CN114896906B - Ice accretion simulation method considering heat conduction in ice layer and solid wall surface - Google Patents

Ice accretion simulation method considering heat conduction in ice layer and solid wall surface Download PDF

Info

Publication number
CN114896906B
CN114896906B CN202210532517.XA CN202210532517A CN114896906B CN 114896906 B CN114896906 B CN 114896906B CN 202210532517 A CN202210532517 A CN 202210532517A CN 114896906 B CN114896906 B CN 114896906B
Authority
CN
China
Prior art keywords
ice
ice layer
water
wall surface
solid wall
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202210532517.XA
Other languages
Chinese (zh)
Other versions
CN114896906A (en
Inventor
陈宁立
易贤
王强
柴得林
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Low Speed Aerodynamics Institute of China Aerodynamics Research and Development Center
Original Assignee
Low Speed Aerodynamics Institute of China Aerodynamics Research and Development Center
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Low Speed Aerodynamics Institute of China Aerodynamics Research and Development Center filed Critical Low Speed Aerodynamics Institute of China Aerodynamics Research and Development Center
Priority to CN202210532517.XA priority Critical patent/CN114896906B/en
Publication of CN114896906A publication Critical patent/CN114896906A/en
Application granted granted Critical
Publication of CN114896906B publication Critical patent/CN114896906B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/08—Fluids
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Fluid Mechanics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Computing Systems (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Algebra (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention is suitable for the technical field of ice prevention and deicer, and provides an icing simulation method considering heat conduction in an ice layer and a solid wall surface, wherein the method considers the heat conduction in the ice layer and the solid wall surface, and simplifies liquid drop impact and flow and phase change of a thin water film on the surface into four energy items of the solid wall surface:
Figure DDA0003640984300000011
a simplified coupling heat transfer model is designed, the heat transfer model comprises convection heat transfer between air and an ice layer, heat conduction inside the ice layer and heat conduction inside a solid wall surface, and four energy items are added to an interface of the air and the ice layer to perform coupling heat transfer simulation calculation so as to simulate ice deposition on the solid wall surface. Compared with the prior art, the method has the advantages that the heat conduction in the ice layer and the solid wall surface is considered, so that the calculation result is more accurate, reasonable model simplification is performed in the calculation process, and the calculation process is relatively simple.

Description

Ice accretion simulation method considering heat conduction in ice layer and solid wall surface
Technical Field
The invention relates to the technical field of ice prevention and deicing, in particular to an ice accretion simulation method considering heat conduction in an ice layer and a solid wall surface.
Background
Icing of the surface of an aircraft occurs when the aircraft passes through a cloud containing supercooled water droplets. Icing can be a serious hazard to flight safety, so that the research on the icing phenomenon of the aircraft is paid more and more attention by scholars, and numerical simulation is an important means for researching the icing of the aircraft. This complex heat transfer phenomenon is involved in the impingement of supercooled water droplets on the icing process. Supercooled water droplets striking the surface release a large amount of latent heat during the freezing process, which is dissipated by evaporation of the water film, heat convection inside the film, and heat transfer from the water film to the outer cold air and ice layers and solid walls. In most existing numerical simulations of ice accretion, the heat conduction in the ice layer and inside the solid wall is usually ignored for simplifying the calculation, and the solid wall is considered to be adiabatic approximately, or the temperature of the solid wall is considered to be equal to the incoming flow temperature. This makes numerical simulation of icing subject to error.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides an ice accumulation simulation method considering heat conduction in an ice layer and a solid wall surface.
An ice accretion simulation method taking into account heat conduction in an ice layer and a solid wall surface, comprising the steps of:
s10, simulating the flow field of air and water drops by adopting an Euler-Euler method to obtain the water drop collection rate beta, the convection heat transfer coefficient h and the shear stress of an air-liquid interface
Figure BDA0003640984280000011
S20, transferring heat from a water film to an ice layer
Figure BDA0003640984280000021
Zero, carrying out numerical simulation, and calculating to obtain the energy brought by the impact liquid drop based on the simulation of the thin water film flow and the phase change
Figure BDA0003640984280000022
Evaporation energy
Figure BDA0003640984280000023
Latent heat of freezing phase change
Figure BDA0003640984280000024
Convection heat transfer inside water film
Figure BDA0003640984280000025
S30. Obtaining the product obtained in the step S20
Figure BDA0003640984280000026
After the heat transfer model is added to the interface of the air and the ice layer, the heat transfer model simulates the coupling heat transfer, wherein the coupling heat transfer comprises the convective heat transfer between the air and the ice layer and the solid wall surface, the heat conduction inside the ice layer and the heat conduction inside the solid wall surface, and the heat transfer from a new water film to the ice layer is calculated
Figure BDA0003640984280000027
S40, judging
Figure BDA0003640984280000028
Whether the convergence is achieved or not, if yes, the calculation is finished; if not, transferring heat from the new water film to the ice layer
Figure BDA0003640984280000029
The numerical simulation calculation in step S20 is substituted, and steps S20 to S40 are repeated.
Further, the step S30 includes the steps of:
s301, calculating wall temperature T according to internal heat conduction equation of solid wall wall ：
Figure BDA00036409842800000210
Figure BDA00036409842800000211
ρ wall Is the density of the solid wall surface, c p,wall Is the specific heat capacity of the solid wall surface,
s302, according to the guide inside the ice layerCalculating the temperature distribution in the ice layer by using a thermal equation, and calculating the internal temperature T of the ice layer i ：
Figure BDA00036409842800000212
Wherein
Figure BDA00036409842800000213
k i Is the thermal conductivity of ice, p i Is the density of ice, c pi Is the specific heat capacity of ice;
the boundary conditions of the contact between the upper surface of the ice layer and the water film are as follows:
Figure BDA0003640984280000031
wherein
Figure BDA0003640984280000032
Normal to the surface of the ice and water films, L f Is the latent heat of phase change per unit mass, H i Is the thickness of the ice layer, n is the nth time step, n +1 is the nth +1 time step, Δ t is the time step,
the boundary conditions of the contact between the lower surface of the ice layer and the solid wall surface are as follows:
Figure BDA0003640984280000033
T i ＝T wall
wherein k is wall Is the thermal conductivity of the wall, n wall Is the normal vector of the wall, T wall Is the wall temperature;
s303, calculating heat transfer from a new water film to an ice layer
Figure BDA0003640984280000034
Figure BDA0003640984280000035
Wherein the content of the first and second substances,
Figure BDA0003640984280000036
is the normal vector of the ice water interface.
Compared with the prior art, the ice accretion simulation method considering the heat conduction in the ice layer and the solid wall surface at least has the following beneficial effects:
the invention considers the heat conduction in the ice layer and the solid wall surface, and simplifies the liquid drop impact and the flow and phase change of the surface thin water film into four energy items of the solid wall surface:
Figure BDA0003640984280000037
a simplified coupling heat transfer model is designed, the heat transfer model comprises convection heat transfer between air and an ice layer, heat conduction inside the ice layer and heat conduction inside a solid wall surface, and four energy items are added to an interface of the air and the ice layer to perform coupling heat transfer simulation calculation so as to simulate ice deposition on the solid wall surface. Compared with the prior art, the method has the advantages that the heat conduction in the ice layer and the solid wall surface is considered, so that the calculation result is more accurate, reasonable model simplification is performed in the calculation process, and the calculation process is relatively simple.
The ice accretion simulation method considering the heat conduction in the ice layer and the solid wall surface is not only suitable for the ice accretion simulation of the surface of an aircraft, but also suitable for the ice accretion simulation of the solid surface of a wind turbine blade, power transmission and the like.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments of the present invention or in the description of the prior art will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of an ice accretion simulation method considering an ice layer and heat conduction in a solid wall surface according to embodiment 1 of the present invention;
FIG. 2 is a schematic heat transfer diagram of the present icing pattern of solid walls, ice layers, water films and air;
FIG. 3 is a simplified model diagram of the coupled heat transfer according to an embodiment of the present invention.
Detailed Description
The following description provides many different embodiments, or examples, for implementing different features of the invention. The particular examples set forth below are illustrative only and are not intended to be limiting.
The impingement of supercooled water droplets on the solid to avoid ice accretion involves this complex heat transfer phenomenon, and as shown in fig. 2, supercooled water droplets impinging on the surface release a large amount of latent heat during icing which is dissipated by evaporation of the water film, heat convection inside the film, and heat transfer from the water film to the outer cold air and ice layers and the solid wall. This complex heat transfer process presents a significant challenge to the numerical simulation process, and in the prior art, in order to simplify the calculation, the heat conduction in the ice layer and inside the solid wall is usually ignored, and the solid wall is considered to be approximately adiabatic, or the temperature of the solid wall is considered to be equal to the incoming flow temperature. This makes numerical simulation of icing subject to error.
The invention simplifies the model, the designed coupling heat transfer model comprises the convective heat transfer between air and an ice layer, the heat conduction in the ice layer and the heat conduction in the solid wall surface, and the liquid drop impact and the flow and phase change of a thin water film on the surface are simplified into four energy items of the solid wall surface:
Figure BDA0003640984280000041
and added to the interface of the air and the ice layer. Therefore, the calculation model of the invention simplifies the heat transfer, but the accuracy of the ice accumulation simulation calculation can be improved by considering the heat conduction in the ice layer and the solid wall surface.
An ice accretion simulation method taking into account the heat conduction in the ice layer and the solid wall surface, as shown in fig. 1, comprises the following steps:
s10, simulating the flow field of air and water drops by adopting an Euler-Euler method to obtain the water drop collection rate beta, the convection heat transfer coefficient h and the shear stress of an air-liquid interface
Figure BDA0003640984280000051
S101, neglecting the influence of water drop items on the air phase, and regarding the simulation of the air phase as single-phase flow.
The control equation adopts a Reynolds average equation, and the mass conservation equation is as follows:
Figure BDA0003640984280000052
where ρ is the density of air and v ai Is the velocity component of the air velocity in the i direction, x i Is a coordinate system, where i =1,2,3 respectively represent the three components of a rectangular coordinate system.
The momentum equation for air is:
Figure BDA0003640984280000053
wherein v is a Representing the air velocity, v ai And v aj Respectively representing the air velocity at the coordinate x i (i =1,2,3) and coordinates x j (j =1,2,3).
Figure BDA0003640984280000054
Is the reynolds stress, which can be modeled using the readable k-epsilon turbulence model and will not be described in detail here. p is pressure, μ a Is the viscosity coefficient of air, g i For gravity on a coordinate axis x i The component (c) above.
Through the simulation of the air field, namely the solution of the formula (1) and the formula (2), the turbulent kinetic energy in the air field can be obtained
Figure BDA0003640984280000059
v′ a1 The air velocity is x 1 The amount of speed pulsation on the shaft,
Figure BDA00036409842800000510
is v' a1 Squared average, the dimensionless speed can be expressed as:
Figure BDA0003640984280000057
wherein C is μ Constant with a value of 0.09. The dimensionless distance of a wall can be expressed as:
Figure BDA0003640984280000058
y p is the actual dimensional distance from the solid wall.
Then, based on the similarity between the velocity boundary layer and the temperature boundary layer, a dimensionless temperature distribution near the solid wall surface can be obtained as follows:
Figure BDA0003640984280000061
wherein Pr is the prandtl number of air, generally takes a constant value, and has a size of 0.71 t The value for turbulent Plantt number is typically 0.85, κ is Von Karman constant, size 0.4187, E is an empirical parameter, and may be 9.793.
Figure BDA0003640984280000062
The thickness of the linear bottom layer of the temperature boundary layer can be considered as
Figure BDA0003640984280000063
r is a constant and can generally take the value of 1/2.
According to the temperature distribution near the wall surface, the convective heat transfer coefficient of the wall surface can be calculated to be
Figure BDA0003640984280000064
S102, regarding the water drop as a continuous term, describing the concentration of the water drop by using the volume fraction alpha, so that the continuous equation of the water drop is as follows:
Figure BDA0003640984280000065
wherein v is i Is at x i Velocity of water in the direction, p w Is the density of water, the momentum equation for the water droplet phase is:
Figure BDA0003640984280000066
wherein, g i Is the gravity of water drop at x i A component of direction; k is the momentum transfer coefficient between air and water droplets, which is defined as:
Figure BDA0003640984280000067
wherein C is d The drag force coefficient can be calculated by a Schiller-Naumann model:
Figure BDA0003640984280000071
wherein Re w Is the relative Reynolds number, which is defined as:
Figure BDA0003640984280000072
wherein v is a Is the velocity vector of the air phase and v is the velocity vector of the water droplet phase.
The velocity of the water drop and the volume fraction alpha thereof can be obtained by iteratively solving the equations (3) and (4), so that the local water collection coefficient beta of the wall surface can be calculated:
Figure BDA0003640984280000073
wherein v is normal Is the normal impact velocity of water drops on the wall surface, U ∞ And LWC are the incoming flow rate and liquid water content, respectively.
S103, airflow shear force
Figure BDA0003640984280000074
Figure BDA0003640984280000075
S20, transferring heat from a water film to an ice layer
Figure BDA0003640984280000076
Zero, carrying out numerical simulation, and calculating to obtain the energy brought by the impact liquid drop based on the simulation of the thin water film flow and the phase change
Figure BDA0003640984280000077
Evaporation energy
Figure BDA0003640984280000078
Latent heat of freezing phase change
Figure BDA0003640984280000079
Convection heat transfer inside water film
Figure BDA00036409842800000710
The icing model is based on the assumption that impingement of supercooled water droplets can form a thin water film on the solid walls, the equation of continuity for the water film being:
Figure BDA00036409842800000711
H w is the thickness of the water film,
Figure BDA00036409842800000712
is the water film velocity, A is the peripheral volume of the control body, A sub The intersecting area of the bottom surface of the control body and the solid wall surface;
the energy conservation equation of the water film is:
Figure BDA0003640984280000081
C pw is the specific heat capacity of water, T w Is the water film temperature;
Figure BDA0003640984280000082
Figure BDA0003640984280000083
Figure BDA0003640984280000084
Figure BDA0003640984280000085
Figure BDA0003640984280000086
wherein U is ∞ And T ∞ Is the speed and temperature of the incoming flow,
Figure BDA0003640984280000087
is the mass of ice formed per unit area and has a magnitude of
Figure BDA0003640984280000088
For the increase in ice thickness between the (n + 1) th time step and the nth time step,
Figure BDA0003640984280000089
for impacting the mass of the water
Figure BDA00036409842800000810
In order to evaporate the mass of water,
Figure BDA00036409842800000811
wherein e (T) = -6.803X 10 3 +27.03T, χ is the evaporation mass transfer coefficient; l is f Is the latent heat of phase change per unit mass, L e Is the latent heat of vaporization per unit mass;
assuming that the water film velocity along the water film thickness is parabolically distributed:
Figure BDA00036409842800000812
wherein
Figure BDA00036409842800000813
Is the pressure gradient of the gas to be treated,
Figure BDA00036409842800000815
is the volumetric force including gravitational centrifugal force and coriolis force, mu is the viscosity coefficient of water, and z is the normal vector at the ice water interface.
The temperature distribution in the water film uses a linear assumption:
Figure BDA00036409842800000814
wherein T is w-i Temperature at ice water interface, assumed to be equilibrium phase transition temperature T freeze ，k w Is the thermal conductivity of water;
the average values of the velocity and temperature in the water film along the thickness direction are:
Figure BDA0003640984280000091
the water film energy and mass conservation can be respectively introduced into the mass conservation and energy conservation equations of the water film, and the equations (10) and (11) become after being dispersed:
Figure BDA0003640984280000092
Figure BDA0003640984280000093
substituting the equations (12), (13) and (14) into the equation (15), H is calculated w And H i At the same time, the energy brought by the impact liquid drop is obtained
Figure BDA0003640984280000094
Evaporation energy
Figure BDA0003640984280000095
Latent heat of freezing phase change
Figure BDA0003640984280000096
Convection heat transfer inside water film
Figure BDA0003640984280000097
S30. Obtaining the product obtained in the step S20
Figure BDA0003640984280000098
After the heat transfer model is added to the interface of the air and the ice layer, the heat transfer model simulates the coupling heat transfer, wherein the coupling heat transfer comprises the convective heat transfer between the air and the ice layer and the solid wall surface, the heat conduction inside the ice layer and the heat conduction inside the solid wall surface, and the heat transfer from a new water film to the ice layer is calculated
Figure BDA0003640984280000099
S301, calculating wall temperature T according to internal heat conduction equation of solid wall wall ：
Figure BDA00036409842800000910
Figure BDA00036409842800000911
ρ wall Is the density of the solid wall surface, c p,wall Is to be fixedThe specific heat capacity of the wall surface of the body,
s302, calculating according to a heat conduction equation inside the ice layer to obtain the temperature distribution inside the ice layer:
Figure BDA0003640984280000101
wherein T is i Is the temperature inside the ice layer, and,
Figure BDA0003640984280000102
k i is the thermal conductivity of ice, p i Is the density of ice, c pi Is the specific heat capacity of the ice,
the boundary conditions of the contact between the upper surface of the ice layer and the water film are as follows:
Figure BDA0003640984280000103
wherein H i Is the thickness of the ice layer or layers,
the boundary conditions of the contact between the lower surface of the ice layer and the solid wall surface are as follows:
Figure BDA0003640984280000104
T i ＝T wall (19)
wherein k is wall Is the thermal conductivity of the wall, n wall Is the normal vector of the wall, T wall Is the wall temperature;
the wall temperature T is calculated by the formula (16) wall The temperature value and the equations (18) and (19) are substituted into the equation (17), and the internal temperature T of the ice layer is calculated i ，
S303, calculating heat transfer from a new water film to an ice layer
Figure BDA0003640984280000105
The obtained internal temperature T of the ice layer i Substituting the following formula to calculate the heat transfer from the new water film to the ice layer:
Figure BDA0003640984280000106
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003640984280000107
is the normal vector of the ice water interface.
S40, judging
Figure BDA0003640984280000108
Whether the convergence is achieved or not, if yes, the calculation is finished; if not, transferring new water film to ice layer
Figure BDA0003640984280000109
The numerical simulation calculation in step S20 is substituted, and steps S20 to S40 are repeated.
As will be understood by those skilled in the art, the method for determining convergence in this step may be to set a set value when calculated
Figure BDA0003640984280000111
If the value is less than the set value, convergence is judged, and if the value is greater than the set value, non-convergence is judged.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (5)

1. An ice accretion simulation method considering heat conduction in an ice layer and a solid wall surface is characterized by comprising the following steps:
s10, simulating the flow field of air and water drops by adopting an Euler-Euler method to obtain the water drop collection rate beta, the convection heat transfer coefficient h and the shear stress of an air-liquid interface
Figure FDA0003640984270000011
S20, making water film to iceHeat transfer of layers
Figure FDA0003640984270000012
Zero, carrying out numerical simulation, and calculating to obtain the energy brought by the impact liquid drop based on the simulation of the thin water film flow and the phase change
Figure FDA0003640984270000013
Evaporation energy
Figure FDA0003640984270000014
Latent heat of freezing phase change
Figure FDA0003640984270000015
Convective heat transfer in water film
Figure FDA0003640984270000016
S30. Obtaining the product obtained in the step S20
Figure FDA0003640984270000017
Adding the water solution into the interface of the air and the ice layer, simulating coupled heat transfer, wherein the coupled heat transfer comprises convection heat exchange between the air and the ice layer and the solid wall surface, heat conduction inside the ice layer and heat conduction inside the solid wall surface, and calculating heat transfer from a new water film to the ice layer
Figure FDA0003640984270000018
S40, judging
Figure FDA0003640984270000019
Whether the convergence is achieved or not, if yes, the calculation is finished; if not, transferring heat from the new water film to the ice layer
Figure FDA00036409842700000110
The numerical simulation calculation in step S20 is substituted, and steps S20 to S40 are repeated.
2. The method for simulating ice accretion considering the heat conduction in the ice layer and the solid wall surface as claimed in claim 1, wherein said step S30 comprises the steps of:
s301, calculating wall temperature T according to internal heat conduction equation of solid wall wall ：
Figure FDA00036409842700000111
Figure FDA00036409842700000112
ρ wall Is the density of the solid wall surface, c p,wall Is the specific heat capacity of the solid wall surface,
s302, calculating to obtain the temperature distribution inside the ice layer according to a heat conduction equation inside the ice layer, and calculating the temperature T inside the ice layer i ：
Figure FDA0003640984270000021
Wherein
Figure FDA0003640984270000022
k i Is the thermal conductivity of ice, p i Is the density of ice, c pi Is the specific heat capacity of ice;
the boundary conditions of the contact between the upper surface of the ice layer and the water film are as follows:
Figure FDA0003640984270000023
wherein
Figure FDA0003640984270000024
Normal to the surface of the ice and water films, L f Is the latent heat of phase change per unit mass, H i Is the thickness of the ice layer, n is the nthA time step, n +1 is the (n + 1) th time step, Δ t is the time step,
the boundary conditions of the contact between the lower surface of the ice layer and the solid wall surface are as follows:
Figure FDA0003640984270000025
T i ＝T wall
wherein k is wall Is the thermal conductivity of the wall, n wall Is the normal vector of the wall, T wall Is the wall temperature;
s303, calculating heat transfer from a new water film to an ice layer
Figure FDA0003640984270000026
Figure FDA0003640984270000027
Wherein the content of the first and second substances,
Figure FDA0003640984270000028
is the normal vector of the ice water interface.
3. The method of claim 2, wherein in step S20, the discrete equation is:
Figure FDA0003640984270000031
Figure FDA0003640984270000032
wherein H w Is the water film thickness, ρ w Is the density of the water and is,
Figure FDA0003640984270000033
is the speed of the water film,
Figure FDA0003640984270000034
normal vector of ice layer and water film surface, A i Is the ith control body peripheral volume, A sub Is the intersecting area of the bottom surface of the control body and the solid wall surface, C pw Is the specific heat capacity of water, T w Is the water film temperature H i Is the thickness of the ice layer, n is the nth time step, b +1 is the nth +1 time step, Δ t is the time step, ρ i Is the density of ice, L f Is the latent heat of phase change per unit mass,
Figure FDA0003640984270000035
respectively, the mass of the impinging water and the mass of the evaporated water, and m is the number of faces of the control body.
4. An ice accretion simulation method taking into account the ice layer and the heat conduction in the solid wall as claimed in claim 3, characterized in that the energy brought in by the impinging liquid droplets
Figure FDA0003640984270000036
Evaporation energy
Figure FDA0003640984270000037
Latent heat of freezing phase change
Figure FDA0003640984270000038
Convection heat transfer inside water film
Figure FDA0003640984270000039
Is calculated as:
Figure FDA00036409842700000310
Figure FDA00036409842700000311
Figure FDA00036409842700000312
Figure FDA00036409842700000313
wherein the content of the first and second substances,
Figure FDA00036409842700000314
is the mass of ice formed per unit area, L e Is the latent heat of vaporization per unit mass, U ∞ And T ∞ Is the incoming flow velocity and temperature.
5. The method of claim 4, wherein in step S20, the boundary conditions of the discrete equations are:
assuming that the water film velocity along the water film thickness is parabolically distributed:
Figure FDA0003640984270000041
wherein
Figure FDA0003640984270000042
Is the pressure gradient of the gas to be treated,
Figure FDA0003640984270000043
is the volume force, mu is the viscosity coefficient of water, z is the normal vector on the ice-water interface;
the temperature distribution in the water film uses a linear assumption:
Figure FDA0003640984270000044
wherein T is w-i Temperature at ice water interface, assumed to be equilibrium phase transition temperature T freeze ，k w Is the thermal conductivity of water.
CN202210532517.XA 2022-05-12 2022-05-12 Ice accretion simulation method considering heat conduction in ice layer and solid wall surface Active CN114896906B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210532517.XA CN114896906B (en) 2022-05-12 2022-05-12 Ice accretion simulation method considering heat conduction in ice layer and solid wall surface

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210532517.XA CN114896906B (en) 2022-05-12 2022-05-12 Ice accretion simulation method considering heat conduction in ice layer and solid wall surface

Publications (2)

Publication Number Publication Date
CN114896906A CN114896906A (en) 2022-08-12
CN114896906B true CN114896906B (en) 2023-03-21

Family

ID=82724260

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210532517.XA Active CN114896906B (en) 2022-05-12 2022-05-12 Ice accretion simulation method considering heat conduction in ice layer and solid wall surface

Country Status (1)

Country Link
CN (1) CN114896906B (en)

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115544818B (en) * 2022-12-05 2023-02-28 中国空气动力研究与发展中心低速空气动力研究所 Grid division and heat conduction calculation method for multilayer heterogeneous thin-wall solid heat conduction calculation
CN115587506B (en) * 2022-12-09 2023-03-10 四川大学 Design method of electric heating ice preventing and removing system
CN115817822B (en) * 2023-02-09 2023-04-18 中国空气动力研究与发展中心低速空气动力研究所 Heat load distribution design method of electric heating anti-icing system
CN117408053B (en) * 2023-10-18 2024-05-07 中国空气动力研究与发展中心计算空气动力研究所 Method for establishing low-temperature flat plate drying mode frosting characteristic curve under strong convection condition

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112989727A (en) * 2021-05-10 2021-06-18 中国空气动力研究与发展中心低速空气动力研究所 Wall surface temperature simulation method of anti-icing system
CN114169077A (en) * 2021-12-13 2022-03-11 南京航空航天大学 Strong-coupling three-dimensional numerical simulation method for hot gas anti-icing of aircraft engine inlet part

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112989727A (en) * 2021-05-10 2021-06-18 中国空气动力研究与发展中心低速空气动力研究所 Wall surface temperature simulation method of anti-icing system
CN114169077A (en) * 2021-12-13 2022-03-11 南京航空航天大学 Strong-coupling three-dimensional numerical simulation method for hot gas anti-icing of aircraft engine inlet part

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
曹广州 ; 吉洪湖 ; 胡娅萍 ; 庞黎刚 ; 斯仁 ; 冯晓星 ; .模拟飞机迎风面三维积冰的数学模型.2011,(第09期),41-51. *
王涛 ; 刘建华 ; 杨亚磊 ; 陈斌 ; .基于灰色组合模型的飞机地面积霜预测.2020,(第07期),78-83. *
苏长明 ; 胡娅萍 ; 曹广州 ; 吉洪湖 ; .考虑水膜蒸发的三维明冰积冰数值研究.2018,(第07期),105-113. *

Also Published As

Publication number Publication date
CN114896906A (en) 2022-08-12

Similar Documents

Publication Publication Date Title
CN114896906B (en) Ice accretion simulation method considering heat conduction in ice layer and solid wall surface
Liu et al. An experimental investigation on the unsteady heat transfer process over an ice accreting airfoil surface
Myers Extension to the Messinger model for aircraft icing
Blake et al. Simulating the freezing of supercooled water droplets impacting a cooled substrate
Villedieu et al. Glaciated and mixed phase ice accretion modeling using ONERA 2D icing suite
CN114169077B (en) Strong-coupling three-dimensional numerical simulation method for hot gas anti-icing of aircraft engine inlet part
Yang et al. Freezing mechanism of supercooled water droplet impinging on metal surfaces
CN114139393B (en) Part electric heating three-dimensional anti-icing numerical simulation method considering water film flow heat transfer
CN111396269B (en) Multi-time-step unsteady icing calculation method and system and storage medium
CN111967201A (en) Method for analyzing critical icing type based on numerical simulation model
Cao et al. Extension to the Myers model for calculation of three-dimensional glaze icing
Son et al. Quantitative analysis of a two-dimensional ice accretion on airfoils
Roisman et al. Wetting and icing of surfaces
CN112678189A (en) Improved icing sensor installation position determining method
Min et al. New roughness-induced transition model for simulating ice accretion on airfoils
CN113779904A (en) Icing phase change calculation method based on coupling of continuous liquid film and discrete liquid film
Homola et al. Turbine size and temperature dependence of icing on wind turbine blades
Shi et al. Research and Development of a Small‐Scale Icing Wind Tunnel Test System for Blade Airfoil Icing Characteristics
Dong et al. Calculation and analysis of runback water flow on anti-icing airfoil surface
CN114398844B (en) Steady-state anti-icing simulation method based on continuous water film flow
Vahab et al. An adaptive coupled level set and moment-of-fluid method for simulating droplet impact and solidification on solid surfaces with application to aircraft icing
Xu et al. Effects of ambient temperature and wind speed on icing characteristics and anti-icing energy demand of a blade airfoil for wind turbine
Lian et al. A modified spongy icing model considering the effect of droplets retention on the ice accretion process
Prince Raj et al. Computational simulation of glaze ice accretion on a rotorcraft engine intake in large supercooled droplet icing conditions
Serkan et al. Parallel computing applied to three-dimensional droplet trajectory simulation in Lagrangian approach

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant