Pressure gradient calculation method for gas-liquid two-phase flow numerical simulation

Abstract

The invention discloses a pressure gradient calculation method for gas-liquid two-phase flow numerical simulation, and relates to the technical field of fluid motion, and the method comprises the steps: for any surface in a computational domain, calculating the driving pressure of the surface through an interpolation method by using the pressure of control units at the two sides of the surface, and calculating the driving pressure of the surface; according to the method, the surface pressure is obtained by combining the hydrostatic pressure at the surface, and finally, the pressure gradient of the center of the control body unit is calculated based on the divergence theorem according to the pressure at each surface of the control body unit, and the method does not directly perform pressure interpolation to obtain the surface pressure, but fully considers the gravity influence in the water-gas two-phase flow. Therefore, the discontinuity of the pressure gradient at the water-air interface is not flattened, the calculation divergence is avoided, and the accuracy and reliability of the calculated pressure gradient of the center of the control body unit are improved.

Description

Technical Field

[0001] This application relates to the technical field of fluid motion, and in particular to a method for calculating pressure gradient for numerical simulation of gas-liquid two-phase flow. Background Art

[0002] One of the main flow characteristics of ship hydrodynamics is the gas-liquid two-phase free surface. The moving interface of the gas-liquid two-phase free surface belongs to a strong discontinuity problem, and its simulation is more difficult than the strong shock wave problem. Therefore, this topic is a more challenging research work and has been highly regarded by scholars at home and abroad since the 1950s and 1960s. In the numerical simulation of the fluid motion interface, it is not only necessary to use a suitable multiphase flow mathematical calculation model to track the moving interface, but also necessary to couple the fluid transport equation to solve the correct pressure field and velocity field. Only in this way can the geometric shape and position information of the fluid interface with physical meaning be obtained, rather than a colorful animation. Finally, from the perspective of engineering applications, two-phase flow is a very complex flow, including high density ratios and high pressure ratios of the two phases, and there are various complex situations such as interface breakup, splash, and fusion. These characteristics make the free surface problem always a major problem in computational fluid dynamics.

[0003] The current classical method for numerical simulation of gas-liquid two-phase flow is to select the RANS equation as the governing equation and use the finite volume method to discretize and solve the governing equations (including the continuity equation, momentum equation, and energy equation) for numerical simulation. The finite volume method is a numerical method based on the integral form. Its core idea is to divide the computational domain into multiple control volume units and integrate the governing equations on each control volume unit, thereby transforming the partial differential equation into an algebraic equation. In the above numerical simulation process, when calculating the pressure source term of the momentum equation, it is necessary to calculate the pressure gradient of each control volume unit. In the finite volume method system, the Green-Gauss formula or the least squares method is generally used for calculation. However, due to the high density ratio of the gas-liquid two-phase flow and the water-gas two-phase free surface in ship hydrodynamics, the conventional Green-Gauss formula or least squares method actually cannot accurately simulate the discontinuity of the pressure gradient at the free surface, which will cause non-physical values to appear in the velocity field near the interface during the solution, and ultimately the entire calculation will diverge, resulting in low reliability of the numerical simulation results of gas-liquid two-phase flow or even inability to complete the numerical simulation. Summary of the Invention

[0004] In view of the above problems and technical requirements, this application proposes a method for calculating pressure gradient for numerical simulation of gas-liquid two-phase flow. The technical solution of this application is as follows:

[0005] A pressure gradient calculation method for gas-liquid two-phase flow numerical simulation, in the process of gas-liquid two-phase flow numerical simulation using a finite volume method combined with a collocated grid, for any control volume unit C in the calculation domain, the pressure gradient calculation method includes:

[0006] For any i-th surface f of the control volume element C i , considering the gravity in the flow field, the pressure p of the control volume unit C is calculated by interpolation method. C and neighboring control volume unit N i Pressure Calculate the surface f i Driving pressure at Among them, the neighbor control volume unit N i is adjacent to the control volume element C and on the surface f i The integer parameter 1≤i≤n, n is the number of surfaces contained in the control volume element C;

[0007] Using the surface f i Driving pressure at Binding surface f i Hydrostatic pressure at Calculate the surface f i The pressure

[0008] According to the pressure at each surface of the control volume unit C The pressure gradient at the center of the control volume unit C is calculated based on the divergence theorem

[0009] Its further technical solution is to interpolate the surface f i Driving pressure at include:

[0010] Considering the gravity in the flow field, the pressure p of the control volume unit C is used C Combined with the hydrostatic pressure at the control volume element C Determine the driving pressure of the control volume element C And use the neighbor control volume unit N i Pressure Combined neighbor control volume unit N i Hydrostatic pressure at Determine the neighbor control volume unit N i Driving pressure

[0011] Using the interpolation coefficient λ i Driving pressure on control unit C and neighboring control volume unit N i Driving pressure According to Interpolate to obtain the driving pressure at the surface f i is For

[0012]

[0013] A further technical solution thereof is that the pressure gradient calculation method further includes:

[0014] Calculate the gravity weighting coefficient as the interpolation coefficient λ according to the gravity of the control volume unit C and the gravity of the neighboring control volume unit N i i .

[0015] A further technical solution thereof is that the calculation formula of the interpolation coefficient λ i is:

[0016]

[0017] Wherein, ρ C is the density at the control volume unit C, and V C is the volume of the control volume unit C; is the density at the neighboring control volume unit N i and is the volume of the neighboring control volume unit N i ; g is the acceleration of gravity.

[0018] A further technical solution thereof is that calculating the pressure at the surface f i includes: For

[0019] Based on the characteristics of the pressure at the surface f i and combining the hydrostatic pressure at the surface f the hydrostatic pressure at the control volume unit C i the hydrostatic pressure at the neighboring control volume unit N the hydrostatic pressure at the control volume unit C the neighboring control volume unit N i the hydrostatic pressure at and combining and arranging to obtain the pressure at the surface f i is: For

[0020]

[0021] Wherein, is the density at the surface f i , is the water depth vector pointing from the water surface reference point to the surface f i ; ρ C is the density at the control volume unit C, and h C ​​​​is the water depth vector from the water surface reference point to the center of the control volume unit C; is the neighbor control volume unit N i where the density is is the water depth vector from the water surface reference point to the center of the neighbor control volume unit N i and g is the acceleration due to gravity; r C represents the vector from the center of the control volume unit C to the center of the surface f i ; represents the vector from the center of the neighbor control volume unit N i to the center of the surface f i .

[0022] Its further technical solution is that the pressure gradient at the center of the control volume unit C is calculated based on the divergence theorem including calculating according to the following formula:

[0023]

[0024] wherein, is the out-of-plane normal vector of the surface f of the control volume unit C i and V C is the volume of the control volume unit C.

[0025] The beneficial technical effect of this application is:

[0026] This application discloses a method for calculating the pressure gradient for numerical simulation of gas-liquid two-phase flow. This method calculates the driving pressure at the surface based on the pressures of the control volume units on both sides of the surface through an interpolation method, then combines the hydrostatic pressure at the surface to obtain the pressure at the surface, and finally calculates the pressure gradient at the center of the control volume unit based on the divergence theorem. This method does not directly perform pressure interpolation to obtain the pressure at the surface, but fully considers the influence of gravity in the gas-liquid two-phase flow. Therefore, it will not smooth out the discontinuity of the pressure gradient at the gas-liquid interface, avoid calculation divergence, and improve the accuracy and reliability of the calculated pressure gradient at the center of the control volume unit, thereby facilitating the improvement of the accuracy and reliability of the numerical simulation of gas-liquid two-phase flow and having good application prospects in scenarios such as ship resistance and flow field simulation with free liquid surfaces in ship CFD simulation.

[0027] When interpolating to obtain the driving pressure at the surface, the conventional distance interpolation is abandoned, and instead the gravity weighting coefficient is used as the interpolation coefficient, which is more in line with physical reality and the obtained calculation results are more accurate, thereby facilitating the further improvement of the accuracy of pressure gradient calculation and the accuracy of numerical simulation of gas-liquid two-phase flow. Description of the Drawings

[0028] Figure 1 is a schematic diagram of the collocated grid of the finite volume method.

[0029] Figure 2 It is a flowchart of the pressure gradient calculation method according to an embodiment of the present application. Detailed implementation manners

[0030] The following further describes the detailed implementation manners of the present application in conjunction with the accompanying drawings.

[0031] The present application discloses a pressure gradient calculation method for numerical simulation of gas-liquid two-phase flow. This method is applied in the process of numerical simulation of gas-liquid two-phase flow using the finite volume method combined with collocated grids. In the process of numerical simulation of gas-liquid two-phase flow using the finite volume method, according to the existing grid data, the computational domain can be divided into multiple control volume units. Each control volume unit includes multiple surfaces, and each surface of the control volume unit is adjacent to another control volume unit. Combining with the collocated grid technology, the flow field variables are stored at the center of the control volume unit.

[0032] For any control volume unit C in the computational domain, the control volume unit C has a total of n surfaces, and any i-th surface is denoted as f i , where the integer parameter 1 ≤ i ≤ n. The neighbor control volume unit of any surface f i of the control volume unit C is denoted as N i , and this neighbor control volume unit N i is the control volume unit that is adjacent to the control volume unit C and coplanar at the surface f i . For example, in an instance, please refer to Figure 1 . Taking the control volume unit C as a hexagonal unit as an example, the control volume unit C includes 6 surfaces respectively denoted as f 1 to f 6 , and the neighbor control volume units of these six surfaces are respectively denoted as N 1 to N 6 .

[0033] The pressure gradient calculation method provided by the present application is used to calculate the pressure source term of the momentum equation during the numerical simulation of gas-liquid two-phase flow, and replaces the traditional Green-Gauss formula or least square method to calculate the pressure gradient at the center of any control volume unit C. Therefore, other contents of the numerical simulation of gas-liquid two-phase flow in the present application will not be elaborated.

[0034] Please refer to Figure 2 The flow schematic diagram shown. The pressure gradient calculation method provided by the present application is based on the divergence theorem, and transforms the pressure gradient at the center of the control volume unit C into the solution of the pressure at each surface of the control volume unit C. Therefore, the key point of this method is to calculate the pressure at each surface of the control volume unit C.

[0035] For any i-th surface f i of the control volume unit C, the conventional method will process the surface fi The control volume units C on both sides and the neighbor control volume units N i The pressure of is directly calculated for the surface f using the pressure interpolation format i the pressure at. However, in the numerical simulation of gas-liquid two-phase flow, since the density of the liquid phase is much greater than that of the gas phase, the gradient of the pressure in the direction of gravity increases sharply at the fluid interface. Therefore, this approach will smooth out the discontinuity of the pressure gradient at the fluid interface like the conventional Green-Gauss formula or the least squares method, resulting in an incorrect calculation of the pressure gradient at the center of the control volume unit near the fluid interface.

[0036] To solve this problem, the present application considers the gravity effect in the flow field and divides the pressure i at the surface f into two parts and writes it as:

[0037]

[0038] Among them, is the driving pressure at the surface f i used to drive the flow of the flow field. And is the hydrostatic pressure at the surface f i used to balance the gravity effect. Among them, the hydrostatic pressure i at the surface f is:

[0039]

[0040] Among them, is the density at the surface f i , is the water depth vector pointing from the water surface reference point to the surface f i , and g is the acceleration of gravity.

[0041] For the driving pressure i at the surface f is obtained by interpolating the pressure p C of the control volume unit C and the pressure i of the neighbor control volume unit N . Specifically:

[0042] Considering the gravity effect in the flow field, the pressure p C of the control volume unit C and the pressure i of the neighbor control volume unit N can also be divided into two parts, namely the driving pressure and the hydrostatic pressure, and there is:

[0043]

[0044] Among them, Denotes the driving pressure at the control volume unit C, Denotes the hydrostatic pressure at the control volume unit C. Denotes the neighbor control volume unit N i At the driving pressure, Denotes the neighbor control volume unit N i At the hydrostatic pressure.

[0045] Due to the surface f i At the driving pressure The interpolation coefficient λ can be utilized i Through the driving pressure at the control volume unit C And the neighbor control volume unit N i At the driving pressure Interpolated to obtain, which can be expressed as:

[0046]

[0047] Therefore, when determining the driving pressure of the control volume unit C according to Equation (3) And the driving pressure of the neighbor control volume unit N i And substituting it into Equation (4), the driving pressure at the surface f can be calculated by the interpolation method according to the pressure p of the control volume unit C And the pressure of the neighbor control volume unit N C And the neighbor control volume unit N i Of the pressure Calculated to obtain the driving pressure at the surface f i At is: Is:

[0048]

[0049] And the hydrostatic pressure at the control volume unit C And the hydrostatic pressure at the neighbor control volume unit N i At the hydrostatic pressure The calculation formula is:

[0050]

[0051] Where ρ C Is the density at the control volume unit C, h C Is the water depth vector pointing from the water surface reference point to the center of the control volume unit C; Is the density of the neighbor control volume unit N i At, Is the water depth vector pointing from the water surface reference point to the center of the neighbor control volume unit N i Center.

[0052] Further substituting Equation (6) into Equation (5) can obtain the driving pressure at the surface f i At The calculation formula is:

[0053]

[0054] In one embodiment, in order to further improve the calculation accuracy and better conform to the physical reality, the interpolation coefficient λ i does not use distance interpolation as in the traditional method, but calculates the gravity-weighted coefficient as the interpolation coefficient λ according to the gravity of the control volume cell C and the gravity of the neighboring control volume cell N i . Since the air density is much smaller than the water density, the pressure value at the two-phase interface should be closer to the pressure at the control volume containing the gas phase. Therefore, the calculation formula of the interpolation coefficient λ i is: i

[0055]

[0056] where ρ C is the density at the control volume cell C, and V C is the volume of the control volume cell C; is the density at the neighboring control volume cell N i , is the volume of the neighboring control volume cell N i .

[0057] Then, substitute the interpolated formula (7) into formula (1), and combine it with the hydrostatic pressure calculation formula of formula (2), and the pressure i at the surface f can be sorted out as:

[0058]

[0059] Therefore, formula (9) can be further sorted out to obtain:

[0060]

[0061] where r C represents the vector from the center of the control volume cell C to the center of the surface f i , represents the vector from the center of the neighboring control volume cell N i to the center of the surface f i .

[0062] For each surface of the control volume cell C, the pressure at the surface can be obtained separately by the above method. Then, based on the pressure at each surface of the control volume cell C the pressure gradient at the center of the control volume cell C can be calculated based on the divergence theorem The calculation formula is:

[0063] ​

[0064] in, is the surface f of the control volume element C i The out-of-plane normal vector.

[0065] The above is only a preferred embodiment of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and changes directly derived or associated by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the protection scope of the present application.

Claims

1. A pressure gradient calculation method for numerical simulation of gas-liquid two-phase flow, characterized in that: In the numerical simulation of gas-liquid two-phase flow using the finite volume method combined with the collocated grid, the pressure gradient calculation method for any control volume unit C in the calculation domain includes: For any i-th surface f of the control volume element C i , considering the gravity in the flow field, the pressure p of the control volume unit C is calculated by interpolation method. C and neighboring control volume unit N i Pressure Calculate the surface f i Driving pressure at Among them, the neighbor control volume unit N i is adjacent to the control volume element C and on the surface f i The integer parameter 1≤i≤n, n is the number of surfaces contained in the control volume element C; Using the surface f i Driving pressure at Binding surface f i Hydrostatic pressure at Calculate the surface f i The pressure According to the pressure at each surface of the control volume unit C The pressure gradient at the center of the control volume unit C is calculated based on the divergence theorem 2. The pressure gradient calculation method according to claim 1, characterized in that: Interpolation obtains the surface f i Driving pressure at include: Considering the gravity in the flow field, the pressure p of the control volume unit C is used C Combined with the hydrostatic pressure at the control volume element C Determine the driving pressure of the control volume element C And use the neighbor control volume unit N i Pressure Combined neighbor control volume unit N i Hydrostatic pressure at Determine the neighbor control volume unit N i Driving pressure Using the interpolation coefficient λ i Driving pressure on control unit C and neighboring control volume unit N i Driving pressure according to Interpolation obtains the surface f i Driving pressure at for 3. The pressure gradient calculation method according to claim 2, characterized in that: The pressure gradient calculation method further includes: According to the gravity of control volume C and neighbor control volume N i The gravity weighting coefficient is used as the interpolation coefficient λ i .

4. The pressure gradient calculation method according to claim 3, characterized in that: Interpolation coefficient λ i The calculation formula is: Among them, ρ C is the density at the control volume unit C, V C is the volume of the control unit C; is the neighbor control volume unit N i The density at is the neighbor control volume unit N i volume; g is the acceleration due to gravity.

5. The pressure gradient calculation method according to claim 2, characterized in that: Calculate the surface f i The pressure include: Based on the surface i The pressure The characteristics of the combined surface f i Hydrostatic pressure at Control the hydrostatic pressure at element C Neighbor control volume unit N i Hydrostatic pressure at Combination Finishing to get the surface f i The pressure for: in, is the surface f i The density at is the water surface reference point pointing to the surface f i The water depth vector; ρ C is the density at the control volume unit C, h C It is the water depth vector from the water surface reference point to the center of the control volume unit C; is the neighbor control volume unit N i The density at It is the water surface reference point pointing to the neighboring control volume unit N i The water depth vector at the center, g is the acceleration due to gravity; r C Indicates that the center of the control volume unit C points to the surface f i The center vector, Represents the neighbor control volume unit N i The center points to the surface f i The center vector.

6. The pressure gradient calculation method according to claim 1, characterized in that: The pressure gradient at the center of the control volume unit C is calculated based on the divergence theorem Including calculation according to the following formula: in, is the surface f of the control volume element C i The out-of-plane normal vector, V C is the volume of the control unit C.

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