CN107506543A - High-voltage direct-current submarine cable simulation method and system - Google Patents
High-voltage direct-current submarine cable simulation method and system Download PDFInfo
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- 238000005485 electric heating Methods 0.000 claims abstract description 5
- 239000013535 sea water Substances 0.000 claims description 24
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Abstract
The invention relates to a high-voltage direct-current submarine cable simulation method and system, wherein an electric-thermal-current multi-physical-field coupling simulation method is provided for a high-voltage direct-current submarine cable by establishing an electric field module control equation, a flow field module control equation, a solid heat transfer module control equation, a fluid heat transfer module control equation and an electric heating coupling module control equation.
Description
Technical field
The present invention relates to electric analog technical field, more particularly to a kind of HVDC submarine cable emulation mode and is
System.
Background technology
Radial temperature profile and Electric Field Distribution when high voltage direct current cable is run are the operation ginsengs for reflecting that cable performance is important
Number, determines the long-term safety stable operation of cable.The difference of high voltage direct current cable and ac cable essentially consists in insulating barrier electricity
Field distribution and its influence factor are different.Under DC condition, loss (normal operation caused by conductor losses and insulated leakage current
When the latter ignore) be that cable has the reason for temperature gradient distribution, and the change of temperature and electric-field intensity can make insulation
Significant change occurs for material electric conductivity, and insulating barrier Electric Field Distribution depends on distribution of conductivity, therefore the electricity of high voltage direct current cable
Field distribution and Temperature Distribution are the relations to intercouple.Secondly, high voltage direct current cable is operationally except considering conductor temperature, also
Need to consider insulating barrier Temperature Distribution and its with the limitation of the coupling of Electric Field Distribution to current-carrying capacity.
Extra large cable is in marine environment, and the running and seawater of extra large cable are closely bound up.It is hot caused by extra large cable conductor losses
Amount carries out solid heat transfer in extra large cable body, soil, and fluid heat transferring is carried out in water.The flowing of seawater is constantly taken away caused by extra large cable
Heat, heat caused by extra large cable also constantly give heating of seawater.The flow velocity and temperature change of seawater can change the flowing feelings of seawater
Condition, the Temperature Distribution of extra large cable change therewith, and then changing insulating materials electrical conductivity makes insulating barrier Electric Field Distribution change, and electric
The change of field distribution influences electrical conductivity and then influences Temperature Distribution in turn again, so research considers the extra large cable electro thermal coupling in flow field
Rule have great importance.
Various operating modes and experimental program can be simulated by numerical simulation, result is relatively accurately obtained, turn into recent years
Study hotspot, but most of research is in electric heating, electromagnetism-heat and heat-stream (air-flow) just for coupling etc., and concentrate on pair
The research of land cable, and simply apply corresponding environment for electric-thermal-stream (current) coupling Simulation shorter mention of extra large cable, some
Parameter and boundary condition are simulated, and emulation accuracy is relatively low.
The content of the invention
Based on this, it is necessary to for emulating the problem of accuracy is relatively low, there is provided a kind of HVDC submarine cable emulation side
Method and system.
A kind of HVDC submarine cable emulation mode, comprises the following steps：
Establish extra large cable body and its lay the threedimensional model of environment；
According to the governing equation of the three-dimension modeling electric-thermal-stream coupling Simulation；Wherein, the governing equation includes
Electric field module governing equation, flow field module governing equation, solid heat transfer module governing equation, fluid heat transferring module governing equation and
Electro thermal coupling module governing equation；
Passed according to the electric field module governing equation, flow field module governing equation, solid heat transfer module governing equation, fluid
Thermal modules governing equation and electro thermal coupling module governing equation carry out HVDC submarine cable emulation.
A kind of HVDC submarine cable analogue system, including：
Model building module, for establishing extra large cable body and its laying the threedimensional model of environment；
Establishing equation module, for the governing equation according to the three-dimension modeling electric-thermal-stream coupling Simulation；Wherein,
The governing equation includes electric field module governing equation, flow field module governing equation, solid heat transfer module governing equation, fluid and passed
Thermal modules governing equation and electro thermal coupling module governing equation；
Emulation module, for according to the electric field module governing equation, flow field module governing equation, solid heat transfer module control
Equation, fluid heat transferring module governing equation and electro thermal coupling module governing equation processed carry out HVDC submarine cable emulation.
Above-mentioned HVDC submarine cable emulation mode and system, by establishing electric field module governing equation, flow field module
Governing equation, solid heat transfer module governing equation, fluid heat transferring module governing equation and electro thermal coupling module governing equation, for height
Pressure direct current submarine cable provides a kind of electric-thermal-stream multiple physical field coupling simulation method, this method direct-coupling electric-thermal-stream
The physical process of multiple physical field, the fast determination method of a kind of temperature, electric field and flow velocity is provided for HVDC extra large cable, simply
It is general, application easy to spread, have to the safe and reliable operation for ensureing power network and the service life for extending submarine cable important
Meaning.
Brief description of the drawings
Fig. 1 is the HVDC submarine cable emulation mode flow chart of one embodiment；
Fig. 2 is the submarine cable of one embodiment and its geometrical model figure for laying environment；
Fig. 3 (a) is the bulk temperature cloud charts in the simulation result of one embodiment；
Fig. 3 (b) is the extra large cable Temperature Distribution cloud atlas in the simulation result of one embodiment；
Fig. 4 is the Electric Field Distribution cloud atlas in the simulation result of one embodiment；
Fig. 5 is the velocity flow profile cloud atlas in the simulation result of one embodiment；
Fig. 6 is the structural representation of the HVDC submarine cable analogue system of one embodiment.
Embodiment
Technical scheme is illustrated below in conjunction with the accompanying drawings.
As shown in figure 1, the present invention provides a kind of HVDC submarine cable emulation mode, it may include following steps：
S1, establish extra large cable body and its lay the threedimensional model of environment；
Establish extra large cable body and its lay environment three-dimensional model diagram as shown in Fig. 2 including seawater region, soil region and
Submarine cable body；Wherein, the seawater region is located at the upper strata of the soil region, and the submarine cable body passes through institute
State seawater region.Include seawater region, the extra large cable body of soil region and submarine cable body three and its laying by establishing
The threedimensional model of environment, can at utmost simulation extra large cable body and its laying environment, it is larger with actual scene similarity, carry
The high simulation result degree of accuracy.It can be seen from Fig. 2, the laying environment in this step is equivalent to two cuboids in emulation, i.e.,
The upper strata for laying environment is " seawater region " (containing an entrance and an outlet), and lower floor is " soil region ".
S2, according to the governing equation of the three-dimension modeling electric-thermal-stream coupling Simulation；Wherein, the governing equation bag
Include electric field module governing equation, flow field module governing equation, solid heat transfer module governing equation, fluid heat transferring module governing equation
With electro thermal coupling module governing equation；
In this step in the three-dimensional electric heating stream coupling model of extra large cable body and its laying environment, loading is electric in the conductor
Heat transfer, the process of electro thermal coupling can be described using following governing equation in heat transfer, solid in stream, the flowing of water, fluid：
In one embodiment, following electric field module governing equation can be established：
J=σ E+Je
In formula,For vector differentiating operator；J is current density vectors, unit A/m3；QjFor current source, unit A/m3；
σ is electrical conductivity, unit S/m；E is electric field intensity, unit V/m；V is potential, unit V；JeIt is close for outside Injection Current
Degree.In this equation group, the basic parameter of solution is V, and other specification is obtained based on V.
In one embodiment, can establish such as Fluid field module governing equation：
In formula, ρ1For the density of fluent material, unit kg/m3；U is velocity, unit m/s；P is pressure, unit
For Pa；μ is dynamic viscosity, unit Pas；I is unit matrix.
In one embodiment, following fluid heat transferring module governing equation can be established：
In formula, C1For the specific heat capacity under fluent material normal pressure, unit is J/ (kgK)；T1It is single for the temperature of fluent material
Position is K；T is the time；Q is to conduct heat flux, unit W/m2；τ is viscid stress tensor, unit Pa；
For strain rate tensor, unit 1/s；Q1For the thermal source in fluent material, (being free of viscid heating), unit W/m3。
In one embodiment, following solid heat transfer module governing equation can be established：
In formula, ρ2For the density of solid material；C2For the specific heat capacity under solid material normal pressure；λ is the heat conduction system of solid material
Number, unit is W/ (mK)；T2For the temperature of solid material, unit K；Q2For the thermal source in solid material, unit W/m3。
In one embodiment, following electro thermal coupling module governing equation can be established：
In formula, ρ2For the density of solid material；T2For the temperature of solid material, unit K；λ is the heat conduction system of solid material
Number, unit is W/ (mK)；U is velocity；For vector differentiating operator；J is current density vectors；E is electric field intensity.
By establishing above-mentioned five kinds of equations, the equation established required for each physical field that emulation content is related to is specify that,
So as to all-sidedly and accurately carry out HVDC submarine cable emulation, simulation process is more directly perceived.By establishing electro thermal coupling
Equation, electric field and thermal field can be coupled.Because thermal field (Temperature Distribution) change, which can influence distribution of conductivity, makes Electric Field Distribution
Change；And Electric Field Distribution change influences distribution of conductivity in turn and then influences the Temperature Distribution of extra large cable.Therefore high pressure
The Electric Field Distribution of direct current cables and Temperature Distribution are the relations to intercouple.
S3, according to the electric field module governing equation, flow field module governing equation, solid heat transfer module governing equation, stream
Body heat transferring module governing equation and electro thermal coupling module governing equation carry out HVDC submarine cable emulation.
This step can be accomplished by the following way：
Step S3.1, be each layer of extra large cable body and its laying environment added material, the thermal conductivity factor of accurate definition material, often
Press thermal capacitance, density and electrical conductivity；
Step S3.2, addition electric field, flow field, solid heat transfer field and fluid heat transferring field, electric field boundary condition, stream is set respectively
Field boundary condition, solid heat transfer field boundary condition and fluid heat transferring field boundary condition；
Step S3.3, high pressure is loaded on submarine cable conductor, the loading current in the form of normal direction current density, by XLPE
The outer surface of (cross-linked polyethylene insulated cable, crosslinked polyetylene insulated type cable) insulation
It is arranged to be grounded, and the electric field of HVDC submarine cable is imitated according to the electric field module equation and electric field boundary condition
Very；
Step S3.4, flow inlet and water export are respectively equipped with the both ends in seawater region, is given at flow inlet
Flow velocity, and the flow field of HVDC submarine cable is emulated according to the flow field module equation and flow field boundary condition；
Step S3.5, seawater region is set to fluid heat transferring, water temperature is given at flow inlet, water temperature coboundary is set to
To heat flux, simulation is radiated, and according to the fluid heat transferring module equation and solid heat transfer field boundary condition to HVDC sea
The solid heat transfer field of bottom cable is emulated；
Step S3.6, extra large cable and soil region being set to solid heat transfer, the lower boundary for setting soil region is steady temperature,
Represent deep soil, and the stream according to the solid heat transfer equation and fluid heat transferring field boundary condition to HVDC submarine cable
Body heat transferring field is emulated；
Step S3.7, mesh generation is carried out using free tetrahedron, refined net division is carried out to extra large cable body, to laying ring
Border carries out coarse grid division.
The effect of mesh generation is that a complicated model is divided into some simple models, and these simple individuals
Between again connect each other, mutually constraint, form total.These simple structures are solved, with regard to overall variation tendency can be obtained,
Grid is more careful neat, and as a result more accurate, grid is coarse, as a result just has larger error.Aforementioned four module is to carry out side
The setting of boundary's condition and the addition of physical field, mesh generation are carried out after this.After simulation, stable state solver can be used
Unity couping calculate extra large cable Temperature Distribution, Electric Field Distribution and velocity flow profile.Solve can obtain extra large cable Temperature Distribution cloud atlas,
Electric Field Distribution cloud atlas and velocity flow profile cloud atlas are as shown in Fig. 3~Fig. 5.Wherein, Fig. 3 (a) is distributed for bulk temperature, and Fig. 3 (b) is sea
Cable Temperature Distribution.
The present invention considers electric-thermal-stream multiple physical field direct-coupling so complicated physical process simultaneously, accurate
In the case of setting material properties and boundary condition, a kind of temperature, electric field and flow velocity are provided for HVDC submarine cable
Fast determination method, simple general-purpose, application easy to spread, to ensureing the safe and reliable operation of power network and extending submarine cable
Service life is significant.
As shown in fig. 6, the present invention also provides a kind of HVDC submarine cable analogue system, it may include：
Model building module 10, for establishing extra large cable body and its laying the threedimensional model of environment；
Establish extra large cable body and its lay environment three-dimensional model diagram as shown in Fig. 2 including seawater region, soil region and
Submarine cable body；Wherein, the seawater region is located at the upper strata of the soil region, and the submarine cable body passes through institute
State seawater region.Include seawater region, the extra large cable body of soil region and submarine cable body three and its laying by establishing
The threedimensional model of environment, can at utmost simulation extra large cable body and its laying environment, it is larger with actual scene similarity, carry
The high simulation result degree of accuracy.It can be seen from Fig. 2, the laying environment in this step is equivalent to two cuboids in emulation, i.e.,
The upper strata for laying environment is " seawater region " (containing an entrance and an outlet), and lower floor is " soil region ".
Establishing equation module 20, for the governing equation according to the three-dimension modeling electric-thermal-stream coupling Simulation；Its
In, the governing equation includes electric field module governing equation, flow field module governing equation, solid heat transfer module governing equation, stream
Body heat transferring module governing equation and electro thermal coupling module governing equation；
In this module in the three-dimensional electric heating stream coupling model of extra large cable body and its laying environment, loading is electric in the conductor
Heat transfer, the process of electro thermal coupling can be described using following governing equation in heat transfer, solid in stream, the flowing of water, fluid：
In one embodiment, following electric field module governing equation can be established：
J=σ E+Je
In formula,For vector differentiating operator；J is current density vectors, unit A/m3；QjFor current source, unit A/
m3；σ is electrical conductivity, unit S/m；E is electric field intensity, unit V/m；V is potential, unit V；JeFor outside Injection Current
Density.In this equation group, the basic parameter of solution is V, and other specification is obtained based on V.
In one embodiment, can establish such as Fluid field module governing equation：
In formula, ρ1For the density of fluent material, unit kg/m3；U is velocity, unit m/s；P is pressure, unit
For Pa；μ is dynamic viscosity, unit Pas；I is unit matrix.
In one embodiment, following fluid heat transferring module governing equation can be established：
In formula, C1For the specific heat capacity under fluent material normal pressure, unit is J/ (kgK)；T1It is single for the temperature of fluent material
Position is K；T is the time；Q is to conduct heat flux, unit W/m2；τ is viscid stress tensor, unit Pa；
For strain rate tensor, unit 1/s；Q1For the thermal source in fluent material, (being free of viscid heating), unit W/m3。
In one embodiment, following solid heat transfer module governing equation can be established：
In formula, ρ2For the density of solid material；C2For the specific heat capacity under solid material normal pressure；λ is the heat conduction system of solid material
Number, unit is W/ (mK)；T2For the temperature of solid material, unit K；Q2For the thermal source in solid material, unit W/m3。
In one embodiment, following electro thermal coupling module governing equation can be established：
In formula, ρ2For the density of solid material；T2For the temperature of solid material, unit K；λ is the heat conduction system of solid material
Number, unit is W/ (mK)；U is velocity；For vector differentiating operator；J is current density vectors；E is electric field intensity.
By establishing above-mentioned five kinds of equations, the equation established required for each physical field that emulation content is related to is specify that,
So as to all-sidedly and accurately carry out HVDC submarine cable emulation, simulation process is more directly perceived.By establishing electro thermal coupling
Equation, electric field and thermal field can be coupled.Because thermal field (Temperature Distribution) change, which can influence distribution of conductivity, makes Electric Field Distribution
Change；And Electric Field Distribution change influences distribution of conductivity in turn and then influences the Temperature Distribution of extra large cable.Therefore high pressure
The Electric Field Distribution of direct current cables and Temperature Distribution are the relations to intercouple.
Emulation module 30, for according to the electric field module governing equation, flow field module governing equation, solid heat transfer module
Governing equation, fluid heat transferring module governing equation and electro thermal coupling module governing equation carry out HVDC submarine cable emulation.
The function of this module can be accomplished by the following way：
Step S3.1, be each layer of extra large cable body and its laying environment added material, the thermal conductivity factor of accurate definition material, often
Press thermal capacitance, density and electrical conductivity；
Step S3.2, addition electric field, flow field, solid heat transfer field and fluid heat transferring field, electric field boundary condition, stream is set respectively
Field boundary condition, solid heat transfer field boundary condition and fluid heat transferring field boundary condition；
Step S3.3, high pressure is loaded on submarine cable conductor, the loading current in the form of normal direction current density, by XLPE
The outer surface of insulation is arranged to be grounded, and according to the electric field module equation and electric field boundary condition to HVDC submarine cable
Electric field emulated；
Step S3.4, flow inlet and water export are respectively equipped with the both ends in seawater region, is given at flow inlet
Flow velocity, and the flow field of HVDC submarine cable is emulated according to the flow field module equation and flow field boundary condition；
Step S3.5, seawater region is set to fluid heat transferring, water temperature is given at flow inlet, water temperature coboundary is set to
To heat flux, simulation is radiated, and according to the fluid heat transferring module equation and solid heat transfer field boundary condition to HVDC sea
The solid heat transfer field of bottom cable is emulated；
Step S3.6, extra large cable and soil region being set to solid heat transfer, the lower boundary for setting soil region is steady temperature,
Represent deep soil, and the stream according to the solid heat transfer equation and fluid heat transferring field boundary condition to HVDC submarine cable
Body heat transferring field is emulated；
Step S3.7, mesh generation is carried out using free tetrahedron, refined net division is carried out to extra large cable body, to laying ring
Border carries out coarse grid division.
The effect of mesh generation is that a complicated model is divided into some simple models, and these simple individuals
Between again connect each other, mutually constraint, form total.These simple structures are solved, with regard to overall variation tendency can be obtained,
Grid is more careful neat, and as a result more accurate, grid is coarse, as a result just has larger error.Aforementioned four module is to carry out side
The setting of boundary's condition and the addition of physical field, mesh generation are carried out after this.After simulation, stable state solver can be used
Unity couping calculated.Solution can obtain the Temperature Distribution cloud atlas, Electric Field Distribution cloud atlas and velocity flow profile cloud atlas of extra large cable such as
Shown in Fig. 3~Fig. 5.Wherein, Fig. 3 (a) is distributed for bulk temperature, and Fig. 3 (b) is extra large cable Temperature Distribution.
The present invention considers electric-thermal-stream multiple physical field direct-coupling so complicated physical process simultaneously, accurate
In the case of setting material properties and boundary condition, a kind of temperature, electric field and flow velocity are provided for HVDC submarine cable
Fast determination method, simple general-purpose, application easy to spread, to ensureing the safe and reliable operation of power network and extending submarine cable
Service life is significant.
The HVDC submarine cable emulation mode one of the HVDC submarine cable analogue system of the present invention and the present invention
One correspondence, the technical characteristic illustrated in the embodiment of above-mentioned HVDC submarine cable emulation mode and its advantage are applicable
In the embodiment of HVDC submarine cable analogue system, hereby give notice that.
Expression or logic and/or step described otherwise above herein in flow charts, for example, being considered use
In the order list for the executable instruction for realizing logic function, may be embodied in any computer-readable medium, for
Instruction execution system, device or equipment (such as computer based system including the system of processor or other can be held from instruction
The system of row system, device or equipment instruction fetch and execute instruction) use, or combine these instruction execution systems, device or set
It is standby and use.For the purpose of this specification, " computer-readable medium " can any can be included, store, communicate, propagate or pass
Defeated program is for instruction execution system, device or equipment or the dress used with reference to these instruction execution systems, device or equipment
Put.
The more specifically example (non-exhaustive list) of computer-readable medium includes following：Connected up with one or more
Electrical connection section (electronic installation), portable computer diskette box (magnetic device), random access memory (RAM), read-only storage
(ROM), erasable edit read-only storage (EPROM or flash memory), fiber device, and portable optic disk is read-only deposits
Reservoir (CDROM).In addition, computer-readable medium, which can even is that, to print the paper of described program thereon or other are suitable
Medium, because can then enter edlin, interpretation or if necessary with it for example by carrying out optical scanner to paper or other media
His suitable method is handled electronically to obtain described program, is then stored in computer storage.
It should be appreciated that each several part of the present invention can be realized with hardware, software, firmware or combinations thereof.Above-mentioned
In embodiment, software that multiple steps or method can be performed in memory and by suitable instruction execution system with storage
Or firmware is realized.If, and in another embodiment, can be with well known in the art for example, realized with hardware
Any one of row technology or their combination are realized：With the logic gates for realizing logic function to data-signal
Discrete logic, have suitable combinational logic gate circuit application specific integrated circuit, programmable gate array (PGA), scene
Programmable gate array (FPGA) etc..
In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show
The description of example " or " some examples " etc. means specific features, structure, material or the spy for combining the embodiment or example description
Point is contained at least one embodiment or example of the present invention.In this manual, to the schematic representation of above-mentioned term not
Necessarily refer to identical embodiment or example.Moreover, specific features, structure, material or the feature of description can be any
One or more embodiments or example in combine in an appropriate manner.
Each technical characteristic of embodiment described above can be combined arbitrarily, to make description succinct, not to above-mentioned reality
Apply all possible combination of each technical characteristic in example to be all described, as long as however, the combination of these technical characteristics is not deposited
In contradiction, the scope that this specification is recorded all is considered to be.
Embodiment described above only expresses the several embodiments of the present invention, and its description is more specific and detailed, but simultaneously
Can not therefore it be construed as limiting the scope of the patent.It should be pointed out that come for one of ordinary skill in the art
Say, without departing from the inventive concept of the premise, various modifications and improvements can be made, these belong to the protection of the present invention
Scope.Therefore, the protection domain of patent of the present invention should be determined by the appended claims.
Claims (9)
1. a kind of HVDC submarine cable emulation mode, it is characterised in that comprise the following steps：
Establish extra large cable body and its lay the threedimensional model of environment；
According to the governing equation of the three-dimension modeling electric-thermal-stream coupling Simulation；Wherein, the governing equation includes electric field
Module governing equation, flow field module governing equation, solid heat transfer module governing equation, fluid heat transferring module governing equation and electric heating
Coupling module governing equation；
According to the electric field module governing equation, flow field module governing equation, solid heat transfer module governing equation, fluid heat transferring mould
Block governing equation and electro thermal coupling module governing equation carry out HVDC submarine cable emulation.
2. HVDC submarine cable emulation mode according to claim 1, it is characterised in that the threedimensional model includes
Seawater region, soil region and submarine cable body；
Wherein, the seawater region is located at the upper strata of the soil region, and the submarine cable body passes through the sea-water area
Domain.
3. HVDC submarine cable emulation mode according to claim 1, it is characterised in that according to the threedimensional model
The step of governing equation for establishing electric-thermal-stream coupling Simulation, includes：
Establish following electric field module governing equation：
▽ J=Qj
J=σ E+Je
E=- ▽ V
In formula, ▽ is vector differentiating operator；J is current density vectors, QjFor current source, σ is electrical conductivity, and E is electric field intensity, and V is
Potential, JeFor outside injected current density.
4. HVDC submarine cable emulation mode according to claim 1, it is characterised in that according to the threedimensional model
The step of governing equation for establishing electric-thermal-stream coupling Simulation, also includes：
Establish such as Fluid field module governing equation：
▽·(ρ1U)=0
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<mo>&dtri;</mo>
<mo>&CenterDot;</mo>
<mo>{</mo>
<mi>&mu;</mi>
<mo>&lsqb;</mo>
<mo>&dtri;</mo>
<mi>u</mi>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mo>&dtri;</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mo>&rsqb;</mo>
<mo>-</mo>
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
<mi>&mu;</mi>
<mrow>
<mo>(</mo>
<mo>&dtri;</mo>
<mo>&CenterDot;</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mi>I</mi>
<mo>}</mo>
</mrow>
In formula, ρ1For the density of fluent material, u is velocity, and p is pressure, and μ is dynamic viscosity, and I is unit matrix.
5. HVDC submarine cable emulation mode according to claim 1, it is characterised in that according to the threedimensional model
The step of governing equation for establishing electric-thermal-stream coupling Simulation, also includes：
Establish following fluid heat transferring module governing equation：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&rho;</mi>
<mn>1</mn>
</msub>
<msub>
<mi>C</mi>
<mn>1</mn>
</msub>
<mo>&lsqb;</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>T</mi>
<mn>1</mn>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>&CenterDot;</mo>
<mo>&dtri;</mo>
<mo>)</mo>
</mrow>
<msub>
<mi>T</mi>
<mn>1</mn>
</msub>
<mo>&rsqb;</mo>
<mo>=</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mo>&dtri;</mo>
<mo>&CenterDot;</mo>
<mi>q</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>&tau;</mi>
<mo>:</mo>
<mi>S</mi>
<mo>-</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mfrac>
<msub>
<mi>T</mi>
<mn>1</mn>
</msub>
<msub>
<mi>&rho;</mi>
<mn>1</mn>
</msub>
</mfrac>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>&rho;</mi>
<mn>1</mn>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<msub>
<mi>T</mi>
<mn>1</mn>
</msub>
</mrow>
</mfrac>
<msub>
<mo>|</mo>
<mi>p</mi>
</msub>
<mo>&lsqb;</mo>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>&rho;</mi>
<mn>1</mn>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>u</mi>
<mo>&CenterDot;</mo>
<mo>&dtri;</mo>
<mo>)</mo>
</mrow>
<mi>p</mi>
<mo>&rsqb;</mo>
<mo>+</mo>
<msub>
<mi>Q</mi>
<mn>1</mn>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula, C1For the specific heat capacity under fluent material normal pressure, T1For the temperature of fluent material, q is conduction heat flux, and τ answers to be viscid
Power tensor, S=0.5 [▽ u+ (▽ u)T] it is strain rate tensor, Q1For the thermal source in fluent material.
6. HVDC submarine cable emulation mode according to claim 1, it is characterised in that according to the threedimensional model
The step of governing equation for establishing electric-thermal-stream coupling Simulation, also includes：
Establish following solid heat transfer module governing equation：
ρ2C2▽ T=▽ (λ ▽ T)+Q2
In formula, ρ2For the density of solid material, C2For the specific heat capacity under solid material normal pressure, λ is the thermal conductivity factor of solid material,
Q2For the thermal source in solid material.
7. HVDC submarine cable emulation mode according to claim 1, it is characterised in that according to the threedimensional model
The step of governing equation for establishing electric-thermal-stream coupling Simulation, also includes：
Establish following electro thermal coupling module governing equation：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&rho;</mi>
<mn>2</mn>
</msub>
<mi>C</mi>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>T</mi>
<mn>2</mn>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>t</mi>
</mrow>
</mfrac>
<mo>+</mo>
<msub>
<mi>&rho;</mi>
<mn>2</mn>
</msub>
<mi>C</mi>
<mi>u</mi>
<mo>&CenterDot;</mo>
<mo>&dtri;</mo>
<msub>
<mi>T</mi>
<mn>2</mn>
</msub>
<mo>=</mo>
<mo>&dtri;</mo>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>&dtri;</mo>
<msub>
<mi>T</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>Q</mi>
<mo>=</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>&dtri;</mo>
<mo>&CenterDot;</mo>
<mrow>
<mo>(</mo>
<mi>&lambda;</mi>
<mo>&dtri;</mo>
<msub>
<mi>T</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>J</mi>
<mo>&CenterDot;</mo>
<mi>E</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
In formula, ρ2For the density of solid material；T2For the temperature of solid material, unit K；λ is the thermal conductivity factor of solid material,
Unit is W/ (mK)；U is velocity；▽ is vector differentiating operator；J is current density vectors；E is electric field intensity.
8. HVDC submarine cable emulation mode according to claim 1, it is characterised in that according to the electric field module
Governing equation, flow field module governing equation, solid heat transfer module governing equation, fluid heat transferring module governing equation and electro thermal coupling
The step of module governing equation progress HVDC submarine cable emulation, includes：
Electric field, flow field, solid heat transfer field and fluid heat transferring field are added, electric field boundary condition, flow field boundary condition is set respectively, consolidates
Body heat transferring field boundary condition and fluid heat transferring field boundary condition；
High pressure is loaded on submarine cable conductor, the loading current in the form of normal direction current density, the outer surface that XLPE is insulated
It is arranged to be grounded, and the electric field of HVDC submarine cable is imitated according to the electric field module equation and electric field boundary condition
Very；
Flow inlet and water export are respectively equipped with the both ends in seawater region, flow velocity is given at flow inlet, and according to institute
State flow field module equation and flow field boundary condition emulates to the flow field of HVDC submarine cable；
Seawater region is set to fluid heat transferring, water temperature is given at flow inlet, water temperature coboundary is set to heat flux, simulation
Radiating, and the solid of HVDC submarine cable is passed according to the fluid heat transferring module equation and solid heat transfer field boundary condition
Thermal field is emulated；
Extra large cable and soil region are set to solid heat transfer, the lower boundary for setting soil region is steady temperature, represents deep soil,
And the fluid heat transferring field of HVDC submarine cable is carried out according to the solid heat transfer equation and fluid heat transferring field boundary condition
Emulation；
The electric field is carried out by coupling with the solid heat transfer field and fluid heat transferring field by electro thermal coupling module governing equation respectively
Close；
Mesh generation is carried out using free tetrahedron, refined net division is carried out to extra large cable body, coarse grid is carried out to laying environment
Division.
A kind of 9. HVDC submarine cable analogue system, it is characterised in that including：
Model building module, for establishing extra large cable body and its laying the threedimensional model of environment；
Establishing equation module, for the governing equation according to the three-dimension modeling electric-thermal-stream coupling Simulation；Wherein, it is described
Governing equation includes electric field module governing equation, flow field module governing equation, solid heat transfer module governing equation, fluid heat transferring mould
Block governing equation and electro thermal coupling module governing equation；
Emulation module, for according to the electric field module governing equation, flow field module governing equation, solid heat transfer module controlling party
Journey, fluid heat transferring module governing equation and electro thermal coupling module governing equation carry out HVDC submarine cable emulation.
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| CN112100809B (en) * | 2020-08-10 | 2022-06-14 | 华南理工大学 | Method for designing three-phase coaxial superconducting cable based on multi-physical field coupling simulation |
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Application publication date: 20171222 |