CN115329693A - Magnetic-flow-force-thermal coupling modeling and numerical simulation method for magnetic gas dynamics in circular tube - Google Patents
Magnetic-flow-force-thermal coupling modeling and numerical simulation method for magnetic gas dynamics in circular tube Download PDFInfo
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Abstract
The invention discloses a magnetic-flow-force-thermal coupling modeling and numerical simulation method for magnetopneumatics in a circular tube. According to the method, a physical model and a mathematical model of the magneto-aerodynamic flow in the circular tube under the action of a transverse magnetic field are constructed according to the influence of the conductivity of the wall surface of the circular tube and the insufficient development of turbulence at an inlet, numerical solution is completed based on a computational fluid mechanics theory, the influence rule of factors such as a Hartmann number Ha and a wall surface conductivity ratio C on the flow and heat transfer characteristics in the circular tube is obtained, the regulation and control mechanism of the flow and heat transfer characteristics by a magnetic field is clarified by analyzing the spatial distribution of induced current, electromagnetic force and Joule heat, the limitation problem existing in the prior art is effectively solved, the method can be widely applied to application scenes such as thrust vector control of an aircraft engine, thermal protection of a tail jet pipe of the engine, thermal regulation and control of a magnetic fluid power generation channel, ablation resistance of a body pipe weapon and the like, and has important theoretical significance and practical application value.
Description
Technical Field
The invention belongs to the technical field of magnetic-fluid-force-thermal coupling simulation of magnetic gas, and relates to a magnetic-fluid-force-thermal coupling modeling and numerical simulation method of magnetic-gas dynamics in a circular tube.
Background
The magnetic field can react with the conductive fluid to form a magnetohydrodynamic effect, and electromagnetic force and joule heat are generated in the fluid, so that the flow and heat transfer characteristics of the fluid are changed. Based on the phenomenon, the regulation and control of the magnetic-gas dynamic flow and the heat transfer characteristic in the high-temperature pipeline have wide application prospects in the fields of aerospace, military and the like, and therefore the importance of the influence analysis of the magnetic-gas dynamic flow and the heat transfer characteristic in the pipeline is highlighted.
At present, although the magnetic field regulation plasma/magnetofluid technology is widely applied to magnetofluid acceleration, magnetofluid power generation and other aspects in the aerospace field, most of the application scenarios only concern the influence of a magnetic field on indexes such as flow characteristics or electric energy extraction efficiency, and the magnetic control thermal protection technology related to heat transfer control generally adopts the flow around the outer surface of an aircraft rather than the flow inside the aircraft, so that the current technology lacks the fundamental analysis of the influence of the magnetic field on the aerodynamic flow and the heat transfer characteristics inside a pipeline, particularly inside a conductive pipeline, and further has the following problems:
firstly, most of the existing analysis technologies for magnetofluid in a pipeline are focused on liquid magnetofluids such as liquid metal, nano magnetofluid and the like, the attention on the gaseous magnetofluid is very little, and thermodynamic parameters of the gaseous magnetofluid are obviously different from those of the liquid magnetofluid, so that the changes of flow and heat transfer characteristics under the action of a magnetic field are different;
secondly, thermodynamic parameters such as density, viscosity, specific heat, heat conductivity and the like of the high-temperature gas change along with the temperature, and further influence is generated on the flow and heat transfer characteristics, and the influence is generally ignored in the existing analysis on the magnetic fluid;
third, in the current related art, the joule heating effect caused by the presence of the induced current in the fluid after the magnetic field is applied is generally ignored, while the joule heating in the magnetopneumatic flow is very significant, and generates an effect that cannot be ignored on the flow and the heat transfer;
fourthly, the analysis of the heat transfer of the magnetic fluid in the pipe is generally a boundary condition of constant wall temperature or constant heat flow density at present, and the heat transfer problem of the magnetoaerodynamic flow in the pipe is generally forced convection heat transfer of the fluid to the pipe wall, belonging to the Robin boundary condition;
fifth, the existing numerical simulation and experimental analysis for the flow and heat transfer characteristics of the magnetic fluid in the pipeline generally focus on describing phenomena and results, and the physical mechanism for the change of the flow and heat transfer characteristics from the perspective of the distribution rule of induced current, electromagnetic force and joule heat is lacked.
In summary, the prior art has problems of insufficient analysis basis, limited analysis and one-sidedness.
Disclosure of Invention
In view of the above, to solve the problems in the background art, magnetic-flow-force-thermal coupling modeling and numerical simulation methods for magnetic gas dynamics in a circular pipe are proposed;
the purpose of the invention can be realized by the following technical scheme:
the invention provides a magnetic-flow-force-thermal coupling modeling and numerical simulation method for magnetic gas dynamics in a circular tube, which comprises the following steps:
s1: constructing a physical model, comprising:
s11: reasonably simplifying the model and parameter setting, and making assumptions;
s12: on the basis of hypothesis, a physical model of the circular tube structure is constructed, and conditions are set;
s13: calculating parameters by using an empirical formula;
s2: constructing a mathematical model comprising:
s21: respectively adding electromagnetic force and Joule heat into a momentum equation and an energy equation to construct a non-constant incompressible magnetic-flow-force-thermal coupling dimensionless control equation, and carrying out dimensionless operation on the equation;
s23: carrying out equation optimization;
s3: the numerical solving algorithm and the verification comprise the following steps:
s31: solving an algorithm and boundary conditions;
s32: characterizing parameters of convective heat transfer strength;
s33: example verification;
s34: checking the independence of grids;
s4: simulating and analyzing an experiment;
s5: and drawing a conclusion.
Compared with the prior art, the invention has the beneficial effects that:
(1) The invention constructs a physical model and a mathematical model of the magnetic-pneumatic dynamic flow in the circular tube under the action of a transverse magnetic field, obtains the influence rule of factors such as Hartmann number Ha and wall surface conductivity ratio C on the flow and heat transfer characteristics in the circular tube, further clarifies the regulation mechanism of the magnetic field on the flow and heat transfer characteristics by analyzing the space distribution of induced current, electromagnetic force and joule heat, effectively solves the problem of thermodynamic parameter change of the magnetic-pneumatic dynamic flow which is not considered in the existing analysis technology of the magnetic-pneumatic dynamic flow and heat transfer characteristics, breaks through the limitation in the existing technology of the magnetic-pneumatic dynamic flow and heat transfer characteristics, fully considers the joule heat effect problem and Robin boundary conditions in the magnetic-pneumatic flow and heat transfer characteristics, deduces a solution method for deriving the convective heat transfer parameters between the magnetic-pneumatic dynamic flow and the wall surface of the circular tube, analyzes the change rule of the magnetic-pneumatic flow and heat transfer characteristics in the insulating circular tube or conductive circular tube under the regulation of the transverse magnetic field, and the like, and can be widely applied to the practical ablation significance and the vector regulation and ablation in the application of controlling the thrust of aircraft engine tail nozzle, the heat protection, the power generation channel, weapon and the weapon resistance.
(2) The method takes the magnetopneumatic flow in the circular tube as an analysis object, considers the factors such as the conductivity of the wall surface of the circular tube and the insufficient development of the turbulent flow in the fluid inlet area, adopts a numerical simulation method to analyze the regulation and control mechanism of the magnetopneumatic flow in the insulating circular tube or the conductive circular tube by a transverse magnetic field, and analyzes the influence rule of the magnetic induction intensity and the wall surface conductivity on the flow and heat transfer characteristics, thereby providing an analysis reference for the related application fields such as flow control and heat energy regulation of the conductive gas in the circular tube, and fully considers the influence of the thermodynamic parameters such as the density, the viscosity, the specific heat, the heat conductivity and the like of the high-temperature gas on the flow and the heat transfer characteristics when constructing a mathematical model, so that the accuracy and the reliability of the mathematical model are further improved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart of the steps of the present invention;
FIG. 2 is a schematic diagram of a physical model of the present invention;
FIG. 3 is a flow chart of a numerical simulation algorithm;
FIG. 4 is a numerical contrast chart of flow velocity along the z =0 direction on yz cross section of a circular tube under different Ha;
fig. 5 is a numerical contrast graph of flow velocity along the z =0 direction on yz cross section of a circular tube when Re =21375, ha =320, c = 0.0457;
FIG. 6 is a graph comparing the Nuoseir number value solution and the Gnieinsk empirical solution at the wall surface of a round tube under different Re along the flow direction;
FIG. 7 is a cloud chart of velocity amplitude distribution on a section x =200mm of a circular tube under different Ha and different C conditions;
fig. 8 is a graph of the dimensionless velocity profile along the line y =0 and along the line z =0 for a circular tube x =200mm, x =300mm cross-section;
FIG. 9 is a cloud diagram of turbulent kinetic energy distribution on a section x =200mm of a circular tube with different Ha and different C;
fig. 10 is a graph of turbulent kinetic energy distribution along line z =0 for y =0 on a section of a circular tube x =200mm and x =300 mm;
FIG. 11 is a cloud of temperature profiles of x =300mm cross-section of a circular tube with different Ha and different C;
FIG. 12 shows the local Nuosels number in the x-direction at different Ha lower circular tubes y =0, z = r0 and z =0, y = r0 walls, with C being 0 and 6667, respectively
A graph;
FIG. 13 shows the average Knoop number of the wall of a circular tube under different conditions C
Graph as a function of Ha;
fig. 14 is a graph showing the induced current distribution on a x =200mm cross section of a circular tube under three conditions of C0,66.67,6667;
FIG. 15 is a vector diagram of the electromagnetic force along the x-axis direction on the cross section of a circular tube;
fig. 16 is a graph of joule heating distribution at the y =0 section and the z =0 section of the circular tube under the three conditions of 0,66.67, and 6667 of C.
Detailed Description
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Referring to fig. 1 to 2, the present invention provides a magnetic-flow-force-thermal coupling modeling and numerical simulation method for magnetopneumatics in a circular tube, the method comprising the following steps:
s1: constructing a physical model comprising:
s11: reasonably simplifying the model and parameter setting, and making assumptions;
specifically, making assumptions specifically includes the following aspects:
1) The magnetoaerodynamic flow satisfies the local thermodynamic equilibrium state and the continuous medium hypothesis;
it is necessary to supplement that the microscopic collision effect among particles can be ignored, so that the magnetohydrodynamics theory can be adopted to solve, and the thermal ionization type conductive gas generally meets the assumption;
2) The conductivity of the fluid in the circular tube is a constant value and does not change along with the change of the flowing state;
3) Besides the electric conductivity, other physical parameters and transport parameters of the fluid are consistent with the air,
4) The natural convection heat transfer coefficient of the outer wall surface of the circular tube and the external air is constant;
5) The flow velocity of the fluid in the pipe is low, and the fluid can be regarded as incompressible fluid to be numerically solved according to the gas dynamics theory, namely the change of the gas density caused by the pressure change in the round pipe can be ignored.
S12: on the basis of hypothesis, a physical model of the circular tube structure is constructed, and conditions are set;
wherein the physical model is 400mm long and has a diameterd 0 30mm, pipe wall thickness 1 mm's pipe structure, carry out compulsory convection heat transfer between intraductal fluid and the pipe internal wall, heat transfer coefficient is h, and the outside wall of pipe carries out natural convection heat transfer with outside air simultaneously, and heat transfer coefficient is he, exerts horizontal magnetic field along perpendicular to pipe axial direction, and magnetic induction amplitude is B 0 And the length and the thickness of the pipe wall are respectively marked as L 0 And L w And the origin of coordinates of the three-dimensional rectangular coordinate system in the physical model is positioned at the circle center of the inlet section of the circular tube.
Further, the specific setting mode of the setting condition is as follows: setting the temperature T of the magnetoaerodynamic flow at the inlet of a circular tube 0 =500K, initial velocity u of magnetic gas in x-direction 0 Setting the initial temperature of the pipe wall to 300K and the outside air temperature to be consistent with each other by =20m/s, recording the outside air temperature as T ∞, and setting the thermal conductivity lambda of the pipe wall w = 200W/(M · K), conductivity σ of the magnetoaerodynamic flow within the tube g =1000S/m, wall conductivity σ, taking into account both insulation and conductivity of the tube wall w Set to 0,1e2S/m,1e4S/m,1e6S/m,1e8S/m, respectively, and wall conductivity ratios C of 0,0.0067,0.667,66.67, and 6667, respectively, where C = σ w L w /σ g r 0 ，r 0 The radius of the circular tube is shown,
s13: and (3) calculating parameters by adopting an empirical formula: calculating density, specific heat at constant pressure, viscosity coefficient and heat conductivity coefficient, and respectively recording as rho and C p μ and λ;
wherein the density ρ is expressed by
T is the temperature;
specific heat at constant pressure C p Is obtained by searching thermodynamic parameter database provided by national standard and technical research institute of the U.S. department of commerce and fitting by using least square method, and the specific expression is C p ＝4.4438*10 -10 T 4 -1.49758*10 -6 T 3 +0.001934077T 2 -0.8141577T+1113.69，
The viscosity coefficient mu is expressed as
The expression of the thermal conductivity λ is λ = (C) 1 T -1 +C 2 T -2/3 +C 3 T -1/3 +C 4 +C 5 T 1/3 +C 6 T 2/3 +C 7 T+C 8 T 4/3 +C 9 T 5 /3 ) Λ, wherein C1 to C9 and Λ are constants;
s2: constructing a mathematical model comprising:
s21: respectively adding electromagnetic force and Joule heat into a momentum equation and an energy equation, constructing a non-constant incompressible magnetic-flow-force-thermal coupling dimensionless control equation, and carrying out dimensionless transformation on the equation;
illustratively, the magnetic-flow-force-thermal coupling dimensionless control equation is as follows:
▽·(ρu)＝0，
wherein u is a velocity vector, p is a pressure, t is a time, J is a current density vector, B is a magnetic induction vector, and J Web with two or more webs Is the induced current amplitude, σ is the conductivity, and T is the temperature of the magnetoaerodynamic flow;
as another example, the magneto-flow-force-thermal coupling dimensionless control equation is dimensionless, and the expression form after dimensionless tempering is as follows:
▽ * ·u * ＝0，
in the formula u * 、t * 、ρ * 、p * 、μ * 、J * 、B * 、Θ、λ * 、C p * 、J Web with two or more webs * Expressed as dimensionless speed, dimensionless time, dimensionless density, dimensionless pressure, dimensionless viscosity coefficient, dimensionless current vector, dimensionless magnetic induction intensity vector, dimensionless temperature, dimensionless heat conductivity coefficient, dimensionless specific heat, dimensionless current amplitude, dimensionless parameters Re, N, ha, pe and E, respectively c Respectively representing the reynolds number, stewart number, hartmann number, peclet number and ektex number.
In addition, u is * ＝u/u 0 ，t * ＝tu 0 /d 0 ，ρ * ＝ρ/ρ 0 ，p * ＝p/(ρ 0 u 0 )，J * ＝J/(σ g B 0 u 0 )，B * ＝B/B 0 ，Θ＝(T-T∞)/(T 0 -T∞)，λ * ＝λ/λ 0 ，C p * ＝C p /C p0 ，
Where ρ is 0 、μ 0 、λ 0 、C p0 Respectively expressed as initial density, initial viscosity coefficient, initial heat conductivity coefficient, initial constant pressure specific heat, v 0 Expressed as the initial velocity of the barrel inlet in the y-direction.
In a specific embodiment, to achieve the coupled solution of the flow field and the electromagnetic field in the dimensionless magnetic-flow-force-thermal coupling dimensionless control equation, the complementary electromagnetic equation is needed, where the conservation of charge law is ∑ v * ·J * ＝0；
Ohm's law of induced current is J * ＝-▽ * φ * +u * ×B * ；
Potential Poisson equation of ^ *2 φ * ＝▽ * ·(u * ×B * )，φ * Is a dimensionless potential of phi * ＝φ/(B 0 u 0 d 0 )。
S23: and (3) carrying out turbulence equation correction: solving turbulence parameters by adopting an SSTk-omega model, and correcting the conventional SSTk-omega model to obtain a corrected turbulence control equation, wherein the specific expression of the corrected turbulence control equation is as follows:
k equation:
the ω equation:
in the above formula, x j The coordinates are coordinates under a Cartesian coordinate system; u. of i 、u j Respectively the velocity component under a Cartesian coordinate system, k is turbulent kinetic energy, omega is the specific dissipation ratio of the turbulent kinetic energy, and tau ij For turbulent stress, σ k And σ ω Prandtl number, mu, for turbulent kinetic energy transport and specific dissipation rate transport, respectively t Is turbulent dynamic viscosity; v. of t Is specific turbulent kinematic viscosity; alpha is alpha m Being anisotropy parameters under the influence of magnetic fields, gamma, beta 1 、β 2 Are all correlation coefficients in the turbulence model, and F1 is a mixing function in the turbulence model.
Understandably, the reynolds number at the inlet of the circular tube is about 40000 which is a typical turbulent flow known by a reynolds number formula, momentum and energy transport caused by turbulent pulsation cannot be calculated only by a magnetic-flow-force-thermal coupling dimensionless control equation after non-quantity tempering, so that a turbulent equation capable of solving an additional term of the turbulent pulsation value needs to be supplemented, and the turbulent equation is corrected;
it is also understood that the solution of turbulence parameters by the SST k- ω model is because the SST k- ω model uses a k- ω model on the near wall surface and uses a k- ε model in the far field, which can compensate the distortion problem in the solution of the near wall region compared to the k- ε model, thereby better characterizing the flow and heat transfer near the wall surface.
S3: the numerical solving algorithm and the verification comprise the following steps:
s31: solving algorithm and boundary conditions: carrying out numerical simulation under a theoretical framework of a finite volume method, controlling the dispersion of diffusion terms in a magnetic-flow-force-thermal coupling dimensionless control equation after non-quantity tempering, a supplemented electromagnetic equation and a corrected turbulence control equation to adopt a central difference format, adopting a three-order QUICK format for internal grid nodes of a convection term, and processing nodes close to a wall surface by adopting a first-order windward format; adopting a second-order fully-implicit discrete format discrete time item; the improved PISO algorithm is adopted to process the pressure-speed coupling term, and in addition, the potential Poisson equation also adopts a third-order QUICK format; and finally, solving the discrete control equation set by adopting a Gauss-Seidel point-by-point iteration method. Wherein, the flow of the magneto-pneumatic transient flow and heat transfer numerical simulation algorithm in the round tube is shown in figure 3,
it is added that the PISO algorithm has sub-iterative processes in each time step, thus ensuring that the speed of each time step meets the conservation of momentum, the improved PISO algorithm comprises a prediction step and two correction steps for the prediction, correction and re-correction of speed and pressure variables, so that the obtained speed field better meets the continuity and momentum equations, and the second correction step can accelerate the convergence speed in a single iterative step. In addition, compared with the traditional algorithms such as SIMPLE and SIMPLE, the PISO algorithm has obvious advantages in unsteady flow. The specific implementation steps of the improved PISO algorithm are as follows:
a prediction step: to pressure field p | The prediction is carried out, and the predicted speed component u is obtained by solving the discrete momentum equation | 、v | And w | ；
Primary correction: setting pressure correction parameter p'And velocity correction parameters u ', v ', w ' are obtained by solving a pressure correction equation and a velocity correction equation respectively || And the corrected velocity component u || 、v || 、w || The relationship between the correction parameter and the correction value may be expressed as: p is a radical of || ＝p|+p′；u || ＝u | +u′；v || ＝v | +v′；w || ＝w | +w′；
And (5) correcting again: setting a secondary pressure correction parameter p 'and secondary velocity correction parameters u', v ', w', and obtaining a final pressure value p by solving a secondary pressure correction equation and a secondary velocity correction equation ||| And a final speed value u ||| 、v ||| 、w ||| Similarly, the relationship between the secondary correction parameter and the secondary correction value may be expressed as p ||| ＝p || +p″；u ||| ＝u || +u″；v ||| ＝v || +v″；w ||| ＝w || +w″；
Further, in conjunction with the physical model, dimensionless boundary conditions for the flow and heat transfer of the magnetoaerodynamic flow in the circular duct are set as follows:
velocity and thermal boundary conditions at the entrance to the tube are u * ＝1,v * ＝1,Θ＝1，u * ,v * And w * Dimensionless components of the velocity of the magnetic gas in x, y and z directions of the circular tube, respectively;
the velocity and thermal boundary conditions at the exit of the pipe are
The boundary conditions of the speed and the magnetic field at the wall surface of the circular tube are
r * Is a dimensionless coordinate along the radial direction;
the boundary condition of the insulation potential is
Understandably, for the conductive pipeline, because the pipe wall is thinner than the diameter of the circular pipe, the thin-wall approximation can be adopted, namely, the current is discharged along the tangential direction of the wall surface, at the moment, the electric potential boundary condition of the outer wall surface of the circular pipe is consistent with the expression of the insulation electric potential boundary condition, and the electric potential boundary condition of the inner wall surface of the circular pipe is
Γ represents the component tangent to the pipe wall;
it can be understood that, since the thermal boundary condition at the wall of the circular tube is Robin condition, when the flow and the heat transfer are basically stable, the balance of the heat transfer amount between the fluid and the inner wall surface of the circular tube and between the outer wall surface of the circular tube and the outside air is achieved, and at this time, the dimensionless thermal boundary condition at the wall of the circular tube is
Theta wf is a dimensionless value of the temperature at the f-th position of the inner wall surface of the circular tube, and theta wg A dimensionless value of the temperature at the g-th position of the outer wall surface of the circular tube, wherein f represents the number of each position of the inner wall surface of the circular tube, f =1,2,... M, g represents the number of each position of the outer wall surface of the circular tube, g =1,2,... S, Θ b Is a dimensionless value, λ, of the mean temperature of the fluid over the cross-section of the pipe 0 Expressed as the initial thermal conductivity at the entrance of the pipe;
s32: the parameter characterization of the convection heat exchange strength specifically comprises the following steps:
A. the Knudel number is used for representing the convective heat transfer strength between the magnetopneumatic flow and the wall surface of the circular tube, and when the flow is basically stable, the local instantaneous Knudel number at a certain position of the wall surface can be expressed as
q w Is the heat flux, T, at a certain position of the inner wall surface of the circular tube b Is the average temperature of the fluid in a cross section of the tube along the x-axis, where T b Is calculated as
Theta representsThe coordinate of the circular tube along the angular direction;
B. the local instantaneous Nu of Knudel number l (x, theta, t) obtaining the time-averaged Knudsen number at a certain position by time averaging
To pair
The integral average is obtained on the wall surface of the whole circular tube to obtain the average Nossel number on the wall surface, which is specifically expressed as
S33: example verification:
specifically, the effectiveness of the numerical simulation algorithm adopted by the invention is verified by adopting three calculation examples, firstly, the experimental results of Takeuchi J and the like about the influence of a transverse magnetic field on the turbulent flow of the KOH aqueous solution in the acrylic round tube are contrastively analyzed, the effectiveness of the algorithm of the invention under the condition of low Ha in the insulating tube is verified, and the verification results are shown in a figure 4; secondly, zhang et al are adopted to compare and verify the effectiveness of the algorithm under the high Ha condition in the conductive round pipe according to the experimental example of the turbulent flow characteristics of the liquid metal magnetofluid in the 304 stainless steel round pipe, and the verification result is shown in figure 5; finally, the effectiveness of the algorithm in solving the problem of the convective heat transfer between high-temperature gas in the round tube and the wall surface is verified by comparison by adopting a Gnielinski empirical formula for convective heat transfer in the tube, and the verification result is shown in a figure 6;
further, based on fig. 4, a numerical simulation result can be obtained, and the experimental result keeps better consistency, based on fig. 5, the numerical simulation result and the experimental result have higher goodness of fit in the core flow area, a certain error occurs in the speed of the boundary layer, the speed is related to the contact resistance of the wall surface and the measurement error of the electromagnetic velocimeter adopted in the experiment, the algorithm is verified to be capable of effectively solving the turbulent flow problem in the conductive circular tube, based on fig. 6, the numerical simulation result and the result obtained by the gnilinski empirical formula calculation keep better consistency, and particularly, the error between the numerical simulation result and the experimental result is smaller as the flow extends to the outlet. Therefore, the three examples verify that the algorithm can effectively solve the magneto-aerodynamic flow and heat transfer characteristics in the circular tube.
S34: and (3) grid independence test: aiming at the circular tube structure, a structured grid is adopted, the grid near the wall surface is encrypted, and the grid independence test is carried out according to the computational fluid mechanics theory;
in the above, when SST k-omega turbulence model is adopted, it is necessary to satisfy y of the first layer grid of the fluid at the wall-attached position + The value is about 1, wherein,
Δ y is the height of the first layer of mesh at the wall, τ w Is wall shear stress;
in one embodiment, to satisfy y of the first layer mesh of fluid at the wall of the body + The value is about 1, the initial value of delta y is determined through theoretical analysis, and the y at the wall surface is obtained through numerical simulation according to the initial value + And on the basis, completing 6 mesh divisions with different sizes by adjusting mesh transition gradient, carrying out numerical simulation on the flow and heat transfer characteristics in the round tube when Ha =148 and C =66.67, and carrying out average Knudel number on the wall surface of the round tube under different mesh sizes
The calculation results and errors are shown in table 1:
TABLE 1 different grid size settings and the corresponding Nonsell number calculation results and errors
S4: experiment simulation and analysis: based on the model and the numerical solution algorithm, the numerical simulation under the conditions of different magnetic induction intensities and different wall conductivities is respectively carried out, the influence of factors such as different Ha and wall conductivity ratio C on the aerodynamic flow and heat transfer characteristics in the circular tube is explored, and the regulation and control mechanism of the transverse magnetic field on the aerodynamic flow and heat transfer characteristics in the insulating tube and the conductive circular tube is obtained, and the method specifically comprises the following steps:
s4-1, analyzing the influence of the magnetic field on the flow characteristics:
referring to fig. 7, the velocity distribution of the cross section of the circular tube under the action of the transverse magnetic field is anisotropic, and the velocity anisotropic distribution becomes more and more obvious with the increase of Ha, when the tube wall is insulated, the velocity gradient near the Hartmann boundary layer increases with the increase of Ha, and the velocity distribution along the radial direction parallel to the magnetic field becomes flat; with the increase of C, the direction of the velocity anisotropic distribution changes, and the anisotropic velocity distribution caused by different C is derived from the differential distribution of induced current and electromagnetic force on the section of the circular tube caused by the change of the wall surface conductivity;
referring to fig. 8, the velocity of the core flow region in the circular tube is suppressed under the action of the transverse magnetic field; for the C =0 insulated pipe, the velocity gradient at the Roberts boundary layer is gradually reduced and the boundary layer is thickened as Ha is increased, and the velocity gradient at the Hartmann boundary layer shows an increasing trend; but for conductive round tubes, the velocity gradients at the Roberts and Hartmann boundary layers both increase with Ha, where in fig. 8, (a) is x =200mm cross section and y =0 direction; (b) is a cross-section of x =200mm, z =0 direction; (c) x =300mm cross section, y =0 direction; (d) Is a cross-section of x =300mm, z =0 direction, wherein the z =0 direction is a radial direction parallel to the magnetic field;
referring to fig. 9, in different C, the turbulent kinetic energy on the cross section of the circular tube is in anisotropic distribution, the turbulent kinetic energy near the Roberts boundary layer is significantly greater than that near the Hartmann boundary layer, when Ha is smaller, i.e. Ha <148, the influence of the wall conductivity on the turbulent kinetic energy is insignificant, but when Ha exceeds a certain range, i.e. Ha >222, the turbulent kinetic energy near the Roberts boundary layer under the conductive wall condition is lower than that under the insulating wall condition, and the turbulent kinetic energy near the Roberts boundary layer shows a tendency of first decreasing and then increasing with the increase of C;
referring to fig. 10, when no magnetic field is applied, the isotropic turbulent kinetic energy is larger near the wall and the core flow area is smaller; under the action of a transverse magnetic field, the turbulence kinetic energy of a core flow area is not obviously changed, the turbulence kinetic energy near a Roberts boundary layer is reduced in certain intensity but not greatly reduced in amplitude, and the turbulence kinetic energy near a Hartmann boundary layer is significantly reduced, wherein (a) in FIG. 10 is a section of x =200mm, and y =0 direction; (b) a cross-section of x =200mm, z =0 direction; (c) a cross-section of x =300mm, y =0 direction; (d) a cross-section of x =300mm, z =0 direction;
s4-2, analyzing the influence of the magnetic field on the heat transfer characteristic:
referring to fig. 11, when the pipe wall is insulated, the anisotropy of the temperature distribution on the section of the circular pipe is more and more obvious along with the increase of Ha, the temperature of the wall surface near the Roberts boundary layer is higher than that of the wall surface at the Hartmann boundary layer, the anisotropy distribution characteristic of the temperature is gradually weakened along with the increase of C under the same Ha, and when the temperature of the core flow area is gradually increased to C =6667 and Ha =370, a large-range high-temperature area appears at the core flow, and the phenomenon is caused by Joule heating effect generated by current in the circular pipe. Therefore, under the conditions of large C value and high Ha number, the temperature in the circular tube is increased due to the accumulation of a large amount of joule heat;
referring to fig. 12, in the insulating wall surface condition, as the flow extends, y =0, z = r0 wall surface
Slightly decreased with increasing Ha, but the degree of decrease was not significant; in the case of conductive walls, i.e. at the C =6667, y =0, z = r0 wall
The trend of decreasing first and then increasing is shown along with the increase of Ha; in general, the convective heat transfer at the wall y =0, z = r0 under the condition of the conductive wall is strongDegree of wall surface Condition less than that of wall surface Condition, at the wall surface of z =0, y = r0 as the flow extends
The decrease is significant, as Ha increases,
is first decreased and then increased, and has =148
The lowest; at the conductive wall, z =0, y = r0 wall
Shows a complex variation, and when Ha =74, can be observed
A certain reduction occurs, to Ha =148 and 370,
the value of (d) does not change much compared to Ha =0, until Ha =555,
again a small amplitude decrease in value of (c); in fig. 12, (a) is a y =0 direction, z = r0 wall surface, and (b) is a z =0 direction, y = r0 wall surface.
Referring to FIG. 13, as Ha increases, the values at different C
All show a tendency of decreasing and then increasing, that is, the transverse magnetic field has an inhibiting effect on the heat transfer of the magnetoaerodynamic flow in the circular tube, but the inhibiting effect has a "saturation effect", and when the heat transfer inhibiting effect is the best, the Ha value is about 222 and when C =0, 66.67,6667
Reduced amplitude divisionRespectively 12.03%,12.40% and 11.09%; when the conductivity of the wall surface is smaller, namely C is less than or equal to 0.67, the convection heat exchange characteristic change under the condition of the conductive wall surface is basically consistent with that of the insulating wall surface; however, when C exceeds a certain range, namely C is greater than or equal to 66.67, the heat transfer characteristics of the insulation wall surface are different from those of the insulation wall surface, and the heat transfer characteristics are specifically shown in the condition of small Ha
Increased, and under Ha conditions
And is reduced.
S4-3, comparing and analyzing the induced current, the electromagnetic force and the space distribution of Joule heat in the circular tubes under different C to obtain a regulation and control mechanism of the magnetic field on the aerodynamic flow and the heat transfer characteristics of the magnetic gas in the insulating circular tube or the conductive circular tube, wherein the regulation and control mechanism specifically comprises the following steps:
s4-3-1, distribution of induced current: taking Ha =74 as an example, referring to fig. 14, when C =66.67, the circular loop of the current still exists, but because the wall is conductive, part of the current passes through the wall to form a path, and the resistance of the wall is lower than that of the fluid, which causes the induced current density value of the core flow area to show a certain increase compared with the insulating wall condition, when C =6667, the induced current almost entirely passes through the wall, the induced current in the cross section almost entirely passes along the positive z-axis direction, and the current loop near the Hartmann boundary layer almost disappears, which also causes the induced current density values of the core flow area and the Roberts boundary layer to be significantly larger than those near the Hartmann boundary layer, where (a) in fig. 14 is C =0; (b) is C =66.67; (C) is C =6667.
S4-3-2, electromagnetic force distribution and regulation mechanism: taking Ha =74 as an example, referring to fig. 15, the profiles of the electromagnetic force distribution on the cross sections under different wall conductivities have similarities, and the main difference is that the value of the electromagnetic force is different, and the value of the electromagnetic force is gradually reduced as C increases. In the core flow region, the electromagnetic force is negative due to the induced current in the positive y-axis direction, and is expressed as a "blocking force" opposite to the flow direction, while the induced current at the Hartmann boundary layer is in the negative y-axis direction, and is expressed as a "pushing force" same as the flow direction; when C is not large, the "drag" at the core flow is significantly less than the "push" at the boundary layer, when C is large, i.e., C =6667, the "push" at the hartmann boundary layer is very small, thereby making the velocity gradient change at this boundary layer less pronounced than at low C values; since the "drag" of the core flow region at large C and high Ha values is very large, the fluid is forced out of the region near the boundary layer, where in fig. 15, (a) is C =0; (b) is C =66.67; (C) is C =6667.
S4-3-3, distribution and regulation mechanism of joule heat: taking Ha =74 as an example, referring to fig. 16, in the insulated wall condition, joule heat is mainly distributed in the thin wall near the Hartmann boundary layer, and the core flow area is smaller at the y =0 section and the z =0 section; with the increase of the wall surface conductivity, when C =66.7, the joule heat of the core flow area is increased, but the maximum value of the joule heat is still distributed near the Hartmann layer; when C =6667, joule heating is more pronounced at the core flow and less at the Roberts boundary layer; when Ha is smaller, the Joule heating effect is not obvious, and the inhibition effect of the magnetic field on turbulent flow is dominant, so that the convective heat transfer strength is reduced along with the increase of Ha; when Ha reaches a certain range, namely Ha is larger than or equal to 222, joule heat in the round tube is accumulated due to the increase of induced current, and the enhancement effect of the joule heat on heat transfer exceeds the inhibition of electromagnetic force on turbulent flow and heat transfer, so that the convective heat transfer strength begins to increase reversely, wherein (a) in fig. 16 is a section of C =0, y =0; (b) is a C =0, z =0 cross-section; (C) is a C =66.67, y =0 cross section; (d) is a C =66.67, z =0 cross section; (e) is a C =6667, y =0 cross section; (f) is a C =6667, z =0 cross section.
The embodiment of the invention takes the magnetopneumatic flow in the circular tube as an analysis object, considers the factors of insufficient development of the conductivity of the wall surface of the circular tube and the turbulence of a fluid inlet area and the like, adopts a numerical simulation method to analyze the regulation and control mechanism of the transverse magnetic field on the magnetopneumatic flow in the insulating circular tube or the conductive circular tube, and analyzes the influence rule of the magnetic induction intensity and the wall surface conductivity on the flow and heat transfer characteristics, thereby providing an analysis reference for the related application fields of flow control, heat energy regulation and the like of the conductive gas in the circular tube, fully considering the influence of the thermodynamic parameters of the high-temperature gas such as density, viscosity, specific heat, heat conductivity and the like on the flow and heat transfer characteristics when constructing a mathematical model, and further improving the accuracy and reliability of the mathematical model.
S5: and (5) drawing a conclusion that: the invention obtains the law of the influence of Hartmann number and wall conductance-conductivity ratio C on the flow and heat transfer characteristics in the round pipe by applying a physical model and a mathematical model of the magnetic-aerodynamic flow in the round pipe under the action of a transverse magnetic field and analyzing the flow and heat transfer characteristics of the magnetic-aerodynamic flow in the insulating round pipe or the conductive round pipe under the action of the transverse magnetic field by adopting a numerical simulation method, and obtains the regulation and control mechanism of the flow and heat transfer characteristics of the magnetic field by analyzing the spatial distribution of induced current, electromagnetic force and joule heat, and the main conclusion is as follows:
(1) The speed on the section of the circular tube shows anisotropic distribution under the action of a transverse magnetic field. In the insulated pipe, the velocity gradient near the Hartmann boundary layer becomes large, but in the conductive pipe with the large C value condition, the velocity gradient in the Roberts boundary layer increases, and the velocity along the line y =0 shows an M-shaped distribution. Furthermore, the anisotropy of the velocity profile becomes more and more pronounced with the increase of Ha and the extension of the flow;
(2) The inhibition effect of the transverse magnetic field on the turbulent flow in the circular tube also has anisotropy, and the turbulent flow kinetic energy near the Hartmann boundary layer is obviously lower than that near the Roberts boundary layer. When Ha is smaller, namely Ha <148, the influence of different C values on turbulent flow energy is not obvious, but when Ha exceeds a certain range, namely Ha >222, the suppression of the turbulent flow kinetic energy near a Roberts boundary layer by a magnetic field under the condition of a conductive wall is larger than that under the condition of an insulating wall;
(3) The transverse magnetic field can inhibit convective heat transfer between the magnetoaerodynamic flow and the wall surface of the circular tube, but the inhibition effect has a saturation effect, namely Ha has an optimal value. When the conductivity of the wall surface is smaller, C is less than or equal to 0.67, under the condition of conductive wall
Substantially in line with the insulating wall; however, when C exceeds a certain range, namely C is more than or equal to 66.67, under the condition of small Ha value
Compared with the insulating wall surface is raised, and the condition of Ha is large
The amount is reduced;
(4) In a round tube
The complex change of the magnetic field is caused by the combined action of the suppression of the turbulent flow by the transverse magnetic field and the joule heating effect, when Ha is smaller, the suppression of the turbulent flow by the magnetic field is dominant,
decreases with increasing Ha; when Ha exceeds a certain value, namely Ha is more than or equal to 222, the heat transfer is enhanced due to the large accumulation of joule heat in the circular tube, so that
Begins to increase in reverse as Ha continues to increase.
The invention obtains the law of the influence of factors such as Hartmann number Ha and wall conductivity ratio C on the flow and heat transfer characteristics in the circular tube by constructing a physical model and a mathematical model of the magnetic-gas dynamic flow in the circular tube under the action of a transverse magnetic field, further clarifies the regulation and control mechanism of the flow and heat transfer characteristics by a magnetic field by analyzing the spatial distribution of induced current, electromagnetic force and Joule heat, effectively solves the problem of the change of thermodynamic parameters of the magnetic-gas dynamic flow which is not considered in the existing analysis technology of the magnetic-gas dynamic flow and heat transfer characteristics, and breaks through the limitations in the existing technology of the magnetic-gas dynamic flow and heat transfer characteristics, the method fully considers the problem of the Joule thermal effect and Robin boundary conditions in the magnetohydrodynamic flow and heat transfer characteristics, deduces a solving method for the convection heat transfer parameter between the magnetohydrodynamic flow and the wall surface of the circular tube, analyzes the change rule of the magnetoaerodynamic flow and the heat transfer characteristics in the insulating circular tube or the conductive circular tube under the control of the transverse magnetic field based on a calculation example, can be widely applied to application scenes of thrust vector control of an aircraft engine, thermal protection of an engine tail jet pipe, thermal control of a magnetohydrodynamic power generation channel, ablation resistance of a body-tube weapon and the like, and has important theoretical significance and practical application value.
The foregoing is merely exemplary and illustrative of the principles of the present invention and various modifications, additions and substitutions of the specific embodiments described herein may be made by those skilled in the art without departing from the principles of the present invention or exceeding the scope of the claims set forth herein.
Claims (10)
1. The magnetic-flow-force-thermal coupling modeling and numerical simulation method of the magnetic gas dynamics in the circular tube is characterized in that: the method comprises the following steps:
s1: constructing a physical model, comprising:
s11: reasonably simplifying the model and parameter setting, and making assumptions;
s12: on the basis of hypothesis, a physical model of a circular tube structure is constructed, and conditions are set;
s13: calculating parameters by adopting an empirical formula;
s2: constructing a mathematical model comprising:
s21: respectively adding electromagnetic force and Joule heat into a momentum equation and an energy equation, constructing a non-constant incompressible magnetic-flow-force-thermal coupling dimensionless control equation, and carrying out dimensionless transformation on the equation;
s22: carrying out turbulence equation correction;
s3: the numerical solving algorithm and the verification comprise the following steps:
s31: solving an algorithm and boundary conditions;
s32: characterizing parameters of convective heat transfer strength;
s33: example verification;
s34: checking the independence of grids;
s4: simulating and analyzing an experiment;
s5: and drawing a conclusion.
2. The method of magnetoaerodynamic magnetohydrodynamic-fluidforcing-thermocoupling modeling and numerical simulation within a tubular of claim 1, wherein: the physical model in the step S12 is 400mm long and d 0 The tube structure with the thickness of 30mm and the thickness of 1mm is characterized in that forced convection heat exchange is carried out between fluid in the tube and the inner wall surface of the tube, the heat exchange coefficient is h, meanwhile, the outer wall surface of the tube and external air carry out natural convection heat exchange, the heat exchange coefficient is he, a transverse magnetic field is applied along the axial direction perpendicular to the tube, and the amplitude of magnetic induction intensity is B 0 And the length and the thickness of the pipe wall are respectively marked as L 0 And L w 。
3. The method of magnetoaerodynamic magneto-fluid-force-thermal coupling modeling and numerical simulation within a circular tube of claim 1, wherein: in the step S12, conditions are set, and the specific setting mode is as follows:
setting the temperature T of the magnetoaerodynamic flow at the inlet of a circular tube 0 =500K, initial velocity u of magnetic gas in x-direction 0 Setting the initial temperature of the pipe wall to 300K and the outside air temperature to be consistent with each other, recording the outside air temperature as T ∞ and setting the thermal conductivity lambda of the pipe wall w = 200W/(M.K), conductivity σ of magnetoaerodynamic flow within a circular tube g =1000S/m, wall conductivity σ in view of both insulation and conductivity of the tube wall w Set to 0,1e2S/m,1e4S/m,1e6S/m,1e8S/m, respectively, and wall conductivity ratios C of 0,0.0067,0.667,66.67, and 6667, respectively, where C = σ w L w /σ g r 0 ，r 0 Which represents the radius of the circular tube,
4. the method of magnetoaerodynamic magneto-fluid-force-thermal coupling modeling and numerical simulation within a circular tube of claim 1, wherein: in the step S13The empirical formula is adopted for parameter calculation, specifically for density, constant pressure specific heat, viscosity coefficient and heat conductivity coefficient calculation, and the parameters are respectively recorded as rho and C p Mu and lambda, where p, C p Mu and lambda correspond to the following expressions:
C p ＝4.4438*10 -10 T 4 -1.49758*10 -6 T 3 +0.001934077T 2 -0.8141577T+1113.69；
λ＝(C 1 T -1 +C 2 T -2/3 +C 3 T -1/3 +C 4 +C 5 T 1/3 +C 6 T 2/3 +C 7 T+C 8 T 4/3 +C 9 T 5/3 )*Λ，
where C1 through C9 and Λ are constants.
5. The method of magnetoaerodynamic magnetohydrodynamic-fluidforcing-thermocoupling modeling and numerical simulation within a tubular of claim 1, wherein: the magnetic-flow-force-thermal coupling dimensionless control equation in the step S21 is as follows:
▽·(ρu)＝0，
wherein u is a velocity vector, p is a pressure, t is a time, J is a current density vector, B is a magnetic induction vector, and J Web with two or more webs Is the induced current amplitude, σ is the conductivity, and T is the temperature of the magnetoaerodynamic flow;
carrying out non-dimensionalization on the magnetic-flow-force-thermal coupling dimensionless control equation, wherein the expression form after non-dimensionalization is as follows:
▽ * ·u * ＝0，
in the formula u * 、t * 、ρ * 、p * 、μ * 、J * 、B * 、Θ、λ * 、C p * 、J Web with two or more webs * Expressed as dimensionless speed, dimensionless time, dimensionless density, dimensionless pressure, dimensionless viscosity coefficient, dimensionless current vector, dimensionless magnetic induction intensity vector, dimensionless temperature, dimensionless heat conductivity coefficient, dimensionless specific heat, dimensionless current amplitude, dimensionless parameters Re, N, ha, pe and E, respectively c Respectively representing the reynolds number, stewart number, hartmann number, peclet number and ektex number.
6. The method of magnetoaerodynamic magneto-fluid-force-thermal coupling modeling and numerical simulation within a circular tube of claim 1, wherein: and in the step S23, turbulence equation correction is performed, turbulence parameters are solved and corrected by adopting an SSTK-omega model, and an optimized turbulence control equation is obtained, wherein the optimized turbulence control equation has the expression:
k equation:
the ω equation:
in the above formula, x j The coordinates are coordinates under a Cartesian coordinate system; u. of i 、u j Respectively the velocity component under a Cartesian coordinate system, k is turbulent kinetic energy, omega is the specific dissipation ratio of the turbulent kinetic energy, and tau ij For turbulent stress, σ k And σ ω Prandtl number, mu, for turbulent kinetic energy transport and specific dissipation rate transport, respectively t Is turbulent dynamic viscosity; v. of t Is specific turbulent kinematic viscosity; alpha is alpha m Being anisotropy parameters under the influence of magnetic fields, gamma, beta 1 、β 2 Are all correlation coefficients in the turbulence model, and F1 is a mixing function in the turbulence model.
7. The method of magnetoaerodynamic magnetohydrodynamic-fluidforcing-thermocoupling modeling and numerical simulation within a tubular of claim 1, wherein: the solving algorithm in the step S31 is used for developing a numerical simulation algorithm of the transient flow and the heat transfer of the magnetohydrodynamics in the circular tube under a theoretical framework of a finite volume method; the specific expression form of the boundary condition is as follows:
velocity and thermal boundary conditions at the entrance to the tube are u * ＝1,v * ＝1,Θ＝1，u * ,v * And w * The non-dimensional components of the speed of the magnetic gas in the x, y and z directions of the circular tube are respectively;
the velocity and thermal boundary conditions at the exit of the pipe are
The boundary condition of the velocity and the magnetic field at the wall surface of the circular tube is u * ＝0,v * ＝0,
r * Is a dimensionless coordinate along the radial direction;
the boundary condition of the insulation potential is
φ * Represents a dimensionless potential;
the boundary condition of the potential of the inner wall surface of the circular tube is
Gamma represents a component tangent to the wall surface of the circular tube, and the potential boundary condition of the inner wall surface of the circular tube is consistent with the expression form of the insulation potential boundary condition;
the dimensionless thermal boundary condition at the wall surface of the round tube is
Theta wf is a dimensionless value of the temperature at the f-th position of the inner wall surface of the circular tube, and theta wg Is a dimensionless value of the temperature of the g-th position of the outer wall surface of the circular tube, wherein f represents the number of each position of the inner wall surface of the circular tube, f =1,2 b Is a dimensionless value, λ, of the mean temperature of the fluid over the cross-section of the pipe 0 Expressed as the initial thermal conductivity at the entrance of the round tube.
8. The method of magnetoaerodynamic magnetohydrodynamic-fluidforcing-thermocoupling modeling and numerical simulation within a tubular of claim 1, wherein: s32, the parameter characterization of the convective heat exchange strength specifically comprises the following steps:
A. the Knudel number is used for representing the convective heat transfer strength between the magnetopneumatic flow and the wall surface of the circular tube, and when the flow is basically stable, the local instantaneous Knudel number at a certain position of the wall surface can be expressed as
q w Is the heat flux, T, at a certain position of the inner wall surface of the circular tube b Is the average temperature of the fluid in a cross section of the pipe along the x axis, wherein T b Is calculated as
Theta is expressed as the coordinate of the circular tube along the angular direction;
B. the local instantaneous Nu of Knudel number l (x, theta, t) obtaining the time-averaged Knudsen number at a certain position by time averaging
To pair
The integral average is obtained on the wall surface of the whole circular tube to obtain the average Nossel number on the wall surface, which is specifically expressed as
9. The method of magnetoaerodynamic magnetohydrodynamic-fluidforcing-thermocoupling modeling and numerical simulation within a tubular of claim 1, wherein: and S4, respectively carrying out numerical simulation under the conditions of different magnetic induction intensities and different wall surface conductivities according to the constructed model and the numerical solving algorithm, analyzing the influence of the magnetic field on the magnetic-gas dynamic flow and heat transfer characteristics in the circular tube, and obtaining a regulation and control mechanism of the transverse magnetic field on the magnetic-gas dynamic flow and heat transfer characteristics in the insulating tube and the conductive circular tube.
10. The method of magnetoaerodynamic magnetohydrodynamic-fluidforcing-thermocoupling modeling and numerical simulation within a tubular of claim 1, wherein: in the step S5, the flow and heat transfer characteristics of the magnetic aerodynamic flow in the insulating circular tube or the conductive circular tube under the action of the transverse magnetic field are researched by using a physical model and a mathematical model of the magnetic aerodynamic flow in the circular tube under the action of the transverse magnetic field and a numerical simulation method, so that the influence rule of the Hartmann number and the wall surface conductivity ratio C on the flow and heat transfer characteristics in the circular tube is obtained, and meanwhile, the regulation and control mechanism of the magnetic field on the flow and heat transfer characteristics is obtained by analyzing the spatial distribution of the induced current, the electromagnetic force and the Joule heat.
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| CN117542423A (en) * | 2023-03-24 | 2024-02-09 | 中国人民解放军陆军装甲兵学院 | Multi-physical process coupling modeling and multi-model collaborative solving method during gun firing |
| CN117542423B (en) * | 2023-03-24 | 2024-04-05 | 中国人民解放军陆军装甲兵学院 | Multi-physical process coupling modeling and multi-model collaborative solving method during gun firing |
| CN116519738A (en) * | 2023-03-31 | 2023-08-01 | 中国人民解放军陆军装甲兵学院 | Method for testing and analyzing heat transfer parameters of plasma jet in circular tube under magnetic-flow-thermal multi-field coupling |
| CN116256390A (en) * | 2023-04-19 | 2023-06-13 | 中国人民解放军陆军装甲兵学院 | Experimental test method for forced convection heat exchange parameters of air flow in cylinder under condition of thermal physical property parameters |
| CN116256390B (en) * | 2023-04-19 | 2024-01-23 | 中国人民解放军陆军装甲兵学院 | Experimental test method for forced convection heat exchange parameters of air flow in cylinder under condition of thermal physical property parameters |
| CN117313586A (en) * | 2023-11-28 | 2023-12-29 | 中国人民解放军陆军装甲兵学院 | Magneto-aerodynamic flow behavior anisotropy analysis method under magneto-rheological multi-field coupling |
| CN117313585A (en) * | 2023-11-28 | 2023-12-29 | 中国人民解放军陆军装甲兵学院 | Analysis method for influencing flow and heat transfer characteristics of conductive airflow by magnetic field direction |
| CN117313586B (en) * | 2023-11-28 | 2024-02-09 | 中国人民解放军陆军装甲兵学院 | Magneto-aerodynamic flow behavior anisotropy analysis method under magneto-rheological multi-field coupling |
| CN117313585B (en) * | 2023-11-28 | 2024-02-20 | 中国人民解放军陆军装甲兵学院 | Analysis method for influencing flow and heat transfer characteristics of conductive airflow by magnetic field direction |
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