Rapid calculation method for water-sand two-phase flow of suspended load fine particles in water pump

Abstract

The invention relates to the technical field of engineering computational fluid mechanics, and provides a rapid calculation method for water-sediment two-phase flow of suspended load fine particles in a water pump, and the rapid calculation method comprises the following steps: firstly, under the nominal sediment concentration condition, defining an interaction retardation factor to represent the interaction retardation effect between water-sediment two-phase movement; determining a sand phase velocity calculation formula; then determining an interactive retardation source item, and adding the interactive retardation source item into a water phase momentum equation to reflect the momentum change of a water phase under the influence of suspended load fine particles; and finally, sequentially solving the sand phase velocity and the water phase velocity under a transient numerical calculation framework of the water pump. According to the rapid calculation method, separated solution of the concentration field and the velocity field of the water-sand two-phase flow of the suspended load fine particles in the water pump is fully achieved, the characteristics of the water-sand two-phase flow of the suspended load fine particles in the water pump can be accurately and efficiently predicted, and the aim of considering calculation precision and calculation efficiency is achieved; therefore, a new thought is provided for large-scale complex engineering calculation.

Description

Technical Field

[0001] The invention relates to the technical field of engineering computational fluid dynamics, and in particular to a fast calculation method for water-sand two-phase flow of suspended fine particles inside a water pump. Background Art

[0002] The water-sand two-phase flow of suspended fine particles inside a water pump is the most common flow in engineering. In numerical calculations, the high-precision two-fluid algorithm recognized in engineering can fully describe the dynamic characteristics of the water and sand phases and their coupling effects, but it has the defects of a large number of equations, high coupling between equations, and a large amount of calculation. It is only suitable as a high-precision verification algorithm and is not suitable for large-scale complex engineering calculations.

[0003] There are two main simplified algorithms to improve computational efficiency: the miscible algorithm and the single-phase algorithm. The miscible algorithm treats the water and sediment phases as a mixed phase through concentration-weighted averaging and obtains the miscible control equations. The concentration field and velocity field are coupled and solved. The velocity slip caused by the interaction between the water and sediment phases is described by the algebraic slip model. The single-phase algorithm takes the water phase as the main research subject, and the interphase coupling effect is completely abandoned. The sediment movement is passively attached to the water flow movement. The water phase flow field is solved by the single-phase flow algorithm, and based on this result, the sediment diffusion equation is used to solve the sand phase concentration field.

[0004] Comparing these two simplified algorithms, we can see that the prediction accuracy of the mixed phase algorithm is relatively higher, but due to the forced coupling of the concentration field and the velocity field, the iterative calculation of the slip velocity and its related terms, the calculation efficiency and flexibility are relatively low; the single-phase calculation method allows the concentration field and the velocity field to be solved separately, and the calculation efficiency and flexibility are relatively high, but the prediction accuracy is relatively low due to the neglect of the water-sand phase interaction. Obviously, these two simplified algorithms cannot accurately and efficiently predict the suspended fine particle water-sand two-phase flow characteristics inside the pump, which seriously limits the development of large-scale complex engineering calculations. Summary of the invention

[0005] The present invention provides a fast calculation method for the two-phase flow of suspended fine particles in a water pump, so as to solve the problem that the related technology is currently unable to efficiently calculate the two-phase flow characteristics of suspended fine particles in a water pump. The fast calculation method of the present invention can overcome the common defects of the existing simplified algorithms, thereby achieving the goal of balancing calculation accuracy and calculation efficiency.

[0006] The present invention provides a fast calculation method for water-sand two-phase flow of suspended fine particles inside a water pump, comprising: Defining the interaction blocker , the mutual retardation factor is used to characterize the retardation between the movement of the sand phase and the movement of the water phase; Based on the interaction inhibitor , determine the sand phase velocity u s The algebraic formula of ; Using the interaction inhibitor and the sand phase velocity u s The algebraic formula for determining the interaction retardation source term , the interaction blocking source term It is used to characterize the effect of sand phase motion on water phase momentum; The interaction blocking source term Added to the water phase momentum equation to reflect the momentum change of the water phase under the influence of suspended fine particles; Using the transient numerical calculation framework of the water pump, the sand phase velocity is solved u s The algebraic formula for obtaining the sand phase velocity u s ; Solve to add the interaction blocking source term The water phase momentum equation is used to obtain the water phase velocity.

[0007] According to a fast calculation method for suspended fine particle water-sand two-phase flow in a water pump provided by the present invention, the defined interaction retardation factor , obtained from the following expression: Expression 1: In the formula, r f is the density of the water phase, r s is the density of the sand phase, α s is the nominal volume concentration of the sand phase, α f =1- α s is the nominal volume concentration of the aqueous phase, d s is the diameter of the sediment particles, u f is the water phase velocity vector, u s is the sand phase velocity vector, Re s = r f | u f - u s | / m f is the sand phase particle Reynolds number, m f is the dynamic viscosity of the water phase, m1、 m 2、 m 3、 m 4、 m 5、 m 6、 m 7、 m 8、 m 9 are all empirical coefficients.

[0008] According to a fast calculation method for water-sand two-phase flow of suspended fine particles in a water pump provided by the present invention, the empirical coefficient in the interaction retardation factor is: m 1=1, m 2=1, m 3 = -1, m 4=18, m 5 = -2.65, m 6 = -1, m 7=2.7, m 8 = -1.963, m 9=0.313.

[0009] According to a fast calculation method for water-sand two-phase flow of suspended fine particles in a water pump provided by the present invention, the sand phase velocity u s , obtained from the following expression 2: Expression 2: In the formula, δt is the time step used in transient numerical calculations, u s is the sand phase velocity vector that needs to be solved at the current moment, u ʹ s is the sand phase velocity vector solved at the previous moment, m s is the dynamic viscosity of the sand phase, g is the acceleration due to gravity, m ts is the turbulent viscosity of the sand phase, is the Laplace term of the sand phase velocity solved at the previous moment, is the pressure gradient.

[0010] According to a fast calculation method for suspended fine particle water-sand two-phase flow in a water pump provided by the present invention, the interactive retardation source term , obtained from the following expression three: Expression three: In the formula, r s is the density of the sand phase, α s is the nominal volume concentration of the sand phase, α f =1- α s is the nominal volume concentration of the aqueous phase, u f is the water phase velocity vector, u s is the sand phase velocity vector.

[0011] According to a fast calculation method for suspended fine particle water-sand two-phase flow in a water pump provided by the present invention, in the interaction retardation factor The expression of the interaction blocking source term In the expression, the nominal volume concentration of the sand phase is α s It is the average sand phase volume concentration of the inflow from the water intake pump.

[0012] According to a fast calculation method for water-sand two-phase flow of suspended fine particles in a water pump provided by the present invention, under a certain working condition that the user is concerned about, α s It is a constant value and does not change with time and space.

[0013] The present invention provides a fast calculation method for the two-phase flow of water and sand with suspended fine particles inside a water pump. The fast calculation method of the present invention fully realizes the separate solution of the concentration field and the velocity field of the two-phase flow of water and sand with suspended fine particles inside the water pump, and can accurately and efficiently predict the two-phase flow characteristics of water and sand with suspended fine particles inside the water pump, achieving the goal of balancing calculation accuracy and calculation efficiency, thereby providing a new idea for large-scale complex engineering calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the technical solutions in the present invention or related technologies, the following briefly introduces the drawings required for use in the embodiments or related technical descriptions. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0015] Figure 1 It is a comparison diagram of the predicted effects of the water pump suspended fine particle water-sand two-phase flow characteristics provided by the present invention.

[0016] Figure 2 It is a schematic diagram of the water pump impeller flow channel monitoring line provided by the present invention.

[0017] Figure 3 The present invention provides an operation flow chart of a fast calculation method for water pump suspended fine particle water-sand two-phase flow. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] Combine the following Figure 1-Figure 3 The invention describes a fast calculation method for water-sand two-phase flow of suspended fine particles inside a water pump.

[0020] It is understandable that, referring to Figure 3 In an embodiment of the present invention, the present invention provides a fast calculation method for water-sand two-phase flow of suspended fine particles inside a water pump, comprising: A1: Define the interaction blocker , the mutual retardation factor is used to characterize the retardation between the movement of the sand phase and the movement of the water phase; A2: Based on the interaction retardation factor , determine the sand phase velocity u s The algebraic formula of ; A3: Using cross-reaction blocking factors and sand phase velocity u s The algebraic formula for determining the interaction retardation source term , the interaction blocking source term It is used to characterize the effect of sand phase motion on water phase momentum; A4: Interaction blocking source Added to the water phase momentum equation to reflect the momentum change of the water phase under the influence of suspended fine particles; A5: Using the well-known water pump transient numerical calculation framework in the field of engineering computational fluids, solve the A2 sand phase velocity u s The algebraic formula for obtaining the sand phase velocity u s ; Solve A4 and add interactive blocking source terms The water phase momentum equation is used to obtain the water phase velocity.

[0021] The present invention provides a fast calculation method for the two-phase flow of water and sand with suspended fine particles inside a water pump. The fast calculation method of the present invention fully realizes the separate solution of the concentration field and the velocity field of the two-phase flow of water and sand with suspended fine particles inside the water pump, and can accurately and efficiently predict the two-phase flow characteristics of water and sand with suspended fine particles inside the water pump, achieving the goal of balancing calculation accuracy and calculation efficiency, thereby providing a new idea for large-scale complex engineering calculations.

[0022] In the embodiment of the present invention, when defining the interaction retardation factor Before, obtain the relevant operating parameters of the water pump, including: rated speed n d , Design flow Q d and design head H d .

[0023] Specifically, the embodiment is a typical water-sand two-phase flow calculation example of suspended fine particles in a water pump. The research object is a vertical centrifugal pump with a specific speed of 106 and a rated speed of n d =800r / min, design flow rate Q d =286m 3 / s, design head H d =36m, sand phase particle density r s 2650kg∙m -3 , sand phase particle diameter d s 25 μm, nominal volume concentration of sand phase (i.e. average volume concentration of sand phase at the pump inlet) α s Under the condition of 0.38%, for this example, the calculation idea of ​​the fast calculation method for water-sand two-phase flow of suspended fine particles in water pumps is implemented.

[0024] In the embodiment of the present invention, the interaction retardation factor is defined as , obtained from the following expression: Expression 1: In the formula, r f is the density of the water phase, r s is the density of the sand phase, α s is the nominal volume concentration of the sand phase, α f =1- α sis the nominal volume concentration of the aqueous phase, d s is the diameter of the sediment particles, u f is the water phase velocity vector, u s is the sand phase velocity vector, Re s = r f | u f - u s | / m f is the sand phase particle Reynolds number, m f is the dynamic viscosity of the water phase, m 1、 m 2、 m 3、 m 4、 m 5、 m 6、 m 7、 m 8、 m 9 are all empirical coefficients.

[0025] Among them, in the embodiment of the present invention, through optimization, the empirical coefficient in the interaction retardation factor is: m 1=1, m 2=1, m 3 = -1, m 4=18, m 5 = -2.65, m 6 = -1, m 7=2.7, m 8 = -1.963, m 9=0.313.

[0026] It should be noted that the relevant empirical coefficient m 1- m 9 was obtained for the first time through a research method that combines “theoretical analysis – experimental measurement – ​​engineering experience”.

[0027] Further, in the embodiment of the present invention, the sand phase velocity u s , obtained from the following expression 2: Expression 2: In the formula, δtis the time step used in transient numerical calculations, u s is the sand phase velocity vector that needs to be solved at the current moment, u ʹ s is the sand phase velocity vector solved at the previous moment, m s is the dynamic viscosity of the sand phase, g is the acceleration due to gravity, m ts is the turbulent viscosity of the sand phase, is the Laplace term of the sand phase velocity solved at the previous moment, is the pressure gradient.

[0028] Furthermore, in an embodiment of the present invention, the interaction blocking source term , obtained from the following expression three: Expression three: In the formula, r s is the density of the sand phase, α s is the nominal volume concentration of the sand phase, α f =1- α s is the nominal volume concentration of the aqueous phase, u f is the water phase velocity vector, u s is the sand phase velocity vector.

[0029] It is understandable that in the embodiment of the present invention, in the above-mentioned interaction blocking factor The expression and interactive blocking source terms of In the expression of α s It is the average sand phase volume concentration of the water pump inlet flow. Under a certain working condition that the user is concerned about, α s It is a constant value and does not change with time and space.

[0030] It is understandable that in the embodiment of the present invention, under the well-known water pump transient numerical calculation framework in the field of engineering computational fluid, high-quality hexahedral grids are used to spatially discretize the computational domain, and the total number of grids is about 4 million. The new method proposed in the present invention is introduced and transient calculation is carried out, and the time step is δt = 60 / n d / 180 = 4.16710 -4 s (the time required for the impeller to rotate 2°). In addition, Figure 1As shown in the figure, in order to better demonstrate the advantages of the fast calculation method, the calculation results of the high-precision two-fluid algorithm recognized in engineering and the calculation results of the fast calculation method proposed in the present invention are compared. Taking the prediction results of the high-precision two-fluid algorithm as the standard, the impeller flow channel monitoring line ( Figure 2 ) flow data on the flow data show that: (1) the prediction results of the fast calculation method proposed by the present invention are compared with the prediction results of the high-precision two-fluid algorithm, and the relative error does not exceed 5%. The calculation time per 100 steps is 1200 seconds, and the time cost is reduced by 80%; (2) the prediction results of the mixed phase calculation method are compared with the prediction results of the high-precision two-fluid algorithm, and the relative error does not exceed 5%, which is almost consistent with the fast calculation method of the present invention. The calculation time per 100 steps is 3600 seconds, and the time cost is only reduced by 40%; (3) The single-phase calculation method does not consider the interphase effect, and the calculation time per 100 steps is 600 seconds. Although the time cost is reduced by 90%, it is impossible to predict the slip velocity. In summary, the present invention has the outstanding advantages of fully realizing the separate solution of the concentration field and velocity field of the suspended fine particle water-sand two-phase flow inside the water pump, and can accurately and efficiently predict the suspended fine particle water-sand two-phase flow characteristics inside the water pump, that is, it achieves the goal of taking into account both calculation accuracy and calculation efficiency, thereby making large-scale complex engineering calculations possible.

[0031] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fast calculation method for water-sand two-phase flow of suspended fine particles inside a water pump, characterized in that: including: Defining the interaction blocker , the mutual retardation factor is used to characterize the retardation between the movement of the sand phase and the movement of the water phase; Based on the interaction inhibitor , determine the sand phase velocity u s The algebraic formula of ; Using the interaction inhibitor and the sand phase velocity u s The algebraic formula for determining the interaction retardation source term , the interaction blocking source term It is used to characterize the effect of sand phase motion on water phase momentum; The interaction blocking source term Added to the water phase momentum equation to reflect the momentum change of the water phase under the influence of suspended fine particles; Using the transient numerical calculation framework of the water pump, the sand phase velocity is solved u s The algebraic formula for obtaining the sand phase velocity u s ; Solve to add the interaction blocking source term The water phase momentum equation is used to obtain the water phase velocity.

2. The rapid calculation method for water-sand two-phase flow of suspended fine particles inside a water pump according to claim 1 is characterized in that: The defined interaction inhibitor , obtained from the following expression: Expression 1: In the formula, ρ f is the density of the water phase, ρ s is the sand phase density, α s is the nominal volume concentration of the sand phase, α f =1- α s is the nominal volume concentration of the aqueous phase, d s is the diameter of the sediment particles, u f is the water phase velocity vector, u s is the sand phase velocity vector, Re s = ρ f | u f - u s | / μ f is the sand phase particle Reynolds number, μ f is the dynamic viscosity of the water phase, m 1、 m 2、 m 3、 m 4、 m 5、 m 6、 m 7、 m 8、 m 9 are all empirical coefficients.

3. The rapid calculation method for water-sand two-phase flow of suspended fine particles inside a water pump according to claim 2 is characterized in that: The empirical coefficient in the interaction retardation factor is: m 1=1, m 2=1, m 3 = -1, m 4=18, m 5 = -2.65, m 6 = -1, m 7=2.7, m 8 = -1.963, m 9=0.

313.

4. The rapid calculation method for water-sand two-phase flow of suspended fine particles inside a water pump according to claim 2 is characterized in that: The sand phase velocity u s , obtained from the following expression 2: Expression two: In the formula, δt is the time step used in transient numerical calculations, u s is the sand phase velocity vector that needs to be solved at the current moment, u ʹ s is the sand phase velocity vector solved at the previous moment, μ s is the dynamic viscosity of the sand phase, g is the acceleration due to gravity, μ ts is the turbulent viscosity of the sand phase, is the Laplace term of the sand phase velocity solved at the previous moment, is the pressure gradient.

5. The rapid calculation method for water-sand two-phase flow of suspended fine particles inside a water pump according to claim 4 is characterized in that: The interaction blocking source term , obtained from the following expression three: Expression three: In the formula, ρ s is the sand phase density, α s is the nominal volume concentration of the sand phase, α f =1- α s is the nominal volume concentration of the aqueous phase, u f is the water phase velocity vector, u s is the sand phase velocity vector.

6. The rapid calculation method for water-sand two-phase flow of suspended fine particles inside a water pump according to claim 5 is characterized in that: In the interaction inhibitor The expression of the interaction blocking source term In the expression, the nominal volume concentration of the sand phase is α s It is the average sand phase volume concentration of the inflow from the water intake pump.

7. The rapid calculation method for water-sand two-phase flow of suspended fine particles inside a water pump according to claim 5 is characterized in that: Under a certain working condition that the user is concerned about, α s It is a constant value and does not change with time and space.

Images