CN103321779B - Supersonic Nonuniform incoming flow Maximum Thrust Nozzle and wall defining method thereof - Google Patents

Abstract

The invention provides a kind of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle and wall defining method thereof.The wall defining method of this Supersonic Nonuniform incoming flow Maximum Thrust Nozzle comprises the following steps: S1: according to heterogeneous loose body parameter, determines the initial boundary of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle; S2: according to initial boundary, utilizes method of characteristics, determines the nucleus of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle; S3: according to conservation of mass theorem and method of characteristics, solves in nucleus inner iteration, determines the wall molded line of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle; S4: according to the wall of the wall molded line determination Supersonic Nonuniform incoming flow Maximum Thrust Nozzle of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.According to Supersonic Nonuniform incoming flow Maximum Thrust Nozzle of the present invention and wall defining method thereof, a kind of Maximum Thrust Nozzle being suitable for Supersonic Nonuniform incoming flow can be obtained.

Description

Supersonic Nonuniform incoming flow Maximum Thrust Nozzle and wall defining method thereof

Technical field

The present invention relates to aerodynamic design field, more specifically, relate to a kind of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle and wall defining method thereof.

Background technique

For the hypersonic aircraft using scramjet engine, the ram drag of scramjet engine is very large, and gross thrust is increased to 10 with the ratio of net thrust by 1 of traditional airbreathing motor.Ejector exhaust pipe is the critical piece that motor produces thrust, and when flight Mach number is 6.0, the thrust that it produces can account for about 70% of motor gross thrust, is not difficult to find out thus, and the quality of ejector exhaust pipe design directly can have influence on the performance of whole motor.Paper " ExhaustNozzleContourforOptimumThrust " (G.V.R.Rao, JetPropulsion, Vol.28, No.6June1958) proposes the Maximum Thrust Nozzle design method based on uniform incoming flow, and the design process of the method is as follows:

(1) given nozzle entry uniformity parameter distribution, jet pipe length and external pressure.

(2) at venturi place to the circular arc of several angle as initial bubble section, utilize irrotationality method of characteristics to solve the domain of influence of initial bubble circular arc, this domain of influence is core area.

(3) in core area, carry out iterative, finally determine 1 D, the nozzle contour that this D the is corresponding maximum thrust met under this external pressure requires and the restriction of jet pipe length.

(4) conservation of mass and irrotationality method of characteristics is utilized to solve the wall molded line of jet pipe.

Under uniform incoming flow condition, above-mentioned design method can realize the maximum thrust of jet pipe, but ultrasound velocity jet pipe incoming flow exists heterogeneity, and existing method can not directly expand in the design of nonuniform flow nozzle contour curve.

Summary of the invention

The present invention aims to provide a kind of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle and wall defining method thereof, can obtain a kind of Maximum Thrust Nozzle being suitable for Supersonic Nonuniform incoming flow.

For solving the problems of the technologies described above, according to an aspect of the present invention, provide a kind of wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, comprise the following steps: S1: according to heterogeneous loose body parameter, determine the initial boundary of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle; S2: according to initial boundary, utilizes method of characteristics, determines the nucleus of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle; S3: according to conservation of mass theorem and method of characteristics, solves in nucleus inner iteration, determines the wall molded line of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle; S4: according to the wall of the wall molded line determination Supersonic Nonuniform incoming flow Maximum Thrust Nozzle of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.

Further, in the step of S1, the method that heterogeneous loose body parameter adopts numerical simulation or test to measure is determined.

Further, in the step of S1, the Mach number of the discrete point on initial boundary is greater than 1.0.

Further, the scope of the Mach number of the discrete point on initial boundary is 1.01 to 1.10.

Further, the step of S2 comprises: with the first end points of initial boundary for true origin, and initial boundary is the axis of Y-axis determination Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, and the axis of the Supersonic Nonuniform incoming flow Maximum Thrust Nozzle determined overlaps with X-axis.

Further, the step of S2 also comprises: the domain of influence utilizing method of characteristics determination initial boundary.

Further, the step of S2 also comprises: after determining the domain of influence, and at the double-pointed downstream given initial bubble wall molded line near initial boundary, wherein, the first end points of initial bubble wall molded line overlaps with the second end points of initial boundary.

Further, the step of S2 also comprises: after given initial bubble wall molded line, utilize method of characteristics, determine the left lateral characteristic line that the discrete point on initial bubble wall molded line sends and right lateral characteristic line, the net region of left lateral characteristic line and right lateral characteristic line composition is nucleus.

Further, the step of S3 comprises: S31: set up chain of command, make chain of command crossing with the meridian plane of any point crossed in nucleus, and their intersection line overlaps with the left lateral characteristic line of initial bubble wall molded line, the flow parameter of any point wherein in nucleus is determined by initial boundary and initial bubble wall molded line.

Further, the step of S3 also comprises: S32: utilize conservation of mass theorem, method of characteristics and equation (1) and (2) to determine coordinate and the flow parameter of the discrete point on intersection line,

$\frac{V\cos (\mathrm{\θ}-\mathrm{\α})}{\cos \mathrm{\α}}=C_1---\left(1\right)$

yρV ²sin ²θtanα=C ₂（2）

Wherein, V is speed of incoming flow, and y is the y coordinate of the discrete point on intersection line, and θ is the flow angle of the discrete point on intersection line, and α is the Mach angle of the discrete point on intersection line, and ρ carrys out current density, C ₁, C ₂it is constant.

Further, the step of S3 also comprises: S33: the flow parameter of the end points away from X-axis on intersection line is substituted into equation (3) and equation (4), if the end points away from X-axis on intersection line does not meet equation (3) and equation (4), then repeat the step of S31 to S32; If the end points away from X-axis on intersection line meets equation (3) and equation (4), be then the outlet end points of the wall of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle away from the end points of X-axis,

$L=x_C+{\∫}_C^E\cot \mathrm{\φdy}---\left(3\right)$

$\sin 2\mathrm{\θ}=\frac{p-p_{\mathrm{amb}}}{\frac{1}{2}\mathrm{\ρ}{V}_1^2}\cot \mathrm{\α}---\left(4\right)$

Wherein, x _cbe the abscissa of intersection line close to the end points of X-axis, L is the length of given jet pipe, and φ is the inclination angle of outlet end points relative to the axis of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, p _ambbe given external pressure, p is the pressure of outlet end points, V ₁be the speed of outlet end points, α is the Mach angle of outlet end points, and θ is the flow angle of outlet end points, and E represents the end points away from X-axis of intersection line, and C represents the end points close to X-axis of intersection line.

Further, the step of S3 also comprises: S34: after determining the outlet end points of the wall of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, according to conservation of mass theorem and method of characteristics, determines the wall molded line of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.

Further, further comprising the steps of: S5: after determining the wall of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, adopt momentum integral relation to solve the displacement thickness that ultrasound velocity obtains uniform incoming flow Maximum Thrust Nozzle boundary layer, carry out boundary layer viscous correction.

Further, method of characteristics revolves method of characteristics for having.

According to a further aspect in the invention, provide a kind of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, this Supersonic Nonuniform incoming flow Maximum Thrust Nozzle comprises wall, and the wall of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle is determined by above-mentioned method.

Apply technological scheme of the present invention, the wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle comprises the following steps: according to heterogeneous loose body parameter, determines the initial boundary of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle; According to initial boundary, utilize method of characteristics, determine the nucleus of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle; According to conservation of mass theorem and method of characteristics, solve in nucleus inner iteration, determine the wall molded line of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle; According to the wall of the wall molded line determination Supersonic Nonuniform incoming flow Maximum Thrust Nozzle of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.According to method of the present invention, the ultrasound velocity Maximum Thrust Nozzle being suitable for heterogeneous loose body can be obtained, the design process of this jet pipe considers the situation of heterogeneous loose body, can be combined well, improve the thrust of supersonic nozzle with the actual application environment of jet pipe.

Accompanying drawing explanation

The accompanying drawing forming a application's part is used to provide a further understanding of the present invention, and schematic description and description of the present invention, for explaining the present invention, does not form inappropriate limitation of the present invention.In the accompanying drawings:

Fig. 1 diagrammatically illustrates the heterogeneity of incoming flow flow angle in the present invention;

Fig. 2 diagrammatically illustrates the heterogeneity of speed of incoming flow in the present invention;

Fig. 3 diagrammatically illustrates geometrical shape and the flow field model figure of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle of the present invention;

Fig. 4 diagrammatically illustrates the flowing of the infinitesimal of chain of command of the present invention; And

Fig. 5 diagrammatically illustrates the solution procedure of method of characteristics of the present invention.

Embodiment

Below in conjunction with accompanying drawing, embodiments of the invention are described in detail, but the multitude of different ways that the present invention can be defined by the claims and cover is implemented.

According to embodiments of the invention, the wall of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle is determined by following defining method.

Shown in composition graphs 1 and Fig. 2, first, carry out step S1: according to heterogeneous loose body parameter, determine the initial boundary of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.Particularly, the heterogeneous loose body parameter of the method determination nozzle entry measured by numerical simulation or test, incoming flow parameter here comprises flow angle, speed, temperature and pressure.These four parameters can be expressed as with the function of coordinate y successively: θ=θ (y), V=V (y), T=T (y), p=p (y), and these four functions are subtraction function.

Shown in composition graphs 3, after determining heterogeneous loose body parameter, according to known heterogeneous loose body parameter, determine the initial boundary of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.Preferably, the Mach number of the discrete point on initial boundary is greater than 1.0.More preferably, the scope of the Mach number of the discrete point on initial boundary is 1.01 to 1.10.In order to indicate the border of jet pipe, the Mach number that also show nozzle entry in Fig. 3 is greater than the border IT of the 1 and border it of upstream wall.

After carrying out step S1, carry out step S2: according to initial boundary, utilize method of characteristics, determine the nucleus of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.Particularly, with the first end points O of initial boundary OT for true origin, initial boundary OT is the axis of Y-axis determination Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, and the axis of the Supersonic Nonuniform incoming flow Maximum Thrust Nozzle determined overlaps with X-axis.

After determining the axis of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, method of characteristics is utilized to solve the domain of influence TOT ' of initial boundary OT, coordinate and the flow parameter distribution of the characteristic line TT ' of a T must be, determine that the nucleus of the maximum jet pipe of Supersonic Nonuniform incoming flow is prepared for follow-up.Wherein, T ' is positioned in the X-axis of coordinate axes.

Determine that domain of influence TOT ' afterwards, the given initial bubble wall molded line TB near T point downstream (forward of X-axis), wherein initial bubble wall molded line TB is circular arc, the center of circle of circular arc is positioned in Y-axis, and this center of circle is greater than the distance of a T to true origin O to the distance of coordinate axes initial point O, the radius of circular arc is given according to the designing requirement of actual design Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.

After given initial bubble wall molded line TB, in conjunction with the characteristic line TT ' determined above, the left lateral characteristic line utilizing the discrete point on method of characteristics determination initial bubble wall molded line TB to send and right lateral characteristic line, the net region of left lateral characteristic line and right lateral characteristic line composition is the nucleus of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.

After determining nucleus, carry out step S3: according to conservation of mass theorem and method of characteristics, solve in nucleus inner iteration, determine the wall molded line of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.Particularly, comprise S31: set up a chain of command (not shown), make this chain of command crossing with the meridian plane (not shown) of any point D crossed in nucleus, and their intersection line is the left lateral characteristic line CDE of initial bubble wall molded line, C and E represents the point close to X-axis and the point away from X-axis of this left lateral characteristic line respectively, and the flow parameter of any point D wherein in nucleus is determined by initial boundary OT and initial bubble wall molded line TB.In other embodiments of the invention, any D in nucleus also can determine according to the mode of the left lateral characteristic line sent along the discrete point of X or Y of initial bubble wall molded line TB, can simplify iterative process to a certain extent like this.

After determining the intersection line CDE between chain of command and the meridian plane crossing D point, carry out S32: bring the flow parameter of D point into equation (1) and (2), determine constant C ₁, C ₂.The coordinate of discrete point on DE is brought into and determines C ₁, C ₂in the equation (1) of constant and (2), in conjunction with characteristic line valve and mass-conservation equation, solve the physical parameter of discrete point on DE.Wherein, equation (1) and (2) as follows:

$\frac{V\cos (\mathrm{\θ}-\mathrm{\α})}{\cos \mathrm{\α}}=C_1---\left(1\right)$

yρV ²sin ²θtanα=C ₂（2）

Wherein, V is speed of incoming flow, and y is the y coordinate of the discrete point on intersection line, and θ is the flow angle of the discrete point on intersection line, and α is the Mach angle of the discrete point on intersection line, and ρ carrys out current density, C ₁, C ₂it is constant.

The derivation of equation (1) and (2) and constant is as follows:

In order to calculate the thrust of jet pipe and the mass flowrate by jet pipe, choose a chain of command by nozzle exit.In Fig. 3, CE represents the intersection of chain of command and meridian plane.φ is the angle of line CE and axis, and it is the function of y.On axis, position sum functions φ (y) of C point determines chain of command completely.An infinitesimal length ds at distance axis y place is considered, as shown in Figure 4 along CE.Unit dimension dA=2 π yds is obtained by rotating about the axis.Wherein ds=dy/sin φ.

ρ, V and θ represent the density of incoming flow, speed and flow direction respectively, wherein think that the flow direction on micro-ds is identical.As follows by the mass flowrate of unit dimension

$\mathrm{\ρV}\frac{\sin (\mathrm{\φ}-\mathrm{\θ})}{\sin \mathrm{\φ}}2\mathrm{\πydy}$

The momentum flux in x direction is

${\mathrm{\ρV}}^2\frac{\sin (\mathrm{\φ}-\mathrm{\θ})\cos \mathrm{\θ}}{\sin \mathrm{\φ}}2\mathrm{\πydy}$

By can obtain the mass flowrate by chain of command along CE integration

$\mathrm{massflow}={\∫}_C^E\mathrm{\ρV}\frac{\sin (\mathrm{\φ}-\mathrm{\θ})}{\sin \mathrm{\φ}}2\mathrm{\πydy}---\left(a\right)$

Similarly, the thrust of jet pipe can be obtained along CE integral pressure difference and momentum flux

$\mathrm{thrust}={\∫}_C^E[(p-p_a)+{\mathrm{\ρV}}^2\frac{\sin (\mathrm{\φ}-\mathrm{\θ})\cos \mathrm{\φ}}{\sin \mathrm{\φ}}]2\mathrm{\πydy}---\left(b\right)$

In current problem, suppose that the entry condition of jet pipe is given, the condition therefore maximizing representation is above abundant.Axial distance between C and E is

$x_E-x_C={\∫}_C^E\cot \mathrm{\φdy}$

Therefore, nozzle-divergence segment length is

$\mathrm{length}=x_C+{\∫}_C^E\cot \mathrm{\φdy}---\left(c\right)$

The change of nozzle contour needs the change of corresponding chain of command.Immovable point C, changes φ and can obtain different chains of command.Given jet pipe length is depended in the position of some C.Can be regarded as fixing, because the change of nozzle contour is limited to given jet pipe length at problem mid point C herein.Therefore the condition below is satisfied.

${\∫}_C^E\cot \mathrm{\φdy}=\mathrm{const}---\left(d\right)$

The mass flowrate that conservation of mass requirement equation (a) provides equals the mass flowrate by jet pipe, and it does not change with the change of nozzle contour.Therefore the maximum thrust solving jet pipe is limited to equation (a) and (d).Utilize Lagrange multiplier method, this problem can be reduced to the maximum value solving lower Line Integral.

$I={\∫}_C^E(f_1+{\mathrm{\λ}}_2{f}_2+{\mathrm{\λ}}_3{f}_3)\mathrm{dy}---\left(e\right)$

Wherein

$f_1=[(p-p_a)+{\mathrm{\ρV}}^2\frac{\sin (\mathrm{\φ}-\mathrm{\θ})\cos \mathrm{\φ}}{\sin \mathrm{\φ}}]y$

$f_2={\mathrm{\ρV}}^2\frac{\sin (\mathrm{\φ}-\mathrm{\θ})}{\sin \mathrm{\φ}}y$

f ₃=cotφ

Wherein λ ₂, λ ₃it is Lagrange multiplier constant.

This problem to solve the first variation being to get I be 0, obtain the chain of command that needs and the flow direction along chain of command.First all possible variation of physical quantity in integral type is listed.In the following discussion, δ is the variation symbol of function, represents branch's differential by respective subscript.

Jet pipe region initial bubble hypothesis is below along profile line TBB'.B point represents the point producing initial bubble, and the right lateral characteristic line that B point sends and chain of command meet at a D.The change of B point downstream nozzle contour can not affect the flowing between CD.

In order to easy, the chain of command hypothesis between C and D is consistent with the left lateral characteristic line of characteristic line grid " core area ".This makes δ C, δ M in this region and δ θ be 0.φ=θ+α along CD is a known quantity, therefore δ φ=0.The position of some D, the namely place that extends to of initial bubble, be unknown quantity, therefore δ D is not equal to 0.

$\mathrm{\δI}=0={\∫}_{\mathrm{yD}}^{\mathrm{yE}}\{(f_{1M}+{\mathrm{\λ}}_2{f}_{2M}+{\mathrm{\λ}}_3{f}_{3M})\mathrm{\δM}+(f_{1\mathrm{\θ}}+{\mathrm{\λ}}_2{f}_{2\mathrm{\θ}}+{\mathrm{\λ}}_3{f}_{3\mathrm{\θ}})\mathrm{\δ\θ}$

（f）

$+(f_{1\mathrm{\φ}}+{\mathrm{\λ}}_2{f}_{2\mathrm{\φ}}+{\mathrm{\λ}}_3{f}_{3\mathrm{\φ}})\mathrm{\δ\φ}\}\mathrm{dy}+\mathrm{\δ}{y}_E{(f_1+{\mathrm{\λ}}_2{f}_2+{\mathrm{\λ}}_3{f}_3)}_{\mathrm{atE}}$

Between D and E, δ D, δ M, δ θ and δ φ are not all 0.Because only there is jet pipe length fixed, δ y is not equal to 0.Being continuous print at inner M and θ of flowing, is also therefore continuous print along CDE, φ.Therefore integral equation (e) is also continuous print.Therefore put D not enter in the first variation of I, can obtain

$\mathrm{\δI}=0={\∫}_{\mathrm{yD}}^{\mathrm{yE}}\{(f_{1M}+{\mathrm{\λ}}_2{f}_{2M}+{\mathrm{\λ}}_3{f}_{3M})\mathrm{\δM}+(f_{1\mathrm{\θ}}+{\mathrm{\λ}}_2{f}_{2\mathrm{\θ}}+{\mathrm{\λ}}_3{f}_{3\mathrm{\θ}})\mathrm{\δ\θ}$

（g）

$+(f_{1\mathrm{\φ}}+{\mathrm{\λ}}_2{f}_{2\mathrm{\φ}}+{\mathrm{\λ}}_3{f}_{3\mathrm{\φ}})\mathrm{\δ\φ}\}\mathrm{dy}+\mathrm{\δ}{y}_E{(f_1+{\mathrm{\λ}}_2{f}_2+{\mathrm{\λ}}_3{f}_3)}_{\mathrm{atE}}$

Because M, θ, φ and y _eit is arbitrary for obtaining variation, has equation above to derive

f _1M+λ ₂f _2M+λ ₃f _3M=0（h）

f _1θ+λ ₂f _2θ+λ ₃f _3θ=0（i）

f _1φ+λ ₂f _2φ+λ ₃f _3φ=0（j）

Along DE,

f ₁+λ ₂f ₂+λ ₃f ₃=0atE（k）

Because f _3Mand f _{3 θ}be not all 0, can f be obtained by equation (g) (h) _1Mf _{2 θ}=f _{1 θ}f _2M

Notice, cancellation y in equation, can obtain

φ=θ+αalongDE（l）

The Representation Equation chain of command is above consistent with the last item left lateral characteristic line of jet pipe.This relation is brought into equation (h) (i), the condition along this line can be obtained, therefore

$\frac{V\cos (\mathrm{\θ}-\mathrm{\α})}{\cos \mathrm{\α}}=-{\mathrm{\λ}}_2---\left(m\right)$

With

yρV ²sin ²θtanα=-λ ₃（n）

-λ ₂,-λ ₃the symbol of constant, the constant C namely in the application ₁, C ₂, formula (m) and (n) are namely equation (1) and (2).

After the coordinate having determined the discrete point on intersection line and flow parameter, carry out step S33: the flow parameter of the end points E away from X-axis on intersection line is substituted into equation (3) and equation (4), flow parameter as fruit dot E meets equation (3) and equation (4), then E point is now the outlet end points of the wall of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.As fruit dot E does not meet equation (3) and equation (4), then repeat to set up chain of command to determining that 1 E can meet the process of equation (3) and equation (4), until obtaining till 1 E meets equation (3) and equation (4).Equation (3) and equation (4) as follows:

$L=x_C+{\∫}_C^E\cot \mathrm{\φdy}---\left(3\right)$

$\sin 2\mathrm{\θ}=\frac{p-p_{\mathrm{amb}}}{\frac{1}{2}\mathrm{\ρ}{V}_1^2}\cot \mathrm{\α}---\left(4\right)$

Wherein, x _cbe the abscissa of intersection line close to the end points of X-axis, L is the length of given jet pipe, and φ is the inclination angle of outlet end points relative to the axis of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, p _ambbe given external pressure, p is the pressure of outlet end points, V ₁be the speed of outlet end points, α is the Mach angle of outlet end points, and θ is the flow angle of outlet end points, and E represents the end points away from X-axis of intersection line, and C represents the end points close to X-axis of intersection line.

Then step S34 is carried out: after having determined the outlet end points of the wall of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, according to the wall molded line TE of conservation of mass theorem and method of characteristics determination Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.Carry out step S4 again: the wall determining Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to wall molded line TE.In the process, determine the process of wall molded line TE actual be the process of the coordinate of the end points away from X-axis of all left lateral characteristic lines before the left lateral characteristic line at E point place determined in nucleus, these end points determined are coupled together the wall molded line TE namely obtaining Supersonic Nonuniform incoming flow Maximum Thrust Nozzle of the present invention.

In an embodiment, the process utilizing method of characteristics to solve as shown in Figure 5.Specifically, the solution procedure of method of characteristics is: suppose two point (x on known wall curve ₁, r ₁, M ₁, θ ₁), (x ₂, r ₂, M ₂, θ ₂), need to solve thirdly (x ₃, r ₃, M ₃, θ ₃) time, the process utilizing Fig. 5 to show solves.

Wherein, conservation of mass formula is as follows:

ρ ₁V ₁A ₁=ρ ₂V ₂A ₂

In solution procedure, first according to estimating step to thirdly solving, then correcting solving value, obtaining the coordinate thirdly after correcting, Mach number and flow direction angle.

Estimate step to comprise:

First solve (x ₃, r ₃),

μ ₁=sin ^-1(1/M ₁)

μ ₂=sin ^-1(1/M ₂)

h ₁=tan[θ ₁+μ ₁]

h ₂=tan[θ ₂-μ ₂]

Have according to difference equation:

r ₃-r ₁=h ₁(x ₃-x ₁)

r ₃-r ₂=h ₂(x ₃-x ₂)

Two formulas are subtracted each other and can be obtained:

r ₁-r ₂={h ₂-h ₁}x ₃+x ₁h ₁-x ₂h ₂

Try to achieve coordinate thirdly

$\left\{\begin{array}{c}{x}_3=\frac{(r_1-r_2)-(x_1{h}_1-x_2{h}_2)}{h_2-h_1}\\ r_3=h_1(x_3-x_1)+r_1\end{array}\right.$

Solve compatibility relation formula below:

Order:

$g_1=\frac{{({M_1}^2-1)}^{1/2}}{1+(\mathrm{\γ}-1){M_1}^2/2}\frac{1}{M_1}$

$g_2=\frac{{({M_2}^2-1)}^{1/2}}{1+(\mathrm{\γ}-1)M_2^2/2}\frac{1}{M_2}$

$f_1=\mathrm{\δ}\frac{\tan \mathrm{\θ}}{{(M^2-1)}^{1/2}\tan \mathrm{\θ}+1}\frac{r_3-r_1}{r_1}$

$f_2=\mathrm{\δ}\frac{\tan \mathrm{\θ}}{{(M^2-1)}^{1/2}\tan \mathrm{\θ}-1}\frac{r_3-r_2}{r_2}$

Then have:

g ₁(M ₃-M ₁)-(θ ₃-θ ₁)-f ₁=0

g ₂(M ₃-M ₂)+(θ ₃-θ ₂)-f ₂=0

Thus obtain Mach number and the flow direction angle at thirdly position place:

$M_3=\frac{f_1-{\mathrm{\θ}}_1+g_1{M}_1+f_2+{\mathrm{\θ}}_2+g_2{M}_2}{g_1+g_2}$

θ ₃=g ₁(M ₃-M ₁)+θ ₁-f ₁

μ ₃=sin ^-1(1M ₃)

In above-mentioned equation, M ₁be the Mach number at first position place, μ ₁be the Mach angle at first position place, θ ₁be the flow direction angle at first position place, x ₁be the abscissa at first position place, r ₁be the y coordinate at first position place, γ is the specific heat at constant pressure of gas and the ratio of specific heat of specific heat at constant volume, and M is local Mach number and M>1, δ are pattern of flow parameter, for two-dimensional flow δ=0, and Three-dimensional Axisymmetric flowing δ=1, r ≠ 0.

M ₂for the Mach number at second point position place, μ ₂for the Mach angle at second point position place, θ ₂for the flow direction angle at second point position place, x ₂for the abscissa at second point position place, r ₂for the y coordinate at second point position place.

M ₃for the Mach number at thirdly position place, μ ₃for the Mach angle at thirdly position place, θ ₃for the flow direction angle at thirdly position place, x ₃for the abscissa at thirdly position place, r ₃for the y coordinate at thirdly position place.

Estimate in step solve thirdly position place coordinate, after Mach number and flow direction angle, the coefficient of equation or parameter are averaged and repeat to estimate the computational process of step, Mach number thirdly and flow direction angle are corrected.This parameter or coefficient mean value solve by the Mach number thirdly of trying to achieve and flow direction angle, order

${M_1}^{\′}=\frac{(M_1+M_3)}{2}$

${M_2}^{\′}=\frac{(M_1+M_3)}{2}$

Wherein M ₁' be first correct after Mach number mean value, M ₂' for second point correct after Mach number mean value, then by M ₁' and M ₂' value substitute into and estimate in step and proceed to solve, until correction of a final proof walk the thirdly Mach number of trying to achieve and estimates the thirdly Mach number M tried to achieve in step ₃location of equal, the final Mach number after the Mach 2 ship correction at thirdly present position place now.In like manner, thirdly the flow direction angle at position place also can obtain final flow direction angle by correcting step.

Preferably, the present embodiment also comprises step S5: after having determined the wall of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, adopt momentum integral relation to solve the displacement thickness in Supersonic Nonuniform incoming flow Maximum Thrust Nozzle boundary layer, carry out boundary layer viscous correction.Equal proportion convergent-divergent can be carried out to boundary layer like this, make the starting point of the actual jet pipe of jet pipe equal with the t point y coordinate of upstream wall.

Due to the existence of gas viscosity, can boundary layer be there is near jet pipe wall profile TB, thus affect nozzle flow field quality, therefore need to carry out viscous correction to jet pipe wall molded line TB.

The step of viscous correction:

A. coefficient of viscosity is solved:

$\frac{\mathrm{\μ}}{{\mathrm{\μ}}_0}={\left(\frac{T}{T_0}\right)}^{1.5}\left(\frac{T_0+T_s}{T+T_s}\right)$

Wherein T ₀=273.16K, μ ₀be T under a barometric pressure ₀the dynamic viscosity coefficient of gas during=273.16K, T _sfor Sutherland constant, relevant with the character of gas, for air, μ ₀=1.7161 × 10 ^-5, T _s=124K, T represent local observed temperature.

B. static temperature is solved:

$T_e=T_0(1+\frac{\mathrm{\γ}-1}{2}{M}^2)$

C. static pressure is solved:

$p_e=p_0{(1+\frac{\mathrm{\γ}-1}{2}{M}^2)}^{\frac{\mathrm{\γ}}{1-\mathrm{\γ}}}$

D. density is solved:

${\mathrm{\ρ}}_e=\frac{p_e}{R{T}_e}$

For air:

R=287J/(kg·mol)

E. the velocity of sound is solved:

$a_e=\sqrt{\mathrm{\γ}{\mathrm{RT}}_e}$

F. solving speed:

u _e=M _e*a _e

G. adiabatic wall temperature is solved:

$T_{\mathrm{aw}}\≈T_e(1+\frac{\mathrm{\γ}-1}{2}{\mathrm{Pr}}^{1/3}{M}_e^2)$

H. the reference length of Re number is solved:

$x=\sqrt{\frac{\mathrm{\γ}+1}{2}{r}^{*}{R}^{*}}$

Wherein r ^*for nozzle entry half height, R ^*for nozzle entry wall radius.

I. Re number is solved:

${\mathrm{Re}}_x=\frac{{\mathrm{\ρ}}_e{u}_{e}x}{{\mathrm{\μ}}_e}$

J. reference temperature is solved:

T′=0.5(T _w+T _e)+0.22(T _aw-T _e)

Wherein T _wrepresent local actual measurement surface temperature.

What k. solve correspondence can not press friction factor:

L. the pass of shape factor and friction factor can not be pressed to be:

$H_i=\frac{1}{1-7\sqrt{C_{\mathrm{fi}}/2}}$

M. can press shape factor and can not press the pass of shape factor to be:

$H=\frac{T_w}{T_e}{H}_i+\frac{T_{\mathrm{aw}}}{T_e}-1$

N. can press friction factor and can not press the pass of friction factor to be:

By the C tried to achieve _fimomentum integral relation is updated to H:

$\frac{\mathrm{d\τ}}{\mathrm{dx}}+\mathrm{\τ}[\frac{2-M^2+H}{M(1+\frac{\mathrm{\γ}-1}{2}{M}^2)}\frac{\mathrm{dM}}{\mathrm{dx}}+\frac{1}{y}\frac{\mathrm{dy}}{\mathrm{dx}}]=\frac{C_f}{2}\sec \mathrm{\φ}$

$\mathrm{\φ}={\tan }^{-1}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)$

$H=\frac{{\mathrm{\δ}}^{*}}{\mathrm{\τ}}$

Wherein, τ is momentum loss thickness, δ ^*for boundary layer displacement thickness, φ is flow direction angle, and H is boundary layer shape factor.This is an ordinary differential system, adopts four step runge kutta methods to solve, obtains boundary layer displacement thickness, displacement thickness is attached to wall molded line TB and obtains the actual wall of jet pipe.Obtain the nozzle contour after viscous correction, overcome near the wall curve that causes due to gas viscosity and can there is boundary layer, thus affect the problem of flow field quality, further increase precision and the quality of the supersonic nozzle of shared throat.

According to another embodiment of the present invention, provide a kind of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, this Supersonic Nonuniform incoming flow Maximum Thrust Nozzle comprises jet pipe wall, and the method that the wall of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle is above-mentioned is determined.According to the present embodiment, Supersonic Nonuniform incoming flow Maximum Thrust Nozzle is suitable for heterogeneous loose body, also contemplates the viscous correction of the jointing of jet pipe in the design process, adds the thrust of jet pipe.

As can be seen from the above description, the above embodiments of the present invention achieve following technique effect: the wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle of the present invention comprises the following steps: determine heterogeneous loose body parameter; According to incoming flow parameter, determine the initial boundary of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, wherein, the first end points of initial boundary is true origin, and the second end points of initial boundary is that Mach number is greater than 1 and is positioned at the point in Y-axis; According to initial boundary, utilize method of characteristics, determine the nucleus of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle; According to the conservation of mass and method of characteristics, solve in nucleus inner iteration, determine the wall molded line of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle; According to the wall of wall molded line determination Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.According to method of the present invention, the ultrasound velocity Maximum Thrust Nozzle being suitable for heterogeneous loose body can be obtained, the design process of this jet pipe considers the situation of heterogeneous loose body, can be combined well, improve the thrust of supersonic nozzle with the actual application environment of jet pipe.

The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention, for a person skilled in the art, the present invention can have various modifications and variations.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (15)

1. a wall defining method for Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, is characterized in that, comprise the following steps:

S1: according to heterogeneous loose body parameter, determines the initial boundary of described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle;

S2: according to described initial boundary, utilize method of characteristics, determines the nucleus of described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle;

S3: according to conservation of mass theorem and described method of characteristics, solves in described nucleus inner iteration, determines the wall molded line of described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle;

S4: the wall determining described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to the wall molded line of described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.

2. the wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 1, is characterized in that, in the step of described S1, the method that described heterogeneous loose body parameter adopts numerical simulation or test to measure is determined.

3. the wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 1, is characterized in that, in the step of described S1, the Mach number of the discrete point on described initial boundary is greater than 1.0.

4. the wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 3, is characterized in that, the Mach number of the discrete point on described initial boundary is in the scope of 1.01 to 1.10.

5. the wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 1, it is characterized in that, the step of described S2 comprises:

With the first end points of described initial boundary for true origin, described initial boundary is the axis that Y-axis determines described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, and the axis of the described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle determined overlaps with X-axis.

6. the wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 5, it is characterized in that, the step of described S2 also comprises:

Described method of characteristics is utilized to determine the domain of influence of described initial boundary.

7. the wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 6, it is characterized in that, the step of described S2 also comprises:

After determining the described domain of influence, at the double-pointed downstream given initial bubble wall molded line near described initial boundary, wherein, described first end points of initial bubble wall molded line overlaps with the second end points of described initial boundary.

8. the wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 7, it is characterized in that, the step of described S2 also comprises:

After given described initial bubble wall molded line, utilize described method of characteristics, determine the left lateral characteristic line that the discrete point on described initial bubble wall molded line sends and right lateral characteristic line, the net region of described left lateral characteristic line and described right lateral characteristic line composition is described nucleus.

9. the wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 7, it is characterized in that, the step of described S3 comprises:

S31: set up chain of command, make described chain of command crossing with the meridian plane of any point crossed in described nucleus, and their intersection line overlaps with the left lateral characteristic line of described initial bubble wall molded line, the flow parameter of any point in wherein said nucleus is determined by described initial boundary and described initial bubble wall molded line.

10. the wall defining method of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 9, it is characterized in that, the step of described S3 also comprises:

S32: utilize described conservation of mass theorem, described method of characteristics and equation (1) and (2) to determine coordinate and the flow parameter of the discrete point on described intersection line,

$\frac{Vcos(\mathrm{\θ}-\mathrm{\α})}{cos\mathrm{\α}}=C_1---\left(1\right)$

yρV ²sin ²θtanα＝C ₂(2)

Wherein, V is speed of incoming flow, and y is the y coordinate of the discrete point on described intersection line, and θ is the flow angle of the discrete point on described intersection line, and α is the Mach angle of the discrete point on described intersection line, and ρ carrys out current density, C ₁, C ₂it is constant.

The wall defining method of 11. Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 10, it is characterized in that, the step of described S3 also comprises:

S33: the flow parameter of the end points away from described X-axis on described intersection line is substituted into equation (3) and equation (4), if the end points away from described X-axis on described intersection line does not meet equation (3) and equation (4), then repeat the step of described S31 to described S32; If the described end points away from described X-axis on described intersection line meets equation (3) and equation (4), then the described end points away from described X-axis is the outlet end points of the wall of described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle,

$L=x_C+{\∫}_C^E\cot \mathrm{\φ}dy---\left(3\right)$

$sin2\mathrm{\θ}=\frac{p-p_{amb}}{\frac{1}{2}{{\mathrm{\ρV}}_1}^2}\cot \mathrm{\α}---\left(4\right)$

Wherein, x _cbe the abscissa of described intersection line close to the end points of described X-axis, L is the length of given jet pipe, and φ is the inclination angle of described outlet end points relative to the axis of described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, p _ambbe given external pressure, p is the pressure of described outlet end points, V ₁be the speed of described outlet end points, α is the Mach angle of described outlet end points, and θ is the flow angle of described outlet end points, and E represents the end points away from described X-axis of described intersection line, and C represents the end points close to described X-axis of described intersection line.

The wall defining method of 12. Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 11, it is characterized in that, the step of described S3 also comprises:

S34: after determining the outlet end points of the wall of described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, according to described conservation of mass theorem and described method of characteristics, determines the wall molded line of described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle.

The wall defining method of 13. Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to claim 1, is characterized in that, further comprising the steps of:

S5: after determining the wall of described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, adopts momentum integral relation to solve the displacement thickness that described ultrasound velocity obtains uniform incoming flow Maximum Thrust Nozzle boundary layer, carries out boundary layer viscous correction.

The wall defining method of 14. Supersonic Nonuniform incoming flow Maximum Thrust Nozzle according to any one of claim 1 to 13, it is characterized in that, described method of characteristics revolves method of characteristics for having.

15. 1 kinds of Supersonic Nonuniform incoming flow Maximum Thrust Nozzle, comprise wall, it is characterized in that, the method for wall according to any one of claim 1 to 14 of described Supersonic Nonuniform incoming flow Maximum Thrust Nozzle is determined.