CN109887550B - Modeling method of energy dissipation regulation model under MIHA pure pneumatic operation condition - Google Patents

Modeling method of energy dissipation regulation model under MIHA pure pneumatic operation condition Download PDF

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CN109887550B
CN109887550B CN201910019394.8A CN201910019394A CN109887550B CN 109887550 B CN109887550 B CN 109887550B CN 201910019394 A CN201910019394 A CN 201910019394A CN 109887550 B CN109887550 B CN 109887550B
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张志炳
周政
陈思
田洪舟
李磊
张锋
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Nanjing University
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Abstract

The invention relates toThe method for modeling the energy dissipation regulation model under the MIHA pure pneumatic operation condition comprises the steps of establishing an energy conversion model in a bubble breaker by analyzing the bubble generation process under the pure pneumatic condition; and calculating the liquid flow based on an energy conversion model and liquid circulation in the bubble breaker, and finally obtaining the energy dissipation rate of the gas-liquid intensive mixing area. The method establishes an energy dissipation regulation and control model under pure pneumatic operation condition aiming at MIHA, comprehensively reflects the structure, the physical property and the operation parameters of a reactor, and the input energy pair epsilonmixThe influence of the energy dissipation regulation model is further researched on the average diameter d of the micro-bubble Sauter, such as the reactor structure, the system physical property, the operation parameters and the like32The key of the influence can realize the guidance of the design of the reactor and the design of the MIHA reaction system, and guide the design of the high-efficiency reactor structure and the reaction system.

Description

Modeling method of energy dissipation regulation model under MIHA pure pneumatic operation condition
Technical Field
The invention belongs to the technical field of reactors and modeling, and particularly relates to a modeling method of an energy dissipation regulation model under an MIHA pure pneumatic operation condition.
Background
For global environmental protection, the sulfur content of bunker fuel oil is reduced, for example, the sulfur content of bunker fuel oil for open sea is reduced to 0.5%, so that it is imperative to replace high-sulfur residual fuel oil with low-sulfur distillate fuel oil. The majority of sulfur in crude oil is present in the resid, which is distributed primarily in aromatics, gums, and asphaltenes, with the majority being present as five-membered ring thiophenes and thiophene derivatives. The method is generally to break the C-S bond of the macromolecule of the residual oil through hydrogenolysis reaction so as to convert sulfur into hydrogen sulfide to remove the sulfur in the residual oil. The sulfur in non-asphaltene is easy to remove under hydrogenation condition, and can reach higher conversion depth. However, as asphaltenes are macromolecules with the largest relative molecular mass, the most complex structure and the strongest polarity in residual oil, sulfur in the asphaltenes is difficult to remove, so that the desulfurization rate in the residual oil hydrodesulfurization process is limited.
The conversion of sulfur-containing asphaltenes is critical during the hydrodesulfurization (hereinafter MIHA) of residua. The core moiety of asphaltenes is a highly condensed fused aromatic ring system. The fused aromatic ring system is surrounded by alkyl and cycloalkyl structures with different numbers and sizes, is the component with the highest condensation degree in the residual oil, simultaneously contains heteroatoms such as S, N, O, metals and the like, and has complex morphology and molecular structure. In the process of residual oil hydroconversion, asphaltene mainly undergoes two reactions of cracking in which macromolecules are changed into small molecules and condensation in which the small molecules are dehydrogenated and polymerized to generate macromolecules in opposite directions. The method takes asphaltene hydrodesulfurization reaction as model reaction of residual oil hydrogenation process, and inspects the influence of reactor structure, system physical property, operation parameters and input energy on energy dissipation in the bubble breaker.
Disclosure of Invention
The invention aims to provide a modeling method of an energy dissipation regulation and control model under the MIHA pure pneumatic operation condition so as to research the structure, the physical property and the operation parameters of a reactor and the input energy pair epsilonmixThereby realizing the guidance of MIHA reactor design and MIHA reaction system design.
MIHA microbubble formation can take three forms, namely: pure hydraulic, pure pneumatic and gas-liquid linkage. Under the conditions of pure hydraulic and pure pneumatic operation, the energy required by system operation and microbubble formation is completely provided by liquid mechanical energy or gas static pressure energy; under the condition of gas-liquid linkage operation, the gas static pressure energy and the liquid mechanical energy simultaneously provide energy required by system operation and micro-bubble formation. The invention discusses a modeling method of an energy dissipation regulation model under a pure pneumatic operation condition, which comprises the following steps:
s100, analyzing a bubble generation process under a pure pneumatic condition, and establishing an energy conversion model in a bubble breaker;
under purely pneumatic operating conditions, liquidVolume flow rate QL<<Gas flow rate QGBefore the gas is not introduced, the bubble breaker is filled with static reaction liquid; the liquid of the system is assumed to be in closed cycle, namely the liquid amount does not change in the whole process; due to the gas entering, part of the liquid is forced to enter the external circulation pipeline of the bubble breaker; the length of the bubble breaker is set to be L, and the diameter is set to be D1Cross sectional area S1＝πD1 2(ii)/4; nozzle diameter DN；
Assumptions are made as follows:
(1) steady state operation, operating pressure PmConstant;
(2) the actual operation pressure is higher, so that the change of the liquid potential energy and the change of the gas pressure in the air bubbles caused by the interfacial tension of the air bubbles are ignored;
(3) since the gas density is much less than that of the liquid, the kinetic energy of the input gas is ignored;
taking a bubble breaker as a control body, and carrying out energy balance under a steady state condition; under pneumatic conditions, the pressure is PG0Volume flow of QG0Is constant at a gas inlet operating pressure of PmWhen the bubble breaker is used, partial static pressure energy is released by the gas and is converted into liquid kinetic energy and bubble surface energy; the static pressure energy released by the gas is equivalent to the work W of the gas on the systemGAccording to the work definition:
Figure BDA0001940239030000021
QGfor the gas flow in the bubble breaker, assuming that the gas is an ideal gas, the following can be obtained according to the ideal gas state equation:
Figure BDA0001940239030000022
in the formula (2), ρG0And MA(gas density and gas molar mass entering the cracker; R and T are gas constant and gas temperature, respectively;
formula (2) is substituted for formula (1) and integrated to obtain:
Figure BDA0001940239030000023
let the difference between the gas pressure at the gas inlet of the bubble breaker and the operating pressure be Δ P, i.e.:
ΔP＝PG0-Pm(29)
since Δ P > 0, WGLess than 0, namely the mechanical energy of the gas is reduced after the gas enters the bubble breaker; due to bubble breaker operating pressure PmConstant and relatively negligible gravitational potential energy of the liquid, so the reduced mechanical energy of the gas will be converted into kinetic energy of the liquid and interfacial energy of the gas bubbles; therefore, the following relationships can be obtained from the equations (3) and (4):
Figure BDA0001940239030000031
equation (5) left of the equal sign is the reduction in gas static pressure energy, i.e., -WG(ii) a The two terms on the right of the equal sign of the equation (5) are liquid kinetic energy and gas-liquid interfacial energy respectively; where ρ isLAnd σLLiquid density and interfacial tension, respectively; u shapeLIs the linear velocity of the liquid flowing out of the disrupter; d32The Sauter average diameter of the bubbles flowing out of the bubble breaker; according to a mass balance, QGAnd QG0The following relationships exist:
Figure BDA0001940239030000032
since Δ P < PmThus QG≈QG0(ii) a Preliminary calculations indicate that the gas-liquid interfacial energy value is negligible relative to the liquid kinetic energy value, and therefore equation (5) can be simplified as:
Figure BDA0001940239030000033
s200, calculating the liquid flow based on an energy conversion model and liquid circulation in the bubble breaker;
because the liquid that advances out of the knapper is closed cycle, and the business turn over liquid flow is equal promptly, so have:
QL＝ULS1(1-φG) (33)
wherein, the gas content in the bubble breaker is phiGCalculated as follows:
Figure BDA0001940239030000034
is obtained from the formulae (8) and (9):
Figure BDA0001940239030000035
ULsubstituting equation (10) for the apparent velocity of the gas-liquid mixture in the bubble breaker can give:
Figure BDA0001940239030000036
from equation (11), the liquid flow Q at the nozzle diameter due to gas input can be calculatedLFrom equation (7), we can derive:
Figure BDA0001940239030000037
under purely pneumatic operating conditions, QL<<QGThen equation (11) is simplified to:
Figure BDA0001940239030000041
this gives:
Figure BDA0001940239030000042
from the ideal equation of state, the following relationship exists:
Figure BDA0001940239030000043
substituting equation (15) into equation (14) yields:
Figure BDA0001940239030000044
as can be seen from equation (16): bubble breaker cross-sectional area S1For liquid circulation flow QLThe influence is larger; because:
Figure BDA0001940239030000045
in the formula VNIs the flow velocity at the nozzle;
when V isNAt a certain timing, it can be obtained from equations (16) and (17):
Figure BDA0001940239030000046
when D is presentNAt a certain timing, it can be obtained from equations (16) and (17):
Figure BDA0001940239030000047
from formulas (10) and (16):
Figure BDA0001940239030000048
thereby completing the Q pair under pure pneumatic conditionL(ii) estimating;
s300, calculating the energy dissipation rate epsilon of the gas-liquid intensive mixing areamix；
According to the first law of thermodynamics:
Figure BDA0001940239030000051
in the above formula, LmixThe length of a gas-liquid intensive mixing area in bubble crushing is m; lambda [ alpha ]1Is the ratio of the gas-liquid volume flow rate, λ1＝QG/QL；K1The ratio of the bubble breaker nozzle diameter to the breaker diameter, K1 ═ DN/D1；
LmixThe maximum flow rate of the liquid in the process of the attenuation is related to the length of the liquid which is attenuated until the liquid disappears in the bubble-breaking zone, and the central linear velocity U of the liquidjmThe attenuation law of (2) is not influenced by the disturbance of the bubbles around the attenuation law and conforms to the following attenuation law:
Figure BDA0001940239030000052
in equation (22), x is the horizontal distance from the bubble breaker core to the maximum velocity. When U is turnedjmDamping to apparent velocity U of gas-liquid mixtureLThen the gas disappears at a high speed, and then a uniform gas-liquid mixture flow is formed; thus, LmixIs Ujm＝ULThe value of x when, i.e.:
Figure BDA0001940239030000053
simplifying equation (23) yields:
Figure BDA0001940239030000054
substituting equation (24) into (21) and simplifying to obtain:
Figure BDA0001940239030000055
by combining equations (16), (20) and equation (25), ε may be calculatedmix。
The invention also aims to provide an energy dissipation regulation and control model under the MIHA pure pneumatic operation condition, which is constructed by the method.
It is a further object of the present invention to provide a reactor designed for the above process.
The reactor structure of the present invention can be found in the patent CN106187660A previously filed by the inventor, and the details in the present invention are not repeated. The invention utilizes the structure, system physical property and operation parameter of the constructed model reactor, and input energy pair epsilonmixSo that the design of relevant reactor structural parameters can be carried out according to requirements.
The method establishes an energy dissipation regulation and control model under pure pneumatic operation condition aiming at MIHA, comprehensively reflects the structure, the physical property and the operation parameters of a reactor, and the input energy pair epsilonmixThe influence of the energy dissipation regulation model is further researched on the average diameter d of the micro-bubble Sauter, such as the reactor structure, the system physical property, the operation parameters and the like32The key of the influence can realize the guidance of the design of the reactor and the design of the MIHA reaction system, and guide the design of the high-efficiency reactor structure and the reaction system.
Drawings
FIG. 1 is a schematic diagram of a physical model of a bubble generation process under purely pneumatic conditions;
FIG. 2 is a graph of the supply air pressure differential Δ P versus the energy dissipation ratio εmixThe influence of (c);
FIG. 3 is a graph of the pressure difference Δ P of supplied gas versus the gas content φGThe influence of (a);
FIG. 4 shows the ventilation QGFor energy dissipation rate epsilonmixThe influence of (a);
FIG. 5 shows ventilation QGTo gas content rate phiGThe influence of (c).
Detailed Description
The technical scheme of the invention is further explained by combining the description of the attached drawings and the detailed description.
Example 1
S100, analyzing a bubble generation process under a pure pneumatic condition, and establishing an energy conversion model in a bubble breaker;
before the gas is not introduced, the bubble breaker is filled with the static reaction liquid. When the gas introduction is started, the gas pressure P is increasedGAnd system operating pressure PmThere is a pressure difference ap between, the static pressure of the gas will be transferred to the liquid, causing the liquid to turbulence, and the gas pressure itself rapidly drops to the operating pressure within the MIHA. Due to the flow of the gas phase and the liquid phase, the gas phase and the liquid phase flow out of the bubble breaker. For pneumatic operating conditions, the liquid flow rate QLMuch less than the gas flow QGThe energy required for the system operation is almost completely provided by gas pressure energy.
Establishing a physical model diagram as shown in FIG. 1:
the system liquid is assumed to be a closed loop cycle, namely, the liquid amount does not change in the whole process. Due to the gas ingress, part of the liquid will be forced into the bubble breaker external circulation line. The length of the bubble breaker is set to be L (m) and the diameter is set to be D1(m) cross-sectional area S1(m2)(S1＝πD1 2/4). Nozzle diameter DN(m)。
Assumptions are made as follows:
(1) steady state operation, operating pressure PmConstant;
(2) the actual operation pressure is higher, so that the change of the liquid potential energy and the change of the gas pressure in the air bubbles caused by the interfacial tension of the air bubbles are ignored;
(3) since the gas density is much less than the liquid, the kinetic energy of the input gas is neglected.
And (4) taking the bubble breaker as a control body to carry out energy balance under a steady state condition. Under pneumatic conditions, the pressure is PG0(Pa) and a volume flow rate of QG0(m3Gas inlet operating pressure of/s) is constant at Pm(Pa), the gas releases part of the static pressure energy and is converted into the kinetic energy of the liquid and the surface energy of the bubbles. The static pressure energy released by the gas is equivalent to the work W of the gas on the systemG(W), defined in terms of work:
Figure BDA0001940239030000071
QG(m3/s) is the gas flow rate in the bubble breaker, and for the sake of simplicity, assuming that the gas is an ideal gas within the scope of the present invention, the equation of state for the ideal gas can be obtained:
Figure BDA0001940239030000072
in the formula (2), ρG0(Kg/m3) And MA(Kg/mol) are the density and molar mass of the gas entering the cracker, respectively; r (8.314J/mol. K) and T (K) are the gas constant and gas temperature, respectively.
Formula (2) is substituted for formula (1) and integrated to obtain:
Figure BDA0001940239030000073
let the difference between the gas pressure at the gas inlet of the bubble breaker and the operating pressure be Δ p (pa), i.e.:
ΔP＝PG0-Pm(54)
since Δ P > 0, WG< 0, i.e. the mechanical energy of the gas after it enters the bubble breaker will be reduced. Due to bubble breaker operating pressure PmConstant and relatively speaking, the gravitational potential energy of the liquid is negligible, so the reduced mechanical energy of the gas will be converted into kinetic energy of the liquid and the interfacial energy of the gas bubbles. Therefore, the following relationships can be obtained from the equations (3) and (4):
Figure BDA0001940239030000074
equation (5) left is the reduction of the gas static pressure energy (W)G) I.e. the energy source required for the system operation; the two terms on the right side of equation (5) are the kinetic energy of the liquid and the interfacial energy of the gas-liquid, respectively. Where ρ isL(Kg/m3) And σL(N/m) are liquid density and interfacial tension, respectively; u shapeL(m/s) linear velocity of the liquid flowing out of the disruptor; d32(m) is the Sauter mean diameter of the bubbles flowing out of the bubble breaker; according to a mass balance, QGAnd QG0The following relations exist:
Figure BDA0001940239030000081
for the studies of the present invention, Δ P < PmThus, QG≈QG0. For convenience of description, the gas flow rates into and out of the reactor are indicated below as QGAnd (4) showing. Preliminary calculations show that the gas-liquid interfacial energy value is negligible relative to the liquid kinetic energy value. This term is first ignored herein, and then checked by calculation. Therefore, equation (5) can be simplified as:
Figure BDA0001940239030000082
s200, calculating liquid flow based on an energy conversion model and liquid circulation in the bubble breaker;
according to the closed loop assumption above, the liquid flows in and out are equal, so there are
QL＝ULS1(1-φG) (58)
Wherein, the gas content in the bubble breaker is phiGCan be calculated as follows:
Figure BDA0001940239030000083
the following formulae (8) and (9) can be used:
Figure BDA0001940239030000084
obviously, ULIs the superficial velocity of the gas-liquid mixture in the bubble breaker. General formula (10)) Substituting equation (7) yields:
Figure BDA0001940239030000085
from equation (11), the liquid flow Q at the nozzle diameter due to gas input can be calculatedLHowever, the form is complex, and should be reasonably simplified according to the actual situation of the project. From equation (7) we can derive:
Figure BDA0001940239030000086
the calculations show that, under the conditions of the present study, QL<<QG. Equation (11) can be simplified as:
Figure BDA0001940239030000087
this gives:
Figure BDA0001940239030000091
in fact, from the ideal equation of state, the following relationship exists:
Figure BDA0001940239030000092
substituting equation (15) into equation (14) yields:
Figure BDA0001940239030000093
as can be seen from equation (16): bubble breaker cross-sectional area S1For liquid circulation flow QLThe influence is larger;
due to the following:
Figure BDA0001940239030000094
in the formula VNIs the flow velocity at the nozzle;
when V isNAt a certain timing, it can be obtained from equations (16) and (17):
Figure BDA0001940239030000095
when D is presentNAt a certain timing, the following equations (16) and (17) can be obtained:
Figure BDA0001940239030000096
from formulas (10) and (16):
Figure BDA0001940239030000097
the above is based on the fact that Q is applied under full pneumatic conditionsLThe coarse calculation of (3). Further according to the known VNDetermination of the diameter DN(when D isNAt a certain time, V can also be obtainedN)。
S300, calculating the energy dissipation rate epsilon of the gas-liquid intensive mixing areamix；
d32Energy dissipation rate epsilon of gas-liquid intensive mixing area in bubble breakermixAre closely related. According to the first law of thermodynamics:
Figure BDA0001940239030000098
in the above formula, LmixThe length of a gas-liquid intensive mixing area in bubble crushing is m; lambda [ alpha ]1Is the ratio of the gas-liquid volume flow (lambda)1＝QG/QL)。K1Is the ratio of the diameter of the bubble breaker nozzle to the diameter of the breaker (K)1＝DN/D1)。
Evans et al have derived L based on the principle of conservation of kinetic energymixA mathematical model of (2), butAre not applicable to the situation in which the present invention is studied, and therefore, the derivation thereof needs to be repeated. The present inventors considered that LmixRelated to the length of decay to disappearance of the highest flow rate of liquid in the bubble collapse zone. The highest flow rate of the liquid is in the process of attenuation, and the central linear velocity U of the liquidjmThe attenuation law of (2) is not influenced by the disturbance of the bubbles around the attenuation law and conforms to the following attenuation law:
Figure BDA0001940239030000101
in equation (22), x is the horizontal distance from the bubble breaker core to the maximum velocity. When U is turnedjmDamping to apparent velocity U of gas-liquid mixtureLAt high speed, and then a homogeneous gas-liquid mixture flow is formed. Thus, LmixIs Ujm＝ULThe value of x. Namely:
Figure BDA0001940239030000102
simplifying equation (23) yields:
Figure BDA0001940239030000103
substituting equation (24) into (21) and simplifying it can be:
Figure BDA0001940239030000104
by combining equations (16), (20) and equation (25), ε can be calculatedmix。
Example 2
This example specifically illustrates an energy dissipation regulation model constructed based on the method of example 1.
The energy dissipation regulation model obtained based on the modeling method of example 1 is as follows:
Figure BDA0001940239030000105
Figure BDA0001940239030000106
Figure BDA0001940239030000107
Figure BDA0001940239030000111
example 3
This example was based on the modeling method of example 1, and the gas supply pressure difference Δ P and the ventilation Q were studied for a specific reactor structure and reaction systemGFor energy dissipation rate epsilonmixThe influence of (c).
(1) Air supply pressure difference delta P to energy dissipation rate epsilonmixThe influence of (a);
the calculation conditions were as follows:
diameter D of the breaker10.02 m; ratio K of bubble breaker nozzle diameter to breaker diameter1＝0.5；
Density p of residual oilL＝800Kg/m3(ii) a Operating pressure Pm14 MPa; the air supply pressure difference delta P is 1-10 MPa; the gas temperature T-450 ℃.
Air supply pressure difference delta P to energy dissipation rate epsilonmixThe effect of (c) is shown in FIG. 2 (ventilation 80L/h);
(2) differential pressure of supplied air Δ P vs. gas content phiGThe influence of (a);
the calculation conditions are the same as those in (1); the results are shown in FIG. 3;
it can be seen that the air supply pressure difference increases, the energy dissipation rate of the bubble breaker increases, and the air inclusion rate decreases. The air supply pressure difference mainly changes the liquid circulation flow, further influences the size of air bubbles and the gas-liquid interfacial area, and finally influences the mass transfer and the macroscopic reaction rate.
(3) Air flow rate QGFor energy dissipation rate epsilonmixThe influence of (a);
the calculation conditions were as follows:
diameter D of the breaker10.02 m; ratio K of bubble breaker nozzle diameter to breaker diameter1＝0.5；
Air flow rate QG1-100L/h; density p of residual oilL＝800Kg/m3(ii) a Operating pressure Pm14 MPa; the air supply pressure difference delta P is 0.1-10 MPa; the gas temperature T is 500 ℃.
The results are shown in FIG. 4;
(4) air flow rate QGTo gas content rate phiGThe influence of (a);
the calculation conditions are the same as (3), and the results are shown in FIG. 5;
it can be seen that the energy dissipation rate in the bubble breaker increases approximately linearly with increasing aeration, and the gas content in the reactor increases with increasing aeration.

Claims (2)

1. A modeling method of an energy dissipation regulation and control model under the MIHA pure pneumatic operation condition is characterized by comprising the following steps:
s100, analyzing a bubble generation process under a pure pneumatic condition, and establishing an energy conversion model in a bubble breaker;
liquid flow rate Q under purely pneumatic operating conditionsL<<Gas flow rate QGBefore the gas is not introduced, the bubble breaker is filled with static reaction liquid; the liquid of the system is assumed to be in closed cycle, namely the liquid amount does not change in the whole process; due to the gas entering, part of the liquid is forced to enter the external circulation pipeline of the bubble breaker; the length of the bubble breaker is set to be L, and the diameter is set to be D1Cross sectional area S1＝πD1 2(ii)/4; nozzle diameter DN；
Assumptions are made as follows:
(1) steady state operation, operating pressure PmConstant;
(2) the actual operation pressure is higher, so that the change of the liquid potential energy and the change of the gas pressure in the air bubbles caused by the interfacial tension of the air bubbles are ignored;
(3) since the gas density is much less than that of the liquid, the kinetic energy of the input gas is ignored;
taking a bubble breaker as a control body, and carrying out energy balance under a steady state condition; under pneumatic conditions, the pressure is PG0Volume flow of QG0Is constant at a gas inlet operating pressure of PmWhen the bubble breaker is used, the gas releases partial static pressure energy and is converted into liquid kinetic energy and bubble surface energy; the static pressure energy released by the gas is equivalent to the work W of the gas on the systemGAccording to the work definition:
Figure FDA0003509880010000011
QGfor the gas flow in the bubble breaker, assuming that the gas is an ideal gas, the following can be obtained according to the ideal gas state equation:
Figure FDA0003509880010000012
in the formula (2), ρG0And MAThe gas density and the gas molar mass entering the crusher are respectively; r and T are respectively a gas constant and a gas temperature;
formula (2) is substituted for formula (1) and integrated to obtain:
Figure FDA0003509880010000021
let the difference between the gas pressure at the gas inlet of the bubble breaker and the operating pressure be Δ P, i.e.:
ΔP＝PG0-Pm (4)
since Δ P > 0, WGLess than 0, namely the mechanical energy of the gas is reduced after the gas enters the bubble breaker; due to bubble breaker operating pressure PmConstant, and relatively speaking, the gravitational potential of the liquid is negligible, and therefore that of the gasSmall mechanical energy is converted into liquid kinetic energy and bubble interfacial energy; therefore, the following formulas (3) and (4) can be obtained:
Figure FDA0003509880010000022
equation (5) left of the equal sign is the reduction in gas static pressure energy, i.e., -WG(ii) a The two terms on the right of the equal sign of the equation (5) are liquid kinetic energy and gas-liquid interfacial energy respectively; where ρ isLAnd σLLiquid density and interfacial tension, respectively; u shapeLIs the linear velocity of the liquid flowing out of the disrupter; d32The Sauter average diameter of the bubbles flowing out of the bubble breaker; according to a mass balance, QGAnd QG0The following relationships exist:
Figure FDA0003509880010000023
since Δ P < PmThus QG≈QG0(ii) a Preliminary calculations show that the gas-liquid interfacial energy value is negligible relative to the liquid kinetic energy value, and therefore equation (5) is simplified as:
Figure FDA0003509880010000024
s200, calculating the liquid flow based on an energy conversion model and liquid circulation in the bubble breaker;
because the liquid that advances out of the knapper is closed cycle, and the business turn over liquid flow is equal promptly, so have:
QL＝ULS1(1-φG) (8)
wherein, the gas content in the bubble breaker is phiGCalculated as follows:
Figure FDA0003509880010000025
the following formulae (8) and (9) can be used:
Figure FDA0003509880010000031
ULsubstituting equation (10) for the apparent velocity of the gas-liquid mixture in the bubble breaker can give:
Figure FDA0003509880010000032
from equation (11), the liquid flow Q at the nozzle diameter due to gas input can be calculatedLFrom equation (7), we can derive:
Figure FDA0003509880010000033
under purely pneumatic operating conditions, QL<<QGThen equation (11) is simplified to:
Figure FDA0003509880010000034
this gives:
Figure FDA0003509880010000035
from the ideal equation of state, the following relationship exists:
Figure FDA0003509880010000036
substituting equation (15) into equation (14) yields:
Figure FDA0003509880010000037
as can be seen from equation (16): bubble breaker cross-sectional area S1For liquid circulation flow rate QLThe influence is larger;
because:
Figure FDA0003509880010000038
in the formula VNIs the flow velocity at the nozzle;
when V isNAt a certain timing, it can be obtained from equations (16) and (17):
Figure FDA0003509880010000041
when D is presentNAt a certain timing, the following equations (16) and (17) can be obtained:
Figure FDA0003509880010000042
from formulas (10) and (16):
Figure FDA0003509880010000043
thereby completing the Q pair under pure pneumatic conditionLEstimating;
s300, calculating the energy dissipation rate epsilon of the gas-liquid intensive mixing areamix；
According to the first law of thermodynamics:
Figure FDA0003509880010000044
in the above formula, LmixThe length of a gas-liquid intensive mixing area in bubble crushing is m; lambda [ alpha ]1Is the ratio of the gas-liquid volume flow rate, λ1＝QG/QL；K1For bubble breaker nozzle diameter and breakerRatio of diameters, K1＝DN/D1；
LmixThe maximum flow rate of the liquid in the process of the attenuation is related to the length of the liquid which is attenuated until the liquid disappears in the bubble-breaking zone, and the central linear velocity U of the liquidjmThe attenuation law of (2) is not influenced by the disturbance of the bubbles around the attenuation law and conforms to the following attenuation law:
Figure FDA0003509880010000045
in equation (22), x is the horizontal distance of the bubble breaker core to the maximum velocity; when U is turnedjmDamping to apparent velocity U of gas-liquid mixtureLThen the gas disappears at a high speed, and then a uniform gas-liquid mixture flow is formed; thus, LmixIs Ujm＝ULThe value of x when, i.e.:
Figure FDA0003509880010000051
simplifying equation (23) yields:
Figure FDA0003509880010000052
substituting equation (24) into (21) and simplifying to obtain:
Figure FDA0003509880010000053
by combining equations (16), (20) and equation (25), ε may be calculatedmix。
2. A reactor designed by the method of claim 1.
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