CN114609456A - Thermal regulation and control osmotic energy conversion analysis method for salt difference power generation device - Google Patents

Thermal regulation and control osmotic energy conversion analysis method for salt difference power generation device Download PDF

Info

Publication number
CN114609456A
CN114609456A CN202210115306.6A CN202210115306A CN114609456A CN 114609456 A CN114609456 A CN 114609456A CN 202210115306 A CN202210115306 A CN 202210115306A CN 114609456 A CN114609456 A CN 114609456A
Authority
CN
China
Prior art keywords
dimensionless
potential
control parameter
equation
control
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.)
Pending
Application number
CN202210115306.6A
Other languages
Chinese (zh)
Inventor
屈治国
朱黄祎
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xian Jiaotong University
Original Assignee
Xian Jiaotong University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xian Jiaotong University filed Critical Xian Jiaotong University
Priority to CN202210115306.6A priority Critical patent/CN114609456A/en
Publication of CN114609456A publication Critical patent/CN114609456A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N25/00—Investigating or analyzing materials by the use of thermal means
    • G01N25/20—Investigating or analyzing materials by the use of thermal means by investigating the development of heat, i.e. calorimetry, e.g. by measuring specific heat, by measuring thermal conductivity

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
  • General Health & Medical Sciences (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Investigating Or Analyzing Materials Using Thermal Means (AREA)

Abstract

The invention discloses a thermal regulation and control osmotic energy conversion analysis method of a salt difference power generation device, which comprises the following steps: describing physical mathematical characteristics of heat regulation and control permeation energy conversion of the salt difference power generation device, wherein the physical mathematical characteristics comprise a physical field, a control equation, physical parameters and output performance; carrying out similarity analysis on the control equation by utilizing a similarity principle to obtain a dimensionless control parameter set pii(ii) a Carrying out dimension analysis on the physical parameters by utilizing Pi theorem to obtain a dimensionless control parameter group Pii(ii) a For dimensionless control parameter group piiAnd dimensionless control parameter group ΠiAnalyzing to determine a dimensionless number of thermal control osmotic energy conversion in a nanochannel of the salt-difference power generation device and to clarify the connection between two dimensionless control parameter sets; analyzing the output performance through a similarity principle to define a dimensionless physical quantity, unifying a plurality of groups of experimental samples into a dimensionless sample,or expand a set of dimensionless samples into multiple different sets of experimental samples.

Description

Thermal regulation and control osmotic energy conversion analysis method for salt difference power generation device
Technical Field
The disclosure belongs to the technical field of new energy, and particularly relates to a thermal regulation and control osmotic energy conversion analysis method of a salt tolerance power generation device.
Background
The nano-channel internal permeation energy conversion is an energy conversion mode that the salinity difference of electrolyte is used as source power to drive ion carriers to selectively and directionally migrate through the nano-channel to form ion flux, and salinity energy is directly converted into electric energy, so that a new way can be provided for the efficient utilization of low-grade salt difference energy. The electrical double layer formed by the surface charging of the nanochannels affects the ion distribution when the electrolyte flows through the nanochannels. Due to the extremely small size of the nanochannel, the electric double layer formed on the surface may generate an overlap effect, thereby exhibiting ion selectivity. Due to the ion selectivity of the nanochannel, the mixed gibbs free energy between salt solutions of different concentrations is converted in the form of a potential difference across the nanochannel.
In order to improve the power generation effect of the permeation energy conversion in the nano channel, the thermal regulation means is the most common. Uniformly increasing the overall operating temperature of osmotic energy conversion affects the physical parameters such as ion diffusion coefficient and dielectric constant to affect the power generation effect. And if the working temperature of osmotic energy conversion is not uniformly increased, if the temperature difference exists at the two ends, physical property parameters can be influenced on one hand, and on the other hand, the temperature difference can also be used as a part of driving force to enable ions to migrate. In general, power generation systems exhibit superior performance whether uniformly or non-uniformly increasing operating temperatures for osmotic energy conversion.
In experimental research, the unified cognition on the physical process of the heat regulation and control osmotic energy conversion in the nano-channel is lacked, and the unified standard of the power generation effect of the heat regulation and control osmotic energy conversion in the nano-channel is also lacked; the large number of samples required to obtain the I-V curve of the power generation system or to calculate the maximum output power can cost a significant economic, time cost.
Disclosure of Invention
In view of the deficiencies in the prior art, the present disclosure provides a thermal regulation and control osmotic energy conversion analysis method for a salt tolerance power generation device, which obtains a dimensionless control parameter set for thermal regulation and control osmotic energy conversion through analysis of a similar principle, wherein the parameter set covers physical laws of non-uniform thermal regulation, uniform thermal regulation and non-thermal regulation and control osmotic energy conversion in a nanochannel, so as to generate a universal guidance for osmotic energy conversion of the nanochannel.
In order to achieve the above object, the present disclosure provides the following technical solutions:
a thermal control osmotic energy conversion analysis method of a salt difference power generation device comprises the following steps:
s100: describing physical mathematical characteristics of heat regulation and control permeation energy conversion of the salt difference power generation device, wherein the physical mathematical characteristics comprise a physical field, a control equation, physical parameters and output performance;
s200: carrying out similar analysis on the control equation by utilizing a similar principle to obtain a dimensionless control parameter group pi for representing the osmotic energy conversion of the non-uniform thermal regulation, the uniform thermal regulation and the non-thermal regulation of the salt-difference power generation devicei；
S300: carrying out dimension analysis on the physical parameters by utilizing Pi theorem to obtain a dimensionless control parameter group Pii；
S400: for the dimensionless control parameter group piiAnd dimensionless control parameter group ΠiPerforming analysis to determine a dimensionless number of thermally regulated osmotic energy conversions in nanochannels of a salt-difference power plant and to clarify the dimensionless set of control parameters πiAnd dimensionless control parameter group piiThe contact of (1);
s500: and analyzing the output performance through a similarity principle to define a non-dimensional potential and a non-dimensional current, so as to unify a plurality of groups of experimental samples into a non-dimensional sample, or expand a group of non-dimensional samples into a plurality of different groups of experimental samples.
Preferably, in step S100, the physical field includes a concentration field, a potential field, a velocity field, and a temperature field, and the concentration field, the potential field, the velocity field, and the temperature field have a coupling effect therebetween.
Preferably, in step S100, the control equation includes:
poisson equation:
Figure BDA0003495519230000031
flux continuity equation:
Figure BDA0003495519230000032
nernst-planck equation:
Figure BDA0003495519230000033
velocity continuity equation:
Figure BDA0003495519230000034
the Navier-Stokes equation:
Figure BDA0003495519230000035
energy equation:
Figure BDA0003495519230000036
nanochannel boundary equation:
Figure BDA0003495519230000037
wherein,
Figure BDA0003495519230000038
is a partial differential operator,. epsilon.is the dielectric constant,. phi.is the potential, F is the Faraday constant, c is the concentration, z is the number of valence charges, i is the ith ion, n is the total number of ion species, J is the ion flux, u is the velocity, D is the diffusion coefficient, R is the general gas constant, T is the temperature, S is the temperatureTIs Soret coefficient, p is pressure, mu is viscosity coefficient, E is electric field strength, rho is density, CpIs specific heat, lambda is the thermal conductivity, sigmafAs conductivity, σ is the surface charge density.
Preferably, in step S100, the physical parameters include: working medium parameters, channel parameters, working condition parameters and constants, wherein,
the working medium parameters comprise: dielectric constant ε, diffusion coefficient D, Soret coefficient STViscosity coefficient mu, thermal diffusivity alpha, thermal conductivity lambda, electrical conductivity sigmaf；
The channel parameters include: characteristic length l, surface charge density σ;
the working condition parameters comprise: potential phi, concentration c, velocity u, temperature T, pressure p;
the constants include: faraday constant F, universal gas constant R.
Preferably, in step S100, the output performance includes: I-V curve, diffusion potential, permeation current and output power.
Preferably, in step S200, the dimensionless control parameter set piiThe method comprises the following steps:
Figure BDA0003495519230000041
π5＝TST、
Figure BDA0003495519230000042
Figure BDA0003495519230000043
wherein,
Figure BDA0003495519230000044
representing the relative size of space potential collection electric quantity and space charge quantity in the nano channel;
Figure BDA0003495519230000045
representing the electrical relative magnitude of the surface potential collection electric quantity and the surface charge density collection electric quantity of the nano-channel;
Figure BDA0003495519230000046
characterizing the relative strength of ion convection and ion diffusion;
Figure BDA0003495519230000047
characterizing the relative strengths of ionic electromigration and ionic diffusion; pi5＝TSTCharacterizing the relative strength of ion thermal migration and ion diffusion;
Figure BDA0003495519230000048
characterizing the relative magnitude of pressure and viscous forces;
Figure BDA0003495519230000049
characterizing the relative magnitude of the electrostatic force and the viscous force;
Figure BDA00034955192300000410
the relative strength of thermal convection and thermal diffusion is characterized;
Figure BDA00034955192300000411
the relative magnitude of joule heating and heat diffusion is characterized.
Preferably, in step S300, the dimensionless control parameter group ΠiThe method comprises the following steps:
Figure BDA0003495519230000051
∏5＝TST、
Figure BDA0003495519230000052
Figure BDA0003495519230000053
preferably, in step S400, the dimensionless control parameter set piiAnd dimensionless control parameter group ΠiAfter conversion, it is expressed as:
Figure BDA0003495519230000054
π2＝∏1，
Figure BDA0003495519230000055
π5＝∏5，
Figure BDA0003495519230000056
Figure BDA0003495519230000057
π9＝∏9；
or as:
∏1＝π2，
Figure BDA0003495519230000058
∏5＝π5，
Figure BDA0003495519230000059
Figure BDA00034955192300000510
∏9＝π9。
preferably, in the step S500,
the dimensionless potential is defined as:
Figure BDA00034955192300000511
the dimensionless current is defined as:
Figure BDA00034955192300000512
wherein phi is*To a dimensionless potential, I*For dimensionless current, L is the nanochannel length, R is the nanochannel radius, φ is the potential, σ is the charge density, ε is the dielectric constant, I is the current, F is the Faraday constant, c is the concentration, R is the universal gas constant, and D is the diffusion coefficient.
Preferably, in step S500, normalization processing is further performed on the defined dimensionless potential and dimensionless current to obtain a normalized dimensionless potential and a normalized dimensionless current;
the normalized dimensionless potential is expressed as:
Figure BDA0003495519230000061
the normalized dimensionless current is expressed as:
Figure BDA0003495519230000062
wherein,
Figure BDA0003495519230000063
is the normalized non-dimensional potential,
Figure BDA0003495519230000064
is a normalized dimensionless current, phi*To a dimensionless potential, I*Is a dimensionless current of phi0 *To a dimensionless diffusion potential, I0 *Is a dimensionless penetration current.
Compared with the prior art, the beneficial effect that this disclosure brought does:
1. through a similarity principle analysis method, a dimensionless control parameter group for thermal regulation and control of osmotic energy conversion is obtained, the physical significance of each dimensionless control parameter is determined, and concentration field, potential field, speed field and temperature field equations and parameters are unified.
2. By ensuring that dimensionless control parameters are unchanged, a plurality of groups of different samples can be unified into a group of dimensionless samples under the guidance of a similarity principle, and the inherent unified physical law is explained; and a group of dimensionless samples can be expanded into a plurality of groups of different samples, and a modeling experiment of thermal regulation and permeation energy conversion in the nano-channel can be carried out.
3. The obtained dimensionless control parameter set covers the physical laws of inhomogeneous thermal regulation, homogeneous thermal regulation and athermal regulation of osmotic energy conversion in the nanochannel, the dimensionless control parameter set can be simplified according to the actual situation to match the corresponding physical process, and the dimensionless control parameter set has a universal guiding value for osmotic energy conversion of the nanochannel.
Drawings
FIG. 1 is a flow chart of a method for analyzing thermal control osmotic energy conversion of a salt-difference power plant according to an embodiment of the present disclosure;
FIG. 2 is a graphical illustration of a dimensional I-V curve for a similar experiment of thermally regulated osmotic energy conversion provided by another embodiment of the present disclosure;
FIG. 3 is a graphical illustration of a dimensionless normalized I-V curve for a similar experiment for thermally regulated osmotic energy conversion, provided in accordance with another embodiment of the present disclosure.
Detailed Description
Specific embodiments of the present disclosure will be described in detail below with reference to fig. 1 to 3. While specific embodiments of the disclosure are shown in the drawings, it should be understood that the disclosure can be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the disclosure, but is made for the purpose of illustrating the general principles of the disclosure and not for the purpose of limiting the scope of the disclosure. The scope of the disclosure is to be determined by the claims appended hereto.
For the purpose of facilitating an understanding of the embodiments of the present disclosure, the following detailed description is to be construed in conjunction with the accompanying drawings, and the various drawings are not intended to limit the embodiments of the present disclosure.
In one embodiment, as shown in fig. 1, the present disclosure provides a method for analyzing thermal control osmotic energy conversion of a salt tolerance power plant, including the following steps:
s100: describing physical mathematical characteristics of heat regulation and control permeation energy conversion of the salt difference power generation device, wherein the physical mathematical characteristics comprise a physical field, a control equation, physical parameters and output performance;
s200: carrying out similarity analysis on the control equation by utilizing a similarity principle to obtain the non-uniform heat tone for representing the salt difference power generation deviceDimensionless control parameter set pi for osmotic energy conversion with controlled, uniform thermal regulation and no thermal regulationi；
S300: carrying out dimension analysis on the physical parameters by utilizing Pi theorem to obtain a dimensionless control parameter group Pii；
S400: for the dimensionless control parameter group piiAnd dimensionless control parameter group ΠiPerforming analysis to determine a dimensionless number of thermally regulated osmotic energy conversions in nanochannels of a salt-difference power plant and to clarify the dimensionless set of control parameters πiDimensionless control parameter group IIiThe contact of (1);
s500: and analyzing the output performance through a similarity principle to define a non-dimensional potential and a non-dimensional current, so as to unify a plurality of groups of experimental samples into a non-dimensional sample, or expand a group of non-dimensional samples into a plurality of different groups of experimental samples.
The above embodiments constitute a complete technical solution of the present disclosure. The dimensionless parameter set obtained by the analysis of the similarity principle covers the physical laws of non-uniform thermal regulation, uniform thermal regulation and non-thermal regulation osmotic energy conversion in the nanochannel, and the dimensionless parameter set can be simplified according to the actual situation to match the corresponding physical process. A modeling experiment of thermal regulation and control of osmotic energy conversion in a nano channel is guided by a similarity principle, dimensionless control parameters are guaranteed to be unchanged through different parameter combinations, multiple groups of experimental samples can be unified into a dimensionless sample on the physical law, and in engineering application, the dimensionless sample can be expanded into multiple groups of different experimental samples under the guidance of the similarity principle.
In another embodiment, in step S100, the physical field includes a concentration field, a potential field, a velocity field, and a temperature field, and the concentration field, the potential field, the velocity field, and the temperature field have a coupling effect therebetween.
In another embodiment, in step S100, the control equation includes:
poisson equation:
Figure BDA0003495519230000091
flux continuity equation:
Figure BDA0003495519230000092
nernst-planck equation:
Figure BDA0003495519230000093
velocity continuity equation:
Figure BDA0003495519230000094
the Navier-Stokes equation:
Figure BDA0003495519230000095
energy equation:
Figure BDA0003495519230000096
nanochannel boundary equation:
Figure BDA0003495519230000097
wherein,
Figure BDA0003495519230000098
is a partial differential operator,. epsilon.is the dielectric constant,. phi.is the potential, F is the Faraday constant, c is the concentration, z is the number of valence charges, subscript i is the ith ion, superscript n is the total number of ion species, J is the ion flux, u is the velocity, D is the diffusion coefficient, R is the general gas constant, T is the temperature, S is the temperatureTIs Soret coefficient, p is pressure, mu is viscosity coefficient, E is electric field strength, rho is density, CpIs specific heat, lambda is the thermal conductivity, sigmafAs conductivity, σ is the surface charge density.
In another embodiment, in step S100, the physical parameters include: working medium parameters, channel parameters, working condition parameters and constants, wherein,
the working medium parameters comprise: dielectric constant epsilon, diffusion coefficient D, Soret seriesNumber STViscosity coefficient μ, thermal diffusivity α (α ═ λ/ρ C)p) Coefficient of thermal conductivity λ, conductivity σf；
The channel parameters include: characteristic length l, surface charge density σ;
the working condition parameters comprise: potential phi, concentration c, velocity u, temperature T, pressure p;
the constants include: faraday constant F, universal gas constant R.
In another embodiment, in step S100, the output performance includes: I-V curve, diffusion potential, permeation current and output power.
In another embodiment, in step S200, the dimensionless control parameter set piiThe method comprises the following steps:
Figure BDA0003495519230000101
π5＝TST、
Figure BDA0003495519230000102
Figure BDA0003495519230000103
wherein,
Figure BDA0003495519230000104
representing the relative size of space potential collection electric quantity and space charge quantity in the nano channel;
Figure BDA0003495519230000105
representing the electrical relative magnitude of the surface potential collection electric quantity and the surface charge density collection electric quantity of the nano-channel;
Figure BDA0003495519230000106
characterizing the relative strength of ion convection and ion diffusion;
Figure BDA0003495519230000107
characterizing the relative strengths of ionic electromigration and ionic diffusion; pi5＝TSTCharacterizing the relative strength of ion thermal migration and ion diffusion;
Figure BDA0003495519230000108
characterizing the relative magnitude of pressure and viscous forces;
Figure BDA0003495519230000111
characterizing the relative magnitude of the electrostatic force and the viscous force;
Figure BDA0003495519230000112
the relative strength of thermal convection and thermal diffusion is characterized;
Figure BDA0003495519230000113
the relative magnitude of joule heating and heat diffusion is characterized.
In this embodiment, taking poisson equation as an example, the process of performing dimensional analysis on poisson equation by using the similarity principle is as follows:
assume a condition 1 and a condition 2, wherein,
working condition 1:
Figure BDA0003495519230000114
working condition 2:
Figure BDA0003495519230000115
to satisfy the similarity between condition 1 and condition 2, the equation is further transformed:
working condition 1:
Figure BDA0003495519230000116
working condition 2:
Figure BDA0003495519230000117
in the above formula, if l is a characteristic length, then
Figure BDA0003495519230000118
Then can ensureThe consistency of the physical fields of the Poisson equation under different working conditions is proved. Therefore, it is not only easy to use
Figure BDA0003495519230000119
I.e. dimensionless control parameters of the poisson equation.
In another embodiment, said non-dimensional control parameter set IIiThe method comprises the following steps:
Figure BDA00034955192300001110
∏5＝TST、
Figure BDA00034955192300001111
Figure BDA00034955192300001112
in this embodiment, the physical parameters have 6 basic dimensions, including M, L, T, N, I, Θ, and the dimensions of the parameters are as follows using the { MLTNI Θ } dimension system:
working medium parameters: ε { M-1L-3T4I2}，D{L2T1}，ST{Θ-1}，μ{ML-1T1}，α{L2T1}，σf/λ{M2L-4T6I2Θ}
Working condition parameters are as follows: phi { ML2T3I-1}，c{L-3N}，u{LT-1}，T{Θ}，p{ML-1T-2}
And (3) channel parameters: l { L }, σ { L }-2TI}
Constant: f { TN-1I}，R{ML2T2N-1Θ-1}
To simplify the number of parameters, the heat conductivity coefficient lambda, the density rho and the specific heat capacity C in the energy equationpThe combination forms a combination parameter of thermal diffusivity alpha, and the combination of thermal conductivity lambda and electric conductivity forms sigmafAnd/lambda. Selecting phi, F, l, sigma, u and T as basic dimension group, and using the basic dimension group and the rest parametersThe power multiplication division combination forms a Pi group, dimensions of the Pi group are all 1, and the Pi group is a dimensionless control parameter group.
In another embodiment, in step S400, the dimensionless control parameter set piiAnd dimensionless control parameter group ΠiAfter conversion, it is expressed as:
Figure BDA0003495519230000121
π5＝∏5，
Figure BDA0003495519230000122
Figure BDA0003495519230000123
π9＝∏9；
or as:
∏1＝π2，
Figure BDA0003495519230000124
∏5＝π5，
Figure BDA0003495519230000125
Figure BDA0003495519230000126
∏9＝π9。
in another embodiment, in step S500,
the dimensionless potential is defined as:
Figure BDA0003495519230000131
the dimensionless current is defined as:
Figure BDA0003495519230000132
wherein phi is*Is made withoutDimensional potential, I*For dimensionless current, L is the nanochannel length, R is the nanochannel radius, φ is the potential, σ is the charge density, ε is the dielectric constant, I is the current, F is the Faraday constant, c is the concentration, R is the universal gas constant, and D is the diffusion coefficient.
Further, the dimensionless potential and the dimensionless current are normalized, and the dimensionless potential after normalization is represented as:
Figure BDA0003495519230000133
the normalized dimensionless current is expressed as:
Figure BDA0003495519230000134
wherein,
Figure BDA0003495519230000135
is the normalized non-dimensional potential,
Figure BDA0003495519230000136
is a normalized dimensionless current, phi*To a dimensionless potential, I*Is a dimensionless current of phi0 *To a dimensionless diffusion potential, I0 *Is a dimensionless penetration current.
And normalizing the I-V curves of different working conditions by using the dimensionless diffusion potential and the dimensionless penetration current. The working condition of the superposition of the dimensionless normalized I-V curves shows that the dimensionless normalized I-V curves have the same physical law and the dimensionless control parameter group is the same.
FIG. 2 is a schematic of a dimensional I-V curve of a similar experiment for thermally regulated osmotic energy conversion; FIG. 3 is a graphical representation of a dimensionless normalized I-V curve for a similar experiment for thermally regulated osmotic energy conversion. For a known dimensional operating condition, the non-dimensional form of the operating condition can be obtained by the definition of the non-dimensional potential and current. And for the working condition that the value of the dimensionless control parameter group is not changed by other parameter combinations, the dimensionless form is the dimensionless form of the known working condition. I.e., the dimensionless I-V curve for one of the operating conditions of fig. 3 reflects the dimensionless I-V curve for these operating conditions. By using the inverse process of the dimensionless number definition,
Figure BDA0003495519230000141
Figure BDA0003495519230000142
and substituting different dimensional parameters to obtain the dimensional potential and current of the working conditions, further obtaining the dimensional I-V curve of the figure 2, and realizing the purpose of expanding the sample. Comparing fig. 2 and fig. 3, when different parameter combinations are selected so that the values of the dimensionless control parameter sets are not changed, the dimensionless I-V curves of the respective working conditions in fig. 2 are different, while the dimensionless normalized I-V curves in fig. 3 are completely overlapped. Therefore, the dimensionless control parameter group of the similar principle reveals the internal rule among the parameters of the dimensionless physical field, and when the dimensionless control parameter group is ensured to be unchanged, one dimensionless working condition can be expanded into a plurality of working conditions, so that the experiment cost is greatly reduced.
In one embodiment, in order to research the physical laws of the non-uniform thermal regulation, the uniform thermal regulation and the non-thermal regulation osmotic energy conversion of the salt tolerance power generation device, the dimensionless control parameter group is analyzed,
the non-uniform thermal regulation osmotic energy conversion physical phenomenon can be directly applied to the non-dimensional control parameter set.
The heat transfer phenomenon and the derived heat diffusion and heat migration problems are not involved in the uniform heat regulation and non-heat regulation osmotic energy conversion physical phenomenon, and the control equations are the same as follows:
poisson equation:
Figure BDA0003495519230000143
flux continuity equation:
Figure BDA0003495519230000144
nernst-planck equation:
Figure BDA0003495519230000151
velocity continuity equation:
Figure BDA0003495519230000152
the Navier-Stokes equation:
Figure BDA0003495519230000153
nanochannel boundary equation:
Figure BDA0003495519230000154
the meaning of the parameters is the same as above. The obtained dimensionless control parameter group is simplified into
Figure BDA0003495519230000155
Figure BDA0003495519230000156
There are 6 dimensionless numbers. Although the set of dimensionless control parameters for uniform thermal regulation and non-thermal regulation of osmotic energy conversion in the nanochannel is the same, the specific values are different, and uniform thermal regulation relates to the values of the physical parameters affected by temperature.
In a specific embodiment, in order to quantitatively measure the guiding significance of a modeling experiment of the thermal control permeation energy conversion in the nano-channel by the similarity principle, on the premise of ensuring that the dimensionless control parameter group value is not changed, numerical simulation is carried out on working conditions A, B, C and D of the thermal control permeation energy conversion in the nano-channel, and a Poisson-Nernst-Planck equation, a momentum equation, an energy equation and a boundary equation are solved by using a finite element method. The calculation formula of the generated power is as follows:
P＝I0φ0/4
wherein, P is the output power (W) of the thermal control osmotic energy conversion in the nano-channel.
The dimensionless output power expression is:
Figure BDA0003495519230000157
the output power, the penetration current, the diffusion potential and the dimensionless parameter values of the output power, the penetration current and the diffusion potential under different working conditions are shown in the following tables 1 and 2:
TABLE 1 dimensional physical parameter values and errors under different working conditions
Figure BDA0003495519230000161
TABLE 2 dimensionless physical parameter values and errors under different working conditions
Figure BDA0003495519230000162
As can be seen from tables 1 and 2, although the physical fields under different working conditions are different, and the maximum error of the physical quantity of the output characteristic is up to 145.88%, the dimensionless physical fields under these working conditions show the same regularity because the dimensionless control parameter sets have the same values, and the maximum error of the dimensionless physical quantity is only 10-9Magnitude. The results fully demonstrate the correctness of the dimensionless control parameters and can be used for guiding modeling experiments.
The present disclosure has been described in detail, and the principles and embodiments of the present disclosure have been explained herein by using specific examples, which are provided only for the purpose of helping understanding the method and the core concept of the present disclosure; meanwhile, for those skilled in the art, according to the idea of the present disclosure, there may be variations in the specific embodiments and the application scope, and in summary, the content of the present description should not be construed as a limitation to the present disclosure.

Claims (10)

1. A thermal control osmotic energy conversion analysis method of a salt difference power generation device comprises the following steps:
s100: describing physical mathematical characteristics of heat regulation and control permeation energy conversion of the salt difference power generation device, wherein the physical mathematical characteristics comprise a physical field, a control equation, physical parameters and output performance;
s200: carrying out similar analysis on the control equation by utilizing a similar principle to obtain a dimensionless control parameter group pi for representing the osmotic energy conversion of the non-uniform thermal regulation, the uniform thermal regulation and the non-thermal regulation of the salt-difference power generation devicei；
S300: carrying out dimension analysis on the physical parameters by utilizing Pi theorem to obtain a dimensionless control parameter group Pii；
S400: for the dimensionless control parameter group piiAnd dimensionless control parameter group ΠiPerforming analysis to determine a dimensionless number of thermally regulated osmotic energy conversions in nanochannels of a salt-difference power plant and to clarify the dimensionless set of control parameters πiAnd dimensionless control parameter group piiThe contact of (1);
s500: and analyzing the output performance through a similarity principle to define a non-dimensional potential and a non-dimensional current, so as to unify a plurality of groups of experimental samples into a non-dimensional sample, or expand a group of non-dimensional samples into a plurality of different groups of experimental samples.
2. The method according to claim 1, wherein in step S100, the physical field comprises a concentration field, a potential field, a velocity field and a temperature field, and there is a coupling effect among the concentration field, the potential field, the velocity field and the temperature field.
3. The method of claim 1, wherein in step S100, the governing equation comprises:
poisson equation:
Figure FDA0003495519220000011
flux continuity equation:
Figure FDA0003495519220000021
nernst-planck equation:
Figure FDA0003495519220000022
velocity continuity equation:
Figure FDA0003495519220000023
the Navier-Stokes equation:
Figure FDA0003495519220000024
energy equation:
Figure FDA0003495519220000025
nanochannel boundary equation:
Figure FDA0003495519220000026
wherein,
Figure FDA0003495519220000027
is a partial differential operator,. epsilon.is the dielectric constant,. phi.is the potential, F is the Faraday constant, c is the concentration, z is the number of valence charges, i is the ith ion, n is the total number of ion species, J is the ion flux, u is the velocity, D is the diffusion coefficient, R is the general gas constant, T is the temperature, S is the temperatureTIs Soret coefficient, p is pressure, mu is viscosity coefficient, E is electric field strength, rho is density, CpIs specific heat, lambda is the thermal conductivity, sigmafAs conductivity, σ is the surface charge density.
4. The method of claim 1, wherein in step S100, the physical parameters comprise: working medium parameters, channel parameters, working condition parameters and constants, wherein,
the working medium parameters comprise: dielectric constant ε, diffusion coefficientD, Soret coefficient STViscosity coefficient mu, thermal diffusivity alpha, thermal conductivity lambda, electrical conductivity sigmaf；
The channel parameters include: characteristic length l, surface charge density σ;
the working condition parameters comprise: potential phi, concentration c, velocity u, temperature T, pressure p;
the constants include: faraday constant F, universal gas constant R.
5. The method of claim 1, wherein in step S100, the output performance comprises: I-V curve, diffusion potential, permeation current and output power.
6. The method of claim 1, wherein in step S200, the dimensionless control parameter set isiThe method comprises the following steps:
Figure FDA0003495519220000031
π5＝TST、
Figure FDA0003495519220000032
Figure FDA0003495519220000033
wherein,
Figure FDA0003495519220000034
representing the relative size of the space potential collection electric quantity and the space charge quantity in the nano channel;
Figure FDA0003495519220000035
representing the electrical relative magnitude of the surface potential collection electric quantity and the surface charge density collection electric quantity of the nano-channel;
Figure FDA0003495519220000036
characterization of ion convection and ion diffusion phasesFor the strength and weakness;
Figure FDA0003495519220000037
characterizing the relative strengths of ionic electromigration and ionic diffusion; pi5＝TSTCharacterizing the relative strength of ion thermal migration and ion diffusion;
Figure FDA0003495519220000038
characterizing the relative magnitude of pressure and viscous forces;
Figure FDA0003495519220000039
characterizing the relative magnitude of the electrostatic force and the viscous force;
Figure FDA00034955192200000310
the relative strength of thermal convection and thermal diffusion is characterized;
Figure FDA00034955192200000311
the relative magnitude of joule heating and heat diffusion is characterized.
7. The method according to claim 1, wherein in step S300, the dimensionless control parameter set ΠiThe method comprises the following steps:
Figure FDA00034955192200000312
∏5＝TST、
Figure FDA00034955192200000313
Figure FDA00034955192200000314
8. the method of claim 1, wherein in step S400, the set of dimensionless control parameters is piiAnd dimensionless control parameter group ΠiAfter conversion, it is expressed as:
Figure FDA0003495519220000041
π2＝∏1，
Figure FDA0003495519220000042
π5＝∏5，
Figure FDA0003495519220000043
Figure FDA0003495519220000044
π9＝∏9；
or as:
∏1＝π2，
Figure FDA0003495519220000045
П5＝π5，
Figure FDA0003495519220000046
Figure FDA0003495519220000047
∏9＝π9。
9. the method of claim 1, wherein, in step S500,
the dimensionless potential is defined as:
Figure FDA0003495519220000048
the dimensionless current is defined as:
Figure FDA0003495519220000049
wherein phi is*To a dimensionless potential, I*For dimensionless current, L is the nanochannel length, R is the nanochannel radius, φ is the potential, σ is the charge density, ε is the dielectric constant, I is the current, F is the Faraday constant, c is the concentration, R is the universal gas constant, and D is the diffusion coefficient.
10. The method according to claim 1, wherein in step S500, the defined dimensionless potential and dimensionless current are normalized to obtain a normalized dimensionless potential and a normalized dimensionless current;
the normalized dimensionless potential is expressed as:
Figure FDA00034955192200000410
the normalized dimensionless current is expressed as:
Figure FDA0003495519220000051
wherein,
Figure FDA0003495519220000052
is the normalized non-dimensional potential,
Figure FDA0003495519220000053
is a normalized dimensionless current, phi*To a dimensionless potential, I*Is a dimensionless current of phi0 *To a dimensionless diffusion potential, I0 *Is a dimensionless penetration current.
CN202210115306.6A 2022-01-30 2022-01-30 Thermal regulation and control osmotic energy conversion analysis method for salt difference power generation device Pending CN114609456A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210115306.6A CN114609456A (en) 2022-01-30 2022-01-30 Thermal regulation and control osmotic energy conversion analysis method for salt difference power generation device

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210115306.6A CN114609456A (en) 2022-01-30 2022-01-30 Thermal regulation and control osmotic energy conversion analysis method for salt difference power generation device

Publications (1)

Publication Number Publication Date
CN114609456A true CN114609456A (en) 2022-06-10

Family

ID=81859411

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210115306.6A Pending CN114609456A (en) 2022-01-30 2022-01-30 Thermal regulation and control osmotic energy conversion analysis method for salt difference power generation device

Country Status (1)

Country Link
CN (1) CN114609456A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115420605A (en) * 2022-09-15 2022-12-02 中国石油大学(华东) Experimental device and method for transmitting chloride ions in concrete with temperature difference on two sides

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115420605A (en) * 2022-09-15 2022-12-02 中国石油大学(华东) Experimental device and method for transmitting chloride ions in concrete with temperature difference on two sides

Similar Documents

Publication Publication Date Title
Kientiz et al. Interfacial water transport effects in proton-exchange membranes
Roos et al. Efficient simulation of fuel cell stacks with the volume averaging method
Andreassi et al. Experimental and numerical analysis of a radial flow solid oxide fuel cell
Chanda et al. Numerical simulation of renewable power generation using reverse electrodialysis
CN110750912B (en) Battery thermal parameter identification method based on non-dimensionalized model
CN114609456A (en) Thermal regulation and control osmotic energy conversion analysis method for salt difference power generation device
Cole et al. Microchannel heat transfer with slip flow and wall effects
CN116595491A (en) Energy efficiency prediction method for ion salt difference power generation under temperature gradient
Meiler et al. An empirical stationary fuel cell model using limited experimental data for identification
Daghighi et al. Numerical studies of electrokinetic control of DNA concentration in a closed‐end microchannel
Huang et al. Effect of hydrodynamic slip on thermoelectric response in negatively-charged nanofluidic channels
Hughes et al. One-dimensional axial simulation of electric double layer overlap effects in devices combining micro-and nanochannels
Inoue et al. Prediction method for drying time of wet porous material in humid hot air and superheated steam
Abdollahzadeh Jamalabadi et al. Effects of thermal boundary conditions on the joule heating of electrolyte in a microchannel
Rastgoftar et al. Boundary Control of Temperature Distribution in a Rectangular Functionally Graded Material Plate
Shi et al. Inverse estimation of electrode microstructure distributions in NASA Bi-electrode supported solid oxide fuel cells
Chen et al. COMPUTATIONAL OPTIMAL CONTROL OF 1D COLLOID TRANSPORT BY SOLUTE GRADIENTS IN DEAD-END MICRO-CHANNELS.
Kaneda et al. Pneumatic handling of droplets on‐demand on a microfluidic device for seamless processing of reaction and electrophoretic separation
Vijayaraghavan et al. Multiphysics-Based Statistical Model for Investigating the Mechanics of Carbon Nanotubes Membranes for Proton-Exchange Membrane Fuel Cell Applications
Wright et al. Plasma Decomposition of Carbon Dioxide: Simulations and Experiments
Hsieh et al. Simulation guided design of a microfluidic device for electrophoretic stretching of DNA
Bittanti et al. Molten carbonate fuel cell dynamical modeling
Olshanski et al. Heat and mass transfer in the processes of drying thin natural leathers pasted on smooth surfaces
CN112765841B (en) Pretreatment lattice Boltzmann method for solving fluid variational calculation
Meng et al. Simulation analysis and experimental verification of thermodynamic characteristics of integrated droplet digital PCR chip

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