CN105022928B - A kind of digitlization of aircraft fuel system position of centre of gravity determines method in real time - Google Patents

Abstract

A digital real-time determination method for the position of the center of gravity of the aircraft fuel system. The smooth kernel function is used to perform kernel approximation to the continuous function describing the fuel characteristics, and the superposition and summation of particle correlation values are used to replace the corresponding integral term in the kernel approximation equation to realize fuel control. The particle approximation of the equation discretizes the continuous fuel oil into a series of fuel particles; when solving the fuel particle control equation, there is no need to divide the control grid, which avoids the common grid distortion problem of other methods, and can capture the fuel free surface more accurately ;According to the fuel tank motion parameters corresponding to the flight attitude of the aircraft, the spatial coordinates of all fuel particles are calculated in real time at each moment; the position of the center of gravity of the fuel system is calculated in real time based on the spatial coordinates of all fuel particles, and the coordinates of the center of gravity of the fuel system change with time. The invention improves the efficiency and accuracy of real-time calculation of the position of the center of gravity of the fuel system during aircraft flight.

Description

A digital real-time determination method for the center of gravity position of aircraft fuel system

technical field

The invention relates to the technical field of determining the center of gravity of an aircraft fuel system, in particular to a digital real-time determination method for the position of the center of gravity of an aircraft fuel system.

Background technique

During the flight of the aircraft, the change of the flight attitude will cause the fuel system of the aircraft to slosh, and the fuel slosh changes the center of gravity of the fuel, which in turn causes changes in the distribution of the center of gravity of the whole aircraft. Fast and real-time acquisition of the position of the fuel center of gravity of the aircraft, and determining the distribution of the center of gravity of the entire aircraft are crucial to controlling the flight stability of the aircraft. Conventionally, computational fluid dynamics is used to solve aircraft fuel slosh. When solving the fuel control equation, the calculation grid needs to be divided. However, when the actual fuel slosh, the free liquid surface is extremely irregular, and even broken and splashed, causing grid distortion. eventually leading to the termination of the computation.

Contents of the invention

In order to overcome the above-mentioned shortcomings of the prior art, the object of the present invention is to provide a digital real-time determination method for the position of the center of gravity of the aircraft fuel system, which improves the real-time calculation efficiency and accuracy of the position of the center of gravity of the fuel system.

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

A digital real-time determination method for the position of the center of gravity of an aircraft fuel system, comprising the following steps:

1) According to the actual structural size of the fuel storage tank of the aircraft fuel system, that is, the overall length, overall width, and overall height, build a digital model of the fuel storage tank structure, which limits the fuel space movement limit;

2) Obtain the fuel oil quantity information in the fuel storage tank and the initial fuel level information;

3) Approximate and discretize the continuous fuel particle in the fuel tank into a series of interacting fuel particles with independent mass. These fuel particles are the subsequent calculation objects, and the space occupied by the fuel particles is the subsequent particleization Fuel digital calculation field;

4) Applying the boundary conditions of the digital calculation domain of particle fuel;

5) Determine the motion parameters of the fuel system based on the flight attitude of the aircraft;

6) Solve the digital calculation model of the particle fuel system in real time, that is, the fuel particle control equation;

7) Real-time calculation of the coordinates of the center of gravity of the fuel system (x _t , y _t , z _t );

8) Finally, obtain the change curve of the center of gravity position coordinates (x _t , y _t , z _t ) of the fuel system with time.

The continuous fuel particleization approximation and discreteness in the step 3) includes the following steps:

3.1) Use the smooth kernel function to perform kernel approximation to the continuous function describing the fuel characteristics, that is, the N-S equation;

Specifically, the following formula is used to perform kernel approximation to the continuous function f(x) describing fuel characteristics:

Among them, W is any smooth kernel function, h is the smooth length that determines the size of the support domain of the smooth kernel function, x is the spatial coordinate of the fuel particle at the center point of the kernel function, and x' is the position of any other fuel particle in the support domain of the fuel particle x Space coordinates, Ω is the support domain of fuel particle x, that is, the numerical calculation domain of particle fuel;

3.2) The particle approximation is used to approximate the kernel approximation equation by replacing the corresponding integral term in the kernel approximation equation with the superposition and summation of all particle correlation values in the support domain of the kernel function;

Specifically, the infinitesimal voxel dx' at the particle j is replaced by the volume ΔV _j of the particle j to realize the particle-based approximation of the equation, then the expression of the function f(x) after particle-based approximation is:

Among them, N is the total number of discrete fuel particles,

If the density of particle j is ρ _j , then the mass of particle j m _j =ρ _j ·ΔV _j ,

The function f(x) is further modified as Then the particle-based approximate expression of the continuous function f(x) describing fuel characteristics at particle i is:

In the step 4), the boundary conditions of the particleized fuel digital calculation domain are applied, which specifically includes the application of the fuel particle space movement boundary and the determination of the fuel free surface boundary, specifically:

For the imposition of the fuel particle space motion limit, the specific method is: one is to set a group of virtual particles at the motion limit, and use the repulsion force generated by the virtual particles to the real particles adjacent to the motion limit to prevent the real particles from penetrating the motion limit; The other is to set the mirror particles outside the motion limit. The mirror particles and the internal real particles are symmetrical about the motion limit. The mirror particles are opposite to the real particle speed, and the real particles are prevented from crossing the motion limit by applying a pressure gradient;

For the determination of the boundary of the free liquid surface of fuel, the specific methods are: one is that the particle density at the free liquid surface is determined by the weighted average of the surrounding particle densities, if the density of a certain particle is less than the actual particle density, the particle is deemed It is located on the free liquid surface, and the particle density is forced to be equal to the actual particle density; another method is that if the number of particles in a particle support domain is smaller than the number of particles in the support domain of the same scale as the internal particles, the particle is considered to be on the free liquid surface.

In step 7), the coordinates (x t , y _{t , z t ) of the center of gravity of the fuel system are calculated in real time, and the three-dimensional coordinates (x t , y t , z t ) of the} spatial position of the center of gravity of the fuel system at any time _t are respectively Determined by the following formula:

Among them, x _i , y _i , _zi are the coordinates of fuel particle i at time t; m _i is the mass of fuel particle i; N is the number of fuel particles.

Beneficial effects of the present invention: the present invention sequentially performs kernel approximation and particle approximation on the continuous function describing fuel characteristics, discretizes the continuous fuel oil into a series of interacting fuel particles with independent mass, and obtains all fuel particle control equations by solving The spatial coordinates of the fuel particles, and then calculate the spatial coordinates of the center of gravity of the fuel system. After the continuous fuel is approximated and discrete by particleization, the calculation process does not need to divide the calculation grid, avoiding the problem of grid distortion, and the calculation efficiency is high and the accuracy is good. .

Description of drawings

Figure 1 is a schematic diagram of continuous fuel particle approximation and discretization inside the fuel tank, where Figure 1(a) is a schematic diagram before particle approximation and discretization, and Figure 1(b) is a schematic diagram after particle approximation and discretization.

Fig. 2 is a schematic diagram of the virtual particle method to define the boundary of spatial motion.

Fig. 3 is a schematic diagram of defining the boundary of spatial motion by the mirror image particle method.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings.

A digital real-time determination method for the position of the center of gravity of an aircraft fuel system, comprising the following steps:

1) According to the actual structural size of the aircraft fuel system fuel storage tank, that is, the overall length, overall width, and overall height, build a digital model of the fuel storage tank structure, which limits the fuel space movement limit;

2) Obtain the fuel oil quantity information in the fuel storage tank and the fuel level information at the initial moment, as shown in Figure 1(a);

3) Approximate and discretize the continuous fuel particle in the fuel tank into a series of interacting fuel particles with independent mass. These fuel particles are the subsequent calculation objects, and the space occupied by the fuel particles is the subsequent particleization Fuel digital computing domain, as shown in Figure 1(b);

Continuous fuel particle approximation and discrete, including the following steps:

3.1) Use the smooth kernel function to perform kernel approximation to the continuous function describing the fuel characteristics, that is, the N-S equation;

Specifically, the following formula is used to perform kernel approximation to the continuous function f(x) describing fuel characteristics:

Among them, W is any smooth kernel function, h is the smooth length that determines the size of the support domain of the smooth kernel function, x is the spatial coordinate of the fuel particle at the center point of the kernel function, and x' is the position of any other fuel particle in the support domain of the fuel particle x Space coordinates, Ω is the support domain of fuel particle x, that is, the numerical calculation domain of particle fuel;

3.2) The particle approximation is used to approximate the kernel approximation equation by replacing the corresponding integral term in the kernel approximation equation with the superposition and summation of all particle correlation values in the support domain of the kernel function;

Specifically, the infinitesimal voxel dx' at the particle j is replaced by the volume ΔV _j of the particle j to realize the particle-based approximation of the equation, then the expression of the function f(x) after particle-based approximation is:

Among them, N is the total number of discrete fuel particles,

If the density of particle j is ρ _j , then the mass of particle j m _j =ρ _j ·ΔV _j ,

The function f(x) is further modified as Then the particle-based approximate expression of the continuous function f(x) describing fuel characteristics at particle i is:

4) Applying the boundary conditions of the particleized fuel digital calculation domain, specifically including the application of the fuel particle space movement boundary and the determination of the fuel free surface boundary;

For the imposition of the fuel particle space motion limit, the specific method is: one is to set a group of virtual particles at the motion limit, and use the repulsion force generated by the virtual particles to the real particles adjacent to the motion limit to prevent the real particles from penetrating the motion limit, As shown in Figure 2; the other is to set the mirror particles outside the motion limit, the mirror particles and the internal real particles are symmetrical about the motion limit, the mirror particles are opposite to the real particle speed, and the real particles are prevented from crossing the motion limit by applying a pressure gradient, as shown in the figure 3 shown;

For the determination of the boundary of the free liquid surface of fuel, the specific methods are: one is that the particle density at the free liquid surface is determined by the weighted average of the surrounding particle densities, if the density of a certain particle is less than the actual particle density, the particle is deemed is located on the free liquid surface, and the particle density is forced to be equal to the actual particle density; another method is to determine that the particle is located on the free liquid surface if the number of particles in the support domain of a certain particle is less than the number of particles in the support domain of the same scale as the internal particles;

5) Determine the motion parameters of the fuel system based on the flight attitude of the aircraft;

6) Real-time solution of the digital calculation model of the particle fuel system, that is, the fuel particle control equation:

Among them, α and β represent the direction, (α, β=1,2,3); r _i represents the displacement of fuel particle i;

7) Calculate the position coordinates (x _t , y _t , z _t ) of the center of gravity of the fuel system in real time, and the three-dimensional coordinates (x _t , y _t , z _t ) of the center of gravity of the fuel at any time (time t) are determined by the following formulas:

Among them, x _i , y _i , z _i are the coordinates of fuel particle i at time t; m _i is the mass of fuel particle i; N is the number of fuel particles;

8) Finally, obtain the change curve of the center of gravity position coordinates (x _t , y _t , z _t ) of the fuel system with time.

The above embodiments are only to illustrate the technical ideas of the present invention, and can not limit the protection scope of the present invention with this. All technical ideas proposed in accordance with the present invention, any changes made on the basis of technical solutions, all fall within the protection scope of the present invention. In; technologies not involved in the present invention can be realized by existing technologies.

Claims (3)

1. a kind of digitlization of aircraft fuel system position of centre of gravity determines method in real time, it is characterised in that comprise the following steps：

1) store oil box structure is built according to the practical structures size of aircraft fuel system oil tank, i.e. overall length, beam overall, total height Digital model；

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

3) by the continuity fuel particleization in oil tank approximately with being separated into a series of interactions with independent mass Fuel particle, these fuel particles are follow-up resolving 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) aircraft flight posture is based on, fuel system kinematic parameter is determined；

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

7) real-time resolving fuel system position of centre of gravity coordinate (x_t,y_t,z_t)；

8) it is final to obtain fuel system position of centre of gravity coordinate (x_t,y_t,z_t) versus time curve,

Described step 3) in continuity fuel particleization approximately with it is discrete, comprise the steps of：

3.1) kernel approximation is carried out using continuous function of the smoothing kernel function to description fuel characteristic, i.e. N-S equations；

Kernel approximation is specially carried out to the continuous function f (x) for describing fuel characteristic using following formula：

<mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>&amp;ap;</mo> <munder> <mo>&amp;Integral;</mo> <mi>&amp;Omega;</mi> </munder> <mi>f</mi> <mrow> <mo>(</mo> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <mi>h</mi> <mo>)</mo> </mrow> <msup> <mi>dx</mi> <mo>&amp;prime;</mo> </msup> </mrow>

Wherein, W is any smoothing kernel function, and h is determines that smoothing kernel function supports the smooth length of domain sizes, and x is in kernel function The space coordinate of heart point fuel particle, x ' is the space coordinate of other any fuel particles in fuel particle x support region, and Ω is Fuel particle x support region, i.e. particlized digital fuel data computational fields；

3.2) application particle is approximate carries out approximate estimation to kernel approximation equation, and method is using all particles in kernel function support region Corresponding integral term in the superposition summation substitution kernel approximation equation of correlation；

Specifically by the volume delta V of the infinitely small volume elements dx' particle j at particle j_jInstead of, realize that the particlized of equation is approximate, Then expression formulas of the function f (x) after particlized is approximate is：

<mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>&amp;ap;</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>,</mo> <mi>h</mi> <mo>)</mo> </mrow> <msub> <mi>&amp;Delta;V</mi> <mi>j</mi> </msub> </mrow>

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

If particle j density is ρ_j, then particle j quality m_j=ρ_j·ΔV_j,

Function f (x) is further modified toThe continuous of fuel characteristic is then described at particle i Function f (x) particlized approximate expression is：

<mrow> <mo>&lt;</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&gt;</mo> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <msub> <mi>m</mi> <mi>j</mi> </msub> <msub> <mi>&amp;rho;</mi> <mi>j</mi> </msub> </mfrac> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mi>W</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>,</mo> <mi>h</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow>

2. a kind of digitlization of aircraft fuel system position of centre of gravity according to claim 1 determines method in real time, it is special Levy and be, described step 4) the middle boundary condition for applying particlized digital fuel data computational fields, specifically include fuel particle space The application on motion limit border and the judgement on fuel oil free surface border, be specially：

For the application on fuel particle spatial movement boundary border, specific method is：One kind is that one group is set at motion limit Virtual particle, the repulsive force produced by virtual particle to the real particles of neighbouring motion limit moves boundary to prevent real particles from penetrating Limit；Another is the setting mirror image particle outside motion limit, and mirror image particle is symmetrical on motion limit with internal real particles, Mirror image particle is with real particles speed on the contrary, preventing real particles from passing through motion limit by applying barometric gradient；

For the judgement on fuel oil free surface border, specific method is：It is a kind of be because of free surface at particle density be to pass through What the weighted average of ambient particles density was determined, if the density of a certain particle is less than actual particle density, assert particle position Forced in free surface, and by the particle density equal to actual particle density；If another method is in a certain particle support region Number of particles be less than internal particle same scale support region in number of particles, then assert the particle be located at free surface.

3. a kind of digitlization of aircraft fuel system position of centre of gravity according to claim 1 determines method in real time, it is special Levy and be, described step 7) in real-time resolving fuel system position of centre of gravity coordinate (x_t,y_t,z_t), any t fuel system Center of gravity locus three-dimensional coordinate (x_t,y_t,z_t) determined respectively by below equation：

<mrow> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>i</mi> </msub> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> <msub> <mi>y</mi> <mi>t</mi> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>i</mi> </msub> <msub> <mi>y</mi> <mi>i</mi> </msub> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>,</mo> <msub> <mi>z</mi> <mi>t</mi> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>i</mi> </msub> <msub> <mi>z</mi> <mi>i</mi> </msub> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>m</mi> <mi>i</mi> </msub> </mrow> </mfrac> </mrow>

Wherein, x_i, y_i, z_iRespectively coordinates of the fuel particle i in t；m_iFor fuel particle i quality；N is fuel particle number Mesh.