A universal turbulence noise calculation method and device

Abstract

The invention discloses a universal turbulence noise calculation method and device, which belongs to the field of aeroacoustics and can effectively filter or reduce vortex modes or entropy modes. The method is as follows: a differential operator is applied to a non-homogeneous convective wave equation with a source term, the convective arterial momentum is filtered, the non-acoustic mode is eliminated or greatly weakened, a new non-homogeneous convective wave equation is obtained, and the sound pressure of a far-field observation point is obtained by solving the equation through a Green's function method. The invention can eliminate or greatly weaken the pseudo-noise caused by turbulence passing through an acoustic integral surface, thereby improving the accuracy of far-field noise calculation.

Description

Technical Field

[0001] The invention belongs to the field of aeroacoustics, and in particular relates to a universal turbulence noise calculation method and device. Background Art

[0002] When studying aeroacoustic problems, the sound field can be divided into three regions: sound source, sound propagation, and sound radiation. In the sound source region, there is a strong coupling between the flow field and the sound field, and the high physical nonlinearity can only be described by the NS equation. In the sound propagation region, there is a weak coupling between the flow field and the sound field, and the influence of the sound field on the flow field can be ignored. The sound propagation equation is generally solved on a non-uniform background flow. In the sound radiation region, it is assumed that there is no coupling between the flow field and the sound field. The flow field in this region is often a uniform flow field or a stationary flow field, and is generally solved by an integral method. Due to the high storage and time costs, it is unrealistic to directly use computational fluid dynamics (CFD) or computational aeroacoustics (CAA) methods to accurately calculate the far field, so a hybrid method is usually used. That is, high-fidelity numerical simulation is performed in the near field to calculate turbulence, and the flow variable is used as the input for the sound radiation calculation, and the far-field directivity is calculated by a method based on the FW-H equation or the Kirchhoff formula.

[0003] However, in practice, in order to ensure the accuracy of the calculation, the acoustic integration surface should be placed in an area with small numerical dissipation, but in this area, non-acoustic fluctuations also decay slowly. Non-acoustic fluctuations are inevitably collected as input for acoustic radiation calculations. If the volume integral is ignored when calculating the far-field noise, the far-field prediction results will be contaminated. To solve this problem, a variety of strategies have been proposed. One is to assume that the influence of near-field flow on sound propagation is not important, and use the solid wall surface as the integration surface in the FW-H method. The second is to use multiple integration surfaces to record data and average the calculation results of multiple integration surfaces. The third is to use an open integration surface and ignore the contribution of the open part to the far-field noise (both acoustic and non-acoustic fluctuations), but there is controversy about the effectiveness of using open integration surfaces. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention provides a universal turbulence noise calculation method to solve the pseudo noise problem caused by calculating turbulence noise through a penetrable acoustic integral surface.

[0005] The technical solution adopted by the present invention is as follows: A general turbulence noise calculation method, the steps are as follows:

[0006] Step 1: Apply differential operators to the nonhomogeneous convective wave equation with source terms to filter the convective arterial momentum and eliminate or significantly reduce the non-acoustic modes.

[0007] The non-homogeneous convective wave equation with source term is:

[0008]

[0009]

[0010] The source term on the right side of the equation is:

[0011]

[0012]

[0013] Among them, ρ ∞ 、u ∞ 、p ∞ are the density, velocity, and pressure of the far-field free flow, respectively. Ignoring the effect of viscosity, then τ = 0,

[0014] The differential operator is Among them, u c is the average flow velocity;

[0015] Step 2: Obtain a new non-homogeneous convective wave equation, which is:

[0016]

[0017] in, is the far-field sound speed, T v is the volume source, includes the acoustic mode; the source term on the right side of the equation is

[0018]

[0019]

[0020] Step 3: Use the Green's function method to obtain the far-field observation point sound pressure of the new non-homogeneous convective wave equation. The calculation formula is as follows:

[0021]

[0022] in, is the Mach number corresponding to the integrated surface velocity at the time of launch, Represents the variable value here as the value at the time of sound wave emission, τ e =tR / c ∞ ;

[0023] For the far field, let |x|>>|y|, in the frequency domain p′ a and Has the following relationship:

[0024]

[0025]

[0026]

[0027]

[0028] in, represents Fourier transform, ω is the frequency;

[0029] The obtained time domain sound pressure is:

[0030]

[0031] On the other hand, the object of the present invention is to be implemented by a computer system, which includes a processor and a computer-readable storage medium communicatively connected to the processor, wherein computer instructions are stored in the computer-readable storage medium, and when the computer instructions are executed by the processor, the steps of the method of the present invention as described above are implemented.

[0032] On the other hand, the object of the present invention is to be implemented by a computer-readable storage medium, on which computer instructions are stored. When the computer instructions are executed by a processor, the steps of the method of the present invention as described above are implemented.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] (1) It can eliminate or significantly reduce the pseudo-noise caused by turbulence passing through the acoustic integration surface, thus improving the accuracy of far-field noise calculation;

[0035] (2) The computation and storage costs of the equivalent sound source are comparable to or even smaller than those of conventional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Multiple FW-H integration surfaces are set for calculating the jet far-field noise;

[0037] Figure 2 The performance comparison between the present invention and multiple FW-H integral surface averaging methods is shown in FIG. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical scheme and advantages of the implementation of the present invention clearer, the technical scheme of the present invention will be described in detail in conjunction with the accompanying drawings. In the accompanying drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. It should be understood here that the described embodiments are partial embodiments of the present invention, rather than all embodiments. The following embodiments are exemplary and are intended to be used to explain the present invention, and should not be construed as limitations on the present invention. Based on the embodiments of the present invention, other embodiments obtained by ordinary technicians in this field without making creative work are all within the scope of protection of the present invention.

[0039] In practical applications, CFD numerical simulation can provide the input data required for integral calculation. For three-dimensional scenes, the required data are q′, Five variables. c There is no unique definition. Different selection methods may affect the distribution range of the equivalent sound source. Therefore, try to select a u that has physical meaning. c If you are solving the Euler equations or Navier-Stokes equations, you can use the Favier average (density-weighted average) velocity as the convection velocity. When the flow Mach number is small, the time-averaged velocity is usually sufficient. For many aeroacoustic problems, if the numerical calculation is based on the linear Euler equations or linear Navier-Stokes, u c The average flow velocity may be used.

[0040] Example 1

[0041] A general method for calculating turbulence noise is as follows:

[0042] Assume that the flow fluctuations contain acoustic and non-acoustic modes, but the acoustic mode propagates at the speed of sound, and the vortex mode and entropy mode are mainly affected by the mean flow. On this basis, the differential operator is applied to the fluctuation variable If the appropriate convection velocity is selected, the vortex mode or entropy mode can be effectively filtered or reduced, and the accuracy of far-field noise calculation can be improved.

[0043] The flow is described by the non-conservative form of the Navier–Stokes equations:

[0044]

[0045] Among them, γ is the specific heat ratio, for air, γ = 1.4, ρ, u and p are density, velocity and pressure respectively, κ is the thermal conductivity, T is the temperature, τ is the stress tensor, and considering the influence of steady-state background flow on sound wave propagation, each flow variable is divided into a steady-state background flow part and a non-steady-state fluctuation part, that is:

[0046]

[0047] Among them, the variables with subscript (·)0 are the steady-state flow part, and the variables with superscript (·)′ are the unsteady-state wave part, including all possible sound waves and vortex waves. Assuming that the steady-state background flow satisfies the conservation law, equation (1) will be simplified to an equation about the wave variable. Rearrangement can obtain the inhomogeneous convective wave equation with source term:

[0048]

[0049] The source term on the right side of the equation is:

[0050]

[0051] Among them, ρ ∞ 、u ∞ 、p ∞ are the density, velocity and pressure of the far-field free flow, respectively. Ignoring the effect of viscosity, τ = 0. The source term takes into account the effects of non-uniform background flow and nonlinear coupling effects of wave variables.

[0052] Introducing differential operators Filter the fluctuation variable, u c To average the flow velocity and eliminate or greatly reduce the non-acoustic modes, equation (3) becomes:

[0053]

[0054] in, The source term on the right side of the equation is:

[0055]

[0056] The nonhomogeneous convective wave equation can be obtained:

[0057]

[0058] in, is the far-field sound speed, T v is the volume source, Mainly contains acoustic modes.

[0059] Introduce f = 0 to express a certain penetrable integral surface. The internal area of ​​the integral surface is f < 0, and the external area of ​​the integral surface is f > 0. Let T of the external area be v Ignoring, the unit external normal vector of the integration surface is The function f satisfies

[0060] The Heaviside step function H(f) is correspondingly defined as:

[0061]

[0062] According to the chain rule, the gradient of H(f) is:

[0063]

[0064] Where δ(f) is the Dirac delta function and the time derivative of H(f) is:

[0065]

[0066] Among them, v is the velocity of the integral surface, and the non-homogeneous convection wave equation is:

[0067]

[0068] The detailed expression of the right side of the equation is:

[0069]

[0070] Equation (7) can be solved using the Green’s function method. The free space Green’s function of the convective wave equation is:

[0071]

[0072] Among them, x and y are the positions of the observer and the sound source, respectively, t and τ are the time when the observer receives the sound wave and the time when the sound wave is emitted from the sound source, respectively, and the variable and R is defined as follows:

[0073]

[0074] Where r = xy, r =|r|;

[0075] The time and space derivatives of the Green's function are related as follows:

[0076]

[0077] in, The spatial derivatives of and R can be calculated as follows:

[0078]

[0079] Therefore, the observation point (x, t) The calculation formula is as follows:

[0080]

[0081] in, is the Mach number corresponding to the integrated surface velocity at the time of launch, Represents the variable value here as the value at the time of sound wave emission, τ e =tR / c ∞ ;

[0082] For the far field, let |x|>>|y|, in the frequency domain p′ a and Has the following relationship:

[0083]

[0084] in, represents Fourier transform, ω is the frequency;

[0085] The obtained time domain sound pressure is:

[0086]

[0087] Example 2

[0088] Take the calculation of far-field directivity of jet noise as an example. Figure 1 As shown, the background flow Mach number M ∞ is 0.2, the jet Mach number is 0.8, and the Reynolds number is 8000. Multiple integral surfaces are arranged in the wake area where the jet is fully developed. The width of the integral surface is 5r0, r0 is the nozzle radius, and the distance from the end face of the integral surface to the nozzle is l s The minimum value is 30r0, the maximum value is 70r0, and a total of 21 equally spaced end faces are arranged. For the problem of pseudo-noise pollution, a commonly used engineering treatment method is to use multiple integral surfaces, perform FW-H integration separately, and finally average the results. However, this method is empirical, and there are no specific criteria for the location, number, size of the integral surface and its dependence on the sound wave and turbulence characteristics under investigation.

[0089] The calculation results of Example 1 are compared with those of the multi-integral surface average method. Figure 2 As shown, if there is only one integration surface ( Figure 2 N=1,l s =45r0 and N=1,l s =50r0), the calculated far-field directivity is completely unable to identify the sound pressure level peak at around 30°, and the results obtained from different integration surfaces are completely different. As the number of integration surfaces increases, the directivity results continue to converge, and finally approach the results of the general far-field noise calculation method proposed in the present invention. Even if 21 integration surfaces are used, the calculation results of the FW-H method still fail to converge completely. Therefore, in order to obtain more accurate results, it is still necessary to add more integration surfaces and collect and store more data. The general far-field noise calculation method proposed in the present invention only requires 1 integration surface and only needs to store 4 variables, so the calculation cost is also greatly reduced.

[0090] The above is only a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any simple replacement or change within the technical idea disclosed by the present invention and the technical solution of the present invention should be within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A general turbulence noise calculation method, characterized in that: Here are the steps: Step 1: Apply differential operators to the nonhomogeneous convective wave equation with source terms to filter the convective arterial momentum and eliminate or significantly reduce the non-acoustic modes. The non-homogeneous convective wave equation with source term is: The source term on the right side of the equation is: Among them, ρ ∞ 、u ∞ 、p ∞ are the density, velocity and pressure of the far-field free flow respectively. Ignoring the effect of viscosity, then τ = 0, and the differential operator is Among them, u c is the average flow velocity; Step 2: Obtain a new non-homogeneous convective wave equation, which is: in, is the far-field sound speed, T v is the volume source, Contains the acoustic modes; the source term on the right side of the equation is: Step 3: Use the Green's function method to obtain the far-field observation point sound pressure of the new non-homogeneous convective wave equation. The calculation formula is as follows: in, is the Mach number corresponding to the integrated surface velocity at the time of launch, Represents the variable value here as the value at the time of sound wave emission, τ e =tR / c ∞ ; For the far field, let |x|>>|y|, in the frequency domain p′ a and Has the following relationship: in, represents Fourier transform, ω is the frequency; The obtained time domain sound pressure is:

2. A computer system comprising a processor and a computer-readable storage medium communicatively connected to the processor, wherein the computer-readable storage medium stores computer instructions, characterized in that: When the computer instructions are executed by the processor, the steps of the method according to claim 1 are implemented.

3. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the computer instructions are executed by a processor, the steps of the method according to claim 1 are implemented.

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