CN111144012B - Calculation method for ice particle deposition process in cold space - Google Patents
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Abstract
The invention discloses a calculation method for an ice particle deposition process in a cold space, which is based on a snow accumulation phenomenon, analyzes the deposition process of ice particles on a cold wall surface from a gas-solid two-phase flow, establishes the calculation method for the ice particle deposition process in the cold space, explores the influence of an initial position of the ice particles, the diameters of the ice particles and a tube bundle arrangement mode on an ice particle motion track and the deposition position, intuitively reflects the deposition process of the ice particles on a single tube bundle and a fork tube bundle in the cold space by using calculation data, and ensures that the research of the ice particle deposition process is more perfect; the calculation result can be used for guiding actual production, namely, the tube bundles related to frosting working conditions are more suitable for adopting fork tube bundles; and the ice particle deposition amount on the surface of the tube bundle can be reduced by reducing the initial temperature of the humid air.
Description
Technical Field
The invention belongs to the field of a calculation method of an ice particle deposition process, and particularly relates to a calculation method for an ice particle deposition process in a cold space.
Background
In recent years, studies on the phenomenon of ice particle deposition have been attracting attention of students. The research of the ice particle deposition process has important theoretical value and wide application value, such as meteorology (snow transportation and deposition), food field (ice cream production), engineering material (cold spray deposition) and the like. Therefore, understanding the dynamic behavior of the ice particle deposition process is of great importance for scientific research and device design. The frosting mechanism of the wet air near the cold wall surface can be known, the deposition process of ice particles on the cold wall surface determines the geometric structure of the frost layer, and the frosting mechanism has important significance for researching the structure and physical properties of the frost layer. From the snow accumulation phenomenon, the ice particle deposition process near the cold wall surface can be divided into three steps: (1) suspending: ice particles located far from the cold wall are transported from the fluid to the vicinity of the stationary cold wall. Wherein, the transportation process of the ice particles doing Brownian motion is mainly convection and diffusion, and the transportation process of the ice particles doing non Brownian motion is mainly physical force caused by gravity and fluid resistance; (2) deposition: ice particles are deposited near the cold wall, the deposition process being primarily affected by various short-range interactions of chemical colloids between the ice particles and the cold wall, including primarily the interaction of the two electron layers with van der waals interactions, hydrodynamic forces, hydration (structural) forces, hydrophobic surface hydrophobicity, and interactions between polymer adsorption layers when macromolecules or polymers adsorb to the ice particle surface and interface. Deposition mechanisms mainly include inertial collision, gravity sedimentation, static electricity, thermophoresis, brown diffusion and lift force; (3) crawling: the ice particles may "roll" or jump a small amount on the snow surface. Experimental results show that if the formed ice particles cannot adhere to the cold wall surface, the growth of the frost layer can be inhibited, i.e. the frosting amount is reduced when the wet air flows through the cold wall surface at high speed. However, due to limitations of experimental techniques (e.g., it is difficult to accurately determine continuous motion trajectories of individual micrometer-sized ice particles by experimental methods), further research on the ice particle deposition process is required. In mathematical models involving turbulent Navier-Stokes equations, snow is typically added in some fashion, and one or both steps in the process of crawling, jumping, and levitation are ignored for the most part. Since ice particle movement involves not only interactions between the fluid and the solid, fluid flow is also affected by the complex boundaries formed by the ice particle deposition. Thus, the conventional CFD method cannot completely predict the ice particle deposition process. In 1998, masselot and Chopard combined the lattice Boltzmann method with the cellular automaton method, established a new mathematical model describing the snow deposition process, namely an LBM-LGA (Lattice Gas Automata) deposition model, and studied the influence of wind on the snow deposition morphology by using the model to reproduce the oscillation ripple formed on the snow deposition surface. Unlike the conventional lagrangian tracking method, the method is less computationally intensive, mainly because it performs numerical simulation calculations with ice particles as particles moving on a grid with a certain probability. Thereafter, the model is also widely used in particle deposition processes. However, in describing the ice particle deposition process, the consideration of ice particle stress is not comprehensive, and certain errors exist in the ice particle deposition judgment mode, so that a new mathematical model needs to be established to solve the problem. In the current research results, the research on the ice particle deposition process in the cold space and the influence of the initial ice particle position, the ice particle diameter and the tube bundle arrangement mode on the motion track and the deposition position of the ice particles is very limited.
Disclosure of Invention
In order to better solve the problem of the ice particle deposition process on the single-row tube bundles and the fork-row tube bundles in the cold space, the influence of the initial position of the ice particles, the diameter of the ice particles and the arrangement mode of the tube bundles on the motion track and the deposition position of the ice particles is explored, so that the research of the ice particle deposition process is more perfect.
Aiming at the problems, the invention provides a calculation method for the ice particle deposition process in the cold space, which is based on the snow accumulation phenomenon, analyzes the deposition process of ice particles on the cold wall surface from the gas-solid two-phase flow, and establishes the calculation method for the ice particle deposition process in the cold space. The method comprises the steps that the ice particles are not broken when collision occurs between the ice particles and the cold wall surface, and the crawling process of the ice particles on the cold wall surface is ignored; assuming that fluid and ice particles move on the same grid node, simulating a flow field and an ice particle movement process by using a grid Boltzmann model and an LGA model respectively, wherein the probability of the ice particles moving to adjacent grid points depends on local flow velocity and other external forces acting on the ice particles; neglecting the crawling process of the ice particles, the movement process of the ice particles mainly comprises two parts of transportation and deposition.
In order to solve the technical problems, the invention adopts the following technical scheme:
the calculation method for the ice particle deposition process in the cold space mainly comprises the following steps:
step one, according to the calculation domain and the grid size required by the physical model calculation, carrying out grid division, as shown in figure 1;
initializing the density and the speed of the model calculation domain and the initial position and the initial speed of ice particles;
step three, solving a flow field of the calculation domain;
the flow field evolution equation is:
where f is the particle distribution function and τ is the relaxation time.
Equilibrium distribution functionThe method comprises the following steps:
wherein c s Is the lattice sound velocity omega i Is weight coefficient, ρ is density, e i Is a discrete velocity. Equilibrium speed u eq The method comprises the following steps:
the intermolecular interaction force is:
F(x)＝F f (x)+F g (x)
wherein, the interaction force between fluids is:
where ψ (ρ) =ρ * [1-exp(-ρ/ρ * )]Is an effective density. G 1 And G 2 The coefficients of interaction between the fluids at adjacent and sub-adjacent locations, respectively.
The gravity is as follows:
F g (x)＝ρ(x)g
solving the density and the speed of each node in the computing domain;
the density and velocity are calculated as:
(step five) calculating the displacement and the speed of the ice particles;
(1) Transport: at the next moment, the ice particles at any point in the flow field move to the adjacent grid point or stay at the original position with a certain probability. As shown in fig. 2, let t be time, grid node r p And an ice particle is arranged on the ice particle. t+delta t At this moment, whether the ice particles move to the nearest neighbor or stay at the original node depends mainly on the transport probabilities p in directions 1, 3, 5 and 7 α The final lattice point positions of the corresponding ice particles are as follows:
r′ p ＝r p +(v 1 e 1 +v 2 e 2 +v 3 e 3 +v 4 e 4 )δ t
wherein v is α Is as followsThe probability of the mechanical Boolean variable with the value of 1 is p α 。
In the D2Q9 model, t+delta t At the moment, the ice particles move to east, north, west, south (i.e. p 1 、p 3 、p 5 And p 7 ) Is a transport probability p of (2) α The expression is:
wherein,for time step delta t The actual displacement of the ice particles +.>
The equation of motion of the ice particles taking into account drag forces, gravity and buoyancy is:
wherein F is d For drag force, F g Is gravity and buoyancy.
Gravity and buoyancy expressions are:
F g ＝(m p -m g )g
wherein,is ice particle mass ρ i Is ice density, r i In order to obtain the radius of the ice particles,for the buoyancy force, ρ, of ice particles g G is gravity acceleration, which is the gas density.
In the particle tracking method, the speed and displacement of the ice particles are solved through an ice particle motion equation, and the specific expression is as follows:
wherein τ p For the relaxation time of the ice particles, the specific value is Stokes number St=τ p u/L determination. Time step delta t The actual displacement of the ice particles is
(2) And (3) deposition: when the ice particles collide with the cold wall surface, part of the ice particles do not move any more and start to deposit on the cold wall surface, and finally become a part of the frost layer on the cold wall surface. Using critical deposition rate V cr As a criterion for judging whether or not ice particles are deposited. When the normal speed of the ice particles impacting the cold wall surface is smaller than the critical deposition speed V cr During this time, ice particles are deposited on the cold wall surface. Based on the operation of branch and Dunn, critical deposition rate V cr Can be expressed as:
V cr ＝[2K/(D i R 2 )] 10/7
wherein D is i Is the ice particle diameter.Is an effective stiffness coefficient. Related parametersE s And E is p Young's moduli of the cold wall surface and the ice particles, respectively. V (v) s And v p Poisson's ratio for cold wall and ice particles, respectively. R is a motion recovery coefficient, and is usually 0.9.
And (step six), returning to the cyclic calculation in the step three until all ice particles are deposited on the wall surface of the tube bundle or move outside the calculation domain, and ending the procedure.
The invention has the following advantages and beneficial effects:
according to the calculation method for the ice particle deposition process in the cold space, the influence of the initial position of the ice particles, the diameters of the ice particles and the arrangement mode of the tube bundles on the motion track and the deposition position of the ice particles is explored, and the deposition processes of the ice particles on the single-row tube bundles and the fork-row tube bundles in the cold space are intuitively embodied by using calculation data, so that the study of the ice particle deposition process is more perfect; the calculation result can be used for guiding actual production, namely, the tube bundles related to frosting working conditions are more suitable for adopting fork tube bundles; and the ice particle deposition amount on the surface of the tube bundle can be reduced by reducing the initial temperature of the humid air.
Drawings
FIG. 1 illustrates meshing and velocity vectors of a D2Q9 model;
wherein, fig. 1 (a) is a grid division diagram of the D2Q9 model; fig. 1 (b) is a velocity vector diagram of the D2Q9 model.
FIG. 2 is a chart of ice particle transport rules for an LBM-LGA ice particle deposition model.
FIG. 3 is a physical model of the ice particle deposition process on a single row tube bundle and a fork row tube bundle;
wherein, FIG. 3 (a) is a single row tube bundle physical model; fig. 3 (b) is a fork tube bundle physical model.
FIG. 4 shows a single row tube bundle velocity field, ice particle motion trajectories and deposition positions of 50 μm and 200 μm diameters, respectively;
wherein FIG. 4 (a) is a single row tube bundle velocity field; FIG. 4 (b) is a motion profile and deposition location of ice particles 50 μm in diameter in a single row of tube bundles; FIG. 4 (c) is a motion profile and deposition position of ice particles 200 μm in diameter in a single row tube bundle.
FIG. 5 shows the velocity field of the fork tube bundle, the motion trajectory and the deposition position of ice particles with diameters of 50 μm and 200 μm, respectively;
wherein fig. 5 (a) is a fork tube bundle velocity field; FIG. 5 (b) is a motion profile and deposition position of ice particles 50 μm in diameter in a fork tube bundle; FIG. 5 (c) is a motion profile and deposition position of 200 μm diameter ice particles in a fork tube bundle.
Fig. 6 is a physical model of the ice particle swarm deposition process on a interdigitated tube bundle.
Fig. 7 shows the deposition of ice particle groups on the surface of the tube bundle at t=1 s with different relative humidity of the humid air inlet;
wherein fig. 7 (a) is a view of the deposition of ice particles on the surface of the tube bundle with the relative humidity of the wet air inlet in case_1, fig. 7 (b) is a view of the deposition of ice particles on the surface of the tube bundle with the relative humidity of the wet air inlet in case_2, and fig. 7 (c) is a view of the deposition of ice particles on the surface of the tube bundle with the relative humidity of the wet air inlet in case_3.
Fig. 8 shows the deposition of ice particles on the surface of the tube bundle at t=1s at different initial temperatures of humid air;
fig. 8 (a) shows the bundle surface ice particle group deposition condition of the initial temperature of the humid air in case_1, fig. 8 (b) shows the bundle surface ice particle group deposition condition of the initial temperature of the humid air in case_4, and fig. 8 (c) shows the bundle surface ice particle group deposition condition of the initial temperature of the humid air in case_5.
Detailed Description
The invention is illustrated in further detail by the following examples.
Example 1
And respectively simulating the ice particle deposition processes of the ice particles in the single-row tube bundles and the staggered tube bundles by using a calculation method of the ice particle deposition process in the cold space. FIG. 3 shows a corresponding physical model, the selected calculation domain is 0.25mX0.02 m, the calculation grid number is 500X 40, the single-row tube bundle and the fork-row tube bundle are composed of five rows of circular tubes, and the diameters of the circular tubes are D t =0.01m, tube spacing s t The upper and lower boundaries are symmetric boundaries, the left boundary is a velocity boundary, the right boundary is an outflow boundary, and the tube bundle wall is a non-slip wall boundary. The air flow rate was v=0.05 m/s. In the simulation process, 30000 steps are operated without adding ice particles, so that the flow field is irrelevant to the initial value. Subsequently, numerical simulation calculations were performed on two groups of ice particles having diameters of 50 μm and 200 μm, respectively, each group having eleven ice particles located at eleven different positions (A (0.0 m,0.001 m), B (0.0 m, 0.003m), C (0.0 m,0.005 m), D (0.0 m, 0.0070 m), E (0.0 m,0.009 m), F (0.0 m, 0.010m), G (0.0 m, 0.01m), H (0.0 m)0.013 m), I (0.0 m,0.015 m), J (0.0 m,0.017 m), K (0.0 m,0.019 m)), and the relevant parameters are shown in Table 1.
TABLE 1 parameters relating to ice particles of different diameters
FIG. 4 shows the velocity field of a single row tube bundle, the motion profile and the deposition position of ice particles with diameters of 50 μm and 200 μm, respectively. From the simulation results, the motion trace of the ice particles with the size of 50 μm in the inlet area is basically matched with the streamline. On the windward side of the circular tube, 50 μm ice particles are relatively smaller in St number, the motion of the ice particles is less influenced by inertia of the ice particles, the motion track of the ice particles is basically consistent with a streamline, part of the ice particles directly impact the wall of the circular tube, and the ice particles impact the wall surface of the circular tube along the normal direction and are deposited due to the smaller volume of the ice particles and larger critical deposition speed, so that 50 μm ice particles E, F and G are deposited on the windward side of the first row of circular tube. The 50 μm ice particles D and H are deposited on the leeward side of the second row and the third row of circular tubes respectively, influenced by the leeward side reflux entrainment effect of the circular tubes. Since the windward side of the rear row of circular tubes is positioned in the wake area of the front row of circular tubes, the influence of flow field disturbance is relatively large, and 50 mu m ice particles C and I are deposited on the windward side of the fourth row of circular tubes. In addition, since the 50 μm ice particles A, B, J and K are relatively far from the tube wall, the ice particles A, B, J and K do not deposit on the tube. The ice particles of 200 μm have a large St number, and the ice particle movement is greatly affected by the inertia of the ice particles. On the windward side of the circular tube, the motion track of the ice particles deviates from the streamline, so that the ice particles are easier to strike the wall of the circular tube, and as the normal speed of the ice particles striking the wall of the circular tube is smaller than the critical deposition speed, 200 mu m ice particles D, E, F, G and H are deposited on the windward side of the first row of circular tubes. Meanwhile, 200 mu m ice particles C and I are deposited on the windward side of the fifth row of circular tubes, mainly because the windward side of the rear row of circular tubes is positioned in the wake zone of the front row of circular tubes, and are influenced by flow field disturbance, and the ice particles are more easy to deposit in the zone. In addition, since the ice particles A, B, J and K are far from the tube wall, 200 μm ice particles A, B, J and K do not deposit on the tube.
FIG. 5 shows the velocity field of the fork tube beam and the trajectories and deposition positions of ice particles with diameters of 50 μm and 200 μm, respectively. The simulation results show that the motion track of the 50 mu m ice particles in the inlet area is basically matched with the streamline. On the windward side of the circular tube, the motion track of the 50 mu m ice particles is matched with the streamline because of being less influenced by the inertia of the circular tube, part of the ice particles directly impact the wall of the circular tube, and the ice particles are deposited after impacting the wall surface of the circular tube along the normal direction because of the high critical deposition speed of the ice particles, so that the 50 mu m ice particles E, F, A, J, K and G are respectively deposited on the windward sides of the circular tubes in the first row, the second row and the third row. The 50 mu m ice particles D are deposited on the leeward side of the third row of circular tubes under the influence of the back-flow entrainment effect on the leeward side of the circular tubes. Since the ice particles B, C, H and I are relatively far from the tube wall, the 50 μm ice particles B, C, H and I do not deposit on the tube. For 200 μm ice particles, the St number is relatively larger, the motion of the ice particles is greatly influenced by the inertia of the ice particles, the motion track of the ice particles is difficult to change, so the ice particles are easier to strike the windward side of the circular tube, and 200 μm ice particles E, F, G, A, J and K are respectively deposited on the windward sides of the circular tubes of the first row and the second row because the normal speed of the ice particles striking the wall of the circular tube is smaller than the critical deposition speed of the ice particles. 200 μm ice particles B, C, D, H and I do not deposit on the tube because the ice particles B, C, D, H and I are relatively far from the tube wall and the larger volume of ice particles are more difficult to entrain by air in the back-flow region on the lee side of the tube.
Comparing fig. 4 and fig. 5, it can be seen that the amount of ice particles deposited in the fork tube bundle is smaller than that in the single row tube bundle under the same condition, mainly because the windward side of the rear row of round tubes of the fork tube bundle is less affected by the leeward side of the front row of round tubes. Therefore, in order to reduce the frosting amount, the tube bundle arrangement mode related to the frosting working condition is more suitable for adopting the staggered tube bundles.
Example 2
And simulating the deposition process of the ice particle group in the fork tube bundle by using a calculation method of the ice particle deposition process in the cold space. FIG. 6 shows a corresponding physical model, the calculation domain is selected to be 0.03mX0.003 m, the calculation grid number is 1200X 120, and five columns and seven roots with the diameter D are arranged in the calculation domain t Round tubes with 0.002m in equilateral triangle cross arrangement with a tube spacing s t =0.003 m, the upper and lower boundaries are symmetric boundaries,the left boundary is a speed boundary, the right boundary is an outflow boundary, and the wall surface of the tube bundle is a non-slip wall surface boundary. The wet air inlet flow rate was v=10m/s, reynolds number was re=66, stokes number was 0.01.
Assuming that the water vapor in the wet air forms ice particles in a uniform and in-phase nucleation mode and the formed ice particles are spherical, according to a classical nucleation theory, the nucleation rate is calculated as follows:
wherein n is c In order to achieve a nucleation coefficient,for the temperature correction coefficient, γ is equal to 1.32, Δh is the phase change process specific enthalpy, R= 461.4J/(kg.K) is the gas constant, T g Is the water vapor temperature ρ g For the water vapor density ρ i Is ice density, sigma i Is the interfacial free energy of ice particles, M w For the quality of water molecule, < > and->Is Kelvin-Helmholtz critical radius, p va For water vapour pressure, p sat Is saturated with water vapor pressure, K b ＝1.3807×10 - 23 J/K is the Boltzmann constant. The number of ice particles formed in unit time in the calculation domain under different simulation working conditions can be calculated by the formula (1), and is shown in the table 2. In the simulation process, 30000 steps are operated without adding ice particles, so that the flow field is irrelevant to the initial value. By 30000 steps, a corresponding number of ice particles are randomly thrown into grid points in the calculation domain x=0.006-0.02 m and y=0-0.003 m.
TABLE 2 calculation of the number of ice particles formed per unit time in the field for different simulation conditions
Fig. 7 shows the ice particle swarm deposition on the tube bundle surface at t=1 s for different relative humidities of the humid air inlet. Wherein red represents non-deposited ice particles and blue represents deposited ice particles. As shown by simulation results, for the first row of tube bundles, on the windward side of the circular tube, due to the large critical deposition speed of the ice particles, part of the ice particles impact the wall of the circular tube along the normal direction and then are deposited. At the position of + -45 DEG on the leeward side of the circular tube, partial ice particles are affected by flow field disturbance to deposit. Although the windward side of the third row of circular pipes is positioned in the wake area of the first two rows of circular pipes, the front ends of the circular pipes in the row are slightly influenced by the first two rows of circular pipes (the first two rows of the fork row pipe bundles are staggered with each other), so that the deposition amount of ice particles on the windward side of the third row of circular pipes is slightly increased compared with that of the first row of circular pipes. In addition, the higher the relative humidity of the wet air inlet, the larger the amount of ice particles deposited on the tube bundle surface. Fig. 8 shows the deposition of ice particle clusters on the surface of the tube bundle at t=1 s with different initial temperatures of the humid air. Simulation results show that the higher the initial temperature of the humid air is, the larger the deposition amount of ice particles on the surface of the tube bundle is.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.
Claims (1)
1. The calculation method for the ice particle deposition process in the cold space is characterized by mainly comprising the following steps of:
step one, calculating a required calculation domain and grid size according to a physical model, and dividing grids;
initializing the density, the speed and the initial position and the initial speed of ice particles of a model calculation domain;
step three, outputting a flow field of a calculation domain;
the flow field evolution equation is:
where f is the particle distribution function and τ is the relaxation time;
equilibrium distribution function f i (eq) (x, t) is:
wherein c s Is the lattice sound velocity omega i Is weight coefficient, ρ is density, e i Is a discrete speed; equilibrium speed u eq The method comprises the following steps:
the intermolecular interaction force is:
F(x)＝F f (x)+F g (x)
wherein, the interaction force between fluids is:
where ψ (ρ) =ρ * [1-exp(-ρ/ρ * )]Is an effective density; g 1 And G 2 The coefficients of interaction between the fluids at adjacent and sub-adjacent locations, respectively;
the gravity is as follows:
F g (x)＝ρ(x)g
outputting the density and the speed of each node in the calculation domain;
the density and velocity are calculated as:
step five, outputting the displacement and the speed of the ice particles;
(1) Transport: at the next moment, the ice particles at any point in the flow field move to adjacent grid points or stay at the original position with a certain probability; let t be time, grid node r p An ice particle is arranged on the ice particle; t+delta t At this moment, whether the ice particles move to the nearest neighbor or stay at the original node depends mainly on the transport probabilities p in directions 1, 3, 5 and 7 α The final lattice point positions of the corresponding ice particles are as follows:
r p '＝r p +(v 1 e 1 +v 2 e 2 +v 3 e 3 +v 4 e 4 )δ t
wherein v is α The probability of taking 1 as a random Boolean variable is p α ；
In the D2Q9 model, t+delta t At the moment, the ice particles move to east, north, west and south, namely p 1 、p 3 、p 5 And p 7 Is a transport probability p of (2) α The expression is:
wherein,for time step delta t The actual displacement of the ice particles +.>
The equation of motion of the ice particles taking into account drag forces, gravity and buoyancy is:
wherein F is d For drag force, F g Gravity and buoyancy;
gravity and buoyancy expressions are:
F g ＝(m p -m g )g
wherein,is ice particle mass ρ i Is ice density, r i For the radius of ice particles>For the buoyancy force, ρ, of ice particles g G is gravity acceleration, which is the gas density;
in the particle tracking method, the speed and displacement of the ice particles are solved through an ice particle motion equation, and the specific expression is as follows:
wherein τ p For the relaxation time of the ice particles, the specific value is Stokes number St=τ p u/L determination; time step delta t The actual displacement of the ice particles is
(2) And (3) deposition: when the ice particles collide with the cold wall surface, part of the ice particles do not move any more and start to deposit on the cold wall surface, and finally become a part of a frost layer on the cold wall surface; using critical deposition rate V cr As a criterion for judging whether or not ice particles are deposited; when the normal speed of the ice particles impacting the cold wall surface is smaller than the critical deposition speed V cr During the process, ice particles are deposited on the cold wall surface;critical deposition rate V cr The method comprises the following steps:
V cr ＝[2K/(D i R 2 )] 10/7
wherein D is i Is the diameter of ice particles;is an effective stiffness coefficient; related parametersE s And E is p Young's moduli of the cold wall surface and the ice particles, respectively; v (v) s And v p Poisson ratio of the cold wall surface and the ice particles respectively; r is a motion recovery coefficient, and 0.9 is taken;
and step six, returning to the step three for circular calculation until all ice particles are deposited on the wall surface of the tube bundle or move outside the calculation area, and ending the program.
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| CN109583066A (en) * | 2018-11-22 | 2019-04-05 | 南京工程学院 | A kind of direct current overhead transmission line insulator surface filth deposition analogy method |
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