CN115616909A - Local time homogenization model control parameter calculation method based on rotational turbulence energy spectrum distribution and application method thereof - Google Patents

Local time homogenization model control parameter calculation method based on rotational turbulence energy spectrum distribution and application method thereof Download PDF

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CN115616909A
CN115616909A CN202211239314.8A CN202211239314A CN115616909A CN 115616909 A CN115616909 A CN 115616909A CN 202211239314 A CN202211239314 A CN 202211239314A CN 115616909 A CN115616909 A CN 115616909A
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刘本庆
杨魏
顾延东
成立
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Abstract

The invention discloses a local time homogenization model control parameter calculation method based on rotational turbulence energy spectrum distribution and an application method thereof, wherein the control parameter calculation method comprises the following steps of: wave number kappa solved by RANS method l Wavenumber k resolvable by the DNS method η (ii) a Step two, introducing Zeman number kappa Ω K to be solved l ～κ η Dividing the energy spectrum into two parts; step three, according to the definition of the turbulent kinetic energy and the energy spectrum distribution of the rotating turbulent flow, combining the position of the grid scale delta in the energy spectrum, and integrating and calculating the modeled turbulent kinetic energy k in the PANS model u And total turbulence energy k t (ii) a Step four, according to the control parameter f in the PANS model k In combination with modelled turbulence energy k u And total turbulence energy k t The expression (c) of (a),and calculating the expression of the corresponding control parameter. The calculation method simultaneously considers the balance of the calculated amount and the calculation precision in numerical simulation, and provides a powerful tool for efficiently solving the rotating flow field in the hydraulic machinery.

Description

Local time homogenization model control parameter calculation method based on rotational turbulence energy spectrum distribution and application method thereof
Technical Field
The invention belongs to the field of turbulence numerical simulation, relates to a calculation method, and particularly relates to a local time homogenization model control parameter calculation method based on rotational turbulence energy spectrum distribution and an application method thereof.
Background
In the field of numerical simulation of turbulence, achieving balance between the calculation amount and the calculation accuracy is always a research hotspot. In engineering applications of complex rotational turbulence such as hydraulic machinery, efficient numerical calculation is particularly important. However, under the influence of strong rotation, large curvature, multi-wall surface and other factors, the internal rotating turbulence of hydraulic machines such as water pumps and the like has the characteristics of rotation, transient property, pulsation and the like. In the numerical simulation of the turbulence, a reynolds time averaging method (RANS) cannot accurately capture flow characteristics such as reverse transfer of energy of the rotating turbulence, and methods such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) have high calculation accuracy, but have great difficulty in simulation of high-reynolds-number and multi-wall-surface hydraulic machines.
In recent years, girimaji et al have proposed a method of local time averaging (PANS) which can be performed by controlling the parameter f k The variation of (a) enables efficient solution of multiple flows. Control parameter f k Defined as the ratio of the modeled turbulent kinetic energy to the total turbulent kinetic energy, and a turbulent energy spectrum chart can well describe the distribution of the turbulent kinetic energy at different scales, so that f is calculated according to the turbulent energy spectrum k Is the most reasonable way. At present, different researchers have deducted PANS calculation methods based on the spectrum distribution of the non-rotational turbulence, which are respectively marked as PANS-ES1 and PANS-ES2. Research shows that energy is reversely transferred in the rotating flow, so that the energy spectrum distribution of the rotating flow is different from that of the non-rotating flow, and the wave number is kappa Ω ＝(Ω 3 /ε) 1/2 Determines the length-scale distribution of turbulence, and influences the energy spectrum transmission and energy spectrum form in the rotating flow, wherein k Ω In order of Zeman number, Ω represents a rotation speed. The existing PANS method has no calculation method aiming at the rotational turbulence, and the difference of the energy spectrum distribution of the rotational turbulence provides a new idea for solving the rotational turbulence.
Disclosure of Invention
In view of the defects and application requirements, the invention provides a method for calculating dynamic control parameters of a PANS model based on the energy spectrum distribution of rotational turbulence, aims to solve the problem that the flow characteristics of the rotational turbulence cannot be accurately reflected by the conventional PANS model, and provides a powerful tool for efficiently analyzing the rotational turbulence in a hydraulic machine.
In order to achieve the above object, the present invention provides a method for calculating control parameters of a local time-averaging model based on a rotational turbulence energy spectrum distribution, which has the following characteristics: the method comprises the following steps:
step one, in the process of solving the turbulence by using a numerical simulation method, the range of a turbulence model coupling NS (Navier-Stokes) equation which can be modeled or directly solved for a turbulence energy spectrum is as follows: wave number kappa that can be solved by RANS method (Reynolds time average method) l Wavenumber k resolvable by the DNS method (direct numerical simulation) η ；
Step two, introducing Zeman number kappa Ω K to be solved l ～κ η Dividing the energy spectrum into two parts to obtain the energy spectrum distribution of the rotating turbulence;
step three, according to the definition of the turbulent kinetic energy and the energy spectrum distribution of the rotating turbulent flow, combining the position of the grid scale delta in the energy spectrum, and integrating and calculating the modeled turbulent kinetic energy k in the PANS model u And total turbulence energy k t ；
Step four, according to the control parameter f in the PANS model k In combination with modelled turbulence energy k u And total turbulence energy k t Calculating the corresponding control parameter f k Is described in (1).
Further, the invention provides a local time homogenization model control parameter calculation method based on the rotating turbulence energy spectrum distribution, which can also have the following characteristics: wherein, in the step one, in the turbulent energy spectrum, the wave number kappa which can be solved by the RANS method l The expression is as follows:
Figure BDA0003884407030000031
in the formula I turb Is a turbulence length scale that can be solved by the RANS method;
Figure BDA0003884407030000032
in the formula, k T Is the total turbulence energy, k, in the RANS process T ＝k R +k U ，k U Is modelled turbulent kinetic energy, k R Is the turbulence energy that is directly solved,
Figure BDA0003884407030000033
U i is the speed of the moment in time,
Figure BDA0003884407030000034
is the time-averaged velocity; epsilon is the turbulent kinetic energy dissipation ratio;
wave number kappa capable of being solved by DNS method in turbulent energy spectrum η The expression of (c) is:
Figure BDA0003884407030000035
in the formula, η is a length scale that can be solved by the DNS method, called Kolmogorov length scale, and the expression is:
Figure BDA0003884407030000036
where ν is the kinematic viscosity of the fluid.
Further, the invention provides a local time homogenization model control parameter calculation method based on the rotating turbulence energy spectrum distribution, which can also have the following characteristics: in the second step, in the numerical simulation calculation, the calculation method of the grid scale Δ is as follows:
Δ＝(ΔxΔyΔz) 1/3 ；
where Δ x, Δ y, and Δ z are the dimensions of the grid cell in the x, y, and z directions, respectively;
wave number kappa corresponding to grid scale Δ Comprises the following steps:
Figure BDA0003884407030000041
zeman number kappa in rotational turbulence Ω The expression of (a) is:
κ Ω ＝(Ω 3 /ε) 1/2 ；
wherein omega is the rotating speed, epsilon is the turbulent kinetic energy dissipation ratio;
the energy spectral distribution of the rotating turbulence is:
when k is Δ ＞κ Ω The energy spectrum E (κ) and the wavenumber κ satisfy the relationship: e (κ) = α ∈ 2/3 κ -5/3 And alpha is a first empirical coefficient of the energy spectrum;
when k is Δ ＜κ Ω The energy spectrum E (κ) and the wavenumber κ satisfy the relationship: e (kappa) = beta (omega epsilon) 1/2 κ -2 And beta is a second empirical coefficient of the energy spectrum.
Further, the invention provides a local time homogenization model control parameter calculation method based on the rotating turbulence energy spectrum distribution, which can also have the following characteristics: wherein, in step three, it is assumed that in the PANS calculation, the grid scale is between the turbulence length scale and the Kolmogorov length scale;
total kinetic energy of turbulence k t Calculated from the following formula:
Figure BDA0003884407030000042
further, the invention provides a local time homogenization model control parameter calculation method based on the rotating turbulence energy spectrum distribution, which can also have the following characteristics: wherein the wavenumber is κ Δ ～κ η The turbulent kinetic energy is solved through modeling;
when k is Δ ＜κ Ω Time, modeled turbulent kinetic energy k u Comprises the following steps:
Figure BDA0003884407030000051
when k is Δ ＞κ Ω Time, modeled turbulent kinetic energy k u Comprises the following steps:
Figure BDA0003884407030000052
further, the invention provides a local time homogenization model control parameter calculation method based on the rotating turbulence energy spectrum distribution, which can also have the following characteristics: wherein, in step four, the control parameter f k Is defined as: f. of k ＝k u /k t 。
Further, the invention provides a local time homogenization model control parameter calculation method based on the rotating turbulence energy spectrum distribution, which can also have the following characteristics: wherein, the first empirical coefficient alpha and the second empirical coefficient beta of the energy spectrum are both 1.8;
control parameter f k The expression of (c) is:
Figure BDA0003884407030000053
when k is Δ ＝κ Ω The two expression forms of the above segments can be unified.
The present invention also provides a computer-readable storage medium storing a computer program having the features of: the computer program causes a computer to execute the method for calculating the control parameters of the local time homogenization model based on the energy spectrum distribution of the rotational turbulence.
The present invention also provides an electronic device having the features of: the device comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the computer program to realize the method for calculating the control parameter of the local time homogenization model based on the rotating turbulence energy spectrum distribution.
The invention also provides an application method of the local time homogenization model control parameter calculation method based on the energy spectrum distribution of the rotational turbulence in the numerical calculation of the rotational turbulence, which is characterized in that: on rotatingWhen the calculation is carried out by converting turbulent flow application, firstly, a classical SST k-omega model is taken as a base RANS model, and a corresponding PANS model is deduced; then, according to the method for calculating the control parameter of the local time homogenization model based on the energy spectrum distribution of the rotational turbulence, calculating the control parameter f derived based on the energy spectrum of the rotational turbulence k And substituting into a PANS model expression of the SST k-omega model; and then, coupling the corrected PANS model with an NS equation to form a nonlinear equation system, and calculating a numerical model which can be used for the rotating turbulence after the equation is dispersed by a finite volume method.
The present invention also provides a computer-readable storage medium storing a computer program having the features of: the computer program causes a computer to execute the application method of the control parameter calculation method based on the local time homogenization model of the energy spectrum distribution of the rotational turbulence in the numerical calculation of the rotational turbulence.
The present invention also provides an electronic device having the features of: the device comprises a memory, a processor and a computer program which is stored on the memory and can run on the processor, wherein the processor realizes the application method of the control parameter calculation method based on the local time homogenization model of the energy spectrum distribution of the rotational turbulence in the numerical calculation of the rotational turbulence when executing the computer program.
The invention has the beneficial effects that: the invention provides a local time homogenization model control parameter calculation method based on rotational turbulence energy spectrum distribution and an application method thereof. The method is more complete in theoretical basis and more suitable for solving the phenomena of turbulence intensity change, energy reverse transfer and the like induced by the rotation effect. The method has better catching capacity on the rotation effect of the rotating turbulence, can realize the balance between the calculated amount and the calculation precision when calculating the rotating turbulence, and provides a powerful tool for the efficient calculation of the rotating turbulence in hydraulic machinery such as a centrifugal pump and the like.
Drawings
FIG. 1 is a flow chart of a method of local time averaging model control parameter calculation based on a rotating turbulence spectral distribution;
FIG. 2 is a rotational turbulence spectrum profile;
FIG. 3 is a flow chart of a method implementation of a local time averaging model control parameter calculation based on a rotational turbulence energy spectral distribution;
FIG. 4 is a schematic diagram of a rotating channel flow example computational domain;
FIG. 5 is a schematic diagram of an example computational domain of a centrifugal pump;
FIG. 6 is a comparison of flow direction average velocity near the rotating channel flow arithmetic suction surface;
FIG. 7 is a graph comparing radial velocity at an exemplary monitoring location of a centrifugal pump.
Detailed Description
The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the present application without making any creative effort belong to the protection scope of the present application.
As shown in fig. 1, the present embodiment is a method for calculating control parameters of a local time-averaging model based on a rotational turbulence energy spectrum distribution, and the method includes the following steps:
step one, in the process of solving the turbulence by using a numerical simulation method, the range of a turbulence model coupling NS (Navier-Stokes) equation which can be modeled or directly solved for a turbulence energy spectrum is as follows: wave number kappa that can be solved by RANS method (Reynolds time average method) l Wave number kappa resolvable by the DNS method (direct numerical simulation) η 。
In particular, in a turbulent energy spectrum, the wave number kappa solved by the RANS method l The expression is as follows:
Figure BDA0003884407030000081
in the formula I turb Is a turbulence length scale that can be solved by the RANS method;
Figure BDA0003884407030000082
in the formula, k T Is the total turbulence energy, k, in the RANS process T ＝k R +k U ，k U Is modelled turbulent kinetic energy, k R Is the turbulence energy that is directly solved,
Figure BDA0003884407030000083
U i is the speed of the moment in time,
Figure BDA0003884407030000084
is the time-averaged velocity; epsilon is the turbulent kinetic energy dissipation ratio.
Wave number kappa capable of being solved by DNS method in turbulent energy spectrum η The expression of (a) is:
Figure BDA0003884407030000085
in the formula, η is a length scale which can be solved by the DNS method, and is called Kolmogorov length scale, and the expression is:
Figure BDA0003884407030000091
where ν is the kinetic viscosity of the fluid.
Step two, introducing Zeman number kappa Ω K to be solved l ～κ η The energy spectrum of the vortex is divided into two parts, and the energy spectrum distribution of the rotating turbulence is obtained.
Specifically, in the numerical simulation calculation, the method for calculating the grid scale Δ is as follows:
Δ＝(ΔxΔyΔz) 1/3 ；
where Δ x, Δ y, and Δ z are dimensions of the grid cell in the x, y, and z directions, respectively.
Wave number kappa corresponding to grid scale Δ Comprises the following steps:
Figure BDA0003884407030000092
zeman number kappa in rotational turbulence Ω The expression of (c) is:
κ Ω ＝(Ω 3 /ε) 1/2 ；
where Ω is the rotational speed and ε is the turbulent kinetic energy dissipation ratio.
The energy spectral distribution of the rotating turbulence is:
when k is Δ ＞κ Ω The energy spectrum E (κ) and the wavenumber κ satisfy the relationship: e (κ) = α ∈ 2/3 κ -5/3 Alpha is a first empirical coefficient of the energy spectrum;
when k is Δ ＜κ Ω The energy spectrum E (κ) and the wavenumber κ satisfy the relationship: e (kappa) = beta (omega epsilon) 1/2 κ -2 And beta is a second empirical coefficient of the energy spectrum.
Step three, according to the definition of the turbulent kinetic energy and the energy spectrum distribution of the rotating turbulent flow, the position of the grid size delta in the energy spectrum is combined, and the modeled turbulent kinetic energy k in the PANS model is calculated through integration u And total turbulence energy k t 。
In particular, it is assumed that in the PANS calculation, the mesh scale is between the turbulence length scale and the Kolmogorov length scale.
Total turbulent kinetic energy k t Calculated from the following formula:
Figure BDA0003884407030000101
as shown in FIG. 2, for smaller turbulence scales (i.e., larger wavenumbers, the wavenumber is κ) Δ ～κ η ) The turbulent kinetic energy is solved through modeling;
when k is Δ ＜κ Ω Time, modeled turbulent kinetic energy k u Comprises the following steps:
Figure BDA0003884407030000102
when k is Δ ＞κ Ω Time, modeled turbulent kinetic energy k u Comprises the following steps:
Figure BDA0003884407030000103
step four, according to the control parameter f in the PANS model k In combination with modelled turbulence energy k u And total turbulence energy k t And calculating the expression of the corresponding control parameter.
Control parameter f k Is defined as: f. of k ＝k u /k t 。
Specifically, both the first empirical coefficient α and the second empirical coefficient β of the energy spectrum are 1.8;
control parameter f k The expression of (c) is:
Figure BDA0003884407030000111
it is noteworthy that when κ Δ ＝κ Ω The two expression forms of the above segments may be unified.
As shown in fig. 3, the present embodiment also provides an implementation of the local time homogenization model control parameter calculation method based on the energy spectrum distribution of the rotational turbulence, that is, an application method thereof in the numerical calculation of the rotational turbulence:
correction of transport equation: firstly, according to the theory of PANS, the form of the corresponding PANS model is deduced based on SST k-omega model, and f containing the rotation speed omega is k The expression is put into the SST k- ω PANS transport equation. Wherein f is k ε = β in the expression 1 kω，β 1 Is the model coefficient and ω is the specific dissipation ratio of the turbulent kinetic energy.
The application of the new method is as follows: and coupling the transport equation of the modified SST k-omega PANS model with an NS equation closed control equation set, and recording as PANS-RCES. And (4) carrying out numerical model calculation on the rotational turbulence after the equation set is dispersed by a finite volume method.
In a specific embodiment, as shown in FIG. 4 and5, respectively, a schematic diagram of a calculation domain of a rotating channel flow example and a schematic diagram of a calculation domain of a centrifugal pump example, wherein the two examples are both the classical cases containing rotating turbulence and can be used for verifying the accuracy of turbulence model calculation. Reynolds number Re = U in the rotating channel flow example m h/v =7000, number of rotations Ro =2 ω h/U m =0.3, where h is half the height of the channel, ν is the kinetic viscosity of the fluid, ω is the rotational speed of the channel stream,
Figure BDA0003884407030000112
is the volume average velocity in the flow direction, with the x-axis forward being the flow direction, and the entire flow being driven by the flow direction pressure gradient. In the case of a centrifugal pump, the impeller speed is 725r/min and the inlet diameter D 1 =71mm, exit radius R 2 =95mm, number of blades 6, rated flow rate Q 0 3.06L/s, measured from the diameter D of the impeller outlet 2 And impeller exit circumferential velocity U 2 Reynolds number defined as Re = U 2 D 2 /υ＝1.4×10 6 . The calculation domain is divided into an inlet domain, an impeller domain and an outlet domain.
In this case, openFOAM is used to calculate the rotation channel flow calculation example, the number of nodes of the regular hexahedron grid is 39.3 ten thousand, the pressure-velocity coupling adopts the PISO algorithm, the gradient term and the divergence term adopt the 'Gauss linear' format, and the time term adopts the backsward format. The average CFL number in the calculation process is kept within 1, and the calculation result of the method PANS-RCES provided by the invention and the two existing dynamics f based on the non-rotation energy spectrum k Comparing the PANS-ES1, PANS-ES2 and DNS results, and calculating by coupling the three methods with an SST k-omega PANS model. In the case of the centrifugal pump, ANSYS CFX is adopted for calculation, the number of hexahedron grid nodes is 256.6 thousands, 15 rotation periods are calculated in the unsteady calculation, and the time average is carried out on the next 10 rotation periods. In the calculation process, a high-order solving format is adopted for a convection term, a central difference format is adopted for a diffusion term, and a second-order backward Euler difference format is adopted for a transient term. Step of time of 1 × 10 -4 s, convergence residual of 1 × 10 -5 The calculation result of the method PANS-RCES (abbreviated as PANS in the figure) proposed by the present invention and the commonly used SST k-The results of the ω model (abbreviated SST in the figure) and the results of the PIV test (abbreviated PIV in the figure) were compared.
As shown in FIG. 6, near the suction surface where turbulence is suppressed in the rotating channel flow, three methods all predicted a velocity profile consistent with DNS, but the two SST k- ω PANS-ES1 and SST k- ω PANS-ES2 models based on the non-rotating spectrum had large deviations from DNS results, which were well matched with DNS. As shown in fig. 7, in the radial velocity profile at the centrifugal pump monitoring position, the SST k- ω PANS-RCES model obtained results more in agreement with the experimental values than the SST model.
In the embodiments disclosed herein, a computer storage medium may be a tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. A computer storage medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of a computer storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (10)

1. A local time homogenization model control parameter calculation method based on rotational turbulence energy spectrum distribution is characterized in that:
the method comprises the following steps:
step one, in the process of solving the turbulence by using a numerical simulation method, the range of turbulence energy spectrum which can be modeled or directly solved by a turbulence model coupling NS equation is as follows: wave number kappa solved by RANS method l Wavenumber k resolvable by the DNS method η ；
Step two, introducing Zeman number kappa Ω K to be solved l ～κ η Dividing the energy spectrum into two parts to obtain the energy spectrum distribution of the rotating turbulence;
step three, according to the definition of the turbulent kinetic energy and the energy spectrum distribution of the rotating turbulent flow, combining the position of the grid scale delta in the energy spectrum, and integrating and calculating the modeled turbulent kinetic energy k in the PANS model u And total turbulence energy k t ；
Step four, according to the control parameter f in the PANS model k In combination with modelled turbulence energy k u And total turbulence energy k t Calculating the corresponding control parameter f k Is described in (1).
2. The method of calculating control parameters of a local time averaging model based on a rotational turbulence energy spectrum distribution according to claim 1, wherein:
wherein, in the step one, in the turbulent energy spectrum, the wave number kappa which can be solved by the RANS method l The expression is as follows:
Figure FDA0003884407020000011
in the formula I turb Is the RANS methodA solvable turbulence length scale;
Figure FDA0003884407020000012
in the formula, k T Is the total turbulent kinetic energy, k, of the RANS process T ＝k R +k U ，k U Is modelled turbulent kinetic energy, k R Is the turbulence energy that is directly solved,
Figure FDA0003884407020000013
U i is the speed of the moment of time,
Figure FDA0003884407020000014
is the time-averaged velocity; epsilon is the turbulent kinetic energy dissipation ratio;
wave number kappa capable of being solved by DNS method in turbulent energy spectrum η The expression of (a) is:
Figure FDA0003884407020000021
in the formula, η is a length scale which can be solved by the DNS method, and is called Kolmogorov length scale, and the expression is:
Figure FDA0003884407020000022
where ν is the kinetic viscosity of the fluid.
3. The method of calculating control parameters of a local time averaging model based on a rotational turbulence energy spectrum distribution according to claim 1, wherein:
in the second step, in the numerical simulation calculation, the grid scale Δ is calculated by:
Δ＝(ΔxΔyΔz) 1/3 ；
wherein Δ x, Δ y, and Δ z are the dimensions of the grid cell in the x, y, and z directions, respectively;
wave number kappa corresponding to grid scale Δ Comprises the following steps:
Figure FDA0003884407020000023
zeman number kappa in rotational turbulence Ω The expression of (a) is:
κ Ω ＝(Ω 3 /ε) 1/2 ；
in the formula, omega is the rotating speed, and epsilon is the turbulent kinetic energy dissipation rate;
the energy spectral distribution of the rotating turbulence is:
when k is Δ ＞κ Ω The energy spectrum E (κ) and the wavenumber κ satisfy the relationship: e (κ) = α ∈ 2/3 κ -5/3 And alpha is a first empirical coefficient of the energy spectrum;
when k is Δ ＜κ Ω The energy spectrum E (κ) and the wavenumber κ satisfy the relationship: e (kappa) = beta (omega epsilon) 1/2 κ -2 And beta is a second empirical coefficient of the energy spectrum.
4. The method of calculating control parameters of a local time averaging model based on a rotational turbulence energy spectrum distribution according to claim 3, wherein:
wherein, in step three, it is assumed that in the PANS calculation, the grid scale is between the turbulence length scale and the Kolmogorov length scale;
total kinetic energy of turbulence k t Calculated from the following formula:
Figure FDA0003884407020000031
5. the method of calculating control parameters of a local time averaging model based on a rotational turbulence energy spectrum distribution according to claim 4, wherein:
wherein κ is the wavenumber Δ ～κ η The turbulent kinetic energy is solved through modeling;
when k is Δ ＜κ Ω Time, modeled turbulent kinetic energy k u Comprises the following steps:
Figure FDA0003884407020000032
when k is Δ ＞κ Ω Time, modeled turbulent kinetic energy k u Comprises the following steps:
Figure FDA0003884407020000033
6. the method of calculating control parameters of a local time averaging model based on a rotational turbulence energy spectrum distribution according to claim 5, wherein:
wherein, in the fourth step, the control parameter f k Is defined as: f. of k ＝k u /k t 。
7. The method of calculating control parameters of a local time averaging model based on a rotational turbulence energy spectrum distribution according to claim 6, wherein:
wherein, the first empirical coefficient alpha and the second empirical coefficient beta of the energy spectrum are both 1.8;
control parameter f k The expression of (a) is:
Figure FDA0003884407020000041
8. the method for applying the calculation method of the control parameters of the local time homogenization model based on the energy spectrum distribution of the rotational turbulence to the numerical calculation of the rotational turbulence according to any one of claims 1 to 7, characterized in that:
when calculation is applied to the rotational turbulence, firstly, a classical SST k-omega model is used as a base RANS model, and a corresponding PANS model is deduced;
then, according to the method for calculating the control parameter of the local time homogenization model based on the energy spectrum distribution of the rotational turbulence, calculating the control parameter f derived based on the energy spectrum of the rotational turbulence k And bringing the expression into a PANS model expression of the SST k-omega model;
and then, coupling the corrected PANS model with an NS equation to form a nonlinear equation system, and calculating a numerical model which can be used for the rotating turbulence after the equation is dispersed by a finite volume method.
9. A computer-readable storage medium storing a computer program, characterized in that: the computer program causes a computer to execute the method of local time-averaging model control parameter calculation based on rotational turbulence energy spectral distribution according to any of claims 1-7.
10. An electronic device, characterized in that: comprising a memory, a processor and a computer program stored on the memory and executable on the processor, when executing the computer program, implementing the method for calculating control parameters based on a local time averaging model of a rotational turbulence energy spectrum distribution according to any one of claims 1 to 7.
CN202211239314.8A 2022-10-11 2022-10-11 Local time homogenization model control parameter calculation method based on rotational turbulence energy spectrum distribution and application method thereof Pending CN115616909A (en)

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