CN115329567A - Three-dimensional turbulent jet flow state numerical simulation method based on turbulent flow characteristics - Google Patents

Three-dimensional turbulent jet flow state numerical simulation method based on turbulent flow characteristics Download PDF

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CN115329567A
CN115329567A CN202210961437.6A CN202210961437A CN115329567A CN 115329567 A CN115329567 A CN 115329567A CN 202210961437 A CN202210961437 A CN 202210961437A CN 115329567 A CN115329567 A CN 115329567A
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黄玄
徐津
乌景秀
王玲玲
杨帆
张先飞
刘国庆
范子武
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Nanjing Hydraulic Research Institute of National Energy Administration Ministry of Transport Ministry of Water Resources
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Abstract

The invention provides a three-dimensional turbulent jet flow state numerical simulation method based on turbulent flow characteristics, which comprises the following steps: establishing a three-dimensional jet numerical model based on NSEs (non-subsampled contourlet-Stokes equations) in a Cartesian coordinate system; based on the jet flow turbulence structure, a trigonometric function numerical disturbance equation set is established; and (3) acting the disturbance function on the outer layer grid of the jet orifice in time-sharing steps, calibrating parameters in the outer layer grid of the jet orifice, and performing three-dimensional turbulent jet flow state simulation. The invention can solve the problems of insufficient turbulent development and inaccurate flow state simulation in the jet flow numerical simulation process, can more quickly obtain turbulent jet flow with various anisotropic characteristics, greatly saves computing resources, simultaneously enables the simulation result to be more accurate, and has important significance in the jet flow mechanism research aspect.

Description

Three-dimensional turbulent jet flow state numerical simulation method based on turbulent flow characteristics
Technical Field
The invention relates to a numerical method for turbulent jet flow state simulation, in particular to a numerical perturbation method for a jet orifice.
Background
The discharge of substances in nature, such as waste water, oil pipeline leaks in the sea, submarine thermal liquid plumes, and exhaust gas emissions in the atmosphere, volcanic soot, etc., occurs frequently, and these discharge of substances can be generalized to jet motion in a receiving fluid. Jet flow problems in natural environment are mostly turbulent jet flow, a high-precision fine numerical simulation method such as direct numerical simulation is not suitable for turbulent flow with high Reynolds number at the present stage, a small-scale vortex structure can be modeled by a large vortex simulation method, so that turbulent flow development is slow and insufficient, and a common solution is to artificially add numerical disturbance to promote turbulent flow development.
The traditional jet numerical disturbance method generally cannot accurately simulate the flow state characteristics of the three-dimensional turbulent jet, for example, a white noise (white noise) disturbance method only considers the randomness of turbulence and cannot simulate the periodicity of jet turbulence. Although the sine function or cosine function perturbation method can simulate the jet flow with the periodic turbulent fluctuation law, the anisotropy of the three-dimensional jet flow cannot be accurately simulated. The method is characterized in that the velocity components of u and v of the initial jet flow are simulated to have obvious correlation, and the flow velocity in the x direction and the y direction at the same simulation moment is the positive direction or the negative direction, so that the cross section shape of the initial jet flow on the x-y cross section is calculated to be a strip shape forming an angle of 45 degrees with the x axis. The phenomenon can increase the simulation time required by the jet to reach the fully turbulent development state, and the calculation cost can be obviously increased in the high-precision three-dimensional turbulent jet numerical simulation, so that a numerical perturbation method considering the randomness, periodicity and anisotropy of the turbulent jet at the same time is urgently needed.
Disclosure of Invention
The invention aims to provide a trigonometric function numerical perturbation method capable of simultaneously simulating jet randomness, periodicity and anisotropy aiming at the numerical method problem of three-dimensional turbulent jet flow state simulation.
The technical scheme of the invention is as follows:
the invention provides a three-dimensional turbulent jet flow state numerical simulation method based on turbulent flow characteristics, which comprises the following steps:
step 1, establishing a three-dimensional jet numerical model based on NSEs (non-subsampled contourlet-Stokes equations) in a Cartesian coordinate system;
step 2, establishing a trigonometric function numerical disturbance equation set based on the jet flow turbulent flow structure;
and 3, acting the disturbance function on the outer layer grid of the jet orifice in time-sharing steps, calibrating parameters of the outer layer grid of the jet orifice, and performing three-dimensional turbulent jet flow state simulation.
Further, the specific perturbation function adopted by the trigonometric function numerical perturbation in the step 2 is as follows:
Figure BDA0003793356410000021
Figure BDA0003793356410000022
Figure BDA0003793356410000023
wherein: x, y and z represent directions in a Cartesian coordinate system, and u, v and w are speeds in the x, y and z directions respectively; a. The w ，A u ，A v Disturbance amplitudes in the w, u and v directions respectively; w is a 0 Is emitted toA flow initial axis velocity; t is simulation time; n is a disturbance period; theta.theta. r Is a random angle between 0 and pi; f is the disturbance frequency.
Further, the amplitude of the disturbance A w The value of (b) is determined according to the actual condition of the jet flow, and the range is 0.1-0.2; a. The u ，A v Value ratio of A w One order of magnitude smaller, ranging from 0.01 to 0.02; and N takes a value of 4-8.
Further, f is the disturbance frequency, and the value is determined by the Strouhal number, which is a similarity criterion for characterizing the flow periodicity.
Further, step 3 specifically comprises:
step 3-1, subdividing the three-dimensional simulation area by using a rectangular computational grid;
step 3-2, applying a triangular disturbance function to two peripheral layers of two layers of grids at the top end of the jet orifice in the z direction, wherein the vertical flow velocity after disturbance is added is w 0 The flow rates in the + w ', x and y directions are u ' and v ', respectively;
step 3-3, adjusting the disturbance amplitude A w ，A u ，A v And carrying out parameter calibration.
Further, in the step 3-1, the grids at the jet opening are required to be encrypted, the grids are required to be divided into 8 layers of grids within the range of 2cm at the bottom of the water tank, and when a square jet opening is simulated, the grids are at least divided into 8 multiplied by 8 grids in the x-y direction; when simulating a circular jet orifice, the x-y direction is subdivided into at least 68 square grids.
The invention has the beneficial effects that:
the invention is applied to three-dimensional high-precision turbulent jet numerical simulation, and provides a numerical disturbance method capable of simultaneously simulating jet randomness, periodicity and anisotropy. By adopting the method, the problems of insufficient turbulent development and inaccurate flow state simulation in the jet flow numerical simulation process can be solved, the turbulent jet flow with various anisotropic characteristics can be obtained more quickly, the calculation resources are greatly saved, the simulation result is more accurate, and the method has important significance in the jet flow mechanism research aspect.
Additional features and advantages of the invention will be set forth in the detailed description which follows.
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The above and other objects, features and advantages of the present invention will become more apparent by describing in more detail exemplary embodiments thereof with reference to the attached drawings, in which like reference numerals generally represent like parts throughout.
Fig. 1 is a conceptual diagram of the present invention.
Fig. 2A and 2B are schematic views of a numerical water tank.
FIG. 3 is a schematic diagram for verifying the on-way flow rate decay law of the jet simulated by the invention.
FIG. 4 is a schematic view of the simulated jet radius verification of the present invention.
FIG. 5 is a schematic diagram of a simulated x-y profile velocity profile verification of the present invention.
FIG. 6 is a schematic diagram of the x-y profile concentration profile verification of a jet simulated by the present invention.
FIG. 7 is a diagram showing the comparison result of u and v velocity components simulated by the method of the present invention and the conventional sine function disturbance method.
Fig. 8A to 8D are schematic diagrams comparing the velocity and concentration distribution on x-y section of jet flow simulated by the method of disturbance with the conventional sine function according to the present invention.
Wherein fig. 8A and 8B are schematic diagrams of velocity distributions on x-y cross-sections simulated by the conventional method and the inventive method, respectively, and fig. 8C and 8D are schematic diagrams of concentration distributions on x-y cross-sections simulated by the conventional method and the inventive method, respectively.
Detailed Description
Preferred embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While the preferred embodiments of the present invention are shown in the drawings, it should be understood that the present invention may be embodied in various forms and should not be limited to the embodiments set forth herein.
The invention provides a three-dimensional turbulent jet flow state numerical simulation method based on turbulent flow characteristics, which realizes numerical disturbance of a jet orifice and comprises the following steps:
step 1, establishing a three-dimensional jet numerical model based on NSEs (non-stationary dimensional equations) in a Cartesian coordinate system;
step 2, establishing a trigonometric function numerical disturbance equation set based on the jet flow turbulent flow structure, wherein the specific disturbance function adopted by the trigonometric function numerical disturbance is as follows:
Figure BDA0003793356410000031
Figure BDA0003793356410000032
Figure BDA0003793356410000041
wherein: x, y and z represent directions in a Cartesian coordinate system, and u, v and w are speeds in the x, y and z directions respectively; a. The w ，A u ，A v Disturbance amplitudes in the w, u and v directions respectively; w is a 0 Is the jet initial axis velocity; t is simulation time; n is a disturbance period; theta r Is a random angle between 0 and pi; f is the disturbance frequency; amplitude of disturbance A w The value of (a) is determined according to the actual condition of the jet flow, and the range is 0.1-0.2; a. The u ，A v Value ratio of A w One order of magnitude smaller, ranging from 0.01 to 0.02; n takes a value of 4 to 8; f is the disturbance frequency, the value is determined by the Strouhal number, which is a similarity criterion for characterizing the flow periodicity.
Step 3, acting the disturbance function on the outer layer grid of the jet orifice in time-sharing steps and calibrating parameters thereof, and carrying out three-dimensional turbulent jet flow state simulation, specifically:
step 3-1, subdividing a three-dimensional simulation area by using a rectangular computational grid; the meshes at the jet orifice need to be encrypted, the water tank bottom needs to be divided into 8 layers of meshes within the range of 2cm, and when a square jet orifice is simulated, the x-y direction is divided into at least 8 multiplied by 8 meshes; when a circular jet orifice is simulated, the x-y direction is at least divided into 68 square grids;
step 3-2, applying a triangular disturbance function to two peripheral layers of two layers of grids at the top end of the jet orifice in the z direction, and adding the disturbed vertical flow velocityIs w 0 The flow rates in the + w ', x and y directions are u ' and v ', respectively;
step 3-3, adjusting disturbance amplitude A w ，A u ，A v And carrying out parameter calibration.
In the specific implementation:
1. numerical model building
Under a Cartesian coordinate system, assuming that a water body is not compressible, the Navier-Stokes equation set (NSEs) approximated by Boussinesq is as follows:
the continuous equation:
Figure BDA0003793356410000042
a momentum equation set:
Figure BDA0003793356410000043
Figure BDA0003793356410000044
Figure BDA0003793356410000045
wherein: u, v, w and g x 、g y 、g z The velocity and the gravitational acceleration in the directions of x, y and z respectively, p is the pressure, rho a The density of the water body is 998kg/m under the condition of pure water 3 (ii) a Rho is the actual density of solute-containing water body, tau xx 、τ xy 、τ xz 、τ yx 、τ yy 、τ yz 、τ zx 、τ zy 、τ zz The viscous force term is mainly related to the velocity gradient and the vortex viscosity coefficient v, and the expression is as follows:
Figure BDA0003793356410000051
as shown in FIG. 2A, in a numerical tank of 1m 0.5m, the jet opening is located at the center of the bottom of the tank, and the opening area A 0 ＝7.8×10 -5 m 2 . The whole numerical water tank is divided into 100 multiplied by 80 non-uniform rectangular grids, the grid at the jet orifice is finest, the bottom of the water tank is divided into 8 layers of grids within 2cm vertical range, the grids are divided horizontally according to the shape of the jet orifice, the rectangular jet orifice is divided into 8 multiplied by 8 grids, the circular jet orifice is simulated approximately by 68 square grids, and a grid division schematic diagram is shown in fig. 2B.
2. Jet orifice numerical value disturbance method
The perturbation function of the trigonometric function numerical perturbation method is as follows:
Figure BDA0003793356410000052
Figure BDA0003793356410000053
Figure BDA0003793356410000054
wherein A is w The value of disturbance amplitude is between 0.1 and 0.2, A u ，A v The disturbance amplitude in the u and v directions respectively, and the value ratio A w The smaller one is between 0.01 and 0.02, and the disturbance amplitude needs to be calibrated according to the actual condition of the jet flow; w is a 0 Is the jet initial axis velocity; t is simulation time, and the disturbance value is different under each time step; the constant N is related to disturbance periodicity, the larger N is, the stronger the disturbance periodicity is, and N =6 is usually taken during jet simulation; theta r The random angle is between 0 and pi and is used for simulating the randomness of turbulent flow; f is disturbance frequency, the value is determined by Strouhal number, and the disturbance frequency is a similarity criterion for representing flow periodicity.
The numerical disturbance acts on the periphery of the top 2 layers of grids in the z direction of the jet ports, as shown in figure 1 (oblique line filling area in the figure), and the vertical flow velocity after the disturbance is addedIs w 0 The flow velocities in the + w ', x and y directions are u ' and v ', respectively, and the disturbance amplitude A is adjusted w ，A u ，A v And carrying out parameter calibration.
3. Simulation result validation
In the numerical water tank shown in fig. 2, two sets of momentum jet working conditions in the homogeneous environment shown in table 1 are provided in total, and the numerical simulation results when the numerical perturbation method provided by the invention is applied to the square-hole jet and the circular-hole jet are verified respectively. The flow velocity distribution, concentration distribution and jet radius of the jet are mainly verified.
Table 1 verification of operating conditions settings
Figure BDA0003793356410000061
Verifying the attenuation rule of the vertical flow velocity of the jet flow: the non-dimensional vertical flow velocity on-way attenuation rule consistent with the previous basin experimental result and empirical formula can be obtained by using the square hole jet flow and the circular hole jet flow which are simulated based on the disturbance method provided by the invention. The water tank experiment of momentum jet flow in a homogeneous environment is carried out in the creep mountain, the on-way speed attenuation rule of the jet flow, which is consistent with an Albertson empirical formula, is obtained, and the speed distribution on the x-y section of the jet flow is consistent with Gaussian distribution. Working conditions 1 and 2 refer to the experimental setting of the bradyseism, a square jet orifice and a round jet orifice which have the same experimental area as the bradyseism are adopted, and the initial flow speed w 0 =0.88m/s. For ease of tracing, the jet is assigned a trace concentration scalar of 10mg/L, which does not affect the jet density.
Time-averaged simulation results within t = 10-20 s are adopted to verify the in-path axis velocity w of the jet under the working conditions 1 and 2 c And (4) attenuation law. FIG. 3 shows the result of the verification, L 0 Representing jet orifice size, for a square-hole jet L 0 Representing side length, circular orifice jet L 0 Representing the diameter. It can be seen that both the square-hole jet flow and the circular-hole jet flow simulated by the numerical perturbation method provided by the invention can obtain a dimensionless on-way velocity attenuation rule which is consistent with the results of the previous turbulent jet flow experiment.
And (3) verifying the radius of the jet flow: the current research shows that the ratio of the jet radius to the rise heightThe relation between the two is in accordance with r = k r/z z, different experimental environments and jet initial conditions all affect the jet radius, resulting in k r/z There is a debate on the value of (a). The invention only verifies that the jet radius is in a reasonable range compared with the experimental result of the prior person. Fig. 4 compares the simulation results of the operating conditions 1 and 2 with the previous experimental results, in which the gray lines are the previous experimental results of negative-buoyancy or positive-buoyancy jet flow, the red lines are the previous experimental results of momentum jet flow, and the black lines are the numerical simulation results of the operating conditions 1 and 2. It can be seen that the ratio of the radius to the height of the jet obtained by simulation varies slightly along the way, mainly occurring near the jet orifice (z/L) 0 <10.0 And near the water surface (z/L) 0 >45.0 K) total r/z The numerical values are distributed in the range of experimental results of predecessors, which shows that the perturbation method provided by the invention can accurately simulate the on-way radius of the jet.
And (3) verifying the flow velocity and concentration distribution of the jet flow x-y section: for the jet with fully developed flow state and turbulence, the x-y section velocity and concentration of the jet are in accordance with Gaussian distribution:
Figure BDA0003793356410000062
Figure BDA0003793356410000071
wherein w c Is the jet axis vertical velocity; c. C c Is the jet axis concentration; b is the half width of the jet and is defined as the position where the vertical flow rate is equal to 1/e of the axial flow rate of the jet, namely, the condition that w = (1/e) w is satisfied c The jet radius of the condition.
Fig. 5 and 6 show the time-averaged velocity and concentration profiles of the jet at two sections z =0.1m,0.3m for conditions 1 and 2, respectively. It can be seen that on the cross sections with three different heights, the jet velocity and the concentration distribution both accord with Gaussian distribution, which indicates that the jet meets the flow state requirement of the turbulent jet.
In conclusion, it is verified from three aspects that the disturbance method provided by the invention can obtain accurate dimensionless rules when simulating square-hole jet flow and circular-hole jet flow: 1) The jet velocity decay law; 2) The radius of the jet; 3) The horizontal cross-sectional velocity and concentration distribution of the jet conforms to a gaussian distribution.
4. Compared with the conventional method
Taking a hole jet as an example, two groups of working conditions shown in table 2 are set to compare the numerical disturbance effects of the trigonometric function numerical disturbance method (hereinafter referred to as the "method of the present invention") and the traditional sine disturbance method (hereinafter referred to as the "traditional method").
TABLE 2 disturbance Effect comparative Condition settings
Figure BDA0003793356410000072
And comparing the u and v velocity component correlation simulated by the method and the traditional method by adopting a time-average numerical simulation result within t =10 s-20 s. 64 scattered points which are uniformly distributed are extracted on the section of z =0.2m of the working conditions 3 and 4 respectively, and the u/w of the scattered points is shown in figure 7 c And v/w c And (4) relationship. It can be seen that, since the conventional method only adds numerical disturbance in the vertical direction, the velocities u and v with initial values of 0 show a clear correlation at the section of z =0.2m and the correlation coefficient is 0.63 through the development of a distance under the action of the numerical disturbance of the vertical flow velocity. The horizontal velocities u and v of the jet flow obtained by the perturbation method provided by the invention have no obvious correlation, and the correlation coefficient is 0.06, so that the correlation coefficient is obviously improved.
The jet turbulence development speed and flow regime based on the method of the invention and the conventional method were further compared. Fig. 8 shows the time-average velocity and concentration distribution of the jet z =0.2m section in the range of t = 10-20 s, fig. 8A and B show the velocity distribution on the x-y section of the jet simulated by the conventional method and the method of the present invention, respectively, and C and D show the corresponding concentration distribution, respectively. It can be seen that the velocity components of the jet flow u and v based on the traditional method have higher correlation, and the situation that the jet flow is in the positive direction or in the negative direction at the same simulation moment is easier to occur, so that the sectional shape of the x-y section of the jet flow in the initial calculation stage is developed into a strip shape forming an angle of 45 degrees with the x axis. The method of the invention obtains more accurate jet horizontal profile speed and concentration distribution under the same simulation duration condition, and the turbulent fluctuation development speed is faster and more accurate than that of the traditional method.
Having described embodiments of the present invention, the foregoing description is intended to be exemplary, not exhaustive, and not limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims (6)

1. A three-dimensional turbulent jet flow state numerical simulation method based on turbulent flow characteristics is characterized by comprising the following steps:
step 1, establishing a three-dimensional jet numerical model based on NSEs (non-stationary dimensional equations) in a Cartesian coordinate system;
step 2, establishing a trigonometric function numerical disturbance equation set based on the jet flow turbulent flow structure;
and 3, acting the disturbance function on the outer layer grid of the jet orifice in time-sharing steps, calibrating parameters of the outer layer grid of the jet orifice, and performing three-dimensional turbulent jet flow state simulation.
2. The three-dimensional turbulent jet flow regime numerical simulation method based on turbulence characteristics of claim 1, wherein: the specific disturbance function adopted by the trigonometric function numerical disturbance in the step 2 is as follows:
Figure FDA0003793356400000011
Figure FDA0003793356400000012
Figure FDA0003793356400000013
wherein: x, y, z denote directions in a Cartesian coordinate systemU, v, w are the velocities in the x, y, z directions, respectively; a. The w ，A u ，A v Disturbance amplitudes in the w, u and v directions respectively; w is a 0 Is the jet initial axis velocity; t is simulation time; n is a disturbance period; theta r Is a random angle between 0 and pi; f is the disturbance frequency.
3. The three-dimensional turbulent jet flow regime numerical simulation method based on turbulent flow characteristics according to claim 2, wherein the three-dimensional turbulent jet flow regime numerical simulation method comprises the following steps of: amplitude of disturbance A w The value of (a) is determined according to the actual condition of the jet flow, and the range is 0.1-0.2; a. The u ，A v Value ratio of A w One order of magnitude smaller, ranging from 0.01 to 0.02; and N takes a value of 4-8.
4. The three-dimensional turbulent jet flow regime numerical simulation method based on turbulence characteristics of claim 2, wherein: f is the disturbance frequency, the value is determined by the Strouhal number, which is a similarity criterion for characterizing the flow periodicity.
5. The three-dimensional turbulent jet flow regime numerical simulation method based on turbulence characteristics of claim 1, wherein: the step 3 specifically comprises the following steps:
step 3-1, subdividing a three-dimensional simulation area by using a rectangular computational grid;
step 3-2, applying a triangular disturbance function to two peripheral layers of two layers of grids at the top end of the jet orifice in the z direction, wherein the vertical flow velocity after disturbance is added is w 0 The flow rates in the + w ', x and y directions are u ' and v ', respectively;
step 3-3, adjusting the disturbance amplitude A w ，A u ，A v And carrying out parameter calibration.
6. The three-dimensional turbulent jet flow regime numerical simulation method based on turbulent flow characteristics according to claim 5, wherein the numerical simulation method comprises the following steps of: in the step 3-1, the grids at the jet opening are required to be encrypted, 8 layers of grids are required to be split within the range of 2cm at the bottom of the water tank, and when a square jet opening is simulated, at least 8 multiplied by 8 grids are split in the x-y direction; when simulating a circular jet orifice, the x-y direction is divided into at least 68 square grids.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116337396A (en) * 2023-05-30 2023-06-27 中国航空工业集团公司哈尔滨空气动力研究所 Method for actively simulating wind tunnel test by using high-altitude atmospheric turbulence

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116337396A (en) * 2023-05-30 2023-06-27 中国航空工业集团公司哈尔滨空气动力研究所 Method for actively simulating wind tunnel test by using high-altitude atmospheric turbulence
CN116337396B (en) * 2023-05-30 2023-07-21 中国航空工业集团公司哈尔滨空气动力研究所 Method for actively simulating wind tunnel test by using high-altitude atmospheric turbulence

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