first right-going expansion wave L according to the Mach number of the outlet of the Laval nozzle1Equation of the straight line, right-hand expansion wave L1The intersection point of the lower wall surface of the transition section, namely the bending starting point B of the lower wall surface of the vortex generation section1；
(6) Solving a first right-going expansion wave L according to the Laval nozzle outlet Mach number, the total static temperature relational expression and the energy equation1The later flow field parameters;
(7) solving the second right-going expansion wave L according to the geometric relation between the arc radius R and the deflection angle delta theta2
Starting point A2Coordinates; and solving the nth right-going expansive wave L according to the relation2Starting point AnCoordinates;
(8) l obtained according to step (6)1Back flow field parameters, and solving a second right-going expansion wave L2The linear equation of (a);
(9) l obtained according to step (6)1Back flow field parameters, solving for streamline m2The linear equation of (a);
(10) simultaneous L2、m2Linear equation to obtain the second right-going expansion wave L2Intersection point B with lower wall surface of transition section2；
(11) Repeating the steps (6) to (10), and respectively solving the B3，B4…BnThe coordinates of (a); wherein B isnIs divided intoRespectively is the intersection point of the nth right-going expansion wave and the lower wall surface of the transition section;
(12) calculating the displacement thickness of the local boundary layer based on the solved flow field parameters, and amplifying A1～AnAnd B1～BnThe area of the flow channel formed.
The key of the design method of the single-pair supersonic flow direction vortex generating device provided by the invention is as follows: according to the requirements of the outlet Mach number of the Laval nozzle and the design Mach number of a test window, the radius of an upper wall surface arc is specified, a vortex generation section is divided into a plurality of infinitesimal sections with equal deflection angles, a streamline equation is gradually solved from the end point of the lower wall surface of a transition section to the downstream by solving an ultrasonic speed arc outer flow field, so that lower wall surface profile line discrete points are obtained, and the discrete points form the lower wall surface; and then, calculating an equivalent expansion angle based on the displacement thickness of the outlet boundary layer of the vortex generation section, and designing the molded lines of the upper wall surface and the lower wall surface of the test window.
Compared with the prior art, the invention has the following beneficial effects:
the design method skillfully utilizes the supersonic speed circular arc outer flow field flow line to construct the vortex generation section, can effectively avoid generating unnecessary background wave systems in the vortex generation section, is simple and convenient, is easy to realize programs, and can realize the control of the strength and the scale of the supersonic speed flow direction vortex only by changing the curvature radius of the vortex generation section. The design method of the test device is feasible for carrying out experimental research on the interference mechanism of shock wave clusters and supersonic flow direction vortexes in the scramjet engine.
Drawings
FIG. 1 is a schematic diagram illustrating the flow field parameters and design of a single pair of supersonic flow direction vortex generating devices without background wave system.
FIG. 2 is a graph showing the relationship between the vortex intensity and the radius of curvature of the upper wall surface of the vortex generation section, wherein Q is the vortex intensity.
FIG. 3 is a schematic view of a profile correction method, wherein CiThe curve is the profile after the test window is corrected.
FIG. 4 shows the profile of the vortex generation section and the test window designed by the method of the present invention.
FIG. 5 is a flow chart of the design of a vortex generating section of a single pair of supersonic flow direction vortex generating devices without background wave system.
Detailed Description
The invention discloses a design method of a single-pair supersonic flow direction vortex generating device without a background wave system. Referring now to FIG. 1, the method of the present invention is described in detail with reference to the preferred embodiments.
(1) Based on the laboratory's existing vacuum source, its volume is 400m 33 vacuum pumps. Determining the Mach number M of the outlet of the Laval nozzle according to the suction flow of the vacuum pump based on a flow equation and by considering the test time 02, the throat area is 23703mm2. According to the equal relation between the throat and the outlet flow of the Laval nozzle, the height of the outlet of the Laval nozzle can be determined to be 200mm, and the width of the outlet of the Laval nozzle can be determined to be 200 mm;
(2) the molded line from the throat section to the outlet section of the laval nozzle is designed by a characteristic line method, and the characteristic line method design can refer to known prior art documents Maurice J.Zucrow, Joe D.Hoffman, Gas dynamic, Volume II, pp 83;
(3) the upper and lower wall surfaces of the transition section have micro-expansion, and the expansion angle is 0.5 degrees;
(4) the detailed flow of the design of the vortex generation section is as follows:
1) setting the Mach number M of the test window n3, by the prant-meier relationship:
θ＝ν(M0)-ν(Mn)
and obtaining the total deflection angle theta of the vortex generation section. In the formula, gamma is a specific heat ratio, 1.4 is taken for air gamma, and Ma is Mach number after an expansion wave;
2) averagely dividing the total deflection angle theta of the vortex generation section into 23 parts, wherein the deflection angle delta theta of each part is approximately equal to 1 degree;
3) giving the radius of curvature of the upper wall surface of the vortex generation section as R1 m;
4) the first right-going expansion wave L in the vortex generation section1Starting point A1A rectangular coordinate system is established for the origin, and the outlet airflow direction 7 of the vortex generation section 3 is taken as the positive direction of the x axis;
5) calculating to obtain a first right-going expansion wave L according to the Mach number of the outlet of the Laval nozzle1Equation of straight line L1：y＝-tan(α1+ θ) × x, wherein α1The Mach angle of the first right-going expanding wave is calculated by referring to the following formula. L is1The point of intersection with the wall profile 6 of the vortex generation section, namely the starting point B of the wall curvature of the vortex generation section1At point B1Before, the wall profile 6 of the vortex generation section is consistent with the wall profile of the transition section 2:
in the above formula, αi、MiRespectively obtaining a Mach angle and a Mach number after the ith right-row expansion wave, and setting the first right-row expansion wave i to be 1;
6) given total temperature T*Calculating the ith right-going expansion wave L as 300KiThe latter flow field parameters are sequentially solved T, V, and finally the right-going expansion wave L is solvediRear velocity component Vxi、VyiThe calculation process is as follows:
Vxi＝VcosΔθ；
Vyi＝VsinΔθ；
wherein, T*T is the total temperature and the static temperature after the ith right-going expansion wave, Vxi、VyiRespectively the velocity components of the velocity vector V in the flow field after the ith right-line bulge wave in the x direction and the y direction; rgTaken as a constant, 287;
7) setting the upper wall surface point AiThe coordinate is (x)i，yi) Wall lower point BiThe coordinate is (k)i，ji) The center O coordinate is (x)o＝x1+Rsinθ,yo＝y1+ Rcos theta), solving the starting point A of the i +1 th right-going expansion wave according to the geometric relation between the arc radius R and the deflection angle delta thetai+1(xi+1,yi+1) Coordinates;
xi+1＝xO-Rsin(θ-iΔθ)；
yi+1＝yO-Rcos(θ-iΔθ)；
8) according to the obtained speed components V in the x and y directions after the ith right-going expansion wavexi、VyiSolving straight line mi+1Slope g ofi；
According to the right-hand line-expansion wave Mach angle αiSolving straight line L in relation to deflection angle delta thetai+1Slope h ofiNamely:
hi＝-tan(αi+1+θ-iΔθ)；
9) according to the right-hand bulge wave end point Bi(ki,ji) Coordinate and straight line mi+1Slope g ofiGive a straight line mi+1According to the right-hand bulge wave starting point Ai+1(xi+1,yi+1) Coordinates and straight line Li+1Slope h ofiGives a straight line Li+1The equation of (c):
10) simultaneous straight line Li+1Line mi+1Solving the intersection point B of the equationsi+1Coordinates;
11) repeating the above process, respectively solving for B2，B3，B4…BnThe coordinates of (a);
12) will find the point BiSequentially connected to form a wall surface type of the vortex generation sectionA wire;
13) referring to fig. 3, B may be derived based on the solved flow field parametersi-1And BiPoint coordinates, perpendicular to the tangent line of the two points, and calculating the displacement thickness of the local boundary layer at Bi-1And BiOn the perpendicular line of the point tangent line with Bi-1、BiTaking a point C of length equal to the starting pointi-1、CiNote that this time at Bi-1、BiTwo points are respectively arranged above and below the flow channel, and the point for expanding the flow channel is taken to enlarge A1-AnAnd B1-BnThe area of the formed flow passage is determined by finding the straight line Ci-1CiThe intercept of (2) is a straight line with a smaller intercept on the lower wall surface of the channel. A straight line with a large intercept is taken on the upper wall surface of the channel. The local boundary layer displacement thickness is calculated as follows:
wherein, RexIs the local Reynolds number;
(5) referring to fig. 4, the profile of the vortex generation section and the test window are designed by the above method, and when the profile is corrected, the upper and lower wall surfaces of the test window are deflected outwards by 0.5 degrees compared with the upper and lower wall surfaces of the outlet of the vortex generation section. A flow chart of the above-described vortex generation section design method is shown in fig. 5.
In addition, the present invention has many specific implementations and ways, and the above description is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be construed as the protection scope of the present invention.
Claims (6)
1. A design method of a single pair of supersonic flow direction vortex generating devices is characterized in that: the single-pair supersonic flow direction vortex generating device comprises a Laval nozzle (1), a transition section (2), a vortex generating section (3) and a test window which are connected in sequence; wherein the design of the vortex generation section (3) comprises the following steps:
(1) calculating to obtain the total deflection angle theta of the vortex generation section (3) according to the Mach number of the outlet of the Laval nozzle and the Mach number requirement of a test window by using a Prandtl-Meyer relational expression;
(2) averagely dividing the total deflection angle theta of the vortex generation section (3) into n parts of deflection angles delta theta, wherein each part of deflection angle delta theta corresponds to an arc infinitesimal section;
(3) setting the curvature radius of the upper wall surface (5) of the vortex generation section as R;
(4) the first right-going expansion wave L in the vortex generation section1Starting point A1Establishing a rectangular coordinate system for an origin, wherein two coordinate axes of the rectangular coordinate system are an x axis and a y axis, and the outlet airflow direction (7) of the vortex generation section (3) is taken as the positive direction of the x axis;
(5) calculating to obtain a first right-going expansion wave L according to the Mach number of the outlet of the Laval nozzle1Equation of the straight line, right-hand expansion wave L1The intersection point of the lower wall surface of the transition section (2) and the lower wall surface of the vortex generation section is the bending starting point B of the lower wall surface of the vortex generation section1；
(6) Solving the ith right-going expansion wave L according to the Mach number of the outlet of the Laval nozzle, the relation of the total static temperature and the energy equationiThe latter flow field parameters, i ═ 1 to n,
wherein the total static temperature is given by
The energy equation is
Wherein, T*T is the total temperature and the static temperature after the ith right-going expansion wave, Vxi、VyiRespectively the velocity components of the velocity vector V in the flow field after the ith right-line bulge wave in the x direction and the y direction; rgIs a constant; miThe Mach number of the ith channel after the right-going expansion wave; gamma is the specific heat ratio;
(7) solving the i +1 th right-going expansion wave L according to the geometric relation between the arc radius R and the deflection angle delta thetai+1Starting point Ai+1(xi+1,yi+1) Coordinates; 1,2, … n-1;
xi+1＝xO-Rsin(θ-i△θ)；
yi+1＝yO-Rcos(θ-i△θ)；
wherein xO、yOA coordinate as a circle center O;
(8) l obtained according to step (6)iThe flow field parameters are then solved for the i +1 th right-going expansion wave Li+1The linear equation of (a);
(9) l obtained according to step (6)iThe later flow field parameters, solving the streamline mi+1The linear equation of (a);
(10) simultaneous Li+1、mi+1Linear equation to obtain the i +1 th right-going expansion wave Li+1The intersection point B of the lower wall surface of the transition section (2)i+1；i＝1,2,…n-1；
(11) Repeating the steps (6) to (10), increasing the value of i by 1 in each repetition, and respectively solving the A3，A4…AnAnd B3，B4…BnThe coordinates of (a); wherein B isnNamely the intersection points of the nth right-going expansion wave and the lower wall surface of the transition section (2);
(12) calculating the displacement thickness of the local boundary layer based on the solved flow field parameters, and amplifying A1～AnAnd B1～BnThe area of the flow channel formed.
2. The design method according to claim 1, wherein: the geometrical configuration of the Laval nozzle is a binary nozzle, the throat area of the Laval nozzle is determined according to the laboratory gas source capacity, and the exit Mach number in the design state is determined according to the test requirement.
3. The design method according to claim 1, wherein: the molded line of the Laval nozzle from the throat section to the outlet section is designed by a characteristic line method.
4. The design method according to claim 1, wherein: the width of the transition section is consistent with that of the Laval nozzle, the upper wall surface and the lower wall surface of the transition section are slightly expanded, and the expansion angle is 0-1 degrees.
5. The design method according to claim 1, wherein: the upper wall surface and the lower wall surface of the test window (4) are deflected outwards compared with the upper wall surface and the lower wall surface of the outlet of the vortex generation section to form a micro-expansion pipeline, and the unilateral expansion angle delta beta is 0.5-1.0 degrees.
6. The design method according to claim 1, wherein: and establishing a mapping relation between the vortex intensity of the test window and the curvature radius R of the upper wall surface (5) of the vortex generation section by a simulation method or a test method, and selecting a proper curvature radius R of the upper wall surface (5) of the vortex generation section according to the mapping relation.
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