CN102302990A - 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 article confrontation equipment has significant effects.Obtain suitable jet pipe wall surface curve through the certain designed technology, 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 quickened at contraction section gradually, and near throat, reaches the velocity of sound; Continue to quicken at expansion segment then, until going out the supersonic flow that required Mach number of interruption-forming and flow direction angle distribute.

Toroidal nozzle is different from traditional two-dimensional 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 existing multiple at present comparatively ripe two dimension or axisymmetric nozzle method for designing, 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-dimensional 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 a current of spring; Transition is evenly to flow then, and proposes a cover empirical equation to 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 like 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 through 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 an empirical equation, and jet pipe is difficult to accomplish optimize.Sivells inherits the design philosophy of Cresci; Transonic speed theoretical (I.M.Hall.TransonicFlowinTwo-dimensionalandAxially-symmet ricNozzles.QuarterlyJournalofMechanicsandAppliedMathemat ics in conjunction with Hall; XV:487-508; 1962.); By setting the pneumatic profile of jet pipe (J.C.Sivells.AComputerProgramfortheAerodynamicsDesignofAx isymmetricandPlanarNozzlesforSupersonicandHypersonicWind 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 on structural design, does not go through but the design of jet pipe profile curve done.U.S.'s patent of invention 3940067 has proposed a kind of plug nozzle that is used for rocket engine; Actual is a kind of toroidal nozzle; Its design object is under the prerequisite that guarantees combustion chamber and extraneous pressure reduction, to realize shortest length; 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 curve that this method is designed 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, a kind of annular supersonic nozzle method for designing is provided, has comprised according to inlet geometric parameter, throat opening area and confirm 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; Confirm 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 confirm 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 an abscissa, and r is an 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, after the supersonic speed curved wall profile of confirming jet pipe, also comprise: adopt the momentum integral relational expression to calculate the boundary layer displacement thickness of supersonic speed inner and outer ring, confirm 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 a 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, confirming also to comprise before the subsonic speed section curve according to inlet geometric parameter, throat opening area: confirm 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, confirming that according to the isentropic relation formula throat opening area also comprises before: the straight wall of confirming jet pipe according to the structural requirement of jet pipe.

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

Subsonic speed section curve is two circular curves.

Further, Asia transonic speed section flow field parameter adopts the approximate Riemann solver of a Roe definite with the Runge-Kutta method, and concrete steps are following:

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

Where,

is the conserved quantity,

is the flux, Ω for the control of body,

for the control surface;

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

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

Which left the two represents the difference between the flux,

to Roe matrix, the subscripts L and R represent the left and right state, I indicates the reference numeral grid cells;

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 through tabling look-up,

Represent that the k step is by separating

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 confirm the initial characteristics line according to local flow direction angle and Mach angle (arcsin (1/M)), confirm the Mach number of axis initial point and along the first derivative of axis direction.

Further, throat flow parameters include: the density ρ, speed

temperature T, pressure p and Mach number M.

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

Further, confirming that according to the isentropic relation formula throat opening area also comprises before: confirm the jet pipe flow according to outlet density, speed and area.

According to a further aspect in the invention, a kind of annular supersonic nozzle is provided, has 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 confirm 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; Confirm 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 the precision and the quality of annular supersonic nozzle.The Mach Number Distribution of the straight wall of supersonic speed is adjusted through the two-dimensional spline curve, makes the Mach Number Distribution of supersonic region of annular supersonic nozzle have adjustability, can control the Mach Number Distribution of the supersonic region of jet pipe more accurately, makes it satisfy design demand.

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 to explain the present invention, does not constitute improper qualification of the present invention.In the accompanying drawings:

Fig. 1 shows the configuration sketch map according to annular supersonic nozzle of the present invention;

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

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

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

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

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

Fig. 7 shows the actual wall sketch map 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 with reference to the accompanying drawings and combine embodiment to describe the present invention in detail.Need to prove that under the situation of not conflicting, embodiment and the characteristic among the embodiment among the application can make up each other.

In the present invention; The subsonic speed section is meant that air-flow gets into 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 promptly transonic speed the section; Be meant that air-flow gets into the 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 confirm internal face be straight wall still be outside wall surface be straight wall; (a) and (b) among Fig. 1 with (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 confirming the straight wall of jet pipe according to annular supersonic nozzle structural requirement, the angle of straight wall and axis is confirmed 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, the angle of then straight wall and axis can be on the occasion of, promptly expand outwardly, with reference to (b) among the figure 1 with (f); If require acceleration distance longer, the angle of then straight wall and axis can be negative value, promptly inwardly shrinks, with reference to (c) among the figure 1 with (e).

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

$\stackrel{.}{m}=\mathrm{\ρVA}$

Where:

is the nozzle flow rate, ρ the density of the nozzle outlet, V is the nozzle outlet velocity, A is the nozzle exit area.

Confirm 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 confirming inlet geometric parameter and nozzle throat area, confirm subsonic speed section curve according to inlet 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 confirmed according to Structural Design Requirement; The starting point and the slope thereof of 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 gets into the supersonic speed section obtain better fluidised form.

After definite subsonic speed section curve, adopt transonic speed section flow field parameter of 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 through numerical solution and obtain throat's flow parameter distribution:

Where,

is the conserved quantity,

is the flux, Ω for the control of the body, on behalf of grid cells, for the control surface, on behalf of grid cell surface.

Throat flow parameters including density ρ, speed

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

corresponding density ρ, speed

temperature T, pressure p and the Mach number M is solved, all supersonic nozzle flow parameter distribution,

represent the solution process parameters required for solution flux.

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

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

Which left the two represents the difference between the flux,

to Roe matrix, the subscripts L and R represent the left and right state, I represents grid cell label.

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 separating

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, confirm the initial characteristics line, confirm the Mach number of axis initial point and along the first derivative of axis direction according to local flow direction angle and Mach angle (arcsin (1/M)).

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 a 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; Like Fig. 4 and shown in Figure 5; Fig. 4 is the configuration picture of the annular supersonic nozzle after the Mach Number Distribution of confirming 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 sketch map on the axis direction; According to the structure of setting; Confirm the throat's Mach number of annular supersonic nozzle and the design Mach number in exit; Use two-dimensional spline curve adjustment Mach Number Distribution then, the flow field Mach Number Distribution is met design requirement.Can find out in conjunction with Fig. 4 and Fig. 5; When the Mach Number Distribution of the straight wall configuration line of confirming supersonic nozzle; At first confirm 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; Adjust the Mach Number Distribution of the intermediate point B of straight wall configuration curve between the terminal point C in the trunnion Mach number of initial point A and exit and the relation between the axis by the quadratic spline curve then, make the flow field Mach Number Distribution satisfy the jet pipe designing requirement.

After the Mach Number Distribution of confirming initial characteristics line and the straight wall of annular supersonic nozzle,, obtain supersonic speed curved wall profile structure, as shown in Figure 6 according to method of characteristic curves iterative supersonic speed curved wall profile parameter.Here, because the initial characteristics line confirmed, therefore, according to the initial point of the supersonic speed curved wall face configuration line of the annular supersonic nozzle that can confirm 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; Confirm to go up the curved wall face configuration line each point Mach Number Distribution of Mach Number Distribution, and finally confirm the upper wall surface of jet pipe supersonic speed curved wall profile corresponding to line segment AC.

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 an abscissa, and r is an 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 relation 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 relation 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 relation 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 a 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 the 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 straight wall profile of determined supersonic speed and the formed annular supersonic nozzle of supersonic speed curved wall profile; And through 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 the 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 confirm 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; Can find out; 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 confirm 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; Confirm 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 the precision and the quality of annular supersonic nozzle.The Mach Number Distribution of the straight wall of supersonic speed is adjusted through the two-dimensional spline curve, makes the Mach Number Distribution of supersonic region of annular supersonic nozzle have adjustability, can control the Mach Number Distribution of the supersonic region of jet pipe more accurately, makes it satisfy design demand.

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.All within spirit of the present invention and principle, any modification of being done, be equal to replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (18)

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

Confirm subsonic speed section curve according to inlet geometric parameter, throat opening area;

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

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

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

2. annular supersonic nozzle method for designing according to claim 1 is characterized in that, said 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 an abscissa, and r is an 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.

3. annular supersonic nozzle method for designing according to claim 1; It is characterized in that; After the supersonic speed curved wall profile of confirming said 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; Confirm 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 a 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, and γ is the specific heat at constant pressure of gas and the specific heat ratio of specific heat at constant volume.

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

5. annular supersonic nozzle method for designing according to claim 1; It is characterized in that; Confirming that according to said inlet geometric parameter, said throat opening area said subsonic speed section curve also comprises before: confirm said throat opening area according to the isentropic relation formula, said 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.

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

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

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

9. annular supersonic nozzle method for designing according to claim 1 is characterized in that, said Asia transonic speed section flow field parameter adopts approximate Riemann solver of Roe and Runge-Kutta method to confirm that concrete steps are following:

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

Where,

is conserved quantities,

as the flux, Ω for the control of body,

for the control surface;

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

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

Which left the two represents the difference between the flux,

as the Roe matrix, the subscripts L and R represent the left and right state, I said that grid cell labeling;

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 separating

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 confirm the initial characteristics line according to local flow direction angle and Mach angle (arcsin (1/M)), confirm the Mach number of axis initial point and along the first derivative of axis direction.

A process according to claim 9, wherein the annular supersonic nozzle design, characterized in that the throat flow parameters include: the density ρ, speed

temperature T, pressure p and Mach number M.

11. annular supersonic nozzle method for designing according to claim 1 is characterized in that the Mach Number Distribution of the straight wall of said supersonic speed is adjusted through the two-dimensional spline curve.

12. annular supersonic nozzle method for designing according to claim 5 is characterized in that, is confirming that according to said isentropic relation formula said throat opening area also comprises before: confirm the jet pipe flow according to outlet density, speed and area.

13. an annular supersonic nozzle is characterized in that, comprises 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.

14. annular supersonic nozzle according to claim 13 is characterized in that, also comprises the subsonic speed section curve that two circular curves form.

15. annular supersonic nozzle according to claim 14 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.

16. annular supersonic nozzle according to claim 15 is characterized in that, also comprises the wall curve that obtains the viscosity correction.

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

18. annular supersonic nozzle according to claim 13 is characterized in that, also comprises according to the straight wall of the determined supersonic speed of the structural requirement of said jet pipe.

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