CN110298063B - Non-compact permeable boundary aerodynamic noise numerical integral calculation method - Google Patents
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Abstract
The invention discloses a non-compact permeable boundary aerodynamic noise numerical integral calculation method, which belongs to the technical field of fluid mechanics and acoustics, and adopts flow calculation software to disperse a flow field calculation area into K grid units to obtain sound source information; selecting boundary S in the vicinity of object P And S is combined with P Discretizing into L grid cells, typically selected as the same boundary as the flowing discrete grid; calculation S P Upper equivalent diffuse sound source p a (z, ω) calculating the sound pressure p of the far-field monitoring point x a (x, ω). The invention adopts the object surface as the integral boundary, and combines the boundary element method to implement the integral calculation, and has the problems of low calculation efficiency, high calculation complexity, value singularity and the like.
Description
Technical Field
The invention belongs to the technical field of hydrodynamics and acoustics, and relates to a non-compact permeable boundary aerodynamic noise value integral calculation method.
Background
In recent years, the problems of noise of aviation aircrafts, civil aircrafts, high-speed trains and impeller machines are greatly solved, so that the demand for the study of aerodynamic noise values is continuously increased. The complex structure surface often has sharp angles or structures such as concave and convex structures, such as a three-section wing model and a fan blade model, and the pneumatic noise numerical value research work is not easy to develop. In practical application, flow high-precision calculation is often adopted, and the calculation load is increased due to the calculation amount. However, the low-precision flow calculation cannot obtain accurate sound source information. Especially when the boundary shape is complex, the numerical value singularity problem exists in the traditional calculation means, and the numerical value calculation difficulty is increased undoubtedly.
If the geometry of the boundary is much smaller than the wavelength of the sound wave, the boundary can be regarded as compact, and the sound wave can continue to radiate forward when propagating to the boundary, and can be regarded as sound propagation in free space; conversely, if the geometry of the boundary is greater than or near the wavelength of the sound wave, the boundary may be considered non-compact, and the sound wave propagates into space to produce an outwardly radiated sound wave, while scattering at the boundary to produce a secondarily radiated sound wave. There is a significant difference in the propagation of sound in non-compact structures from free space.
The boundary integral equation method combines the thought of boundary elements, and effectively improves the calculation efficiency of the pneumatic noise problem. In recent years, a great number of students have carried out many researches on non-compact structures by adopting the method, and the method is basically divided into two types, wherein one type is to seek an accurate green function solution meeting given boundary conditions, and the method obtains the green function by a method of constructing the green function and combines low-precision flow calculation to carry out acoustic calculation; and the second is to combine the pressure variable decomposition expression, provide an acoustic integral equation for far-field sound pressure calculation, and complete far-field noise calculation by capturing a scattered sound source on the object plane boundary.
The current relevant research work is applicable to simple boundaries, and the problems of low calculation efficiency and high calculation complexity exist under the complex boundary condition.
Disclosure of Invention
The invention aims to overcome the defects of low calculation efficiency, high calculation complexity and numerical value singularity in the process of carrying out integral calculation by adopting the object surface as an integral boundary and combining a boundary element method in the calculation method in the prior art, develop the research work of the pneumatic noise numerical value calculation of a complex structure, and provide a pneumatic noise numerical value integral calculation method with a non-compact permeable boundary.
The above object of the present invention is achieved by the following technical solutions:
a method for calculating the numerical integral of pneumatic noise of a non-compact permeable boundary,
the method comprises the following steps:
step 1: dispersing the flow field calculation region into K grid units by adopting flow calculation software (such as Fluent) to obtain sound source information including density ρ and pressure p h Speed u i (i=1, 2, 3), ρ for low mach number flow h ≈ρ；
Step 2: selecting boundary S in the vicinity of object P And S is combined with P Discretizing into L grid cells, typically selected as the same boundary as the flowing discrete grid;
step 3: using the formula
Calculation S P Upper equivalent diffuse sound source p a (z, ω) can be rearranged into a system of linear equations:
Where m=1, 2,3, … L, n=1, 2,3, … L, L being the number of units contained in the boundary S;
step 4: using the formula
In the above calculation expression, ω represents the circumferential frequency, c 0 Representing the propagation velocity of sound waves, V k Representing the area or volume of the kth flow field grid cell [] k Representing information on the kth flow field grid cell [] l Representing information on the first border element, p a (z l ω) represents the point z on the boundary l Sound pressure at omega frequency, p a (x, ω) represents the sound pressure of the far field monitoring point x at ω frequency, and j represents an imaginary unit in the last term. Delta ij Representing a second order tensor,
further, when the problem is a two-dimensional model, the two-dimensional model calculates the free space green's function G (y) by the following formula in the implementation of steps 3, 4 m ,y n ,ω)
Further, when the problem is a three-dimensional model, the steps 3 and 4 are implemented by the following stepsThe column formula calculates the free space green's function G (y m ,y n ,ω)
Determining y m Point and y n Free space green's function edge y of point n External normal partial derivative of point
Comprising the following steps:
when the problem is a two-dimensional model, the implementation process of the steps 3 and 4 is determined by the following formula
When the problem is a three-dimensional model, the implementation process of the steps 3 and 4 is determined by the following formula
Determining y m Point and y n Free space green's function edge y of point n Second partial derivative of point
Comprising the following steps:
when the problem is a two-dimensional model, the implementation process of the steps 3 and 4 is determined by the following formula
Further, when the problem is a three-dimensional model, the implementation process of the steps 3 and 4 is determined by the following formula
Determining x-point and y n Free space green's function edge y of point n External normal partial derivative of point
Comprising the following steps:
when the problem is a two-dimensional model, the implementation process of the steps 3 and 4 is determined by the following formula
When the problem is a three-dimensional model, the implementation process of the steps 3 and 4 is determined by the following formula
Determining x-point and y n Free space green's function edge y of point n Second partial derivative of point
Comprising the following steps:
when the problem is a two-dimensional model, the implementation process of the steps 3 and 4 is determined by the following formula
Further, when the problem is a three-dimensional model, the implementation process of the steps 3 and 4 is determined by the following formula
Wherein the subscripts M, n=1, 2,3, …, M is the grid cell number,
for the first class 0 th order Hankel function, < >>
First class 1 order Hankel function, k=ω/c 0 Is the number of sound waves.
The object plane scattering sound source is calculated through the step 3, and on the premise that the right-end term solving is completed, the object plane scattering sound source can be calculated by calculation
Obtaining a matrix:
sub-item H of H mn To-be-solved sound source point y m The corresponding matrix column entries are:
wherein s=s 1 ∪S 1 …∪S L ，y m Point and y n When overlapped, H mn ＝0。
And 4, calculating the sound pressure of the far-field monitoring point, and directly obtaining the sound pressure on the premise of completing the solution of the right-end term.
The invention has the advantages and beneficial effects that:
1. according to the invention, the flow field sound source information is obtained by adopting second-order precision flow calculation, so that the workload of numerical calculation is effectively improved;
2. according to the invention, the equivalent scattering sound source is obtained by calculating the sound source on the permeable boundary, so that the problem of the calculation complexity of the complex object plane boundary scattering sound source is reduced;
2. the invention obtains far-field noise by calculating radiation noise and scattering noise, and the radiation part and the scattering part can be distinguished in sound pressure information;
3. the invention can solve the problem of aerodynamic noise propagation calculation in complex configuration or in a plurality of object flow fields, and has strong applicability.
Drawings
FIG. 1 is a flow field calculation partial mesh map;
FIG. 2 is a schematic illustration of point source acoustic propagation;
FIG. 3 is a graph of permeable boundary and object boundary position profiles;
FIG. 4 is a laminar cylindrical flow field calculation region;
FIG. 5 is a grid density distribution near a laminar flow cylinder;
fig. 6 is a far-field sound pressure directivity calculated by low-frequency lower laminar flow cylindrical boundary integration, where (a) f=f 0 ，(b)f＝2f 0 ；
FIG. 7 is a position distribution of laminar cylindrical surfaces and permeable boundaries;
fig. 8 is a far-field sound pressure directivity obtained by different integration boundaries, where (a) f=f 0 ，(b)f＝2f 0 ；
FIG. 9 is a position distribution of turbulent cylindrical surfaces and permeable boundaries;
fig. 10 is a far-field sound pressure level distribution obtained by different integration boundaries, where (a) f=f 0 ，(b)f＝2f 0 。
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the accompanying drawings and the detailed description.
The sound field calculation in the invention is based on flow calculation, and takes the acoustic calculation of cylinders and airfoils in two-dimensional space as an example, as shown in figure 1, each grid is regarded as a sound source, and the sound signals received by the far-field detector are the sum of sound signals sent by all the sound sources.
The point sound source propagation is known to follow wave equation (1),
each flow field sound source can be equivalently regarded as a point source, and simultaneously follows the flow propagation rule to meet the lightill wave equation (2)
The density ρ, pressure p and velocity u are decomposed into the following form in consideration of compressibility of the flow
By a series of integral deductions, the following acoustic calculation model in the frequency domain space can be obtained
Wherein ω=2pi f represents a circumferential frequency; the point Z is the monitor position and,
c (z) =1/2 corresponding to smooth integral boundary, far field monitoring point pairC (z) =1, v 0 Representing the flow field region between the object plane boundary and the integration boundary, V-V 0 Representing the area of the flow field outside the integration boundary.
From the above acoustic calculation model, it can be seen that:
1. on the basis of the completion of the flow calculation, each grid cell density ρ obtained by the flow calculation is stored in the time direction h Pressure p h And speeds u in different coordinate directions i ,u j 。
2. To monitor acoustic information, the monitor can be placed at any location, and generally comprises two types: an object surface and a non-object surface, wherein the non-object surface may be within the flow calculation region or outside the flow calculation region,
taking propagation of a single sound source as an example, as shown in fig. 2, a sound source point is placed at a point a, a monitor is placed at a point C, B is an object surface boundary, and a sound signal received at the point C includes two parts: (1) A.fwdarw.C; (2) A, B and C
Wherein the noise obtained by the path (1) is radiated sound and the noise obtained by the path (2) is scattered sound. On the premise of completing the flow calculation, the radiation noise can be directly calculated; after the calculation of the scattered sound sources distributed on the object plane B is completed, the scattered noise can be calculated. For the actual flow problem, starting from a model equation, acoustic calculation can be performed by selecting S as the boundary of the object surface.
However, when the object surface structure is complex or there are a plurality of objects in the flow field, two-dimensional problems are taken as an example, for example, two objects including an airfoil and a cylinder are included in fig. 3, and the airfoil boundary and the cylinder boundary are S, respectively C And S is D . When the integral calculation is performed by using the object surface boundary, the integral boundary s=s C +S D The scattering sound source calculation needs to disperse the object plane boundary into a fine boundary unit, and the problems of high calculation complexity, numerical value singularity and the like exist. In view of the above, a permeable boundary S surrounding an object is employed P Integral calculation is performed, at which time s=s in model equation (4) P The specific implementation steps are as follows:
1: dispersing a flow field calculation region into K grid cells by adopting flow calculation software (such as Fluent), and storing flow field information, namely sound source information, of all grid cells which change along with time;
2: selecting boundary S in the vicinity of object P And S is combined with P Discretizing into L boundary units, wherein the boundary units are generally selected to be the same as the boundary of the flowing discrete grid so as to reduce the calculation workload;
3: calculating S by using formula (5) P Upper equivalent diffuse sound source p a (z, ω) can be rearranged into a linear system of equations (6).
4: calculating the sound pressure p of the far-field monitoring point x by adopting a formula (7) a (x,ω)。
Equation (5) is shown below:
equation (6) is shown below:
where l=1, 2,..l, E is an identity matrix, H is a symmetric matrix with diagonal zero
Where m=1, 2,3, … L, n=1, 2,3, … L, L is the number of units contained in the boundary S.
Equation (7) is shown below:
when the problem is a two-dimensional model, the free space green's function G (y m ,y n ,ω)
When the problem is a three-dimensional model, the free space green's function G (y m ,y n ,ω)
Determining y m Point and y n Free space green's function edge y of point n External normal partial derivative of point
Comprising the following steps:
when the problem is a two-dimensional model, it is determined by the following formula
When the problem is a three-dimensional model, it is determined by the following formula
Determining y m Point and y n Free space green's function edge y of point n Second partial derivative of point
Comprising the following steps:
when the problem is a two-dimensional model, it is determined by the following formula
When the problem is a three-dimensional model, it is determined by the following formula
Determining x-point and y n Free space green's function edge y of point n External normal partial derivative of point
Comprising the following steps:
when the problem is a two-dimensional model, it is determined by the following formula
When the problem is a three-dimensional model, it is determined by the following formula
Determining x-point and y n Free space green's function edge y of point n Second partial derivative of point
Comprising the following steps:
when the problem is a two-dimensional model, it is determined by the following formula
When the problem is a three-dimensional model, it is determined by the following formula
Wherein the subscripts M, n=1, 2,3, …, M is the grid cell number,
for the first class 0 th order Hankel function, < >>
First class 1 order Hankel function, k=ω/c 0 Number of sound waves, c 0 Is the speed at which sound waves propagate in the medium.
Calculating an object plane scattering sound source by adopting a formula (6), and on the premise that the solution of a right-end term is completed, calculating
Obtaining the subitem H of matrix H mn To-be-solved sound source point y m The corresponding matrix column items are
Wherein s=s 1 ∪S 1 …∪S L ，y m Point and y n When overlapped, H mn ＝0。
Calculating the sound pressure of a far-field monitoring point by adopting a formula (7), and solving the right-end term on the premise of completionUnder the condition, p can be directly obtained a (x,ω)。
Further, the contributions of the sound source items are analyzed:
calculating boundary scattering sound source by adopting a formula (6), wherein the first term at the right end
The second term on the right side representing the radiation contribution of the sound source signal of the computing unit
Representing flow field regions V-V 0 Radiation contribution of inner flow field grid cell sound source signal to z, third term at right end
Representing the radiation contribution of the sound source signal of other elements on the boundary S to z, the last term
Representing a flow field region V 0 The equivalent radiated sound of the internal sound source signal to z, thereby obtaining the contribution of all sound sources to the boundary observation point, namely, the scattered sound source.
When far-field monitoring point sound pressure is carried out by adopting formula (7), the first term at the right end
Representing flow field regions V-V 0 The radiation contribution of all flow field grid cell sound source signals to x, the second term at the right end
Representing the radiation contribution of the sound source signal to x on boundary S, third term on right
The contribution of the scattering sound source on the boundary S to x is indicated as scattering noise. Last item
Representing a flow field region V 0 Equivalent radiated sound of the sound source signal in the range to x, so that the contribution of all sound sources to far-field observation points is obtained.
The specific application proves that the invention has the following characteristics:
the invention adopts the permeable boundary surrounding the object as an integral boundary, and obtains an equivalent scattering sound source by calculating the sound source on the permeable boundary; the radiation noise and the scattering noise can be effectively distinguished in the far-field noise;
the invention breaks through the limit of calculating the scattering sound source by adopting the object plane boundary in the traditional method, and can obtain the near-field equivalent scattering sound source; meanwhile, the noise contribution of the near-field flow region can be considered;
the invention can solve the propagation calculation of aerodynamic noise with complex configuration or aerodynamic noise in flow fields of a plurality of objects, and has stronger applicability.
The invention does not need to adopt high-precision calculation, and greatly improves the calculation efficiency.
The invention selects the smooth flow field grid boundary surrounding all objects as a permeable boundary, and is easy to implement.
The specific application cases are as follows:
example 1 laminar cylindrical noise prediction
A two-dimensional cylinder with a diameter d=1m is selected as a study object, and the incoming flow mach number ma=0.15 and the reynolds number re=100. This section mainly examines the reliability of non-tight permeable integration boundaries. The flow field calculation area and grid distribution are shown in figure 4, the cylinder center coincides with the origin of coordinates, and the flow field calculation area is defined in the horizontal direction [ -12D,24D]And in the vertical direction[-12D，12D]Within the range, 44,080 quadrilateral grid cells are contained, U represents the incoming flow velocity, u=ma×c 0 . The local area grid distribution map is shown in fig. 5. For numerical comparison with the DNS method calculation result of khali, 180 observation points are uniformly arranged on the circumference with (1.86D, 0) as the center and r=12.9d as the radius as the circumference.
First, to verify the validity of the calculation method. The diffuse sound source is calculated using a Cylinder boundary (Cylinder wall). Fig. 6 shows a sound pressure directivity diagram at a low frequency, wherein a red circle represents a calculation result of khali using DNS (direct numerical simulation), and a blue solid line represents a result obtained by integrating calculation using a cylindrical surface in the current calculation method, and the two methods coincide.
To verify the validity of the permeable boundary, a permeable boundary S as shown in FIG. 7 is selected 1 、S 2 、S 3 For the integral boundaries, fig. 8 shows far-field sound pressure directivity obtained by calculating equivalent scattered sound sources for different integral boundaries. As can be seen from fig. 8, the calculation result obtained by integrating the different permeable boundaries is quite consistent with the cylindrical surface. The permeable boundary integral calculation method can accurately capture the equivalent scattered sound source. Wherein in FIG. 8, f 0 Representing vortex shedding frequency.
Example 2 turbulent cylindrical noise prediction
The calculation example mainly analyzes turbulence noise distribution, takes a three-dimensional cylindrical model as a research object, and selects physical parameters as follows: cylinder diameter d=0.019 m, incoming flow mach number ma=0.2, corresponding to Re number 9×10 4 . Fluid motion induced noise in the x-direction (-15 d,20 d), y-direction (-15 d,15 d), and z-direction (0,4D) ranges was computationally analyzed with the cylinder center as the origin of coordinates. Fig. 9 shows the position distribution of the cylindrical surface and the different permeable boundaries.
Fig. 10 shows far-field sound pressure level distributions obtained for different integration boundaries. As can be seen from fig. 10, when f=f 0 、f＝2f 0 The maximum radiation directions of the sound waves are respectively expressed as vertical and horizontal directions, which are consistent with the results obtained by the boundary element method based on green's function numerical solution, such as Hu, and also consistent with vortex sheddingFrequency (f=f) 0 ) And second harmonic frequency (f=2f) 0 ) Aerodynamic noise mainly presents the physical fact of dipole distribution. The three integration boundaries can accurately vortex shedding frequencies (f=f 0 ) Is a noise distribution of (a). The difference is that S is selected 3 For integration boundaries, at the second harmonic frequency (f=2f 0 ) The lower sound pressure level on the left side indicates that a proper permeable boundary needs to be selected in practical engineering problems.
In the foregoing, the protection scope of the present invention is not limited to the preferred embodiments of the present invention, and any simple changes or equivalent substitutions of the technical solutions that can be obviously obtained by those skilled in the art within the technical scope of the present invention disclosed in the present invention fall within the protection scope of the present invention.
Claims (4)
1. The method for calculating the pneumatic noise numerical integral of the non-compact permeable boundary is characterized by comprising the following steps of:
step 1: dispersing a flow field calculation region into K grid units by adopting flow calculation software to obtain sound source information comprising density ρ and pressure p h Speed u i I=1, 2,3, ρ for low mach number flows h ≈ρ；
Step 2: selecting boundary S in the vicinity of object P And S is combined with P Discretizing into L grid units, and selecting the L grid units as boundaries identical to the flowing discrete grids;
step 3: using the formula
Calculation S P Upper equivalent diffuse sound source p a (z, ω) rearranged into a linear system of equations:
where l=1, 2..i.l, E is an identity matrix and H is a symmetric matrix with zero diagonal
Where m=1, 2,3, … L, n=1, 2,3, … L, L being the number of units contained in the boundary S;
step 4: using the formula
Calculating sound pressure p of far-field monitoring point x a (x,ω)，
In the above calculation expression, ω represents the circumferential frequency, c 0 Representing the propagation velocity of sound waves, V k Representing the area of the kth flow field grid cell [] k Representing information on the kth flow field grid cell [] l Representing information on the first border element, p a (z l ω) represents the point z on the boundary l Sound pressure at omega frequency, p a (x, ω) represents the sound pressure of the far field monitoring point x at ω frequency, and j represents the imaginary unit, δ in the last term ij Representing a second order tensor,
2. the method for calculating the aerodynamic noise value integral of the non-tight permeable boundary according to claim 1, wherein when the study object is a two-dimensional model, the steps 3 and 4 are implemented as follows:
1) The free space green's function G (y) is calculated by the following formula m ,y n ,ω)
2) Y is determined by the following formula m Point and y n Free space green's function edge y of point n External normal partial derivative of point
3) Y is determined by the following formula m Point and y n Free space green's function edge y of point n Second partial derivative of point
4) The x-point and y are determined by the following formula n Free space green's function edge y of point n External normal partial derivative of point
5) The x-point and y are determined by the following formula n Free space green's function edge y of point n Second partial derivative of point
3. The method for calculating the aerodynamic noise value integral of the non-tight permeable boundary according to claim 1, wherein when the study object is a three-dimensional model, the steps 3 and 4 are implemented in the following steps:
1) Free space green is calculated by the following formulaFunction G (y) m ,y n ,ω)：
2) Y is determined by the following formula m Point and y n Free space green's function edge y of point n External normal partial derivative of point
3) Y is determined by the following formula m Point and y n Free space green's function edge y of point n Second partial derivative of point
4) The x-point and y are determined by the following formula n Free space green's function edge y of point n External normal partial derivative of point
5) The x-point and y are determined by the following formula n Free space green's function edge y of point n Second partial derivative of point
Wherein the subscripts M, n=1, 2,3, …, M is the grid cell number,
for the first class 0 th order Hankel function, < >>
First class 1 order Hankel function, k=ω/c 0 Is the number of sound waves.
4. The method for calculating the aerodynamic noise numerical integral of a non-tight permeable boundary according to claim 3, wherein the object plane scattering sound source is calculated by the step 3, and the object plane scattering sound source is calculated by the calculation on the premise that the right-hand term solving is completed
Obtaining a matrix:
sub-item H of H mn To-be-solved sound source point y m The corresponding matrix column entries are:
wherein s=s 1 ∪S 1 …∪S L ，y m Point and y n When overlapped, H mn ＝0；
And 4, calculating the sound pressure of the far-field monitoring point through the step, and directly obtaining the sound pressure on the premise of completing the solution of the right-end term.
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