CN102302990B - Annular supersonic velocity spray pipe and design method thereof - Google Patents

Abstract

The invention provides an annular supersonic velocity spray pipe and a design method thereof. The design method for the annular supersonic velocity spray pipe comprises the following steps of: predicting a flow field parameter in a transonic velocity segment area, and extracting an initial characteristic line from the flow field parameter; determining the mach number distribution of a supersonic velocity upright wall of the spray pipe according to design requirements; and determining a supersonic velocity curved wall molded surface of the spray pipe by a characteristic line method according to the initial characteristic line and the mach number distribution of the supersonic velocity upright wall. According to the design method for the annular supersonic velocity spray pipe, compression waves are not concentrated in a flow field of the designed annular supersonic velocity spray pipe, the distribution of the flow field parameter can be optimized according to actual application, and the quality of the flow field of the annular supersonic velocity spray pipe can be greatly improved. According to the annular supersonic velocity spray pipe, the design method for the annular supersonic velocity spray pipe is utilized.

Description

Annular supersonic nozzle and method for designing thereof

Technical field

The present invention relates to field of fluid power, in particular to a kind of annular supersonic nozzle and method for designing thereof.

Background technology

Supersonic nozzle is widely used in the equipment such as high-speed aircraft, rocket, supersonic wind tunnel, high-energy laser, injection vavuum pump, and the performance of nozzle flow field product confrontation equipment has significant effects.Obtain suitable jet pipe wall surface curve by certain designing technique, can improve the nozzle flow field quality greatly, improve equipment performance, save reasearch funds.Supersonic nozzle generally is made up of contraction section and expansion segment, under certain pressure drove, gas accelerated gradually at contraction section, and reaches the velocity of sound near throat, continue to accelerate at expansion segment then, until going out the supersonic flow that the required Mach number of interruption-forming and flow direction angle distribute.

Toroidal nozzle is different from traditional two dimension or axisymmetric nozzle, from the angle of geometry, is not simple linear relationship (two-dimensional nozzle) or quadratic relationship (axisymmetric nozzle) between its area of section and the channel height.Complex relationship on this geometry makes the expansion characteristics of annular channel be different from two dimension or circular pipe, and therefore also different to the accelerating performance of gas, the particularity of this geometry and fluidal texture has been brought certain difficulty to method for designing.Though have multiple comparatively ripe two dimension or axisymmetric nozzle method for designing at present, and can realize higher exit flow field quality, existing method can not directly expand in the design of toroidal nozzle profile curve.Its subject matter that faces comprises: one, existing flow model and empirical equation are difficult to direct application; The 2nd, the expansion of annular channel and wave absorption have certain particularity, obviously are different from traditional two dimension or axial symmetry wind tunnel nozzle; The 3rd, the ring wall surface boundary layer is revised and also is different from the axial symmetry wind tunnel nozzle.

Conventional two-dimensional and axisymmetric nozzle method for designing mainly comprise following several.A kind of approximation method (K.Foelsch.The Analytical Design of an Axially Symmetric Laval Nozzle for a Parallel and Uniform Jet.J.of the Aeronaut that Foelsch proposes, Sci.16:161-188,1948.) adopt experience curve to design the subsonic speed section, for the supersonic speed section, the a certain zone of supposing jet pipe is current of spring, transition is evenly to flow then, and proposes a cover empirical equation at the initial bubble district.People have carried out a lot of improvement to this method subsequently, the improvement of its empirical equation being carried out as Crown (J.C.Crown.Supersonic Nozzle Design.NACATN-1651,1948.).Because all based on current of spring hypothesis, in order to reduce error, jet pipe is generally very long for these methods, and since on axis the current of spring district directly and homogeneity range join and cause the axial velocity gradient discontinuous, influence flow field quality.For fear of these problems, Cresci by a part of wave absorption district is set in profile to before method improve (R.J.Cresci.Tabulation of Coordinates for Hypersonic Axisymmetric Nozzles Part I-Analysis and Coordinates for Test Section Mach Numbers of 8,12 and 20.WADD-TN-58-300,1958.), but the method initial bubble section still is empirical equation, and jet pipe is difficult to accomplish optimize.Sivells inherits the design philosophy of Cresci, transonic speed theoretical (I.M.Hall.Transonic Flow in Two-dimensional and Axially-symmetric Nozzles.Quarterly Journal of Mechanics and Applied Mathematics in conjunction with Hall, XV:487-508,1962.), by setting the pneumatic profile of jet pipe (J.C.Sivells.A Computer Program for the Aerodynamics Design of Axisymmetric and Planar Nozzles for Supersonic and Hypersonic Wind Tunnels.AEDC-TR-78-63,1978.) that axis Mach Number Distribution or VELOCITY DISTRIBUTION obtain having continuous curvature.Monograph " the pneumatic and structural design of high low-speed wind tunnel " (Liu Zhengchong, National Defense Industry Press, 2003) has been introduced multiple jet pipe designing technique, and corresponding mentality of designing and preceding method are similar, repeat no more.

Conventional two-dimensional and axisymmetric nozzle method for designing can reach certain flow field quality, but existing toroidal nozzle mainly is to adopt taper or experience curve to design, and flow field quality is difficult to control.U.S.'s patent of invention 3289946 discloses the annular shrinkage expansion jet pipe that a kind of engine is used, and its target is to increase thrust, reduce resistance, and this invention has proposed improvement project in structural design, is not discussed in detail but the design of jet pipe profile curve done.U.S.'s patent of invention 3940067 has proposed a kind of plug nozzle for rocket engine, actual is a kind of toroidal nozzle, its design object is to realize shortest length under the prerequisite that guarantees combustion chamber and extraneous pressure reduction, this invention mainly improves the jet pipe design from the angle of structure and material thermal protective performance, according to the principle design plug vertebra of trajectory optimisation and the curve of jet pipe outer wall, the designed curve that goes out of this method can't guarantee the uniformity at flow field Mach number and flow direction angle, also is difficult to solve problems such as supersonic region wave absorption and viscosity correction.

Summary of the invention

The present invention aims to provide a kind of annular supersonic nozzle and method for designing thereof, reduces or eliminates the concentrated compressional wave in the flow field of annular supersonic nozzle, thereby improves annular supersonic nozzle flow field quality greatly.

To achieve these goals, according to an aspect of the present invention, provide a kind of annular supersonic nozzle method for designing, comprised according to entrance geometric parameter, throat opening area and determine subsonic speed section curve; According to subsonic speed section curve prediction Asia section flow field parameter transonic speed, and extract the initial characteristics line from flow field parameter; Determine the Mach Number Distribution of the straight wall of supersonic speed of jet pipe according to the Structural Design Requirement of annular supersonic nozzle; Mach Number Distribution according to initial characteristics line and the straight wall of supersonic speed adopts the method for characteristic curves to determine the supersonic speed curved wall profile of jet pipe.

Further, method of characteristic curves iterative formula is:

$\left\{\begin{array}{c}\frac{\mathrm{\Δr}}{\mathrm{\Δx}}=\tan [\mathrm{\θ}\±{\sin }^{-1}(1/M)]\\ \frac{{(M^2-1)}^{1/2}}{1+(\mathrm{\γ}-1)M^2/2}\frac{\mathrm{\ΔM}}{M}\stackrel{\‾}{+}\mathrm{\Δ\θ}-\mathrm{\δ}\frac{\tan \mathrm{\θ}}{{(M^2-1)}^{1/2}\tan \mathrm{\θ}\±1}\frac{\mathrm{\Δr}}{r}=0\end{array}\right.$

Wherein, x is abscissa, and r is ordinate, and θ is local flow direction angle, and M is local Mach number and M＞1, and δ is the pattern of flow parameter, for two dimension δ=0 of flowing, and axial symmetry δ=1 of flowing, r ≠ 0, γ is the specific heat at constant pressure of gas and the specific heat ratio of specific heat at constant volume.

Further, also comprise after the supersonic speed curved wall profile of determining jet pipe: adopt the momentum integral relational expression to calculate the boundary layer displacement thickness of supersonic speed inner and outer ring, determine viscosity wall curve, the momentum integral relational expression is:

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

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

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

Wherein, τ is momentum loss thickness, δ ^*Be boundary layer displacement thickness, φ is the flow direction angle, and H is the boundary layer form factor, C _fFor pressing coefficient of friction.

Further, after definite viscosity wall curve, also comprise: carry out the boundary layer and revise, obtain the wall curve of viscosity correction.

Further, also comprise before the subsonic speed section curve determining according to entrance geometric parameter, throat opening area: determine throat opening area according to the isentropic relation formula, the isentropic relation formula is:

$\frac{A}{A^{*}}=\frac{1}{M_t}{\left[\left(\frac{2}{\mathrm{\γ}+1}\right)(1+\frac{\mathrm{\γ}-1}{2}{M}_t^2)\right]}^{(\mathrm{\γ}+1)/2(\mathrm{\γ}-1)}$

Wherein, A is the nozzle exit area, A ^*Be nozzle throat area, M _tBe the nozzle throat Mach number, γ is the specific heat ratio of gas.

Further, before determining throat opening area according to the isentropic relation formula, also comprise: the straight wall of determining jet pipe according to the structural requirement of jet pipe.

Further, after the straight wall of determining jet pipe, also comprise: the angle that requires to determine straight wall and axis according to the acceleration distance of jet pipe.

Subsonic speed section curve is two circular curves.

Further, the Asia transonic speed the section flow field parameter adopt the approximate Riemann solver of a Roe and Runge-Kutta method to determine that concrete steps are as follows:

Do not have sticking conservation form Euler equation by numerical solution and obtain throat's flow parameter distribution:

Wherein,

Be conserved quantity,

Be flux, Ω is control volume,

Be the control volume surface;

Adopt the approximate Riemann solver of Roe with formula (1) space product subitem discretization:

${\left({\stackrel{\→}{F}}_c\right)}_R-{\left({\stackrel{\→}{F}}_c\right)}_L={\left({\stackrel{\‾}{A}}_{\mathrm{Roe}}\right)}_{I+1/2}({\stackrel{\→}{W}}_R-{\stackrel{\→}{W}}_L)---\left(2\right)$

Wherein two of the left side the expression flux differences,

Be the Roe matrix, subscript L and R represent left and right sides state respectively, and I represents the label of grid cell;

The time integral item that adopts the Runge-Kutta method to find the solution formula (1):

${\stackrel{\→}{W}}_I^{\left(0\right)}={\stackrel{\→}{W}}_I^n$

${\stackrel{\→}{W}}_I^{\left(1\right)}={\stackrel{\→}{W}}_I^{\left(0\right)}-{\mathrm{\α}}_1\frac{{\mathrm{\Δt}}_I}{{\mathrm{\Ω}}_I}{\stackrel{\→}{R}}_I^{\left(0\right)}$

$\begin{array}{c}{\stackrel{\→}{W}}_I^{\left(2\right)}={\stackrel{\→}{W}}_I^{\left(0\right)}-{\mathrm{\α}}_2\frac{{\mathrm{\Δt}}_I}{{\mathrm{\Ω}}_I}{\stackrel{\→}{R}}_I^{\left(1\right)}---\left(3\right)\\ .\\ .\\ .\end{array}$

${\stackrel{\→}{W}}_I^{(n+1)}={\stackrel{\→}{W}}_I^{\left(m\right)}={\stackrel{\→}{W}}_I^{\left(0\right)}-{\mathrm{\α}}_m\frac{{\mathrm{\Δt}}_I}{{\mathrm{\Ω}}_I}{\stackrel{\→}{R}}_I^{(m-1)}$

α in following formula _kThe coefficient of representing each step can obtain by tabling look-up, Represent that the k step is by solution

The residual error that obtains, m=3, α ₁=0.1918, α ₂=0.4929, α ₃=1,

Employing formula (1)-(3) are tried to achieve flow parameter and are distributed, and determine the initial characteristics line according to local flow direction angle and Mach angle (arcsin (1/M)), determine the Mach number of axis initial point and along the first derivative of axis direction.

Further, throat's flow parameter comprises: density p, speed

Temperature T, pressure p and Mach number M.

Further, the Mach Number Distribution of the straight wall of supersonic speed is adjusted by the two-dimensional spline curve.

Further, before determining throat opening area according to the isentropic relation formula, also comprise: determine the jet pipe flow according to outlet density, speed and area.

According to a further aspect in the invention, provide a kind of annular supersonic nozzle, comprised that the Mach Number Distribution according to initial characteristics line and the straight wall of supersonic speed adopts the definite supersonic speed curved wall profile of the method for characteristic curves.

Further, annular supersonic nozzle also comprises the subsonic speed section curve that two circular curves form.

Further, annular supersonic nozzle also comprises the determined viscosity wall of the boundary layer displacement thickness curve that adopts the momentum integral relational expression to calculate the supersonic speed inner and outer ring.

Further, annular supersonic nozzle also comprises the wall curve that obtains the viscosity correction.

Further, the characteristic curve of initial characteristics line for transonic speed extracting in the section flow field parameter according to the Asia of subsonic speed section curve prediction.

Further, annular supersonic nozzle also comprises according to the determined straight wall of the structural requirement of jet pipe.

According to technical scheme of the present invention, the supersonic speed curved wall profile of jet pipe adopts the method for characteristic curves to determine according to the Mach Number Distribution of initial characteristics line and the straight wall of supersonic speed, can pass through method of characteristic curves wave absorption, make and do not have the compressional wave of concentrating in the flow field, flow field parameter distributes and can be optimized according to practical application, can effectively guarantee the uniformity at flow field Mach number and flow direction angle, improve flow field quality greatly.Adopt the momentum integral relational expression to calculate the boundary layer displacement thickness of supersonic speed inner and outer ring, determine viscosity wall curve, can there be the boundary layer near having overcome the wall curve that causes owing to gas viscosity, thereby influence the problem of rhomboid flow field quality, further improved precision and the quality of annular supersonic nozzle.The Mach Number Distribution of the straight wall of supersonic speed is adjusted by the two-dimensional spline curve, makes the Mach Number Distribution of supersonic region of annular supersonic nozzle have adjustability, and the Mach Number Distribution of supersonic region that can more accurate control jet pipe makes it satisfy the design needs.

Description of drawings

The accompanying drawing that constitutes a part of the present invention is used to provide further understanding of the present invention, and illustrative examples of the present invention and explanation thereof are used for explaining the present invention, do not constitute improper restriction of the present invention.In the accompanying drawings:

Fig. 1 shows the configuration schematic diagram according to annular supersonic nozzle of the present invention;

Fig. 2 shows the subsonic speed section curve configuration schematic diagram according to annular supersonic nozzle of the present invention;

Fig. 3 shows the Flow Field Distribution schematic diagram according to annular supersonic nozzle of the present invention;

Fig. 4 shows the straight wall configuration schematic diagram according to annular supersonic nozzle of the present invention;

Fig. 5 shows the straight wall Mach Number Distribution schematic diagram according to annular supersonic nozzle of the present invention;

Fig. 6 shows the supersonic speed curved wall profile schematic diagram according to annular supersonic nozzle of the present invention;

Fig. 7 shows the actual wall schematic diagram according to annular supersonic nozzle of the present invention; And

Fig. 8 shows the structural representation according to annular supersonic nozzle of the present invention.

The specific embodiment

Hereinafter will describe the present invention with reference to the accompanying drawings and in conjunction with the embodiments in detail.Need to prove that under the situation of not conflicting, embodiment and the feature among the embodiment among the application can make up mutually.

In the present invention, the subsonic speed section refers to that air-flow enters after the jet pipe contraction section its flow velocity less than the part of the velocity of sound, the Asia transonic speed the section also namely transonic speed the section, refer to that air-flow enters boundary part between the supersonic speed state from the subsonic speed state, usually, the Mach number of subsonic speed section is less than 0.8, and the Mach number of inferior transonic speed section is between 0.8 to 1.2, and the Mach number of supersonic speed section is greater than 1.2.

As shown in Figure 1, according to annular supersonic nozzle method for designing of the present invention, at first according to structural requirement determine internal face be straight wall still be outside wall surface be straight wall, (a) and (b) among Fig. 1 and (c) be that straight wall, outside wall surface are the configuration picture of the supersonic speed toroidal nozzle of curved wall for internal face, (d), (e) and (f) be that curved wall, outside wall surface are the configuration picture of the supersonic speed toroidal nozzle of straight wall for internal face, they all are the axle center rotation with the rotation, and finally form needed nozzle structure.

After determining the straight wall of jet pipe according to annular supersonic nozzle structural requirement, the angle of straight wall and axis is determined in requirement according to the jet pipe acceleration distance, if the requirement of no acceleration distance then is the cylinder wall, with reference to (a) among the figure 1 with (d); If require acceleration distance short, then the angle of straight wall and axis can be on the occasion of, namely expand outwardly, with reference to (b) among the figure 1 with (f); If require acceleration distance longer, then the angle of straight wall and axis can be negative value, namely inwardly shrinks, with reference to (c) among the figure 1 with (e).

After the angle of determining between straight wall and the axis, determine the jet pipe flow according to outlet density, speed and area; Nozzle flowmeter is calculated formula:

$\stackrel{.}{m}=\mathrm{\ρVA}$

Wherein:

Be the jet pipe flow, ρ is nozzle exit density, and V is nozzle velocity, and A is the nozzle exit area.

Determine the area of throat's anchor ring afterwards according to the isentropic relation formula; The isentropic relation formula is:

$\frac{A}{A^{*}}=\frac{1}{M_t}{\left[\left(\frac{2}{\mathrm{\γ}+1}\right)(1+\frac{\mathrm{\γ}-1}{2}{M}_t^2)\right]}^{(\mathrm{\γ}+1)/2(\mathrm{\γ}-1)}$

Wherein, A ^*Be nozzle throat area, M _tBe the nozzle throat Mach number, γ is the specific heat at constant pressure of gas and the specific heat ratio of specific heat at constant volume.

As shown in Figure 2, after definite entrance geometric parameter and nozzle throat area, determine subsonic speed section curve according to entrance geometric parameter and nozzle throat area, subsonic speed section curve is the part of R1 and R2 indication.In the present invention, adopt two circular curves that subsonic speed section curve is set, two circular arcs can connect with straightway, wherein the center of circle and radius are determined according to Structural Design Requirement, starting point and the slope thereof of the two-end-point corresponding jet pipe wall entrance of difference and slope thereof, the actual wall of jet pipe supersonic speed section, this structure can guarantee that the subsonic speed section curve of designing can have good transition and natural being connected with supersonic speed section curved portion, make annular supersonic nozzle have the pneumatic profile of jet pipe of continuous curvature, thereby make the air-flow that enters the supersonic speed section obtain better fluidised form.

After definite subsonic speed section curve, adopt transonic speed section flow field parameter of the approximate Riemann solver of Roe and Runge-Kutta method prediction Asia, and therefrom extract the initial characteristics line;

Do not have sticking conservation form Euler equation by numerical solution and obtain throat's flow parameter distribution:

Wherein,

Be conserved quantity, Be flux, Ω is control volume, represents grid cell,

Be the control volume surface, represent the surface of grid cell.

Throat's flow parameter comprises density p, speed

Temperature T, pressure p and Mach number M, in the formula

The corresponding density p of difference, speed

Temperature T, pressure p and Mach number M find the solution, and each flow parameter that obtains supersonic nozzle distributes,

Represent the flux of the parameter that will find the solution in the solution procedure respectively.

Adopt the approximate Riemann solver of Roe with formula (1) space product subitem discretization afterwards:

${\left({\stackrel{\→}{F}}_c\right)}_R-{\left({\stackrel{\→}{F}}_c\right)}_L={\left({\stackrel{\‾}{A}}_{\mathrm{Roe}}\right)}_{I+1/2}({\stackrel{\→}{W}}_R-{\stackrel{\→}{W}}_L)---\left(2\right)$

Wherein two of the left side the expression flux differences,

Be the Roe matrix, subscript L and R represent left and right sides state respectively, and I represents the label of grid cell.

The time integral item that adopts the Runge-Kutta method to find the solution formula (1):

${\stackrel{\→}{W}}_I^{\left(0\right)}={\stackrel{\→}{W}}_I^n$

${\stackrel{\→}{W}}_I^{\left(1\right)}={\stackrel{\→}{W}}_I^{\left(0\right)}-{\mathrm{\α}}_1\frac{{\mathrm{\Δt}}_I}{{\mathrm{\Ω}}_I}{\stackrel{\→}{R}}_I^{\left(0\right)}$

$\begin{array}{c}{\stackrel{\→}{W}}_I^{\left(2\right)}={\stackrel{\→}{W}}_I^{\left(0\right)}-{\mathrm{\α}}_2\frac{{\mathrm{\Δt}}_I}{{\mathrm{\Ω}}_I}{\stackrel{\→}{R}}_I^{\left(1\right)}---\left(3\right)\\ .\\ .\\ .\end{array}$

${\stackrel{\→}{W}}_I^{(n+1)}={\stackrel{\→}{W}}_I^{\left(m\right)}={\stackrel{\→}{W}}_I^{\left(0\right)}-{\mathrm{\α}}_m\frac{{\mathrm{\Δt}}_I}{{\mathrm{\Ω}}_I}{\stackrel{\→}{R}}_I^{(m-1)}$

α in following formula _kThe coefficient of representing each step, Represent that the k step is by solution

The residual error that obtains, m=3, α ₁=0.1918, α ₂=0.4929, α ₃=1.

Adopt formula (1)-(3) to try to achieve flow parameter then and distribute, determine the initial characteristics line according to local flow direction angle and Mach angle (arcsin (1/M)), determine the Mach number of axis initial point and along the first derivative of axis direction.

Determined annular supersonic nozzle Flow Field Distribution image as shown in Figure 3, wherein L is the initial characteristics line, the curve of initial characteristics line L both sides is for waiting mach line.The initial characteristics line is the nozzle throat of section transonic speed from the Asia, and the angle of the tangential direction of initial characteristics line and local flow direction is Mach angle.

Then according to the Structural Design Requirement of annular supersonic nozzle, the Mach Number Distribution of the straight wall of given its supersonic speed, as shown in Figure 4 and Figure 5, Fig. 4 is the configuration picture of the annular supersonic nozzle after the Mach Number Distribution of determining the straight wall of supersonic speed according to the Structural Design Requirement of jet pipe, Fig. 5 is that the straight wall of supersonic speed is along the Mach Number Distribution schematic diagram on the axis direction, according to the structure of setting, determine throat's Mach number of annular supersonic nozzle and the design Mach number in exit, use the two-dimensional spline curve to adjust Mach Number Distribution then, the flow field Mach Number Distribution is met design requirement.In conjunction with Fig. 4 and Fig. 5 as can be seen, when the Mach Number Distribution of the straight wall configuration line of determining supersonic nozzle, at first determine the Mach Number Distribution of the initial point A that is positioned at the supersonic speed section of straight wall configuration line according to initial characteristics line and throat's Mach number, obtain being positioned at the Mach Number Distribution that reaches the terminal point C that designs Mach number of outside nozzle then according to Structural Design Requirement, by the Mach Number Distribution of the intermediate point B of the straight wall configuration of quadratic spline curve adjustment curve between the terminal point C in the trunnion Mach number of initial point A and exit and the relation between the axis, make the flow field Mach Number Distribution satisfy the jet pipe designing requirement then.

After the Mach Number Distribution of determining initial characteristics line and the straight wall of annular supersonic nozzle, according to method of characteristic curves iterative supersonic speed curved wall profile parameter, obtain supersonic speed curved wall profile structure, as shown in Figure 6.Here, because the initial characteristics line determined, therefore, according to the initial point of the supersonic speed curved wall face configuration line of the annular supersonic nozzle that can determine from the initial characteristics line of A point to order corresponding to A.According to the initial characteristics line and etc. mach line, in conjunction with the quality that flow to its corresponding initial point on curved wall face configuration line from the A point, the jet pipe flow of trying to achieve with reference to the front, according to conservation of mass theorem, determine to go up corresponding to line segment AC the curved wall face configuration line each point Mach Number Distribution of Mach Number Distribution, and finally determine the upper wall surface of jet pipe supersonic speed curved wall profile.

Method of characteristic curves iterative formula is:

$\left\{\begin{array}{c}\frac{\mathrm{\Δr}}{\mathrm{\Δx}}=\tan [\mathrm{\θ}\±{\sin }^{-1}(1/M)]\\ \frac{{(M^2-1)}^{1/2}}{1+(\mathrm{\γ}-1)M^2/2}\frac{\mathrm{\ΔM}}{M}\stackrel{\‾}{+}\mathrm{\Δ\θ}-\mathrm{\δ}\frac{\tan \mathrm{\θ}}{{(M^2-1)}^{1/2}\tan \mathrm{\θ}\±1}\frac{\mathrm{\Δr}}{r}=0\end{array}\right.$

Wherein, x is abscissa, and r is ordinate, and θ is local flow direction angle, and M is local Mach number and M＞1, and δ is the pattern of flow parameter, for two dimension δ=0 of flowing, and axial symmetry δ=1 of flowing, r ≠ 0, γ is the specific heat at constant pressure of gas and the specific heat ratio of specific heat at constant volume.In the present embodiment, because for axial symmetry flows, so δ=1, r ≠ 0.

As shown in Figure 7, because can there be the boundary layer in the existence of gas viscosity near the desirable wall curve of jet pipe, thereby influences the rhomboid flow field quality, therefore need the desirable wall curve of jet pipe supersonic speed section is carried out the viscosity correction, obtain jet pipe supersonic speed section actual wall surface curve.

The step of viscosity correction:

A. find the solution viscosity:

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

T wherein ₀=273.16K, μ ₀Be T under the atmospheric pressure ₀The dynamics viscosity of gas during=273.16K, T _sBe the 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. find the solution static temperature:

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

C. find the solution static pressure:

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

D. find the solution density:

${\mathrm{\ρ}}_e=\frac{p_e}{{\mathrm{RT}}_e}$

For air:

R＝287J/(kg·mol)

E. find the solution the velocity of sound:

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

F. find the solution speed:

u _e＝M _e*a _e

G. find the solution adiabatic wall temperature:

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

H. find the solution the reference length of Re number:

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

R wherein ^*Be throat's half height, R ^*Be the nozzle throat radius of curvature.

I. find the solution the Re number:

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

J. find the solution reference temperature:

T′＝0.5(T _w+T _e)+0.22(T _aw-T _e)

T wherein _wRepresent local actual measurement surface temperature.

That k. finds the solution correspondence can not press coefficient of friction:

(10 ⁵＜Re _x＜10 ⁹)

1. can not press the pass of form factor and coefficient of friction to be:

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

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

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

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

With the C that tries to achieve _FiBe updated to the momentum integral relational expression with 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 ^*Be boundary layer displacement thickness, φ is the flow direction angle, and H is the boundary layer form factor.This is an ODE group, adopts four step Runge-Kutta methods to find the solution, and obtains boundary layer displacement thickness, displacement thickness is appended to desirable wall curve obtain the actual wall of jet pipe.Obtain the revised annular supersonic nozzle curved wall profile of viscosity, can have the boundary layer near having overcome the wall curve that causes owing to gas viscosity, thereby influence the problem of rhomboid flow field quality, further improved precision and the quality of annular supersonic nozzle.

As shown in Figure 8, according to annular supersonic nozzle of the present invention, has the determined subsonic speed nozzle section of subsonic speed section curve that two circular curves form; According to the straight wall profile of the determined supersonic speed of the structural requirement of jet pipe, Mach Number Distribution according to initial characteristics line and the straight wall of supersonic speed adopts the definite supersonic speed curved wall profile of the method for characteristic curves, and according to the supersonic nozzle section of the straight wall profile of determined supersonic speed and the formed annular supersonic nozzle of supersonic speed curved wall profile, and by carry out the actual wall surface curve that the viscosity correction obtains according to viscosity wall curve subsonic speed nozzle section and supersonic nozzle section are revised, finally obtain subsonic speed nozzle section 1 and the supersonic nozzle section 2 of revised annular supersonic nozzle.Wherein viscosity wall curve adopts the boundary layer displacement thickness of momentum integral relational expression calculating supersonic speed inner and outer ring to determine that the initial characteristics line transonic speed extracts the section flow field parameter from the Asia according to subsonic speed section curve prediction.

From above description, as can be seen, the above embodiments of the present invention have realized following technique effect: the supersonic speed curved wall profile of jet pipe adopts the method for characteristic curves to determine according to the Mach Number Distribution of initial characteristics line and the straight wall of supersonic speed, can pass through method of characteristic curves wave absorption, make and do not have the compressional wave of concentrating in the flow field, flow field parameter distributes and can be optimized according to practical application, can effectively guarantee the uniformity at flow field Mach number and flow direction angle, improves flow field quality greatly.Adopt the momentum integral relational expression to calculate the boundary layer displacement thickness of supersonic speed inner and outer ring, determine viscosity wall curve, can there be the boundary layer near having overcome the wall curve that causes owing to gas viscosity, thereby influence the problem of rhomboid flow field quality, further improved precision and the quality of annular supersonic nozzle.The Mach Number Distribution of the straight wall of supersonic speed is adjusted by the two-dimensional spline curve, makes the Mach Number Distribution of supersonic region of annular supersonic nozzle have adjustability, and the Mach Number Distribution of supersonic region that can more accurate control jet pipe makes it satisfy the design needs.

The above is the preferred embodiments of the present invention only, is not limited to the present invention, and for a person skilled in the art, the present invention can have various changes and variation.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (15)

1. an annular supersonic nozzle method for designing is characterized in that, comprises

Determine subsonic speed section curve according to entrance geometric parameter, throat opening area;

According to described subsonic speed section curve prediction section district's flow field parameter transonic speed, and extract the initial characteristics line from described flow field parameter;

Determine the Mach Number Distribution of the straight wall of supersonic speed of described jet pipe according to the Structural Design Requirement of described annular supersonic nozzle;

According to the Mach Number Distribution of described initial characteristics line and the straight wall of described supersonic speed, adopt the method for characteristic curves to determine the supersonic speed curved wall profile of described jet pipe;

Described method of characteristic curves iterative formula is:

$\left\{\begin{array}{c}\frac{\mathrm{\Δr}}{\mathrm{\Δx}}=\tan [\mathrm{\θ}\±{\sin }^{-1}(1/M)]\\ \frac{{(M^2-1)}^{1/2}}{1+(\mathrm{\γ}-1)M^2/2}\frac{\mathrm{\ΔM}}{M}\stackrel{-}{+}\mathrm{\Δ\θ}-\mathrm{\δ}\frac{\tan \mathrm{\θ}}{{(M^2-1)}^{1/2}\tan \mathrm{\θ}\±1}\frac{\mathrm{\Δr}}{r}=0\end{array}\right.$

Wherein, x is abscissa, and r is ordinate, and θ is local flow direction angle, and M is local Mach number and M〉1, δ is the pattern of flow parameter, for two dimension δ=0 of flowing, axial symmetry δ=1 of flowing, r ≠ 0, γ is the specific heat at constant pressure of gas and the specific heat ratio of specific heat at constant volume;

Described transonic speed section flow field parameter adopts the approximate Riemann solver of Roe and Runge-Kutta method to determine that concrete steps are as follows:

Do not have sticking conservation form Euler equation by numerical solution and obtain throat's flow field parameter distribution:

Wherein,

Be conserved quantity,

Be flux, Ω is control volume,

Be the control volume surface, t is the time;

Adopt the approximate Riemann solver of Roe with formula (1) space product subitem discretization:

${\left({\stackrel{\→}{F}}_c\right)}_R-{\left({\stackrel{\→}{F}}_c\right)}_L={\left({\stackrel{\‾}{A}}_{\mathrm{Roe}}\right)}_{I+1/2}({\stackrel{\→}{W}}_R-{\stackrel{\→}{W}}_L)---\left(2\right)$

Wherein two of the left side the expression flux differences,

Be the Roe matrix, subscript L and R represent left and right sides state respectively, and I represents the label of grid cell;

The time integral item that adopts the Runge-Kutta method to find the solution formula (1):

${\stackrel{\→}{W}}_I^{\left(0\right)}={\stackrel{\→}{w}}_I^n$

${\stackrel{\→}{W}}_I^{\left(1\right)}={\stackrel{\→}{W}}_I^{\left(0\right)}-{\mathrm{\α}}_1\frac{\mathrm{\Δ}{t}_I}{{\mathrm{\Ω}}_I}{\stackrel{\→}{R}}_I^{\left(0\right)}$

${\stackrel{\→}{W}}_I^{\left(2\right)}={\stackrel{\→}{W}}_I^{\left(0\right)}-{\mathrm{\α}}_2\frac{\mathrm{\Δ}{t}_I}{{\mathrm{\Ω}}_I}{\stackrel{\→}{R}}_I^{\left(1\right)}---\left(3\right)$

. . .

${\stackrel{\→}{W}}_I^{(n+1)}={\stackrel{\→}{W}}_I^{\left(m\right)}={\stackrel{\→}{W}}_I^{\left(0\right)}-{\mathrm{\α}}_m\frac{\mathrm{\Δ}{t}_I}{{\mathrm{\Ω}}_I}{\stackrel{\→}{R}}_I^{(m-1)}$

α in following formula _kThe coefficient of representing each step,

Represent that the k step is by solution

The residual error that obtains, m=3,

α ₁＝0.1918，α ₂＝0.4929，α ₃＝1，

Employing formula (1)-(3) are tried to achieve flow field parameter and are distributed, and determine the initial characteristics line according to local flow direction angle and Mach angle (arcsin (1/M)), determine the Mach number of axis initial point and along the first derivative of axis direction;

The Mach Number Distribution of the straight wall of described supersonic speed is adjusted by the two-dimensional spline curve.

2. annular supersonic nozzle method for designing according to claim 1, it is characterized in that, after the supersonic speed curved wall profile of determining described jet pipe, also comprise: adopt the momentum integral relational expression to calculate the boundary layer displacement thickness of annular supersonic nozzle inner and outer ring, determine viscosity wall curve, the momentum integral relational expression is:

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

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

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

Wherein, τ is momentum loss thickness, δ ^*Be boundary layer displacement thickness, φ is the flow direction angle, and H is the boundary layer form factor, C _fFor pressing coefficient of friction, M is local Mach number and M〉1, γ is the specific heat at constant pressure of gas and the specific heat ratio of specific heat at constant volume.

3. annular supersonic nozzle method for designing according to claim 2 is characterized in that, also comprises after determining described viscosity wall curve: carry out the boundary layer and revise, obtain the wall curve of viscosity correction.

4. annular supersonic nozzle method for designing according to claim 1, it is characterized in that, also comprise before the described subsonic speed section curve determining according to described entrance geometric parameter, described throat opening area: determine described throat opening area according to the isentropic relation formula, described isentropic relation formula is:

$\frac{A}{A^{*}}=\frac{1}{M_t}{\left[\left(\frac{2}{\mathrm{\γ}+1}\right)(1+\frac{\mathrm{\γ}-1}{2}{M_t}^2)\right]}^{(\mathrm{\γ}+1)/2(\mathrm{\γ}-1)}$

Wherein, A is the nozzle exit area, A ^*Be nozzle throat area, M _tBe the nozzle throat Mach number, γ is the specific heat at constant pressure of gas and the specific heat ratio of specific heat at constant volume.

5. annular supersonic nozzle method for designing according to claim 4 is characterized in that, is determining also to comprise before the described throat opening area according to described isentropic relation formula: the straight wall of determining described jet pipe according to the structural requirement of described jet pipe.

6. annular supersonic nozzle method for designing according to claim 5 is characterized in that, also comprises after the straight wall of determining described jet pipe: the angle that requires to determine straight wall and axis according to the acceleration distance of described jet pipe.

7. annular supersonic nozzle method for designing according to claim 1 is characterized in that, described subsonic speed section curve is two circular curves.

8. annular supersonic nozzle method for designing according to claim 1 is characterized in that, described throat flow parameter comprises: density p, speed Temperature T, pressure p and Mach number M.

9. annular supersonic nozzle method for designing according to claim 4 is characterized in that, is determining also to comprise before the described throat opening area according to described isentropic relation formula: determine the jet pipe flow according to outlet density, speed and area.

10. a kind of annular supersonic nozzle that designs of method for designing according to claim 1 is characterized in that, comprises the supersonic speed curved wall profile that the Mach Number Distribution according to initial characteristics line and the straight wall of supersonic speed adopts the method for characteristic curves to determine.

11. annular supersonic nozzle according to claim 10 is characterized in that, also comprises the subsonic speed section curve that two circular curves form.

12. annular supersonic nozzle according to claim 11 is characterized in that, also comprises the determined viscosity wall of the boundary layer displacement thickness curve that adopts the momentum integral relational expression to calculate the supersonic speed inner and outer ring.

13. annular supersonic nozzle according to claim 12 is characterized in that, also comprises the wall curve that obtains the viscosity correction.

14. annular supersonic nozzle according to claim 11 is characterized in that, the characteristic curve of described initial characteristics line for transonic speed extracting in the section flow field parameter according to the Asia of subsonic speed section curve prediction.

15. annular supersonic nozzle according to claim 10 is characterized in that, also comprises according to the straight wall of the determined supersonic speed of the structural requirement of described jet pipe.

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