CN106777542A - Spring leaf propeller flow noise prediction method - Google Patents

Spring leaf propeller flow noise prediction method Download PDF

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CN106777542A
CN106777542A CN201611060235.5A CN201611060235A CN106777542A CN 106777542 A CN106777542 A CN 106777542A CN 201611060235 A CN201611060235 A CN 201611060235A CN 106777542 A CN106777542 A CN 106777542A
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propeller
fluid
rho
flow
flow noise
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邹丽
鲁建华
孙铁志
宗智
姜胜超
于游
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Dalian University of Technology
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Abstract

The invention discloses a kind of spring leaf propeller flow noise prediction method, comprise the following steps:- set up the full scale model of propeller to be analyzed and fluid domain, the model is included the rotational domain of rotation and the static domain not rotated with spiral;Full scale model described in gridding;The sampled point of noise is set;For the full scale model of gridding sets the solution parameter of flow field and sound field;- it is the renewal dynamic grid of described full scale model;The material properties of solid portion propeller are set.Mesh generation and coupling surface parameter;Fluid and structural simulation procedure parameter and fluid structurecoupling governing equation are set;Wherein:It is stress;N is normal vector;D is displacement;Subscript f and s represent fluid and solid respectively;Fluid and structural simulation is carried out, until algorithmic statement;Flow field data at the monitoring point are obtained, the sound pressure level at monitoring point is calculated according to FW H equations;The power spectral density plot of sound field is obtained according to Fast Fourier Transform (FFT) FFT functions.

Description

Spring leaf propeller flow noise prediction method
Technical field
The present invention relates to a kind of Forecasting Methodology of spring leaf propeller flow noise, design patent classification number G06 is calculated;Push away Calculate;Count digital calculating equipment or data processing that G06F electricity Digital data processing G06F17/00 is particularly well-suited to specific function Equipment or data processing method G06F17/50 CADs.
Background technology
Propeller noise is the major part of submarine noise, by formation mechanism can be divided into blade vibration noise, cavitation erosion, Flow noise, wherein blade vibration noise and cavitation erosion are the major parts of propeller noise, and as propeller optimization sets The theoretical progressively maturation of meter, the vibration noise and cavitation erosion of blade can be obtained to a certain extent by optimizing Design of Propeller Solution.Propeller flow noise refers to that turbulent flow interacts with propeller and produces vortex shedding etc. at pressure fluctuation and blade tip and produce Raw noise, its Producing reason is mainly the interaction of current and oar.For submarine, during its lowsteaming, spiral Although oar flow noise proportion very little, it has a huge impact to sonar signal to noise ratio.Propeller flow noise can increase The ambient noise of sonar, reception of the influence sonar to target acoustic signal, so as to have impact on the fight capability of submarine.Submarine is at a high speed During navigation, noise is mainly flow noise, so as to reduce the disguise of submarine, increased exposed risk.Therefore, by spiral shell Revolve the research of oar flow noise to optimize Design of Propeller, reduce propeller noise, the performance for lifting submarine is significant.
Due to there are problems that in propeller flow noise fest hydrophone installation difficulty, experiment sound reflecting, therefore state The inside and outside research to propeller flow noise is main based on numerical simulation, and such as Seol H are by potential flow theories and sound Analogy knot Close, the vacuole and non-cavitation erosion of propeller are forecast by numerical method;Thank build ripple et al. in Lighthill acoustic analogy theories and On the basis of FW-H equations, theoretical sum is carried out to propeller radiation spectral noise using the Green's function with mean flow effect Value analysis;The method that Gong Jing wind et al. is combined with large eddy simulation and K-FWH equations, is carried out to Propeller noise Forecast, it was demonstrated that large eddy simulation combination K-FWH models carry out the feasibility of propeller noise forecast.
But in past research, scholars are main to be considered as propeller rigid body or only carries out fluid-structure , then be delivered to pressure result in structure, it is not intended that two-way between fluid-structure by unidirectional couplings, i.e., first computational flow Coupling.Development and people with composite are goed deep into flexible surface Research of Noise Reduction, by changing propeller blade Elasticity come reduce propeller flow noise as scientific research personnel new problem.Can not necessarily be regarded again using the propeller of spring leaf It is rigid body, this requires the bilateral coupled effect between considering fluid-structure during numerical simulation, the stream after coupling Field computation carries out the analysis of flow noise after finishing.
The content of the invention
Proposition for problem above of the invention, and a kind of spring leaf propeller flow noise prediction method developed, bag Include following steps:
- full scale model of propeller to be analyzed and fluid domain is set up, the model includes the rotation that will be rotated with spiral Turn domain and the static domain not rotated;Full scale model described in gridding;The sampled point of noise is set;It is complete for gridding Dimension model sets the solution parameter of flow field and sound field;
- it is the renewal dynamic grid of described full scale model;The material properties of solid portion propeller are set.Grid Divide and coupling surface parameter;Fluid and structural simulation procedure parameter and fluid structurecoupling governing equation are set;
Wherein:τ is stress;N is normal vector;D is displacement;Subscript f and s represent fluid and solid respectively;
- fluid and structural simulation is carried out, until algorithmic statement;Flow field data at the monitoring point are obtained, according to FW-H equations Calculate the sound pressure level at monitoring point;The power spectral density plot of sound field is obtained according to Fast Fourier Transform (FFT) FFT functions, to gained Result carries out acoustic analysis, completes the prediction of spring leaf propeller flow noise.
As the full scale model correctness that preferred embodiment, before calculating elastic model step also there is checking to set up The step of:
- calculation assumption is the data in rigid propeller sound field and flow field;
- by the contrast rigid rotor for obtaining and the sound field and flow field numerical value tested, verify the full scale model Correctness;
If-meet correctness requirement, continue to calculate elastic oar flow field harmony field data.
Used as preferred embodiment, described projected propeller principle and Formula of Coordinate System Transformation complete propeller blade tangent plane Two-dimensional plane coordinate to three dimensional space coordinate conversion, and then complete propeller blade tangent plane contour curve drafting;
Wherein:φ is the angle of pitch;θ is Angle of Trim;L is distance between maximum gauge line and reference line;R is blade section half Footpath;X1、Y1、Z1It is the coordinate value under local coordinate system;X, Y, Z are coordinate value under global coordinate system.
As preferred embodiment, the governing equation of described fluid structurecoupling for meet continuity equation and Na Wei-this Lentor equation N-S equations, equation functions form is as follows:
Wherein:ρ is fluid density;T is the time;ux、uy、uzRespectively speed rectangular coordinate system in space x, y, z axle point Amount;P is pressure;X, Y, Z are respectively external force component in the x, y, z-directions;μ is fluid dynamic viscosity;Δ is La Pula This operator.
Further, turbulent flow field computation uses RNGk- ε turbulence models during fluid and structural simulation:
Wherein:ρ is fluid density;It is material derivative;K is Turbulent Kinetic;ε is turbulence dissipation rate;μ is viscous for fluid dynamic Property coefficient;αk、αεIt is the inverse of turbulent prandtl number;μeffIt is corrected parameter with R;GkAnd GbRespectively laminar velocity gradient and floating The Turbulent Kinetic that power causes;YMFor compressible fluid turbulent flow expands contribution amount;C、C、CIt is empirical.
Used as preferred embodiment, described solution parameter at least includes that the selection of flow field portion turbulence model, fluid are close Degree, rotary shaft, rotating speed and boundary condition;
Acoustic module part at least includes the velocity of sound in far field density/the i.e. density of fluid water, water and the reference sound in water Pressure;
Solving part at least includes setting derivation algorithm, convergence residual error and time step.
Used as preferred embodiment, described acoustic analysis at least includes that the sound pressure level of forecast propeller flow noise is big It is small;
By being calculated Changing Pattern of the flow noise sound pressure level size with propeller advance coefficient J, and then obtain spiral Oar flow noise;
Wherein v is propeller speed, is the flow velocity of Inlet water in calculating, and n is rotating speed, and D is airscrew diameter.
Brief description of the drawings
For clearer explanation embodiments of the invention or the technical scheme of prior art, below will be to embodiment or existing The accompanying drawing to be used needed for having technology description does one and simply introduces, it should be apparent that, drawings in the following description are only Some embodiments of the present invention, for those of ordinary skill in the art, on the premise of not paying creative work, may be used also Other accompanying drawings are obtained with according to these accompanying drawings.
Fig. 1 is broad flow diagram of the present invention
Fig. 2 is projected propeller principle schematic
Fig. 3 is propeller threedimensional model schematic diagram
Fig. 4 is rotational domain and static domain schematic diagram
Fig. 5 is to be calculated fluid domain scale diagrams
Fig. 6 is fluid domain and domain mesh generation schematic diagram
Fig. 7 is open water performance of propeller curve computable value with test value comparison diagram
Fig. 8 is propeller flow noise with advance coefficient change curve
Specific embodiment
To make the purpose, technical scheme and advantage of embodiments of the invention clearer, with reference to the embodiment of the present invention In accompanying drawing, clearly complete description is carried out to the technical scheme in the embodiment of the present invention:
As shown in figures 1 to 6:
Step one Geometric Modeling:The software used in this step is Solidworks, the projected propeller according to Fig. 2 Principle schematic and Formula of Coordinate System Transformation:
Wherein:φ is the angle of pitch;θ is Angle of Trim;L is distance between maximum gauge line and reference line;R is blade section half Footpath;X1、Y1、Z1It is the coordinate value under local coordinate system;X, Y, Z are coordinate value under global coordinate system.
The propeller blade tangent plane two-dimensional plane coordinates of DTMB 4119 can be converted into three dimensional space coordinate, so that Propeller blade tangent plane contour curve is obtained in Solidworks,
Then curved surface setting-out is carried out as setting-out curve using each blade section guide margin and with sideline.The curved surface that will be formed again enters The curved surface of closing is then converted to entity and obtains a leaf model by row repairing, the curved surface closed.Next oar is set up Hub model, array processing is carried out to blade, complete the modeling of propeller, as shown in Figure 3.
Numerical simulation is carried out to propeller and belongs to typical rotating machinery problem, therefore to the modeling use rotation of fluid domain The general modeling method of machinery, that is, set up static domain and rotational domain,
Wherein rotational domain is the part for being rotated together with propeller in simulations, and static domain does not rotate.Fluid The modeling in domain is mainly in SolidWorks to be made and static domain and rotational domain diameter identical cylinder respectively.Then quiet Boolean calculation is only carried out on the cylinder of domain and cuts away rotational domain cylinder, formed final static domain, cloth is carried out on rotational domain cylinder Your computing cuts away propeller, forms final rotational domain, as shown in Figure 4.Rotational domain and static domain are carried out into assembly manipulation, is obtained To final calculating fluid domain, size is as shown in Figure 5.The propeller and fluid domain model that will be set up are derived with .stp files, For subsequently using.
After model is obtained, also with proving correctness the step of, in the present embodiment, calculate the gained spacious water of propeller Performance curve (such as Fig. 7, including thrust coefficient, moment coefficient, efficiency) is contrasted, result of calculation phase in embodiment with test value 5% is less than to error.In general, numerical simulation error is up to more accurate within 5%, it is possible to which decision model is correct 's.
Step 2 fluid domain mesh generation:This step is entered with meshing modules in ANSYS Workbench to fluid domain Row mesh generation.Preference is set to CFD analyses during division;
Need to carry out the setting of dynamic mesh in fluid calculation in view of wind-structure interaction, while the structure of model itself Form is more complicated, in order that the grid for being divided more preferably expresses airfoil shape, using destructuring tetrahedral grid to fluid Domain is divided, and the grid at propeller is suitably encrypted, especially in such as blade tip part change of flow state than larger local grid Than close elsewhere, to keep computational accuracy.
Fluid domain mesh generation is as shown in Figure 6.
Step 3 sets CFD software for calculation:CFD is calculated and is met the conservation of mass and the law of conservation of momentum in this step, i.e., full Sufficient continuity equation and N-S equations, therefore governing equation is:
Wherein:ρ is fluid density;T is the time;ux、uy、uzRespectively speed rectangular coordinate system in space x, y, z axle point Amount;P is pressure;X, Y, Z are respectively external force component in the x, y, z-directions;μ is fluid dynamic viscosity;Δ is La Pula This operator.
Selection transient state first is calculated, and RNGk- ε are then selected in the Model options Viscous of ANSYS Fluent softwares Turbulence model, remaining keeps acquiescence.
RNGk- ε models have precision higher in the turbulent flow field computation for having whirlpool, and its equation is:
Wherein:ρ is fluid density;It is material derivative;K is Turbulent Kinetic;ε is turbulence dissipation rate;μ is viscous for fluid dynamic Property coefficient;αk、αεIt is the inverse of turbulent prandtl number;μeffIt is corrected parameter with R;GkAnd GbRespectively laminar velocity gradient and floating The Turbulent Kinetic that power causes;YMFor compressible fluid turbulent flow expands contribution amount;C、C、CIt is empirical.
The static domain of rotational domain is set to fluid in Cell Zone Condition, rotational domain chooses MRF (i.e. Multiple references System) option, the parameters such as rotary shaft, rotating speed are configured according to studied operating mode.
Boundary condition is configured the present invention and is gone out using speed import, pressure by Boundary Condition options Mouthful, inlet velocity, if actual condition is non-uniform flow, needs to be configured using UDF according to actual condition value, outlet pressure Power is set to 0, and import, exit turbulent parameters select turbulence intensity and turbulent viscosity ratio according to universal experience, take 2%.Rotation The face that domain is connected with static domain is set to interface, and the face of cylinder in static domain is set to static without sliding wall, and blade and propeller hub set It is set to without sliding wall.
Treatment is carried out to sound field to be needed to open the acoustic module of Fluent, i.e. FW-H models in Model options, and is carried out Set.
Acoustic analogy theory is that N-S equations are deformed into inhomogeneous wave equation by Lighthill in research turbulent flow sound is excited, Hydrodynamics harmony student's federation is tied and is formed, improved by later scholar and form FW-H equations, its fundamental form Formula is as follows:
Wherein:It is monitoring location;T is the time;pTIt is thickness noise;pLIt is load noise;pQIt is quadrapole noise.
Fluid density presses the density 998.2kg/m of liquid water in Fluent databases3The velocity of sound is set to 1500m/ in setting, water The reference sound pressure that s, free stream velocity are in inlet velocity, water is set to 1 × 10-6Pa, sound source are set to blade.Test point is set to sit Mark, as flow noise sampled point below, to predict the propeller flow noise of this point.
In example of the invention in order to other documents carry out contrast be being respectively 0 away from the central axial distance of oar axle, 0.5R, 0.7R, radial distance are respectively at 0.3R, 0.7R, R, 1.2R, 2R and set altogether 15 sampled points and monitor noise.
Arrangement above is finished and set according to actual needs the parameters such as Fluent algorithms, convergence residual error, time step, is carried out just The rigid oar of beginning is calculated, and obtains flow field and sound field data and comparison of test results, is conducive to selecting suitable algorithm and checking mould The accuracy of type is so as to follow-up calculating.The open water performance of propeller curve that present example is obtained in calculating is with test value to such as Shown in Fig. 6.
Step 4 dynamic mesh is set:When elastic oar is calculated, blade is in deformation state, and the shape in flow field domain can be caused to send out Changing, therefore need to be updated the grid of fluid domain after fluid structurecoupling calculates finish for the first time.ANSYS Fluent There is provided the fairing of grid spring, three kinds of grid updating modes of grid reconstruction and dynamic layer grid, wherein dynamic layer grid application in Hexahedral mesh, and fluid domain is tetrahedral grid in simulating, therefore only need to the grid genial grid reconstruction of spring light Two ways carries out grid updating.The genial grid reconstruction function of grid spring light is activated first in dynamic mesh option, spring is normal Number is set to 0.6, border relaxation factor and is set to 0.6, and other specification first uses default value, is progressively adjusted according to the result for calculating It is whole.Parameter setting finish after selection dynamic mesh region, it is main in calculating to consider spring leaf propeller, so by blade and week Enclose rotational domain and be set to dynamic mesh region, wherein blade is set to System Coupling, and rotational domain is set to Deforming.
Step 5 domain is set:First according to the material of calculated propeller in Transient Structural modules Material sets material properties.Then meshing is opened, preference is set to mechanical analyses, and automatic division of selection is met meter Calculate desired grid as shown in Figure 6.Then it is fluid structurecoupling face, the constraint of structure and time step to set blade.Time step Length is set to identical with fluid section calculatings, and fluid structurecoupling face is corresponding with dynamic mesh region in Fluent to be set to blade, setting Propeller hub is clamped end.
Structure division only considers elastic deformation, therefore governing equation is:
σ=E ε
Wherein:σ is stress;E is elastic modelling quantity;ε is strain.
Step 6 fluid structurecoupling is set:System Coupling modules can realize that fluid is handed over the data of Structure Calculation Change, coupling setting need to be carried out in this module, mainly time step, data exchange face and Structure matrix are configured.When Between step-length set to meet make fluid, structure, coupling time step-length completely to should ensure that coupling calculate accuracy.By fluid and Blade in structure solver is set to data exchange face, and data transfer is carried out during fluid structurecoupling.Deformation in calculating Process for when propeller is moved in a fluid stress cause blade to deform, subsequent blade deformation again cause the shape of fluid domain to be sent out Changing, therefore Structure matrix should be that solid after first fluid, i.e. Fluent are set to 1, Transient Structural and are set to 2.After setting completed, click on Update and start two-way fluid and structural simulation until convergence.
Generally the convergence residual error of fluid structurecoupling is all dynamic equilibrium, and the condition of convergence may be referred to residual error but not Place one's entire reliance upon residual error.Fluid and structural simulation is due to carrying out grid updating, so convergence residual error is fluctuation.In a time step In long, from large to small, from large to small, residual error maximum is less than the previous time to residual error to convergence residual error in next time step Step, therefore growth over time, if being always this rule, the maximum for restraining residual error can be tapered into, is finally reached Dynamic equilibrium.
The present invention judges that reaching the condition of convergence will ensure at 2 points:1. residual error reaches dynamic equilibrium;2. in each time step Last time iteration, calculate give tacit consent on interface display physics numerical quantity it is basically identical, illustrate that the result gone down of continuation is It is basically unchanged.
Fluid structurecoupling part should meet that fluid is equal with each variable in structure intersection or conservation, and calculating of the invention does not consider Temperature, therefore fluid structurecoupling governing equation is:
Wherein:τ is stress;N is normal vector;D is displacement;Subscript f and s represent fluid and solid respectively.
Step 7 Analysis of The Acoustic Fields:ANSYS Fluent modules are turned again to, acoustic part is processed, read monitoring point Place's flow field data, the sound pressure level at monitoring point is calculated according to FW-H equations, while can be according to built-in fast of ANSYS Fluent Fast Fourier transformation (FFT) function obtains the power spectral density plot of sound field, and acquired results are carried out with acoustic analysis, completes to bullet The prediction of property blade propeller flow noise.
Propeller flow noise sound size under different operating modes is calculated in present example, and have found flow noise acoustic pressure Level size is with propeller advance coefficient J:
Wherein v be propeller speed, in calculating for Inlet water flow velocity, n is rotating speed, and D is airscrew diameter) change rule Rule:General, constantly increasing with advance coefficient, propeller flow noise constantly reduces.
The above, the only present invention preferably specific embodiment, but protection scope of the present invention is not limited thereto, Any one skilled in the art the invention discloses technical scope in, technology according to the present invention scheme and its Inventive concept is subject to equivalent or change, should all be included within the scope of the present invention.

Claims (7)

1. a kind of spring leaf propeller flow noise prediction method, it is characterised in that comprise the following steps:
- full scale model of propeller to be analyzed and fluid domain is set up, the model includes the rotational domain that will be rotated with spiral The static domain not rotated;Full scale model described in gridding;The sampled point of noise is set;It is full-scale for gridding Model sets the solution parameter of flow field and sound field;
- it is the renewal dynamic grid of described full scale model;The material properties of solid portion propeller are set.Mesh generation With coupling surface parameter;Fluid and structural simulation procedure parameter and fluid structurecoupling governing equation are set;
τ f · n f = τ s · n s d f = d s
Wherein:τ is stress;N is normal vector;D is displacement;Subscript f and s represent fluid and solid respectively;
- fluid and structural simulation is carried out, until algorithmic statement;Flow field data at the monitoring point are obtained, is calculated according to FW-H equations Sound pressure level at monitoring point;The power spectral density plot of sound field is obtained according to Fast Fourier Transform (FFT) FFT functions, to acquired results Acoustic analysis is carried out, the prediction of spring leaf propeller flow noise is completed.
2. spring leaf propeller flow noise prediction method according to claim 1, is further characterized in that and is calculating elasticity The step of also there is the full scale model correctness that checking is set up before model step:
- calculation assumption is the data in rigid propeller sound field and flow field;
- by the contrast rigid rotor for obtaining and the sound field and flow field numerical value tested, verify the correct of the full scale model Property;
If-meet correctness requirement, continue to calculate elastic oar flow field harmony field data.
3. spring leaf propeller flow noise prediction method according to claim 1, is further characterized in that according to propeller Projection theory and Formula of Coordinate System Transformation complete the conversion of propeller blade tangent plane two-dimensional plane coordinate to three dimensional space coordinate, and then complete Into the drafting of propeller blade tangent plane contour curve;
X Y Z = Z 1 sin φ + X 1 cos φ + L sin φ - r tan θ r cos ( Z 1 cos φ - X 1 sin φ + L cos φ r ) r sin ( Z 1 cos φ - X 1 sin φ + L cos φ r )
Wherein:φ is the angle of pitch;θ is Angle of Trim;L is distance between maximum gauge line and reference line;R is blade section radius;X1、 Y1、Z1It is the coordinate value under local coordinate system;X, Y, Z are coordinate value under global coordinate system.
4. spring leaf propeller flow noise prediction method according to claim 1, is further characterized in that described stream is consolidated The governing equation of coupling is to meet continuity equation and Navier Stokes equation N-S equations, and equation functions form is as follows:
∂ ρ ∂ t + ∂ ( ρu x ) ∂ x + ∂ ( ρu y ) ∂ y + ∂ ( ρu z ) ∂ z = 0
ρ du x d t = - ∂ p ∂ x + ρ X + μΔu x ρ du y d t = - ∂ p ∂ y + ρ Y + μΔu y ρ du z d t = - ∂ p ∂ z + ρ Z + μΔu z
Wherein:ρ is fluid density;T is the time;ux、uy、uzRespectively component of the speed in rectangular coordinate system in space x, y, z axle;p It is pressure;X, Y, Z are respectively external force component in the x, y, z-directions;μ is fluid dynamic viscosity;Δ is Laplce's calculation Son.
5. spring leaf propeller flow noise prediction method according to claim 4, is further characterized in that fluid structurecoupling meter Turbulent flow field computation uses RNGk- ε turbulence models during calculation:
ρ D k D t = ∂ ∂ y ( α k μ e f f ∂ k ∂ y ) + G k + G b - ρ ϵ - Y M ρ D ϵ D t = ∂ ∂ y ( α ϵ μ e f f ∂ ϵ ∂ y ) + C 1 ϵ ϵ k ( G k + C 3 ϵ G b ) - C 2 ϵ ρ ϵ 2 k - R
Wherein:ρ is fluid density;It is material derivative;K is Turbulent Kinetic;ε is turbulence dissipation rate;μ is fluid dynamic viscosity system Number;αk、αεIt is the inverse of turbulent prandtl number;μeffIt is corrected parameter with R;GkAnd GbRespectively laminar velocity gradient and buoyancy draw The Turbulent Kinetic for rising;YMFor compressible fluid turbulent flow expands contribution amount;C、C、CIt is empirical.
6. spring leaf propeller flow noise prediction method according to claim 1, is further characterized in that:Described solution Parameter at least includes the selection of flow field portion turbulence model, fluid density, rotary shaft, rotating speed and boundary condition;
Acoustic module part at least includes the velocity of sound in far field density/the i.e. density of fluid water, water and the reference sound pressure in water;
Solving part at least includes setting derivation algorithm, convergence residual error and time step.
7. spring leaf propeller flow noise prediction method according to claim 1, is further characterized in that described acoustics Analysis at least includes the sound pressure level size of forecast propeller flow noise;
By being calculated Changing Pattern of the flow noise sound pressure level size with propeller advance coefficient J, and then obtain propeller flow Noise;
J = v n D
Wherein v is propeller speed, is the flow velocity of Inlet water in calculating, and n is rotating speed, and D is airscrew diameter.
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CN113343499B (en) * 2021-07-06 2022-10-28 西安交通大学 Flow noise prediction method for naval vessel shell
CN113343499A (en) * 2021-07-06 2021-09-03 西安交通大学 Flow noise prediction method for naval vessel shell
CN113392600B (en) * 2021-07-12 2022-11-01 东南大学 Relevance analysis method for propeller low-frequency line spectrum characteristics in non-uniform inflow
CN113392600A (en) * 2021-07-12 2021-09-14 东南大学 Relevance analysis method for propeller low-frequency line spectrum characteristics in non-uniform inflow
CN113643679B (en) * 2021-10-14 2021-12-31 中国空气动力研究与发展中心低速空气动力研究所 Rotor wing and tail rotor aerodynamic noise separation method based on cascade filter
CN113643679A (en) * 2021-10-14 2021-11-12 中国空气动力研究与发展中心低速空气动力研究所 Rotor wing and tail rotor aerodynamic noise separation method based on cascade filter
CN117556720A (en) * 2023-10-19 2024-02-13 上海慕灿信息科技有限公司 Pneumatic acoustic frequency domain solving method based on Lighthill sound analogy

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