CN109800488B - Numerical calculation method for bottom thermal environment of liquid rocket in high-altitude environment - Google Patents
Numerical calculation method for bottom thermal environment of liquid rocket in high-altitude environment Download PDFInfo
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Abstract
The invention discloses a numerical calculation method for a bottom thermal environment of a liquid rocket in an overhead environment, which comprises the steps of firstly establishing a three-dimensional geometric model of the liquid rocket; then, carrying out grid division on the three-dimensional model by using a multi-block structured grid method and encrypting; then establishing a convection/heat radiation coupling model of the carrier rocket fuel gas plume containing supersonic velocity free flow at high altitude: and then, dispersing convection terms in the N-S equation: dispersing by adopting a second-order windward TVD format; and finally, establishing a radiation model by adopting a discrete coordinate method, carrying out large-scale parallel calculation on the rocket total flow field and the heat flow at the bottom of the rocket total flow field, and outputting Mach number, temperature, pressure flow field and convection/coupling heat flow cloud pictures. The invention provides a numerical simulation method which is high in precision, low in calculation cost and in accordance with engineering practice.
Description
Technical Field
The invention belongs to the field of numerical simulation of a thermal environment of a supersonic aircraft, and particularly relates to a numerical calculation method of a bottom thermal environment of a liquid rocket in an overhead environment.
Background
In recent years, with the successive development of a series of important space activities such as manned landing, space station construction, deep space exploration and the like, the research work of heavy carrier rockets and power systems thereof is increased in China, and the fact that liquid oxygen kerosene engines and liquid hydrogen liquid oxygen engines are the best choices of the power systems of the carrier rockets is determined. When the liquid carrier rocket engine works, because the pressure of the external environment is too low, the gas flow expands rapidly after entering the external environment, the backflow is formed at the bottom of the rocket, the convection heating effect is formed at the bottom of the rocket body, and meanwhile, hot CO is injected into high-temperature gas 2 、H 2 The mixed gas flow of O and the like forms a radiation heating effect on the bottom of the rocket. The bottom of the rocket is equivalent to a leeward surface and is easily subjected to the coupling action of convection heating and radiation heating caused by the jet flow backflow of the engine, so that the temperature is rapidly increased. The low estimation of the thermal environment at the bottom of the rocket brings great threat to the overall safety of the rocket, even induces major accidents such as explosion and the like to cause flight failure, and the high estimation of the thermal environment at the bottom of the rocket leads to conservative design of thermal protection equipment and increases the launching cost, so that the thermal environment analysis and research on the bottom of the liquid carrier rocket becomes the current focus.
Compared with the foreign research degree of the thermal environment at the bottom of the rocket, the foreign research degree of the thermal environment at the bottom of the rocket is still in an early stage at present in China, especially, few flight test data of liquid carrier rockets in China exist, most of domestic scholars research the thermal environment at the bottom of the rocket in the aspect of numerical simulation, and the lack of comparative analysis causes the effectiveness of a simulation method to be difficult to verify. And because the computing resources are limited, most scholars simplify the numerical model to different degrees, for example, the geometric model only considers one quarter, the grid has no boundary layer, the thermal radiation computation adopts a P-1 model with lower precision, and the like, which influence the computation precision to a great extent.
With the continuous development of computational fluid mechanics and the continuous improvement of computer performance, numerical simulation has become an effective means for studying flow fields. With the development of aerospace science and technology, rocket load is increased, the size is increased, the calculation area of the whole rocket flow field is large, the grid scale is large, the calculation amount is increased, large-scale parallel calculation is needed for solving, and a numerical simulation method with high precision and low calculation cost is urgently needed for simulating the bottom thermal environment of the liquid rocket in the high-altitude environment.
Disclosure of Invention
The invention aims to provide a numerical calculation method for a bottom thermal environment of a liquid rocket in an overhead environment so as to realize the prediction problem of the thermal environment of the liquid rocket in the overhead environment.
The technical scheme for realizing the purpose of the invention is as follows:
a numerical calculation method for a bottom thermal environment of a liquid rocket in a high-altitude environment is characterized by comprising the following steps:
and 4, dispersing convection items in the N-S equation: dispersing by adopting a second-order windward TVD format;
and 5, performing large-scale parallel calculation on the rocket full flow field and the heat flow at the bottom of the rocket full flow field by using a Discrete-coordinates method (DOM) in the radiation model, and outputting Mach number, temperature, pressure flow field and convection/coupling heat flow cloud pictures.
Compared with the prior art, the invention has the following remarkable advantages:
(1) according to the numerical calculation method for the bottom thermal environment of the liquid rocket in the high-altitude environment, a multi-structured grid method is adopted for grid division, so that the problems that the whole flow field area of the liquid rocket is large, the grid scale is large and calculation is difficult are effectively solved, and the problem that convection/radiation coupling heat transfer is difficult to calculate is solved;
(2) according to the numerical calculation method for the bottom thermal environment of the liquid rocket in the high-altitude environment, the adopted second-order windward TVD format is most suitable for solving the problem of highly compressible flow, the shock wave capturing capability is high, and due to the design of the flux limiter with strong robustness, not only can a complex wave system structure with high resolution be obtained, but also the non-physical oscillation of strong intermittent solution can be inhibited;
(3) the invention relates to a numerical calculation method for a bottom thermal environment of a liquid rocket in an overhead environment.A turbulence model adopts a readable k-epsilon two-equation model, and compared with a standard k-epsilon two-equation model, a generation item in a turbulence dissipation rate epsilon equation does not contain a generation item G in a turbulence energy k equation any more k And turbulent viscosity mu t Coefficient C of μ Not constant but related to strain rate, such a form better represents energy conversion;
(4) the invention relates to a numerical calculation method of a bottom thermal environment of a liquid rocket in a high-altitude environment, which solves the radiant heat flow by adopting a discrete coordinate system (DOM), and has the characteristics of easiness in processing scattering problems, easiness in simultaneous solution with a flow equation and higher calculation accuracy.
Drawings
FIG. 1 is a flow chart of a numerical calculation method for the bottom thermal environment of a liquid rocket in an overhead environment.
FIG. 2 is a three-dimensional model diagram of a liquid rocket.
FIG. 3 is a multi-nozzle liquid rocket multi-block structured grid diagram.
FIG. 4 is a multi-nozzle liquid rocket Mach number field cloud diagram.
FIG. 5 is a cloud view of the temperature field of a multi-nozzle liquid rocket.
FIG. 6 is a cloud view of a multi-nozzle liquid rocket pressure field.
FIG. 7 is a bottom convection/radiant heat flux coupled cloud view of a multi-nozzle liquid rocket.
FIG. 8 is a schematic diagram showing comparison between numerical simulation results and actual measurement results of monitoring points at the bottom of a multi-nozzle liquid rocket.
Detailed Description
For the purpose of illustrating the technical solutions and technical objects of the present invention, the present invention will be further described with reference to the accompanying drawings and specific embodiments.
With reference to fig. 1, the method for calculating the value of the bottom thermal environment of the liquid rocket in the high altitude environment of the invention comprises the following steps:
1.1, drawing a model according to a ratio 1:1 of a real rocket;
1.2, in conjunction with fig. 2, the three-dimensional geometric model requires the following parameters: the height and radius of the core stage-1, the warhead-2 curvature of the core stage, the length of the nozzle-3, the radius of the inlet and outlet of the nozzle-3 and the radius of the throat-4 of the nozzle.
2.1, combining with the figure 3, carrying out block processing on the multi-nozzle rocket three-dimensional model, and dividing the total calculation domain into two sub-domains: a core stage and an outer domain-1 surrounding the core stage; a spray pipe and a fuel gas plume region-2 below the spray pipe;
and 2.2, encrypting the grids of the spray pipe and the plume region, wherein the whole calculation domain adopts a structural grid to ensure the orthogonality and the smoothness of the grids. During numerical calculation, due to the fact that physical quantities such as temperature and pressure at the boundary change violently, the flow near the wall face cannot be accurately calculated through the wall face function, therefore, grids of the boundary layer calculation domain are further encrypted, and the Y + value of the grids near the wall face is guaranteed to be smaller than 3.
because the multi-nozzle rocket mostly adopts gas fuel, the gas component contains H 2 O，CO 2 ，CO，H 2 ，N 2 Etc., so that a gas and air multi-component flow model is employed.
3.1, the gas jet flow is set to meet the following requirements: the ideal gas is continuous and the components are directly free from chemical reaction; namely:
(1) the gas jet flow meets the requirement of a continuous medium; (2) the gas jet is a compressible pure gas phase medium; (3) no chemical reaction occurs inside the gas jet; (4) a multi-component mixed flow model of gas and air is adopted, and various components all meet an ideal gas state equation;
3.2, establishing a gas multi-component transport equation as
Wherein, Y l Is the mass fraction of the fuel gas component l of the liquid rocket, R l Is the net generation rate of the fuel gas component l of the liquid rocket after chemical reaction, S l The generation rate caused by the discrete phases of the source items is customized. J. the design is a square l The diffusion flux of the components of the liquid rocket fuel gas is represented by t, the rocket flight time is represented by ρ, the fluid density of the rocket fuel gas is represented by v, and the vector of the rocket velocity is represented by divergence of gas flow microelements;
wherein the diffusion flux of the components of the rocket fuel gas is
In the formula, D l，m As liquid rocket fuel gasMass dissipation factor of component l, D T，l The thermal diffusion coefficient of the fuel gas component l of the liquid rocket;
3.3, establishing a compressible N-S equation model of a single component l under a rectangular coordinate system:
in the formulas (3) to (6), U is a liquid rocket fuel gas flow variable; F. g, H is the liquid rocket gas flow flux vector, F v 、G v 、H v The viscous flux vector of the liquid rocket fuel gas is obtained, and K is the heat conduction coefficient of the liquid rocket fuel gas; t is the ambient temperature; p, rho, e, tau and mu are respectively rocket gas pressure, density, specific kinetic energy, stress and viscosity coefficient, u, v and w are respectively components of the liquid rocket gas velocity in the x, y and z directions, the center of the bottom of the rocket is an original point, the rocket flight direction is the z direction, and the connecting lines of the centers of the inlets of the non-adjacent spray pipes are respectively in the x and y directions;
3.4, establishing a turbulence model of the plume in the rocket flight process by adopting a Realizable k-epsilon two-equation model:
compared with a standard k-epsilon two-equation model, the model has clearer description on the flow characteristics such as high streamline curvature, vortex and the like;
the equation of the turbulence kinetic energy k and the equation of the turbulence dissipation rate epsilon are
In formulae (7) and (8), G k For the generation term of the turbulent kinetic energy k due to the mean velocity gradient, mu t For turbulent viscosity, σ k And σ ε Prandtl numbers, C, of turbulence energy k and turbulence dissipation factor epsilon, respectively 1 And C 2 Is a constant coefficient of equation, C 1 ＝1.44，C 2 ＝1.9。
And 4, dispersing convection items in the N-S equation: dispersing by adopting a second-order windward TVD format;
the carrier rocket adopts a design scheme of a high-thrust engine, the total temperature and total pressure of a combustion chamber are high, jet flow is high under-expansion supersonic jet flow, the wave system structure is complex, and the second-order windward TVD format is most suitable for solving the problem of high compressible flow;
4.1, performing numerical integration on each volume grid unit by adopting a finite volume method:
the volume of the flow variable U at the center of the body unit averages:
in the formula, V i,j , k To compute volumetric grid cells.
And 4.2, discretizing the traffic by adopting a second-order windward TVD format.
In the formula, numerical flux
Respectively as follows:
in the formula, λ k ，μ k ，ν k To linearize the eigenvalues of the replacement matrix, alpha k 、β k 、γ k Coefficient of expansion terms for linearizing the replacement matrix, e k (A)、e k (B)、e k (C) And in order to linearize the eigenvector of the replacement matrix, i, j and k are unit vectors in the directions of x, y and z respectively, and the viscous flux adopts second-order central difference dispersion.
And 5, establishing a radiation model by using a Discrete-coordinates method (DOM), carrying out large-scale parallel calculation on the rocket full flow field and the heat flow at the bottom of the rocket full flow field, and outputting Mach number, temperature, pressure flow field and convection/coupling heat flow cloud pictures.
5.1, integral-differential basic equation for defining radiation heat transfer:
analyzing components of engine fuel gas to obtain mole percent of components of the rocket fuel gas, measuring to obtain environment temperature, flight speed, environment pressure, pressure inside the nozzle, initial temperature of the wall surface of the nozzle and the bottom of the rocket body and temperature inside the nozzle, and substituting into an integral-differential basic equation of radiation heat transfer:
in the formula: s is a direction vector;
the gas diffusion term is the gas medium radiation intensity; i is b Radiation intensity of a black body; k is a radical of a ，k s The absorption coefficient and the scattering coefficient of a multi-nozzle rocket jet wake flow medium are respectively;
is a gas phase function;
5.2, dispersing the radiation heat transfer basic equation by using a DOM model:
the discrete coordinate method has the characteristics of higher calculation precision and easy simultaneous solution with a flow equation;
discretization along the s direction by the radiation transfer equation yields:
the spectral intensity I obtainable from formula (13) λ The radiation transfer equation for (r, s) is:
where r is a position vector, s is a direction vector, s' is a scattering direction vector, s is a gas layer thickness, a is an absorption coefficient, n is a refractive index, σ is a black body radiation constant, and s is scattering coefficient, I is spectral radiation intensity, T is thermodynamic temperature of black body, phi is scattering phase function, omega' is solid angle, lambda is wavelength, I bλ Black body intensity given for planck's equation.
5.3, carrying out large-scale parallel calculation on the rocket total flow field and the heat flow at the bottom of the rocket total flow field, and outputting Mach number, temperature and pressure flow fields and convection/coupling heat flow cloud charts
Examples
A numerical calculation method for the bottom thermal environment of a liquid rocket in a high-altitude environment comprises the following steps according to the steps in the specific implementation mode:
in connection with fig. 2, the three-dimensional geometric model requires the following parameters: the height and the radius of the core stage-1, the warhead-2 curvature of the core stage, the length of the spray pipe-3, the inlet and outlet radii of the spray pipe-3 and the radius of the throat-4 of the spray pipe are determined, and then the model is established at a ratio of 1: 1.
and (3) carrying out multiple block structured grid processing on the geometric model by combining with the graph 3, and dividing grids for the multi-nozzle liquid rocket, wherein the total number of the grids is 892 ten thousand finally.
the fuel gas component comprises H 2 O、CO 2 、CO、H 2 The molar mass percentages are respectively 38%, 26%, 25%, 9% and 2%, and the solution is substituted into a multi-component equation.
and 5, performing large-scale parallel calculation on the rocket total flow field and the heat flow at the bottom of the rocket by the radiation model by adopting a discrete coordinate method, and outputting Mach number, temperature, pressure flow field and convection/coupling heat flow cloud pictures.
The following parameters were entered:
flight height: 20km ambient temperature: 216k flight speed: 1.2Ma ambient pressure: 6587Pa
Pressure inside the nozzle: 1.8*10 7 Pa initial temperature of the wall surface of the spray pipe and the bottom of the arrow body: 300k
Internal temperature of the nozzle: 3400k radiation absorption coefficient: 0.3
The numerical calculation method for the bottom thermal environment under the high altitude environment of the liquid rocket outputs a Mach number field, a temperature field, a pressure field and a total heat flow distribution cloud map in two days under the condition of parallel calculation by using 32 CPUs, fig. 4 shows that Mach waves of the multi-nozzle liquid rocket expand and interact with each other, fig. 5 shows that the highest temperature value of the multi-nozzle liquid rocket is at a nozzle and a shock wave intersection position, fig. 6 shows that the pressure at the bottom plume intersection of the multi-nozzle liquid rocket is high and is caused by the mutual interference of the plumes, fig. 7 shows that the numerical value of the bottom heat flow of the rocket is larger as the bottom heat flow of the rocket approaches to the central position and is uniformly distributed outwards in a circular shape, fig. 8 shows that the numerical calculation result is high in goodness of fit with similar engineering test results, and shows that the simulation method has higher precision. The method can improve the calculation precision and reduce the calculation cost, and the calculation result can provide guidance for the thermal protection of the bottom of the rocket.
Claims (3)
1. A numerical calculation method for a bottom thermal environment of a liquid rocket in a high-altitude environment is characterized by comprising the following steps:
step 1, establishing a three-dimensional geometric model of the liquid rocket; the method specifically comprises the following steps:
1.1, performing model drawing according to the ratio of a real rocket to be 1: 1;
1.2, the three-dimensional geometric model needs the following parameters: the height and the radius of the core stage, the warhead curvature of the core stage, the length of the spray pipe, the inlet and outlet radii of the spray pipe and the radius of the throat part of the spray pipe;
step 2, carrying out grid division on the three-dimensional model by using a multiple-block structured grid method and carrying out encryption; the method specifically comprises the following steps:
2.1, carrying out blocking processing on the multi-nozzle rocket three-dimensional model, and dividing the overall calculation domain into two sub-domains: a core stage and an outer domain surrounding the core stage; the spray pipe and a fuel gas plume region below the spray pipe;
2.2, encrypting the grids of the spray pipe and the plume area, and further encrypting the grids of the boundary layer calculation domain;
step 3, establishing a convection/thermal radiation coupling model of the carrier rocket fuel gas plume containing the supersonic velocity free flow at high altitude: establishing a convection/thermal radiation coupling model of a carrier rocket gas plume containing supersonic free flow at high altitude based on a Navier-Stokes equation and a readable k-epsilon two-equation turbulence model of gas multi-component transport; the method comprises the following specific steps:
3.1, the gas jet flow is set to meet the following requirements: the ideal gas is continuous and the components are directly free from chemical reaction;
3.2, establishing a Navier-Stokes equation for multi-component gas transportation
Wherein Y is l Is the mass fraction of the fuel gas component l of the liquid rocket, R l The net generation rate of the liquid rocket fuel gas component l after chemical reaction, S l Discrete facies induction for custom source itemsThe generation rate of (2); j. the design is a square l The diffusion flux of the components of the liquid rocket fuel gas is shown, t is the rocket flight time, rho is the fluid density of the rocket fuel gas, and v is the rocket velocity vector;
3.3, establishing a compressible gas multi-component transport Navier-Stokes equation model with a single component l under a rectangular coordinate system:
wherein U is a liquid rocket fuel gas flow variable; F. g, H is the liquid rocket fuel gas flow flux vector, F v 、G v 、H v Is a viscous flux vector of the fuel gas of the liquid rocket;
3.4, establishing a turbulence model of the plume in the rocket flight process by adopting a Realizable k-epsilon two-equation model:
the equation of the turbulence kinetic energy k and the equation of the turbulence dissipation rate epsilon are
In formulae (7) and (8), G k For the generation term of the turbulent kinetic energy k due to the mean velocity gradient, mu t For turbulent viscosity, σ k And σ ε Prandtl numbers, C, of turbulence energy k and turbulence dissipation factor epsilon, respectively 1 And C 2 Is the equation constant coefficient;
step 4, carrying out dispersion on convection terms in a gas multi-component transport Navier-Stokes equation: dispersing by adopting a second-order windward TVD format;
and 5, establishing a radiation model by adopting a discrete coordinate method, carrying out large-scale parallel calculation on the rocket total flow field and the heat flow at the bottom of the rocket total flow field, and outputting Mach number, temperature, pressure flow field and convection/coupling heat flow cloud pictures.
2. The numerical calculation method for the bottom thermal environment of the liquid rocket in the high altitude environment according to claim 1, wherein the step 4 specifically comprises the following steps for dispersing convection terms in a Navier-Stokes equation for gas multi-component transport:
4.1, performing numerical integration on each volume grid unit by adopting a finite volume method:
the volume of the flow variable U at the center of the volume unit averages:
in the formula, V i,j,k In order to compute the volume grid cells,
4.2, dispersing the convection traffic by adopting a second-order windward TVD format;
in the formula, λ k ，μ k ，ν k To linearize the eigenvalues of the replacement matrix, alpha k 、β k 、γ k Coefficient of expansion terms for linearizing the replacement matrix, e k (A)、e k (B)、e k (C) To linearize the eigenvectors of the replacement matrix, i, j, k are the unit vectors in the x, y, z directions respectively,
second order central difference discretization is used for the numerical flux viscous flux of the equation.
3. The numerical calculation method for the bottom thermal environment of the liquid rocket in the high altitude environment according to claim 2 is characterized in that the radiation model in the step 5 adopts a discrete coordinate method:
5.1, defining an integral-differential basic equation of radiation heat transfer:
establishing an integral-differential basic equation of radiation heat transfer:
in the formula: (ii) a
The gas diffusion term is the gas medium radiation intensity; I.C. A b Radiation intensity of a black body; k is a radical of a ，k s The absorption coefficient and the scattering coefficient of a multi-nozzle rocket jet wake flow medium are respectively;
is a gas phase function;
5.2, modeling a discrete radiation heat transfer basic equation by using a discrete coordinate method:
spectral intensity I λ The radiation transfer equation for (r, s) is:
where r is a position vector, s is a direction vector, s' is a scattering direction vector, a is an absorption coefficient, n is a refractive index, σ is a black body radiation constant, and σ is a black body radiation constant s Is scattering coefficient, I is spectral radiation intensity, T is thermodynamic temperature of black body, phi is scattering phase function, omega' is solid angle, lambda is wavelength, I bλ Black body intensity given for planck's equation;
5.3, carrying out large-scale parallel computation on the rocket total flow field and the heat flow at the bottom of the rocket total flow field, and obtaining a simulation result after computation.
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