A high-density ratio multiphase flow particle simulation method based on near-field dynamics

Abstract

This invention discloses a particle simulation method for high-density-ratio multiphase flow based on peri-field dynamics, relating to the field of computer graphics. This invention is the first to introduce a state-based peri-field dynamics method into fluid simulation within computer graphics physics simulations, performing stable simulations of high-density-ratio multiphase flow by calculating integral forms of the fluid continuity equation and the dynamic equation. This method also introduces an advanced particle mass exchange strategy to address the problem of non-conservation of mass in multiphase flow. This method is the first to be able to simulate particle densities as high as 1:1000 (e.g., the density ratio of air to water is approximately 1:800), achieving a maximum density ratio tens of times higher than previous methods.

Description

Technical Field

[0001] This invention relates to the field of computer graphics technology, and in particular to a high-density ratio multiphase flow particle simulation method based on near-field dynamics. Background Technology

[0002] Multiphase flow simulation has always been an important branch of physical graphics simulation, mainly including the simulation of multi-component fluids and the interaction and transformation of solid, liquid, and gas phases. Multi-component fluids, in particular, have received extensive research from the graphics community due to their complex and visually interesting phenomena. In recent years, many simulation methods for multiphase flows have emerged, including mesh-based methods, particle-based methods, and hybrid methods that combine mesh and particle approaches. Among particle methods, the most well-known is a hybrid model method based on SPH (Smoothed Particle Hydrodynamics). Its basic idea is to have each particle carry the volume fraction of each phase component, and update the volume fraction in each iteration step by calculating the particle's drift velocity, ultimately simulating the separation and merging of components in a multiphase flow. Following this method, many particle methods and hybrid methods based on hybrid models have emerged. However, these methods all face a difficult but crucial problem—the high density ratio problem. Multiphase flows with high density ratios are very common in life and exhibit a wide variety of phenomena. Whether it's the massive movement of bubbles in a liquid or the explosions that occur in chemical reactions due to drastic changes in density ratio, the simulation of high-density-ratio multiphase flow is indispensable. However, the methods mentioned above cannot stably simulate high-density-ratio multiphase fluids.

[0003] Therefore, both academia and industry need a new perspective to address the instability issues caused by high density ratios. Summary of the Invention

[0004] This invention aims to solve the problem that multiphase flow particle simulation methods cannot stably simulate high density ratios, and therefore proposes a multiphase flow simulation method based on near-field dynamics.

[0005] This invention is achieved through the following technical solution

[0006] A high-density-ratio multiphase flow particle simulation method based on near-field dynamics is proposed. In addition to carrying physical quantities such as mass and velocity, the multiphase flow particles also carry the volume fraction and mass fraction of each component. After initializing the various physical quantities of the particles, an iterative loop is performed across all particles, including the following steps:

[0007] Step 1: Calculate the mixing density and pressure of particles in each iteration step using the density and pressure calculation methods mentioned in smooth particle hydrodynamics;

[0008] Step 2: Calculate the particle drift velocity using a multiphase flow mixing model that represents each phase component by volume fraction;

[0009] Step 3: Calculate the particle's shape tensor and deformation gradient tensor based on the relevant content in perifield dynamics (for the description of states);

[0010] Step 4: Calculate the change in particle volume fraction using the integral form of the continuity equation;

[0011] Step 5: Calculate the mass transfer of particles based on the change in volume fraction, obtain the updated particle mass and static density from the mass transfer, then obtain the mass fraction of each phase of the particles from the particle mass, and normalize the volume fraction of the particles accordingly.

[0012] Step 6: Solve for the particle's acceleration and velocity using the momentum equation, and update the particle's displacement.

[0013] Return to step 1 of the loop and proceed with the calculation process for the next iteration until the simulation is complete.

[0014] According to the simulated cycle process provided by the present invention, the formula for calculating the mixing density is as follows:

[0015]

[0016] In the formula, i and j are the particle indices (representing the particle indices to which the physical quantity belongs), ρ m，i Let m be the mixing density of each phase for particle i (hereinafter referred to as i-particle), m be the particle mass, W be the Cubic-Spline kernel function, and ξ = x. j -x i Let be the relative displacement between particle j and particle i, x represent the displacement of the particle, and h be the search radius.

[0017] The pressure calculation formula is as follows:

[0018]

[0019] Where γ = 7 is a commonly used value set manually; reducing this value will weaken the incompressibility of the liquid. B is a pressure constant, and ρ... m0 The static density of the mixed particles.

[0020] The formula for calculating particle drift velocity in the hybrid model is as follows:

[0021]

[0022] Where k represents the ordinal number of each phase, ranging from 0 to n-1, n is the number of phases in the simulation, c is the mass fraction, α is the volume fraction, and τ and σ are constant coefficients reflecting the pressure and diffusion components, respectively, of the volume fraction change. Generally, increasing τ will accelerate pressure-related phenomena, such as causing liquid stratification to occur faster, while increasing σ will make the diffusion phenomenon more apparent in the simulation. The acceleration 'a' in the formula is calculated using the following formula:

[0023]

[0024] In the formula, the acceleration is the combined acceleration due to gravity and the velocity v. m material derivative The difference.

[0025] The formula for calculating the shape tensor of the particle is:

[0026]

[0027] in For interpolation mixing density, This is a binary product operator.

[0028] The formula for calculating the deformation gradient tensor of the particle is:

[0029]

[0030] The formula for calculating the continuity equation through integration, that is, the formula for calculating the change in volume fraction, is as follows:

[0031]

[0032]

[0033]

[0034] Where S represents the volume fraction change contributed by the total volume change of the particles, S k V represents the volume fraction change contributed by the volume change of the k-th phase contained within the particle, where V is the volume of the particle.

[0035] The formula for calculating the particle mass transfer amount is:

[0036] Δm k，i =∑ρ k V i Δα k，i ,

[0037] Then, the mass fraction is obtained based on the amount of mass transferred.

[0038]

[0039] In the formula m k Let be the mass of the k-th phase of the particle, and ∑ in the denominator k′ This represents the summation over the range from k′ = 0 to k′ = n-1.

[0040] The volume fraction in the normalization method uses the following formula:

[0041]

[0042] The formula for calculating particle acceleration using the momentum equation is as follows:

[0043]

[0044] in

[0045]

[0046]

[0047] In the formula f p For pressure volume density (pressure per unit volume), f μ Given the density of a viscous body, the velocity is obtained using acceleration, as shown in the formula:

[0048]

[0049] In the formula The velocity represents the velocity at time t during the simulation. The superscript (t) indicates the time position of the physical quantity. Δt is the time step in the simulation. Displacement is obtained from the velocity.

[0050]

[0051] Advantages and beneficial effects of the present invention:

[0052] This invention reduces the instability caused by computational errors in particle methods that typically calculate differential equations by calculating integral equations based on peridynamics. Furthermore, the mass exchange strategy described herein significantly improves the problem of non-conservation of mass between phases. The invention effectively solves the high density ratio problem in particle methods by calculating integral equations based on peridynamics and employing the mass exchange strategy. This method is the first particle method capable of simulating densities as high as 1:1000 (e.g., the density ratio of air to water is approximately 1:800), achieving a maximum density ratio several tens of times higher than previous methods. Attached Figure Description

[0053] To more clearly illustrate the technical solutions of the present invention, the accompanying drawings used in the description of the embodiments or prior art will be briefly introduced below. The accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0054] Figure 1 Figure 1 shows the experimental results comparing the stability of the method of this invention with existing advanced methods; (a) The explicit multiphase flow mixing model method based on SPH has a density ratio of 1:20 for light-colored liquid to dark-colored liquid; (b) The method of this invention has a density ratio of 1:20 for light-colored liquid to dark-colored liquid; (c) The explicit multiphase flow mixing model method based on SPH has a density ratio of 1:50 for light-colored liquid to dark-colored liquid. This method cannot simulate multiphase fluids with a density ratio of 1:50; (d) The method of this invention has a density ratio of 1:50 for light-colored liquid to dark-colored liquid, which can be stably simulated.

[0055] Figure 2 Figure 2 shows the experimental results comparing the stability of the method of this invention with existing advanced methods; (a) The explicit multiphase flow mixing model method using particle number density, with a density ratio of 1:50 for the light-colored liquid and 1:50 for the dark-colored liquid, simulates a collapse at an early time point; (b) The method of this invention using particle number density, with a density ratio of 1:50 for the light-colored liquid and 1:50 for the dark-colored liquid, can be simulated stably; (c) The method of this invention, with a density ratio of 1:200 for the light-colored liquid and 1:200 for the dark-colored liquid, can be simulated stably; (d) The implicit multiphase flow mixing model method based on constrained dynamics, with a density ratio of 1:10 for the light-colored liquid and 1:10 for the dark-colored liquid, will cause the simulation to become unstable when the two phases come into contact; (e) The implicit multiphase flow mixing model method that ensures incompressibility by calculating the deformation gradient, with a density ratio of 1:10 for the light-colored liquid and 1:10 for the dark-colored liquid, will cause the simulation to collapse at an early time point.

[0056] Figure 3 The following are experimental results demonstrating the effectiveness of the particle mass exchange strategy described in this invention: (a) Without using the particle mass exchange strategy described in this invention, the density ratio of the dark liquid to the light liquid is 1:50, and the volume of the dark liquid is significantly reduced; (b) With the method of this invention, the density ratio of the dark liquid to the light liquid is 1:50, and the volumes of the dark liquid and the light liquid can be well maintained consistent with the initial state.

[0057] Figure 4 This is a diagram showing the experimental results of the gas-liquid two-phase interaction of the present invention.

[0058] Figure 5 This is a flowchart of a high-density ratio multiphase flow particle simulation method based on near-field dynamics according to the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. The following embodiments are used to illustrate this invention but should not be used to limit its scope.

[0060] In the description of the embodiments of the present invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of the present invention based on the specific circumstances.

[0061] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and / or combine the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0062] The following is combined with Figure 3 This invention describes a high-density-ratio multiphase flow particle simulation method based on near-field dynamics:

[0063] This invention provides a multiphase flow simulation method based on near-field dynamics. The simulation method flow is as follows: Figure 5 As shown, it includes the following steps:

[0064] After initializing the simulation scenario and various particle physical quantities (including setting the density to 1000 kg / m³, setting the particle displacement, and adjusting the volume fraction of each phase to the initial values ​​required for the experiment), the following loop is performed:

[0065] The mixing density and pressure of each particle are calculated using the density and pressure calculation formulas mentioned in the SPH method.

[0066] The drift velocity of each particle is calculated based on a multiphase flow mixing model that uses volume fraction to represent each phase component.

[0067] Calculate the shape tensor and deformation gradient tensor of the particle based on the description of state in peri-field dynamics;

[0068] The change in particle volume fraction in each iteration step is calculated using the continuity equation in integral form derived by this method.

[0069] The amount of mass transfer between particles is calculated based on the change in volume fraction, and the particle mass and static density are updated for the next iteration using the calculated amount of mass transfer.

[0070] The mass fraction of each phase of the particle is obtained from the mass calculated in the previous step, and the volume fraction of the particle is normalized accordingly.

[0071] Based on the calculated physical quantities, the acceleration and velocity of the particle are solved, and the force on the particle is calculated and the particle position is updated according to the momentum equation derived by this method.

[0072] Return to the first step of the loop and proceed with the calculation process for the next iteration until the simulation is complete.

[0073] It is worth noting that the essential difference between the method of this invention and existing multiphase flow simulation methods is that the method of this invention uses near-field dynamics-based state description to calculate the integral form of the momentum equation and the continuity equation.

[0074] To demonstrate the stability of the high-density-ratio multiphase flow particle simulation method based on near-field dynamics provided in this invention, we compared its stability with current advanced multiphase flow particle simulation methods in dam-break experiments. These comparison methods include explicit multiphase flow mixing models based on SPH, explicit multiphase flow mixing models based on SPH using particle number density, implicit multiphase flow mixing models based on constrained dynamics, and implicit multiphase flow mixing models that guarantee incompressibility by calculating deformation gradients.

[0075] Figure 1 and Figure 2 A comparison chart of dam-break test stability provided by this invention with other advanced methods.

[0076] Figure 1 In Figures (a) and (c), the explicit multiphase flow mixing model method based on SPH is used, with the density ratios of the light-colored liquid to the dark-colored liquid being 1:20 and 1:50, respectively. Figures (b) and (d) show the method provided by this invention, with density ratios of 1:20 and 1:50, respectively. It is clearly visible from the figures that the explicit multiphase flow mixing model method based on SPH simulates a collapse when the density ratio is 1:50.

[0077] Figure 2 (a) is an explicit multiphase flow mixing model using particle number density, with a density ratio of 1:50 for the light-colored liquid and 1:50 for the dark-colored liquid. The simulation collapses at an early time point. (b) is the method provided by this invention using particle number density, with a density ratio of 1:50 for the light-colored liquid and 1:50 for the dark-colored liquid. The simulation is stable. (c) is the method provided by this invention, with a density ratio of 1:200 for the light-colored liquid and 1:200 for the dark-colored liquid. (d) is an implicit multiphase flow mixing model based on constrained dynamics, with a density ratio of 1:10 for the light-colored liquid and 1:10 for the dark-colored liquid. During the simulation, the light-colored liquid exhibits instability, including chaotic particle motion and the appearance of non-physical cavities. (e) is an implicit multiphase flow mixing model that ensures incompressibility by calculating deformation gradients, with a density ratio of 1:10 for the light-colored liquid and 1:10 for the dark-colored liquid. It also exhibits instability. This example illustrates that the method provided by this invention can simulate density ratios tens of times higher than existing advanced methods, and can still perform stable multiphase flow simulations at normal time steps even with density ratios as high as 1:200.

[0078] One reason why this invention can stably simulate high density ratios is that it solves the momentum equation and continuity equation for the state-based description of near-field dynamics:

[0079]

[0080] in

[0081]

[0082]

[0083] as well as

[0084]

[0085]

[0086]

[0087] In the above formula, f p For pressure volume density, f μ Let S be the density of the viscous mass, and let S represent the volume fraction change contributed by the total volume change of the particles. k V represents the volume fraction change contributed by the volume change of the k-th phase contained within the particle, where V is the volume of the particle.

[0088] Figure 3This is a volume conservation experiment. (a) Without using the particle mass exchange strategy described in this invention, the density ratio of the dark liquid to the light liquid is 1:50. The volume reduction of the dark liquid is very significant. (b) The method of this invention. The density ratio of the dark liquid to the light liquid is 1:50. The volumes of the dark liquid and the light liquid can be well maintained consistent with the initial state. This example illustrates that the particle mass exchange strategy provided by this invention can very effectively solve the problem of mass non-conservation in current multiphase flow simulation methods (because the density of each phase remains unchanged in multiphase flow simulation, the visual effect of mass conservation is directly reflected in volume conservation). The particle mass exchange strategy is: to calculate the mass transfer of particles using pairwise changes in volume fraction:

[0089] Δm k，i =∑ρ k V i Δα k，i ,

[0090] And the normalized volume fraction is calculated using the mass fraction:

[0091]

[0092] Figure 4 This is a gas-liquid two-phase interaction experiment. Gas is intermittently injected into a container filled with liquid through a pipe at the bottom of the container, forming individual bubbles. The bubbles deform as they rise, eventually leaping out of the water and bursting. In this experiment, the density ratio of gas to liquid is 1:100. This example demonstrates the versatility of the method of this invention, which can handle many gas-liquid interaction problems that particle-based multiphase flow simulation methods cannot.

[0093] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A high density ratio multiphase flow particle simulation method based on near field dynamics, characterized in that, In addition to carrying physical quantities such as mass and velocity, the multiphase flow particles also carry the volume fraction and mass fraction of each component. After initializing the various physical quantities of the particles, the following iterative loop is performed on all particles, including the following steps: Step 1: Calculate the mixing density and pressure of particles in each iteration step using the density and pressure calculation methods mentioned in smooth particle hydrodynamics; the formula for calculating the mixing density is: wherein denotes the particle order number to which the physical quantity belongs, is the phase mixing density of the particle with order number is the particle mass, is the Cubic-Spline kernel function, is the particle and the relative displacement of the particle denotes the displacement of the particle, is the search radius;​​ The pressure calculation formula is as follows: in This is a manually set value; reducing this value will weaken the incompressibility of the liquid. It is a constant pressure coefficient. The static density of the particle mixture; Step 2: Calculate the particle drift velocity using a multiphase flow mixing model that represents each phase component by volume fraction. The formula for calculating the particle drift velocity is as follows: in The ordinal number representing each phase, with a value ranging from 0 to... , The number of phases in the simulation, For quality fraction, It is the volume fraction. and These are the constant coefficients for the pressure component and the diffusion component, respectively, reflecting changes in volume fraction. (Increase) This will accelerate pressure-related phenomena and increase... This will allow the simulation to show more diffusion phenomena; the acceleration in the formula Calculated using the following formula: In the formula, acceleration is the sum of gravitational acceleration and the combined velocity. The difference in the material derivatives; Step 3: Calculate the particle shape tensor and deformation gradient tensor based on near-field dynamics; the formula for calculating the particle shape tensor is: in For interpolation mixing density, This is a binary product operator; The formula for calculating the deformation gradient tensor of the particle is: ； Step 4: Calculate the change in particle volume fraction using the integral form of the continuity equation; the formula for calculating the change in volume fraction is as follows: in, This represents the change in volume fraction contributing to the total volume change of particles. Indicates the first number contained within the particle. The change in volume fraction contributed by the volume change of the phase. The volume of the particle; Step 5: Calculate the mass transfer of particles based on the change in volume fraction, obtain the updated particle mass and static density from the mass transfer, then obtain the mass fraction of each phase of the particles from the particle mass, and normalize the volume fraction of the particles accordingly. Step 6: Solve for the acceleration and velocity of the particle using the momentum equation, and update the particle's displacement. Return to step 1 of the loop and proceed with the calculation process for the next iteration until the simulation is complete.

2. The high-density ratio multiphase flow particle simulation method based on near-field dynamics according to claim 1, characterized in that, The change in particle volume fraction calculated using the integral form of the continuity equation can be used to further calculate the mass transfer between particles, with the following formula: In the formula The volume of the particle; Then, the mass fraction is obtained based on the amount of mass transferred. In the formula For the first particle The mass of the phase, in the denominator Indicates to arrive Summing these values, we obtain the normalized volume fraction: 。 3. The high-density ratio multiphase flow particle simulation method based on near-field dynamics according to claim 2, characterized in that, The acceleration of the particle is calculated using the momentum equation, and the formula is as follows: in , In the formula For pressure volume density, Given the density of a viscous body, the velocity is obtained using acceleration, as shown in the formula: In the formula Represents time points during the simulation process Speed, superscript Used to refer to the moment in which a physical quantity is located. The displacement is obtained using velocity as the time step in the simulation. 。

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