1. A flow noise simulation method based on a disturbance equation is characterized by comprising the following steps:

step 1: introducing a compact disturbance equation CDE to replace a numerical simulation NS equation;

step 1-1: the flow variable is decomposed in different scales, and the original flow variable U is decomposed into basic partsAnd disturbance U':

wherein rho, p, u, v and w respectively represent density, pressure and velocity components in XYZ three directions; the upper dash line represents the time average of the variable, and the wavy symbol represents the Favre average of the variable; the disturbance amounts corresponding to the time average and the Favre average, respectively;

step 1-2: decomposition of a conservative variable Q into a reference streamAnd disturbance solution Q':

wherein e represents an internal energy;

step 1-3: will not have adhesive flux F_jDecomposing into:

wherein the content of the first and second substances,and F'_jReference quantity and disturbance quantity u representing flux respectively_jRepresenting a velocity component, p_xj、p_yjAnd p_zjRespectively representing the pressure in three directions of XYZ;

step 2: moving unknown terms containing disturbance in the three equations in the step 1 to the left end of the equation to obtain a generalized disturbance equation:

the fifth term and the seventh term at the left end are nonlinear disturbance terms, and alpha epsilon (0,1) is a switch of the nonlinear term; tau is_ijRepresenting the tensor of shear stress, τ_xj、τ_yj、τ_zjRespectively representing shear stress tensors in three directions of XYZ; u. of_iRepresenting a velocity component;

the decomposition formula of partial conservation variables and flux in the formula (4) is specifically developed as follows:

and (3) obtaining:

wherein γ represents the specific heat ratio;

when α ═ 1, the nonlinear term exists, equation (4) is a recombined version of the complete NS equation;

when α is 0, the non-linear term is ignored;

further represented by the following matrix:

wherein V represents the velocity, δ_xj、δ_yj、δ_zjKronecker symbols respectively representing three directions of XYZ, the term with a sharp superscript representing a correction term containing a weighting factor α;

and step 3: for a jacobian matrix without viscous fluxWhen non-linear terms are included, the CDE and NS equations are the same; when the non-linear terms are ignored, each term is replaced by its corresponding reference stream parameter; therefore, seamless switching between the NS equation and the control equation when the nonlinear term is ignored can be realized by adjusting the value of the weighting coefficient alpha in the CDE;

and 4, step 4: for numerical simulation of a complex turbulence phenomenon, firstly performing RANS simulation in a specified calculation region, then performing grid division in a concerned calculation region, and solving an unsteady CDE by taking an RANS solution as a reference flow to obtain turbulence pulsation, thereby realizing a mixed RANS/LES simulation method;

and 5: performing RANS simulation on the numerical simulation of the complex stream-sound interference in the whole domain, dividing a concerned area into a local sound source area and a sound propagation area, and performing grid division; and taking the RANS simulation result as a reference solution, adopting the LES simulation based on the CDE in the sound source area, and adopting the LEE simulation based on the CDE in the sound propagation area.

Background

During high-speed flight of the aircraft, engine tail jet flow, an engine boundary layer and the like can generate extremely strong noise radiation. These aerodynamic noises are generated by turbulence of the surrounding air by turbulent vortices of different dimensions in the region of the smaller turbulent acoustic source and propagate in a region of great acoustic propagation. Turbulent eddies in the sound source region have large amplitude and small time/space dimensions, most turbulent kinetic energy is converted into heat energy through nonlinear viscous dissipation, and only a small part of turbulent kinetic energy is radiated into the environment in the form of sound waves. While the noise pulsations within the acoustic propagation region have a very small amplitude and a large time/space scale, the propagation of which is almost non-dissipative. Meanwhile, when the radiated sound wave is reflected on the surface of the body, the reflected sound wave thereof may generate reverse interference to the turbulent sound source.

Aerodynamic noise is essentially a particular flow phenomenon created by constant turbulence. On the one hand, even in a very small turbulent sound source region, a Direct Numerical Simulation (DNS) method that employs turbulence itself has computational resource consumption that is hard to be borne by the most advanced supercomputers at present. On the other hand, because very different amplitudes and characteristic scales exist in the sound source region and the flow parameter pulsation in the sound propagation region, the turbulence pulsation and the noise pulsation are simultaneously analyzed by using the complete NS equation, so that the calculation cost is hard to bear, and the requirements of the sound source region and the noise pulsation on the numerical errors of the calculation method are difficult to reconcile. Therefore, in practical applications, different forms of simplified control equations are required to describe different flow phenomena.

For a high-precision Computational Fluid Dynamics (CFD) method of turbulence itself, a RANS (Reynolds-Averaged Navier Stokes) simulation method can efficiently predict the statistical average amount of turbulence, but cannot resolve the non-constant evolution of turbulent eddies. The high-precision LES (Large-Eddy Simulation) method can resolve Large-scale turbulent flow structures and model the influence of small-scale structures, but the numerical Simulation cost of real high-Re-number flow is still hard to bear. The hybrid RANS/LES method (such as Detached-Eddy Simulation, DES) combines the advantages of both methods, reduces the calculation cost by adopting RANS at the wall boundary layer and adopting LES method at other parts, but has the problem of insufficient modeling stress at the interface of the two methods because turbulent eddies with different sizes cannot be fully analyzed.

For the high-precision Computational aeroacoustic (CAA) method of flow noise, the hybrid LES/FWH acoustic simulation method is the most effective high-precision numerical simulation method when the back interference of radiated sound waves to a near-field turbulent sound source is negligible. According to the method, firstly, an unsteady turbulent sound source is analyzed in a near-field turbulent sound source region by adopting an LES method, and then in the second step of calculation, the sound pressure of any point of a far field is directly predicted through a semi-analytic solution of an FWH sound simulation equation, so that the extremely high calculation cost required by simulation of broadband noise long-range propagation is avoided. However, when the flow-acoustic double interference is strong, such as the interference of turbulent sound sources of a hoisting engine under the wing and the wing surface reflection noise, the computational cost of this hybrid method increases by several orders of magnitude compared to the non-hoisting state. At present, some researches adopt simplified equations, such as Linear Euler Equation (LEE), to simulate noise propagation, and the calculation cost is reduced by coupling the LES of the sound source area and the LEE of the sound propagation area, but the problems of Equation transformation, inconsistent solution variables, non-physical reflection of a partition interface and the like of different partition equations cannot be effectively solved, so that no numerical simulation research report of the method for the complex flow-sound interference phenomenon is found.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a flow noise simulation method based on a disturbance equation, which comprises the steps of firstly introducing a compact disturbance equation CDE to replace a numerical simulation NS equation, and then aiming at a multi-scale turbulence phenomenon, realizing a novel mixed RANS/LES simulation method so as to solve the problems of overhigh LES simulation cost and insufficient modeling stress of the mixed RANS/LES method at a partition interface; and aiming at the phenomenon of complex bidirectional flow-sound interference, a flow-sound partition coupling CFD/CAA simulation method is realized, so that the problem that the high-precision flow-sound interference simulation is difficult to carry out by partition coupling of different equations and solving of variables in the existing method is solved. The invention can not only keep or improve the simulation precision, but also greatly reduce the calculation cost; for complex aeroacoustic problems, the calculation cost can be further obviously reduced through load balancing optimization.

The technical scheme adopted by the invention for solving the technical problem comprises the following steps:

step 1: introducing a compact disturbance equation CDE to replace a numerical simulation NS equation;

step 1-1: the flow variable is decomposed in different scales, and the original flow variable U is decomposed into basic partsAnd disturbance U':

wherein rho, p, u, v and w respectively represent density, pressure and velocity components in XYZ three directions; the upper dash line represents the time average of the variable, and the wavy symbol represents the Favre average of the variable; the disturbance amounts corresponding to the time average and the Favre average, respectively;

step 1-2: decomposition of a conservative variable Q into a reference streamAnd disturbance solution Q':

wherein e represents an internal energy;

step 1-3: will not have adhesive flux F_jDecomposing into:

wherein the content of the first and second substances,and F'_jReference quantity and disturbance quantity u representing flux respectively_jRepresenting a velocity component, p_xj、p_yjAnd p_zjRespectively representing the pressure in three directions of XYZ;

step 2: moving unknown terms containing disturbance in the three equations in the step 1 to the left end of the equation to obtain a generalized disturbance equation:

the fifth term and the seventh term at the left end are nonlinear disturbance terms, and alpha epsilon (0,1) is a switch of the nonlinear term; tau is_ijRepresenting the tensor of shear stress, τ_xj、τ_yj、τ_zjRespectively representing shear stress tensors in three directions of XYZ; u. of_iRepresenting a velocity component;

the decomposition formula of partial conservation variables and flux in the formula (4) is specifically developed as follows:

and (3) obtaining:

wherein γ represents the specific heat ratio;

when α ═ 1, the nonlinear term exists, equation (4) is a recombined version of the complete NS equation;

when α is 0, the non-linear term is ignored;

further represented by the following matrix:

wherein V represents the velocity, δ_xj、δ_yj、δ_zjKronecker symbols respectively representing three directions of XYZ, the term with a sharp superscript representing a correction term containing a weighting factor α;

and step 3: for a jacobian matrix without viscous fluxWhen non-linear terms are included, the CDE and NS equations are the same; when the non-linear terms are ignored, each term is replaced by its corresponding reference stream parameter; therefore, seamless switching between the NS equation and the control equation when the nonlinear term is ignored can be realized by adjusting the value of the weighting coefficient alpha in the CDE;

and 4, step 4: for numerical simulation of a complex turbulence phenomenon, firstly performing RANS simulation in a specified calculation region, then performing grid division in a concerned calculation region, and solving an unsteady CDE by taking an RANS solution as a reference flow to obtain turbulence pulsation, thereby realizing a mixed RANS/LES simulation method;

and 5: performing RANS simulation on the numerical simulation of the complex stream-sound interference in the whole domain, dividing a concerned area into a local sound source area and a sound propagation area, and performing grid division; using the RANS simulation result as a reference solution, and adopting an LES simulation based on CDE in a sound source area; CDE-based LEE simulation is employed in the acoustic propagation region.

The invention has the following beneficial effects:

the hybrid RANS/LES method and the flow-sound subarea coupling simulation method based on the CDE have the main advantages that the simulation precision can be kept or improved, and the calculation cost can be greatly reduced; for complex aeroacoustic problems, the calculation cost can be further obviously reduced through load balancing optimization.

Drawings

Fig. 1 is a flow chart of the CDE based hybrid RANS/LES method of the present invention.

FIG. 2 is a flow chart of a CDE-based stream-sound partition coupling CFD/CAA method according to the present invention.

Fig. 3 is a comparison graph of the computational cost between the flow-sound partition coupling simulation and the NLNS method in the second embodiment of the present invention.

Fig. 4 is a diagram illustrating a partitioning of a local unsteady computing domain according to a first embodiment of the present invention.

Fig. 5 shows simulation results of the first embodiment of the present invention.

Fig. 6 shows three dividing manners of the sound source region and the sound propagation region in the second embodiment of the present invention.

FIG. 7 is a schematic diagram showing the temporal variation of the transient pressure disturbance at three locations in the second embodiment of the present invention.

FIG. 8 is a graph showing the distribution of Reynolds stress components at two locations in a second embodiment of the present invention.

Detailed Description

The invention is further illustrated with reference to the following figures and examples.

Step 1: introducing a compact disturbance equation CDE to replace a numerical simulation NS equation;

step 1-1: the flow variable is decomposed in different scales, and the original flow variable U is decomposed into basic partsAnd disturbance U':

wherein rho, p, u, v and w respectively represent density, pressure and velocity components in XYZ three directions; the upper dash line represents the time average of the variable, and the wavy symbol represents the Favre average of the variable; the disturbance amounts corresponding to the time average and the Favre average, respectively;

step 1-2: decomposition of a conservative variable Q into a reference streamAnd disturbance solution Q^′：

Wherein e represents an internal energy;

step 1-3: will not have adhesive flux F_jDecomposing into:

wherein the content of the first and second substances,and F'_jReference quantity and disturbance quantity u representing flux respectively_jRepresenting a velocity component, p_xj、p_yjAnd p_zjRespectively representing the pressure in three directions of XYZ;

step 2: moving unknown terms containing disturbance in the three equations in the step 1 to the left end of the equation to obtain a generalized disturbance equation:

the fifth term and the seventh term at the left end are nonlinear disturbance terms, and alpha epsilon (0,1) is a switch of the nonlinear term; tau is_ijRepresenting the tensor of shear stress, τ_xj、τ_yj、τ_zjRespectively representing shear stress tensors in three directions of XYZ; u. of_iRepresenting a velocity component;

the decomposition formula of partial conservation variables and flux in the formula (4) is specifically developed as follows:

and (3) obtaining:

wherein γ represents the specific heat ratio;

when α ═ 1, the nonlinear term exists, equation (4) is a recombined version of the complete NS equation;

when α is 0, the non-linear terms are ignored, and each term may be replaced by its corresponding reference flow variable.

When deriving the flux term (e.g., the second equation above), the appearance is asWhen α is 0, this term leaves only the reference flow variable

Further represented by the following matrix:

each element in the matrix is replaced by their corresponding reference solution, where V denotes velocity, δ_xj、δ_yj、δ_zjKronecker symbols respectively representing three directions of XYZ, the term with a sharp superscript representing a correction term containing a weighting factor α;

and step 3: for a jacobian matrix without viscous fluxWhen non-linear terms are included, the CDE and NS equations are the same; when the non-linear terms are ignored, each term is replaced by its corresponding reference stream parameter; therefore, seamless switching between the NS equation and the control equation when the nonlinear term is ignored can be realized by adjusting the value of the weighting coefficient alpha in the CDE;

and 4, step 4: for numerical simulation of the complex turbulence phenomenon, RANS simulation is firstly carried out in a complex and large calculation area, then grids are divided in a concerned small calculation area, and an unsteady CDE is solved by taking an RANS solution as a reference flow to obtain turbulence pulsation, so that a mixed RANS/LES simulation method is realized. Because the RANS/LES partition interface in the DES method does not exist, the method has lower calculation cost compared with the existing mixed RANS/LES, and avoids the defects of other methods.

And 5: for numerical simulation of complex stream-acoustic interference, RANS simulation is performed on the whole domain, a concerned area is divided into a local sound source area and an acoustic propagation area, and gridding division is performed; by taking the RANS simulation result as a reference solution, the CDE can be restored to LES simulation in the near-field turbulent sound source area, and meanwhile, the reference solution required by the simplified LEE equation is provided in the sound propagation area, so that the noise propagation simulation is realized. Therefore, by seamlessly switching different forms of CDE in different partitions and simultaneously solving the disturbance equation taking the RANS solution as reference, a flow-sound partition coupling simulation algorithm can be realized, and the problem that the existing method is difficult to couple different equations and solve variables in different partitions to carry out high-precision flow-sound interference simulation is effectively solved. In addition, the numerical algorithm with respectively optimal turbulence and noise is adopted in different partitions, so that the calculation cost can be obviously reduced under the condition of maintaining or improving the calculation accuracy.

The specific embodiment is as follows:

the first embodiment is as follows: a hybrid RANS/LES method based on CDE.

Example a selected simulation object was a two-dimensional compressible shear layer flow with superimposed initial pressure pulsations, formed by a blunt trailing edge splitter plate, with incoming flow mach numbers of 0.1 and 0.6 in the upper and lower regions separated by the splitter plate, respectively, and with x ═ x₁The thickness of the boundary layer momentum is theta. Selecting theta as reference length, c_∞For reference speed, θ/c_∞To reference time, p_∞c_∞ ²Is a reference pressure. The diverter plate geometry is given by the following equation:

wherein AR is 2.5, m is 6 and dimensionless plate width ω is 2. Reynolds number Re of low-speed part incoming flow_θ＝ρ₁u₁θ₁/μ₁250. The initial pressure perturbation superimposed on the steady elementary stream is:

U′＝[0,0.05f(x,y)/(γ-1),0,0,0]

f(x,y)＝exp{-ln2[(x+20/4)²+(y+20/4)²]}

the initial pressure disturbance, which develops freely before contacting the spoiler, is then reflected by the lower surface of the spoiler and diffracted by the trailing edge into the flow area of the upper surface.

As shown in fig. 4, stationary simulations over a larger computational domain calculate viscous shear layers by solving the NS equation in full form, while non-stationary simulations are limited to a smaller flow region within the dashed line and predict the development of an unsteady disturbance by solving the CDE. Only 14 ten thousand grid points are set in the steady calculation domain because only the flow gradient near the shear layer is large; the unsteady calculation adopts 2.6 ten thousand nodes, and can be restored into high-precision LES simulation based on NS equation by adopting CDE equation in complete form in the near-field sound source area.

Fig. 5 shows the simulation result of the first embodiment, in which fig. 5(a) is an instantaneous pressure cloud at time t-90, which includes propagation and scattering of the pressure wave. Fig. 5(b) is a graph of the change in pressure disturbance at (x, y) — (50, 50) with time. The result is almost completely consistent with the result of universe calculation by utilizing NS equation and 24.7 ten thousand nodes at Stanford university, which shows that the method has the calculation precision consistent with the calculation by utilizing NS equation, but the calculation cost is reduced by one order of magnitude.

Example two: CDE-based stream-sound partition coupling simulations.

The second embodiment and the first embodiment select the same simulation object, and the initial pressure disturbance is as follows:

p′＝A·exp{-ln2[(x+20/4)²+(y+20/4)²]}

wherein a is 0.01/(γ -1), 0.05/(γ -1), 0.1/(γ -1).

In consideration of the strong non-linear and viscous effects of the shear layer and the initial perturbation, a full form of NS equation, i.e., α ═ 1 in CDE, is used in this region, and LEE, i.e., α ═ 0, is used in other regions.

Fig. 3 counts the grid size of the CFD computational domain and the comparison of CPU time with NLNS (non-linear NS equation) calculations.

In order to research the influence of the division mode of the flow-sound partition calculation domain on the result, three groups of comparison calculation tests are carried out, the range of the CFD calculation domain of the first group is-10 and y is less than or equal to 10, and only a shear layer is included; the range of the second group is-35 is less than or equal to y and less than or equal to 10, and the initial disturbance area is further included; the third group has a range of y is more than or equal to-35 and less than or equal to 15. These three sets of experiments were scored as M10P10, M35P10, M35P15, respectively. As shown in fig. 6.

Fig. 7 is a schematic diagram of the temporal variation of the instantaneous pressure disturbance at three positions when the initial disturbance amplitude is maximum, i.e. a is 0.1/(γ -1), and it can be seen that a large error is brought about when the nonlinear and viscous effects are neglected in the initial disturbance region, while the flow-acoustic zoning coupling algorithm makes the calculation result closer to the NLNS result due to the introduction of the effect at the required part.

Fig. 8 is a distribution of reynolds stress components < u "> at-30 and 50. It can be seen that the conventional LEE-based simulation method neglects the viscous term, and the predicted Reynolds stress is significantly different from the calculation using the complete NS. The method adopted by the invention can accurately predict the Reynolds stress, which is very important for high-precision numerical simulation of a turbulent sound source and radiation noise thereof.