Liquid oxygen flowmeter fluid-solid coupling particle simulation method for liquid rocket engine

Abstract

A liquid rocket engine liquid oxygen flowmeter fluid-solid coupling particle simulation method, through analyzing the driving effect of the fluid working medium on the rotating part of the turbine flowmeter, the stable rotating speed of the rotating part is obtained, and the flow of the fluid working medium is further converted; first, the numerical analysis model of the physical field to be solved is determined, and the accurate analysis model of the physical field to be solved is constructed, then the meshless particle method is used to disperse the solving domain, the position information of the inflow boundary and the outflow boundary of the solving domain is represented by constructing a Cartesian coordinate system, and the position information of all particles is also represented, in each iteration step in the solving process, the position information of each particle is identified and judged, when the particle is located outside the solving domain, it is reset back to the inflow boundary and redefined according to the preset inflow boundary condition, and subsequent iteration solving is carried out; the present application can solve the coupling process of complex physical field, and has lower calculation cost.

Description

Technical Field

[0001] This invention belongs to the field of liquid oxygen flow meter technology, specifically relating to a fluid-structure interaction particle simulation method for liquid oxygen flow meters in liquid rocket engines. Background Technology

[0002] Liquid oxygen, as a commonly used and pollution-free oxidizer in liquid rocket engines, is widely used in aerospace liquid rocket engines. Accurate measurement of liquid oxygen flow rate is crucial for engine development and obtaining accurate engine characteristics. The most commonly used instrument for flow measurement is the turbine flow meter, a velocity-type flow measurement instrument with advantages such as high precision and wide measurement range, widely used in the aerospace field. Because liquid oxygen operates at low temperatures, controlling its operating temperature in a laboratory environment is often difficult. Therefore, precise numerical simulation analysis of the liquid oxygen flow meter's operating status is necessary to ensure its performance reliability. The above analysis often involves coupled calculations of complex physical fields. Balancing computational efficiency and time cost, numerical analysis methods are commonly used in engineering. Currently, commonly used numerical analysis methods include the finite element method and the finite volume method.

[0003] Both the finite element method (FEM) and the finite volume method discretize the computational domain by dividing it into meshes, approximating the solution for each mesh element, and then solving for an approximate solution for the entire computational domain. However, when dealing with problems involving complex physical field coupling, the mesh-based FEM and finite volume methods suffer from mesh distortion and high computational costs, leading to a sharp decrease in computational accuracy. The meshless particle method can solve this problem by addressing mesh distortion. The meshless particle method describes the computational domain using a group of interacting particles. By solving the dynamic equations of the particle group and tracking the trajectory of each particle, the dynamic behavior of the entire computational domain is obtained. Since there is no mesh relationship between the particles, it avoids a series of problems such as accuracy loss caused by large mesh deformation. Furthermore, the meshless particle method requires continuous injection of particles into the given computational domain to ensure the continuity of the simulation analysis. However, as the analysis time increases, the number of particles required also increases, which leads to an increase in computational cost that cannot be ignored. This makes it difficult to meet the requirements of stable and efficient analysis. Therefore, there is an urgent need for a numerical analysis method that can solve the coupling process of complex physical fields while having a lower computational cost. Summary of the Invention

[0004] To overcome the shortcomings of the above-mentioned technologies, the present invention aims to provide a fluid-structure interaction particle simulation method for liquid oxygen flowmeters in liquid rocket engines, which can solve the coupling process of complex physical fields and has a low computational cost.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A fluid-structure interaction particle simulation method for liquid oxygen flowmeters in liquid rocket engines includes the following steps:

[0007] 1) Determine the numerical analysis model of the physical field to be solved:

[0008] Import the true geometric configuration of the problem to be solved, define the geometric coefficients representing the known solution region, i.e., the shape control points of the solution region, and establish a complete set of analysis node vectors and shape interpolation basis functions in the parametric coordinate system based on spline curves, according to the accuracy requirements of geometric modeling. Take 9 control points to construct a cubic B-spline curve, whose node vector is a non-decreasing sequence ξ = {ξ1, ξ2, ..., ξ1} between 0 and 1. m+p+1 The recursive formula for the B-spline basis functions is as follows:

[0009]

[0010] Where i = 1, 2, ..., m + p + 1; N is the basis function of the B-spline curve, p is the order of the basis function, and ξ is the node in the parametric coordinate system;

[0011] Based on the node vectors and shape control points obtained in the above process, the physical domain is divided. Rational B-spline surfaces are obtained using B-spline basis functions and weighting coefficients, thus initially generating a numerical analysis model for computational analysis. The rational B-spline basis function is expressed as follows:

[0012]

[0013] Where R is the bilinear rational B-spline basis function, and ω is the projection weight factor;

[0014] 2) Construct an accurate analytical model for the physical problem to be solved:

[0015] For the numerical analysis model established in step 1), depending on the different computational accuracy requirements and computational capability constraints, the methods of inserting geometric operation nodes and increasing the order of rational B-spline basis functions at different nodes are adopted to refine the solution domain boundary and the curve, thereby obtaining an accurate analysis model of the physical problem to be solved.

[0016] 3) Discretize the solution domain:

[0017] The solution domain within the exact analytical model is discretized using a particle-based approach, and the kernel function of the particles is expressed using a Gaussian function as follows:

[0018]

[0019] Where r is the distance from the central particle, and h is the smooth length;

[0020] The motion of fluid particles in the solution domain is controlled by the Navier-Stokes equations. The particle-based Lagrangian Navier-Stokes equations after the kernel approximation are as follows:

[0021]

[0022]

[0023] Where ρ is the fluid density, t is time, M is the particle mass, v is the particle velocity, P is the pressure, μ is the dynamic viscosity, g is the gravitational acceleration, and l ij Let be the distance between particle i and particle j. The gradient of the kernel function;

[0024] 4) Construct a Cartesian coordinate system to determine the coordinate information of the solution domain:

[0025] Based on the discretized solution domain obtained in step 3), particle inflow boundary and particle outflow boundary are set on both sides of it. Particles enter the solution domain from the inflow boundary and flow out of the solution domain from the outflow boundary. The position parameters of the precise analysis model constructed in step 2) and the discretized particles in step 3) are represented by the Cartesian coordinate system. In the Cartesian coordinate system, the particle inflow boundary and outflow boundary in the solution domain are represented by uniquely determined coordinates.

[0026] 5) Determine if the particle's position is within the solution domain:

[0027] During the solution process, the position information of each particle in the solution domain is updated with each iteration. When the position coordinates of a particle exceed the position coordinates of the outflow boundary, the particle no longer participates in the calculation within the solution domain.

[0028] 6) Place the particles that have flowed out of the solution domain back into the boundary:

[0029] According to the judgment condition in step 5), when the coordinate information of the particle is not within the range defined by the solution domain, it is reset back to the inflow boundary and redefined according to the pre-set inflow boundary conditions, i.e., pressure inflow or velocity inflow, and then the subsequent solution is performed.

[0030] 7) Analysis and Calculation:

[0031] Based on the Cartesian coordinate system determined in step 4), the position information of the solution domain is uniquely determined. The motion of particles in the solution domain is controlled by Lagrange-type Navier-Stokes equations, and the updating of particle positions follows the Lagrange method, with the equations as follows:

[0032]

[0033] Where v x (t), v y (t), vz (t) represents the components of the particle's velocity along the three axes in the Cartesian coordinate system. In each iteration step, the flow field is first analyzed and solved. Then, the flow field solution obtained in this iteration step is applied to the fluid-structure interaction calculation to analyze the driving process of the working fluid on the turbine rotor in the turbine flowmeter and solve for the turbine rotor speed. When the turbine rotor speed no longer changes between adjacent iteration steps, the calculation process converges. Finally, the input flow rate of the working fluid is obtained by converting the turbine rotor speed. The conversion equation is as follows:

[0034]

[0035] Where n is the rotational speed, K is the instrument coefficient, and Q is the flow rate.

[0036] The present invention has the following beneficial effects:

[0037] This invention proposes a fluid-structure interaction particle simulation method for liquid oxygen flowmeters in liquid rocket engines. It uses a meshless particle discretization method to discretize the solution domain, which can meet the analysis and calculation of multi-physics coupling in complex flow states. Furthermore, this invention puts the particles that flow out of the calculation domain boundary back into the inlet boundary for cyclic calculation, avoiding the problems of increased analysis time and reduced calculation efficiency caused by the continuous increase of particle number, thus achieving stable and efficient analysis and calculation. Attached Figure Description

[0038] Figure 1 This is a flowchart of the present invention.

[0039] Figure 2 This is a schematic diagram of a turbine flow meter assembly according to an embodiment of the present invention.

[0040] Figure 3 This is a schematic diagram of the internal piping of a certain type of turbine flow meter according to an embodiment of the present invention.

[0041] Figure 4 A schematic diagram of the discrete solution domain and the filling of particles.

[0042] Figure 5 A schematic diagram for identifying particle position information.

[0043] Figure 6 A schematic diagram of particle reset for the outflow solution domain. Detailed Implementation

[0044] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It is used for the analysis and calculation of flow control systems in high-thrust aerospace engines. This embodiment takes the flow field analysis within the pipeline system of a certain type of turbine flowmeter as an example. Figure 2 and Figure 3As shown, this model of turbine flow meter consists of an upstream guide vane 1, a turbine rotor 2, and a downstream guide vane 3. The turbine flow meter assembly is located in a horizontal pipe 4 with a length of 9m and a distance of 6m from the inlet 5. The working fluid is liquid oxygen, which flows in from the inlet 5 of the pipe 4, flows out from the outlet 6 after passing through the turbine flow meter assembly, and the turbine rotor 2 rotates stably under the drive of the working fluid. Its rotational speed is converted to obtain the input flow rate of the working fluid.

[0045] like Figure 1 As shown, a fluid-structure interaction particle simulation method for liquid oxygen flowmeters in liquid rocket engines includes the following steps:

[0046] 1) Determine the numerical analysis model of the physical field to be solved:

[0047] Importing the actual geometric configuration of this embodiment, we define the geometric coefficients representing the known solution region, i.e., the shape control points of the solution region. Based on the accuracy requirements of the geometric configuration, and using spline curves, we establish complete analysis node vectors and shape interpolation basis functions in the parametric coordinate system. We construct a cubic B-spline curve using 9 control points, with its node vectors being a non-decreasing sequence ξ = {ξ1, ξ2, ..., ξ...} between 0 and 1. m+p+1 The recursive formula for the B-spline basis functions is as follows:

[0048]

[0049] Where i = 1, 2, ..., m + p + 1; N is the basis function of the B-spline curve, p is the order of the basis function, and ξ is the node in the parametric coordinate system;

[0050] Based on the node vectors and shape control points obtained in the above process, the physical domain is divided. Rational B-spline surfaces are obtained using B-spline basis functions and weighting coefficients, thus initially generating a numerical analysis model for computational analysis. The rational B-spline basis function is expressed as follows:

[0051]

[0052] Where R is the bilinear rational B-spline basis function, and ω is the projection weight factor;

[0053] 2) Construct an accurate analytical model for the physical problem to be solved:

[0054] For the numerical analysis model established in step 1), depending on the different computational accuracy requirements and computational capability constraints, the methods of inserting geometric operation nodes and increasing the order of rational B-spline basis functions at different nodes are adopted to refine the solution domain boundary and the curve, thereby obtaining an accurate analysis model of the physical problem to be solved.

[0055] 3) Discretize the solution domain

[0056] like Figure 4 As shown, the solution domain within the exact analysis model is discretized using a particle-based approach. The kernel function of fluid particle 7, expressed using a Gaussian function, is as follows:

[0057]

[0058] Where r is the distance from the central particle, and h is the smooth length;

[0059] The motion of fluid particle 7 in the solution domain is controlled by the Navier-Stokes equations. The particle-based Lagrangian Navier-Stokes equations after the kernel approximation are as follows:

[0060]

[0061]

[0062] Where ρ is the fluid density, t is time, M is the particle mass, v is the particle velocity, P is the pressure, μ is the dynamic viscosity, g is the gravitational acceleration, and l ij Let be the distance between particle i and particle j. The gradient of the kernel function;

[0063] 4) Construct a Cartesian coordinate system to determine the coordinate information of the solution domain:

[0064] Based on the discretized solution domain obtained in step 3), particle inflow boundaries x are set on both sides of it. L and particle outflow boundary x R The particle inflow boundary corresponds to inlet 5 in the geometric model, and the particle outflow boundary corresponds to outlet 6 in the geometric model. Fluid particles 7 enter the solution domain from the inflow boundary and flow out of the solution domain from the outflow boundary. The position parameters of the precise analysis model constructed in step 2) and the discretized fluid particles 7 in step 3) are both represented using Cartesian coordinates. In Cartesian coordinates, both the particle inflow boundary and the outflow boundary in the solution domain can be uniquely represented by coordinates, where the center coordinates of the inflow boundary are (x... L y L z L The coordinates of the outflow boundary center are (x R y R z R The center coordinates of fluid particle 7 are (x... i y i z i ), i = 1, 2, ..., q, where q is the total number of particles;

[0065] 5) Determine if the particle's position is within the solution domain:

[0066] During the solution process, the position information of each particle in the solution domain is updated with each iteration, such as... Figure 5 (a) and Figure 5 As shown in (b), when viewed from the xy plane, when x i >x R At that time, it can be concluded that the particle has flowed out of the solution domain. From the perspective of the yz plane, when (y i -y R ) 2 +(z i -z R ) 2 >D 2 When the value of D is 4, it can be determined that the particle has flowed out of the solution domain. In this embodiment, the value of D is 590mm, which is the inner diameter of the horizontal pipe 4. In each iteration step, the position information of the particle is compared and judged. When one or both of the above two conditions are met, it is considered that the particle has flowed out of the solution domain and no longer participates in the calculation within the solution domain.

[0067] 6) Place the particles that have flowed out of the solution domain back into the boundary:

[0068] like Figure 6 As shown, according to the judgment condition in step 5), when the coordinate information of fluid particle 7 is not within the range defined by the solution domain, it is reset back to the inflow boundary, that is, the center coordinates of fluid particle 7 are set to be equal to the center coordinates x of the inflow boundary inlet. i =x L y i =y L , z i =z L The inflow boundary conditions (pressure inflow or velocity inflow) are then redefined according to the pre-defined inflow boundary conditions for subsequent solution.

[0069] 7) Analysis and Calculation:

[0070] Based on the Cartesian coordinate system determined in step 4), the position information of the solution domain is uniquely determined. The motion of fluid particle 7 in the solution domain is controlled by the Lagrange-type Navier-Stokes equations. The update of the position of fluid particle 7 follows the Lagrange method, and the equations are as follows:

[0071]

[0072] Where v x (t), v y (t), v z(t) represents the components of the particle's velocity along the three axes in the Cartesian coordinate system. In each iteration step, the flow field is first analyzed and solved. Then, the flow field solution obtained in this iteration step is applied to the fluid-structure interaction calculation to analyze the driving process of the working fluid on the turbine rotor 2 in the turbine flowmeter. The rotational speed of the turbine rotor 2 is solved. When the rotational speed of the turbine rotor 2 no longer changes between adjacent iteration steps, the calculation process converges. Finally, the input flow rate of the working fluid is obtained by converting the rotational speed of the turbine rotor 2. The conversion equation is as follows:

[0073]

[0074] Where n is the rotational speed, K is the instrument coefficient, and Q is the flow rate.

Claims

1. A fluid-structure interaction particle simulation method for liquid oxygen flowmeters in liquid rocket engines, characterized in that, Includes the following steps: 1) Determine the numerical analysis model of the physical field to be solved: Import the true geometric configuration of the problem to be solved, define the geometric coefficients representing the known solution region, i.e., the shape control points of the solution region, and establish a complete set of analysis node vectors and shape interpolation basis functions in the parametric coordinate system based on spline curves, according to the accuracy requirements of geometric modeling. Take 9 control points to construct a cubic B-spline curve, whose node vector is a non-decreasing sequence ξ = {ξ1, ξ2, ..., ξ1} between 0 and 1. m+p+1 The recursive formula for the B-spline basis functions is as follows: Where i = 1, 2, ..., m + p + 1; N is the basis function of the B-spline curve, p is the order of the basis function, and ξ is the node in the parametric coordinate system; Based on the node vectors and shape control points obtained in the above process, the physical domain is divided. Rational B-spline surfaces are obtained using B-spline basis functions and weighting coefficients, thus initially generating a numerical analysis model for computational analysis. The rational B-spline basis function is expressed as follows: Where R is the bilinear rational B-spline basis function, and ω is the projection weight factor; 2) Construct an accurate analytical model for the physical problem to be solved: For the numerical analysis model established in step 1), depending on the different computational accuracy requirements and computational capability constraints, the methods of inserting geometric operation nodes and increasing the order of rational B-spline basis functions at different nodes are adopted to refine the solution domain boundary and the curve, thereby obtaining an accurate analysis model of the physical problem to be solved. 3) Discretize the solution domain: The solution domain within the exact analytical model is discretized using a particle-based approach, and the kernel function of the particles is expressed using a Gaussian function as follows: Where r is the distance from the central particle, and h is the smooth length; The motion of fluid particles in the solution domain is controlled by the Navier-Stokes equations. The particle-based Lagrangian Navier-Stokes equations after the kernel approximation are as follows: Where ρ is the fluid density, t is time, M is the particle mass, v is the particle velocity, P is the pressure, μ is the dynamic viscosity, g is the gravitational acceleration, and l ij Let be the distance between particle i and particle j. The gradient of the kernel function; 4) Construct a Cartesian coordinate system to determine the coordinate information of the solution domain: Based on the discretized solution domain obtained in step 3), particle inflow boundary and particle outflow boundary are set on both sides of it. Particles enter the solution domain from the inflow boundary and flow out of the solution domain from the outflow boundary. The position parameters of the precise analysis model constructed in step 2) and the discretized particles in step 3) are represented by the Cartesian coordinate system. In the Cartesian coordinate system, the particle inflow boundary and outflow boundary in the solution domain are represented by uniquely determined coordinates. 5) Determine if the particle's position is within the solution domain: During the solution process, the position information of each particle in the solution domain is updated with each iteration. When the position coordinates of a particle exceed the position coordinates of the outflow boundary, the particle no longer participates in the calculation within the solution domain. 6) Place the particles that have flowed out of the solution domain back into the boundary: According to the judgment condition in step 5), when the coordinate information of the particle is not within the range defined by the solution domain, it is reset back to the inflow boundary and redefined according to the pre-set inflow boundary conditions, i.e., pressure inflow or velocity inflow, and then the subsequent solution is performed. 7) Analysis and Calculation: Based on the Cartesian coordinate system determined in step 4), the position information of the solution domain is uniquely determined. The motion of particles in the solution domain is controlled by Lagrange-type Navier-Stokes equations, and the updating of particle positions follows the Lagrange method, with the equations as follows: Where v x (t), v y (t), v z (t) represents the components of the particle's velocity along the three axes in the Cartesian coordinate system. In each iteration step, the flow field is first analyzed and solved. Then, the flow field solution obtained in this iteration step is applied to the fluid-structure interaction calculation to analyze the driving process of the working fluid on the turbine rotor in the turbine flowmeter and solve for the turbine rotor speed. When the turbine rotor speed no longer changes between adjacent iteration steps, the calculation process converges. Finally, the input flow rate of the working fluid is obtained by converting the turbine rotor speed. The conversion equation is as follows: Where n is the rotational speed, K is the instrument coefficient, and Q is the flow rate.

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