In-cylinder fuel-gas mixing optimization method based on droplet phase transition state in high-density environment

Abstract

The present invention discloses an in-cylinder oil-gas mixing optimization method based on the phase change state of droplets in a high-density environment, which belongs to the technical field of in-cylinder oil-gas mixing. The specific process is as follows: Step 1, selecting an alkane component whose density changes monotonically at the gas-liquid interface in a binary mixture as a reference component; Step 2, calculating the density distribution and influencing parameters of the reference component in the normal direction of the gas-liquid interface; Step 3, calculating the characteristic interface thickness and surface tension of the gas-liquid interface based on the density distribution of the reference component in the normal direction of the gas-liquid interface; Step 4, calculating the average molecular free path and Knudsen number based on the interface temperature, equilibrium pressure and average molecular hard sphere diameter; Step 5, jointly predicting the evolution of the spatial structure of the gas-liquid interface through the interface thickness, surface tension, average molecular free path and Knudsen number; Step 6, when the result predicted in Step 5 is that the droplets undergo a supercritical phase change, increasing the Reynolds number of the airflow in the cylinder to optimize the oil-gas mixing in the cylinder.

Description

Technical Field

[0001] The present invention belongs to the technical field of in-cylinder oil-gas mixing, and in particular relates to an in-cylinder oil-gas mixing optimization method based on droplet phase change state under a high-density environment. Background Art

[0002] Yang, Meng, and their team have made outstanding contributions to the study of the phase transition and mixing characteristics of fuel droplets in supercritical environments. They investigated the transport, mixing, and dynamic evolution of single LOX droplets in supercritical laminar flow, focusing on two environmental factors: ambient pressure and convective velocity. Their results confirmed that increasing ambient pressure enhances droplet elongation. Subsequently, Yang, Meng, and their colleagues investigated the oil-gas mixing process of two LOX droplets in a supercritical convective nitrogen environment, providing further information on the impact of front-to-back droplet interactions on oil-gas mixing. Sierra-Pallares et al. investigated the effects of droplet size, ambient pressure, and convective velocity on the oil-gas mixing process of fuel droplets in supercritical environments. Their results showed that droplet size had no effect on the droplet dynamics. Chae et al. investigated the effects of ambient pressure and convective velocity on the dynamic evolution and vaporization characteristics of supercritical LOX droplets. They found that increasing ambient pressure accelerates droplet elongation. They also concluded that, under supercritical conditions, increasing ambient pressure inhibits diffusion, leading to a shortened droplet lifetime. Lee et al. simulated the mixing and deformation of a supercritical n-heptane droplet in a nitrogen atmosphere well above the fuel's critical point. Their numerical results showed that the initially spherical fuel droplet deformed significantly due to the disappearance of the gas-liquid interface and surface tension, forming a toroidal vortex at its tail. However, their thermodynamic model did not consider real gas effects in the thermodynamic properties of both the fuel and the gas, and assumed a constant fluid density, resulting in certain limitations in their results. Research on optimizing in-cylinder fuel-gas mixtures based on gas-liquid interface thickness can help optimize in-cylinder fuel-gas mixing at the microscopic level. This allows for predicting the supercritical phase transition of the fuel and thus controlling the in-cylinder airflow to optimize fuel-gas mixing. However, because the gas-liquid interface thickness is at the nanometer scale, traditional optical experimental methods cannot capture the evolution of the gas-liquid interface structure and are insufficient to reveal the mechanism of the supercritical phase transition of liquid fuel jets under transcritical / supercritical conditions. Therefore, it is crucial to analyze the timing of the transition from traditional two-phase evaporation-dominated mixing behavior to supercritical unidirectional diffusion-dominated mixing behavior from the perspective of the microscopic gas-liquid interface. Summary of the Invention

[0003] The purpose of the present invention is to provide an in-cylinder oil-gas mixing optimization method based on the phase change state of droplets in a high-density environment, so as to solve the problems existing in the prior art that traditional optical experimental means cannot capture the evolution process of the gas-liquid interface structure, and the traditional thermodynamic models do not consider the real gas effect and the poor uniformity of oil-gas mixing.

[0004] To achieve the above objectives, the present invention provides an in-cylinder oil-gas mixing optimization method based on the phase change state of droplets in a high-density environment, comprising the following steps:

[0005] Step 1: selecting an alkane component whose density changes monotonically at the gas-liquid interface in the binary mixture as a reference component, wherein the gas-liquid interface is the region between the alkane / nitrogen binary mixture in a gas-liquid equilibrium state;

[0006] Step 2: Calculate the density distribution and influencing parameters of the reference component in the normal direction of the gas-liquid interface;

[0007] Step 3: Calculate the characteristic interface thickness and surface tension of the gas-liquid interface based on the density distribution of the reference component in the normal direction of the gas-liquid interface;

[0008] Step 4, calculating the average molecular free path and Knudsen number based on the interface temperature, equilibrium pressure and average molecular hard sphere diameter;

[0009] Step 5: The evolution of the spatial structure of the gas-liquid interface is predicted by the interface thickness, surface tension, average molecular free path, and Knudsen number. Specifically, when the Knudsen number is greater than 0.1, the interface thickness increases, the surface tension decreases, and the average molecular free path shortens, but it does not reach a limit. When the Knudsen number is not greater than 0.1, the interface thickness is the thickest, the surface tension is the smallest, and the average molecular free path is the shortest. It is predicted that the mixed fluid at the gas-liquid interface will transform from a discontinuous fluid to a continuous fluid, and a supercritical phase transition will occur. At this time, the gas-liquid interface disappears and transforms into a supercritical fluid boundary mixing layer.

[0010] Step 6: When the result predicted in step 5 is that the droplets undergo a supercritical phase transition, increase the Reynolds number of the airflow in the cylinder, establish a subcritical evaporation mixing model of droplets in a high-density convective environment and a supercritical diffusion mixing model of droplets in a high-density convective environment to jointly optimize the oil-gas mixing in the cylinder.

[0011] Preferably, the calculation expression for the density distribution of the reference component in the normal direction of the gas-liquid interface in step 2 is as follows:

[0012]

[0013] Where, ρ I,L is the liquid density, ρ I,V is the gas phase density, Δρ I is the density increment, N is the number of discrete grid nodes at the gas-liquid interface, ρi Represents the density of the liquid phase.

[0014] Preferably, the influencing parameter κ in step 2 i,j The calculation expression is as follows:

[0015]

[0016] c 0,i =-2.985+4.332Z c,i +10.859Z c,i 2 -1.990ω i +1.798ω i 2 -5.436×10 -6 (θ r,i ) 2

[0017] c 1,i =-0.965+1.405Z c,i +2.746Z c,i 2 -0.963ω i +1.346ω i 2 -1.110×10 -6 (θ r,i ) 2

[0018] c 2,i =-0.121+0.156Z c,i +0.540Z c,i 2 -0.123ω i +0.090ω i 2 -0.219×10 -6 (θ r,i ) 2

[0019] Where, β i,j represents the binary interaction parameter, κ i represents the influence parameter of pure component i, κ j represents the influence parameter of pure component j, a i and b i are all constants, N A represents Avogadro's constant, c 0,i 、c 1,i and c 2,i are the correlation coefficients of pure substances, T' r represents the characteristic temperature, Z c,i represents the critical compressibility factor, ωi represents the eccentricity factor, θ r,i represents the contrast dipole moment.

[0020] Preferably, the specific calculation process of the surface tension of the gas-liquid interface in step 3 is as follows:

[0021] S31. The expression of surface tension σ1 in spatial coordinate form in the normal direction of the gas-liquid interface is as follows:

[0022]

[0023] S32. Convert the spatial coordinate form in the normal direction of the gas-liquid interface into the density distribution form in the normal direction of the gas-liquid interface by using the coordinate conversion rule. The specific calculation expression is as follows:

[0024]

[0025] Where, ρ M,i and ρ M,j are the densities of the liquid and gas components in the mixture, respectively. Subscript I represents the reference component, subscripts V and L represent the gas and liquid phases in phase equilibrium, respectively. i and ρ j are the densities of the liquid and gas phases, respectively, and σ represents the surface tension in the form of density distribution in the normal direction of the gas-liquid interface.

[0026] Preferably, the characteristic interface thickness l of the gas-liquid interface in step 3 is VLE The calculation expression is as follows:

[0027]

[0028] Where, ρ I,0 is the gas phase density of reference component I at the initial integration point, z0 represents ρ I,0 The position, z represents ρ I The location, represents the giant thermodynamic potential energy density of the mixture, Indicates a negative value of the equilibrium pressure, is the huge thermodynamic potential energy density difference, the huge thermodynamic potential energy density difference The calculation expression is as follows:

[0029]

[0030] Where, ρ M,i represents the density of the liquid phase in the mixture, ρ M,j represents the density of the gas phase in the mixture.

[0031] Preferably, the calculation expression for calculating the average molecular free path in step 4 based on the interface temperature, equilibrium pressure and average molecular hard sphere diameter is as follows:

[0032]

[0033] Where, d i is the diameter of the chain hard ball, m i is the hard sphere number, is the hard sphere diameter, d is the average molecular hard sphere diameter, x i is, Λ is the average molecular free path, k B is the Boltzmann constant, T is the interface temperature, and P is the equilibrium pressure;

[0034] The ratio of the average molecular free path to the characteristic interface thickness is the Knudsen number, which is calculated as follows:

[0035]

[0036] Where Kn is the Knudsen number.

[0037] Preferably, in step 6, a subcritical evaporation mixing model of droplets in a high-density convective environment is established based on the VOF method, including the continuity equation, momentum equation, energy equation, and component equation, as follows:

[0038] The VOF method is used to capture the interface between the gas and liquid phases, and the piecewise linear interface algorithm is used to reconstruct the high-resolution gas-liquid interface. In the VOF method, the sum of the volume fractions of the liquid and gas phases in any control volume is always 1. The specific expression is as follows:

[0039]

[0040] Where, α l is the liquid phase volume fraction;

[0041] The calculation expression of the continuity equation is as follows:

[0042]

[0043] Where ρ is the density, is the velocity, α is the volume fraction, subscript q is the phase q, S m,q Represents the mass source term, which is used to describe the mass transfer process between gas and liquid phases. Specifically, the mass transfer rate at the gas-liquid interface is calculated by a mass transfer model with a physical basis. Based on this mass transfer model, the mass transfer rate Calculated by the following equation:

[0044]

[0045] Where δ is the evaporation coefficient, R is the universal gas constant, and T ν Indicates the saturation temperature, P ν is the saturation pressure, Pi is the vapor partial pressure at the gas-liquid interface, and finally, combined with the Clausius-Clapeyron relationship, the mass transfer rate in the above formula is Converted to the following form:

[0046]

[0047] Where ΔH represents the enthalpy difference, T i represents the temperature at the gas-liquid interface, ρ v Represents density, and the above formula is the mass source term S used in this model m,q The final form of

[0048] The calculation expression of the momentum equation is as follows:

[0049]

[0050] In the formula, P represents pressure, μ represents viscosity, represents the gradient, It represents the surface tension existing at the gas-liquid interface. The surface tension is calculated by the following formula:

[0051]

[0052] Where κ represents the curvature, ρ l represents the liquid side density, ρ g represents the gas phase density, σ is the surface tension coefficient, and the surface tension coefficient σ under subcritical conditions is calculated by the following relationship:

[0053]

[0054] Where, P c represents the critical pressure, T c represents the critical temperature, ω represents the eccentricity factor, and T represents the interface temperature;

[0055] The calculation expression of the energy equation is as follows:

[0056]

[0057] Where E represents the energy of the binary mixture, which is calculated using the mass average method, and λ represents the thermal conductivity. is the stress tensor, T is the temperature, h i,q is the enthalpy of component i in phase q, is the diffusion flux, S h represents the energy source term, and the calculation expression is as follows:

[0058]

[0059] The calculation expression of the component equation is as follows:

[0060]

[0061] Where Y i.q is the mass fraction of component i in phase q, S s,q represents the component source term, α q represents the volume fraction, ρ q represents density, represents the diffusion flux of component i in phase q. In all the above equations, the density ρ, thermal conductivity λ, and viscosity μ of the binary mixture are calculated by the volume fraction averaging method, and the constant pressure specific heat cp of the binary mixture is calculated by the mass averaging method.

[0062] Preferably, the high-density convective environment droplet supercritical diffusion mixing model established in step 6 includes four control equations, specifically the continuity control equation, the momentum control equation, the energy control equation, and the component control equation. The calculation expression of each control equation is as follows:

[0063] Continuity equation:

[0064]

[0065] Momentum equation:

[0066]

[0067] Where, I represents impulse;

[0068] Energy equation:

[0069]

[0070] Where h j represents the enthalpy of component j; the second term on the right side of the above formula represents the temperature gradient due to component diffusion, i.e., the Dufour effect;

[0071] Component equation:

[0072]

[0073] Where, is the diffusion flux of component i, and the calculation expression is as follows:

[0074]

[0075] Where D i,m represents the mass diffusion coefficient of component i, D T,i represents the thermal diffusivity of component i, Represents the mass fraction gradient of component i, the second term on the right side of the above formula It represents the transport of components due to the additional concentration gradient caused by the temperature gradient, namely the Soret effect.

[0076] Therefore, the present invention adopts the above-mentioned in-cylinder oil-gas mixing optimization method based on the phase change state of droplets under high-density environment. By establishing a gas-liquid interface model, it can quickly and accurately determine whether the droplets have entered the supercritical state, and by establishing a subcritical evaporation mixing model and a supercritical diffusion mixing model under high-density convection environment, it is obtained that when the droplets enter the supercritical state, the Reynolds number of the airflow in the cylinder is increased, thereby promoting oil-gas mixing.

[0077] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 This is an overall flow chart of the in-cylinder oil-gas mixing optimization method based on the phase change state of droplets under high-density environment of the present invention;

[0079] Figure 2 It is a graph showing the change of the giant thermodynamic potential energy density difference with the density distribution at the gas-liquid interface;

[0080] Figure 3 It is a graph showing the change of the average molecular free path with the composition of the saturated gas phase mixture under different ambient pressures;

[0081] Figure 4 is a graph showing the variation of Knudsen number with interface temperature at different equilibrium pressures;

[0082] Figure 5 It is a graph showing the change of gas-liquid interface thickness with interface temperature at different pressures;

[0083] Figure 6 It is a graph showing the change of surface tension of gas-liquid interface with interface temperature under different pressures;

[0084] Figure 7 Figure 1 shows the effect of airflow velocity on the dynamic evolution of droplets and the oil-gas mixing process in different modes. (a) shows the effect of the dynamic evolution of droplets and the oil-gas mixing process in the subcritical evaporation mixing mode, and (b) shows the effect of the dynamic evolution of droplets and the oil-gas mixing process in the supercritical diffusion mixing mode.

[0085] Figure 8 This is a curve showing the change in the average mass fraction of n-heptane in n-heptane droplets at different air flow rates;

[0086] Figure 9 The influence diagram of droplets under different Reynolds numbers; (a) is the distribution diagram of n-heptane mass fraction, (b) is the vorticity distribution diagram;

[0087] Figure 10The influence curves of different Reynolds numbers on the properties of n-heptane droplets; (a) is the influence curve of the stratification coefficient, and (b) is the influence curve of the droplet phase change rate;

[0088] Figure 11 This is a graph showing the effect of Reynolds number on the thermodynamic state evolution of a binary mixture of n-heptane and nitrogen. DETAILED DESCRIPTION

[0089] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0090] See also Figure 1-11 , an in-cylinder oil-gas mixing optimization method based on droplet phase change state under high-density environment, comprising the following steps:

[0091] Step 1: selecting an alkane component whose density changes monotonically at the gas-liquid interface in the binary mixture as a reference component, wherein the gas-liquid interface is the region between the alkane / nitrogen binary mixture in a gas-liquid equilibrium state;

[0092] Step 2: Calculate the density distribution and influencing parameters of the reference component in the normal direction of the gas-liquid interface;

[0093] The calculation expression for the density distribution of the reference component in the normal direction of the gas-liquid interface is as follows:

[0094]

[0095] Where, ρ I,L is the liquid density, ρ I,V is the gas phase density, Δρ I is the density increment, N is the number of discrete grid nodes at the gas-liquid interface, ρ i Represents the density of the liquid phase.

[0096] Influencing parameter κ i,j The calculation expression is as follows:

[0097]

[0098] c 0,i =-2.985+4.332Z c,i +10.859Z c,i 2 -1.990ω i +1.798ω i 2 -5.436×10 -6(θ r,i ) 2

[0099] c 1,i =-0.965+1.405Z c,i +2.746Z c,i 2 -0.963ω i +1.346ω i 2 -1.110×10 -6 (θ r,i ) 2

[0100] c 2,i =-0.121+0.156Z c,i +0.540Z c,i 2 -0.123ω i +0.090ω i 2 -0.219×10 -6 (θ r,i ) 2

[0101] Where, β i,j represents the binary interaction parameter, κ i represents the influence parameter of pure component i, κ j represents the influence parameter of pure component j, a i and b i are all constants, N A represents Avogadro's constant, c 0,i 、c 1,i and c 2,i are the correlation coefficients of pure substances, T' r represents the characteristic temperature, Z c,i represents the critical compressibility factor, ω i represents the eccentricity factor, θ r,i represents the contrast dipole moment.

[0102] Step 3: Calculate the characteristic interface thickness and surface tension of the gas-liquid interface based on the density distribution of the reference component in the normal direction of the gas-liquid interface;

[0103] The specific calculation process of the surface tension of the gas-liquid interface is as follows:

[0104] S31. According to the linear density gradient theory, the surface tension κ1 in the spatial coordinate form in the normal direction of the gas-liquid interface is expressed as follows:

[0105]

[0106] S32. Convert the spatial coordinate form in the normal direction of the gas-liquid interface into the density distribution form in the normal direction of the gas-liquid interface by using the coordinate conversion rule. The specific calculation expression is as follows:

[0107]

[0108] Where, ρ M,i and ρ M,j are the densities of the liquid and gas components in the mixture, respectively. Subscript I represents the reference component, subscripts V and L represent the gas and liquid phases in phase equilibrium, respectively. i and ρ j are the densities of the liquid and gas phases, respectively, and σ represents the surface tension in the form of density distribution in the normal direction of the gas-liquid interface.

[0109] Characteristic interface thickness l of the gas-liquid interface VLE The calculation expression is as follows:

[0110]

[0111] Where, ρ I,0 is the gas phase density of reference component I at the initial integration point, z0 represents ρ I,0 The position, z represents ρ I The location, represents the giant thermodynamic potential energy density of the mixture, Indicates a negative value of the equilibrium pressure, is the huge thermodynamic potential energy density difference, the huge thermodynamic potential energy density difference The calculation expression is as follows:

[0112]

[0113] Where, ρ M,i represents the density of the liquid phase in the mixture, ρ M,j represents the density of the gas phase in the mixture.

[0114] Step 4: Calculate the average molecular free path and Knudsen number based on the interface temperature, equilibrium pressure, and average molecular hard sphere diameter. The specific calculation expressions are as follows:

[0115]

[0116]

[0117] Where, d i is the diameter of the chain hard ball, m i is the hard sphere number, is the hard sphere diameter, d is the average molecular hard sphere diameter, x i is, Λ is the average molecular free path, k Bis the Boltzmann constant, whose value is k B =1.380649×10 -23 J / K, T is the interface temperature, and P is the equilibrium pressure;

[0118] The ratio of the average molecular free path to the characteristic interface thickness is the Knudsen number, which is calculated as follows:

[0119]

[0120] Where Kn is the Knudsen number.

[0121] Step 5: The evolution of the spatial structure of the gas-liquid interface is predicted by the interface thickness, surface tension, average molecular free path, and Knudsen number. Specifically, when the Knudsen number is greater than 0.1, the interface thickness increases, the surface tension decreases, and the average molecular free path shortens, but it does not reach a limit. When the Knudsen number is not greater than 0.1, the interface thickness is the thickest, the surface tension is the smallest, and the average molecular free path is the shortest. It is predicted that the mixed fluid at the gas-liquid interface will transform from a discontinuous fluid to a continuous fluid, and a supercritical phase transition will occur. At this time, the gas-liquid interface disappears and transforms into a supercritical fluid boundary mixing layer.

[0122] Step 6: When the result predicted in step 5 indicates that the droplets undergo a supercritical phase transition, the Reynolds number of the in-cylinder airflow is increased, and a subcritical evaporation mixing model for droplets in a high-density convective environment and a supercritical diffusion mixing model for droplets in a high-density convective environment are established to jointly optimize the in-cylinder oil-gas mixing. The subcritical evaporation mixing model for droplets in a high-density convective environment is established based on the VOF method, including the continuity equation, momentum equation, energy equation, and component equation, as follows:

[0123] The VOF method is used to capture the interface between the gas and liquid phases, and a piecewise linear interface algorithm is used to reconstruct the high-resolution gas-liquid interface. In the VOF method, the sum of the volume fractions of the liquid and gas phases in any control volume is always 1. In other words, within any given control volume, the variables represent either one of the gas and liquid phases or a two-phase mixture (i.e., the gas-liquid interface). The specific expression is as follows:

[0124]

[0125] Where, α l is the liquid phase volume fraction;

[0126] The continuity equation for a phase q in the gas-liquid two-phase system that supports high-resolution gas-liquid interface reconstruction is as follows:

[0127]

[0128] Where ρ is the density, is the velocity, α is the volume fraction, subscript q is the phase q, S m,q Represents the mass source term, which is used to describe the mass transfer process between gas and liquid phases. Specifically, the mass transfer rate at the gas-liquid interface is calculated by a mass transfer model with a physical basis. Based on this mass transfer model, the mass transfer rate Calculated by the following equation:

[0129]

[0130] Where δ is the evaporation coefficient, R is the universal gas constant, and T ν Indicates the saturation temperature, P ν is the saturation pressure, P i is the vapor partial pressure at the gas-liquid interface, and finally, combined with the Clausius-Clapeyron relationship, the mass transfer rate in the above formula is Converted to the following form:

[0131]

[0132] Where ΔH represents the enthalpy difference, T i represents the temperature at the gas-liquid interface, ρ v Represents density, and the above formula is the mass source term S used in this model m,q The final form of

[0133] Momentum equation. In this model, it is assumed that the momentum equations for the gas and liquid phases in the computational domain are identical, and the calculated velocity field is shared by the gas and liquid phases. The simplified approach of sharing the same velocity field for the gas and liquid phases is inappropriate in high-velocity and turbulent environments, but it is still applicable to the laminar flow environment studied in this paper. The momentum equation is thus obtained as follows:

[0134]

[0135] In the formula, P represents pressure, μ represents viscosity, represents the gradient, It represents the surface tension existing at the gas-liquid interface. The surface tension is calculated by the following formula:

[0136]

[0137] Where κ represents the curvature, ρ l represents the liquid side density, ρ g represents the gas phase density, σ is the surface tension coefficient, and the surface tension coefficient σ under subcritical conditions is calculated by the following relationship:

[0138]

[0139] Where, P c represents the critical pressure, Tc represents the critical temperature, ω represents the eccentricity factor, and T represents the interface temperature;

[0140] Energy equation. In this model, the energy equations for the gas and liquid phases in the computational domain have the same form. The calculated velocity field is shared by the gas and liquid phases, and its expression is as follows:

[0141]

[0142] Where E represents the energy of the binary mixture, which is calculated using the mass average method, and λ represents the thermal conductivity. is the stress tensor, T is the temperature, h i,q is the enthalpy of component i in phase q, is the diffusion flux, S h represents the energy source term, and the calculation expression is as follows:

[0143]

[0144] The calculation expression of the component equation is as follows:

[0145]

[0146] Where Y i.q is the mass fraction of component i in phase q, S s,q represents the component source term, α q represents the volume fraction, ρ q represents density, represents the diffusion flux of component i in phase q. In all the above equations, the density ρ, thermal conductivity λ, and viscosity μ of the binary mixture are calculated by the volume fraction averaging method, and the constant pressure specific heat cp of the binary mixture is calculated by the mass averaging method.

[0147] The above four equations are solved by the commercial software ANSYS Fluent 2021R1, and the simulation is performed using the Pressure-based transient solver based on the SIMPLEPressure-velocity coupling method. The spatial discretization of the momentum equation, energy equation, and component equation uses the second-order upwind format, while the spatial discretization of the pressure equation uses the PRESTO format. The spatial discretization of the volume fraction equation is achieved through the Geo-Reconstruct scheme, and the time discretization method is a first-order implicit format.

[0148] The established supercritical diffusion mixing model for droplets in a high-density convective environment includes four governing equations: continuity, momentum, energy, and composition. Unlike the phase transition mixing of fuel droplets in a subcritical convective environment, in a supercritical convective environment, when the initial temperature of the introduced fuel droplet approaches the critical mixing temperature of the mixture, rapid heat transfer between the droplet and the environment causes the droplet gas-liquid interface to instantly reach a critical mixing state. This allows the assumption that the supercritical phase transition has negligible effects on the droplet's behavior. At this point, the gas-liquid interface with significant surface tension no longer exists between the gas and liquid phases, and the latent heat of vaporization decreases to zero. However, the temperature inside the droplet remains below the critical mixing temperature, indicating that the fluid inside the droplet remains in a liquid-phase thermodynamic state. Therefore, in a supercritical convective environment, the fuel droplet can be assumed to be a dense fluid enclosed by the critical mixing state isosurface. The fluid within the entire flow field can be considered a single-phase continuous medium, with its thermodynamic state distinguishing its phase. Based on this, the supercritical diffusion mixing model is used to describe the droplet dynamics behavior and oil-gas mixing process of fuel droplets in a convective environment after supercritical transition. The calculation expression of each control equation is as follows:

[0149] Continuity governing equation:

[0150]

[0151] Momentum governing equation:

[0152]

[0153] Where, I represents impulse;

[0154] Energy governing equation:

[0155]

[0156] Where h j represents the enthalpy of component j; the second term on the right side of the above formula represents the temperature gradient due to component diffusion, i.e., the Dufour effect;

[0157] Component governing equation:

[0158]

[0159] Where, is the diffusion flux of component i, and the calculation expression is as follows:

[0160]

[0161] Where D i,m represents the mass diffusion coefficient of component i, D T,i represents the thermal diffusivity of component i, Represents the mass fraction gradient of component i, the second term on the right side of the above formula It represents the transport of components due to the additional concentration gradient caused by the temperature gradient, namely the Soret effect.

[0162] Based on the finite volume method, the above basic control equations are solved by the commercial software ANSYS FLUENT 2021R1. The simulation is carried out with the Pressure-based transient solver based on the SIMPLE Pressure-velocity coupling method. The spatial discretization of the gradient and pressure equations adopts the second-order upwind scheme. The spatial discretization method of the momentum control equation, the component control equation, and the energy control equation also adopts the second-order upwind scheme. The time discretization method is a first-order implicit format.

[0163] Under high-density environmental conditions, the droplets first undergo a subcritical evaporation phase transition. As the gas-liquid interface temperature continues to rise, the droplets will enter a supercritical phase transition mode. When the droplets undergo a supercritical phase transition, the gas-liquid interface between the droplets and the gas disappears and transforms into a supercritical fluid boundary mixing layer. Figure 5 As shown in , the thickness of the gas-liquid interface increases exponentially with increasing temperature. Figure 6 As shown in , the surface tension of the gas-liquid interface decreases exponentially with increasing temperature. Figure 3 As shown in , the average molecular free path shortens with the increase of interface temperature. Based on the increase of gas-liquid interface thickness, the decrease of surface tension and the shortening of average molecular free path, it is predicted that the droplet will have a supercritical phase transition trend. Figure 4 As shown in , the Knudsen number of the gas-liquid interface decreases with the increase of the interface temperature. When it is less than 0.1, the mixture in the gas-liquid interface changes from a discontinuous fluid to a continuous fluid, that is, a supercritical transition occurs. At this time, the gas-liquid interface disappears and transforms into a supercritical fluid boundary mixing layer. Figure 7 As shown in Figure 2, increasing the air flow rate can accelerate the phase transition of droplets under subcritical and supercritical conditions, but when the droplets are in the supercritical state, increasing the air flow rate has a more significant effect on the phase transition of the droplets. Figure 8 As shown in Figure 2, under all airflow rate conditions, the movement distance of droplets in the supercritical diffusion mixing mode is always greater than that in the subcritical evaporation mixing mode at the same time, and the greater the airflow rate, the more obvious the advantage of the supercritical diffusion mixing mode. When the droplets are in the supercritical state: Figure 9 As shown in the figure, when the droplet Reynolds number is Red = 1271, due to the increase in air flow velocity, a larger area of ​​vorticity distribution is formed on both sides of the droplet, and the vorticity at this time is significantly greater than that when Red = 85, which ultimately causes the vortex on the weak side of the droplet to continue to curl and expand and cause the droplet to stretch and deform. Figure 10As shown in (a), at all Reynolds numbers, the stratification coefficient of the fuel droplets decreases with time, which is determined by the supercritical diffusion mixing mode. The stratification coefficient of the fuel droplets decreases with the increase of Reynolds number. The reason is that the vortex structure on the weak side of the droplet expands with the increase of Reynolds number. The enhanced component diffusion leads to the generation of more uniform oil-gas mixtures, which indicates that the oil-gas mixing uniformity is higher at higher Reynolds numbers. Figure 10 As shown in (b), the droplet phase change rate increases with the increase of Reynolds number. The reasons are: on the one hand, the high Reynolds number leads to more significant tensile deformation of the droplet, thereby strengthening the heat and mass transfer process between the fuel droplet and the ambient gas; on the other hand, increasing the air flow rate is conducive to "blowing away" the n-heptane vapor generated near the droplet surface, increasing the n-heptane concentration gradient on the droplet surface, thereby accelerating the droplet phase change process dominated by diffusion. Figure 11 As shown in Figure 2, at high Reynolds numbers, the thermodynamic state of the binary mixture in the gas phase is more widely distributed, resulting in faster and more uniform mixing with air.

[0164] Therefore, the present invention adopts the above-mentioned in-cylinder oil-gas mixing optimization method based on the phase change state of droplets under high-density environment. By establishing a gas-liquid interface model, it can quickly and accurately determine whether the droplets have entered the supercritical state, and by establishing a subcritical evaporation mixing model and a supercritical diffusion mixing model under high-density convection environment, it is obtained that when the droplets enter the supercritical state, the Reynolds number of the airflow in the cylinder is increased, thereby promoting oil-gas mixing.

[0165] 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 the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An in-cylinder oil-gas mixing optimization method based on droplet phase change state in a high-density environment is characterized by: The following steps are involved: Step 1: selecting an alkane component whose density changes monotonically at the gas-liquid interface in the binary mixture as a reference component, wherein the gas-liquid interface is the region between the alkane / nitrogen binary mixture in a gas-liquid equilibrium state; Step 2: Calculate the density distribution and influencing parameters of the reference component in the normal direction of the gas-liquid interface; Step 3: Calculate the characteristic interface thickness and surface tension of the gas-liquid interface based on the density distribution of the reference component in the normal direction of the gas-liquid interface; Step 4, calculating the average molecular free path and Knudsen number based on the interface temperature, equilibrium pressure and average molecular hard sphere diameter; Step 5: The evolution of the spatial structure of the gas-liquid interface is predicted by the interface thickness, surface tension, average molecular free path, and Knudsen number. Specifically, when the Knudsen number is greater than 0.1, the interface thickness increases, the surface tension decreases, and the average molecular free path shortens, but it does not reach a limit. When the Knudsen number is not greater than 0.1, the interface thickness is the thickest, the surface tension is the smallest, and the average molecular free path is the shortest. It is predicted that the mixed fluid at the gas-liquid interface will transform from a discontinuous fluid to a continuous fluid, and a supercritical phase transition will occur. At this time, the gas-liquid interface disappears and transforms into a supercritical fluid boundary mixing layer. Step 6: When the result predicted in step 5 is that the droplets undergo a supercritical phase transition, increase the Reynolds number of the airflow in the cylinder, establish a subcritical evaporation mixing model of droplets in a high-density convective environment and a supercritical diffusion mixing model of droplets in a high-density convective environment to jointly optimize the oil-gas mixing in the cylinder.

2. The in-cylinder oil-gas mixing optimization method based on droplet phase change state in a high-density environment according to claim 1 is characterized in that: The calculation expression for the density distribution of the reference component in the normal direction of the gas-liquid interface in step 2 is as follows: Where, ρ I , L is the liquid density, ρ I , V is the gas phase density, Δ PI is the density increment, N is the number of discrete grid nodes at the gas-liquid interface, ρ i Represents the density of the liquid phase.

3. The in-cylinder oil-gas mixing optimization method based on droplet phase change state in a high-density environment according to claim 2 is characterized in that: Influencing parameter κ in step 2 i，j The calculation expression is as follows: c 0，i =-2.985+4.332Z c，i +10.859Z c，i 2 -1,990h i +1.798h i 2 -5.436×10 -6 (i r，i ) 2 c 1，i =-0.965+1.405Z c，i +2.746Z c，i 2 -0.963h i +1.346h i 2 -1.110×10 -6 (i r，i ) 2 c 2，i =-0.121+0.156Z c，i +0.540Z c，i 2 -0.123h i +0.090h i 2 -0.219×10 -6 (i r，i ) 2 Where, β i，j represents the binary interaction parameter, κ i represents the influence parameter of pure component i, κ j represents the influence parameter of pure component j, a i and b i are all constants, N A represents Avogadro's constant, c 0,i 、c 1，i and c 2，i are the correlation coefficients of pure substances, T′ r represents the characteristic temperature, Z c，i represents the critical compressibility factor, ω i represents the eccentricity factor, θ ri represents the contrast dipole moment.

4. The in-cylinder oil-gas mixing optimization method based on droplet phase change state in a high-density environment according to claim 3 is characterized in that: The specific calculation process of the surface tension of the gas-liquid interface in step 3 is as follows: S31. The expression of surface tension σ1 in spatial coordinate form in the normal direction of the gas-liquid interface is as follows: S32. Convert the spatial coordinate form in the normal direction of the gas-liquid interface into the density distribution form in the normal direction of the gas-liquid interface by using the coordinate conversion rule. The specific calculation expression is as follows: Where, ρ M,i and ρ M，j are the densities of the liquid and gas components in the mixture, respectively. Subscript I represents the reference component, subscripts V and L represent the gas and liquid phases in phase equilibrium, respectively. i and ρ j are the densities of the liquid and gas phases, respectively, and σ represents the surface tension in the form of density distribution in the normal direction of the gas-liquid interface.

5. The in-cylinder oil-gas mixing optimization method based on droplet phase change state in a high-density environment according to claim 4 is characterized in that: The characteristic interface thickness l of the gas-liquid interface in step 3 VLE The calculation expression is as follows: Where, ρ I，0 is the gas phase density of reference component I at the initial integration point, z0 represents ρ I,0 The position, z represents ρ I The location, represents the giant thermodynamic potential energy density of the mixture, Indicates a negative value of the equilibrium pressure, is the huge thermodynamic potential energy density difference, the huge thermodynamic potential energy density difference The calculation expression is as follows: Where ρM,i represents the density of the liquid phase in the mixture, and PM,j represents the density of the gas phase in the mixture.

6. The in-cylinder oil-gas mixing optimization method based on droplet phase change state in a high-density environment according to claim 5 is characterized in that: The calculation expression for the average molecular free path in step 4 is as follows based on the interface temperature, equilibrium pressure and average molecular hard sphere diameter: Where, d i is the diameter of the chain hard ball, m i is the hard sphere number, is the hard sphere diameter, d is the average molecular hard sphere diameter, x i is, Λ is the average molecular free path, k B is the Boltzmann constant, T is the interface temperature, and P is the equilibrium pressure; The ratio of the average molecular free path to the characteristic interface thickness is the Knudsen number, which is calculated as follows: Where Kn is the Knudsen number.

7. The method for optimizing in-cylinder oil-gas mixing based on droplet phase transition in a high-density environment according to claim 6, characterized in that: In step 6, a subcritical evaporation mixing model of droplets in a high-density convective environment is established based on the VOF method, including the continuity equation, momentum equation, energy equation, and component equation, as follows: The VOF method is used to capture the interface between the gas and liquid phases, and the piecewise linear interface algorithm is used to reconstruct the high-resolution gas-liquid interface. In the VOF method, the sum of the volume fractions of the liquid and gas phases in any control volume is always 1. The specific expression is as follows: Where, α l is the liquid phase volume fraction; The calculation expression of the continuity equation is as follows: Where ρ is the density, is the velocity, α is the volume fraction, subscript q is the phase q, S m,q Represents the mass source term, which is used to describe the mass transfer process between gas and liquid phases. Specifically, the mass transfer rate at the gas-liquid interface is calculated by a mass transfer model with a physical basis. Based on this mass transfer model, the mass transfer rate Calculated by the following equation: Where δ is the evaporation coefficient, R is the universal gas constant, Tν is the saturation temperature, Pν is the saturation pressure, and P i is the vapor partial pressure at the gas-liquid interface, and finally, combined with the Clausius-Clapeyron relationship, the mass transfer rate in the above formula is Converted to the following form: Where ΔH represents the enthalpy difference, T i represents the temperature at the gas-liquid interface, ρ ν Indicates density; The calculation expression of the momentum equation is as follows: In the formula, P represents pressure, μ represents viscosity, represents the gradient, It represents the surface tension existing at the gas-liquid interface. The surface tension is calculated by the following formula: Where K represents the curvature, ρ l represents the liquid side density, ρ g represents the gas phase density, σ is the surface tension coefficient, and the surface tension coefficient σ under subcritical conditions is calculated by the following relationship: Where, P c represents the critical pressure, T c represents the critical temperature, ω represents the eccentricity factor, and T represents the interface temperature; The calculation expression of the energy equation is as follows: Where E represents the energy of the binary mixture, which is calculated using the mass average method, and λ represents the thermal conductivity. is the stress tensor, T is the temperature, h i，q is the enthalpy of component i in phase q, is the diffusion flux, S h represents the energy source term, and the calculation expression is as follows: The calculation expression of the component equation is as follows: Where Y i.q is the mass fraction of component i in phase q, S s，q represents the component source term, α q represents the volume fraction, ρ q represents density, represents the diffusion flux of component i in phase q.

8. The in-cylinder oil-gas mixing optimization method based on droplet phase change state in a high-density environment according to claim 7 is characterized in that: The supercritical diffusion mixing model of droplets in a high-density convective environment established in step 6 includes four control equations, namely the continuity control equation, the momentum control equation, the energy control equation, and the component control equation. The calculation expression of each control equation is as follows: Continuity equation: Momentum equation: Where, I represents impulse; Energy equation: Where h j represents the enthalpy of component j; Component equation: Where, is the diffusion flux of component i, and the calculation expression is as follows: Where D i，m represents the mass diffusion coefficient of component i, D T，i represents the thermal diffusivity of component i, represents the mass fraction gradient of component i.

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