CN113868758B - Elastic hypersonic aircraft modeling method based on computational mechanics - Google Patents
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Abstract
The invention discloses a modeling method of an elastic hypersonic aircraft based on computational mechanics, which comprises the following steps: step 1: establishing a geometric model of the hypersonic aircraft and performing grid division; step 2: based on computational fluid dynamics and computational structural mechanics, simulating and calculating elastic characteristics and aerodynamic parameters of the hypersonic aircraft under different working conditions to obtain fitting data; step 3: establishing a hypersonic aircraft rigid body dynamics model according to the fitting data and solving deformation angles at different positions according to a vibration equation; step 4: according to the rigid body dynamics model and the vibration equation, combining simulation calculation results in the steps, and obtaining the six-degree-of-freedom elastic dynamics model of the elastic hypersonic aircraft through curve fitting.
Description
Technical Field
The invention belongs to the field of computational mechanics, and particularly relates to an elastic hypersonic aircraft modeling method based on computational mechanics.
Background
The hypersonic aircraft has the characteristics of high flying speed, strong burst prevention capability, large striking range and the like, has important strategic significance and extremely high application value, and is the forefront of the development of the current aerospace technology. But the extremely high flying speed has the characteristics of strong nonlinearity, strong coupling, quick time variation, uncertainty and the like of a control model. From the viewpoint of hydrodynamics, the aerodynamic and thermodynamic environment of the hypersonic aircraft is very complex throughout the body; from the structural mechanics perspective, the complex flow field environment makes the aircraft stress condition very complex, and the influence of elastic characteristics exists at the same time. These complex characteristics make the calculation amount required for establishing the hypersonic aircraft mathematical model with six degrees of freedom larger and the formula derivation difficulty higher under the condition of considering the elastic characteristics.
The modeling of the hypersonic aircraft is mainly divided into two parts, firstly, the elastic characteristics of the aircraft under different working conditions are required to be calculated, and then, the elastic dynamics model is fitted by combining the rigid body dynamics model according to the calculation result. In the elastic characteristic calculation stage, firstly, the problem of model establishment is considered, the complexity of the model influences the calculation time to a certain extent, whether a calculation result has engineering application value or not, and the rationality of the model also determines whether the calculation result has reference significance for subsequent research, so that a simpler aircraft model with certain rationality needs to be established; then considering the grid division problem, the selection of the type and the size of the grid can influence the convergence and the precision of the calculation result, but the undersize of the grid can increase the calculation cost, so that the grid with proper type and size is needed to be selected to balance the contradiction between the calculation cost and the precision; finally, the parameter setting of the solver needs to be considered, the types of models and solving problems adapted to different types of solvers and turbulence models are different, the dependence on grids is also different, the calculation result can be calculated more quickly and accurately by selecting an appropriate solver on the basis of ensuring calculation convergence, meanwhile, the material selection problem of different parts of the aircraft needs to be considered, and the stress condition in actual flight can be simulated more accurately by appropriate material selection, so that the calculation result has more engineering application value. In the elastic dynamics model modeling stage, the selection of six-degree-of-freedom rigid body dynamics models is needed to be considered, the selection of a proper rigid body model can effectively reduce the calculated amount of the fitting process and improve the fitting precision, meanwhile, how the elastic characteristic calculation data are combined with the rigid body model is needed to be considered so as to fit the elastic model, and the proper fitting method can effectively improve the precision of the model.
Disclosure of Invention
The invention aims to provide a modeling method of an elastic hypersonic aircraft based on computational mechanics for a hypersonic aircraft mathematical model considering elastic characteristics. According to the method, on the basis of obtaining elastic characteristics under different working conditions, the rigid body dynamics model of the aircraft is expanded, and the influence of the elastic characteristics is added, so that a six-degree-of-freedom elastic dynamics model of the hypersonic aircraft with half experience is obtained, and a basis is provided for the design of the appearance integration design of the aircraft and the design of the controller.
The invention adopts the following technical scheme:
1. An elastic hypersonic aircraft modeling method based on computational mechanics comprises the following steps:
Step 1: establishing a geometric model of the hypersonic aircraft and performing grid division;
step 2: based on computational fluid dynamics and computational structural mechanics, simulating and calculating elastic characteristics and aerodynamic parameters of the hypersonic aircraft under different working conditions to obtain fitting data;
Step 3: establishing a hypersonic aircraft rigid body dynamics model according to the fitting data and solving deformation angles at different positions according to a vibration equation;
Step 4: according to the rigid body dynamics model and the vibration equation, combining simulation calculation results in the steps, and obtaining a six-degree-of-freedom elastic dynamics model of the hypersonic aircraft through curve fitting: wherein: the fitting data are elastically solved by adopting a bidirectional fluid-solid coupling method:
201. calculating the temperature and heat flux density values of the wall surface of the aircraft under different incoming flow working conditions, and the radiant heat balance boundary conditions:
Wherein T w is the wall temperature value; t cl is the temperature at the center of the grid cell immediately adjacent to the object plane first layer; epsilon is the wall emissivity constant, determined by the wall material of the aircraft; σ=5.6687×10 -8(W/m2K4), is the Stefan-Boltzmann constant;
202. A turbulence calculation model is calculated by the following control equation, wherein:
vt＝Cμfμk2/ε
Wherein f 1f2fμ is a low Reynolds number damping parameter, C ε1Cε2Cμσκσε is a model constant, P κ is a turbulent kinetic energy generation term, τ u is a time scale, DE is an additional source term, The corrected isotropic dissipation ratio;
203. when the solver parameter is set, the values of the turbulence kinetic energy and the dissipation ratio can be calculated by the following formula:
k＝1.5(Uav*I)2
ε＝k1.5Cmu 0.75/l
l＝0.07L
I＝0.16Rel -0.125
Rel＝UavL/v
Wherein U av is the average flow velocity of the fluid, I is the turbulence intensity, L is the turbulence length scale, L is the characteristic length, and C mu is the empirical value.
Further, the geometric model meshing process comprises the following steps:
101. dividing boundary layer grids near the hypersonic aircraft body to capture gradient information in the boundary layer;
102. the boundary layer grid is represented by a dimensionless number y +, and the calculation process is shown in the following formula
Wherein y is the position of the grid node of the first layer boundary layer and the wall surface, U τ is the friction speed, v is the fluid viscosity, τ ω is the shear stress on the wall surface, ρ is the fluid density, C f is the wall surface friction coefficient, U ∞ is the speed when the fluid is fully developed, and Re l is the Reynolds number of the fluid;
103. according to the related parameters of the known fluid environment and the ideal y + value, the value of y can be calculated to control the size of the boundary layer grid;
104. and then proper adjustment is carried out according to engineering experience and simulation results to obtain proper parameters of the boundary layer.
Further, the hypersonic aircraft rigid body dynamics model is:
Wherein x, Y are the forward position and the lateral position under the ground coordinate system respectively, h is the height, V is the speed, the range is between 0 and 6 Mach, χ is the course angle, γ is the course angle, α is the attack angle, the range is between-3 degrees and +3 degrees, μ is the roll angle, p is the roll angle speed, q is the pitch angle speed, γ is the yaw angle speed, g is the gravitational acceleration, M is the mass, I xx,Iyy,Izz is the moment of inertia, L, D, Y, T are the lift force, the resistance, the side force and the thrust respectively, M x,My,Mz is the roll moment, the pitch moment and the yaw moment respectively;
Further, the vibration equation is to respectively establish a bending vibration equation according to the longitudinal section and the transverse section of the aircraft; the vibration equation is:
zx(x,t)＝∑iΦxi(x)ηxi(t),i＝1,2...
zy(y,t)＝∑iΦyi(y)ηyi(t),i＝1,2...
Wherein x, y are the length from any point of the longitudinal and transverse airframe to the aircraft nose respectively, E x(x,t),Ey (y, t) represents the longitudinal and transverse structural elastic modulus, I x(x),Iy (y) is the moment of inertia of the cross section and longitudinal section of the aircraft, m is the mass per unit volume, W x(x,t),Wy (y, t) is the longitudinal and transverse stress of the aircraft, z x(x,t),zy (y, t) is the longitudinal and transverse elastic deformation displacement function of the aircraft, wherein eta xi,ηyi is the longitudinal and transverse ith elastic mode respectively, and phi xi,Φyi is the longitudinal and transverse ith free vibration mode function respectively.
The deformation angles of the front body, the rear body and the two sides obtained according to the vibration equation are as follows:
Further, the aircraft elasto-kinetic model building process:
401. the expressions for generating aerodynamic parameters of an aircraft from aerodynamic discrete trends can be expressed separately as
Wherein phi is the opening degree of the accelerator, and the change of the elastic characteristic on the opening degree of the accelerator is ignored; delta e1,δe2 is elevator deflection angle, reference area S and spreadIs constant,/>For dynamic pressure, ρ is the fluid density and V is the aircraft speed. The control quantity is mainly delta e1,δe2, and the range is between-5 degrees and +5 degrees;
402. The curve fitting polynomial constructed by · is given by C L(·),CD(·),CY(·),CT(·),CM (·) in the form:
Where P (-) represents the basis function that constitutes C L(·),CD(·),CY(·),CT(·),CM (-), which is generally in the form of a polynomial on a certain variable;
403. and (3) determining polynomial coefficients by using a least square method, and performing curve fitting on the C L(·),CD(·),CY(·),CT(·),CM (·) base parameters.
Advantageous effects
1. The invention aims to consider a hypersonic aircraft mathematical model with elastic characteristics, expand an aircraft rigid body dynamics model on the basis of obtaining the elastic characteristics under different working conditions, and add the influence of the elastic characteristics, so that a six-degree-of-freedom elastic dynamics model of a semi-empirical hypersonic aircraft is obtained, and a basis is provided for the design of the appearance integration design of the aircraft and the design of a controller.
2. According to the method, modeling and analysis of the hypersonic aircraft with elastic characteristics are considered, based on computational fluid dynamics and computational structural mechanics, the elastic characteristics and aerodynamic parameters of the hypersonic aircraft under different working conditions are calculated, and a six-degree-of-freedom semi-empirical hypersonic aircraft dynamics model containing the elastic characteristics is established through curve fitting according to the calculated data under different working conditions.
3. According to the invention, the elastic characteristics of the aircraft under different working conditions are obtained through simulation calculation, and the existing six-degree-of-freedom rigid body dynamics model is combined to fit a semi-empirical six-degree-of-freedom elastic dynamics model, so that the calculation amount and the complexity of mathematical deduction are reduced.
Drawings
FIG. 1 is a flow chart of simulation calculation and modeling;
FIG. 2 is a schematic plan view of a hypersonic aircraft;
FIG. 3 is a hypersonic aircraft model map;
fig. 4 is a flow chart of bi-directional fluid-solid coupling.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the following detailed description of the present invention will be given with reference to the accompanying drawings and examples, which are given by way of illustration only, and not by way of limitation, and thus should not be construed as limiting the scope of the present invention.
The hypersonic aircraft has very complex flight environment and flight condition, and needs a complex controller and control algorithm to control the hypersonic aircraft, so that higher requirements are put forward on the model of the controlled object, but the hypersonic aircraft dynamics model with six degrees of freedom and considering the elastic characteristic is complex at present, has the characteristics of nonlinearity, strong coupling and the like, and brings difficulty to the design of the controller. Therefore, the invention provides a method for establishing an elastic model based on simulation data. In the simulation calculation stage, the elastic characteristics of the hypersonic aircraft under different working conditions are calculated and analyzed, so that fitting data such as elastic characteristics, deformation degree and stress conditions of all parts of the aircraft under different working conditions are obtained, and a foundation is provided for fitting an elastic model. In the model building stage, the elastic data obtained by calculation is fitted into elastic parameters by a certain method based on the existing six-degree-of-freedom rigid body model, and the rigid body model is expanded into a semi-empirical elastic model.
The hypersonic speed aircraft has the characteristics of high speed, strong breakthrough capability, large striking range and the like. The control difficulty is high, and in order to obtain a good control effect, a proper controlled object model is needed to be obtained first. However, the flow field environment of the whole aircraft is quite complex, so that the derivation process of the model is complex, the calculation amount is large, and a simple and effective model is difficult to build through a traditional mathematical method. Because hypersonic aircrafts fly at high altitudes where the atmospheric density is very low, the low density effect of hypersonic flow has a significant impact on aerodynamic forces. Because of the low atmospheric density, the air medium is no longer continuous, the conventional continuous flow assumption does not describe the fluid state well, and molecular motion theory must be used as a theoretical basis for research. When the aircraft flies at hypersonic speeds, the flying speed is too fast, so that the temperature of the surface of the aircraft body rises, which causes the boundary layer to become thicker, and the influence of the boundary layer cannot be ignored. At the same time, the viscous interaction of hypersonic flow, i.e. the increase in the thickness of the boundary layer, should also be considered, which influences the state of motion of the non-viscous flow, which in turn counteracts the boundary layer. The existence of the viscous effect enables the effective aerodynamic surface of the hypersonic aircraft to be changed into a boundary layer and an engine body surface, and the engine body surface rubs with external fluid due to the viscous effect, so that the pressure distribution and the resistance of the hypersonic aircraft are obviously changed. A very thin bow-shaped shock wave exists in front of the head of the aircraft, and a subsonic velocity zone is positioned in a region between a sonic velocity line and the wall surface of the head; a more pronounced flow separation zone exists in the flow field near the wall behind the shoulder end point; two more significant vortices exist in the tail region and when the reflux zone flow rate is higher than the local sound velocity, shock waves are generated in the tail region, thereby affecting the convection field conditions to some extent. Due to the viscous disturbance, the thickness of the boundary layer in the hypersonic aircraft flow field increases, and the viscous effect is not negligible.
The fluid environment of the whole aircraft is very complex, and the influence of the elastic characteristic is not negligible. Because of the slim body profile and the light structural design of hypersonic aircraft, the structural rigidity of the aircraft is reduced due to the influence of aerodynamic heat and other factors when the aircraft flies at hypersonic speed, so that a remarkable elastic effect of the aircraft occurs. The existence of the elastic effect enables the states of the aircraft such as rudder deflection angle, pitch angle, attack angle and the like to change, thereby affecting the overall aerodynamic layout of the aircraft, and simultaneously affecting the propulsion system of the aircraft, wherein the change of the propulsion system can cause the change of the control performance of the aircraft and even cause the failure of the original control strategy of the aircraft. In particular, when the transit of the aircraft changes, the lift resistance of the aircraft changes significantly, which is detrimental to the effective control of the flying height. Meanwhile, the change of the rigid motion state, such as the change of the flying speed, attack angle and the like, directly affects the stress of the hypersonic aircraft and further affects the deformation of the elastic body.
The simulation calculation and modeling flow chart of the invention is shown in fig. 1, and the main steps are as follows.
Step 1: and establishing a geometric model of the hypersonic aircraft and performing grid division.
Step 2: based on computational fluid dynamics and computational structural mechanics, the elastic characteristics and the aerodynamic parameters of the hypersonic aircraft under different working conditions are simulated and calculated to obtain fitting data.
Step 3: and establishing a hypersonic aircraft rigid body dynamic model according to the fitting data, and solving deformation angles at different positions according to a vibration equation.
Step 4: based on the rigid body dynamics model and the vibration equation, combining simulation calculation results in the steps, and obtaining the six-degree-of-freedom elastic dynamics model of the hypersonic aircraft through curve fitting.
The specific process of the invention is as follows:
1. Geometric model building
The hypersonic aircraft model adopted by the invention is of a waverider structure, and a schematic plan view is shown in figure 2. The waverider configuration is a hypersonic aircraft configuration with an attached shock wave at all its leading edges. Under hypersonic flight conditions, the lower surface of the body precursor generates an appendage shock wave, so that lift force and head-up moment are formed, and meanwhile, the pressure of incoming flow at an air inlet is increased as an external precompression system. After the combustion chamber and fuel are combusted, the incoming flow expands through the tail nozzle to generate the thrust required by the aircraft, and meanwhile, lift force and low head moment are formed on the lower surface of the rear body of the aircraft body. Because the shock wave generated by the waverider is positioned below the lifting surface of the waverider, the upper surface and the lower surface of the waverider are not in pressure communication, so that the problem of flow field interference between the lower surface and the upper surface of the aircraft is avoided, the upper surface and the lower surface can be treated separately, and the primary design and calculation process of the aircraft are effectively simplified. Therefore, in the hypersonic flight range, waverider has been recognized as the best profile.
In order to perform numerical calculation on the geometric model, the hypersonic aircraft model selected by the invention needs to perform discretization processing on the continuous geometric model, namely, mesh division is performed on the airframe and surrounding flow field areas, and boundary layer meshes are required to be divided near the airframe in the mesh division process so as to capture gradient information in the boundary layer.
Regarding how the boundary layer parameters are selected, the theoretical and actual calculation results are required to be continuously adjusted. For hypersonic outflow fields, the number of boundary layer layers is typically around 5 to 10 layers. For the size of the boundary layer grid, the invention performs size control by selecting the first layer boundary layer distance. In the actual operation process, the boundary layer distance of the first layer is too small to be described conveniently, so the boundary layer is expressed by adopting a dimensionless quantity y +, and the calculation process is shown in the following formula
Where y is the position of the first layer boundary layer grid node and the wall, U τ is the friction speed, v is the fluid viscosity, τ ω is the shear stress on the wall, ρ is the fluid density, C f is the wall friction coefficient, U ∞ is the speed at which the fluid is fully developed, and Re l is the reynolds number of the fluid. From the above equation, if the relevant parameters of the fluid environment and the ideal y + value are known, the y value can be calculated to control the size of the boundary layer grid, and then appropriate parameters can be obtained by appropriate adjustment according to engineering experience and simulation results. In general turbulence, the ideal value of y + ranges between 30 and 300.
2. Elastic property solving
Because the surrounding flow field of the hypersonic aircraft is quite complex when the hypersonic aircraft flies in the atmosphere, shock waves can be generated in the tail area when the flow rate of the reflux area is higher than the local sound velocity, so that the state of the flow field is influenced to a certain extent. The thickness of the boundary layer in hypersonic aircraft flow fields increases due to viscous disturbances, in some cases comparable to the thickness of the shock layer, and therefore the effect of fluid viscosity needs to be taken into account. The fluid part is assumed to be ideal gas, so that the flight environment of the aircraft in the cruising stage is simulated, the external flow field area is assumed to be a pressure far field, and the surface of the aircraft body is a non-slip wall surface. The selected fuselage and wing materials are D6AC high-density alloy steel materials, the density of the steel materials is 7900kg/m 3, the Young modulus is 12 x 10 13 Pa, and the Poisson ratio is 0.3. In the calculation process, the flow field and the structure body can generate interaction, and the flow field and the structure body are divided into unidirectional fluid-solid coupling and bidirectional fluid-solid coupling according to different transmission directions of the interaction. In unidirectional fluid-solid coupling, the flow field calculation is still steady state calculation, only the final flow field calculation result is led into the structure solving module, then the stress condition of the structure is calculated by the structure solving module, the deformation quantity generated after the stress of the structure is not transmitted to the flow field settlement module, namely, the influence of the flow field on the structure is only considered, and the reaction of the structure shape on the flow field is not considered. The invention adopts bidirectional fluid-solid coupling for calculation. The flow of the bidirectional fluid-solid coupling calculation is shown in fig. 4. The bidirectional fluid-solid coupling calculation not only considers the influence of the flow field on the structural body, but also considers the influence of the deformation of the structural body on the flow field. After selecting a suitable iteration format, a solution calculation may be performed. After the solving, aerodynamic data such as the elastic deformation degree, the lifting force, the resistance, the pitching moment and the like of each part of the aircraft under the consideration of the elastic action can be obtained.
In order to simulate the real flight environment as much as possible, the wall temperature conditions used in the calculation process of the invention are two types: isothermal wall boundary conditions and radiant heat balance boundary conditions. For wind tunnel experiments, the blowing time is very short and is generally in the range of 10 < -5 > to 10 < -3 > s, and the surface temperature of the experimental model is not changed so much, so that isothermal wall temperature conditions are reasonable for the experimental model. For an actual hypersonic aircraft, because the temperature values of the wall surface are changed under different flight conditions and even under the same condition, the temperature values at different positions on the surface of the aircraft are different, so that the isothermal wall boundary condition is unreasonable under the condition, and in order to accurately calculate the temperature and the heat flux density values of the wall surface of the aircraft under different incoming flow conditions, the invention adopts the radiant heat balance boundary condition:
Wherein T w is the wall temperature value; t cl is the temperature at the center of the grid cell immediately adjacent to the object plane first layer; epsilon is the wall emissivity constant, determined by the wall material of the aircraft; σ=5.6687×10 -8(W/m2K4), is a Stefan-Boltzmann constant.
Meanwhile, in order to improve the calculation accuracy, the viscosity effect is considered in the calculation process, and a standard k-epsilon turbulence model is selected as a turbulence calculation model, wherein k represents turbulence kinetic energy, and epsilon represents turbulence kinetic energy dissipation rate. The model contains two control equations, shown below, where the equation for the turbulent kinetic energy k is an accurate equation and the equation for the turbulent dissipation ratio epsilon is an empirical equation.
vt＝Cμfμk2/ε
Wherein f 1f2fμ is a low Reynolds number damping parameter, C ε1Cε2Cμσκσε is a model constant, P κ is a turbulent kinetic energy generation term, τ u is a time scale, DE is an additional source term,For the corrected isotropic dissipation ratio. In setting the solver parameters, the values of turbulence kinetic energy and dissipation ratio can be calculated by the following formula.
k＝1.5(Uav*I)2
ε＝k1.5Cmu 0.75/l
l＝0.07L
I＝0.16Rel -0.125
Rel＝UavL/v
Wherein U av is the average flow velocity of the fluid, I is the turbulence intensity, L is the turbulence length scale, L is the characteristic length, and C mu is the empirical value.
3. Building rigid body dynamics model of aircraft
The six-degree-of-freedom rigid body dynamics model of the hypersonic aircraft is shown as follows:
Wherein x, Y are the forward position and the lateral position under the ground coordinate system respectively, h is the height, V is the speed, the range is between 0 and 6 Mach, χ is the course angle, γ is the track angle, α is the attack angle, the range is between-3 degrees and +3 degrees, μ is the roll angle, p is the roll angle speed, q is the pitch angle speed, γ is the yaw angle speed, g is the gravitational acceleration, M is the mass, I xx,Iyy,Izz is the moment of inertia, L, D, Y, T are the lift force, the resistance, the side force and the thrust respectively, and M x,My,Mz is the roll moment, the pitch moment and the yaw moment respectively.
The hypersonic aircraft fuselage with waverider configuration is slender, and the elastic mode can be obviously excited when the aircraft flies at high speed, so that the aircraft fuselage is bent and deformed, and the rigid body state and the aerodynamic parameters of the aircraft are influenced. The elastic influence should therefore be reflected in a rigorous hypersonic aircraft model, and the elastic vibration equation is deduced below.
And respectively establishing bending vibration equations in the longitudinal section and the transverse section of the aircraft to obtain vibration frequency and vibration mode.
The vibration equation is
zx(x,t)＝∑iΦxi(x)ηxi(t),i＝1,2...
zy(y,t)＝∑iΦyi(y)ηyi(t),i＝1,2...
Wherein x, y are the length from any point of the longitudinal and transverse airframe to the aircraft nose respectively, E x(x,t),Ey (y, t) represents the longitudinal and transverse structural elastic modulus, I x(x),Iy (y) is the moment of inertia of the cross section and longitudinal section of the aircraft, m is the mass per unit volume, W x(x,t),Wy (y, t) is the longitudinal and transverse stress of the aircraft, z x(x,t),zy (y, t) is the longitudinal and transverse elastic deformation displacement function of the aircraft, wherein eta xi,ηyi is the longitudinal and transverse ith elastic mode respectively, and phi xi,Φyi is the longitudinal and transverse ith free vibration mode function respectively.
The deformation angles of the front body, the rear body and the two sides are as follows:
4. Building an elastohydrodynamic model of an aircraft
In order to simplify the model and consider the influence of elastic characteristics, the invention adopts a curve fitting method of stepwise regression analysis, and based on pneumatic parameters under different working conditions under the condition of considering the elastic characteristics obtained in the previous step, complex force and moment in the previous step are expressed into a linear combination form of related state quantity and input quantity, thereby obtaining the six-degree-of-freedom elastic dynamics model of the hypersonic aircraft.
By analyzing the calculated pneumatic discrete data trend, the expressions of aerodynamic parameters such as lift force, resistance force, side force and the like can be respectively expressed as
/>
Wherein phi is the opening degree of the accelerator, and the change of the elastic characteristic to the opening degree of the accelerator is ignored. Delta e1,δe2 is elevator deflection angle, reference area S and spreadIs constant,/>For dynamic pressure, ρ is the fluid density and V is the aircraft speed. The control amount is mainly delta e1,δe2, and the range is between-5 degrees and +5 degrees.
C L(·),CD(·),CY(·),CT(·),CM (·) is a curve-fitting polynomial constructed from·in the general form:
Where P (-) represents the basis function that constitutes C L(·),CD(·),CY(·),CT(·),CM (-), which is typically in the form of a polynomial on a certain variable. The specific form of each basis function needs to be determined, and the specific form mainly comprises the steps of determining the degree of a basis function polynomial and each coefficient. The polynomial degree determination mainly considers the requirement of fitting precision, and further determines which control quantity and state quantity and specific times of each item should be contained in the polynomial on the basis of analyzing the variation trend of the elastic pneumatic data obtained in the calculation process and possible coupling conditions. The secondary terms of attack angle and accelerator are added to the resistance and thrust coefficients, and the result shows that the fitting accuracy can be effectively improved. Meanwhile, the lift force and resistance coefficient are added with the coupling items of attack angle and accelerator opening, so that the accuracy is improved, and the coupling effect between the control quantity and the state quantity is also shown. In order to make the model more accurate, not only an appropriate basis function form is sought from the point of view of calculation data, but also whether different variables have influence on pneumatic parameters or not is considered according to a specific physical model. Because the throttle opening, the attack angle and the front and rear body shape variables only affect the model aerodynamic parameters in the longitudinal direction and have no influence on the side force born by the aircraft, the side force coefficient is only composed of the basis functions corresponding to the deformation angles of the two sides. In order to further simplify the model, the throttle opening item is omitted from the lift force, the side force, the rolling moment and the yaw moment coefficient, and the influence of the throttle opening on fitting accuracy is small. The pneumatic parameters obtained by the curve fitting method based on the data simplify the original dynamic model and introduce the influence of the elastic action under the condition of ensuring the accuracy.
Then, a least square method is selected to determine polynomial coefficients, an objective function is defined first, taking a curve fitting process of lift coefficient C L as an example, and the objective function is as follows:
Wherein L, L * are respectively calculated lift values and lift values obtained by fitting various pneumatic parameters. In order to obtain the minimum value of the objective function, a method of obtaining extremum by adopting a multi-element function is adopted, and each variable is sequentially subjected to deviation obtaining to form an equation set as follows:
and solving the equation set to obtain specific parameters of each polynomial, thereby obtaining the complete six-degree-of-freedom elastic model of the hypersonic aircraft.
According to the method, a geometric model is built and grids are divided according to the flow, the aerodynamic parameters and stress conditions of the aircraft in a normal state and in a tail vane fault state are calculated through the processes of arranging a solver, structural materials and the like, and the aerodynamic characteristics and the elastic characteristics of the aircraft are further summarized through analysis of calculation results. The total length of the aircraft body selected by the invention is 100 feet, the front length of the aircraft is 47 feet, the rear length of the aircraft is 33 feet, the included angle between the upper surface and the horizontal direction is 3 degrees, and the included angle between the lower surface and the horizontal direction is 6 degrees. The length of the lower engine is 20 feet, and the lower engine is a hollow cuboid, and the wall surface of the lower engine is a wall without thickness. The aircraft has a width of 1 foot and the overall structure is elongate. The tail rudder is 15 feet long and is in a triangular prism shape. After the geometric model is built, an external flow field is built outside the aircraft to simulate the flight environment of the aircraft, the total length of the external flow field is 200 feet, the front end is 50 feet away from the forefront of the aircraft, the rear end is 150 feet away from the tail of the aircraft, the width and the height are 50 feet, the whole of the geometric model is cuboid, and the variable range of the flow field can be covered. The results of the aerodynamic feature calculation are shown in table 1.
Table 1 partial aerodynamic parameter calculation results
After a specific form of the basis function is obtained, the curve-fitting polynomial can be written as follows. It can be seen that the lift coefficient is mainly related to the aircraft angle of attack, the rudder deflection angles of the two sides, and the transverse and longitudinal deformation angles; the resistance coefficient is mainly equal to the attack angle, the accelerator opening, the deflection angles of the rudders at two sides and the transverse and longitudinal deformation angles, and a quadratic polynomial is adopted for improving the fitting accuracy of the attack angle, and a coupling term of the attack angle and the deflection angle of the rudders is added; the side force coefficient is only related to the lateral deformation; the thrust consists of an attack angle, an accelerator opening and a transverse and longitudinal coupling term, and the coupling term of the attack angle and the accelerator opening and a quadratic form of the accelerator opening are introduced to improve fitting precision; the generalized force coefficient is formed by linearly combining an attack angle, an accelerator opening, a rudder deflection angle and a transverse and longitudinal deformation angle; the roll moment coefficient is only related to the deflection angles of the two rudders; the pitching moment is related to the attack angle, the accelerator opening, the deflection angles of the two rudders and the longitudinal deformation angle, and the influence of the transverse deformation angle is ignored; yaw moment is related to attack angle, deflection angles of two rudders and transverse deformation angle, and influence of longitudinal deformation angle is ignored.
The invention is not limited to the embodiments described above. The above description of specific embodiments is intended to describe and illustrate the technical aspects of the present invention, and is intended to be illustrative only and not limiting. Numerous specific modifications can be made by those skilled in the art without departing from the spirit of the invention and scope of the claims, which are within the scope of the invention.
Claims (5)
1. The modeling method of the elastic hypersonic aircraft based on computational mechanics is characterized by comprising the following steps of:
Step 1: establishing a geometric model of the hypersonic aircraft and performing grid division;
step 2: based on computational fluid dynamics and computational structural mechanics, simulating and calculating elastic characteristics and aerodynamic parameters of the hypersonic aircraft under different working conditions to obtain fitting data;
Step 3: establishing a hypersonic aircraft rigid body dynamics model according to the fitting data and solving deformation angles at different positions according to a vibration equation;
step 4: according to the rigid body dynamics model and the vibration equation, combining simulation calculation results in the steps, and obtaining a six-degree-of-freedom elastic dynamics model of the hypersonic aircraft through curve fitting, wherein: the fitting data are elastically solved by adopting a bidirectional fluid-solid coupling method:
201. calculating the temperature and heat flux density values of the wall surface of the aircraft under different incoming flow working conditions, and the radiant heat balance boundary conditions:
Wherein: t w is the wall temperature value; t cl is the temperature at the center of the grid cell immediately adjacent to the object plane first layer; epsilon is the wall emissivity constant, determined by the wall material of the aircraft; σ=5.6687×10 -8(W/m2K4), is the Stefan-Boltzmann constant;
202. A turbulence calculation model is calculated by the following control equation, wherein:
vt＝Cμfμk2/ε
Wherein f 1、f2、fμ is a low Reynolds number damping parameter, C ε1、Cε2、Cμ、σκ、σε is a model constant, P κ is a turbulent kinetic energy generation term, τ u is a time scale, D, E is an additional source term, V is the fluid viscosity for the corrected isotropic dissipation ratio;
203. when the solver parameter is set, the values of the turbulence kinetic energy and the dissipation ratio are calculated by the following formula:
k＝1.5(Uav*I)2
ε＝k1.5Cmu 0.75/l
l＝0.07L
I＝0.16Rel -0.125
Rel＝UavL/v
Wherein U av is the average flow velocity of the fluid, I is the turbulence intensity, L is the turbulence length scale, L is the characteristic length, and C mu is the empirical value.
2. The elastic hypersonic aircraft modeling method based on computational mechanics according to claim 1 wherein the geometric model meshing process is as follows:
101. dividing boundary layer grids near the hypersonic aircraft body to capture gradient information in the boundary layer;
102. the boundary layer grid is represented by a dimensionless number y +, and the calculation process is shown in the following formula
Wherein y is the position of the grid node of the first layer boundary layer and the wall surface, U τ is the friction speed, tau ω is the shear stress on the wall surface, rho is the fluid density, C f is the friction coefficient of the wall surface, U ∞ is the speed when the fluid is completely developed, and Re l is the Reynolds number of the fluid;
103. according to the related parameters of the known fluid environment and the ideal y + value, calculating the value of y for controlling the size of the boundary layer grid;
104. and then properly adjusting according to engineering experience and simulation results to obtain parameters of the boundary layer.
3. The elastic hypersonic aircraft modeling method based on computational mechanics according to claim 2 wherein the hypersonic aircraft rigid body dynamics model is:
Wherein x, Y are the forward position and the lateral position under the ground coordinate system respectively, h is the height, V is the speed, the range is between 0 and 6 Mach, χ is the course angle, γ is the track angle, α is the attack angle, the range is between-3 degrees and +3 degrees, μ is the roll angle, p is the roll angle speed, q is the pitch angle speed, r is the yaw angle speed, g is the gravitational acceleration, M is the mass, I xx,Iyy,Izz is the moment of inertia, L, D, Y, T are the lift force, the resistance, the side force and the thrust respectively, and M x,My,Mz is the roll moment, the pitch moment and the yaw moment respectively.
4. A method of modeling a hypersonic elastic aircraft based on computational mechanics according to claim 3 wherein the vibration equations are based on the flexural vibration equations established in the longitudinal and transverse cross-sections of the aircraft, respectively; the vibration equation is:
zx(x,t)＝∑iΦxi(x)ηxi(t),i＝1,2...
zy(y,t)＝∑iΦyi(y)ηyi(t),i＝1,2...
Wherein x, y are the length from any point of the longitudinal and transverse airframe to the aircraft nose respectively, E x(x,t),Ey (y, t) represents the longitudinal and transverse structural elastic modulus, I x(x),Iy (y) is the moment of inertia of the cross section and longitudinal section of the aircraft, m is the mass per unit volume, W x(x,t),Wy (y, t) is the longitudinal and transverse stress of the aircraft, z x(x,t),zy (y, t) is the longitudinal and transverse elastic deformation displacement function of the aircraft, wherein eta xi,ηyi is the longitudinal and transverse ith elastic mode respectively, and phi xi,Φyi is the longitudinal and transverse ith free vibration mode function respectively;
The deformation angles of the front body, the rear body and the two sides obtained according to the vibration equation are as follows:
5. The elastic hypersonic aircraft modeling method based on computational mechanics as claimed in claim 4 wherein the aircraft elastic dynamics model building process:
401. The expressions for generating aerodynamic parameters of an aircraft according to aerodynamic discrete trends are respectively expressed as
Wherein phi is the accelerator opening, the elastic characteristic is neglected to change of the accelerator opening, delta e1,δe2 is the elevator deflection angle, the reference area S and the extension lengthIs constant,/>The dynamic pressure is V, the speed of the aircraft is controlled by delta e1,δe2, and the range is between-5 degrees and +5 degrees;
402. The curve fitting polynomial constructed by · is given by C L(·),CD(·),CY(·),CT(·),CM· (·) in the form:
Wherein P (-) represents the basis function constituting C L(·),CD(·),CY(·),CT(·),CM (-) in the form of a polynomial on a certain variable;
403. and (3) determining polynomial coefficients by using a least square method, and performing a curve fitting process on the C L(·),CD(·),CY(·),CT(·),CM (·) base parameters.
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