CN115817822B - Heat load distribution design method of electric heating anti-icing system - Google Patents
Heat load distribution design method of electric heating anti-icing system Download PDFInfo
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Abstract
Disclosed is a heat load distribution design method of an electric heating anti-icing system, comprising: simulating the air and water drop flow field outside the heating coverage area based on preset simulation conditions to obtain the convective heat transfer coefficient and water drop impact quality of each grid unit of the heating coverage area; calculating the heat load of the electric heating anti-icing system in each grid unit based on the preset target anti-icing temperature, the convection heat transfer coefficient and the water drop impact quality; determining a face average anti-icing heat flow for each heating zone of the plurality of heating zones based on the heat load of each grid cell; iteratively calculating the wall temperature for each grid cell based on the average anti-icing heat flow of the surface of each heating region until the wall temperature converges relative to the target anti-icing temperature; and under the condition that the wall surface temperature of each grid unit is converged relative to the target anti-icing temperature, obtaining the finally determined surface average anti-icing heat flow of each heating area, thereby designing the heat load distribution of the electric heating anti-icing system.
Description
Technical Field
The present disclosure relates generally to the field of anti-icing and, more particularly, to a method for designing a heat load distribution of an electrically heated anti-icing system.
Background
Ice accretion on the surface of an aircraft when the aircraft passes through a cloud layer containing supercooled water drops can cause serious damage to the safety of the aircraft, for example, ice accretion on the surface of a wing can cause the lift of the wing to be reduced, the resistance to be increased and the stall to be possibly advanced, so that an anti-icing system is generally required to be designed on a key part (such as the surface of the wing) of the aircraft. The electric heating anti-icing system is one commonly used anti-icing system on the surface of an aircraft, and can effectively protect the aircraft under icing meteorological conditions.
In the design of an electrical heating anti-icing system, it is important to determine the input power of the surface electrical heating system, i.e. the anti-icing heat load. The method for designing the anti-icing heat load in the related art generally comprises the steps of firstly carrying out preliminary design of the anti-icing heat load according to the experience of a designer or the design of the existing similar model, then carrying out anti-icing numerical simulation or an icing wind tunnel test to verify the carried design, increasing or reducing the corresponding anti-icing heat load according to the test result and the design experience, and repeatedly iterating to obtain the finally required heat load; or, firstly, the water collection rate of the surface is obtained by numerical simulation calculation, and the heat distribution required to be provided by the complete evaporation of the water film on the surface (dry anti-icing) is calculated by neglecting the tangential heat conduction of the solid surface according to the amount of the impact water.
However, the anti-icing heat load design method in the related art has many problems, such as that no guidance can be provided for the zone heating design, the internal heat conduction of the multilayer thin-wall solid has defects, or the design of anti-icing on a wet surface (liquid water exists on the surface) has defects or over-protection design.
Disclosure of Invention
The invention provides a heat load distribution design method of an electric heating anti-icing system, which can be used for carrying out heat load distribution design aiming at a plurality of heating areas in a heating coverage area by considering the characteristics of the electric heating anti-icing system, thereby better meeting the heating requirements of different positions and improving the energy utilization efficiency of the electric heating anti-icing system.
In one general aspect, there is provided a heat load distribution design method of an electric heating anti-icing system, wherein the electric heating anti-icing system is used for electrically heating a heating coverage area, the heating coverage area includes a plurality of heating areas, and the heat load distribution design method includes: simulating the air and water drop flow field outside the heating coverage area based on preset simulation conditions to obtain the convective heat transfer coefficient and water drop impact quality of each grid unit of the heating coverage area; calculating the heat load of the electric heating anti-icing system in each grid unit based on a preset target anti-icing temperature, the convection heat exchange coefficient and the water drop impact quality; determining a face average anti-icing heat flow for each heating zone of the plurality of heating zones based on the heat load of each grid cell; iteratively calculating a wall temperature for each grid cell based on the face average anti-icing heat flow of each heating region until the wall temperature converges relative to the target anti-icing temperature; and under the condition that the wall surface temperature of each grid unit converges relative to the target anti-icing temperature, obtaining the finally determined average anti-icing heat flow of each heating area, and designing the heat load distribution of the electric heating anti-icing system according to the finally determined average anti-icing heat flow of each heating area.
Optionally, the simulated conditions include at least one of an incoming flow condition, a cloud condition, and a wall temperature condition, wherein the incoming flow condition includes at least one of an incoming flow velocity, an incoming flow temperature, and a pressure, the cloud condition includes at least one of a water droplet diameter and a liquid water content, and the wall temperature condition includes a given wall temperature, wherein the given wall temperature is determined based on the incoming flow temperature.
Optionally, the heat load of the electrically heated anti-icing system at each grid cell is calculated by the following equation:
wherein the content of the first and second substances,
wherein the content of the first and second substances,
wherein, the first and the second end of the pipe are connected with each other,
indicates heat load, <' > or>
Represents the heat quantity taken away by convective heat exchange>
Indicates the heat removed by the impacting water drop, and>
represents the heat removed by evaporation>
Represents the convective heat transfer coefficient>
Indicates a target anti-icing temperature, <' > is present>
Indicating an incoming flow temperature>
Represents the specific heat capacity of the water>
Indicates drop impact quality>
Indicates the incoming flow velocity, and>
represents the evaporation quality ratio>
Represents the latent heat of evaporation of water>
Represents a mass transfer coefficient>
Represents a predetermined constant, <' > based on the total number of cells in the test area>
Represents the specific heat capacity of the air>
Represents the Liu Yi Si number of water vapor>
Indicating the air pressure.
Optionally, the face average anti-icing heat flow is calculated by the following equation:
wherein the content of the first and second substances,
is shown asNThe area of the individual heating zones is averaged against the heat flow of ice>
Denotes the firstNThe area of each of the heated zones is,
is shown asNIn a heating areaiHeat load of a grid cell->
Is shown asNIn a heating areaiArea of each grid cell.
Optionally, the electrically heated anti-icing system comprises a multilayer thin-walled solid, wherein the iteratively calculating the wall temperature for each grid cell based on the average anti-icing heat flow for each heating zone comprises:
and determining a heat transfer boundary condition of the multilayer thin-wall solid based on the face average anti-icing heat flow of each heating area, and performing heat conduction calculation on the multilayer thin-wall solid under the heat transfer boundary condition to calculate the wall temperature for each grid unit iteratively.
Optionally, the multi-layer thin-walled solid comprises at least a heating layer, wherein the heat transfer boundary conditions comprise a first boundary condition, a second boundary condition, and a third boundary condition, wherein,
the first boundary condition is that the surface average anti-icing heat flow of each heating area is added into the heat conduction calculation of the heating layer in a heat source mode,
the second boundary condition is
A bottom surface for confining the multilayer thin-walled solid,
the third boundary condition is
For confining the upper surface of the multilayer thin-walled solid, wherein,
wherein the content of the first and second substances,
represents the bottom heat flow of a multi-layer thin-wall solid>
Represents an upper surface heat flow of a multi-layered thin-walled solid>
Represents the heat quantity taken away by convective heat transfer calculated according to the wall temperature>
Indicating calculation from wall temperatureIn the presence of impinging water drops, and>
represents the heat removed by evaporation calculated on the basis of the wall temperature>
Indicating the wall temperature.
Optionally, said iteratively calculating, for each grid cell, a wall temperature comprises:
in each iteration of the iterative calculation of the wall temperature, determining whether the wall temperature of any grid cell converges relative to the target anti-icing temperature;
and under the condition that the wall surface temperature of the grid unit is not converged relative to the target anti-icing temperature, updating and calculating the heat load of the grid unit, and re-determining the average anti-icing heat flow of the surface of each heating area based on the updated and calculated heat load.
Alternatively, the convergence of the wall surface temperature with respect to the target anti-icing temperature is represented by the following inequality:
wherein the content of the first and second substances,Cindicating the temperature overshoot.
Optionally, the heat load of the grid cell is updated by the following equation:
wherein the content of the first and second substances,
indicating the heat load of the update calculation.
According to the heat load distribution design method of the electric heating anti-icing system, the characteristics of the electric heating anti-icing system can be considered, the convection heat transfer coefficient distribution and the water drop impact mass distribution are obtained by simulating the air and water drop flow field, and the anti-icing heat flows are respectively determined for the plurality of heating areas in the heating coverage area on the basis, so that the heat load distribution design is carried out on the electric heating anti-icing system based on the anti-icing heat flows of each heating area, on one hand, the heating requirements of different positions are better met, the energy utilization efficiency of the electric heating anti-icing system is improved, on the other hand, the method is suitable for considering the condition of heat conduction inside a multilayer thin-wall solid, the design requirement of dry surface anti-icing can be met, and the design requirement of wet surface anti-icing can also be met.
Additional aspects and/or advantages of the present general inventive concept will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the general inventive concept.
Drawings
The above and other objects and features of the embodiments of the present disclosure will become more apparent from the following description taken in conjunction with the accompanying drawings illustrating embodiments, in which:
FIG. 1 is a schematic structural diagram illustrating a zoned electrically heated anti-icing system for an airfoil surface according to an embodiment of the present disclosure;
FIG. 2 is a schematic structural diagram illustrating a multi-layer material of an electrically heated anti-icing system according to an embodiment of the present disclosure;
FIG. 3 is a flow chart illustrating a heat load distribution design method of an electrically heated anti-icing system according to an embodiment of the present disclosure;
FIG. 4 is a schematic diagram illustrating heat transfer boundary conditions according to an embodiment of the present disclosure.
Detailed Description
The following detailed description is provided to assist the reader in obtaining a thorough understanding of the methods, devices, and/or systems described herein. However, various changes, modifications, and equivalents of the methods, apparatus, and/or systems described herein will be apparent to those skilled in the art after reviewing the disclosure of the present application. For example, the order of operations described herein is merely an example, and is not limited to those set forth herein, but may be changed as will become apparent after understanding the disclosure of the present application, except to the extent that operations must occur in a particular order. Moreover, descriptions of features known in the art may be omitted for clarity and conciseness.
The features described herein may be embodied in different forms and should not be construed as limited to the examples described herein. Rather, the examples described herein have been provided to illustrate only some of the many possible ways to implement the methods, devices, and/or systems described herein, which will be apparent after understanding the disclosure of the present application.
Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs after understanding the present disclosure. Unless explicitly defined as such herein, terms (such as those defined in general dictionaries) should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and the present disclosure, and should not be interpreted in an idealized or overly formal sense.
Further, in the description of the examples, when it is considered that detailed description of well-known related structures or functions will cause a vague explanation of the present disclosure, such detailed description will be omitted.
According to the embodiment of the disclosure, in order to improve the utilization efficiency of energy, the electric heating system of the aircraft does not adopt the same power to heat the whole surface, but different heating units are arranged in different regions of the surface (for example, different heating units are respectively arranged for the A, B, C, D, E, F and the G regions of the wing leading edge shown in fig. 1), and different heating powers are provided for the different heating units, so as to meet the heating requirements of different positions. In addition, the electrical heating anti-icing system on the surface of the aircraft is generally formed by bonding a plurality of thin solid material layers made of different materials due to the constraint of conditions such as the process, and as shown in fig. 2, the plurality of thin solid layers can include a surface protective layer, an internal elastic layer, a heating layer, an insulating layer and the like. The different material layers have a large difference in physical properties such as density, specific heat capacity, and thermal conductivity.
Therefore, according to the heat load distribution design method of the electric heating anti-icing system, the characteristics of the electric heating anti-icing system are considered, the heat load distribution design is carried out on the electric heating anti-icing system aiming at the heating areas in the heating coverage area, the heating requirements of different positions are better met, the energy utilization efficiency of the electric heating anti-icing system is improved, and the method is also suitable for the condition of considering the internal heat conduction of the multilayer thin-wall solid.
A heat load distribution design method of the electric heating anti-icing system according to the embodiment of the present disclosure will be described in detail with reference to fig. 3 and 4.
FIG. 3 is a block diagram illustrating a heat load distribution design method of an electrically heated anti-icing system according to an embodiment of the present disclosure. Here, the electric heating anti-icing system is used to electrically heat a heating coverage area, which includes a plurality of heating areas. It is to be understood that the number of heating zones can be set by one skilled in the art as a practical matter and the present disclosure is not limited thereto. As an example, the heating coverage area may be an airfoil surface as shown in fig. 1, although the disclosure is not limited thereto.
Referring to fig. 3, in step S301, a simulation may be performed on an air and water droplet flow field outside the heating coverage area based on preset simulation conditions, so as to obtain a convective heat transfer coefficient and a water droplet impact quality of each grid unit of the heating coverage area. Here, the simulation condition may include at least one of an inflow condition, a cloud condition, and a wall temperature condition, and the grid cell is a CFD (Computational Fluid Dynamics) Computational grid cell. Further, the inflow condition may include at least one of an inflow velocity, an inflow temperature, and a pressure, the cloud condition may include at least one of a Water droplet Diameter (MVD) and a Liquid Water Content (LWC), and the wall temperature condition may include a given wall temperature. Further, simulation software such as FENSAP-ICE or NNW-ICE may be utilized to simulate air and water droplet flow fields outside the heating footprint, although the present disclosure is not so limited. The convection heat transfer coefficient distribution and the water drop impact mass distribution of the heating coverage area can be obtained simply, conveniently and quickly by simulating the air and water drop flow field outside the heating coverage area by using software FENSAP-ICE or NNW-ICE and the like under the preset inflow condition and cloud and mist condition.
In accordance with an embodiment of the present disclosure, wall temperatures are given during the above-described air and water droplet flow field simulation
Can be based on the incoming flow temperature->
To be determined. As an example, a given wall temperature may be determined as: />
The unit is K, so that the convective heat transfer coefficient at a given wall temperature can be calculated and obtained through software FENSAP-ICE or NNW-ICE in the simulation>
Here, based on>
，/>
Representing heat flow per unit area.
Next, in step S302, the heat load of the electric heating anti-icing system in each grid cell may be calculated based on the preset target anti-icing temperature, the convective heat transfer coefficient and the water droplet impact quality. Here, the target anti-icing temperature may be slightly higher than the icing temperature (273.15K) to ensure that a certain design margin is left, for example, the target anti-icing temperature may be set to be 5 degrees above the freezing point, i.e., 278.15K, although the present disclosure is not limited thereto. Further, with the electric heating anti-icing system, the range of the heating coverage area may be larger than the water droplet striking range, and the water film evaporation mainly occurs in the heating coverage area, so that the temperature of the unheated area is low, and the evaporation rate is relatively small even if the overflow water is present, and thus can be ignored.
According to embodiments of the present disclosure, a one-dimensional thermal conduction simulation may be employed to initially estimate the distribution of thermal load throughout the heating footprint while maintaining a desired target anti-icing temperature. In other words, the heat load of the electrically heated anti-icing system at each grid cell can be calculated by the following equations (1) to (6) while ignoring the effect of aerodynamic heating:
here, the first and second liquid crystal display panels are,
here, the number of the first and second electrodes,
here, the first and second liquid crystal display panels are,
indicating heat load, <' > based on>
Represents the heat quantity taken away by the convection heat exchange>
Indicates the heat removed by the impacting water drop, and>
represents the heat removed by evaporation>
Represents a convective heat transfer coefficient>
Indicates a target anti-icing temperature, <' > is present>
Indicates the incoming flow temperature, <' > or>
Represents the specific heat capacity (constant) of water and/or is present in the water>
Indicates drop impact quality>
Indicates the incoming flow velocity, and>
represents the evaporation quality ratio>
Represents the latent heat of evaporation (constant) of water>
Represents a mass transfer coefficient>
Represents a predetermined constant (a particular value can be determined based on the circumstances, such as, but not limited to 105.4), -or>
Represents the specific heat capacity (constant) of air and/or is present in the air>
Represents the Liu Yi Si number (constant, preferably 0.875) of water vapor and/or (meth) acrylic acid or acrylic acid>
Indicating the air pressure.
Next, in step S303, an average anti-icing heat flow of the face of each heating region of the plurality of heating regions may be determined based on the heat load of each grid cell. Here, the surface average anti-icing heat flow may be calculated by the following equation (7):
here, the first and second liquid crystal display panels are,
is shown asNThe area of the individual heating zones is averaged against the heat flow of ice>
Is shown asNThe area of each of the heating zones is,
is shown asNIn a heating areaiHeat load of a grid cell->
Is shown asNIn a heating areaiArea of individual grid cells. Further, the air conditioner is provided with a fan,Nthe value range of (a) depends on the number of heating zones,iis dependent onNThe number of grid cells in each heating zone, however, the present disclosure does not limit this.
Next, in step S304, the wall temperature may be iteratively calculated for each grid cell based on the face average anti-icing heat flow of each heating region until the wall temperature converges with respect to the target anti-icing temperature. Here, the electrically heated anti-icing system may include a multi-layered thin-walled solid, so that a heat transfer boundary condition of the multi-layered thin-walled solid may be determined based on a face average anti-icing heat flow of each heating region, and a heat conduction calculation may be performed on the multi-layered thin-walled solid under the heat transfer boundary condition to iteratively calculate a wall surface temperature for each mesh unit. Further, a specific algorithm for performing heat conduction calculation on the multilayer thin-wall solid is described in more detail in the patent application 'grid division and heat conduction calculation method for heat conduction calculation of multilayer heterogeneous thin-wall solid' of the patent application No. 202211545866.1 of the present applicant, and a person skilled in the art can refer to the above patent application to iteratively calculate the wall temperature for each grid unit, which is not described herein again in this disclosure. The wall temperature of each grid unit is calculated iteratively in a mode of conducting heat conduction calculation on the multilayer thin-wall solid under the heat conduction boundary condition, the wall temperature of all grid units can be obtained under the condition that the wall characteristics of the electric heating anti-icing system are considered, and therefore the calculated wall temperature is more reasonable and accurate.
According to embodiments of the present disclosure, the multi-layer thin-walled solid may include at least a heating layer, and the heat transfer boundary condition may be a third type of coupling boundary condition, including a first boundary condition, a second boundary condition, and a third boundary condition. For a better understanding of embodiments of the present disclosure, the heat transfer boundary conditions according to embodiments of the present disclosure are described in detail below with reference to fig. 4.
FIG. 4 is a schematic diagram illustrating heat transfer boundary conditions according to an embodiment of the present disclosure.
Referring to fig. 4, the multi-layer thin-walled solid may include a protective layer, an elastic layer, a heating layer, and an insulating layer from top to bottom. Further, the first boundary condition may be an average anti-icing heat flow of the face of each heating zone
Adding the heat source into the heat conduction calculation of the heating layer; the second boundary condition may be->
A bottom surface for confining a multilayer thin-walled solid; the third boundary condition can be expressed as the following equation (8) for confining the upper surface of the multilayer thin-walled solid:
here, the number of the first and second electrodes,
here, the first and second liquid crystal display panels are,
represents the bottom heat flow of a multi-layer thin-wall solid>
Represents upper surface heat flow of multi-layered thin-walled solids>
Represents the heat quantity taken away by convective heat transfer calculated according to the wall temperature>
Represents the heat taken away by the impinging water drops calculated on the basis of the wall temperature>
Represents the heat removed by evaporation calculated on the basis of the wall temperature>
Indicating the wall temperature.
According to the embodiment of the disclosure, in each iteration of iteratively calculating the wall temperature, for any one grid cell, whether the wall temperature of the grid cell converges with respect to the target anti-icing temperature may be determined; then, under the condition that the wall temperature of the grid cell is not converged relative to the target anti-icing temperature, updating calculation is carried out on the heat load of the grid cell, and the average anti-icing heat flow of the surface of each heating area is determined again on the basis of the heat load after updating calculation. It should be understood that in any iteration, in the case where the wall temperature of the grid cell converges with respect to the target anti-icing temperature, the heat load of the grid cell remains unchanged in the iteration, i.e., the calculation is not updated for the heat load of the grid cell in the iteration. Further, after the heat loads of all the grid cells of which the wall temperatures do not converge with respect to the target anti-icing temperature are updated, the average anti-icing heat flow of the surface of each heating region can be determined again by using the above equation (7). By carrying out updating calculation on the heat load of the grid unit with unconverged wall surface temperature and keeping the heat load of the grid unit with unconverged wall surface temperature unchanged, the process of calculating the heat load is simplified, the iterative calculation of the wall surface temperature is simpler, and the calculation resources are saved.
According to an embodiment of the present disclosure, the heat load of the grid cell described above may be updated by the following equation (12):
here, the first and second liquid crystal display panels are,
indicating the heat load of the update calculation.
Referring back to fig. 3, in step S305, a finally determined surface average anti-icing heat flow of each heating region may be obtained under the condition that the wall temperature of each grid cell converges with respect to the target anti-icing temperature, so as to design the heat load distribution of the electric heating anti-icing system according to the finally determined surface average anti-icing heat flow.
According to an embodiment of the present disclosure, convergence of the wall surface temperature with respect to the target anti-icing temperature may be represented by the following inequality (13):
here, the number of the first and second electrodes,Cthe temperature excess is indicated and may be set by a person skilled in the art according to the actual situation, for example 10 degrees, but the disclosure is not limited thereto. It should be understood that,
or (R)>
The case (2) indicates that the wall surface temperature does not converge with respect to the target anti-icing temperature. By reasonably setting the convergence condition of the wall surface temperature, the iterative calculation of the wall surface temperature can be accelerated, and the finally obtained anti-icing heat flow of each heating area is more in line with the heat load design requirement.
According to the heat load distribution design method of the electric heating anti-icing system, the characteristics of the electric heating anti-icing system can be considered, the convection heat transfer coefficient distribution and the water drop impact mass distribution are obtained by simulating the air and water drop flow field, and the anti-icing heat flow is respectively determined for the heating areas in the heating coverage area on the basis, so that the heat load distribution design is carried out on the electric heating anti-icing system based on the anti-icing heat flow of each heating area, the heating requirements of different positions are better met, the energy utilization efficiency of the electric heating anti-icing system is improved, the method is suitable for considering the condition of heat conduction in the multilayer thin-wall solid, the design requirement of dry surface anti-icing can be met, and the design requirement of wet surface anti-icing can also be met.
A heat load distribution design method of an electrically heated anti-icing system according to an embodiment of the present disclosure may be written as a computer program and stored on a computer-readable storage medium. When executed by a processor, the computer program may implement the heat load distribution design method of the electrically heated anti-icing system as described above. Examples of computer-readable storage media include: read-only memory (ROM), random-access programmable read-only memory (PROM), electrically erasable programmable read-only memory (EEPROM), random-access memory (RAM), dynamic random-access memory (DRAM), static random-access memory (SRAM), flash memory, non-volatile memory, CD-ROM, CD-R, CD + R, CD-RW, CD + RW, DVD-ROM, DVD-R, DVD + R, DVD-RW, DVD + RW, DVD-RAM, BD-ROM, BD-R, BD-R LTH, BD-RE, blu-ray or optical disk memory, hard Disk Drives (HDDs), solid-state hard disks (SSDs), card-type memory (such as a multimedia card, a Secure Digital (SD) card, or an extreme digital (XD) card), magnetic tape, floppy disk, magneto-optical data storage, hard disk, solid-state disk, and any other device configured to store and to enable a computer program and any associated data file, data processing structure and to be executed by a computer. In one example, the computer program and any associated data, data files, and data structures are distributed across networked computer systems such that the computer program and any associated data, data files, and data structures are stored, accessed, and executed in a distributed fashion by one or more processors or computers.
Although a few embodiments of the present disclosure have been shown and described, it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the disclosure, the scope of which is defined in the claims and their equivalents.
Claims (4)
1. A heat load distribution design method of an electric heating anti-icing system, wherein the electric heating anti-icing system is used for electrically heating a heating coverage area, and the heating coverage area comprises a plurality of heating areas, wherein the heat load distribution design method comprises the following steps:
simulating the air and water drop flow field outside the heating coverage area based on preset simulation conditions to obtain the convective heat transfer coefficient and water drop impact quality of each grid unit of the heating coverage area;
calculating the heat load of the electric heating anti-icing system in each grid unit based on a preset target anti-icing temperature, the convection heat exchange coefficient and the water drop impact quality;
determining a face average anti-icing heat flow for each heating zone of the plurality of heating zones based on the heat load of each grid cell;
iteratively calculating a wall temperature for each grid cell based on the face average anti-icing heat flow of each heating region until the wall temperature converges relative to the target anti-icing temperature;
under the condition that the wall surface temperature of each grid unit is converged relative to the target anti-icing temperature, obtaining the finally determined surface average anti-icing heat flow of each heating area, and designing the heat load distribution of the electric heating anti-icing system according to the finally determined surface average anti-icing heat flow;
calculating a heat load of the electrically heated anti-icing system at each grid cell by the following equation:
wherein the content of the first and second substances,
indicates heat load, <' > or>
Represents the heat quantity taken away by the convection heat exchange>
Indicating heat carried away by impinging water dropletsThe amount of the compound (A) is,
represents the heat removed by evaporation>
Represents the convective heat transfer coefficient>
Indicates a target anti-icing temperature, <' > is present>
The temperature of the incoming flow is shown,
represents the specific heat capacity of the water>
Indicates drop impact quality>
Indicates the incoming flow velocity, and>
represents the evaporation quality ratio>
Represents the latent heat of evaporation of water>
Represents a mass transfer coefficient, <' > or>
Represents a predetermined constant, is present>
Represents the specific heat capacity of the air>
Represents the Liu Yi Si number of water vapor>
Represents the air pressure;
the electrically heated anti-icing system comprises a multilayer thin-walled solid, wherein the iteratively calculating a wall temperature for each grid cell based on the average anti-icing heat flow for the face of each heating zone comprises:
determining a heat transfer boundary condition of the multilayer thin-walled solid based on the face average anti-icing heat flow of each heating area, and performing heat conduction calculation on the multilayer thin-walled solid under the heat transfer boundary condition to iteratively calculate the wall surface temperature for each grid unit;
the multi-layer thin-walled solid comprises at least a heating layer, wherein the heat transfer boundary conditions comprise a first boundary condition, a second boundary condition, and a third boundary condition, wherein,
the first boundary condition is that the average anti-icing heat flow of the surface of each heating area is added into the heat conduction calculation of the heating layer in a heat source mode,
the second boundary condition is
A bottom surface for confining the multilayer thin-walled solid,
the third boundary condition is
For confining the upper surface of the multilayer thin-walled solid, wherein,
wherein the content of the first and second substances,
represents the bottom heat flow of a multi-layer thin-wall solid>
Represents an upper surface heat flow of a multi-layered thin-walled solid>
Represents the heat quantity taken away by convective heat transfer calculated according to the wall temperature>
Represents the heat quantity taken away by the impinging water drops calculated on the basis of the wall temperature>
Represents the heat removed by evaporation calculated on the basis of the wall temperature>
Represents the wall temperature;
the iteratively calculating the wall temperature for each grid cell includes:
in each iteration of the iterative computation of the wall temperature, determining whether the wall temperature of any grid cell converges relative to the target anti-icing temperature;
under the condition that the wall temperature of the grid unit is not converged relative to the target anti-icing temperature, carrying out updating calculation on the heat load of the grid unit so as to re-determine the average anti-icing heat flow of the surface of each heating area based on the heat load after updating calculation;
the heat load of the grid cell is updated by the following equation:
wherein, the first and the second end of the pipe are connected with each other,
indicating the heat load of the update calculation.
2. The heat load distribution design method of claim 1, wherein the simulated conditions include at least one of an incoming flow condition, a cloud condition, and a wall temperature condition, wherein the incoming flow condition includes at least one of an incoming flow velocity, an incoming flow temperature, and a pressure, wherein the cloud condition includes at least one of a water droplet diameter and a liquid water content, and wherein the wall temperature condition includes a given wall temperature, wherein the given wall temperature is determined based on the incoming flow temperature.
3. The heat load distribution design method of claim 1, wherein the convergence of the wall temperature with respect to the target anti-icing temperature is represented by the following inequality:
wherein the content of the first and second substances,Cindicating a temperature overage.
4. The heat load distribution design method of claim 1, wherein the face average anti-icing heat flow is calculated by the equation:
wherein the content of the first and second substances,
is shown asNThe area of the individual heating zones is averaged against the heat flow of ice>
Is shown asNArea of the individual heating zones->
Is shown asNIn a heating areaiHeat load of grid cells>
Is shown asNIn a heating areaiArea of individual grid cells. />
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310088148.4A CN115817822B (en) | 2023-02-09 | 2023-02-09 | Heat load distribution design method of electric heating anti-icing system |
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| CN116644258B (en) * | 2023-07-19 | 2023-12-22 | 中国空气动力研究与发展中心低速空气动力研究所 | Anti-icing heat load calculation method and system |
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