CN116738665A - Prediction method for heating evaporation process of water-in-oil emulsified oil drops - Google Patents
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Abstract
The invention relates to a prediction method for a heating evaporation process of water-in-oil emulsified oil drops, which specifically comprises a modeling process and a solving process; the modeling process is as follows: step 1: abstract and simplify the water-in-oil type emulsified oil liquid drop; step 2: establishing an equation to describe physical parameters of the water-in-oil emulsified oil; step 3: establishing an equation to describe the diffusion process of dispersed water droplets in the emulsified oil in the oil; step 4: establishing an equation to describe the evaporation process of oil and water on the surface of oil drops; step 5: establishing an equation to describe the heat transfer process in the oil drops; step 6: setting critical conditions to describe the polymerization process of dispersed water drops after the deactivation of the surfactant in oil drops; the solving process is as follows: step 7: and (5) carrying out iterative solution to obtain the temperature and the diameter of the liquid drop in the heating process and the distribution of components in the oil drop. The invention can predict the temperature, diameter and component distribution in the oil drop during the heating and evaporating process of the emulsified oil drop by using the heating and evaporating model.
Description
Technical Field
The invention belongs to the field of heating evaporation models, and particularly relates to a prediction method for a heating evaporation process of water-in-oil emulsified oil drops.
Background
The water-in-oil emulsified oil refers to multiphase dispersion system solution in which oil is a continuous phase, water is a disperse phase, and water is dispersed in the oil in the form of small water drops, and the water-in-oil emulsified oil can be used as a fuel in an internal combustion engine, so that the fuel economy can be improved, and the emission of pollutants such as soot, nitrogen oxides and the like can be reduced. The heating and evaporating process of the water-in-oil emulsified oil has important influence on the formation of spray atomization and mixed gas in a cylinder. However, due to the complex structure of the water-in-oil emulsified oil, the liquid drops have complex physical change process in the heating process, and no accurate method for predicting the heating evaporation process of the water-in-oil emulsified oil liquid drops exists at present.
At present, the common prediction method of the heating evaporation process of the water-in-oil type emulsified oil liquid drops is a prediction method based on multi-component miscible fuel, and the diffusion of dispersed small water drops in the emulsified oil is assumed to be the same as that of the miscible fuel, so that water in the oil drops can be infinitely diffused to the surfaces of the oil drops for evaporation. There are also methods which assume that the dispersed water in the emulsified oil exists in the form of a water droplet in the center of the oil droplet, and does not move and spread during heating. The method does not consider the influence of the surfactant on the heating and evaporating process of the liquid drops, and experimental researches show that the surfactant in the emulsified oil can be deactivated when the temperature exceeds a threshold value, and the dispersed small water drops in the emulsified oil can be quickly polymerized after the surfactant is deactivated, so that the method has an important influence on the heating and evaporating of the emulsified oil. The current prediction methods do not take these factors into account, and the prediction accuracy is low, especially after surfactant failure. The method takes experiments as the basis, fully considers the influence of surfactant inactivation after dispersion water droplet diffusion evaporation in the heating process of the water-in-oil type emulsified oil, has higher accuracy, and provides a new thought for the research of water-in-oil type emulsified oil droplet evaporation.
Disclosure of Invention
The invention aims to provide a prediction method for a heating evaporation process of water-in-oil emulsified oil drops, which solves the problem of low prediction precision in the prior art.
In order to solve the technical problems, the technical scheme of the invention is as follows: the method is characterized by specifically comprising a modeling process and a solving process;
the modeling process is as follows:
step 1: abstract and simplify the water-in-oil emulsified oil drops;
step 2: establishing an equation to describe physical parameters of the water-in-oil emulsified oil;
step 3: establishing an equation to describe the diffusion process of dispersed water droplets in the emulsified oil in the oil;
step 4: establishing an equation to describe the evaporation process of oil and water on the surface of oil drops;
step 5: establishing an equation to describe the heat transfer process in the oil drops;
step 6: setting critical conditions to describe the polymerization process of dispersed water drops after the deactivation of the surfactant in oil drops;
the solving process is as follows:
step 7: and (5) carrying out iterative solution to obtain the temperature and the diameter of the liquid drop in the heating process and the distribution of components in the oil drop.
Further, in the step 1, in order to reduce the modeling difficulty, the process of abstracting and simplifying the water-in-oil type emulsified oil droplets includes:
(1) Assuming that the liquid drops are spherical, and the heat transfer and value transmission process of the liquid drops in the heating process is ball symmetry, simplifying the heating and evaporation process of the liquid drops into a one-dimensional process;
(2) The ratio of the diameter of the dispersed droplets to the diameter of the oil drops in the emulsified oil is less than 1:200, and the droplets are assumed to be uniformly distributed in the oil drops;
(3) When the average temperature of the oil drops reaches the deactivation temperature of the surfactant, in order to reduce the modeling difficulty, the dispersed water drops in the oil drops are assumed to be instantaneously polymerized into a large water drop at the center of the oil drops, and the specific polymerization process is ignored;
(4) Assuming that the gas near the surface of the emulsified oil drops is in a quasi-stable state in the heating evaporation process, and the liquid and the gas near the surface of the oil drops are in a thermodynamic equilibrium state;
(5) In order to reduce the modeling difficulty, the dissolution process of the gas into the oil drops is ignored, and only one-way evaporation of the liquid is considered, so that the evaporation of the oil drops is Stefan flow, and the gas evaporated by the oil drops can be quickly mixed with air to form ideal gas.
Further, in the step 2, an equation is established to describe physical parameters of the water-in-oil emulsified oil, wherein the equation is as follows:
φ l (T)＝∑ i Y l,i φ l,i (T)
wherein ,φl (T) is a physical parameter including gas and liquid, Y l,i Phi is the mass fraction of different components l,i (T) is the physical property of the component i at different temperatures, and T is the temperature (K);
the mass fraction of the components of the physical parameters of the gas and the temperature of the gas are determined by adopting a 1/3 principle, namely
Y ref,i ＝Y vs,i +(Y v∞,i -Y vs,i )/3
T ref ＝T s +(T g -T s )/3
wherein ,Yref,i Is the reference mass fraction of the components of the gas physical parameters, Y vs,i Is the mass fraction of the gas near the surface of the oil drop of component i, Y v∞,i The mass fraction of the gas being the component i at infinity, T ref Is the reference temperature (K), T s Is the oil drop surface temperature (K), T g Is the gas temperature (K).
Further, in the step 3, an equation is established to describe a diffusion process of the dispersed water droplets in the emulsified oil in the oil, and a diffusion equation of the oil and the water in the droplets is as follows:
wherein ,Di Diffusion coefficient (m) for component i 2 /s)，Y l,i The mass fraction of the component i in the oil drop is represented by R as a spherical coordinate, and t asA bay(s);
the initial conditions for the diffusion equation for oil and water in a droplet are:
Y i (R,0)＝Y i,0
wherein ,Yi (R, 0) is the mass fraction of component i at a radius R,0 moment, Y i,0 A representation;
the boundary conditions of the diffusion equation of oil and water in the droplet at the center of the oil droplet are:
wherein ,Yl,i The mass fraction of the component i in the oil drops;
the boundary conditions at the surface of the oil droplet for the diffusion equation of oil and water within the droplet are:
wherein ,evaporation rate of oil droplets (kg/s), Y ls,i The mass fraction of component i in the vicinity of the oil droplet surface, ε i R is the ratio of the evaporation rates of oil and water d Is equivalent radius (m) of oil drop, D w,o Is the diffusion coefficient (m 2 /s)；
In the diffusion equation of oil and water in a droplet D i Diffusion coefficient (m) for component i 2 S), can be expressed as:
where κ is the Boltzmann constant, μ is the viscosity of the fluid (Pa·s), and r is the radius of the sphere (m).
Furthermore, in the step 3, an equation is established to describe the diffusion process of the dispersed water droplets in the emulsified oil in the oil, the emulsified oil droplets are assumed to be spherically symmetrical droplets, and the equation is solved only in the droplets, and after the water in the emulsified oil droplets is polymerized, the equation is not solved any more.
Further, in the step 4, an equation is established to describe the evaporation process of the oil and water on the surface of the oil drop, specifically: when the total evaporation rate isAfter being determined, the evaporation rates of water and oil at the oil droplet surface are expressed as:
wherein ,represents the total evaporation rate (kg/s) of the oil droplets,>indicating the evaporation rate (kg/s) of water and oil at the surface of the oil droplets;
epsilon in the evaporation rate equation of water and oil at the surface of oil droplets i Expressed as:
wherein ,εi (i=w, o) is the ratio of the evaporation rates of oil and water, Y vs,i (i=w, o) is the mass fraction of oil and water vapor at the oil droplet surface;
in the evaporation rate equation of water and oil at the surface of oil dropsThe method comprises the following steps:
wherein ,Rd Is milkInstantaneous radius (m), ρ of the oil droplets g Is the density of the gas (kg/m) 3 )，D v Is the diffusion coefficient (m 2 /s)；
To be solved forThe swood number Sh in the equation needs to be solved, expressed as:
wherein Red and Scd The reynolds number and schmitt number of the oil droplets, respectively;
f in the equation M Is about B M Can be expressed as:
in equation B M Is a spearmint prime number expressed as:
wherein ,Yv∞,i (i=w, o) is the mass fraction of water to oil at infinity, 0, Y vs,i (i=w, o) is the mass fraction of water vapor to oil vapor near the surface of the oil droplets.
Further, in the step 4, the equation established for describing the evaporation process of oil and water on the surface of oil droplets is solved, and the mass fraction Y of the water vapor and the oil vapor on the surface of oil droplets is determined accurately vs,i (i=w, o), which can be expressed as:
wherein ,Mi Is the molar mass (kg/mol) of component i, X vs,i The gas mole fraction of component i near the oil droplet surface can be expressed as: x is X vs,i ＝P v,i /P amb ，P amb Is ambient pressure (Pa), P v,i The vapor pressure (Pa) of component i near the surface of the oil droplets is expressed as:
wherein ,Xls,i Is the molar mass fraction of the liquid component i near the oil droplet surface, gamma i Is the activity coefficient of the component i,the saturated vapor pressure (Pa) of component i at the surface temperature of the oil droplets is expressed as:
wherein ,Tboil,i Is the boiling temperature (K), T of component i s Is the oil drop surface temperature (K), L i For component i, the vaporization potential value (J/kg) at the surface temperature of the oil droplets, R u Is the general gas constant (J/(K. Mol)).
Further, in the step 5, an equation is established to describe a heat transfer process in the oil drop, and a transfer equation of temperature in the oil drop is expressed as:
wherein T is time, R is the radius of the liquid drop under a spherical coordinate system, and T is temperature (K);
the initial conditions of the transfer equation for temperature within the oil droplets are:
T(R,0)＝T 0
wherein T (R, 0) is the temperature at the moment 0 at the spherical position R, and can be set as T 0 Normal temperature 297K;
the boundary conditions of the transfer equation of temperature within the drop at the center of the drop are:
the boundary conditions of the transfer equation of temperature within the oil droplet at the surface of the oil droplet are:
wherein ,Rd Is the equivalent radius (m) of the droplet,k is the heat transferred into the oil drop l Is the heat conductivity coefficient of the solution; alpha in the equation of transfer of temperature within oil droplets l The thermal diffusivity of a solution is expressed as:
α l ＝k l /(C pl ρ l )
wherein ,ρl Density of the solution (kg/m) 3 )，C pl Specific heat capacity (g/(kg×k)) of the solution;
the calculation formula of (2) is as follows:
wherein ,to reach the surface of the oil droplets, the heat is expressed as:
wherein ,Nu* To improve the Nusselt number, k g Is the thermal conductivity (W/(m.K)) of the gas, T g Is the heating temperature (K), T of the gas s Is the oil drop surface temperature (K), B T For the number of Stobetin heat transfers, σ is the Stefan Boltzmann constant, ε d The heat radiation coefficient of the heating cavity;
the energy consumed for evaporation of oil and water at the oil droplet surface is expressed as:
wherein , and />Evaporation rates (kg/s) of water and oil, respectively, L w and Lo Vaporization latent heat value (J/kg) of oil and water, respectively;
for calculationB appearing in the equation T Expressed as:
wherein ,can be expressed as:
wherein ,Cpl Is the specific heat capacity of liquid (J/(kg.K)), C pg Is the specific heat capacity of the gas (J/(kg. K)), le is LivissNumber, expressed as:
the modified nusselt number nux is expressed as:
wherein ,Red Reynolds number, pr d Is the number of the Philippine delta, F T Is a function of the number of heat transfers of the Stollding, expressed as:
further, the step 6 sets critical conditions to describe the polymerization process of dispersing water droplets after the deactivation of the surfactant in the oil droplets, specifically: critical conditions are the deactivation temperature T of the surfactant ds When the average temperature T in the oil drops ave Above the deactivation temperature T of the surfactant ds When the dispersed water in the oil drops is polymerized instantaneously into a big water drop at the center of the oil drops, and only the oil in the oil drops is evaporated.
Further, in the step 7, iterative solution is performed to obtain the temperature and diameter of the liquid drop in the heating process and the distribution of components in the oil drop, and the specific solution process is as follows:
(1) Application Y i (R,0)＝Y i,0 ，T(R,0)＝T 0 Initializing the temperature distribution and the component distribution in the oil drops;
(2) Applying equation phi l (T)＝∑ i Y l,i φ l,i (T) calculating physical properties of the fuel oil and physical properties of the gas;
(3) Applying equation Y vs ＝∑ i Y vs,i Calculating the mass fraction of oil vapor and water evaporation near the surface of the oil drop;
(4) Applying equations separatelyCalculating a Stollding prime number B M And the Stollding heat transfer number B T ；
(5) Applying equations separatelyCalculation of the Serpentis number F M And the Nusselt number F T ；
(6) Applying the equationCalculate the evaporation rate of water and oil at the surface of the oil drop +.>
(7) Updating the radius of the oil drop to obtain the radius of the oil drop at the next moment by using the following equation
wherein ,for the rate of change of the radius of the oil droplet (m/s), Δt is the calculation time step(s), +.>For the initial radius>For the equivalent radius (m) of the oil drop at the next moment,>the equivalent radius (m) of the oil drop at the previous moment;
(8) Applying the equationCalculate the heat transferred into the oil drop +.>
(9) Applying the equationSolving a temperature equation transmitted by temperature in oil drops to obtain temperature distribution in the oil drops, and then solving T ave Updating the average temperature of the oil droplets;
(10) Comparing the average temperature T of the oil droplets ave And deactivation temperature T of surfactant ds If the average temperature of the oil droplets is below the deactivation temperature of the surfactant, the equation is appliedSolving the components in the oil drops; if the average temperature of the oil drops is higher than the deactivation temperature of the surfactant, the dispersed water in the emulsified oil is polymerized into a big water drop at the center of the oil drops, and the component equation in the oil drops is not solved any more;
(11) Repeating the steps (2) - (10) until the temperature of the oil droplets reaches a preset temperature.
Compared with the prior art, the invention has the beneficial effects that:
(1) The heating evaporation model can be used for predicting the temperature, the diameter and the distribution of components in the oil drops in the heating evaporation process of the emulsified oil drops.
(2) The critical condition of deactivation of the surfactant in the oil drop is set, the influence of the surfactant on the heating and evaporating process of the liquid drop is described, and the polymerization process of dispersing water drops after the deactivation of the surfactant is considered, so that the prediction accuracy of the method is further improved.
(3) An equation is established to describe the diffusion process of dispersed water droplets in the emulsified oil in the oil, taking into account the effect of the water droplet diameter on the diffusion of water in the oil.
Drawings
FIG. 1 is a flow chart of a method for predicting the heating evaporation process of water-in-oil emulsified oil droplets.
FIG. 2 is a schematic diagram of a method for predicting the heating evaporation process of water-in-oil emulsified oil droplets.
FIG. 3 shows the development history of the temperature and diameter of the oil droplets when the water-in-oil emulsified oil droplets were not polymerized during heating.
FIG. 4 shows the development history of the temperature and diameter of the oil droplets when the water-in-oil emulsified oil droplets polymerize during heating.
Wherein 1 represents a mixed droplet of oil and water, 2 represents oil, 3 represents a large droplet, 4 represents a process in which no water is polymerized, and small droplets are diffused to the surface of the droplet to evaporate, 5 represents a process in which water is polymerized into a large droplet in oil, no water is evaporated, 9 represents a polymerization point of water in an experiment, and 10 represents a polymerization point of water predicted by this method.
Detailed Description
In order to better understand the present method by those skilled in the art, the present method is further described below with reference to specific embodiments.
The invention provides a prediction method for a heating evaporation process of water-in-oil emulsified oil drops, which specifically comprises a modeling process and a solving process, wherein the step flow is shown in figure 1;
the modeling process is as follows:
step 1: abstract and simplify the water-in-oil type emulsified oil liquid drop: the heating evaporation process of the emulsified oil drops is extremely complex, including the interaction of a gas/liquid interface and an oil/water interface, and it is difficult to directly simulate the heating evaporation process of the oil drops by using a CFD model. Therefore, to reduce the difficulty of modeling, abstracting and simplifying the water-in-oil emulsified oil droplets and simplifying the process includes:
(1) Assuming that the liquid drops are spherical, and the heat transfer and value transmission process of the liquid drops in the heating process is ball symmetry, simplifying the heating and evaporation process of the liquid drops into a one-dimensional process;
(2) Before the dispersed water in the emulsified oil is polymerized, the ratio of the diameter of the dispersed water droplets to the diameter of the oil droplets in the emulsified oil is smaller than 1:200, and the water droplets are assumed to be uniformly distributed in the oil droplets, so that the influence of the oil/water interface on the heating evaporation process can be ignored. However, the diffusion of water within the oil is still affected by the water droplet diameter;
(3) Although the polymerization of the dispersed water droplets in the oil droplets requires a certain time, the specific polymerization process is extremely complex, including the collision, convergence, fusion and other processes of the water droplets, and is difficult to describe accurately, meanwhile, the whole polymerization process is very short compared with the heating process of the oil droplets, so when the average temperature of the oil droplets reaches the deactivation temperature of the surfactant, in order to reduce the modeling difficulty, the dispersed water droplets in the oil droplets are assumed to be polymerized into a large water droplet in the center of the oil droplets instantly, and the specific polymerization process is ignored;
(4) Assuming that the gas near the surface of the emulsified oil drops is in a quasi-stable state in the heating evaporation process, and the liquid and the gas near the surface of the oil drops are in a thermodynamic equilibrium state;
(5) In order to reduce the modeling difficulty, the dissolution process of the gas into the oil drops is ignored, and only one-way evaporation of the liquid is considered, so that the evaporation of the oil drops is Stefan flow, and the gas evaporated by the oil drops can be quickly mixed with air to form ideal gas.
Step 2: the equation is established to describe the physical parameters of the water-in-oil emulsified oil, because the selection of the physical parameters of the liquid and the gas in the model has an important influence on the accuracy of the simulation. Physical property parameter phi of emulsified oil l (T) is determined by the mass fraction of oil and water in the emulsified oil and the temperature of the oil droplets, e.g. the liquid thermal conductivity k l Density ρ of liquid l Constant pressure specific heat capacity C of liquid pl The physical property parameter equation is:
φ l (T)＝∑ i Y l,i φ l,i (T)
wherein ,φl (T) is a physical parameter including gas and liquid, Y l,i Phi is the mass fraction of different components l,i (T) is the physical property of the component i at different temperatures, and T is the temperature (K);
physical properties of gases, e.g. gas thermal conductivity k g Density ρ of gas g Constant pressure specific heat capacity C of gas pg Gas diffusion coefficient D v It is also calculated according to the above equation, but the mass fraction of the gas physical parameter component and the temperature of the gas are determined by using 1/3 principle, namely
Y ref,i ＝Y vs,i +(Y v∞,i -Y vs,i )/3
T ref ＝T s +(T g -T s )/3
wherein ,Yref,i Is the reference mass fraction of the components of the gas physical parameters, Y vs,i Is the mass fraction of the gas near the surface of the oil drop of component i, Y v∞,i The mass fraction of the gas being the component i at infinity, T ref Is the reference temperature (K), T s Is the oil drop surface temperature (K), T g Is the gas temperature (K).
Step 3: the equation is established to describe the diffusion process of dispersed water droplets in the emulsified oil in the oil: the diffusion equation of oil and water in a droplet is:
wherein ,Di Diffusion coefficient (m) for component i 2 /s)，Y l,i The mass fraction of the component i in oil drops is represented by R, the spherical coordinates are represented by t, and the time(s) is represented by t;
the initial conditions for the diffusion equation for oil and water in a droplet are:
Y i (R,0)＝Y i,0
wherein ,Yi (R, 0) is the mass fraction of component i at a radius R,0 moment, Y i,0 A representation;
the boundary conditions of the diffusion equation of oil and water in the droplet at the center of the oil droplet are:
wherein ,Yl,i The mass fraction of the component i in the oil drops;
the boundary conditions of the diffusion equation of oil and water within the droplet at the surface of the oil droplet are coupled by empirical formulas:
wherein ,evaporation rate of oil droplets (kg/s), Y ls,i The mass fraction of component i in the vicinity of the oil droplet surface, ε i R is the ratio of the evaporation rates of oil and water d Is equivalent radius (m) of oil drop, D w,o Is the diffusion coefficient (m 2 /s)；
Since only the diffusion of oil and water is considered in the emulsified oil, the diffusion of water in the oil is equal to the diffusion of oil in the water, so D in the diffusion equation of oil and water in the droplet i Diffusion coefficient (m) for component i 2 S), can be expressed as:
where κ is the Boltzmann constant, μ is the viscosity of the fluid (Pa·s), and r is the radius of the sphere (m).
The method comprises the steps of establishing an equation to describe the diffusion process of dispersed water droplets in the emulsified oil in the oil, assuming the emulsified oil droplets to be spherical symmetrical droplets, and solving the equation only in the droplets, wherein after water in the emulsified oil droplets is polymerized, the equation is not solved any more, and the water in the oil droplets forms a large water droplet which can not be diffused, so that only the oil is evaporated.
Step 4: the set up equation describes the evaporation process of oil and water on the surface of the oil droplets, specifically: when the total evaporation rate isAfter being determined, the evaporation rates of water and oil at the oil droplet surface are expressed as:
wherein ,represents the total evaporation rate (kg/s) of the oil droplets,>indicating the evaporation rate (kg/s) of water and oil at the surface of the oil droplets;
epsilon in the equation i Expressed as:
wherein ,εi (i=w, o) is the ratio of the evaporation rates of oil and water, Y vs,i (i=w, o) is the mass fraction of oil and water vapor at the oil droplet surface;
for aqueous emulsified oil, the oil and water are simultaneously evaporated on the oil droplet surface before the dispersed water droplets polymerize, and only the oil is evaporated after the water has polymerized. The evaporation rate of the oil and water at the oil droplet surface can be determined by its steven flow at the oil droplet surface, then the evaporation rate of the water and oil at the oil droplet surface is determined by the equationThe method comprises the following steps:
wherein ,Rd To emulsify the instantaneous radius (m), ρ of the oil drop g Is the density of the gas (kg/m) 3 )，D v As water vapour in airDiffusion coefficient (m) 2 /s)；
To be solved forThe swood number Sh in the equation needs to be solved, expressed as:
wherein Red and Scd The reynolds number and schmitt number of the oil droplets, respectively;
f in the equation M Is about B M Can be expressed as:
in equation B M Is a spearmint prime number expressed as:
wherein ,Yv∞,i (i=w, o) is the mass fraction of water to oil at infinity, 0, Y vs,i (i=w, o) is the mass fraction of water vapor to oil vapor near the surface of the oil droplets.
Solving an equation established for describing the evaporation process of oil and water on the surface of oil drops, firstly, accurately determining the mass fraction Y of water vapor and oil vapor on the surface of the oil drops vs,i (i=w, o) according to the previous assumption, the oil and water in the oil droplets can be mixed with air rapidly after evaporation, so the mixture can be regarded as ideal gas, which can be expressed as:
wherein ,Mi Is the molar mass (kg/mol) of component i, X vs,i Gas near the surface of oil drop as component iThe volume mole fraction can be expressed as: x is X vs,i ＝P v,i /P amb ，P amb Is ambient pressure (Pa), P v,i The vapor pressure (Pa) of component i near the surface of the oil droplets is expressed as:
wherein ,Xls,i Is the molar mass fraction of the liquid component i near the oil droplet surface, gamma i Is the activity coefficient of the component i,the saturated vapor pressure (Pa) of component i at the surface temperature of the oil droplets is expressed as:
wherein ,Tboil,i Is the boiling temperature (K), T of component i s Is the oil drop surface temperature (K), L i For component i, the vaporization potential value (J/kg) at the surface temperature of the oil droplets, R u Is the general gas constant (J/(K. Mol)).
Step 5: the set-up equation describes the heat transfer process within the oil droplets, and for a spherically symmetric oil droplet, the transfer equation for temperature within the oil droplet is expressed as:
wherein T is time, R is the radius of the liquid drop under a spherical coordinate system, and T is temperature (K);
the initial conditions of the transfer equation for temperature within the oil droplets are:
T(R,0)＝T 0
wherein T (R, 0) is the temperature at the moment 0 at the spherical position R, and can be set as T 0 Normal temperature 297K;
the boundary conditions of the transfer equation of temperature within the drop at the center of the drop are:
the boundary conditions of the transfer equation of temperature within the oil droplet at the surface of the oil droplet are coupled by empirical formulas:
wherein ,Rd Is the equivalent radius (m) of the droplet,k is the heat transferred into the oil drop l Is the heat conductivity coefficient of the solution; alpha in the equation of transfer of temperature within oil droplets l The thermal diffusivity of a solution is expressed as:
wherein ,ρl Density of the solution (kg/m) 3 )，C pl Specific heat capacity (g/(kg×k)) of the solution;
Q d the calculation formula of (2) is as follows:
wherein ,to reach the surface of the oil droplets, the heat is expressed as:
wherein ,Nu* To improve the Nusselt number, k g Is the thermal conductivity (W/(m.K)) of the gas, T g Is the heating temperature (K), T of the gas s Is the oil drop surface temperature (K), B T For the number of Stobetin heat transfers, σ is the Stefan Boltzmann constant, ε d The heat radiation coefficient of the heating cavity;
the energy consumed for evaporation of oil and water at the oil droplet surface is expressed as: />
wherein , and />Evaporation rates (kg/s) of water and oil, respectively, L w and Lo Vaporization latent heat value (J/kg) of oil and water, respectively;
for calculationB appearing in the equation T Expressed as:
wherein ,can be expressed as:
wherein ,Cpl Is the specific heat capacity of liquid (J/(kg.K)), C pg Let is the number of Lives, which is expressed as the specific heat capacity of the gas (J/(kg. K)), and:
the modified nusselt number nux is expressed as:
wherein ,Red Reynolds number, pr d Is the number of the Philippine delta, F T Is a function of the number of heat transfers of the Stollding, expressed as:
step 6: setting critical conditions to describe the polymerization process of dispersed water drops after the deactivation of the surfactant in oil drops; as shown in fig. 2, specifically: critical conditions are the deactivation temperature T of the surfactant ds When the average temperature T in the oil drops ave Below the deactivation temperature T of the surfactant ds When the droplets are assumed to be uniformly distributed in the mixed droplet 1 of oil and water, no water is polymerized, the droplets can spread to the droplet surface to evaporate 4, and as the temperature increases, the average temperature T in the droplet ave Above the deactivation temperature T of the surfactant ds When the dispersed water in the oil drops 2 is polymerized instantly into a big water drop 3 at the center of the oil drops, no water is evaporated 5 after polymerization, and only the oil in the drops is evaporated.
The solving process is as follows:
step 7: and (3) carrying out iterative solution, and obtaining the temperature and the diameter of the liquid drop in the heating process and the distribution of components in the oil drop as shown in figure 1. The specific solving process is as follows:
(1) Applying equation Y i (R,0)＝Y i,0 ，T(R,0)＝T 0 Initializing the temperature distribution and the component distribution in the oil drops;
(2) Applying equation phi l (T)＝∑ i Y l,i φ l,i (T) MeterCalculating physical properties of fuel oil and gas;
(3) Applying equation Y vs ＝Σ i Y vs,i Calculating the mass fraction of oil vapor and water evaporation near the surface of the oil drop;
(4) Applying equations separatelyCalculating a Stollding prime number B M And the Stollding heat transfer number B T ；
(5) Applying equations separatelyCalculation of the Serpentis number F M And the Nusselt number F T ；
(6) Applying the equationCalculate the evaporation rate of water and oil at the surface of the oil drop +.>
(7) Updating the radius of the oil drop to obtain the radius of the oil drop at the next moment by using the following equation
wherein ,for the rate of change of the radius of the oil droplet (m/s), Δt is the calculation time step(s), +.>For the initial radius>For the equivalent radius (m) of the oil drop at the next moment,>the equivalent radius (m) of the oil drop at the previous moment;
(8) Applying the equationCalculate the heat transferred into the oil drop +.>
(9) Applying the equationSolving a temperature equation transmitted by temperature in oil drops to obtain temperature distribution in the oil drops, and then solving T ave Updating the average temperature of the oil droplets;
(10) Comparing the average temperature T of the oil droplets ave And deactivation temperature T of surfactant ds If the average temperature of the oil droplets is below the deactivation temperature of the surfactant, the equation is appliedSolving the components in the oil drops; if the average temperature of the oil drops is higher than the deactivation temperature of the surfactant, the dispersed water in the emulsified oil is polymerized into a big water drop at the center of the oil drops, and the component equation in the oil drops is not solved any more;
(11) Repeating the steps (2) - (10) until the temperature of the oil droplets reaches a preset temperature.
The evaporation process of the water-in-oil emulsified oil in heating is predicted by the method, and compared with an experiment. FIG. 3 shows the development history of the temperature and diameter of the oil droplets during heating, under the conditions that the surfactant in the emulsified oil is not deactivated during heating, and the dispersed water droplets in the oil droplets are not polymerized, with the heating temperature of 383K, the surfactant content in the emulsified oil being 0.5vol%, the water content being 30vol%, and the sauter mean diameter of the dispersed water droplets being 3.7. Mu.m. The squares are experimental results and the curves are predicted results. From the graph, the prediction result is better matched with the experimental result, which shows that the method can well predict the heating evaporation process of the liquid drop under the condition that no polymerization occurs.
FIG. 4 shows the development history of the temperature and diameter of the oil droplets during heating under the condition that the surfactant in the emulsified oil is deactivated during heating and the dispersed water droplets in the oil droplets are polymerized at a heating temperature of 383K, the surfactant content in the emulsified oil is 0.5vol%, the water content is 30vol%, and the sauter average diameter of the dispersed water droplets is 3.7 μm. The square is the experimental result, the solid curve is the predicted result considering water polymerization, the dotted curve is the predicted result not considering water polymerization, 9 represents the polymerization point of water in the experiment, and 10 represents the water polymerization point predicted by the method. From the graph, the predicted result of the method is better matched with the experimental result. This demonstrates that the method can predict well the heating evaporation process of droplets in the case of water polymerization. In the prior art, the polymerization process of water is not considered, and when water is polymerized, the predicted result and the experimental value have larger difference.
The above embodiments are merely illustrative of the preferred embodiments of the present invention, and the present invention is not limited to the above embodiments, and various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the design concept of the present invention should fall within the protection scope of the present invention, and the claimed technical content of the present invention is fully described in the claims.
Claims (10)
1. The method for predicting the heating evaporation process of the water-in-oil emulsified oil drops is characterized by comprising a modeling process and a solving process;
the modeling process is as follows:
step 1: abstract and simplify the water-in-oil type emulsified oil liquid drop;
step 2: establishing an equation to describe physical parameters of the water-in-oil emulsified oil;
step 3: establishing an equation to describe the diffusion process of dispersed water droplets in the emulsified oil in the oil;
step 4: establishing an equation to describe the evaporation process of oil and water on the surface of oil drops;
step 5: establishing an equation to describe the heat transfer process in the oil drops;
step 6: setting critical conditions to describe the polymerization process of dispersed water drops after the deactivation of the surfactant in oil drops;
the solving process is as follows:
step 7: and (5) carrying out iterative solution to obtain the temperature and the diameter of the liquid drop in the heating process and the distribution of components in the oil drop.
2. The method for predicting the heating evaporation process of water-in-oil emulsion droplets according to claim 1, wherein in step 1, in order to reduce modeling difficulty, the process of abstracting and simplifying the water-in-oil emulsion droplets comprises:
(1) Assuming that the liquid drops are spherical, and the heat transfer and value transmission process of the liquid drops in the heating process is ball symmetry, simplifying the heating and evaporation process of the liquid drops into a one-dimensional process;
(2) The ratio of the diameter of the dispersed droplets to the diameter of the oil drops in the emulsified oil is less than 1:200, and the droplets are assumed to be uniformly distributed in the oil drops;
(3) When the average temperature of the oil drops reaches the deactivation temperature of the surfactant, in order to reduce the modeling difficulty, the dispersed water drops in the oil drops are assumed to be instantaneously polymerized into a large water drop at the center of the oil drops, and the specific polymerization process is ignored;
(4) Assuming that the gas near the surface of the emulsified oil drops is in a quasi-stable state in the heating evaporation process, and the liquid and the gas near the surface of the oil drops are in a thermodynamic equilibrium state;
(5) In order to reduce the modeling difficulty, the dissolution process of the gas into the oil drops is ignored, and only one-way evaporation of the liquid is considered, so that the evaporation of the oil drops is Stefan flow, and the gas evaporated by the oil drops can be quickly mixed with air to form ideal gas.
3. The method for predicting the heating evaporation process of water-in-oil emulsified oil droplets according to claim 1, wherein in the step 2, an equation describing physical parameters of the water-in-oil emulsified oil is established, and the equation is:
φ l (T)＝∑ i Y l,i φ l,i (T)
wherein ,φl (T) is a physical parameter including gas and liquid, Y l,i Phi is the mass fraction of different components l,i (T) is the physical property of the component i at different temperatures, and T is the temperature (K);
the mass fraction of the components of the physical parameters of the gas and the temperature of the gas are determined by adopting a 1/3 principle, namely
Y ref,i ＝Y vs,i +(Y v∞,i -Y vs,i )/3
T ref ＝T s +(T g -T s )/3
wherein ,Yref,i Is the reference mass fraction of the components of the gas physical parameters, Y vs,i Is the mass fraction of the gas near the surface of the oil drop of component i, Y v∞,i The mass fraction of the gas being the component i at infinity, T ref Is the reference temperature (K), T s Is the oil drop surface temperature (K), T g Is the gas temperature (K).
4. The method for predicting the heating evaporation process of water-in-oil emulsified oil droplets according to claim 1, wherein the equation established in the step 3 describes the diffusion process of the dispersed water droplets in the emulsified oil in the oil, and the diffusion equation of the oil and water in the droplets is:
wherein ,Di Diffusion coefficient (m) for component i 2 /s)，Y l,i The mass fraction of the component i in oil drops is represented by R, the spherical coordinates are represented by t, and the time(s) is represented by t;
the initial conditions for the diffusion equation for oil and water in a droplet are:
Y i (R,0)＝Y i,0
wherein ,Yi (R, 0) is the mass fraction of component i at a radius R,0 moment, Y i,0 A representation;
the boundary conditions of the diffusion equation of oil and water in the droplet at the center of the oil droplet are:
wherein ,Yl,i The mass fraction of the component i in the oil drops;
the boundary conditions at the surface of the oil droplet for the diffusion equation of oil and water within the droplet are:
wherein ,evaporation rate of oil droplets (kg/s), Y ls,i The mass fraction of component i in the vicinity of the oil droplet surface, ε i R is the ratio of the evaporation rates of oil and water d Is equivalent radius (m) of oil drop, D w,o Is the diffusion coefficient (m 2 /s)；
In the diffusion equation of oil and water in a droplet D i Diffusion coefficient (m) for component i 2 S), can be expressed as:
where κ is the Boltzmann constant, μ is the viscosity of the fluid (Pa·s), and r is the radius of the sphere (m).
5. The method for predicting the heating evaporation process of water-in-oil type emulsified oil droplets according to claim 4, wherein in the step 3, an equation describing the diffusion process of the dispersed water droplets in the emulsified oil is established, the emulsified oil droplets are assumed to be spherically symmetrical droplets, and the equation is solved only in the droplets, and when the water in the emulsified oil droplets is polymerized, the equation is not solved.
6. The method for predicting the heating evaporation process of water-in-oil emulsified oil droplets according to claim 1, wherein the equation describing the evaporation process of oil and water on the surface of oil droplets in step 4 is specifically as follows: when the total evaporation rate isAfter being determined, the evaporation rates of water and oil at the oil droplet surface are expressed as:
wherein ,represents the total evaporation rate (kg/s) of the oil droplets,>indicating the evaporation rate (kg/s) of water and oil at the surface of the oil droplets;
epsilon in the equation i Expressed as:
wherein ,εi (i=w, o) is the ratio of the evaporation rates of oil and waterValue of Y vs,i (i=w, o) is the mass fraction of oil and water vapor at the oil droplet surface;
in the equationThe method comprises the following steps:
wherein ,Rd To emulsify the instantaneous radius (m), ρ of the oil drop g Is the density of the gas (kg/m) 3 )，D v Is the diffusion coefficient (m 2 /s)；
Solving forThe swood number Sh in the equation needs to be solved, expressed as:
wherein Red and Scd The reynolds number and schmitt number of the oil droplets, respectively;
f in the equation M Is about B M Can be expressed as:
in equation B M Is a spearmint prime number expressed as:
wherein ,Yv∞,i (i=w, o) is the mass fraction of water to oil at infinity, 0, Y vs,i (i=w, o) is water near the surface of the oil dropletThe mass fraction of vapor to oil vapor.
7. The method for predicting the heating evaporation process of water-in-oil emulsified oil droplets as set forth in claim 6, wherein said step 4 solves the equation describing the evaporation process of oil and water on the surfaces of oil droplets, and it is necessary to accurately determine the mass fraction Y of water vapor and oil vapor on the surfaces of oil droplets vs,i (i=w, o), which can be expressed as:
wherein ,Mi Is the molar mass (kg/mol) of component i, X vs,i The gas mole fraction of component i near the oil droplet surface can be expressed as: x is X vs,i ＝P v,i /P amb ，P amb Is ambient pressure (Pa), P v,i The vapor pressure (Pa) of component i near the surface of the oil droplets is expressed as:
wherein ,Xls,i Is the molar mass fraction of the liquid component i near the oil droplet surface, gamma i Is the activity coefficient of the component i,the saturated vapor pressure (Pa) of component i at the surface temperature of the oil droplets is expressed as:
wherein ,Tboil,i Is the boiling temperature (K), T of component i s Is the oil drop surface temperature (K), L i For component i, the vaporization potential value (J/kg) at the surface temperature of the oil droplets, R u Is the general gas constant (J/(K. Mol)).
8. The method for predicting the heating evaporation process of water-in-oil emulsified oil droplets according to claim 1, wherein the equation set up in step 5 describes the heat transfer process in the oil droplets, and the equation for the transfer of temperature in the oil droplets is expressed as:
wherein T is time, R is the radius of the liquid drop under a spherical coordinate system, and T is temperature (K);
the initial conditions of the transfer equation for temperature within the oil droplets are:
T(R,0)＝T 0
wherein T (R, 0) is the temperature at the moment 0 at the spherical position R, and can be set as T 0 Normal temperature 297K;
the boundary conditions of the transfer equation of temperature within the drop at the center of the drop are:
the boundary conditions of the transfer equation of temperature within the oil droplet at the surface of the oil droplet are:
wherein ,Rd Is the equivalent radius (m) of the droplet,k is the heat transferred into the oil drop l Is the heat conductivity coefficient of the solution; alpha in the equation of transfer of temperature within oil droplets l The thermal diffusivity of a solution is expressed as:
α l ＝k l /(C pl ρ l )
wherein ,ρl Density of the solution (kg/m) 3 )，C pl Specific heat capacity (g/(kg×k)) of the solution;
the calculation formula of (2) is as follows:
wherein ,to reach the surface of the oil droplets, the heat is expressed as:
where Nu is the modified nucelt number, k g Is the thermal conductivity (W/(m.K)) of the gas, T g Is the heating temperature (K), T of the gas s Is the oil drop surface temperature (K), B T For the number of Stobetin heat transfers, σ is the Stefan Boltzmann constant, ε d The heat radiation coefficient of the heating cavity;
the energy consumed for evaporation of oil and water at the oil droplet surface is expressed as:
wherein , and />Evaporation rates (kg/s) of water and oil, respectively, L w and Lo Vaporization latent heat value (J/kg) of oil and water, respectively;
for calculationB appearing in the equation T Expressed as:
wherein ,can be expressed as:
wherein ,Cpl Is the specific heat capacity of liquid (J/(kg.K)), C pg Let is the number of Lives, which is expressed as the specific heat capacity of the gas (J/(kg. K)), and:
the modified nusselt number nux is expressed as:
wherein ,Red Reynolds number, pr d Is the number of the Philippine delta, F T Is a function of the number of heat transfers of the Stollding, expressed as:
9. the method for predicting the heating evaporation process of water-in-oil emulsified oil droplets according to claim 1, wherein the setting of critical conditions in step 6 describes the polymerization process of dispersed water droplets after deactivation of the surfactant in the oil droplets, specifically: critical conditions are the deactivation temperature T of the surfactant ds When the average temperature T in the oil drops ave Above the deactivation temperature T of the surfactant ds When the dispersed water in the oil drops is polymerized instantaneously into a big water drop at the center of the oil drops, and only the oil in the oil drops is evaporated.
10. The method for predicting the heating and evaporating process of water-in-oil emulsified oil droplets according to claim 1, wherein the iterative solution is performed in the step 7, and the temperature, the diameter and the component distribution in the oil droplets in the heating process are obtained, and the specific solution process is as follows:
(1) Application Y i (R,0)＝Y i,0 ，T(R,0)＝T 0 Initializing the temperature distribution and the component distribution in the oil drops;
(2) Applying equation phi l (T)＝∑ i Y l,i φ l,i (T) calculating physical properties of the fuel oil and physical properties of the gas;
(3) Applying equation Y vs ＝∑ i Y vs,i Calculating the mass fraction of oil vapor and water evaporation near the surface of the oil drop;
(4) Applying equations separatelyCalculating a Stollding prime number B M And the Stollding heat transfer number B T ；
(5) Applying equations separatelyCalculation of the Serpentis number F M And the Nusselt number F T ；
(6) Applying the equationCalculate the evaporation rate of water and oil at the surface of the oil drop +.>
(7) Updating the radius of the oil drop to obtain the radius of the oil drop at the next moment by using the following equation
wherein ,for the rate of change of the radius of the oil droplet (m/s), Δt is the calculation time step(s), +.>For the initial radius>For the equivalent radius (m) of the oil drop at the next moment,>the equivalent radius (m) of the oil drop at the previous moment;
(8) Applying the equationCalculate the heat transferred into the oil drop +.>
(9) Applying the equationSolving a temperature equation transmitted by temperature in oil drops to obtain temperature distribution in the oil drops, and then solving T ave Updating the average temperature of the oil droplets;
(10) Comparing the average temperature T of the oil droplets ave And deactivation temperature T of surfactant ds If the average temperature of the oil droplets is below the deactivation temperature of the surfactant, the equation is appliedSolving the components in the oil drops; if the average temperature of the oil drops is higher than the deactivation temperature of the surfactant, the dispersed water in the emulsified oil is polymerized into a big water drop at the center of the oil drops, and the component equation in the oil drops is not solved any more;
(11) Repeating the steps (2) - (10) until the temperature of the oil droplets reaches a preset temperature.
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| CN103364439A (en) * | 2013-07-15 | 2013-10-23 | 南京理工大学 | Method for determining object surface temperature under fog-comprising condition |
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