CN107563051B - Micro-interface strengthening reactor bubble scale structure imitates regulation-control model modeling method - Google Patents
Micro-interface strengthening reactor bubble scale structure imitates regulation-control model modeling method Download PDFInfo
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Abstract
The present invention relates to a kind of micro-interface strengthening reactor bubble scale structures to imitate regulation-control model modeling method, with micro-interface strengthening reactor largest air bubbles diameter dmaxWith minimum bubble diameter dminFor independent variable, bubble Sauter average diameter d32Its numerical relation is constructed for dependent variable；And it is theoretical based on Kolmogorov-Hinze, construct micro-interface strengthening reactor largest air bubbles diameter dmax, minimum bubble diameter dminRelationship between reactor parameter.Method of the invention contacts reactor bubble scale and the structural parameters, operating parameter and physical parameter of reactor together with specific numerical relation, there is directive significance for the design of reactor, and it is applicable to a variety of reactors, versatility is good, the bubble scale regulation-control model constructed using modeling method of the invention, it can be further by adjusting the structural parameters of reactor and operating parameter to obtain the maximization target that reaction process efficiency object is imitated, or under given reaction target and energy and material consumption, design efficient structure of reactor.
Description
Technical field
The invention belongs to chemical industry manufacture, reactor, modeling technique fields, and in particular to a kind of micro-interface strengthening reactor gas
It steeps scale structure and imitates regulation-control model modeling method.
Background technique
Oxidation plus the heterogeneous reactions such as hydrogen, chlorination are widely present in chemical production process, Global reaction Rate generally by
It is formed on mass transport process.The mass transfer rate of gas liquid reaction is mainly common by liquid side (or gas side) mass tranfer coefficient and gas liquid film product a
It influences.Existing research shows that a is bigger to the influence degree of volume transmission quality coefficient, and is easy regulation.Therefore, increase a to be considered as mentioning
Particularly effective approach of the height by mass transfer limited gas liquid reaction system reaction efficiency.
Bubble Sauter average diameter d32It is one of the key parameter for determining a size, they are mainly between by bubble and gas-liquid
Two alternate interaction forces influence.Bubble coalescence and division are then above two active force respectively as a result, and to influence bubble straight
The size of diameter.Therefore, the meso-scale behavior of bubble coalescence and rupture as bubble is the profound cause for determining a size.It closes
It is long-standing in the research of bubble coalescence and disruptive behaviour, generally believe energy absorbing device and d32It is important influence factor.Thing
In reality, d32A and volume transmission quality coefficient size can be influenced, is the central factor for determining gas-liquid Global reaction Rate[1].Research is aobvious
Show, works as d32When being gradually reduced, volumetric mass transfer rate is gradually increased；Especially work as d32When less than 1mm, volumetric mass transfer rate is with d32
Reduction be similar to exponential form comparatively fast increase.Therefore, reduce d as much as possible32Gas-liquid mass transfer can be strengthened and finally increased
Global reaction Rate.
Bubbling reactor and stirring-bubbling reactor are industrial most traditional and common gas-liquid reactors.As PX is aoxidized
The tower bubbling reactor of TA processed, bubble diameter are typically larger than 10mm or even a few Centimeter Levels, and mass transfer interfacial area extremely has
Limit, it is therefore necessary to reactor is made very big, to improve Global reaction Rate, while liquid must be promoted by increasing air-blowing amount
Body turbulent flow, improves gas holdup, and then increases interfacial area, but this measure necessarily reduces the utilization rate of oxygen in air, increases compression
Machine power and exhaust emissions lead to energy consumption transition and loss of material and environmental pollution.In terms of turbulent flow dynamics angle, traditionally use
It obtains to be formed mostly in most widely stirring-bubble type gas-liquid reactor and has an impact to bubble macroscopic motion but bubble breaking is acted on
Little big whirlpool, bubble cannot be effectively crushed, therefore bubble diameter is bigger than normal, and mass transfer area is limited, so that reaction efficiency is relatively low.It is strong
Change gas-liquid mass transfer, tower bubbling reactor adds the internals such as gas distribution grid, static mixer generally to reinforce mixing, and stirs
Kettle then needs the structures such as agitating paddle or the inner cylinder of installation different structure, to increase the air content of liquid layer.Nevertheless, both are reacted
Bubble diameter in device is usually 5~20mm, and the phase contact area in provided unit volume is extremely limited, generally less than
100m2/m3, therefore reaction efficiency can not obtain breakthrough raising.Therefore, industrially frequently by high temperature and pressure and increasing tolerance
Improve gas holdup and phase contact area, but this has great negative shadow to the energy consumption of reaction process, material consumption and reaction selectivity
It rings.
Since micro- crushing technology of research and development bubble is particularly significant, therefore most in the past 10 years, English, beauty, moral, Deng state university with
Research institution begins to focus on and researches and develops ultra-fine bubbler techniques[2-11], but its research achievement has following common defects:
(1) though the bubble of a certain amount of micron order scale can be obtained using means such as Mechanical Crushing, fluid impact, ultrasounds,
Gas liquid ratio (the ratio between gas volume and liquid volume) is too low, and generally below 1%, the upper limit is no more than 5%.In addition, generating microbubble
Equipment energy consumption and manufacturing cost it is too high.
(2) it is still not based on the microbubble architectural characteristic that liquid phase is continuous phase and high turbulence both at home and abroad, proposed system
The micro-interface mass transfer enhancement of change is theoretical, microbubble is tested and characterizing method, micro-interface strengthening reactor structure effect regulation theory and phase
Close mathematical model.
For these reasons, though there is fragmentary application experiment result to deliver, there has been no the industrial application of scale report,
Especially in the application of chemical industry manufacturing field substantially also in space state.
The Chemical Manufacture of current era totally considers that survival and development are depended on to material based on innovation, green, environmental protection
Material is substantially innovated with process technology.Improve reaction with the Atom economy of separation process to reduction energy consumption, material consumption, enhance the competitiveness
It is most important.Based on this, it is proposed that " micro-interface mass transfer enhancement reaction-finely separate integrated system " new technology, it is intended to from most
Basic ultra-fine gas-liquid particle characteristics research is set out, and is solved under high turbulence state in ultra-fine grain system, micro-interface chemistry
Theory involved in the structures such as fluid flowing, mass transfer, reaction, energy conversion effect regulation overall process, technology are asked with application in reactor
Topic.
Ultra-fine gas-liquid particle of the present invention refers to ultra-fine bubble (or fine droplets), is that particle equivalent diameter is in
1μm≤d0The micron order gas-liquid particle of < 1mm.In the reaction system, ultra-fine gas-liquid particle forms ultra-fine interface (or micro- boundary
Face), the formation at ultra-fine interface substantially enhances mass transfer and reaction rate, especially by mass transfer limited reaction system.
, it is emphasized that classical gas-liquid mixed theory is generally basede on millimeter-Centimeter Level gas-liquid particle characteristic, presently the most
Reasonable method is multiple dimensioned minimum energy principle (EMMS)[12].Current research work mostly is anti-for traditional gas-liquid
Answer bubble on the grade in device[13,14], seldom it is related to ultra-fine grain system.For the mixing of ultra-fine grain system, mass transfer with
Response characteristic, it is necessary to establish new computation model, test and characterizing method and structure effect regulation-control model, must study thus new
Device structure, energy input form and translative mode, to form the completely new calculating for being suitable for ultra-fine grain reaction system
Software and hardware platform, for China process industrial production technology attain a new height the technology that provides and equipment support.
In the prior art for d32There are two types of the research of algorithm is general:
1.Wherein niRepresent bubble number, diRepresent bubble diameter；The shortcomings that this algorithm is to need to know
The bladdery diameter of institute and bubble number in system, this can not accomplish at present, and this formula does not include reactor yet
Structural parameters, operating parameter and physical parameter, directive significance no for the design of reactor is not truly
Structure imitates regulation-control model；
2.d32=α dmax, proportionality coefficient α in this formula is come out by empirical estimating, can only be for certain specific
System, and error is larger.
So-called structure effect regulation mathematical model refers to the reaction efficiency (efficiency and object effect) of ultra-fine gas-liquid particle reaction system
It mathematically associates with system physicochemical property, micro-interface characteristic, mass transfer characteristic and structure of reactor, so that realizing can lead to
Adjustment structural parameters and operating parameter are crossed to obtain the maximization target of reaction process efficiency object effect, or in given reaction target
Under (task) and energy and material consumption, efficient structure of reactor is designed.And for micro-interface strengthening reactor, work in this respect
Make in the world still to be blank.
Bibliography
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with microbubbles[J].Journal of Chemical Engineering of Japan,2006,39(11):
1213-1220.
[4]Muroyama K,Imai K,Oka Y,Hayashi J,Mass transfer properties in a
bubble column associated with micro-bubble dispersions[J].Chemical
Engineering Science,201,100:464-473.
[5]Maeda Y,Hosokawa S,Baba Y,Tomiyama Akio.Generation mechanism of
micro-bubbles in a pressurized dissolution method[J].Experimental Thermal and
Fluid Science,2015,60:201-207.
[6]Hasegawa H,Nagasaka Y,Kataoka H.Electrical potential of
microbubble generated by shear flow in pipe with slits.Fluid Dynamics
Research,2008,40(7-8):554-564.
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Trichodermareesei for cellulase production[J].Process Biochemistry,2005,40
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[8]Rehman F,Medley GJ,Bandulasena H,Zimmerman WB.Fluidic oscillator-
mediated microbubble generation to provide cost effective mass transfer and
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[10]Druzinec D,Salzig De,Kraume M,Czermak P.Micro-bubble aeration in
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cell culture media[J].Chemical Engineering Science,2015,126:160-168.
[11] Li Baozhang, Shang Longan, research [J] the Northwest University journal of the Jiang Xinzhen circulation flow reactor of falling injecting type is (certainly
So science version) .1989,04:65-69.
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exploring the intrinsic similarity between gas-solid and gas-liquid systems
[J].Chinese Journal of Chemical Engineering.2012,20(1):167-177.
[13]Hinze JO.Fundamentals of the hydrodynamic mechanism of splitting
in dispersion processes[J].AIChE Journal.1955,1(3):289-295.
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for measuring bubble parameters[J].Chemical Engineering Science,2016,141(17):
143-153.
Summary of the invention
It is an object of the present invention to overcome the deficiencies of existing technologies, a kind of micro-interface strengthening reactor bubble scale is provided
Structure imitates regulation-control model modeling method.
To achieve the above object, the present invention adopts the following technical scheme:
A kind of micro-interface strengthening reactor bubble scale structure effect regulation-control model modeling method, comprising:
(1) with micro-interface strengthening reactor largest air bubbles diameter dmaxWith minimum bubble diameter dminFor independent variable, bubble
Sauter average diameter d32For dependent variable, d is establishedmax、dminAnd d32Between relationship；Specific step is as follows:
If x, m, n be respectively bubble diameter in reactor gas-liquid system, bubble diameter geometry natural logrithm mean value and
Standard deviation obtains the probability density function of bubble diameter x:
Bubble diameter meets bubble Sauter average diameter d when this distribution32Are as follows:
d32=exp (m+2.5n2) (2)
Bubble diameter x is in logarithm normal distribution, therefore the mathematic expectaion (arithmetic mean of instantaneous value) of lnx are as follows:
Bubble diameter probability density figure is drawn according to the probability density function of bubble diameter x, whenWhen, probability density is most
Greatly；First derivative i.e. herein is 0:
Equation (3) substitution (1) is obtained into equation (4):
It can be obtained by (3), (4):
Due to:
It can be obtained after equation (1) is substituted into (6) and abbreviation:
It enables:Then above formula simplifies are as follows:
Equation (8) left end is error function, with standard error function the difference is that the difference of the limit of integration, formula (5) are divided
Above-mentioned range of integration is not substituted into, and can be obtained after converting standard error function for equation (8):
In equation (9), erf () is error function；
For the error function of following form:
Series expansion can be used in its approximate calculation.Classical Taylor series expansion, convergence rate is compared with Chebyshev
(Chebyshev) series is slow, but has relatively simple quantic, therefore is widely adopted.For engineering research,
Acquisition form is relatively simple, the succinct expression that error can be received by engineering field, without pursuing error in mathematical meaning
Minimum accurate expression.Taylor series expansion is different according to the value range of error function independent variable and uses different forms,
Such as:
As z≤4, erf (z) is deployable are as follows:
Due to:
Work as dmax/dminWhen being 1000:
And according to equation (11):
Therefore, when:
That is:
When, equation (9) is approximate to be set up；
In addition, condition and n and d that equation (9) is set upmax/dminSize it is related, and n is by dmax/dminSize system
About；Bubble diameter cumulative probability density g (n) is constructed to investigate n and dmax/dminInfluence to equation (9) establishment condition, enables bubble
Particle-size accumulation probability density g (n) are as follows:
Draw g (n)~n relation curve；Acquisition ensure equation (9) set up n can value range and dmax/dminPass
System；
Take the equal sign condition of inequality (16), it may be assumed that
M and n are determined by formula (5) and (18), and then d is established by equation (2)32Basic mathematic model；Its result is as follows:
(2) theoretical based on Kolmogorov-Hinze, construct micro-interface strengthening reactor largest air bubbles diameter dmax, it is minimum
Bubble diameter dminRelationship between reactor parameter；
For ultra-fine bubble system, the rupture of bubble and the formation of new bubble betide the biggish bubble breaking area ε,
Since there are efficiencies to gas-liquid interface transmitting energy for turbulence vortex, the minimum turbulence vortex scale of bubbles burst can be made to be
11.4~31.4 times of Kolmogorov scale, it is assumed that this multiplying power is 11.4, is greater than its ruler since turbulence vortex is only capable of broken diameter
The bubble of degree, therefore, bubble diameter minimum value dminIt is consistent with the turbulence vortex scale, it may be assumed that
dmin=11.4 (μL/ρL)0.75ε-0.25 (21)
Based on Kolmogorov-Hinze theory, largest air bubbles diameter dmaxIt is determined by following formula (22):
dmax=ε-2/5(σLWecrit/2ρL)3/5 (22)
Wherein, ε is energy absorbing device；μLFor hydrodynamic viscosity；σLFor surface tension of liquid；ρLFor fluid density；
WecritFor the critical weber number of bubble breaking；
The critical weber number We of bubble breaking used by difference is studiedcritIt is different.This is mainly weber number and bubble week
The flow pattern enclosed is related, and the more difficult quantitative description of flow pattern.Resonance theory in the present invention based on bubble breaking determines Wecrit:
Wherein, α2For bubble volume modulus, α2=2,3 ...；Work as α2Bigger, bubble high frequent vibration is fiercer, and bubble is got over
It is small, α is selected for ultra-fine bubble particles2=2, i.e. Wecrit=1.24；
At this time:
dmax=0.75 (σL/ρL)0.6ε-0.4 (24)
Preferably, the energy absorbing device ε is obtained in the following way:
Step 100: being micro-interface strengthening reactor by the computation partition of the total energy absorbing device ε of micro-interface strengthening reactor
The summation of interior three different zones energy absorbing devices, the energy absorbing device ε including reactor body area bubbling areaR, gas-liquid is broken
The ε in areamixAnd the ε in gas liquid outlet areapl；
Step 110: where the energy absorbing device ε of reactor body area bubbling areaRIt calculates in the following way:
In gas reactor sparging process, do work according to bubble to system, εRIt indicates are as follows:
Wherein, QGFor ventilation volume flow, m in reactor3/s；S0For cross-sectional reactor area, m2；
Step 120: calculating the ε of gas-liquid fracture areamix:
Based on εmixTraditional counting model, it is assumed that gas-liquid mixed is adiabatic process and ignores liquid potential variation, ignores gas
Mass flow, and the unit of energy absorbing device is made to be unified for W/Kg, it is as follows to obtain calculation formula:
Wherein, LmixFor bubble breaking section length, m；P0、P1Respectively bubble breaking area Inlet fluid static pressure and outlet gas-liquid
Mixture pressure, Pa；λ1For the ratio between gas-liquid volume flow: K1For the ratio of nozzle diameter and bubble breaking area diameter, K1=DN/
D1；S1For bubble breaker cross-sectional area, m2；ρLFor fluid density, kg/m3；QLFor liquid circulation volume flow in reactor,
m3/s；
λ1=QG/QL (27)
Step 121: calculating bubble breaking area Inlet fluid static pressure P0And outlet gas-liquid mixture pressure P1:
Ignore bubble breaking area pipe friction loss, then:
Wherein, φmixFor bubble breaking area gas holdup, it is calculated as follows:
Ignore energy loss at pipe friction and nozzle, according to conservation of energy principle, the practical ENERGY E obtained of system0Are as follows:
That is:
It is obtained by formula (28) (31):
Step 122: calculating bubble breaking section length Lmix:
LmixIt is determined, or is determined as follows by measurement gas-liquid fracture area inside pipe wall pressure jump:
Wherein: PHFor air pressure above gas-liquid fracture area, Pa；ρMZFor gas-liquid mixture density in gas-liquid fracture area, Kg/m3；vN
For the effluxvelocity of jet orifice, m/s；Ue,maxFor the maximum return speed of gas-liquid fracture area vortex, m/s；
PHIt is pushed away by Bernoulli equation:
PH≈PG0 (34)
In formula, PG0For supply gas pressure, Pa；
ρMZIt is calculate by the following formula:
ρMZ=ρGφmix+ρL(1-φmix)≈ρL(1-φmix) (35)
In formula, ρGFor gas density, g/m3；
Consider the influence of gas-liquid fracture area gas-liquid mixture flow velocity, Ue,maxFor jet orifice jet velocity and gas-liquid fracture area gas
The Vector modulation of liquid mixture flow velocity as a result, using following formula calculate Ue,max:
Formula (34) (36) are substituted into formula (33), and can be obtained after abbreviation:
Obtain reactor bubble breaker length Lb, and L is calculated according to formula (37)mix；
1. working as Lmix<LbWhen, with the calculated result of formula (37) for LmixActual numerical value；
2. working as Lmix≥LbWhen, illustrate that jet energy approximation consumes in bubble breaker region completely, then:
Lmix=Lb (38)
Step 130: calculating the ε in gas liquid outlet areapl；
Assuming that bubble is evenly distributed state in gas liquid outlet area, the energy dissipation rate ε in this regionplIt is calculated by following formula:
Structure of reactor guarantees λ when designing1Adjustable extent is sufficiently large, is determined by experiment between reactor elementary structure parameter
Relationship be K1=0.5, Lb=13D1；It substitutes into aforementioned corresponding expression formula and abbreviation can obtain:
Step 200: determining εR、εmixAnd εplRespective numerical values recited；
Step 210: it is equal to the gas-liquid flow equilibrium principle of bubble breaking area outlet according to the gas-liquid flow for entering reactor,
It obtains:
In formula, CLFor based on effective volume π D in reactor0 2H0/ 4 liquid circulation multiple, i.e., liquid circulation is total per hour
The ratio of volume and reactor effective volume；u1Gas-liquid mixture linear velocity, m/s are exported for bubble breaker；λ1Value 0.1~
0.5；
From formula (43):Then u1When increase, cross-sectional reactor area S0Also increase；Convolution (25) can
Know, at this time εRReduce；It is compared for the energy absorbing device to reactor different zones, it is assumed that u1=3.0m/s；CL=20；H0
=1.5m；It can be obtained by formula (43), work as λ1When=0.1~0.5:
D0≈19D1 (44)
Selected D1Numerical value calculates simultaneously energy absorbing device of the paralleling reactor different zones under different spray nozzles liquid speed, determines
With the energy absorbing device ε of gas-liquid fracture areamixIt compares, reactor body area, the energy absorbing device in gas liquid outlet area are negligible not
Meter, i.e. εmix≈ε；The then mathematical relationship between the energy absorbing device ε and structure of reactor parameter of entire reactor, can be by formula
(26) it calculates and determines, it may be assumed that
The second object of the present invention is to provide the bubble scale structure effect regulation-control model of above-mentioned modeling method building.
Specifically, the bubble scale structure effect regulation-control model is as follows:
dmin=11.4 (μL/ρL)0.75ε-0.25 (21)
dmax=0.75 (σL/ρL)0.6ε-0.4 (24)
In formula, QLFor liquid circulation volume flow in reactor；LmixFor bubble breaking section length；D1For bubble breaking Guan Zhi
Diameter；λ1For the ratio between gas-liquid volume flow, λ1=QG/QL；QGFor ventilation volume flow in reactor；P0For bubble breaker inlet
The static pressure of liquid；P1Gas-liquid mixture pressure is exported for bubble breaking area；ε is energy absorbing device；μLFor hydrodynamic viscosity；σL
For surface tension of liquid；ρLFor fluid density.
Another object of the present invention is to provide application of the above method in reactor design.
According to required bubble Sauter average diameter d32Numerical value imitates the anti-of regulation-control model establishment by above-mentioned bubble scale structure
Answer device structural parameters, physical parameter, operating condition and bubble Sauter average diameter d32Relationship carries out structural parameters to reactor
With the design of physical parameter so that structure of reactor parameter and physical parameter meet bubble scale structure effect regulation-control model determine number
Value relationship.
Method of the invention is suitable for micro-interface strengthening reactor, and core is bubble breaker.Bubble breaker
Principle is that gas phase entrained by high-speed jet mutually hits progress energy transmission, makes bubble breaking, structural parameters have Lb、D1, in detail
Fine texture is shown in attached drawing 1, and in addition to this other structures parameter of the reactor has D0、H0, specific reactor structure related content is
It is published in the patent CN10618766A of inventor's earlier application, is repeated no more in the present invention.
The invention has the following beneficial effects:
(1) regulation-control model is imitated using the bubble scale structure that modeling method of the invention constructs, constructs dmax、dminAnd d32's
Direct calculated relationship, and d is no longer obtained by the way of experimental fit32Specific value, greatly reduce and answer in the reactor
The error that used time generates；
(2) d of existing method building32Model is directed to bubbling reactor (Bubble column, BC) more and is bubbled
Gas-liquid system or jet pump (gas-liquid in stirred tank reactor (Bubbling-stirred reactor, BSR)
Jet bump, GLJB) in Air-Water system.And for industrial micro-interface reactor (MIR), then it is not necessarily applicable in, reason
Be: 1. bubble breaking mechanism is different from above-mentioned reactor in MIR；2. may relate to high viscosity in industrial gas-liquid reaction system
Liquid, and there is no consider liquid viscosity to d for the prior art (such as formula 46)32Influence；And utilize modeling method structure of the invention
The bubble scale structure effect regulation-control model built is applicable to industrial micro-interface reactor (MIR), and versatility is more preferable；
(3) regulation-control model is imitated using the bubble scale structure that modeling method of the invention constructs, it can be further by adjusting anti-
Structural parameters and the operating parameter of device are answered to obtain the maximization target of reaction process efficiency object effect, or in given reaction target
Under (task) and energy and material consumption, efficient structure of reactor is designed.
Detailed description of the invention
Fig. 1 is a kind of structure of reactor schematic diagram, for illustrating application of the modeling method of the invention in reactor assembly；
Wherein 1- reactor, valve before 2- is pumped, 3- circulating pump, valve after 4- is pumped, 5- fluid flowmeter, 6- heat exchanger, 7- bubble breaker, 8-
Temperature measurer, 9- down-comer, 10- gas trap, 11- gas flowmeter, 12- gas phase entrance, 13- pressure gauge, 14- liquidometer；D0It is anti-
Answer device diameter, H0Initial liquid level height in reactor, D1Bubble breaking pipe diameter, LbBubble breaking section length；
Fig. 2 is n and dmax/dminTo the influence curve figure of bubble diameter cumulative probability density；
Fig. 3 is the prior art and comparison of computational results curve graph of the invention.
Specific embodiment
Embodiment 1
The present embodiment illustrates the modeling method of bubble scale model of the present invention.
Method of the invention, comprising:
(1) with micro-interface strengthening reactor largest air bubbles diameter dmaxWith minimum bubble diameter dminFor independent variable, bubble
Sauter average diameter d32For dependent variable, d is establishedmax、dminAnd d32Between relationship；Specific step is as follows:
If x, m, n be respectively bubble diameter in reactor gas-liquid system, bubble diameter geometry natural logrithm mean value and
Standard deviation obtains the probability density function of bubble diameter x:
Bubble diameter meets bubble Sauter average diameter d when this distribution32Are as follows:
d32=exp (m+2.5n2) (2)
Bubble diameter x is in logarithm normal distribution, therefore the mathematic expectaion (arithmetic mean of instantaneous value) of lnx are as follows:
Bubble diameter probability density figure is drawn according to the probability density function of bubble diameter x, whenWhen, probability density is most
Greatly；First derivative i.e. herein is 0:
Equation (3) substitution (1) is obtained into equation (4):
It can be obtained by (3), (4):
Due to:
It can be obtained after equation (1) is substituted into (6) and abbreviation:
It enables:Then above formula simplifies are as follows:
Equation (8) left end is error function, with standard error function the difference is that the difference of the limit of integration, formula (5) are divided
Above-mentioned range of integration is not substituted into, and can be obtained after converting standard error function for equation (8):
In equation (9), erf () is error function；
For the error function of following form:
Series expansion can be used in its approximate calculation.Classical Taylor series expansion, convergence rate is compared with Chebyshev
(Chebyshev) series is slow, but has relatively simple quantic, therefore is widely adopted.For engineering research,
Acquisition form is relatively simple, the succinct expression that error can be received by engineering field, without pursuing error in mathematical meaning
Minimum accurate expression.Taylor series expansion is different according to the value range of error function independent variable and uses different forms,
Such as:
As z≤4, erf (z) is deployable are as follows:
Due to:
Work as dmax/dminWhen being 1000:
And according to equation (11):
Therefore, when:
That is:
When, equation (9) is approximate to be set up；
In addition, condition and n and d that equation (9) is set upmax/dminSize it is related, and n is by dmax/dminSize system
About；Bubble diameter cumulative probability density g (n) is constructed to investigate n and dmax/dminInfluence to equation (9) establishment condition, enables bubble
Particle-size accumulation probability density g (n) are as follows:
G (n)~n relation curve is drawn, as shown in Figure 2；For determining gas-liquid system, bubble size distribution is (by m and n
Determine) by dmax/dminInfluence；Work as dmax/dminOne timing, n should uniquely determine value, i.e. bubble size distribution is unique.
As shown in Figure 2: ensure equation (9) set up n can value range and dmax/dminIt is closely related, but as n → 0, n and dmax/
dminIt is unrelated；
Take the equal sign condition of inequality (16), it may be assumed that
M and n are determined by formula (5) and (18), and then d is established by equation (2)32Basic mathematic model；Its result is as follows:
(2) theoretical based on Kolmogorov-Hinze, construct micro-interface strengthening reactor largest air bubbles diameter dmax, it is minimum
Bubble diameter dminRelationship between reactor parameter；
For ultra-fine bubble system, the rupture of bubble and the formation of new bubble betide the biggish bubble breaking area ε,
Since there are efficiencies to gas-liquid interface transmitting energy for turbulence vortex, the minimum turbulence vortex scale of bubbles burst can be made to be
11.4~31.4 times of Kolmogorov scale, it is assumed that this multiplying power is 11.4, is greater than its ruler since turbulence vortex is only capable of broken diameter
The bubble of degree, therefore, bubble diameter minimum value dminIt is consistent with the turbulence vortex scale, it may be assumed that
dmin=11.4 (μL/ρL)0.75ε-0.25 (21)
Based on Kolmogorov-Hinze theory, largest air bubbles diameter dmaxIt is determined by following formula (22):
dmax=ε-2/5(σLWecrit/2ρL)3/5 (22)
Wherein, ε is energy absorbing device；μLFor hydrodynamic viscosity；σLFor surface tension of liquid；ρLFor fluid density；
WecritFor the critical weber number of bubble breaking；
The critical weber number We of bubble breaking used by difference is studiedcritIt is different.This is mainly weber number and bubble week
The flow pattern enclosed is related, and the more difficult quantitative description of flow pattern.Resonance theory in the present invention based on bubble breaking determines Wecrit:
Wherein, α2For bubble volume modulus, α2=2,3 ...；Work as α2Bigger, bubble high frequent vibration is fiercer, and bubble is got over
It is small, α is selected for ultra-fine bubble particles2=2, i.e. Wecrit=1.24；
At this time:
dmax=0.75 (σL/ρL)0.6ε-0.4 (24)
Wherein, energy absorbing device ε is calculated in the following way:
Wherein, step 100: being micro-interface reinforcing by the computation partition of the total energy absorbing device ε of micro-interface strengthening reactor
The summation of three different zones energy absorbing devices in reactor, the energy absorbing device ε including reactor body area bubbling areaR, gas
The ε of liquid fracture areamixAnd the ε in gas liquid outlet areapl；
Step 110: where the energy absorbing device ε of reactor body area bubbling areaRIt calculates in the following way:
In gas reactor sparging process, do work according to bubble to system, εRIt indicates are as follows:
Wherein, QGFor ventilation volume flow, m in reactor3/s；S0For cross-sectional reactor area, m2；
Step 120: calculating the ε of gas-liquid fracture areamix:
Based on εmixTraditional counting model, it is assumed that gas-liquid mixed is adiabatic process and ignores liquid potential variation, ignores gas
Mass flow, and the unit of energy absorbing device is made to be unified for W/Kg, it is as follows to obtain calculation formula:
Wherein, LmixFor bubble breaking section length, m；P0、P1Respectively bubble breaking area Inlet fluid static pressure and outlet gas-liquid
Mixture pressure, Pa；λ1For the ratio between gas-liquid volume flow: K1For the ratio of nozzle diameter and bubble breaking area diameter, K1=DN/
D1；S1For bubble breaker cross-sectional area, m2；ρLFor fluid density, kg/m3；QLFor liquid circulation volume flow in reactor,
m3/s；
λ1=QG/QL (27)
Step 121: calculating bubble breaking area Inlet fluid static pressure P0And outlet gas-liquid mixture pressure P1:
Ignore bubble breaking area pipe friction loss, then:
Wherein, φmixFor bubble breaking area gas holdup, it is calculated as follows:
Ignore energy loss at pipe friction and nozzle, according to conservation of energy principle, the practical ENERGY E obtained of system0Are as follows:
That is:
It is obtained by formula (28) (31):
Step 122: calculating bubble breaking section length Lmix:
LmixIt is determined, or is determined as follows by measurement gas-liquid fracture area inside pipe wall pressure jump:
Wherein: PHFor air pressure above gas-liquid fracture area, Pa；ρMZFor gas-liquid mixture density in gas-liquid fracture area, Kg/m3；vN
For the effluxvelocity of jet orifice, m/s；Ue,maxFor the maximum return speed of gas-liquid fracture area vortex, m/s；
PHIt is pushed away by Bernoulli equation:
PH≈PG0 (34)
In formula, PG0For supply gas pressure, Pa；
ρMZIt is calculate by the following formula:
ρMZ=ρGφmix+ρL(1-φmix)≈ρL(1-φmix) (35)
In formula, ρGFor gas density, g/m3；
Consider the influence of gas-liquid fracture area gas-liquid mixture flow velocity, Ue,maxFor jet orifice jet velocity and gas-liquid fracture area gas
The Vector modulation of liquid mixture flow velocity as a result, using following formula calculate Ue,max:
Formula (34) (36) are substituted into formula (33), and can be obtained after abbreviation:
Obtain reactor bubble breaker length Lb, and L is calculated according to formula (37)mix；
1. working as Lmix<LbWhen, with the calculated result of formula (37) for LmixActual numerical value；
2. working as Lmix≥LbWhen, illustrate that jet energy approximation consumes in bubble breaker region completely, then:
Lmix=Lb (38)
Step 130: calculating the ε in gas liquid outlet areapl；
Assuming that bubble is evenly distributed state in gas liquid outlet area, the energy dissipation rate ε in this regionplIt is calculated by following formula:
Structure of reactor guarantees λ when designing1Adjustable extent is sufficiently large, is determined by experiment between reactor elementary structure parameter
Relationship be K1=0.5, Lb=13D1；It substitutes into aforementioned corresponding expression formula and abbreviation can obtain:
Step 200: determining εR、εmixAnd εplRespective numerical values recited；
Step 210: it is equal to the gas-liquid flow equilibrium principle of bubble breaking area outlet according to the gas-liquid flow for entering reactor,
It obtains:
In formula, CLFor based on effective volume π D in reactor0 2H0/ 4 liquid circulation multiple, i.e., liquid circulation is total per hour
The ratio of volume and reactor effective volume；u1Gas-liquid mixture linear velocity, m/s are exported for bubble breaker；λ1Value 0.1~
0.5；
From formula (43):Then u1When increase, cross-sectional reactor area S0Also increase；Convolution (25) can
Know, at this time εRReduce；It is compared for the energy absorbing device to reactor different zones, it is assumed that u1=3.0m/s；CL=20；H0
=1.5m；It can be obtained by formula (43), work as λ1When=0.1~0.5:
D0≈19D1 (44)
Selected D1Numerical value calculates simultaneously energy absorbing device of the paralleling reactor different zones under different spray nozzles liquid speed, determines
With the energy absorbing device ε of gas-liquid fracture areamixIt compares, reactor body area, the energy absorbing device in gas liquid outlet area are negligible not
Meter, i.e. εmix≈ε；The then mathematical relationship between the energy absorbing device ε and structure of reactor parameter of entire reactor, can be by formula
(26) it calculates and determines, it may be assumed that
Embodiment 2
The present embodiment illustrates the model of the building of modeling method described in embodiment 1 in dioxy by taking reactor shown in FIG. 1 as an example
Change the application in carbon and aqueous systems reactor.The structure of reactor of Fig. 1 can be the structure of existing micro-interface strengthening reactor, only adopt
Parameter designing is carried out with method of the invention, the structure of reactor is repeated no more in the present invention.
The bubble scale structure effect regulation-control model constructed according to embodiment 1 is as follows:
dmin=11.4 (μL/ρL)0.75ε-0.25 (21)
dmax=0.75 (σL/ρL)0.6ε-0.4 (24)
In formula, QLFor liquid circulation volume flow in reactor；LmixFor bubble breaking section length；D1For bubble breaking Guan Zhi
Diameter；λ1For the ratio between gas-liquid volume flow, λ1=QG/QL；QGFor ventilation volume flow in reactor；P0For bubble breaker inlet
The static pressure of liquid；P1Gas-liquid mixture pressure is exported for bubble breaking area；ε is energy absorbing device；μLFor hydrodynamic viscosity；σL
For surface tension of liquid；ρLFor fluid density.
The model that embodiment 3 is selected mainly considers LmixLess than LbThe case where, because opposite situation is not common, compare pole
End.Structure of reactor parameter also needs to meet: λ1=0.1~0.5, K1=0.5, Lb=13D1；
For carbon dioxide and aqueous systems, work as operating condition are as follows: QL=2000L/h (5.56 × 10-4m3/ s), gas flow
QG=0.2QL, T=298K, PG0=1atm；And in this system liquid phase physical parameter are as follows: ρL=1000kg/m3, μL=8.9 ×
10-4Pas, σL=7.197 × 10-4N/m；Reactor bubble breaking pipe diameter D1=0.02m；E0The energy of expression system input
Amount, i.e. rated power on circulating pump nameplate, take E0=1000W.
The bubble Sauter average diameter d that can be calculated according to operating condition and above-mentioned model32=0.426mm, and pass
The bubble mean diameter obtained under system process conditions is 1mm or so.It can be seen that the bubble mean diameter of this reactor is than logical
The bubble mean diameter that paradoxical reaction device generates is small more than one times.
Levenspiel thinks that the Global reaction Rate of heterogeneous system can be expressed from the next:
Gas liquid reaction macroscopic view rate equation after abbreviation can simplify are as follows:
Tables 1 and 2 is the comparative situation of the parameters under same system different-grain diameter:
The parameter that 1 different-grain diameter drag formula of table calculates
Three kinds of resistances (air film, liquid film, intrinsic) that 2 different-grain diameter drag formula of table calculates
As shown in table 1, table 2, when bubble diameter becomes original 1/10 and 1/2, gas liquid film integral is not increased
About 467 times and 9 times, Global reaction Rate increases about 4 times and 2 times respectively, and reacts resistance and be gradually transitioned by liquid film controlled
By intrinsic reaction draught control.It can be seen that microbubble scale enhances gas-liquid mass transfer rate really.
Embodiment 3
The present embodiment illustrates the model of the building of modeling method described in embodiment 1 in sky by taking reactor shown in FIG. 1 as an example
Application in air-water system reactor, with existing prediction d32The superior place that model is compared.
For Air-Water system, the prior art generally uses following formula predictions d32:
d32=0.65dmax (46)
Construct the d of above formula and the method for the present invention building32Predictor formula calculated result contrast curve chart, as shown in Figure 3.By scheming
3 it is found that (when ε is less than 10 (W/kg), the calculated result of this research and use formula (46) is basic when energy absorbing device ε is sufficiently small
Unanimously；When ε is gradually increased, the two prediction result has different: for Air-Water system, when ε is greater than 10 (W/kg),
Formula (46) acquired results are relatively small, but error between the two is acceptable.
Formula (46) is disadvantageous in that: 1, the coefficient in the equation is obtained based on experimental fit, can not be associated with
Reactor design parameter；2, d in equationmaxMathematic(al) representation be to be obtained based on isotropic turbulence theory, and the theory is suitable
Premise is energy absorbing device infinity, at this point, influence of the liquid viscosity to Air Bubble Size can be ignored.In recent years, entirely
The bubble size distribution existing research of power spectrum, but form is more complex, wherein also there are some empirical parameters, therefore there is still a need for into one
Walk the reasonable determination of reduced form and model parameter.
And method of the invention is also based on isotropic turbulence theory and obtains, but passes through the probability to bubble size distribution
Statistical analysis, the relational expression obtained by reasonable Mathematical treatment are associated with bubble in this pair of of industrial reactor of liquid viscosity
The physical parameter that size has a major impact can be used as the basis of further industrial application.
Claims (3)
1. a kind of micro-interface strengthening reactor bubble scale structure imitates regulation-control model modeling method characterized by comprising
(1) with micro-interface strengthening reactor largest air bubbles diameter dmaxWith minimum bubble diameter dminFor independent variable, bubble Sauter
Average diameter d32For dependent variable, d is establishedmax、dminAnd d32Between relationship；Specific step is as follows:
If x, m, n are respectively the mean value and standard of bubble diameter in reactor gas-liquid system, bubble diameter geometry natural logrithm
Difference obtains the probability density function of bubble diameter x:
Bubble diameter meets bubble Sauter average diameter d when this distribution32Are as follows:
d32=exp (m+2.5n2) (2)
Bubble diameter x is in logarithm normal distribution, therefore the mathematic expectaion (arithmetic mean of instantaneous value) of lnx are as follows:According to
The probability density function of bubble diameter x draws bubble diameter probability density figure, whenWhen, probability density is maximum；I.e.
First derivative herein is 0:
Equation (3) substitution (1) is obtained into equation (4):
It can be obtained by (3), (4):
Due to:
It can be obtained after equation (1) is substituted into (6) and abbreviation:
It enables:Then above formula simplifies are as follows:
Equation (8) left end is error function, with standard error function the difference is that the difference of the limit of integration, by formula (5) generation respectively
Enter above-mentioned range of integration, and can be obtained after converting standard error function for equation (8):
In equation (9), erf () is error function；
For the error function of following form:
Approximate calculation is carried out using Taylor series expansion, Taylor series expansion is different according to the value range of error function independent variable
And different forms is used, as z≤4, erf (z) is deployable are as follows:
Due to:
Work as dmax/dminWhen being 1000:
And according to equation (11):
Therefore, when:
That is:
When, equation (9) is approximate to be set up；
In addition, condition and n and d that equation (9) is set upmax/dminSize it is related, and n is by dmax/dminSize restriction；Structure
Bubble diameter cumulative probability density g (n) is built to investigate n and dmax/dminInfluence to equation (9) establishment condition, enables bubble diameter
Cumulative probability density g (n) are as follows:
Draw g (n)~n relation curve；Acquisition ensure equation (9) set up n can value range and dmax/dminRelationship；
Take the equal sign condition of inequality (16), it may be assumed that
M and n are determined by formula (5) and (18), and then d is established by equation (2)32Basic mathematic model；Its result is as follows:
(2) theoretical based on Kolmogorov-Hinze, construct micro-interface strengthening reactor largest air bubbles diameter dmax, minimum bubble
Diameter dminRelationship between reactor parameter；
The minimum turbulence vortex scale that can make bubbles burst is 11.4~31.4 times of Kolmogorov scale, it is assumed that this multiplying power is
11.4, since turbulence vortex is only capable of the bubble that broken diameter is greater than its scale, bubble diameter minimum value dminWith the turbulence vortex
Scale is consistent, it may be assumed that
dmin=11.4 (μL/ρL)0.75ε-0.25 (21)
Based on Kolmogorov-Hinze theory, largest air bubbles diameter dmaxIt is determined by following formula (22):
dmax=ε-2/5(σLWecrit/2ρL)3/5 (22)
Wherein, ε is energy absorbing device；μLFor hydrodynamic viscosity；σLFor surface tension of liquid；ρLFor fluid density；WecritFor gas
Bubble is crushed critical weber number；
We is determined based on the resonance theory of bubble breakingcrit:
Wherein, ρGFor gas density；α2For bubble volume modulus, α2=2,3 ...；Work as α2Bigger, bubble high frequent vibration is fiercer,
Bubble selects α with regard to smaller, for ultra-fine bubble particles2=2, i.e. Wecrit=1.24；
At this time:
dmax=0.75 (σL/ρL)0.6ε-0.4 (24)
Bubble Sauter average diameter d is calculated according to formula (20), (21), (24)32。
2. the method according to claim 1, wherein the energy absorbing device ε is obtained in the following way:
Step 100: being three in micro-interface strengthening reactor by the computation partition of the total energy absorbing device ε of micro-interface strengthening reactor
The summation of a different zones energy absorbing device, the energy absorbing device ε including reactor body area bubbling areaR, gas-liquid fracture area
εmixAnd the ε in gas liquid outlet areapl；
Step 110: where the energy absorbing device ε of reactor body area bubbling areaRIt calculates in the following way:
In gas reactor sparging process, do work according to bubble to system, εRIt indicates are as follows:
Wherein, QGFor ventilation volume flow, m in reactor3/s；S0For cross-sectional reactor area, m2；
Step 120: calculating the ε of gas-liquid fracture areamix:
Based on εmixTraditional counting model, it is assumed that gas-liquid mixed is adiabatic process and ignores liquid potential variation, ignores gaseous mass
Flow, and the unit of energy absorbing device is made to be unified for W/Kg, it is as follows to obtain calculation formula:
Wherein, LmixFor bubble breaking section length, m；P0、P1Respectively bubble breaking area Inlet fluid static pressure and outlet gas-liquid mixed
Object pressure, Pa；λ1For the ratio between gas-liquid volume flow: K1For the ratio of nozzle diameter and bubble breaking area diameter, K1=DN/D1；S1
For bubble breaker cross-sectional area, m2；ρLFor fluid density, kg/m3；QLFor liquid circulation volume flow, m in reactor3/s；
λ1=QG/QL (27)
Step 121: calculating bubble breaking area Inlet fluid static pressure P0And outlet gas-liquid mixture pressure P1:
Ignore bubble breaking area pipe friction loss, then:
Wherein, φmixFor bubble breaking area gas holdup, it is calculated as follows:
Ignore energy loss at pipe friction and nozzle, according to conservation of energy principle, the practical ENERGY E obtained of system0Are as follows:
That is:
It is obtained by formula (28) (31):
Step 122: calculating bubble breaking section length Lmix:
LmixIt is determined, or is determined as follows by measurement gas-liquid fracture area inside pipe wall pressure jump:
Wherein: PHFor air pressure above gas-liquid fracture area, Pa；ρMZFor gas-liquid mixture density in gas-liquid fracture area, Kg/m3；vNTo penetrate
The effluxvelocity of head piece, m/s；Ue,maxFor the maximum return speed of gas-liquid fracture area vortex, m/s；
PHIt is pushed away by Bernoulli equation:
PH≈PG0 (34)
In formula, PG0For supply gas pressure, Pa；
ρMZIt is calculate by the following formula:
ρMZ=ρGφmix+ρL(1-φmix)≈ρL(1-φmix) (35)
In formula, ρGFor gas density, g/m3；
Consider the influence of gas-liquid fracture area gas-liquid mixture flow velocity, Ue,maxIt is mixed for jet orifice jet velocity and gas-liquid fracture area gas-liquid
Close logistics speed Vector modulation as a result, using following formula calculating Ue,max:
Formula (34) (36) are substituted into formula (33), and can be obtained after abbreviation:
Obtain reactor bubble breaker length Lb, and L is calculated according to formula (37)mix；
1. working as Lmix<LbWhen, with the calculated result of formula (37) for LmixActual numerical value；
2. working as Lmix≥LbWhen, illustrate that jet energy approximation consumes in bubble breaker region completely, then:
Lmix=Lb (38)
Step 130: calculating the ε in gas liquid outlet areapl；
Assuming that bubble is evenly distributed state in gas liquid outlet area, the energy dissipation rate ε in this regionplIt is calculated by following formula:
Structure of reactor guarantees λ when designing1Adjustable extent is sufficiently large, is determined by experiment the pass between reactor elementary structure parameter
System is K1=0.5, Lb=13D1；By K1Specific value substitute into formula (31), (32), (37) and abbreviation can obtain:
Step 200: determining εR、εmixAnd εplRespective numerical values recited；
Step 210: being equal to the gas-liquid flow equilibrium principle of bubble breaking area outlet according to the gas-liquid flow for entering reactor, obtain
It arrives:
In formula, CLFor based on effective volume π D in reactor0 2H0/ 4 liquid circulation multiple, i.e. liquid circulation total volume per hour
With the ratio of reactor effective volume；u1Gas-liquid mixture linear velocity, m/s are exported for bubble breaker；λ1Value 0.1~0.5；
From formula (43):Then u1When increase, cross-sectional reactor area S0Also increase；Convolution (25) it is found that this
When εRReduce；It is compared for the energy absorbing device to reactor different zones, it is assumed that u1=3.0m/s；CL=20；H0=
1.5m；It can be obtained by formula (43), work as λ1When=0.1~0.5:
D0≈19D1 (44)
Selected D1Numerical value calculates simultaneously energy absorbing device of the paralleling reactor different zones under different spray nozzles liquid speed, determining and gas-liquid
The energy absorbing device ε of fracture areamixIt compares, reactor body area, the energy absorbing device in gas liquid outlet area are negligible, i.e. εmix
≈ε；The then mathematical relationship between the energy absorbing device ε and structure of reactor parameter of entire reactor can be calculated true by formula (26)
It is fixed, it may be assumed that
。
3. a kind of reactor designed using 2 the method for claims 1 or 2.
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| CN109684769B (en) * | 2019-01-09 | 2023-06-13 | 南京大学 | Modeling method of bubble scale regulation model under MIHA pure pneumatic operation condition |
| CN109806815B (en) * | 2019-01-14 | 2020-10-30 | 浙江大学 | Method for detecting gas-liquid dispersion state of jet bubbling reactor based on liquid velocity fluctuation |
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