A method for predicting the spatial structure of gas-liquid interface in high-density environment

Abstract

The invention discloses a method for predicting the spatial structure of a gas-liquid interface under a high-density environment, which belongs to the technical field of fuel spraying. The specific process is as follows: step 1, selecting an alkane component whose density in a binary mixture changes monotonically in a gas-liquid interface as a reference component, wherein the gas-liquid interface is a region between alkane / nitrogen binary mixtures in a gas-liquid phase equilibrium state; 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 according to 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 the Knudsen number according to the interface temperature, equilibrium pressure and the average molecular hard sphere diameter; step 5, predicting the evolution of the spatial structure of the gas-liquid interface by the interface thickness, surface tension, average molecular free path and Knudsen number.

Description

Technical Field

[0001] The invention belongs to the technical field of fuel spraying, and in particular relates to a method for predicting the spatial structure of a gas-liquid interface in a high-density environment. Background Art

[0002] In the field of fuel spray, optical testing methods and numerical simulation methods are constantly developing. In the spray optical testing methods, the use of ultra-high-speed cameras based on backlighting, shadowing and schlieren methods to observe the macroscopic characteristics of fuel spray has been widely used. In the numerical simulation of diesel engine spray combustion, the Euler-Lagrangian model that describes the splitting of liquid jets has become the most widely used numerical model. However, no matter which method is used, the atomization and fragmentation processes such as primary and secondary fragmentation under the dominance of the surface tension, fluid inertia and liquid viscosity at the gas-liquid interface indicate that the existence of a sharp immiscible gas-liquid interface under subcritical conditions is one of the prerequisites for the occurrence of this atomization and fragmentation process.

[0003] As the density of the working fluid in the internal combustion power system continues to increase, the liquid jet will show a pattern of morphological characteristics that are completely different from the subcritical state. For example, in the now publicly available literature Mayer W, Hiroshi, T. Propellant injection in a liquid oxygen / gaseous hydrogen rocket engine [J] Journal of Propulsion and Power, 1996, 12 (6): 1137-1147, it was first confirmed through optical experiments that the classic fragmentation atomization characteristics of liquid fuel jets no longer exist under sufficiently high ambient temperature and pressure, that is, there are certain changes in the gas-liquid interface. Researchers have focused on studying and revealing the transformation mechanism of the dynamic changes of liquid fuel jets and the impact they bring. ; Summary of the invention

[0004] The purpose of the present invention is to provide a method for predicting the spatial structure of the gas-liquid interface in a high-density environment, so as to solve the problem that traditional optical experimental means in the prior art cannot capture the evolution process of the gas-liquid interface structure and is difficult to reveal the mechanism of the morphological structure transformation of the liquid fuel jet in a trans / supercritical environment.

[0005] To achieve the above object, the present invention provides a method for predicting the spatial structure of a gas-liquid interface in a high-density environment, comprising the following steps:

[0006] 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 phase equilibrium state;

[0007] Step 2, calculating the density distribution and influencing parameters of the reference component in the normal direction of the gas-liquid interface;

[0008] Step 3, according to the density distribution of the reference component in the normal direction of the gas-liquid interface, the characteristic interface thickness and surface tension of the gas-liquid interface are calculated;

[0009] Step 4, calculating the average molecular free path and Knudsen number according to the interface temperature, equilibrium pressure and average molecular hard sphere diameter;

[0010] Step 5: Predict the evolution of the spatial structure of the gas-liquid interface through the interface thickness, surface tension, average molecular free path and Knudsen number.

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

[0012] ;

[0013] ;

[0014] In the formula, is the liquid density, is the gas phase density, is the density increment, N is the number of mesh nodes for discretization of the gas-liquid interface, Represents the density of the liquid phase.

[0015] Preferably, the influencing parameters in step 2 are The calculation expression is as follows:

[0016] ;

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] In the formula, represents the binary interaction parameter, Represents pure components i The influencing parameters, represents the influence parameter of pure component j, and are constants, represents Avogadro's constant, , and are the correlation coefficients of pure substances, represents the characteristic temperature, represents the critical compression factor, represents the eccentricity factor, Represents the contrast dipole moment.

[0022] Preferably, the specific calculation process of the surface tension of the gas-liquid interface in step 3 is as follows:

[0023] S31. Surface tension in spatial coordinate form in the normal direction of the gas-liquid interface The expression is as follows:

[0024] ;

[0025] S32. The spatial coordinate form in the normal direction of the gas-liquid interface is converted 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:

[0026] ;

[0027] ;

[0028] In the formula, and are the densities of the liquid and gas components in the mixture, respectively. Denotes reference component, subscript V , L represent the gas phase and liquid phase in phase equilibrium, respectively. and are the densities of the liquid and gas phases, respectively, The surface tension that represents the density distribution in the normal direction of the gas-liquid interface.

[0029] Preferably, the characteristic interface thickness of the gas-liquid interface in step 3 is The calculation expression is as follows:

[0030] ;

[0031] ;

[0032] In the formula, As reference component The gas phase density at the initial integration point is, express Location, express Location, represents the giant thermodynamic potential energy density of the mixture, Indicates a negative value of the equilibrium pressure, is a huge thermodynamic potential energy density difference.

[0033] Preferably, the huge thermodynamic potential energy density difference The calculation expression is as follows:

[0034] ;

[0035] In the formula, represents the density of the liquid phase in the mixture, Represents the density of the gas phase in the mixture.

[0036] Preferably, the calculation expression for calculating the average molecular free path in step 4 according to the interface temperature, equilibrium pressure and average molecular hard sphere diameter is as follows:

[0037] ;

[0038] ;

[0039] ;

[0040] In the formula, is the diameter of the chain hard sphere, is the hard sphere number, is the hard sphere diameter, is the average molecular hard sphere diameter, is the mole fraction corresponding to the average molecular hard sphere diameter, is the average molecular free path, is the Boltzmann constant, is the interface temperature, To balance the pressure.

[0041] Preferably, the Knudsen number is the ratio of the average molecular free path to the characteristic interface thickness, and the calculation expression is as follows:

[0042] ;

[0043] In the formula, is the Knudsen number.

[0044] Preferably, in 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 does not reach the 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 in the gas-liquid interface changes from a discontinuous fluid to a continuous fluid, and a supercritical phase transition occurs. At this time, the gas-liquid interface disappears and changes into a supercritical fluid boundary mixing layer.

[0045] Therefore, the present invention adopts the above-mentioned method for predicting the spatial structure of the gas-liquid interface in a high-density environment. By calculating and judging the spatial structure of the gas-liquid interface, the spatial structure of the gas-liquid interface in a high-density environment can be predicted quickly and accurately, and it can be determined whether the droplets have entered a supercritical state.

[0046] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is an overall flow chart of a method for predicting the spatial structure of a gas-liquid interface under a high-density environment of the present invention;

[0048] Figure 2 is a curve diagram showing the change of the giant thermodynamic potential energy density difference with the density distribution in the gas-liquid interface in an embodiment of the present invention;

[0049] Figure 3 is a curve diagram showing the variation of the average molecular free path with the composition of the saturated gas phase mixture under different ambient pressures in an embodiment of the present invention;

[0050] Figure 4 is a curve diagram showing the variation of the Knudsen number with the interface temperature under different equilibrium pressures in an embodiment of the present invention;

[0051] Figure 5 is a graph showing the change of the gas-liquid interface thickness with the interface temperature under different pressures in an embodiment of the present invention;

[0052] Figure 6 1 is a graph showing the change of the surface tension of the gas-liquid interface with the interface temperature under different pressures in an embodiment of the present invention. DETAILED DESCRIPTION

[0053] 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 invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0054] See also Figure 1-6 , a method for predicting the spatial structure of a gas-liquid interface in a high-density environment, comprising the following steps:

[0055] 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 phase equilibrium state;

[0056] Step 2: Calculate the density distribution and influencing parameters of the reference component in the normal direction of the gas-liquid interface; wherein the calculation expression for the density distribution of the reference component in the normal direction of the gas-liquid interface is as follows:

[0057] ;

[0058] ;

[0059] In the formula, is the liquid density, is the gas phase density, is the density increment, N is the number of mesh nodes for discretization of the gas-liquid interface, Represents the density of the liquid phase.

[0060] Influencing parameters , which characterizes the molecular structure of the gas-liquid interface and determines the response of the density gradient to the local deviation of the chemical potential from its saturation value. The parameters that can be influenced by the pure components and Calculated. is a binary interaction parameter. For the alkane / nitrogen binary system of the present invention, its binary interaction parameter can be set to zero. Therefore, the accurate calculation of the pure component influence parameter is very important for the description of the gas-liquid interface. In the present invention, the influence parameter of the pure component i is is the characteristic temperature = 1-T / Tc. The influence parameter of pure component j is is the characteristic temperature = a function of 1-T / Tc. is Avogadro's constant, = 6.0221415×1023 mol-1, and is the critical pressure of component i , parameters related to critical temperature Tc and eccentricity factor ω. 、 and is the correlation coefficient of pure substances, and these three correlation coefficients are the critical compression factors , eccentricity factor and the contrast dipole moment The function of is calculated as follows:

[0061] ;

[0062] ;

[0063] ;

[0064] ;

[0065] ;

[0066] In the formula, represents the binary interaction parameter, Represents pure components i The influencing parameters, represents the influence parameter of pure component j, and are constants, represents Avogadro's constant, , and are the correlation coefficients of pure substances, represents the characteristic temperature, represents the critical compression factor, represents the eccentricity factor, Represents the contrast dipole moment.

[0067] Step 3: Calculate the characteristic interface thickness and surface tension of the gas-liquid interface according to the density distribution of the reference component in the normal direction of the gas-liquid interface; the specific calculation process of the surface tension of the gas-liquid interface is as follows:

[0068] S31. Surface tension in spatial coordinate form in the normal direction of the gas-liquid interface The expression is as follows:

[0069] ;

[0070] S32. The spatial coordinate form in the normal direction of the gas-liquid interface is converted 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:

[0071] ;

[0072] ;

[0073] In the formula, and are the densities of the liquid and gas components in the mixture, respectively. Indicates reference component, subscript V , L represent the gas phase and liquid phase in phase equilibrium, respectively. and are the densities of the liquid and gas phases, respectively, The surface tension that represents the density distribution in the normal direction of the gas-liquid interface.

[0074] Characteristic interface thickness of the gas-liquid interface The calculation expression is as follows:

[0075] ;

[0076] ;

[0077] In the formula, As reference component The gas phase density at the initial integration point is, express Location, express Location, represents the giant thermodynamic potential energy density of the mixture, Indicates a negative value of the equilibrium pressure, is the giant thermodynamic potential energy density difference, and the geometric structure and surface tension of the interface depend on the giant thermodynamic potential energy density difference. The specific calculation expression is as follows:

[0078] ;

[0079] In the formula, represents the density of the liquid phase in the mixture, Represents the density of the gas phase in the mixture.

[0080] 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 calculation expression of the average molecular free path is as follows:

[0081] ;

[0082] ;

[0083] ;

[0084] In the formula, is the diameter of the chain hard sphere, is the hard sphere number, is the hard sphere diameter, is the average molecular hard sphere diameter, is the mole fraction corresponding to the average molecular hard sphere diameter, is the average molecular free path, is the Boltzmann constant, is the interface temperature, To balance the pressure.

[0085] The Knudsen number is the ratio of the average molecular free path to the characteristic interface thickness, and the calculation expression is as follows:

[0086] ;

[0087] In the formula, is the Knudsen number.

[0088] Step 5. Predict the evolution of the spatial structure of the gas-liquid interface through 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 the 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 in 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.

[0089] Example

[0090] Under high-density environmental conditions, the droplets first undergo a subcritical evaporation phase transition. As the temperature of the gas-liquid interface continues to increase, 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 Figure 1, 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 has a supercritical phase transition trend. Figure 4 As shown in the figure, 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 is transformed into a supercritical fluid boundary mixing layer. Figure 2 The huge thermodynamic potential energy density difference under different pressure conditions is shown in With the change of density distribution in the gas-liquid interface, the distribution of the giant thermodynamic potential energy density difference in the interface is like a "mountain", and = 0, the density value represents the density of the saturated mixture on both sides of the gas-liquid interface. Figure 2 It can be seen that under lower interface temperature conditions (Ts = 350 K), the peak value of the giant thermodynamic potential energy density difference is significantly greater than its peak value at higher interface temperature (Ts = 500 K), and this peak value decreases with the increase of ambient pressure. When the gas-liquid interface temperature approaches the critical mixing temperature, the "foot of the mountain" on both sides of the giant thermodynamic potential energy density difference shrinks and approaches zero as a whole, which means that the density within the entire gas-liquid interface is approaching a unified density value.

[0091] Therefore, the present invention adopts the above-mentioned method for predicting the spatial structure of the gas-liquid interface in a high-density environment. By calculating and judging the spatial structure of the gas-liquid interface, the spatial structure of the gas-liquid interface in the high-density environment can be quickly and accurately predicted to determine whether the droplet has entered the supercritical state, thereby solving the problem that traditional optical experimental methods cannot capture the evolution process of the gas-liquid interface structure and are difficult to reveal the mechanism of the morphological structure transformation of liquid fuel jets in trans / supercritical environments.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. 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 solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for predicting the spatial structure of a gas-liquid interface in a high-density environment, characterized in that: 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 phase equilibrium state; Step 2, calculating the density distribution and influencing parameters of the reference component in the normal direction of the gas-liquid interface; The calculation expression of the density distribution of the reference component in the normal direction of the gas-liquid interface is as follows: ； ； In the formula, is the liquid density, is the gas phase density, is the density increment, N is the number of mesh nodes for discretization of the gas-liquid interface, represents the density of the liquid phase; Influencing parameters The calculation expression is as follows: ； ； ； ； ； In the formula, represents the binary interaction parameter, Represents pure components i The influencing parameters, Represents pure components j The influencing parameters, and are constants, represents Avogadro's constant, , and are the correlation coefficients of pure substances, represents the characteristic temperature, represents the critical compression factor, represents the eccentricity factor, represents the contrast state dipole moment; Step 3, according to the density distribution of the reference component in the normal direction of the gas-liquid interface, the characteristic interface thickness and surface tension of the gas-liquid interface are calculated; S31. Surface tension in spatial coordinate form in the normal direction of the gas-liquid interface The expression is as follows: ； S32. The spatial coordinate form in the normal direction of the gas-liquid interface is converted 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: ； ； In the formula, and are the densities of the liquid and gas components in the mixture, respectively. I Denotes reference component, subscript V , L represent the gas phase and liquid phase in phase equilibrium, respectively. and are the densities of the liquid and gas phases, respectively, The surface tension represents the density distribution in the normal direction of the gas-liquid interface; Characteristic interface thickness of the gas-liquid interface The calculation expression is as follows: ； ； In the formula, As reference component I The gas phase density at the initial integration point is, express Location, express 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; Huge thermodynamic potential energy density difference The calculation expression is as follows: ； In the formula, represents the density of the liquid phase in the mixture, It represents the density of gas phase in the mixture; 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 calculation expression for the average molecular free path is as follows: ； ； ； In the formula, is the diameter of the chain hard sphere, is the hard sphere number, is the hard sphere diameter, is the average molecular hard sphere diameter, for, is the average molecular free path, is the Boltzmann constant, is the interface temperature, To balance the pressure; Step 5: Predict the evolution of the spatial structure of the gas-liquid interface through the interface thickness, surface tension, average molecular free path and Knudsen number.

2. The method for predicting the spatial structure of the gas-liquid interface in a high-density environment according to claim 1, characterized in that: The Knudsen number is the ratio of the average molecular free path to the characteristic interface thickness, and the calculation expression is as follows: ； In the formula, is the Knudsen number.

3. The method for predicting the spatial structure of the gas-liquid interface in a high-density environment according to claim 1, characterized in that: In 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 the 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 in 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.

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