CN105022928A - Digitized real-time determination method for center-of-gravity position of fuel system of aircraft - Google Patents

Abstract

A digitized real-time determination method for a center-of-gravity position of a fuel system of an aircraft comprises: carrying out kernel approximation on a continuous function which describes the fuel characteristics through a smoothing kernel function, replacing a corresponding integral item in a kernel approximation equation by superposed summation of a particle correlation value to realize particlized approximation of a fuel control equation, and discretizing continuous fuel to a series of fuel particles; not dividing control meshes when the fuel particle control equation is resolved to avoid common mesh deformation by other methods, and relatively precisely capturing a free surface of the fuel; resolving space coordinates of all fuel particles at the moments in real time according to oil tank movement parameters corresponding to flight attitudes of the aircraft; and calculating the center-of-gravity position of the fuel system in real time according to the space coordinates of all fuel particles and outputting a curve of the coordinates of the center-of-gravity position of the fuel system changing along with time. According to the method provided by the invention, the real-time resolving efficiency and precision of the center-of-gravity position of the fuel system in the flight process of the aircraft are improved.

Description

A kind of real-time defining method of digitizing of aircraft fuel system centre of gravity place

Technical field

The present invention relates to aircraft fuel system center of gravity determination technical field, be specifically related to a kind of real-time defining method of digitizing of aircraft fuel system centre of gravity place.

Background technology

In aircraft flight process, the change of flight attitude can cause rocking of aircraft fuel system, and fuel oil rocks the center of gravity changing fuel oil, and then causes the change of full machine gravity centre distribution.Fast, the change of Real-time Obtaining aircraft fuel oil centre of gravity place, determine that full machine gravity centre distribution is most important to manipulation aircraft flight stability.Conventional employing computational fluid dynamics solves the method that aircraft fuel oil rocks, need when solving fuel oil governing equation to divide computing grid, and when actual fuel oil rocks, its free surface is extremely irregular, and fragmentation, splashing even can occur, cause mesh distortion, finally cause calculating termination.

Summary of the invention

In order to overcome the shortcoming of above-mentioned prior art, the object of this invention is to provide a kind of real-time defining method of digitizing of aircraft fuel system centre of gravity place, improve real-time resolving efficiency and the precision of fuel system centre of gravity place.

In order to achieve the above object, the technical scheme that the present invention takes is:

The real-time defining method of digitizing of aircraft fuel system centre of gravity place, comprises the following steps:

1) according to the practical structures size of aircraft fuel system oil tank, i.e. the digital model of overall length, beam overall, height overall structure oil tank structure, this model defines fuel space motion limit;

2) the fuel quantity information in oil tank and initial time fuel liquid level information is obtained;

3) the continuity fuel particle in oil tank be similar to and be separated into a series of interactional fuel particle with independent mass, these fuel particle are and follow-up resolve object, and the space occupied by fuel particle is follow-up particlized digital fuel data computational fields;

4) boundary condition of particlized digital fuel data computational fields is applied;

5) based on aircraft flight attitude, fuel system kinematic parameter is determined;

6) real-time resolving particlized fuel system digital computation model, i.e. fuel particle governing equation;

7) real-time resolving fuel system centre of gravity place coordinate (x _t, y _t, z _t);

8) final acquisition fuel system centre of gravity place coordinate (x _t, y _t, z _t) curve over time.

Described step 3) in continuity fuel particleization approximate and discrete, comprise following steps:

3.1) adopt smoothing kernel function to the continuous function describing fuel characteristic, namely N-S equation carries out kernel approximation;

Be specially and adopt following formula to carry out kernel approximation to continuous function f (x) describing fuel characteristic:

$f\left(x\right)\≈\underset{\mathrm{\Ω}}{\∫}f\left(x^{\′}\right)W(x-x^{\′},h){\mathrm{dx}}^{\′}$

Wherein, W is arbitrary smoothing kernel function, h is the smooth length determining smoothing kernel function support region size, x is the volume coordinate of kernel function central point fuel particle, the volume coordinate of other arbitrary fuel particle in the support region that x ' is fuel particle x, Ω is the support region of fuel particle x, i.e. particlized digital fuel data computational fields;

3.2) application particle is approximate carries out approximate estimation to kernel approximation equation, and method adopts the superposition of all particle correlations in kernel function support region summation to replace integration item corresponding in kernel approximation equation;

Specifically by the volume delta V of the infinitely small volume elements dx' particle j at particle j place _jreplace, the particlized realizing equation is similar to, then the expression formula of function f (x) after particlized is similar to is:

$f\left(x\right)\≈\underset{j=1}{\overset{N}{\Σ}}f\left(x_j\right)W(x-x_j,h){\mathrm{\ΔV}}_j$

Wherein, N is the sum of discrete rear fuel particle,

If the density of particle j is ρ _j, then the quality m of particle j _j=ρ _jΔ V _j,

Function f (x) is revised as further then the particlized approximate expression of continuous function f (x) of particle i place description fuel characteristic is:

$<f\left(x_i\right)>=\underset{j=1}{\overset{N}{\&Sigma;}}\frac{m_j}{{\mathrm{\&rho;}}_j}f\left(x_j\right)W(x_i-x_j,h).$

Described step 4) the middle boundary condition applying particlized digital fuel data computational fields, specifically comprise the applying on fuel particle spatial movement boundary border and the judgement on fuel oil free surface border, be specially:

For the applying on fuel particle spatial movement boundary border, concrete grammar is: one arranges one group of virtual particle at motion limit place, and the repulsive force produced by the real particles of virtual particle to contiguous motion limit stops real particles to penetrate motion limit; Another kind is at motion limit outer setting mirror image particle, and mirror image particle and inner real particles are about motion limit symmetry, and mirror image particle is contrary with real particles speed, prevents real particles from passing through motion limit by applying pressure gradient;

For the judgement on fuel oil free surface border, concrete grammar is: a kind of is because the particle density at free surface place is determined by the weighted mean of ambient particles density, if the density of a certain particle is less than actual particle density, then assert that this particle is positioned at free surface, and this particle density is forced to equal actual particle density; If another kind method is the number of particles that the number of particles in a certain particle support region is less than in internal particle same scale support region, then assert that this particle is positioned at free surface.

Described step 7) middle real-time resolving fuel system centre of gravity place coordinate (x _t, y _t, z _t), the three-dimensional coordinate (x of the center of gravity locus of arbitrary t fuel system _t, y _t, z _t) determined by following formula respectively:

$x_t=\frac{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i{x}_i}{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i},y_t=\frac{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i{y}_i}{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i},z_t=\frac{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i{z}_i}{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i}$

Wherein, x _i, y _i, z _ibe respectively the coordinate of fuel particle i in t; m _ifor the quality of fuel particle i; N is fuel particle number.

Beneficial effect of the present invention: the present invention carries out kernel approximation to the continuous function describing fuel characteristic successively and particle is similar to, a series of interactional fuel particle with independent mass is changed into by discrete for continuous fuel oil, by resolving fuel particle governing equation, obtain the volume coordinate of all fuel particle, and then calculate the volume coordinate of fuel system centre of gravity place, continuous fuel oil is after particlized is similar to and is discrete, solution process is without the need to dividing computing grid, avoid mesh distortion problem, resolve that efficiency is high, precision good.

Accompanying drawing explanation

Fig. 1 is the approximate and discrete schematic diagram of the continuous fuel particleization of fuel tank internal, wherein Fig. 1 (a) for particlized be similar to and discrete before schematic diagram, wherein Fig. 1 (b) for particlized be similar to discrete after schematic diagram.

Fig. 2 is virtual particle legal adopted spatial movement boundary border schematic diagram.

Fig. 3 is mirror image particle method definition space motion limit border schematic diagram.

Embodiment

Below in conjunction with accompanying drawing, the present invention is further illustrated.

The real-time defining method of digitizing of aircraft fuel system centre of gravity place, comprises the following steps:

1) according to the practical structures size of aircraft fuel system oil tank, i.e. the digital model of overall length, beam overall, height overall structure oil tank structure, namely this model defines fuel space motion limit;

2) the fuel quantity information in oil tank and initial time fuel liquid level information is obtained, as shown in Fig. 1 (a);

3) the continuity fuel particle in oil tank be similar to and be separated into a series of interactional fuel particle with independent mass, these fuel particle are and follow-up resolve object, space occupied by fuel particle is follow-up particlized digital fuel data computational fields, as shown in Fig. 1 (b);

Continuity fuel particleization is approximate and discrete, comprises following steps:

3.1) adopt smoothing kernel function to the continuous function describing fuel characteristic, namely N-S equation carries out kernel approximation;

Be specially and adopt following formula to carry out kernel approximation to continuous function f (x) describing fuel characteristic:

$f\left(x\right)\&ap;\underset{\mathrm{\&Omega;}}{\&Integral;}f\left(x^{\&prime;}\right)W(x-x^{\&prime;},h){\mathrm{dx}}^{\&prime;}$

Wherein, W is arbitrary smoothing kernel function, h is the smooth length determining smoothing kernel function support region size, x is the volume coordinate of kernel function central point fuel particle, the volume coordinate of other arbitrary fuel particle in the support region that x ' is fuel particle x, Ω is the support region of fuel particle x, i.e. particlized digital fuel data computational fields;

3.2) application particle is approximate carries out approximate estimation to kernel approximation equation, and method adopts the superposition of all particle correlations in kernel function support region summation to replace integration item corresponding in kernel approximation equation;

Specifically by the volume delta V of the infinitely small volume elements dx' particle j at particle j place _jreplace, the particlized realizing equation is similar to, then the expression formula of function f (x) after particlized is similar to is:

$f\left(x\right)\&ap;\underset{j=1}{\overset{N}{\&Sigma;}}f\left(x_j\right)W(x_i-x_j,h){\mathrm{\&Delta;V}}_j$

Wherein, N is the sum of discrete rear fuel particle,

If the density of particle j is ρ _j, then the quality m of particle j _j=ρ _jΔ V _j,

Function f (x) is revised as further then the particlized approximate expression of continuous function f (x) of particle i place description fuel characteristic is:

$<f\left(x_i\right)>=\underset{j=1}{\overset{N}{\&Sigma;}}\frac{m_j}{{\mathrm{\&rho;}}_j}f\left(x_j\right)W(x_i-x_j,h);$

4) apply the boundary condition of particlized digital fuel data computational fields, specifically comprise the applying on fuel particle spatial movement boundary border and the judgement on fuel oil free surface border;

For the applying on fuel particle spatial movement boundary border, concrete grammar is: one arranges one group of virtual particle at motion limit place, the repulsive force produced by the real particles of virtual particle to contiguous motion limit stops real particles to penetrate motion limit, as shown in Figure 2; Another kind is at motion limit outer setting mirror image particle, and mirror image particle and inner real particles are about motion limit symmetry, and mirror image particle is contrary with real particles speed, prevents real particles from passing through motion limit, as shown in Figure 3 by applying pressure gradient;

For the judgement on fuel oil free surface border, concrete grammar is: a kind of is because the particle density at free surface place is determined by the weighted mean of ambient particles density, if the density of a certain particle is less than actual particle density, then assert that this particle is positioned at free surface, and this particle density is forced to equal actual particle density; If another kind method is the number of particles that the number of particles in a certain particle support region is less than in internal particle same scale support region, then assert that this particle is positioned at free surface;

5) based on aircraft flight attitude, fuel system kinematic parameter is determined;

6) real-time resolving particlized fuel system digital computation model, i.e. fuel particle governing equation:

$\frac{{\mathrm{d\&rho;}}_i}{dt}=\underset{j=1}{\overset{N}{\&Sigma;}}{m}_j(v_i^{\mathrm{\&beta;}}-v_j^{\mathrm{\&beta;}})\&CenterDot;\frac{\&part;W_{ij}}{\&part;x_i^{\mathrm{\&beta;}}}$

$\frac{{\mathrm{dv}}_i^{\mathrm{\&alpha;}}}{dt}=\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{m}_j\left(\frac{{\mathrm{\&sigma;}}_i^{\mathrm{\&alpha;}\mathrm{\&beta;}}}{{\mathrm{\&rho;}}_i^2}+\frac{{\mathrm{\&sigma;}}_j^{\mathrm{\&alpha;}\mathrm{\&beta;}}}{{\mathrm{\&rho;}}_j^2}\right)\&CenterDot;\frac{\&part;W_{ij}}{\&part;x_i^{\mathrm{\&beta;}}}+F_{\mathrm{\&alpha;}}$

$\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i\frac{{\mathrm{dr}}_i}{dt}=\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i{v}_i$

Wherein, α and β represents direction, (α, β=1,2,3); r _irepresent the displacement of fuel particle i;

7) real-time resolving fuel system centre of gravity place coordinate (x _t, y _t, z _t), any instant (t) fuel oil center of gravity 3 d space coordinate (x _t, y _t, z _t) determined by following formula respectively:

$x_t=\frac{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i{x}_i}{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i},y_t=\frac{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i{y}_i}{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i},z_t=\frac{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i{z}_i}{\underset{i=1}{\overset{N}{\&Sigma;}}{m}_i}$

Wherein, x _i, y _i, z _ibe respectively the coordinate of fuel particle i in t; m _ifor the quality of fuel particle i; N is fuel particle number;

8) final acquisition fuel system centre of gravity place coordinate (x _t, y _t, z _t) curve over time.

Above embodiment is only and technological thought of the present invention is described, can not limit protection scope of the present invention with this, every technological thought proposed according to the present invention, and any change that technical scheme basis is done, all falls within scope; The technology that the present invention does not relate to all is realized by prior art.

Claims (4)

1. the real-time defining method of the digitizing of aircraft fuel system centre of gravity place, is characterized in that, comprise the following steps:

1) according to the practical structures size of aircraft fuel system oil tank, i.e. the digital model of overall length, beam overall, height overall structure oil tank structure;

2) the fuel quantity information in oil tank and initial time fuel liquid level information is obtained;

3) the continuity fuel particle in oil tank be similar to and be separated into a series of interactional fuel particle with independent mass, these fuel particle are and follow-up resolve object, and the space occupied by fuel particle is follow-up particlized digital fuel data computational fields;

4) boundary condition of particlized digital fuel data computational fields is applied;

5) based on aircraft flight attitude, fuel system kinematic parameter is determined;

6) real-time resolving particlized fuel system digital computation model, i.e. fuel particle governing equation;

7) real-time resolving fuel system centre of gravity place coordinate (x _t, y _t, z _t);

8) final acquisition fuel system centre of gravity place coordinate (x _t, y _t, z _t) curve over time.

2. the real-time defining method of digitizing of a kind of aircraft fuel system centre of gravity place according to claim 1, is characterized in that, described step 3) in continuity fuel particleization approximate and discrete, comprise following steps:

3.1) adopt smoothing kernel function to the continuous function describing fuel characteristic, namely N-S equation carries out kernel approximation;

Be specially and adopt following formula to carry out kernel approximation to continuous function f (x) describing fuel characteristic:

Wherein, W is arbitrary smoothing kernel function, h is the smooth length determining smoothing kernel function support region size, x is the volume coordinate of kernel function central point fuel particle, the volume coordinate of other arbitrary fuel particle in the support region that x ' is fuel particle x, Ω is the support region of fuel particle x, i.e. particlized digital fuel data computational fields;

3.2) application particle is approximate carries out approximate estimation to kernel approximation equation, and method adopts the superposition of all particle correlations in kernel function support region summation to replace integration item corresponding in kernel approximation equation;

Specifically by the volume delta V of the infinitely small volume elements dx' particle j at particle j place _jreplace, the particlized realizing equation is similar to, then the expression formula of function f (x) after particlized is similar to is:

Wherein, N is the sum of discrete rear fuel particle,

If the density of particle j is ρ _j, then the quality m of particle j _j=ρ _jΔ V _j,

Function f (x) is revised as further then the particlized approximate expression of continuous function f (x) of particle i place description fuel characteristic is:

3. the real-time defining method of digitizing of a kind of aircraft fuel system centre of gravity place according to claim 1, it is characterized in that, described step 4) the middle boundary condition applying particlized digital fuel data computational fields, specifically comprise the applying on fuel particle spatial movement boundary border and the judgement on fuel oil free surface border, be specially:

For the applying on fuel particle spatial movement boundary border, concrete grammar is: one arranges one group of virtual particle at motion limit place, and the repulsive force produced by the real particles of virtual particle to contiguous motion limit stops real particles to penetrate motion limit; Another kind is at motion limit outer setting mirror image particle, and mirror image particle and inner real particles are about motion limit symmetry, and mirror image particle is contrary with real particles speed, prevents real particles from passing through motion limit by applying pressure gradient;

For the judgement on fuel oil free surface border, concrete grammar is: a kind of is because the particle density at free surface place is determined by the weighted mean of ambient particles density, if the density of a certain particle is less than actual particle density, then assert that this particle is positioned at free surface, and this particle density is forced to equal actual particle density; If another kind method is the number of particles that the number of particles in a certain particle support region is less than in internal particle same scale support region, then assert that this particle is positioned at free surface.

4. the real-time defining method of digitizing of a kind of aircraft fuel system centre of gravity place according to claim 1, is characterized in that, described step 7) middle real-time resolving fuel system centre of gravity place coordinate (x _t, y _t, z _t), the three-dimensional coordinate (x of the center of gravity locus of arbitrary t fuel system _t, y _t, z _t) determined by following formula respectively:

Wherein, x _i, y _i, z _ibe respectively the coordinate of fuel particle i in t; m _ifor the quality of fuel particle i; N is fuel particle number.