CN109446623B - Solid-state heat storage heating characteristic matching design method based on heat transfer rate balance - Google Patents
Solid-state heat storage heating characteristic matching design method based on heat transfer rate balance Download PDFInfo
- Publication number
- CN109446623B CN109446623B CN201811220025.7A CN201811220025A CN109446623B CN 109446623 B CN109446623 B CN 109446623B CN 201811220025 A CN201811220025 A CN 201811220025A CN 109446623 B CN109446623 B CN 109446623B
- Authority
- CN
- China
- Prior art keywords
- heat
- air
- resistance wire
- temperature
- solid
- 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
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
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- 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
- G06F2119/08—Thermal analysis or thermal optimisation
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y02E60/14—Thermal energy storage
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Central Heating Systems (AREA)
- Investigating Or Analyzing Materials Using Thermal Means (AREA)
Abstract
A solid-state heat storage heating characteristic matching design method based on heat transfer rate balance comprises the following steps: 1) Acquiring structural data material data and operating condition parameters of the high-temperature solid-state heat storage device; 2) Establishing a heat transfer rate balance model between the high-temperature heat storage material and the resistance heating element: 3) And 4) establishing a heat transfer model between the high-temperature heat storage material and the resistance heating element according to a heat transfer rate balance model: 5) Determining the boundary condition of the heat transfer coupling between the air and the surface of the heat accumulator: 6) And judging whether the surface temperature of the resistance wire is in an operation temperature range. 7) Obtaining the air inlet flow speed parameters meeting the design structure of the heat accumulator air channel and each operating temperature interval, and matching the structure and the performance of the electric heating element and the heat storage device, thereby realizing the optimization of the whole structure. (1) The temperature change rate is constant, so that the heat transfer balance can be calculated. And (2) matching the heat storage material with the resistance wire. (3) The shortening of the service life of the electric heating element caused by high-temperature brittleness is avoided.
Description
Technical Field
The invention belongs to the field of high-temperature solid-state heat storage design optimization, and relates to a solid-state heat storage heating characteristic matching design optimization method based on fluid-solid multi-field heat transfer rate balance.
Background
Solid-state high-temperature heat storage is a novel low-cost and large-capacity heat storage mode, has wide application prospect in the fields of high-temperature heat storage, peak regulation of thermal power plants and the like, and has the working principle that: during the electricity consumption valley period or the power grid surplus electricity period, the electric heat energy storage conversion system is started to convert electric energy into heat energy to be stored in the heat storage material, the heat energy is released only in the heat load demand period, and in four energy transfer processes of electric heat energy conversion, heat storage, heat transfer and heat exchange, the system effectively realizes electric heat decoupling and thermoelectric isolation. In recent years, the energy storage device is applied to urban distributed heating and flexible operation transformation equipped with a cogeneration unit on a large scale, is used as one of interruptible loads, effectively solves the problem of consumption of clean energy such as wind power, photovoltaic power, nuclear power and the like, and becomes one of research hotspots of large-scale energy storage.
The heat storage energy storage device stores heat energy generated by surplus electricity or abandoned electricity in the heat storage material through the electric heating device, the resistance-type alloy heating element needs to endure high temperature of hundreds of degrees centigrade after being electrified, the temperature can be reduced to be below 100 ℃ when releasing heat, the resistance-type alloy heating element works in a large temperature difference range, the heating element is easy to have fatigue caused by repeated overheating and cold and heat, the service life of the heating element is seriously influenced, and the phenomenon of frequent maintenance is caused.
In addition, in the design of the solid-state heat storage device, if the surface load of the electric heating element is higher than the heat transfer rate of the heat storage material, the heat generated by the resistance wire exceeds the absorption rate of the heat storage body, the accumulated heat energy can be converted into temperature rise, the temperature rise is too high, the service life of the resistance wire can be shortened, and the reliability and the economic operation of the heat storage device are influenced. Among common heat storage materials, the heat conductivity coefficient of an organic phase change heat storage material is about 0.2W/(m.K), the heat conductivity coefficient of an inorganic phase change material is about 0.5W/(m.K), the heat conductivity coefficient of water is about 0.593W/(m.K), the heat conductivity coefficient of a solid magnesium oxide heat storage material is about 4.6W/(m.K), and the heat conductivity coefficients are all low, so that the heat transfer problem needs to be considered.
Disclosure of Invention
The invention discloses a matching design method for a heat storage material and an electric heating element of a solid-state heat storage system, which aims to solve the problems in the prior art and analyze the heat transfer rate balance relationship and the temperature field between the solid-state heat storage material and the heating element under three different operating conditions of simple heating, simultaneous heating/heat release and simple heat release of a solid-state heat storage device. A solid-state heat storage heating characteristic matching design method based on heat transfer rate balance is designed, so that higher surface load of a heating element is realized, and the service life of the heating element is optimized.
The technical scheme is as follows:
the method comprises the following steps:
1) Acquiring structural data material data and operating condition parameters of the high-temperature solid-state heat storage device;
2) Setting target parameters such as heating power and expected temperature rise rate of the electric heating element, and establishing a heat transfer rate balance model between the high-temperature heat storage material and the resistance heating element:
in the formula: p is the heating power of the electric heating element; j is heat-work equivalent; lambda s Is the solid thermal conductivity; t is s Is the solid surface temperature; s is the heated surface area of the solid; a. The e The surface area of the resistance wire; h is es The radiation heat exchange coefficient of the resistance wire and the heat accumulator is shown; t is e The temperature of the resistance wire; a. The s The surface area of the brick hole is shown; h is sa The heat transfer coefficient is the heat transfer coefficient of convection between the heat accumulator and air; t is a unit of a Is the air temperature; v. of a Is the air flow rate; rho A The areal density of air flowing into the heat exchanger; m is a unit of a Mass of air in the thermal storage body; c. C a The heat capacity of air; t is time; m is e The mass of the resistance wire; c. C e Is the thermal capacity of the resistance wire;
3) According to the heat transfer rate balance model, calculating the convective heat transfer rate phi between the heat accumulator and the air as And the return stroke number, the hole occupying ratio, the area, the length and the air inlet flow of the heat accumulator air channel are designed according to the design;
4) Establishing a heat transfer model between the high-temperature heat storage material and the resistance heating element by using ANSYS finite element analysis software according to the following formula:
(1) The resistance wire conducts heat to the heat accumulator by radiation:
in the formula: i is the radiation intensity; a is the absorption coefficient; sigma s Is the scattering coefficient; n is 0 Is a refractive index; t is e Is the local temperature; omega is a phase function; Ω is a spatial solid angle;
(2) Convection heat transfer of the heat accumulator by the resistance wire:
(3) In the formula: c. C pa Is the specific heat of air; rho a Is the air density; t is a Is the air temperature; lambda a Is the air thermal conductivity; upsilon is a Is an air velocity vector; phi is the airflow viscous dissipation; p is hydrostatic pressure; q. q.s ea The heat flow between the fluid and the resistance wire; q. q.s sa The heat flow between the fluid and the heat accumulator;
heat conduction of heat accumulator solid:
in the formula: c. C ps Is the specific heat of the solid; rho s Is the density of the solid; t is s Is the solid temperature; lambda [ alpha ] s Is the solid thermal conductivity;
5) Determining the boundary condition of the heat transfer coupling between the air and the surface of the heat accumulator:
and (3) when the flow-solid interface meets the energy continuity condition, coupling the three energy equations of heat transfer:
in the formula: t is e ε and σ are radiation temperature, blackness and Stefan-Boltzmann constant, respectively; t is a And h a Fluid temperature and surface heat transfer coefficient, respectively; t is s And λ s Solid temperature and thermal conductivity, respectively; q. q.s e ，q a And q is s Respectively the radiation heat flow density, the convection heat flow density and the heat conduction heat flow density of the fluid side and the solid side on the fluid-solid interface; n is a stream-a solid interface normal vector.
6) And analyzing the change condition of the heat transfer temperature field between the resistance wire and the heat accumulator by using an ANSYS heat transfer model, judging whether the surface temperature of the resistance wire is in an operating temperature range, and changing the inlet air speed to reduce the surface temperature of the resistance wire or increase the surface temperature of the resistance wire when the resistance wire is not in the operating temperature range.
7) Obtaining the air inlet flow speed parameters meeting the design structure of the heat accumulator air duct and each operation temperature interval, and matching the structures and the performances of the electric heating element and the heat storage device, thereby realizing the optimization of the whole structure.
The high-temperature solid-state heat storage system conforms to the law of energy conservation in each working state, and according to the first law of thermodynamics, the heat Q and work W exchanged between the system and the outside and the internal energy variation delta U of the system meet the following requirements:
ΔU＝Q+W (5)
according to the formula (5), part of the heat energy generated by the resistance wire is converted into the internal energy U of the resistance wire, which is reflected as the temperature change of the resistance wire, and the other part of the heat energy is the heat energy Q exchanged between the resistance wire and the other parts of the heat storage device; in the heat storage process of the electric heat storage device, the electric energy is converted into heat energy by the heat element with the heating power being P through joule heat, and the system input power is given by the following formula (5):
ΔU＝Q+PΔt/J (6)
in the formula: j is a thermal equivalent, and the unit is J/cal;
the resistance wire with resistance wire has mass m e The thermal capacity of the resistance wire is c e The rate of heat exchange from the electric heating element to the outside is then:
in the formula: t is e The temperature of the resistance wire;
in the heat exchange Q, the heat exchange Q of the resistance wire and the surrounding air is included ea And the radiation heat Q between the resistance wire and the heat accumulator es Two parts; if the resistance wire exchanges heat with the outsideAt a rate or heat flow of phi e ，Φ ea Indicating the convective heat transfer rate, phi, of the resistance wire and air es The rate of radiant heat of the resistance wire and the heat accumulator is shown as follows:
Φ e ＝Φ es +Φ ea (8)
wherein, the resistance wire and the heat accumulator radiate heat rate phi es Comprises the following steps:
in the formula: a. The e The surface area of the resistance wire; h is es The surface area of the resistance wire is far smaller than the heating surface area of the heat accumulator, and the emissivity of the heat accumulation unit system is epsilon s ＝ε e So the radiation heat exchange coefficient h of the resistance wire and the heat accumulator es The values are:
h es ＝5.67×10 -8 ε e (10)
in the whole heat-accumulating heat-exchanging process, besides the heat exchange on the surface of the resistance wire, the heat exchange also exists between the surface of the heat accumulator and the air, and Q is used sa Represents the heat exchanged by the heat storage body and air, and Q es Is the radiation heat between the resistance wire and the heat accumulator, the net heat conduction quantity Q in the heat accumulator s Can be expressed as:
Q s ＝Q es +Q sa (11)
according to the heat balance relationship expressed by the equation (11), if using phi sa Expressing the convective heat transfer rate of the heat accumulator and air, using phi s Representing the net heat flow from the inner surface of the regenerator, there are:
Φ s ＝Φ es -Φ sa (12)
wherein the net heat flow phi of the inner surface of the heat accumulator s Comprises the following steps:
convective heat transfer rate phi of surface of heat storage body and air sa Comprises the following steps:
Φ sa ＝A s h sa (T s -T a ) (14)
in the formula, A s Is the surface area of the inner surface of the heat accumulator, h sa The heat transfer coefficient is the heat transfer coefficient of convection between the heat accumulator and air; under the condition of forced convection, calculating the heat exchange coefficient h between the inner surface of the heat accumulator and the air by adopting a non-circular pipe groove turbulent forced convection heat transfer correlation Gnielinski formula sa ：
In the formula, d s Equivalent brick hole diameter for heat accumulator: (
A c Is the sectional area of the brick hole, P is the circumference of the brick hole), f is the Darcy resistance coefficient, l s The brick holes are long;
when the formulas (12) and (8) are combined, the following are provided:
Φ e ＝2Φ es +Φ ea -Φ sa -Φ s (16)
in the process of convective heat transfer between the resistance wire and the heat accumulator, the internal energy change of the air and the heat loss generated by the air and the outside during air circulation should be considered, especially, under the working condition of storing/releasing heat at the same time, the heat loss of the air in the heat exchanger can be expressed as follows:
in the formula, v a Is the air velocity, ρ A Is the areal density of the air flowing into the heat exchanger; considering the relationship between air heat loss and convective heat transfer rateIs phi of a It can also be expressed as:
when the formulas (7) and (18) are substituted into the formula (16), the following are provided:
substituting the formula (9), the formula (13), the formula (14) and the formula (17) into the formula (19) to obtain:
equation (15) applies to Re a ＝2300～10 6 ，Pr a ＝0.6～10 5 )
The advantages and effects are as follows:
the invention provides a solid-state heat storage heating characteristic matching design method based on a heat transfer rate balance method, aiming at the heat transfer characteristics of a heat storage unit and the high-temperature oxidation characteristics of a resistance heating element. Compared with the existing design method of the high-temperature solid-state heat storage structure body, the method has the following advantages:
(1) The temperature of the heat accumulator changes greatly in the operation process, the heat accumulator is difficult to design and calculate according to the temperature value of a heat accumulation part, the heat transfer rate can be adopted to assume that the temperature change of the resistance wire in a certain time interval and the temperature change of the surface of the heat accumulator are linear changes, the temperature change rate is a constant value, and accordingly heat transfer balance type calculation can be carried out.
(2) The matching between the heat storage material and the resistance wire is actually the matching between the heat conduction rate of the heat storage material and the surface temperature of the resistance wire. By adopting a heat transfer rate balancing method, the surface temperature of the resistance wire can be reduced under the condition of not reducing the power of the resistance wire, namely, the service life of the heating element is prolonged while high heat storage density is realized.
(3) When the heat storage material and the heating element are matched, the surface temperature of the resistance wire can be controlled in the brittle temperature range of the electric heating material, so that the service life of the electric heating element is prevented from being shortened due to high-temperature brittleness.
Drawings
FIG. 1 is a schematic structural view of a solid state thermal storage device; the device comprises a heat storage module 1, a heat storage module 2, an embedded heating wire 3, a heat exchanger 4, a variable frequency fan 5, a heat preservation shell 6 and an external control;
FIG. 2 is a schematic diagram of solid heat storage and transfer, in which (a) is a schematic diagram of heat transfer of spiral heating wires, and (b) is a schematic diagram of heat transfer of wavy heating wires;
FIG. 3 is a schematic diagram of heat transfer for a solid state heat storage system
FIG. 4 is a flow chart of heat transfer matching design for a solid state thermal storage system
The specific implementation mode is as follows:
the invention mainly aims at the design of a heat storage material and an electric heating wire of a high-temperature solid-state heat storage system, and provides a solid-state heat storage heating characteristic matching design method based on heat transfer rate balance, which is used for solving the problem of the adaptive design of the heat storage material and the electric heating wire of the heat storage system.
The method comprises the following steps:
1) Acquiring structural data material data and operating condition parameters of the high-temperature solid-state heat storage device;
2) Setting target parameters such as heating power of the electric heating element, expected temperature rise rate and the like, and establishing a heat transfer rate balance model between the high-temperature heat storage material and the resistance heating element:
in the formula: p is the heating power of the electric heating element; j is a thermal equivalent; lambda [ alpha ] s Is the solid thermal conductivity; t is s Is the solid surface temperature; s is the heated surface area of the solid; a. The e The surface area of the resistance wire; h is es The radiation heat exchange coefficient of the resistance wire and the heat accumulator is adopted; t is e The temperature of the resistance wire; a. The s The surface area of the brick hole; h is a total of sa The heat transfer coefficient is the heat transfer coefficient of convection between the heat accumulator and air; t is a unit of a Is air temperatureDegree; v. of a Is the air flow rate; rho A The areal density of air flowing into the heat exchanger; m is a Mass of air in the thermal storage body; c. C a The heat capacity of air; t is time; m is e The mass of the resistance wire; c. C e Is the thermal capacity of the resistance wire;
3) According to the heat transfer rate balance model, calculating the convective heat transfer rate phi between the heat accumulator and the air as And the return stroke number, the hole occupying ratio, the area, the length and the air inlet flow of the heat accumulator air channel are designed according to the design;
4) Establishing a heat transfer model between the high-temperature heat storage material and the resistance heating element by using ANSYS finite element analysis software:
5) Determining the boundary condition of the heat transfer coupling between the air and the surface of the heat accumulator:
and (3) when the flow-solid interface meets the energy continuity condition, coupling the three energy equations of heat transfer:
in the formula: t is e ε and σ are radiation temperature, blackness and Stefan-Boltzmann constant, respectively; t is a unit of a And h a Fluid temperature and surface heat transfer coefficient, respectively; t is s And λ s Solid temperature and thermal conductivity, respectively; q. q of e ，q a And q is s Respectively the radiation heat flow density, the convection heat flow density and the heat conduction heat flow density of the fluid side and the solid side on the fluid-solid interface; n is a normal vector of a flow-solid interface;
6) Analyzing the change condition of a heat transfer temperature field between the resistance wire and the heat accumulator by using an ANSYS heat transfer model, judging whether the surface temperature of the resistance wire is in an operation temperature interval, and changing the inlet air speed to reduce the surface temperature of the resistance wire or increase the surface temperature of the resistance wire when the resistance wire is not in the operation temperature interval;
7) Obtaining the air inlet flow speed parameters meeting the design structure of the heat accumulator air channel and each operating temperature interval, and matching the structure and the performance of the electric heating element and the heat storage device, thereby realizing the optimization of the whole structure.
4) In the steps, according to the following formula, establishing a heat transfer model between the high-temperature heat storage material and the resistance heating element by using ANSYS finite element analysis software:
(1) The resistance wire is used for heat radiation transfer of the heat accumulator:
in the formula: i is the radiation intensity; a is the absorption coefficient; sigma s Is the scattering coefficient; n is 0 Is a refractive index; t is a unit of e Is the local temperature; omega is a phase function; Ω is a spatial solid angle;
(2) The resistance wire carries out heat convection on the heat accumulator:
(3) In the formula: c. C pa Is the specific heat of air; rho a Is the air density; t is a Is the air temperature; lambda [ alpha ] a Is the air thermal conductivity; upsilon is a Is an air flow velocity vector; phi is the airflow viscous dissipation; p is hydrostatic pressure; q. q of ea The heat flow between the fluid and the resistance wire; q. q.s sa The heat flow between the fluid and the heat accumulator;
(3) Heat conduction of heat accumulator solid:
in the formula: c. C ps Is the specific heat of the solid; rho s Is the density of the solid; t is a unit of s Is the solid temperature; lambda [ alpha ] s Is the solid thermal conductivity.
The present invention is further described in detail below:
the invention relates to a solid-state heat storage system, which selects high-temperature solid-state heat storage material magnesium oxide and high-density metal alloy heating material iron-chromium-aluminum alloy for resistance heating, analyzes three working condition processes of pure heating, simultaneous heating/heat release and pure heat release of a heat accumulator in order to ensure high efficiency, reliability and stability of system operation, and researches the balance relation of heat transfer rates between the solid-state heat storage material and a heating element. The relation between the heat transfer characteristics of the heat storage material and the heat transfer temperature field change between the heating materials is analyzed, a heating characteristic matching design method based on a heat transfer rate balance method is provided, high heating efficiency is achieved, and the service life of a heating element is prolonged.
1) High temperature heat storage material characteristics
The invention selects magnesium oxide as a high-temperature heat storage material, and the average density of the magnesium oxide is 3000kg/m 3 The average mass specific heat capacity is 1000J/kg per hour ℃, the heat conductivity coefficient is 4.5-6.0W/m per hour, and the melting point is 1600-1700 ℃. The magnesium oxide has extremely high refractory temperature which can reach 2000 ℃ at most according to the purity of the magnesium oxide, and the temperature is far higher than the use temperature of the heating element, so that the structural thermal stability of the heat accumulator can be guaranteed. The magnesium oxide also has higher specific heat capacity, the value of the specific heat capacity is about 1000J/kg DEG C, and under the condition of the same mass and temperature rise, more heat is stored, so that the heat storage device can effectively absorb heat in a heating period.
2) Material properties of heating element
The heating element of the electric heat storage device is made of special alloy materials, the invention adopts iron-chromium-aluminum alloy as the electric heating alloy material, the maximum use temperature can reach 1400 ℃, the melting point is 1500 ℃, and the density is 7.1-7.4 kg/m 3 . The electric heating material can meet the requirements of high-temperature working environment and high electric energy conversion efficiency of the heating element, but the service life of the electric heating material is greatly influenced by the working environment. The iron-chromium-aluminum alloy has brittleness at 475 ℃, brittleness of sigma phase and high-temperature brittleness above 1000 ℃, and the low high-temperature strength caused by the high-temperature brittleness finally causes the short service life of the electric heating element and influences the safety and reliability of the electric heating device.
3) Heat transfer rate balancing method
The solid-state heat storage system is composed of a heat storage structure body (comprising a heat storage module and an embedded heating wire), a heat exchange circulating system (comprising a heat exchanger and a variable frequency fan), a heat preservation shell, an external control and the like, and figure 1 is a schematic structural diagram of the solid heat storage device. The operation of the solid heat storage device is a heat release and heat storage alternate circulation process, and heat energy generated by the electric heating element is brought into the heat accumulator by direct radiation heat transfer and convection heat transfer of air to complete a simple heating process of the heat storage device; after the electric heating element stops heating, the heat energy in the heat accumulator can be brought out of the heat storage device through the convection heat transfer of the air and enters the heat exchanger to finish the pure heat release process; if the electric heating element is heating, the heat exchanger works simultaneously, and the heat storage devices are in the process of heating and releasing heat simultaneously.
In the working process of the solid-state heat storage system, heat exchange among the heat storage structures is related to solid heat conduction, convective heat transfer and thermal radiation heat transfer, so that a heat transfer model of the solid-state heat storage device can be established as follows:
solid heat conduction:
in the formula: c. C ps Is the specific heat of the solid; ρ is a unit of a gradient s Is the density of the solid; t is a unit of s Is the solid temperature; lambda [ alpha ] s Is the solid thermal conductivity.
Convection heat exchange:
in the formula: rho a Is the air density; c. C pa Is the specific heat of air; t is a unit of a Is the air temperature; t is time; lambda [ alpha ] a Is the air thermal conductivity; upsilon is a Is an air velocity vector; phi is the airflow viscous dissipation; p is the hydrostatic pressure.
Radiation heat transfer:
in the formula: i: the intensity of the radiation; s: area of the radiator; a: the absorption coefficient; sigma s : a scattering coefficient; n is 0 : a refractive index; t is a unit of e : the local temperature; ω: a phase function; Ω:the spatial solid angle.
In the heat storage structure, two different heat transfer modes of solid heat conduction and fluid heat transfer exist on a solid-solid interface between air and a heat storage body, the boundary conditions are determined continuously according to the temperature and the heat flow density, the boundary conditions are enabled to meet the energy continuity conditions, and the three heat transfer energy equations are coupled.
In the formula: t is e ε and σ are radiation temperature, blackness and Stefan-Boltzmann constant, respectively; t is a And h a Fluid temperature and surface heat transfer coefficient, respectively; t is a unit of s And λ s Solid temperature and thermal conductivity, respectively; q. q of e ，q a And q is s The radiation heat flow density, the convection heat flow density and the heat conduction heat flow density of the fluid side and the solid side on the fluid-solid interface respectively; n is the normal vector of the flow-solid interface.
The high-temperature solid-state heat storage system conforms to the law of energy conservation in each working state, and according to the first law of thermodynamics, the heat Q and work W exchanged between the system and the outside and the internal energy variation delta U of the system meet the following requirements:
ΔU＝Q+W (5)
according to the formula (5), part of the heat energy generated by the resistance wire is converted into the internal energy U of the resistance wire, which is reflected as the temperature change of the resistance wire, and the other part of the heat energy is the heat energy Q exchanged between the resistance wire and the other parts of the heat storage device. In the heat storage process of the electric heat storage device, the electric energy is converted into heat energy by the heat element with the heating power being P through joule heat, and the system input power is given by the following formula (5):
ΔU＝Q+PΔt/J (6)
in the formula: j is the thermal equivalent in J/cal.
The resistance wire with resistance wire has mass m e The thermal capacity of the resistance wire is c e The rate of heat exchange from the electric heating element to the outside is then:
in the formula: t is a unit of e Is the resistance wire temperature.
In the heat exchange Q, the heat exchange Q of the resistance wire and the surrounding air is included ea And the radiation heat Q between the resistance wire and the heat accumulator es Two parts. If the heat exchange rate or heat flow of the resistance wire and the outside is phi e ，Φ ea Indicating the convective heat transfer rate, phi, of the resistance wire and air es The rate of radiant heat of the resistance wire and the heat accumulator is shown as follows:
Φ e ＝Φ es +Φ ea (8)
wherein, the resistance wire and the heat accumulator radiate heat rate phi es Comprises the following steps:
in the formula: a. The e The surface area of the resistance wire; h is a total of es The surface area of the resistance wire is far smaller than the heating surface area of the heat accumulator, and the emissivity of the heat accumulation unit system is epsilon s ＝ε e So the radiation heat exchange coefficient h of the resistance wire and the heat accumulator es The values are:
h es ＝5.67×10 -8 ε e (10)
in the whole heat-storage heat exchange process, besides the heat exchange on the surface of the resistance wire, the heat exchange also exists between the surface of the heat accumulator and the air, and Q is used sa Representing the heat exchanged by the heat accumulator with air, and Q es Is the radiation heat between the resistance wire and the heat accumulator, the net heat conduction quantity Q in the heat accumulator s Can be expressed as:
Q s ＝Q es +Q sa (11)
according to the heat balance relationship expressed by the equation (11), if phi is used sa Expressing the convective heat transfer rate of the heat accumulator and air, using phi s Representing the net heat flow from the inner surface of the heat accumulator, there are:
Φ s ＝Φ es -Φ sa (12)
wherein the net heat flow phi of the inner surface of the heat accumulator s Comprises the following steps:
convective heat transfer rate phi of surface of heat storage body and air sa Comprises the following steps:
Φ sa ＝A s h sa (T s -T a ) (14)
in the formula, A s Is the surface area of the inner surface of the heat accumulator, h sa Is the heat convection coefficient between the heat accumulator and the air. Under the condition of forced convection, calculating the heat exchange coefficient h of the inner surface of the heat accumulator and the air by adopting a non-circular pipe slot turbulence forced convection heat transfer correlation Gnielinski formula sa ：
In the formula (d) s Brick hole equivalent diameter for heat accumulator
A c Is the sectional area of the brick hole, P is the circumference of the brick hole), f is the Darcy resistance coefficient, l s The brick holes are long. (this formula applies to Re a ＝2300～10 6 ，Pr a ＝0.6～10 5 )
When the formulas (12) and (8) are combined, the following are provided:
Φ e ＝2Φ es +Φ ea -Φ sa -Φ s (16)
in the process of convective heat transfer between the resistance wire and the heat accumulator, the internal energy change of the air and the heat loss generated by the air and the outside during air circulation should be considered, especially, under the working condition of storing/releasing heat at the same time, the heat loss of the air in the heat exchanger can be expressed as follows:
in the formula, v a Is the air velocity, ρ A Is the areal density of the air flowing into the heat exchanger. Considering the relationship between air heat loss and convective heat transfer rate, phi a It can also be expressed as:
when the formulas (7) and (18) are substituted into the formula (16), the following are provided:
substituting the formula (9), the formula (13), the formula (14) and the formula (17) into the formula (19) to obtain:
the formula (20) is a heat transfer rate balance relation among high-temperature solid heat storage systems, and it can be seen from the formula (20) that the temperature of the resistance wire and the heat storage rate of the heat storage body are closely and related to the geometric structure of the system, the power of the resistance wire, the material thermal parameters and the system operating conditions, and the temperature of the resistance wire and the heat storage rate of the heat storage body can be controlled by changing the parameters. Through the optimal design of the structure and the optimal adjustment of system parameters, the heat conduction rate can be balanced, the temperature change of each part of the heat accumulator can be controlled, and the service life of the heating element can be optimized.
Claims (4)
1. A solid-state heat storage heating characteristic matching design method based on heat transfer rate balance is characterized by comprising the following steps: the method comprises the following steps:
1) Acquiring structural data material data and operating condition parameters of the high-temperature solid-state heat storage device;
2) Setting target parameters such as heating power and expected temperature rise rate of the electric heating element, and establishing a heat transfer rate balance model between the high-temperature heat storage material and the resistance heating element:
in the formula: p is the heating power of the electric heating element; j is a thermal equivalent; lambda [ alpha ] s Is the solid thermal conductivity; t is s Is the solid surface temperature; s is the heated surface area of the solid; a. The e The surface area of the resistance wire; h is a total of es The radiation heat exchange coefficient of the resistance wire and the heat accumulator is adopted; t is a unit of e The temperature of the resistance wire; a. The s The surface area of the brick hole is shown; h is a total of sa The heat transfer coefficient is the convective heat transfer coefficient between the heat accumulator and the air; t is a unit of a Is the air temperature; v. of a Is the air flow rate; ρ is a unit of a gradient A The areal density of air flowing into the heat exchanger; m is a Mass of air in the thermal storage body; c. C a The heat capacity of air; t is time; m is e The mass of the resistance wire; c. C e Is the thermal capacity of the resistance wire; n is a normal vector of a flow-solid interface;
3) According to the heat transfer rate balance model, calculating the convective heat transfer rate phi between the heat accumulator and the air as And the return stroke number, the hole occupying ratio, the area, the length and the air inlet flow of the heat accumulator air channel are designed according to the design;
4) Establishing a heat transfer model between the high-temperature heat storage material and the resistance heating element by using ANSYS finite element analysis software:
5) Determining the boundary condition of the heat transfer coupling between the air and the surface of the heat accumulator:
and (3) when the energy continuity condition is met on the fluid-solid interface, coupling the three energy equations of heat transfer:
in the formula: t is e ε and σ are resistance wire temperature, blackness and Stefan-Boltzmann constant, respectively; t is a And h a Air temperature and surface heat transfer coefficient, respectively; t is s And λ s The solid surface temperature and the thermal conductivity are respectively; q. q.s e ，q a And q is s Respectively the radiation heat flow density, the convection heat flow density and the heat conduction heat flow density of the fluid side and the solid side on the fluid-solid interface; n is a normal vector of a flow-solid interface;
6) Analyzing the change condition of a heat transfer temperature field between the resistance wire and the heat accumulator by using an ANSYS heat transfer model, judging whether the surface temperature of the resistance wire is in an operation temperature interval, and changing the inlet air speed to reduce the surface temperature of the resistance wire or increase the surface temperature of the resistance wire when the resistance wire is not in the operation temperature interval;
7) Obtaining the air inlet flow speed parameters meeting the design structure of the heat accumulator air duct and each operation temperature interval, and matching the structures and the performances of the electric heating element and the heat storage device, thereby realizing the optimization of the whole structure.
2. The method for designing matching of heating characteristics of solid state thermal storage based on heat transfer rate balance as claimed in claim 1, wherein: 4) According to the following formula, establishing a heat transfer model between the high-temperature heat storage material and the resistance heating element by using ANSYS finite element analysis software:
(1) And the resistance wire conducts heat to the heat accumulator in a radiation mode:
in the formula: i is the radiation intensity; a is the absorption coefficient; sigma s Is the scattering coefficient; n is a radical of an alkyl radical 0 Is a refractive index; t is a unit of e Is the local temperature; omega is a phase function; omega is a spatial solid angle; s is the heated surface area of the solid;
(2) And convection heat exchange of the heat accumulator by the resistance wire:
(3) In the formula: c. C pa Is the specific heat of air; rho a Is the air density; t is a Is the air temperature; lambda a Is the air thermal conductivity; upsilon is a Is an air velocity vector; phi is the airflow viscous dissipation; p is hydrostatic pressure; t is time;
(3) Solid heat conduction of the heat accumulator:
in the formula: c. C ps Is the specific heat of the solid; ρ is a unit of a gradient s Is the density of the solid; t is s Is the solid temperature; lambda [ alpha ] s Is the solid thermal conductivity; t is time.
3. The solid-state heat storage heating characteristic matching design method based on heat transfer rate balance as claimed in claim 1 or 2, wherein: the high-temperature solid-state heat storage system conforms to the law of energy conservation in each working state, and according to the first law of thermodynamics, the heat Q and work W exchanged between the system and the outside and the internal energy variation delta U of the system meet the following requirements:
ΔU＝Q+W (5)
according to the formula (5), part of the heat energy generated by the resistance wire is converted into the internal energy U of the resistance wire, which is reflected as the temperature change of the resistance wire, and the other part of the resistance wire exchanges heat Q with the other parts of the heat storage device; in the heat storage process of the electric heat storage device, the heating power is P, and the electric energy is converted into heat energy through joule heat by the heat element, and then formula (5) has to the system input power:
ΔU＝Q+PΔt/J (6)
in the formula: j is a thermal equivalent, and the unit is J/cal; Δ t is a time variable;
the resistance wire with resistance wire has mass m e The thermal capacity of the resistance wire is c e Then, the rate of heat exchange from the electric heating element to the outside is:
in the formula: t is a unit of e The temperature of the resistance wire;
in the exchange heat quantity Q, the exchange heat quantity Q containing the resistance wire and the surrounding air ea And the radiation heat Q between the resistance wire and the heat accumulator es Two parts; if the heat exchange rate or heat flow of the resistance wire and the outside is phi e ，Φ ea Indicating convective heat transfer rate, phi, of the resistance wire and air es The radiant heat rate of the resistance wire and the heat accumulator is shown, and the radiant heat rate comprises the following components:
Φ e ＝Φ es +Φ ea (8)
wherein, the resistance wire and the heat accumulator radiate heat rate phi es Comprises the following steps:
in the formula: a. The e The surface area of the resistance wire; h is es Is the radiation heat exchange coefficient, T, of the resistance wire and the heat accumulator e Temperature of resistance wire, T s Is the solid surface temperature; because the surface area of the resistance wire is far smaller than the heating surface area of the heat accumulator, the emissivity epsilon of the heat accumulation unit system s ＝ε e So the radiation heat exchange coefficient h of the resistance wire and the heat accumulator es The values are:
h es ＝5.67×10 -8 ε e (10)
in the whole heat-storage heat exchange process, besides the heat exchange on the surface of the resistance wire, the heat exchange also exists between the surface of the heat accumulator and the air, and Q is used sa Representing the heat exchanged by the heat accumulator with air, and Q es Is the radiation heat between the resistance wire and the heat accumulator, the net heat conduction quantity Q in the heat accumulator s Can be expressed as:
Q s ＝Q es +Q sa (11)
according to the heat balance relationship expressed by the equation (11), if using phi sa Expressing the convective heat transfer rate of the heat accumulator and air by phi s Representing the net heat flow from the inner surface of the heat accumulator, there are:
Φ s ＝Φ es -Φ sa (12)
wherein the net heat flow phi of the inner surface of the heat accumulator s Comprises the following steps:
convective heat transfer rate phi of surface of heat storage body and air sa Comprises the following steps:
Φ sa ＝A s h sa (T s -T a ) (14)
in the formula, A s Is the inner surface area of the heat accumulator, h sa The heat transfer coefficient is the convective heat transfer coefficient between the heat accumulator and the air; under the condition of forced convection, calculating the heat exchange coefficient h between the inner surface of the heat accumulator and the air by adopting a non-circular pipe groove turbulent forced convection heat transfer correlation Gnielinski formula sa ：
In the formula (d) s Brick hole equivalent diameter for heat accumulator
A c Is the sectional area of the brick hole, P is the circumference of the brick hole), f is the Darcy resistance coefficient, l s The brick holes are long; t is a Is the air temperature; t is s Is the solid surface temperature;
when the formulas (12) and (8) are combined, the following are provided:
Φ e ＝2Φ es +Φ ea -Φ sa -Φ s (16)
in the process of convective heat transfer between the resistance wire and the heat accumulator, the internal energy change of the air and the heat loss generated by the air and the outside during air circulation should be considered, especially, under the working condition of storing/releasing heat at the same time, the heat loss of the air in the heat exchanger can be expressed as follows:
in the formula, v a Is the air velocity, ρ A Is the areal density of the air flowing into the heat exchanger; t is a Is the air temperature; considering the relationship between air heat loss and convective heat transfer rate, phi a It can also be expressed as:
when the formulas (7) and (18) are substituted into the formula (16), the following are provided:
substituting the formula (9), the formula (13), the formula (14) and the formula (17) into the formula (19) to obtain:
4. the solid-state thermal storage heating characteristic matching design method based on heat transfer rate balance is characterized in that: equation (15) applies to Re a ＝2300～10 6 ，Pr a ＝0.6～10 5 。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811220025.7A CN109446623B (en) | 2018-10-19 | 2018-10-19 | Solid-state heat storage heating characteristic matching design method based on heat transfer rate balance |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811220025.7A CN109446623B (en) | 2018-10-19 | 2018-10-19 | Solid-state heat storage heating characteristic matching design method based on heat transfer rate balance |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109446623A CN109446623A (en) | 2019-03-08 |
| CN109446623B true CN109446623B (en) | 2022-11-04 |
Family
ID=65546991
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811220025.7A Active CN109446623B (en) | 2018-10-19 | 2018-10-19 | Solid-state heat storage heating characteristic matching design method based on heat transfer rate balance |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109446623B (en) |
Families Citing this family (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110220405B (en) * | 2019-05-22 | 2021-07-27 | 国网辽宁省电力有限公司大连供电公司 | Solid heat storage and transfer control method based on Fourier number consistency |
| CN110472270B (en) * | 2019-06-28 | 2022-09-27 | 合肥通用机械研究院有限公司 | Modeling optimization method of sodium cooled reactor passive waste heat removal system |
| CN110398058A (en) * | 2019-08-26 | 2019-11-01 | 济南世普润节能环保科技有限公司 | The gas inerting processing unit of the displacement method of solid heat collecting system |
| CN110332713A (en) * | 2019-08-26 | 2019-10-15 | 周封 | The gas inerting processing unit of the null method of solid heat collecting system |
| CN112648787A (en) * | 2019-10-10 | 2021-04-13 | 中车石家庄车辆有限公司 | Method and device for determining cold accumulation residual service life and computer equipment |
| CN110765645B (en) * | 2019-11-06 | 2023-05-23 | 国网四川省电力公司电力科学研究院 | Design method of built-in coil type compressed air heat exchange system |
| CN111413364B (en) * | 2020-04-10 | 2022-10-04 | 上海理工大学 | In-situ nondestructive testing method and system for concrete heat storage coefficient in building wall |
| CN115293066B (en) * | 2022-08-09 | 2023-09-01 | 西南石油大学 | Gas well temperature field calculation method considering stratum seepage heat transfer effect |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103420668A (en) * | 2012-05-21 | 2013-12-04 | 天津德仕能科技有限公司 | Heat-storing magnesia brick |
| CN103455684A (en) * | 2013-09-16 | 2013-12-18 | 华东理工大学 | Real-time performance prediction method for industrial steam cracking furnace hearth based on field method |
| CN105651091A (en) * | 2016-02-19 | 2016-06-08 | 上海交通大学 | Heat transfer enhanced chemical heat storage device and heat storage system applying same |
| CN106340583A (en) * | 2011-12-26 | 2017-01-18 | 中沼忠司 | Thermoelectric generator |
| CN106686770A (en) * | 2016-02-03 | 2017-05-17 | 黄伟聪 | Thick film element with coating substrate with high heat conduction capability |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20020162339A1 (en) * | 2001-05-04 | 2002-11-07 | Harrison Howard R. | High performance thermoelectric systems |
-
2018
- 2018-10-19 CN CN201811220025.7A patent/CN109446623B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106340583A (en) * | 2011-12-26 | 2017-01-18 | 中沼忠司 | Thermoelectric generator |
| CN103420668A (en) * | 2012-05-21 | 2013-12-04 | 天津德仕能科技有限公司 | Heat-storing magnesia brick |
| CN103455684A (en) * | 2013-09-16 | 2013-12-18 | 华东理工大学 | Real-time performance prediction method for industrial steam cracking furnace hearth based on field method |
| CN106686770A (en) * | 2016-02-03 | 2017-05-17 | 黄伟聪 | Thick film element with coating substrate with high heat conduction capability |
| CN105651091A (en) * | 2016-02-19 | 2016-06-08 | 上海交通大学 | Heat transfer enhanced chemical heat storage device and heat storage system applying same |
Non-Patent Citations (1)
| Title |
|---|
| 高温蓄热技术的研究现状及展望;韩瑞瑞 等;《建筑节能》;20110930(第9期);第32-38页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109446623A (en) | 2019-03-08 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109446623B (en) | Solid-state heat storage heating characteristic matching design method based on heat transfer rate balance | |
| Liu et al. | Solidification performance of a latent heat storage unit with innovative longitudinal triangular fins | |
| CN106450572B (en) | A kind of system and method based on lithium ion battery component zone heat management | |
| CN105605957B (en) | Solid electric heat-storage device | |
| CN110220405B (en) | Solid heat storage and transfer control method based on Fourier number consistency | |
| Feng et al. | Thermal insulation constructal optimization for steel rolling reheating furnace wall based on entransy dissipation extremum principle | |
| JP2017523378A (en) | Apparatus and method for storing thermal energy | |
| He et al. | A study on latent heat storage exchangers with the high‐temperature phase‐change material | |
| CN202470194U (en) | Centralized heat storage electric heating system | |
| Kumar et al. | Experimental and numerical study of latent heat thermal energy storage with high porosity metal matrix under intermittent heat loads | |
| Said et al. | A study on the thermal energy storage of different phase change materials incorporated with the condenser of air-conditioning unit and their effect on the unit performance | |
| CN204901909U (en) | Indoor phase -change thermal heating system | |
| Srivastava et al. | A review on solar air heater technology | |
| Kalash et al. | Thermal performance improvement of double pass solar air heater | |
| Minakova et al. | Biaxial heat balance model of a solar collector | |
| Li et al. | Characteristics and optimation of heat pipe radiator for space nuclear propulsion spacecraft | |
| Xu et al. | Modeling and analysis of a dual-channel solar thermal storage wall system with phase change material in hot summer and cold winter area | |
| Liu et al. | Numerical study on the thermal performance of a phase change heat exchanger (PCHE) with innovative fractal tree-shaped fins | |
| Ren et al. | Analysis of melting and solidification performance of bionic snowflake fin horizontal Triplex-tube latent heat storage system based on response surface method | |
| Kandilli | A comparative study on the energetic-exergetic and economical performance of a photovoltaic thermal system (PVT) | |
| Shi et al. | Performance of a BAPVT modules coupled TEHR unit fresh air system based on micro heat pipe array | |
| Chu et al. | Smart microchannel heat exchangers with Built-In graded SMA vortex generators that responds to random hotspots | |
| Wang et al. | Experimental study on the new type of electrical storage heater based on flat micro-heat pipe arrays | |
| Afshari | Experimental and numerical study on heat transfer enhancement of home radiators by employing solar cells and fans | |
| Motahar | An analysis of unglazed transpired solar collectors based on exergetic performance criteria |
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 |