JP2017004103A - Turbulence simulation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To improve accuracy of numeric analysis of a flow field in which a swirl occurs.SOLUTION: A turbulence simulation method according to an embodiment acquires a measurement result of a feature of a turbulence which is measured in a flow field in which a swirl occurs. Then, numeric analysis is performed by using a turbulence model and a first turbulence model coefficient corresponding to the turbulence model, then an analysis result of the feature of the turbulence in the flow field is acquired, then a tolerance between the measurement result and the analysis result is calculated. Then, a prescribed parameter having correlation to the tolerance is designated, then correlation between the tolerance and the parameter is digitized over the whole area of the flow field. Then whole area of the flow field is divided into a first analysis area in which a value of the correlation exceeds a threshold and a second analysis area in which a value of the correlation is equal to or less than the threshold. Then, using the turbulence model, and a second turbulence model coefficient obtained by correcting a value of the first turbulence model coefficient, the feature of the turbulence in the first analysis area is digitized and analyzed.SELECTED DRAWING: Figure 6

Description

  Embodiments described herein relate generally to a turbulent flow simulation method.

  With the recent improvement in computational performance in electronic computers, fluid analysis technology has also made rapid progress, and recently fluid simulation is frequently used in the development of fluid machinery. The flow around a fluid machine is mostly turbulent, and although it is inherently desirable to perform direct numerical simulation (DNS) without modeling the turbulent flow, it is the fastest electronic computer today. Even if is used, direct calculation of turbulence is difficult.

  In addition, the turbulent flow length scale and time scale are wide in the analysis target region, and these scales are generally much smaller than the size of the analysis grid used for mesh division. Therefore, it is necessary to model turbulent flow, and the analysis is performed by combining the model equation and the fluid equation of motion. Many turbulent models used for numerical simulation have been proposed to date.

Turbulence Analysis (Computational Fluid Dynamics Series) Computational Fluid Dynamics Committee, University of Tokyo Press Turbulent computational fluid dynamics model and calculation method Hisaaki Omiya, Hiroshi Miyake, Tsuyoshi Yoshizawa, University of Tokyo Press Sadao KUROSAWA, Turblent Flow Simulation for the Draft Tube of a Kaplan Turbine, 23rd IAHR Symposium, 2006

  However, the existing numerical simulation method using the turbulent flow model, for example, for a flow field where swirl (vortex) is generated, analyzes the result of the numerical simulation in the region of the entire flow field. It cannot be said that it is sufficiently simulated, and improvement in analysis accuracy is required.

  Therefore, the problem to be solved by the present invention is to provide a turbulent flow simulation method capable of improving the accuracy of numerical analysis of a flow field in which a swirl is generated.

  The turbulent flow simulation method according to the embodiment includes a step of obtaining a measurement result, a step of obtaining an analysis result, a step of calculating an error, a step of digitizing, a step of dividing, and a step of performing numerical analysis. In the step of acquiring the measurement result, the measurement result of the characteristic of the turbulent flow measured in the flow field where the swirl is generated is acquired. In the step of obtaining the analysis result, a numerical analysis is performed using the turbulent flow model and the first turbulent flow model coefficient corresponding to the turbulent flow model, and an analysis result of the characteristics of the turbulent flow in the flow field is obtained. In the step of calculating an error, an error between the obtained measurement result and the analysis result obtained by performing the numerical analysis is calculated. In the step of quantifying the correlation, a predetermined parameter having a correlation with the calculated error is designated, and the correlation between the error and the parameter is quantified over the entire region of the flow field. In the dividing step, the entire region of the flow field is divided into a first analysis region where the quantified correlation value exceeds a threshold value and a second analysis region where the correlation value is equal to or less than the threshold value. . In the numerical analysis step, the characteristics of the turbulent flow in the first analysis region are numerically analyzed using the turbulent flow model and the second turbulent model coefficient obtained by correcting the value of the first turbulent flow model coefficient. To do.

The functional block diagram which shows the structure of the turbulent flow simulation apparatus which concerns on embodiment. FIG. 2 is a cross-sectional view schematically showing a configuration of a Kaplan turbine that is a target for analyzing a flow field by the turbulent flow simulation apparatus of FIG. 1. The bird's-eye view which shows the state which has arrange | positioned the analysis grid | lattice in the flow field in the Kaplan water turbine of FIG. The figure which shows the relationship between the measurement result of the characteristic of the turbulent flow measured in the flow field in FIG. 2, and the analysis result which analyzed the characteristic of the turbulent flow of this flow field by the conventional numerical simulation. Explanatory drawing in the case of dividing | segmenting an analysis area | region with the turbulent flow simulation apparatus of FIG. The flowchart which shows the simulation method of the turbulent flow which concerns on embodiment.

Hereinafter, embodiments will be described with reference to the drawings.
The turbulent flow simulation method according to the present embodiment is realized using, for example, a turbulent flow simulation device 20 as shown in FIG. As shown in FIG. 1, the turbulent flow simulation apparatus 20 includes a measurement result acquisition unit 21, a numerical analysis unit 22, a condition setting unit 23, an error calculation unit 24, a correlation calculation unit 25, an analysis region division unit 26, a threshold storage. A unit 27, a turbulent model coefficient changing unit 28, and a turbulent model coefficient determining unit 29.

  Here, in this embodiment, as shown in FIG. 2, for example, a case where a numerical simulation is performed on a flow field in which a swirl (vortex) in a Kaplan Turbine 30 is generated is illustrated. As shown in FIG. 2, the Kaplan turbine 30 includes, for example, a casing 31 that is a spiral water pipe, a guide vane 32, a propeller-like impeller (runner) 33 including a runner vane 33a and a runner cone 33b, and a suction pipe. (Draft tube) 34 and the like.

  As shown in FIGS. 1 and 2, the measurement result acquisition unit 21 described above is a turbulence measured (actually measured) using, for example, a hot-wire anemometer or a laser anemometer in the flow field where the swirl in the suction pipe 34 is generated. Acquire measurement results of flow characteristics (measurement results such as flow velocity and pressure). As an example, the measurement result acquisition unit 21 acquires an axial flow velocity (flow velocity along the axial direction of the impeller 33) measured in a region immediately below the runner cone 33b of the impeller 33 in the suction pipe 34, and the like. To do.

  On the other hand, the numerical analysis unit 22 performs a numerical analysis using at least a predetermined turbulent model and a turbulent model coefficient (first turbulent model coefficient) corresponding to the turbulent model, in a flow field where a swirl is generated. Obtain analysis results of turbulent flow characteristics. As an example, the numerical analysis unit 22 acquires an axial flow velocity and the like obtained by numerical analysis of a region near the bottom of the runner cone 33b.

  Here, the numerical simulation using the turbulent flow model is generally RANS (Reynolds Averaged Navier-Stokes Simulation) suitable for steady-state analysis using a time average model such as an eddy viscosity model or a stress equation model (RSM: Reynolds Stress Model). LES (Large-Eddy Simulation), which can also perform transient analysis using a spatial average model. For the latter LES, for example, flow analysis with separation is known to have better analysis results than RANS, but the lattice dependency of the solution and the calculation load are high.

  On the other hand, in the former RANS, as an eddy viscosity model, for example, a zero equation model such as a Baldwin-Lomax model, a one equation model such as a Spalart-Allmaras model, and a two equation model such as a k-ε model or a k-ω model are exemplified. it can. Examples of the stress equation model for solving the Reynolds stress transport equation include the Gibson-Launder model and the Speziale-Sarkar-Gatski model.

  The 0 equation model described above has a low calculation load because it does not solve the transport equation. On the other hand, a flow analysis with separation is underestimated. In addition, the one-equation model solves only the eddy viscosity transport equation, and the flow analysis with separation is overestimated. Further, the two-equation model solves a transport equation of kinetic energy k and dissipation factor ε or specific dissipation factor ω (ε / k), and is not suitable for separation, swirl, and secondary flow analysis. On the other hand, the stress equation model provides better results of analysis of separation, swirling, and secondary flow than the eddy viscosity model.

  In the case of the standard k-ε model, the transport equation of kinetic energy k and dissipation factor ε is defined by the following equation.

In Equations 1 to 3, u represents velocity (flow velocity), ρ represents fluid density, E represents deformation velocity, μ represents eddy viscosity coefficient, and μ _t represents eddy viscosity. Further, C _μ , σ _k , σ _ε , C _1ε , and C _2ε indicate turbulent model coefficients (first turbulent model coefficients) corresponding to the standard k-ε model. The numerical analysis unit 22 of the turbulent flow simulation device 20 uses, for example, a numerical analysis using at least the standard k-ε model and a plurality of turbulent model coefficients (a plurality of first turbulent model coefficients) each having a fixed value. The function to perform.

  FIG. 3 illustrates a state in which an analysis grid (mesh) 35 is formed by the numerical analysis unit 22 with respect to a region in the suction pipe 34 of the Kaplan turbine 30. The numerical analysis unit 22 increases the orthogonality so as to minimize the degree of twist, which is said to have an adverse effect on the analysis result, and forms the analysis grid 35 having, for example, about 1 million grid points.

  As shown in FIGS. 1 and 3, the condition setting unit 23 gives conditions for each of the entrance boundary E1, the exit boundary E2, and the wall boundary E3. That is, the condition setting unit 23 uses the fluid velocity distribution at the inlet portion of the analysis region acquired by the measurement result acquisition unit 21 (the axis of the fluid at the E1 portion in FIGS. 2 and 3) as the boundary condition of the inlet boundary E1. The flow velocity [Axial Velocity] and the distribution of velocity [Tangential Velocity] of the tangential component of the flow in the E1 portion) are set as boundary conditions. In addition, the condition setting unit 23 sets the measurement result of the fluid pressure at the outlet portion of the analysis region acquired by the measurement result acquisition unit 21 as the boundary condition of the outlet boundary E2. Set wall function boundary conditions.

  Further, the numerical analysis unit 22 uses, for example, a finite volume method as a discretization method, a QUICK method as a convection term, and a simple method that integrates pressure and velocity as a differential decomposition method as an analysis method. Apply. Further, the numerical analysis unit 22 has a function of performing numerical analysis by applying, for example, an RSM (Reynolds Stress Model) or, for example, a Cubic k-ε model belonging to the standard k-ε model to the turbulent flow model.

  FIG. 4 shows the results of measurement of the turbulent flow characteristics measured in the flow region immediately below the impeller 33 (runner cone 33b) and the turbulent flow characteristics in this flow region by conventional numerical simulation (turbulent flow model and fixed value turbulence). It is a figure which shows the relationship with the analysis result analyzed by the conventional numerical analysis using a flow model coefficient. Specifically, FIG. 4 shows the radial position of the impeller 33 in the flow region directly below the impeller 33, the measurement result of the axial flow velocity in the flow region directly below the impeller 33, and Cubic k-ε. The relationship between the model and the analysis result of the axial flow velocity by RSM is shown.

  As shown in FIG. 4, the root portion (base end portion of the rotating machine) corresponding to a position of about 70 mm from the rotation center of the impeller 33 (runner) to the outer diameter side, and the impeller 33 on the basis of this rotation center. With the tip part (the tip part of the rotating machine) corresponding to the outer diameter side of about 150 mm to 260 mm, the analysis result of both the Cubic k-ε model and the RSM is appropriate for the measurement result (measured measurement result). It can be seen that it has not been simulated.

  That is, an existing numerical simulation method using a predetermined turbulence model and a fixed turbulence model coefficient corresponding to the turbulence model in a flow field in which a swirl occurs immediately below the impeller (downstream of the rotor blade). Even if the measurement result can be simulated qualitatively, it is difficult to simulate the measurement result quantitatively. In the analysis of the flow field in which the swirl is generated not only in the Kaplan turbine but also in the rotating machine, it is assumed that the same result is obtained.

  Therefore, as shown in FIG. 1, the turbulent flow simulation apparatus 20 according to the present embodiment includes the error calculating unit 24, the correlation calculating unit 25, the analysis region dividing unit 26, the threshold storage unit 27, and the turbulent model coefficient changing unit. 28 and a turbulence model coefficient determination unit 29 are further provided.

  The error calculation unit 24 includes a measurement result such as a flow velocity acquired by the measurement result acquisition unit 21 and an analysis result such as a flow velocity obtained by numerical analysis by the numerical analysis unit 22 (a predetermined turbulence model and a turbulent flow model). And an error from a numerical analysis result using a corresponding fixed value of the first turbulent model coefficient. The correlation calculation unit 25 having a function as a correlation parameter setting unit designates a predetermined parameter such as vorticity (ζ) having a correlation (Correlation) with respect to the error calculated by the error calculation unit 24 (correlation). The parameter is set), and the correlation between the error and the parameter (correlation according to the radial position of the impeller 33) is quantified over the entire flow field that is the target of the error calculation.

  As shown in FIG. 5, the analysis region dividing unit 26 divides the entire region of the flow field, which is an error calculation target by the error calculation unit 24, in the radial direction of the swirl (impeller 33). Specifically, the analysis region dividing unit 26 uses the first analysis region (the correlation value quantified by the correlation calculation unit 25 exceeds the threshold value) as a region of the entire flow field that is an error calculation target. A region A [root portion], a region C [chip portion]) having a large correlation is divided into a second analysis region (region B having a small correlation) whose numerical correlation value is equal to or less than a threshold value. The threshold value storage unit 27 stores in advance a threshold value (threshold value corresponding to the correlation value) that the analysis region dividing unit 26 refers to when dividing the region.

  Further, the numerical analysis unit 22 described above has a predetermined turbulence model such as a Cubic k-ε model or an RSM, and a value of a turbulence model coefficient (first turbulence model coefficient) corresponding to the predetermined turbulence model. The characteristic of the turbulent flow in the first analysis region (region A and region C shown in FIG. 5) is numerically analyzed (numerical simulation) using the second turbulent model coefficient corrected for. Further, the numerical analysis unit 22 uses a predetermined turbulence model and a turbulence model coefficient (first turbulence model coefficient) corresponding to the predetermined turbulence model to generate a second analysis region (FIG. 5). Numerical analysis is performed on the characteristics of turbulent flow in the region B) shown.

  Here, the second turbulent model coefficient described above is obtained as follows. That is, the turbulent model coefficient changing unit 28 increases or decreases the value of the first turbulent model coefficient in stages, and sequentially replaces the first turbulent model coefficient with a plurality of temporary turbulent model coefficients. On the other hand, the numerical analysis unit 22 repeats numerical analysis of the characteristics of the turbulent flow in the first analysis region by sequentially using the predetermined turbulent flow model and one of the plurality of temporary turbulent flow model coefficients ( Perform turbulence model coefficient change analysis). Further, the turbulent model coefficient determining unit 29 is configured to use the temporary turbulent model when the error between the analysis result of the numerical analysis repeatedly performed and the measurement result acquired by the measurement result acquiring unit 21 becomes the smallest. The coefficient value is detected as the second turbulent model coefficient.

Next, a turbulent flow simulation method according to this embodiment will be described mainly based on the flowchart shown in FIG. First, the measurement result acquisition unit 21 acquires a measurement result (Vefd) of a turbulent flow characteristic (such as an axial flow velocity) measured in a flow field in which a swirl is generated (just below the runner cone 33b shown in FIG. 2). On the other hand, the numerical analysis unit 22 includes a predetermined turbulence model (for example, a standard k-ε model) and a first turbulence model coefficient corresponding to the turbulence model (for example, C _μ and σ _k illustrated in Equation 4). , Σ _ε , C _1ε , C _{2ε, and the} like) and obtain an analysis result (Vcfd) of turbulent flow characteristics (axial velocity, etc.) in the flow field where swirling occurs.

  Next, as shown in FIG. 6, the error calculation unit 24 calculates an error (Error) between the measurement result (Vefd) such as the flow velocity and the analysis result (Vcfd) such as the flow velocity obtained by numerical analysis ( S1). Further, the correlation calculation unit 25 designates a predetermined parameter such as vorticity (ζ) having a correlation (Correlation) with respect to this error, and the entire flow field (runner cone) subjected to error calculation is designated. The correlation between the error and the parameter is converted into a numerical value over the region immediately below (33b) (S2).

  Subsequently, as illustrated in FIG. 6, when the quantified correlation exceeds the threshold (Yes in S <b> 3), the analysis region dividing unit 26 determines the flow field that is an error calculation target as illustrated in FIG. 5. The entire region is divided into a first analysis region (region A or region C having a large correlation) such as a route portion or a chip portion where the correlation value exceeds a threshold value, and a first correlation region whose numerical correlation value is equal to or less than the threshold value. It is divided into two analysis regions (region B having a small correlation) (S4).

  Next, the numerical analysis unit 22 includes a second turbulence model coefficient obtained by correcting the value of the first turbulence model coefficient by the turbulence model coefficient changing unit 28 and the turbulence model coefficient determination unit 29, a turbulence model, (By turbulent model coefficient change analysis), numerically analyze the characteristics of turbulent flow in the first analysis region (region A and region C shown in FIG. 5) (S5). Further, the numerical analysis unit 22 performs a numerical analysis on the second analysis region (region B shown in FIG. 5) using the first turbulent model coefficient and the turbulent model.

  As described above, according to the turbulent flow simulation method according to the present embodiment, the measurement result of the turbulent flow characteristic in the flow field where the swirl is generated and the analysis result by the initial numerical analysis are effectively fused. The accuracy of the final numerical analysis (numerical simulation) can be improved without causing a significant increase in cost. Thereby, the performance of the fluid machine which can generate | occur | produce a swirl can be improved.

  As mentioned above, although embodiment of this invention was described, this embodiment is shown as an example and is not intending limiting the range of invention. The novel embodiment can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the scope of the invention. This embodiment and its modifications are included in the scope and gist of the invention, and are included in the invention described in the claims and the equivalents thereof.

  For example, the turbulent flow simulation method and the turbulent flow simulation apparatus 20 according to the present embodiment can be applied not only to Kaplan turbines, but also to Francis turbines and any fluid machine that can generate swirl.

  1 are shown as functional blocks in FIG. 1 including each component (the error calculating unit 24, the analysis region dividing unit 26, the turbulent flow model coefficient changing unit 28, etc.) included in the turbulent flow simulation apparatus 20 of the present embodiment. The turbulent flow simulation program that can be executed by the computer may be configured, and further, the turbulent flow simulation program may be stored in a storage medium such as an optical disk or a semiconductor memory and distributed. It is also possible.

  DESCRIPTION OF SYMBOLS 20 ... Turbulent flow simulation apparatus, 21 ... Measurement result acquisition part, 22 ... Numerical analysis part, 24 ... Error calculation part, 25 ... Correlation calculation part, 26 ... Analysis area division part, 27 ... Threshold storage part, 28 ... Turbulence Model coefficient changing unit, 29... Turbulent model coefficient determining unit.

Claims (5)

Obtaining a measurement result of the characteristics of the turbulent flow measured in the flow field where the swirl is generated;
Performing numerical analysis using a turbulent flow model and a first turbulent flow model coefficient corresponding to the turbulent flow model to obtain an analysis result of characteristics of the turbulent flow in the flow field;
Calculating an error between the obtained measurement result and the analysis result obtained by the numerical analysis;
Specifying a predetermined parameter having a correlation with the calculated error, and quantifying the correlation between the error and the parameter over a region of the entire flow field;
Dividing the region of the entire flow field into a first analysis region where the quantified correlation value exceeds a threshold value and a second analysis region where the correlation value is equal to or less than the threshold value;
Numerically analyzing turbulent flow characteristics in the first analysis region using the turbulent flow model and a second turbulent flow model coefficient obtained by correcting the value of the first turbulent flow model coefficient;
A turbulent flow simulation method comprising: Numerically analyzing turbulent flow characteristics in the second analysis region using the turbulent flow model and the first turbulent model coefficient;
The turbulent flow simulation method according to claim 1, further comprising: Using the turbulence model and one of a plurality of temporary turbulence model coefficients obtained by gradually increasing or decreasing the value of the first turbulence model coefficient in turn, the turbulence model in the first analysis region is used. Numerical analysis of flow characteristics is repeated, and the value of the temporary turbulence model coefficient when the error between the analysis result of the numerical analysis and the measurement result is minimized is detected as the second turbulence model coefficient Step to do,
The turbulent flow simulation method according to claim 1, further comprising: In the dividing step, the first and second analysis regions are set by dividing the entire region of the flow field in the radial direction of the swirl.
The turbulent flow simulation method according to any one of claims 1 to 3. In the step of obtaining the measurement result and the step of obtaining the analysis result, the flow velocity is obtained as the measurement result and the analysis result, respectively.
In the step of quantifying the correlation, vorticity is designated as the parameter.
The turbulent flow simulation method according to any one of claims 1 to 4.

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