Calculation method of turbulent diffusion force in rotating water-sediment two-phase flow based on adaptive scale ratio

Abstract

The present invention discloses a method for calculating the turbulent diffusion force of a rotating water-sand two-phase flow based on an adaptive scale ratio, which belongs to the field of engineering computational fluid dynamics. It mainly includes: introducing an energetic scale ratio and a Coriolis scale ratio with flow adaptability to respectively characterize the regulating effect of rotating turbulence on the following behavior of heavy particles and the gain effect on the momentum exchange of water and sand; calculating the phase diffusion factor, phase turbulence factor, group following factor and coupling intensity factor of the rotating water-sand flow to determine the turbulent diffusion force coefficient suitable for the conditions of rotating water and sand flow; and modifying the classic Favre turbulent diffusion force model to obtain a new model. The present invention introduces a dynamic scale ratio function with flow adaptability to reflect the following behavior of heavy particles of sediment on the turbulent eddy of water flow and their interaction, which can effectively adjust the turbulent diffusion capacity of heavy particles. It can directly adapt to the flow characteristics of the rotating water-sand two-phase flow in hydraulic machinery, and effectively avoid the problems of poor applicability and low prediction accuracy of existing methods.

Description

Technical Field

[0001] The invention belongs to the field of engineering computational fluid dynamics, and in particular relates to a method for calculating turbulent diffusion force of rotating water-sand two-phase flow based on an adaptive scale ratio. Background Art

[0002] Rotating water-sand two-phase flow is a common engineering flow phenomenon in hydraulic machinery. It has a significant impact on the energy conversion characteristics, pressure pulsation characteristics, and abrasion characteristics of equipment such as turbines and pumps. Accurately predicting the characteristics of rotating water-sand two-phase flow fields is an engineering requirement for studying the internal flow characteristics of hydraulic machinery. Rotating turbulence in hydraulic machinery has the characteristics of strong transients and high pulsation. The turbulent diffusion behavior of heavy-grained sediment in it is an important factor affecting the interaction between water and sediment phases. However, existing methods generally model it as a diffusion term in the mass equation and use a constant diffusion coefficient calibrated for gas phase conditions. In actual applications, it is found that this approach often underestimates the turbulent diffusion capacity of heavy-grained sediment in water turbulence, which seriously affects the prediction accuracy of important distributions such as sediment concentration and abrasion rate. Therefore, there is currently a lack of turbulent diffusion force models that are directly applicable to rotating water-sand flow conditions. It is necessary to develop a new turbulent diffusion force calculation method to better serve the engineering calculation of hydraulic machinery. Summary of the invention

[0003] The purpose of the present invention is to propose a method for calculating the turbulent diffusion force of a rotating water-sand two-phase flow based on an adaptive scale ratio, which is characterized by comprising the following steps:

[0004] Step 1: Introduce the energetic scale ratio d e , to characterize the regulatory effect of water turbulence on the sand particle following behavior;

[0005] Step 2: According to the energy scale ratio d e Determining the phase diffusion factor m for rotating water-sand flows d ;

[0006] Step 3: Introduce the Coriolis scale ratio d k , to characterize the gain effect of rotating turbulence on water-sediment momentum exchange;

[0007] Step 4: According to the Korotkoff scale ratio d k Determination of the phase turbulence factor m of rotating water-sand flow t ;

[0008] Step 5: According to the Stokes number S of the sand grain T Concentration C S Determine the group following factor m respectively f and coupling intensity factor m i ;

[0009] Step 6: Use the classic Favre turbulent diffusion force F in multiphase flow numerical calculation TD Based on the phase diffusion factor m d , phase turbulence factor m t , Group following factor m f and coupling intensity factor m i To determine the turbulent diffusion coefficient C required for rotating water-sand flow calculations TD , and the Favre turbulent diffusion force F TD The corrected rotating water-sand turbulent diffusion force F TD* After being added to the momentum equation in the form of a source term, it can be directly used for the numerical calculation of the rotating water-sand two-phase flow field in hydraulic machinery;

[0010] The energetic scale ratio d e It is derived from the following formula:

[0011]

[0012] Among them, d s is the diameter of sand particles, k w is the turbulent kinetic energy of the water phase, ε w is the water phase turbulent dissipation rate;

[0013] The phase diffusion factor m d It is derived from the following formula:

[0014]

[0015] in, Represents the natural exponential function of the variables, f1 is the first diffusion constant, f2 is the second diffusion constant, and f3 is the third diffusion constant.

[0016] The Korotkoff scale ratio d k It is derived from the following formula:

[0017]

[0018] Among them, d s is the diameter of sand particles, υ w is the kinematic viscosity of the water phase, ε w is the water phase turbulent dissipation rate.

[0019] The phase turbulence factor m t It is derived from the following formula:

[0020]

[0021] Among them, f4 is the first turbulence constant and f5 is the second turbulence constant.

[0022] The group following factor m fIt is derived from the following formula:

[0023] m f =1+f6·exp(f7·S Tmax )

[0024] Among them, S Tmax is the maximum Stokes number of sand particles in the computational domain, f6 is the first group following constant, and f7 is the second group following constant.

[0025] The coupling intensity factor m i It is derived from the following formula:

[0026]

[0027] in, is the average sand phase concentration in the calculation domain, f8 is the first coupling intensity constant, and f9 is the second coupling intensity constant.

[0028] The rotating water-sand turbulent diffusion coefficient C TD It is derived from the following formula:

[0029] C TD =m d ·m t ·m f ·m i

[0030] The classical Favre turbulent diffusion force F in multiphase flow TD Based on, the correction is made according to the following formula:

[0031] F TD *=C TD ·F TD

[0032] The first diffusion constant f1=1594.8, the second diffusion constant f2=-1.26, the third diffusion constant f3=2; the first turbulence constant f4=0.00088, the second turbulence constant f5=3;

[0033] The first group follows a constant f6=2, and the second group follows a constant f7=-0.01;

[0034] The first coupling intensity constant f8=1.5, and the second group following constant f9=-1.

[0035] The beneficial effects of the present invention are as follows: (1) a dynamic scale ratio function with flow adaptability is introduced to reflect the following behavior of heavy particle sediment on water flow turbulence and their interaction, which can effectively adjust the turbulent diffusion capacity of particles; (2) the empirical expression can directly adapt to the flow characteristics of rotating water-sand two-phase flow in hydraulic machinery, avoiding the problems of poor applicability and low prediction accuracy of existing methods, and providing new ideas for engineering calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The cross-sectional grid and longitudinal coordinate diagram of the computational domain for the straight pipe water-sand two-phase flow example;

[0037] Figure 2 This is a comparison diagram of the relative concentration distribution of sediment along the water depth direction in the straight pipe example;

[0038] Figure 3 Schematic diagram of the computational domain grid and flow direction coordinates for the example of water-sand two-phase flow in a curved pipe; a is the cross-sectional view of the curved pipe, and b is the schematic diagram of the curved pipe.

[0039] Figure 4 This is a comparison diagram of the depth wear rate distribution of the outer wall along the flow direction in the elbow example;

[0040] Figure 5 The present invention is a flowchart for the implementation of the method for calculating the turbulent diffusion force of rotating water and sand based on the adaptive scale ratio. DETAILED DESCRIPTION

[0041] The present invention proposes a method for calculating the turbulent diffusion force of a rotating water-sand two-phase flow based on an adaptive scale ratio. The present invention is further described below in conjunction with the accompanying drawings and specific implementation methods.

[0042] like Figure 1 and Figure 3 {a, b} show the computational domain and computational grid diagrams of the straight circular pipe water-sand two-phase flow example and the curved pipe water-sand two-phase flow example, respectively. Both examples are classic test cases for the development of rotating water-sand two-phase flow models in hydraulic machinery and their systems. In the straight circular pipe example, the incoming flow Reynolds number Re = 2.2×10 5 , the volume concentration of incoming sediment C S =5%, incoming sand particle diameter d s =440μm; in the elbow calculation example, the incoming flow Reynolds number Re = 2.0×10 5 , the volume concentration of incoming sediment C S =1.13%, incoming sand particle diameter d s =450μm. For these two examples, the above-mentioned method for calculating the turbulent diffusion force of rotating water-sand two-phase flow based on adaptive scale ratio can be implemented according to the following process, which specifically includes the following steps: (e.g. Figure 5 (shown)

[0043] Step 1: Introduce the energetic scale ratio d e To characterize the regulatory effect of water turbulence on sand particle following behavior;

[0044] Step 2: According to the energy scale ratio d e Determining the phase diffusion factor m for rotating water-sand flows d ;

[0045] Step 3: Introduce the Coriolis scale ratio d k To characterize the gain effect of rotating turbulence on water-sediment momentum exchange;

[0046] Step 4: According to the Korotkoff scale ratio d k Determination of the phase turbulence factor m of rotating water-sand flow t ;

[0047] Step 5: According to the Stokes number S of the sand grain T Concentration C S Determine the group following factor m respectively f and coupling intensity factor m i ;

[0048] Step 6: Use the classic Favre turbulent diffusion force F in multiphase flow numerical calculation TD Based on the phase diffusion factor m d , phase turbulence factor m t , Group following factor m f and coupling intensity factor m i To determine the turbulent diffusion coefficient C required for rotating water-sand flow calculations TD , and the Favre turbulent diffusion force F TD The corrected rotating water-sand turbulent diffusion force F TD* After being added to the momentum equation in the form of a source term, it can be directly used for the numerical calculation of the rotating water-sand two-phase flow field in hydraulic machinery;

[0049] The energetic scale ratio d e It is derived from the following formula:

[0050]

[0051] Among them, d s is the diameter of sand particles, k w is the turbulent kinetic energy of the water phase, ε w is the water phase turbulent dissipation rate;

[0052] The phase diffusion factor m d It is derived from the following formula:

[0053]

[0054] in, Represents the natural exponential function of the variables, f1 is the first diffusion constant, f2 is the second diffusion constant, and f3 is the third diffusion constant.

[0055] The Korotkoff scale ratio d k It is derived from the following formula:

[0056]

[0057] Among them, d s is the diameter of sand particles, υ w is the kinematic viscosity of the water phase, ε w is the water phase turbulent dissipation rate.

[0058] The phase turbulence factor m t It is derived from the following formula:

[0059]

[0060] Among them, f4 is the first turbulence constant and f5 is the second turbulence constant.

[0061] The group following factor m f It is derived from the following formula:

[0062] m f =1+f6·exp(f7·S Tmax )

[0063] Among them, S Tmax is the maximum Stokes number of sand particles in the computational domain, f6 is the first group following constant, and f7 is the second group following constant.

[0064] The coupling intensity factor m i It is derived from the following formula:

[0065]

[0066] in, is the average sand phase concentration in the calculation domain, f8 is the first coupling intensity constant, and f9 is the second coupling intensity constant.

[0067] The rotating water-sand turbulent diffusion coefficient C TD It is derived from the following formula:

[0068] C TD =m d ·m t ·m f ·m i

[0069] The classical Favre turbulent diffusion force F in multiphase flow TDBased on, the correction is made according to the following formula:

[0070] F TD *=C TD ·F TD

[0071] Preferably, the first diffusion constant f1 is preferably 1594.8, the second diffusion constant f2 is preferably -1.26, and the third diffusion constant f3 is preferably 2; the first turbulence constant f4 is preferably 0.00088, and the second turbulence constant f5 is preferably 3; the first group following constant f6 is preferably 2, and the second group following constant f7 is preferably -0.01; the first coupling intensity constant f8 is preferably 1.5, and the second group following constant f9 is preferably -1. It should also be noted that in the actual calculation process, the order of each step can be appropriately adjusted according to actual needs, and is not limited here.

[0072] In this embodiment, high-quality hexahedral meshes are used to spatially discretize the computational domain, and the total number of meshes in the two examples is about 1.07 million. After the new method proposed in the present invention is introduced, the full implicit coupling solution technology is used for steady-state calculation. In addition, in order to better show the advantages of the new method, the prediction results of the existing method are also compared. Figure 2 The figure shows the relative concentration distribution of sediment along the water depth in the straight pipe example; Figure 4 The figure shows the comparison of the depth wear rate distribution of the outer wall along the flow direction in the elbow calculation example. It can be seen from the analysis that compared with the existing method, the prediction results of the new method proposed in the present invention are closer to the experimental values, that is, it can more accurately obtain the characteristics of the rotating water-sand flow field and is more suitable for the calculation of water-sand two-phase flow in hydraulic machinery.

[0073] In summary, the outstanding advantages of the method for calculating the turbulent diffusion force of rotating water-sand two-phase flow based on adaptive scale ratio proposed in the present invention are: (1) a dynamic scale ratio function with flow adaptability is introduced to reflect the following behavior of heavy particle sediment on water turbulence and their interaction, which can effectively adjust the turbulent diffusion capacity of particles; (2) the empirical expression can directly adapt to the flow characteristics of rotating water-sand two-phase flow in hydraulic machinery, avoiding the problems of poor applicability and low prediction accuracy of existing methods, and can provide new ideas for engineering calculations.

Claims

1. A method for calculating the turbulent diffusion force of rotating water-sand two-phase flow based on adaptive scale ratio, characterized in that The method comprises the following steps: Step 1: Introduce the energetic scale ratio d e To characterize the regulatory effect of water turbulence on sand particle following behavior; Step 2: According to the energy scale ratio d e Determining the phase diffusion factor m for rotating water-sand flows d ; Step 3: Introduce the Coriolis scale ratio d k To characterize the gain effect of rotating turbulence on water-sediment momentum exchange; Step 4: According to the Korotkoff scale ratio d k Determination of the phase turbulence factor m of rotating water-sand flow t ; Step 5: According to the Stokes number S of the sand grain T Concentration C S Determine the group following factor m respectively f and coupling intensity factor m i ; Step 6: Use the classic Favre turbulent diffusion force F in multiphase flow numerical calculation TD Based on the phase diffusion factor m d , phase turbulence factor m t , Group following factor m f and coupling intensity factor m i To determine the turbulent diffusion coefficient C required for rotating water-sand flow calculations TD , and the Favre turbulent diffusion force F TD The correction is made to the rotating water-sand turbulent diffusion force After being added to the momentum equation in the form of a source term, it can be directly used for the numerical calculation of the rotating water-sand two-phase flow field in hydraulic machinery; The energetic scale ratio d e It is derived from the following formula: Among them, d s is the diameter of sand particles, k w is the turbulent kinetic energy of the water phase, ε w is the water phase turbulent dissipation rate; The phase diffusion factor m d It is derived from the following formula: in, Represents the natural exponential function of the variables, f1 is the first diffusion constant, f2 is the second diffusion constant, and f3 is the third diffusion constant; The Korotkoff scale ratio d k It is derived from the following formula: Among them, d s is the diameter of sand particles, υ w is the kinematic viscosity of the water phase, ε w is the water phase turbulent dissipation rate; The phase turbulence factor m t It is derived from the following formula: Among them, f4 is the first turbulence constant, f5 is the second turbulence constant; The group following factor m f It is derived from the following formula: m f =1+f6·exp(f7·S Tmax ) Among them, S Tmax is the maximum Stokes number of sand particles in the computational domain, f6 is the first group following constant, and f7 is the second group following constant; The coupling intensity factor m i It is derived from the following formula: in, is the average sand phase concentration in the calculation domain, f8 is the first coupling intensity constant, and f9 is the second coupling intensity constant. The rotating water-sand turbulent diffusion coefficient C TD It is derived from the following formula: C TD =m d ·m t ·m f ·m i , The classical Favre turbulent diffusion force F in multiphase flow TD Based on, the correction is made according to the following formula:

2. The method for calculating turbulent diffusion force of rotating water-sand two-phase flow based on adaptive scale ratio according to claim 1 is characterized in that: The first diffusion constant f1=1594.8, the second diffusion constant f2=-1.26, and the third diffusion constant f3=2.

3. The method for calculating turbulent diffusion force of rotating water-sand two-phase flow based on adaptive scale ratio according to claim 1 is characterized in that: The first turbulence constant f4=0.00088, and the second turbulence constant f5=3.

4. The method for calculating turbulent diffusion force of rotating water-sand two-phase flow based on adaptive scale ratio according to claim 1 is characterized in that: The first group follows a constant f6=2, and the second group follows a constant f7=-0.

01.

5. The method for calculating turbulent diffusion force of rotating water-sand two-phase flow based on adaptive scale ratio according to claim 1 is characterized in that: The first coupling intensity constant f8=1.5, and the second group following constant f9=-1.

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