WO2018214657A1 - Equalisation technique for turbulent boundary layer load model - Google Patents

Abstract

An equalisation technique for a turbulent boundary layer load model, comprising the steps of: (1) forming an equivalent completely-random surface pressure load model after a turbulent boundary layer load model is equalised; (2) determining the magnitude of an equivalent correlation function of the equivalent completely-random surface pressure load model; and (3) determining the wavelength of structural bending and a characteristic wavelength of a turbulent boundary layer load, thus calculating the frequency of consistency, and thereby determining an applicable frequency range of the equivalent random surface pressure load model. An equalisation technique for a turbulent boundary layer load model is a technique of equalising a turbulent boundary layer load model to a completely-random surface pressure load model; the technique can effectively reduce the calculated amount of structural dynamic response analysis under the action of a turbulent boundary layer load, shorten a design cycle and save on the design cost.

Description

An Equivalent Technique for a Turbulent Boundary Layer Load Model Technical field

The invention relates to the technical field of random surface pressure load model equivalent, and particularly relates to an equivalent technique of a turbulent boundary layer load model.

Background technique

As spacecraft develop toward higher flight speeds, they face severe random noise and other environments during the mission cycle, which may cause structural failure or failure of precision instruments and instruments. Therefore, in the design of the spacecraft, the effects of mechanical vibration and noise should be considered. Test methods, theoretical methods and numerical methods can be used to predict the dynamic response of the system under random noise excitation. Among them, the test method can obtain reliable results, but the cost of conducting test analysis is high, and the design cycle is long; the theoretical method is only applicable to simple systems, and it is difficult to solve the dynamic response prediction problem of complex systems; the numerical method can save design cost and shorten design Cycle is an effective aid to experimental analysis.

In a currently known turbulent boundary layer load model, the coherence length of the low frequency band is long and the coherence length of the high frequency band is short. When the modal superposition method in the finite element method is used to analyze the random response of the structure in the turbulent boundary layer load excitation, the coherence length of the turbulent boundary layer load is shortened as the analysis frequency increases, and the size of the finite element mesh is required to be smaller. This causes the amount of computation to grow geometrically. Therefore, in the higher frequency band, effective measures need to be taken to solve the problem of low efficiency of the above-mentioned turbulent boundary layer load model analysis, thereby shortening the design cycle and saving design cost.

Summary of the invention

OBJECT OF THE INVENTION In order to overcome the deficiencies in the prior art, the present invention provides an equivalent technique for the turbulent boundary layer load model in view of the existing problems in the application of a turbulent boundary layer load model. It can effectively improve the efficiency of structural dynamic response simulation analysis under turbulent boundary layer load excitation.

Technical Solution: In order to achieve the above object, the technical solution adopted by the present invention is:

An equivalent technique for a turbulent boundary layer load model, comprising the following steps:

(1) The turbulent boundary layer load model is equivalent to form an equivalent completely random surface pressure load model;

(2) determining the magnitude of the equivalent correlation function of the equivalent completely random surface pressure load model;

(3) Determine the applicable frequency range of the equivalent random surface pressure load model according to the structural model and the turbulent boundary layer load model.

Further, the turbulent boundary layer load model in the step (1) is:

Where ξ _x is the distance of the two points in the x-axis direction, ξ _y is the distance of the two points in the y-axis direction, ω is the angular frequency, and S ₀ is the magnitude of the load power spectrum, D _x =α _x /k _c , D _y =α _y /k _c are the coherence lengths of the forward flow direction and the cross flow direction, respectively, the dimensionless constant α _x =8, α _y =1.2, k _c =ω/U _c is the convection wave number, U _c =0.7U For convection speed, U is the incoming flow speed.

Further, the equivalent completely random surface pressure load model in the step (1) is:

S _pp (ξ _x , ξ _y , ω)=S ₀ C ^eq (ω)δ(ξ _x )δ(ξ _y ) (2)

Where C ^eq (ω) is the magnitude of the equivalent correlation function and the function δ(ξ) is the Kroneck function:

Further, the magnitude C ^eq (ω) of the equivalent correlation function of the equivalent completely random surface pressure load model in the step (2) satisfies the following formula:

Further, the magnitude C ^eq (ω) of the equivalent correlation function of the equivalent fully random surface pressure load model is:

Further, the applicable frequency range of the equivalent completely random surface pressure load model in the step (3) is f≥f ^crit , and f ^crit is the critical frequency.

Further, the critical frequency is:

f ^crit =4f _c (6)

Where f _c is the consistency frequency.

Further, the uniform frequency f _c is a uniform frequency when the structural bending wavelength λ _B (ω) and the reverberant field load characteristic wavelength λ _T (ω) are equal, that is, λ _B (ω)=λ _T (ω) :

Where E is the elastic modulus of the material, ρ is the material density, ν is the material Poisson's ratio, and h is the thickness of the structural surface plate member.

Advantageous Effects: The equivalent technology of a turbulent boundary layer load model provided by the present invention is a technique for equivalenting a turbulent boundary layer load model to a completely random surface pressure load model, which can effectively reduce turbulent boundary layer load excitation The calculation of the dynamic response analysis of the lower structure shortens the design cycle and saves the design cost.

DRAWINGS

Figure 1 is a logic flow diagram of the present invention;

Figure 2 is a schematic view of a rectangular simply supported plate;

Figure 3 is a schematic diagram of the displacement response power spectral density at point A on a rectangular simple plate.

detailed description

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

Figure 1 shows a logical flow diagram of an equivalent technique for a turbulent boundary layer load model, which mainly includes the following steps:

Step (1) The turbulent boundary layer load model is equivalent to form an equivalent completely random surface pressure load model;

(1.1) Turbulent boundary layer load model, the cross-spectrum between the surface pressure loads at any two points in space is:

Where ξ _x is the distance of the two points in the x-axis direction, ξ _y is the distance of the two points in the y-axis direction, ω is the angular frequency, and S ₀ is the magnitude of the load power spectrum, D _x =α _x /k _c , D _y =α _y /k _c are the coherence lengths of the forward flow direction and the cross flow direction, respectively, the dimensionless constant α _x =8, α _y =1.2, k _c =ω/U _c is the convection wave number, U _c =0.7U For convection speed, U is the incoming flow speed.

(1.2) Equivalent completely random surface pressure load model, the cross-spectrum of the surface pressure at any two points in space is:

S _pp (ξ _x , ξ _y , ω)=S ₀ C ^eq (ω)δ(ξ _x )δ(ξ _y ) (2)

Where C ^eq (ω) is the magnitude of the equivalent correlation function and the function δ(ξ) is the Kroneck function:

Step (2)) determining the magnitude C ^eq (ω) of the equivalent correlation function of the equivalent completely random surface pressure load model, and determining the equivalent completely random surface pressure load model;

The magnitude of the equivalent correlation function of the equivalent completely random surface pressure load model, C ^eq (ω), satisfies the following equation:

The magnitude C ^eq (ω) of the equivalent correlation function of the equivalent fully random surface pressure load model obtained by solving equation (4) is:

Step (3) determining an applicable frequency range of the equivalent random surface pressure load model according to the structural model and the turbulent boundary layer load model; specifically:

(3.1) Determine the bending wavelength of the structure:

Where E is the elastic modulus of the material, ρ is the material density, ν is the material Poisson's ratio, and h is the thickness of the structural surface plate member.

(3.2) Determine the characteristic wavelength of the turbulent boundary layer load:

λ _T (ω)=2πU _c /ω (7)

(3.3) Calculate the uniform frequency when the structural bending wavelength and the turbulent boundary layer load characteristic wavelength are equal, that is, λ _B (ω)=λ _D (ω):

(3.4) Calculate the critical frequency for the equivalent fully random surface pressure load model:

f ^crit =4f _c (9)

(3.5) Determine the applicable frequency range of the equivalent fully random surface pressure load model in step (2) as f ≥ f ^crit .

Example

As shown in Figure 2, a rectangular simple support plate is taken as an example to calculate the consistency frequency. The dimensions of the rectangular simply supported plate are: x axial length L _x =1 m, y axial length L _y =1 m, thickness h = 0.005 m. The parameters of the material used for the rectangular simply supported plate are: elastic modulus E = 120 GPa, material density ρ = 7800 kg/m ³ , Poisson's ratio υ = 0.3. When the incoming flow velocity U=100 m/s, the value of each parameter is substituted into equation (8) to obtain f _c = 102 Hz.

The critical frequency applicable to the equivalent fully random surface pressure load model calculated by step (3.4) is f ^crit = 408 Hz.

After step (3.5), the applicable frequency range of the equivalent fully random surface pressure load model is f ≥ f ^crit , that is, when the analysis frequency f ≥ 408 Hz, in this example, the equivalent complete randomness shown by equation (2) can be obtained. The surface pressure load model replaces the turbulent boundary layer load model shown in equation (1).

The equivalent fully random surface pressure load obtained by the above steps is applied to the simply supported rectangular plate shown in FIG. 2, and the displacement response power spectral density at point A (0.3 m, 0.2 m) is calculated (in dB). The value is 1m ² Hz ^-1 ), as shown in Figure 3. The results in Fig. 3 show that, in this example, when f ≥ f ^crit , that is, f ≥ 408 Hz, the equivalent fully random surface ballast model obtained in the above step can effectively represent the turbulent boundary layer load model.

The final result of the embodiment shows that the method proposed by the invention can effectively convert the turbulent boundary layer load model into an equivalent completely random surface pressure load model, and improve the efficiency of the subsequent response analysis.

The above description is only a preferred embodiment of the present invention, and it should be noted that those skilled in the art can also make several improvements and retouchings without departing from the principles of the present invention. It should be considered as the scope of protection of the present invention.

Claims (8)

An equivalent technique for a turbulent boundary layer load model, characterized in that it comprises the following steps: (1) The turbulent boundary layer load model is equivalent to form an equivalent completely random surface pressure load model; (2) determining the magnitude of the equivalent correlation function of the equivalent completely random surface pressure load model; (3) Determine the applicable frequency range of the equivalent random surface pressure load model according to the structural model and the turbulent boundary layer load model. The equivalent technique of the turbulent boundary layer load model according to claim 1, wherein the turbulent boundary layer load model in the step (1) is:

Where ξ _x is the distance of the two points in the x-axis direction, ξ _y is the distance of the two points in the y-axis direction, ω is the angular frequency, and S ₀ is the magnitude of the load power spectrum, D _x =α _x /k _c , D _y =α _y /k _c are the coherence lengths of the forward flow direction and the cross flow direction, respectively, the dimensionless constant α _x =8, α _y =1.2, k _c =ω/U _c is the convection wave number, U _c =0.7U For convection speed, U is the incoming flow speed. The equivalent technique of the turbulent boundary layer load model according to claim 1, wherein the equivalent fully random surface pressure load model in the step (1) is: S _pp (ξ _x , ξ _y , ω)=S ₀ C ^eq (ω)δ(ξ _x )δ(ξ _y ) (2) Where C ^eq (ω) is the magnitude of the equivalent correlation function and the function δ(ξ) is the Kroneck function:

The equivalent technique of the turbulent boundary layer load model according to claim 1, wherein the magnitude C ^eq (ω) of the equivalent correlation function of the equivalent completely random surface pressure load model in the step (2) is satisfied. formula:

The equivalent technique of the turbulent boundary layer load model according to claim 1 or 4, characterized in that the magnitude C ^eq (ω) of the equivalent correlation function of the equivalent completely random surface pressure load model is:

The technique according to an equivalent load model turbulent boundary layer as claimed in claim, wherein: the frequency range applicable to the model of the equivalent load pressure of step (3) is completely random surface is f≥f ^crit, f ^crit is Critical frequency. The equivalent technique of the turbulent boundary layer load model according to claim 6, wherein the critical frequency is: f ^crit =4f _c (6) Where f _c is the consistency frequency. The equivalent technique of the random surface pressure load model of the reverberation field according to claim 7, wherein the uniform frequency f _c is such that the structural bending wavelength λ _B (ω) and the reverberant field load characteristic wavelength λ _T Consistent frequency when (ω) is equal, ie λ _B (ω)=λ _T (ω):

Where E is the elastic modulus of the material, ρ is the material density, ν is the material Poisson's ratio, and h is the thickness of the structural surface plate member.

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