CN110083917A - A kind of gas phase-drop phase bidirectional couple numerical computation method - Google Patents
A kind of gas phase-drop phase bidirectional couple numerical computation method Download PDFInfo
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Abstract
The invention belongs to fluid dynamics fields, disclose a kind of gas phase-drop phase bidirectional couple numerical computation method, and step (1) constructs the geometrical model and grid division of object construction, exports grid file；Step (2) reads in grid file, calculates the gas phase flow field parameter information at current time；Step (3) establishes calculation procedure and reads gas phase flow field parameter information file, calculates the movement phase transition parameter of the drop at current time；Step (4) calculates the influence domain radius of drop evaporation；Step (5) recalculates and updates quality source item, component source item, momentum source term and the energy source item that drop acts on gas phase flow field around, and on the grid being loaded within the scope of influence domain radius respectively；The gas phase flow field parameter information of step (6) corrected Calculation subsequent time.Real-time update of the present invention calculates amendment, improves the accuracy and reliability of result；The phenomenon that avoiding Severe distortion in grid makes iterative calculation be easier to restrain.
Description
Technical field
The invention belongs to fluid dynamics field more particularly to a kind of gas phase-drop phase bidirectional couple numerical computation methods.
Background technique
With being widely used for the nuclear power energy, guarantee that the safe and efficient operation of nuclear power generating equipment becomes core objective, either
By improving the drop separation efficiency in steam-water separator, pass through containment under water vapour mass dryness fraction or accident conditions to improve
Spray system sprays fine drop, and to reduce temperature in containment, pressure and radioactive substance concentration, this is all steamed with liquid drop movement
Hair process is closely related.Since liquid drop movement evaporation process is the mistake of the multiple physical fields such as flow field, temperature field, concentration field coupling
Journey, physical phenomenon and mechanism are complex, and therefore, applied fluid dynamics calculation method simulates vapor-liquid two phases flowing as meter
Calculating gas phase-drop phase Flow Field Distribution includes that temperature field, moisture field, velocity field, pressure field, concentration of component distribution etc. have provided
Effect means.
But there are still some problems in the method for numerical simulation of the vapor-liquid two phases flowing in currently available technology, such as greatly
Mostly it is that drop evaporation process is calculated based on gas phase-drop phase unidirectional couplings model, that is, ignores drop evaporation for office around
The influence of portion's gas phase flow field parameter, the environment gas phase parameter around drop are chosen for the parameter of infinite point or incoming flow always,
Therefore, cause to change using the gas and liquid phase characterisitic parameter of this roughization numerical result assumed and actual evaporation process
Between there is relatively large deviation, especially run in equipment such as container spray, steam-water separator, fuel spray, spray scrubbers
Cheng Zhong, more for amount of droplets, the distance between drop is smaller, the operating condition of drop phase density larger (i.e. dense drop stream), liquid
Drop evaporation is more violent, produces a large amount of water vapours and enters in local gaseous environment around, ignores drop at this time to its nearly table
The influence of the gas phase flow field Parameters variation in face, when calculating drop parameter using the gas phase flow field parameter of infinite point, it is clear that can make
Deviation between calculated result and actual result further increases, and result reliability is not high.Although having for high temperature gas cooled reactor
It is used in the numerical simulation of steam-water separator and couples the calculation method of iterative solution between gas-liquid two-phase, but how established out more
Reasonable gas phase-drop phase tow-way coupling model obtains more accurate, reliable numerical simulation result still in exploration.
Vapor-liquid two phases in the prior art flow method for numerical simulation, most of to be built upon liquid drop movement evaporation unidirectionally
It is calculated on the basis of coupling model, i.e. the parameter of drop surrounding environmental gases is selected as the ginseng of infinite point or incoming flow
Number, not accounting for gas phase flow field parameter in the certain influence area of surrounding in drop evaporation process includes flow velocity field, temperature field
With the influence of the variations such as concentration field.However, drop is usually interior movement in a limited space, and close in drop under actual conditions
It is constantly evaporated under the driving of concentration difference in the water vapour film on surface between water vapour component and environmental gas component, drop
The water vapour being evaporated is entered in surrounding environmental gases component by diffusion way, is will cause near drop near surface first
The flowing of water vapour fluid, and heat is mixed and exchanges with the environmental gas component flow near drop near surface, so that drop is close
The parameters such as the gaseous fluid temperature around surface changes, water vapour concentration of component change, in turn, drop near surface week
The variation for the gas phase flow field parameter enclosed will affect the further evaporation of drop again；As a result, drop near surface nearby be heated or
Cooling gaseous fluid, against diffusion and thermally conductive or convection current mode surface constantly remote with drop around gaseous fluid into
One step mass-and heat-transfer.In entire drop evaporation process, the parameters such as droplet radius, drop temperature constantly change, surrounding gas phase stream
The parameters such as temperature, the water vapor concentration of body also constantly change, and influence each other between gas-liquid two-phase, all can be at each moment
Row bidirectional couple influence, until drop be evaporated completely or the water vapor concentration and ambient gas of droplet surface liquid film in water steam
Vapour concentration is consistent, reaches gas-liquid equilibrium again.Although having the calculating for high temperature gas cooled reactor steam-water separator numerical simulation
In method use gas-liquid two-phase between couple iteration calculation method, but how by the reciprocation between gas phase-drop more
Rationally, reliably it is added in gas phase-drop phase tow-way coupling model, establishes out gas phase-liquid more accurate, applied widely
Drop phase tow-way coupling model this study a question still have it is to be solved.
Summary of the invention
The high a kind of mutually two-way coupling of gas phase-drop of good, high reliablity that it is an object of the invention to open accuracys, stability
Close numerical computation method.
The object of the present invention is achieved like this: it comprises the following steps:
Step (1): the geometrical model and grid division of object construction are constructed, to be also directed to during grid division several
The wall area of what model and geometry change more violent texture surface area and carry out local mesh reflnement, then export
Grid file；
Step (2): starting fluid calculation software reads in grid file, selects computation model, calculate the gas phase at current time
Flow field parameter information generates gas phase flow field parameter information file；
Step (3): establish calculation procedure read gas phase flow field parameter information file, and obtain current time apart from drop
Gas phase flow field parameter at the position nr of center, n are positive integers, and r is the radius of drop, select liquid drop movement phase transition model, are calculated
The movement phase transition parameter of the drop at current time；
Step (4): the movement phase transition parameter and gas phase flow field parameter of the drop based on current time calculate drop evaporation
Influence domain radius Rif；
Step (5): the movement phase transition parameter and gas phase flow field parameter of the drop based on current time are recalculated and are updated
Drop acts on the quality source item S of gas phase flow field aroundm, component source item Si, momentum source term F and energy source item SE, and by it is above-mentioned more
Quality source item S after newm, component source item Si, momentum source term F and energy source item SEIt is loaded into shadow respectively according to distance weighting mode
Ring domain radius RifOn grid in range, make quality source item Sm, component source item Si, momentum source term F and energy source item SEDispersion load
In multiple grids in the domain of influence；
Step (6): the gas phase flow field parameter letter of subsequent time is calculated based on the computation model adjustment selected in step (2)
Breath；
Step (7): it repeats step (3) to step (6), constantly updates gas phase-drop phase Flow Field Distribution of subsequent time, directly
It is completed to all iterative steps.
The invention also includes:
1. the gas phase flow field parameter information in step (2) described in includes: density of gas phase ρg, gas phase flowing velocity u, gas phase
Temperature Tg, the pressure P of gas phaseg, fluid kinematic viscosity μg, flow field curl Ω, calculation expression isThe diffusion of steam
Coefficient Dv。
2. the movement phase transition parameter of the drop at the current time in step (3) described in includes: the acceleration a of drop, liquid
The speed v of drop, the position coordinates of drop, the temperature T of dropd, the pressure P of dropd, the density p of dropd, the viscosity, mu of dropd,
The specific heat at constant pressure c of dropp, the latent heat of vaporization γ of drop, the molal weight M of drop, the mixed gas in droplet surface liquid film
Density ps, the temperature of droplet surface and the gas phase temperature at drop centered correspond to TrAnd Tnr。
The gas phase flow field parameter at the position drop centered nr at the acquisition current time in the step (3) described in 3.
Process further include: establish KD searching algorithm and obtain distance objective drop xiM grid section at position within the scope of (n-1) r to nr
The space coordinate of point；The gas phase flow field parameter information at the position drop centered nr is obtained using apart from inverse ratio interpolation method
Fi；Interpolation scheme are as follows:
In above formula, ljIndicate the position vector x of i-th of dropiIt is European between the space coordinate of j-th of grid node
Distance；M is any integer in 1 to 8.
The liquid drop movement phase transition model in step (3) described in 4. are as follows:
In above formula, x is the position vector of drop, and ω is the rotation speed of drop, and v is the speed of drop, and T is the temperature of drop
Degree；G is acceleration of gravity, and R is gas constant；H is convection transfer rate, CMIt is torque coefficient, CDIt is Yi force coefficient, CMaIt is
Magnus lift coefficient, CSaIt is Sa Fuman lift coefficient, BM=(Ys-Y∞)/(1-Ys) it is mass transfer number, Sh=2.0+
0.6Re0.5Sc1/3It is sherwood number, Re=2 ρsvr/μgIt is Reynolds number, Sc=ν/DvIt is Schmidt number；λ1、λ2、λ3、λ4And λ5It is
Normalization coefficient, and
λ1=-15 ρg/16πρd；
λ2=3 ρf/(8ρdr+4ρgr)；
λ3=3 ρg(4ρd+2ρg)；
λ4=[1.615 (μd+2μg/3)2/(μd+μg)2(μgρg)0.5]/(ρdπr/3+ρgπr/6)；
λ5=2 (ρd-ρg)/(2ρd+ρg)。
The influence domain radius R in step (4) described in 5.ifCalculation formula:
In above formula, the temperature difference of the Δ T between drop phase and surrounding gas phase, t is time, Y∞For water vapour quality in gas phase point
Number, P is operating pressure, ξtIt is the correction factor of time, ξYIt is the correction factor of water vapour mass fraction, ξPIt is operating pressure
Correction factor.
The quality source item S in step (5) described in 6.m:
Component source item Si:
Energy source item SE:
Momentum source term F:
F=- ∑ (ma-FG)/Vcell；
In above formula, m is the quality of drop, VcellFor the volume of grid, FGFor the gravity of drop.
7. the gas phase in step (7)-drop phase Flow Field Distribution described in includes the temperature field of gas phase, gaseous pressure field, gas
The velocity field of phase, the water vapor concentration field in gas phase, the spatial position distribution of drop, the radius distribution of drop, the speed of drop
At least one of the temperature field of field and drop.
The invention has the benefit that
1, gas phase flow field parameter in the present invention at the position selected distance drop nr calculates drop parameter, and to nr range
Reasonable value is made local, real around drop for being calculated using the gas phase flow field parameter of infinite point or incoming flow
When gas phase flow field parameter it is more accurate, reliable, more accurate, reliable drop parameter knot can be calculated by substituting into drop model
Fruit makes numerical simulation result be more in line with reality；
2, the present invention real-time update influence domain radius and is loaded into the domain of influence in iterative process each time
Drop source item size carries out calculating amendment with the gas phase flow field parameter information to subsequent time, improves gas phase-drop phase flow field ginseng
The accuracy and reliability of number calculated result, makes numerical simulation result more closing to reality operating condition；
3, in the present invention by drop source item according to being loaded into apart from the inverse ratio method of weighting on the gas phase flow field grid in the domain of influence,
More conducively source item is added to evenly dispersedly in multiple grids around drop, makes on the gas phase flow field grid within the scope of the domain of influence
The source item size variation of load is more continuous, gentle, avoid due to source item is excessive in single grid and other grids around it
Interior source item causes the Severe distortion of gas phase quality in grid, momentum and Energy distribution for 0, or even the phenomenon that singular point occurs, makes to change
Generation calculating more easily restrains, numerical value computational stability is good, result is more accurate and reliable；
4, larger, evaporation that present invention is particularly suitable for dense drop streams or the temperature difference more acutely, between gas-liquid two-phase moves fast
The numerical simulation calculation under the operating conditions such as difference is larger is spent, can effectively solve the problem that two is alternate since the source item of bidirectional couple is larger, makes
The problem of being not easy convergence at calculating, has the characteristics that applied widely, computational accuracy is high；
5, it is combined using local mesh reflnement with nearest point interpolation method in the present invention, reduces the same of grid computing amount
When, guarantee computational accuracy；And using mesh point coordinate nearest around KD searching algorithm quick obtaining to target position, pass through
The gas phase flow field parameter information at object droplet position is obtained apart from inverse ratio interpolation method, not only greatly improves grid computing speed
Degree and guarantee computational accuracy, can be widely applied to containment spray system, steam-water separator, fuel spray system, spray washing
In the numerical simulation of drop evaporation behavior in the equipment running process such as tower.
Other features and advantages of the present invention will be illustrated in the following description, also, partly becomes from specification
It obtains it is clear that understand through the implementation of the invention.The objectives and other advantages of the invention can be by specification, right
Specifically noted structure is achieved and obtained in claim and attached drawing.
Detailed description of the invention
Fig. 1 is a kind of flow chart of gas phase-drop phase bidirectional couple numerical computation method；
Fig. 2 a is a kind of containment spray system device of gas phase-drop phase bidirectional couple numerical computation method embodiment
Overall structure scale diagrams；
Fig. 2 b is two-dimensional axial symmetric geometrical model structural schematic diagram；
Fig. 3 is drop evaporating state schematic diagram；
Fig. 4 a is traditional Lagrange drop source item loading method；
Fig. 4 b is the schematic illustration of drop source item loading method in the domain of influence；
During Fig. 5 is the spray that a kind of embodiment of gas phase-drop phase bidirectional couple numerical computation method is calculated
Temperature versus time curve figure；
During Fig. 6 is the spray that a kind of embodiment of gas phase-drop phase bidirectional couple numerical computation method is calculated
Pressure versus time curve figure；
During Fig. 7 is the spray that a kind of embodiment of gas phase-drop phase bidirectional couple numerical computation method is calculated
Water vapour mass fraction versus time curve figure；
Fig. 8 is that the wall surface of the container near zone of geometrical model carries out the structural schematic diagram of mesh refinement processing；
Fig. 9 is the parameter setting of specific injection drop and environment gas phase.
Specific embodiment
Further describe the present invention with reference to the accompanying drawing:
It is a kind of flow chart of gas phase-drop phase bidirectional couple numerical computation method such as Fig. 1；
Gas phase proposed by the present invention-drop phase bidirectional couple numerical computation method is achieved in that
S1: the geometrical model and grid division of object construction are constructed, grid file is exported；
S2: starting fluid calculation software reads in grid file, selects computation model, calculates the gas phase flow field ginseng at current time
Number information；
S3: establish calculation procedure read gas phase flow field parameter information file, and obtain current time apart from drop (i.e. liquid
Drop center) gas phase flow field parameter at the position nr, computation model is selected, the movement phase transition parameter of the drop at current time is calculated；
S4: the movement phase transition parameter and gas phase flow field parameter of the drop based on current time calculate the influence of drop evaporation
Domain radius Rif (i.e. drop evaporation process influence area range that gas phase flow field around it is had an impact, the abbreviation domain of influence)；
S5: the movement phase transition parameter and gas phase flow field parameter of the drop based on current time recalculate drop and act on
The quality source item S of surrounding gas phase flow fieldm, component source item Si, momentum source termEnergy source item SE, and by above-mentioned updated four
Source item is loaded into influence domain radius R respectivelyifOn grid in range；
S6: the gas phase flow field parameter information of subsequent time is calculated based on the computation model adjustment in the step S2；
The iterative process of step S3~S6 is repeated, to constantly update gas phase-drop phase Flow Field Distribution of subsequent time, until
All iterative steps are completed.
Optionally, in step s3, it establishes calculation procedure and reads gas phase flow field parameter information file, and obtain current time
The gas phase flow field parameter at the position drop nr, select computation model, calculate the drop at current time movement phase transformation ginseng
Number；Wherein, the liquid drop movement phase transition model includes following equation:
Wherein, amount to be asked is in the left side of above-mentioned equation, comprising: the position vector x of drop, the rotation speed ω of drop,
The speed v of drop, the radius r of drop, the temperature T of drop；
The right side physical quantity of equation includes:
1) gas phase flow field parameter information, comprising: density of gas phase ρg, gas phase flowing velocity u, the temperature T of gas phaseg, the pressure of gas phase
Power Pg, fluid kinematic viscosity μg, flow field curl Ω, calculation expression isThe diffusion coefficient D of steamv；
2) the movement phase transition parameter of the drop at current time, comprising: the acceleration a of drop, the speed v of drop, drop
Position coordinates, the temperature T of dropd, the pressure p of dropd, the density p of dropd, the viscosity, mu of dropd, the specific heat at constant pressure of drop
cp, the latent heat of vaporization γ of drop, the molal weight M of drop, the density p of the mixed gas in droplet surface liquid films, droplet surface
Temperature and the gas phase temperature at drop centered nr correspond to TrAnd Tnr；
3) constant, comprising: gravity acceleration g, gas constant R；
4) related coefficient calculated according to gas phase and drop parameter, comprising: evaporative condenser factor alpha, convection transfer rate h,
Torque coefficient CM, Yi force coefficient CD, Magnus lift coefficient CMa, Sa Fuman lift coefficient CSa, mass transfer number BM, calculation expression
ForSherwood number Sh, calculation expression Sh=2.0+0.6Re0.5Sc1/3, reynolds number Re, calculation expression
ForSchmidt number Sc, calculation expression are
5) normalization coefficient λ1~λ5, calculation expression is respectively as follows: λ1=-15 ρg/16πρd、λ2=3 ρf/(8ρdr+4ρgr)、
λ3=3 ρg(4ρd+2ρg)、λ4=[1.615 (μd+2μg/3)2/(μd+μg)2(μgρg)0.5]/(ρdπr/3+ρgπr/6)、λ5=2 (ρd-
ρg)/(2ρd+ρg)。
Optionally, in step s 4, the movement phase transition parameter and gas phase flow field parameter of the drop based on current time calculates
The influence domain radius R of drop evaporationif；Wherein, influence domain radius RifCalculation expression are as follows:
In formula, r is droplet radius, and the temperature difference of the Δ T between drop phase and surrounding gas phase, t is time, Y∞For water in gas phase
Quality of steam score (i.e. water vapor concentration), P are operating pressure, ξt、ξY、ξPRespectively time, water vapour mass fraction, work
The correction factor of pressure.
Optionally, in the step S5, quality source item Sm, component source item Si, momentum source termEnergy source item SEAccording to
Distance weighting mode is loaded on the grid within the scope of the domain of influence, makes quality source item Sm, component source item Si, momentum source termEnergy
Source item SEIn multiple grids that dispersion is loaded into the domain of influence respectively.
Optionally, in the step S5, the quality source item Sm, the component source item Si, the momentum source termInstitute
State energy source item SECalculation expression be respectively as follows:
In formula: m is the quality of drop,For the acceleration of drop, VcellFor the volume of grid, FGFor the gravity of drop；Its
In, component source item SiWith quality source item SmIt is identical.
Optionally, the gas phase-drop Flow Field Distribution includes: the temperature field (i.e. the Temperature Distribution of gas phase) of gas phase, gas phase
The pressure field pressure of gas phase (i.e. distribution), the velocity field (i.e. the flowing velocity distribution of gas phase) of gas phase, the water vapour in gas phase are dense
Spend the field mass fraction of vapour content (i.e. distribution), the spatial position distribution (i.e. liquid drop movement track) of drop, drop half
At least one of diameter distribution, the velocity field of drop and temperature field of drop.
Optionally, in step sl, when carrying out grid dividing to the geometrical model of object construction further include: be directed to geometry mould
The wall area of type and/or geometry change more violent texture surface area and carry out local mesh reflnement.
Optionally, in step s3, the process of the gas phase flow field parameter at the position drop nr at current time is obtained
Further include:
1) it establishes KD searching algorithm and obtains distance objective drop xiM grid node at position within the scope of (n-1) r~nr
Space coordinate；
2) the gas phase flow field parameter at target position (i.e. apart from the position drop nr) is obtained using apart from inverse ratio interpolation method
Information Fi；
Wherein, interpolation scheme are as follows:
In formula: ljIndicate the position vector x of i-th of dropiBetween the space coordinate of j-th of grid node it is European away from
From；M is any integer in 1 to 8.
In order to solve the problems in the existing technology, the present invention is based on the movement of drop in a limited space to evaporate
Journey establishes a kind of gas phase-drop bidirectional couple that the evaporation of consideration drop influences the flow field parameter of gas phase local around it
Calculation method.During realizing the object of the invention, the gas phase flow field parameter at the position drop nr at current time is chosen
The gas phase flow field parameter of infinite point or incoming flow is substituted to solve liquid drop movement phase transition model, and binding isotherm and experience are chosen
The value range of nr keeps the drop parametric results at the current time being calculated more accurate, true；Then, it calculates current
The influence domain radius R of the drop evaporation at momentif, while updating the quality source item S that drop acts on gas phase flow field aroundm, component
Source item Si, momentum source termEnergy source item SE, and four source items are dispersed to be loaded into domain of influence model according to apart from inverse ratio weight mode
In grid in enclosing, the revised gas phase flow field parameter information of subsequent time is calculated, and then using revised
Gas phase flow field parameter information calculates the liquid drop movement phase transition parameter of subsequent time, repeats the iterative process, can constantly update down
The gas phase at one moment-drop phase Flow Field Distribution, until all iterative steps are completed, finally realize it is a kind of more rationally, it is true,
The numerical simulation method of accurate liquid drop movement evaporation process.
Specifically, in conjunction with Fig. 1, (Fig. 1 is gas phase-drop phase bidirectional couple numerical computation method stream of the embodiment of the present invention
Journey schematic diagram) shown in, implementation process of the invention includes the following steps:
S1: firstly, according to the geometric dimension of object construction, using modeling software, (such as Solidworks software or UG are soft
Part or Proe software etc.) geometrical model and grid division of object construction are drawn, and it is directed to the chamber wall close to geometrical model
Face near zone carries out mesh refinement, exports grid file.
S2: net is read in starting fluid calculation software (such as FLUENT software or CFX software or STAR-CCM software)
Lattice file；The calculation of boundary conditions consistent with the actual design parameter of geometrical model is specified in grid file, selection is suitable
Gas phase flow field parameter computation model (i.e. gas-phase governing equations), discrete method for solving and other correlation solve parameters；It calculates
Obtain the gas phase flow field parameter information at current time；Wherein, the space coordinate of grid node gas phase corresponding with the grid node
It is in one-to-one relationship between flow field parameter information.
S3: being added in fluid calculation software by independently writing UDF calculation procedure, reads gas phase flow field parameter information text
Part selects liquid drop movement phase transition model (such as formula 1), and obtains the gas phase flow field parameter at the position drop nr at current time
Liquid drop movement phase transition model is substituted into, to calculate the movement phase transition parameter of the drop at current time.
Specifically, being solved to collect around more accurate drop local, real-time gas phase flow field parameter
Liquid drop movement phase transition model, the present invention in, as shown in Figure 3, it is assumed that around drop any position flow field parameter it is known that and
Gas phase flow field Parameters variation is not very acutely, then to choose the gas phase flow field ginseng at the position drop centered nr at current time
Number, i.e., the surface at the position nr can take the arbitrary value in the range of n=5~30 as boundary, n is calculated, it is preferable that and n=5~
10, it is derived by liquid drop movement phase transition model through theory, concrete model includes following expression:
Wherein, amount to be asked is in the left side of above-mentioned equation, comprising: the position vector x of drop, the rotation speed ω of drop,
The speed v of drop, the radius r of drop, the temperature T of drop；
The right side physical quantity of equation includes:
1) gas phase flow field parameter information, comprising: density of gas phase ρg, gas phase flowing velocity u, the temperature T of gas phaseg, the pressure of gas phase
Power Pg, fluid kinematic viscosity μg, flow field curl Ω, calculation expression isThe diffusion coefficient D of steamv；
2) the movement phase transition parameter of the drop at current time, comprising: the acceleration a of drop, the speed v of drop, drop
Position coordinates, the temperature T of dropd, the pressure p of dropd, the density p of dropd, the viscosity, mu of dropd, the specific heat at constant pressure of drop
cp, the latent heat of vaporization γ of drop, the molal weight M of drop, the density p of the mixed gas in droplet surface liquid films, droplet surface
Temperature and the gas phase temperature at drop centered nr correspond to TrAnd Tnr；
3) constant, comprising: gravity acceleration g, gas constant R；
4) related coefficient calculated according to gas phase and drop parameter, comprising: evaporative condenser factor alpha, convection transfer rate h,
Torque coefficient CM, Yi force coefficient CD, Magnus lift coefficient CMa, Sa Fuman lift coefficient CSa, mass transfer number BM, calculation expression
ForSherwood number Sh, calculation expression Sh=2.0+0.6Re0.5Sc1/3, reynolds number Re, calculation expression
ForSchmidt number Sc, calculation expression are
5) normalization coefficient λ1~λ5, calculation expression is respectively as follows: λ1=-15 ρg/16πρd、λ2=3 ρf/(8ρdr+4ρgr)、
λ3=3 ρg(4ρd+2ρg)、λ4=[1.615 (μd+2μg/3)2/(μd+μg)2(μfρg)0.5]/(ρdπr/3+ρgπr/6)、λ5=2 (ρd-
ρg)/(2ρd+ρg)。
Compared to using the gas phase flow field parameter of infinite point or incoming flow to calculate drop parameter in Traditional calculating methods
Speech, the gas phase flow field parameter at the position drop nr at current time is chosen in the embodiment of the present invention to calculate drop parameter,
And binding isotherm and experience carry out reasonable value to nr range, so that acquiring gas phase within the scope of effective domain of influence of evaporation drop
Flow field parameter value makes real-time gas local around drop to collect local, real-time gas phase flow field parameter around drop
Phase flow field parameter is more accurate, reliable, substitutes into revised liquid drop movement phase transition model and is solved, can be obtained it is more accurate,
Reliable liquid drop movement phase transition parameter is as a result, make numerical simulation result be more in line with reality.
Further, it is also wrapped during obtaining the gas phase flow field parameter at the position drop nr at current time
It includes: 1) establishing KD searching algorithm and obtain distance objective droplet position xiLocate the sky of M grid node within the scope of (n-1) r~nr
Between coordinate；2) the gas phase flow field parameter at target position (i.e. apart from the position drop nr) is obtained using apart from inverse ratio interpolation method
Information Fi；
Wherein, interpolation scheme are as follows:
In formula: xiIndicate the position vector of i-th of drop, FiIndicate the gas phase flow field parameter information of i-th of drop, ljTable
Show drop xiEuclidean distance at position between the space coordinate of j-th of grid node；Any integer in M desirable 1 to 8.
In the embodiment of the present invention, in order to choose the grid at target position (i.e. apart from the position drop about nr) as much as possible
Background gas phase flow field parameter of the gas phase flow field parameter corresponding to node as drop, the present invention in using r as numerical search model
The error criterion enclosed increases grid section by expanding the corresponding grid node search range of target location gas phase flow field parameter
The volumes of searches of point improves gas phase flow field parametric reliability, in combination with most to get the grid node closer to target position
Neighbor interpolation method, to guarantee to seek the high efficiency of gas phase flow field parameter.
In addition, also being combined by using local mesh reflnement with nearest point interpolation method in the embodiment of the present invention, realize
While reducing grid computing amount, computational accuracy ensure that；It establishes KD searching algorithm to match with apart from inverse ratio interpolation method, most
Efficient, high-precision numerical simulation calculation process is realized eventually, can be widely applied to containment spray system, steam-water separator, combustion
In the numerical simulation calculation of drop evaporation behavior in the equipment running process such as oily spraying system, spray scrubber.
S4: the movement phase transition parameter (such as calculated result of step S3) and gas phase flow field parameter of the drop based on current time
(such as calculated result of step S2) calculates the radius R of the domain of influence of evaporation dropif(such as formula 2)；
It is easily understood that during drop evaporates in certain condition gaseous environment, it can be in a certain range around
Gas phase flow field have an impact, the present inventor be based on existing research conclusion (such as Constant et al. research shows that drop with
The heat transfer of gas phase is confined in the range of 10~30 times of droplet radius the influence that drop evaporates) and early period investigation in it is a large amount of
Numerical result proposes the domain of influence (gray area as shown in Figure 3) concept of evaporation drop, i.e., in the domain of influence, due to
The presence of drop, drop can constantly be evaporated and be exchanged heat with flow field, and flow field parameter variation is more violent around drop, with drop
The increase (along radial direction) of centre distance, temperature gradient, the mass fraction of the water vapour component in gas phase gradually decrease simultaneously
Tend to 0 (reasonability of the hypothesis is verified in the massive values computation result in investigation early period).Further, have
Influence domain sizes, the influence that drop evaporation process generates gas phase flow field Parameters variation around can be by by the source of drop
Item (including quality source item, momentum source term, component source item and energy source item) load is realized on the grid within the scope of the domain of influence.
The present inventor is from theory, and (i.e. influence domain radius is defined as R to the influence domain sizes of dropif) mainly and drop
Water vapour mass fraction Y in temperature difference T, time t, gas phase between radius r, drop and surrounding gas phase∞, operating pressure P or
Drop temperature T is related, as multi-variable function, and expression formula is represented by Rif=f (r, Δ T, Y∞,P,t).By largely counting
Value calculates and analytic induction summarizes, influence domain radius RifCalculation expression may be expressed as:
In formula, ξt、ξY、ξPRespectively the time, water vapour mass fraction, operating pressure correction factor, can express respectively
Are as follows:
It should be pointed out that above-mentioned relation formula is obtained under certain operating condition, the scope of application are as follows: 0.1MPa≤P≤
0.5MPa, 0≤Y∞≤ 0.7,5 μm≤r≤1000 μm.
S5: the movement phase transition parameter (such as calculated result of step S3) and gas phase flow field parameter of the drop at current time are utilized
(such as calculated result of step S2) recalculates the quality source item S that drop acts on gas phase flow field aroundm, component source item Si, it is dynamic
Measure source itemEnergy source item SE, to four source items carry out real-time updates (source item, which is calculated, is calculated as parallel procedure with influence domain radius,
Sequence interchangeable is only one of embodiment herein)；And updated four source items are loaded into the domain of influence half respectively
Diameter RifOn grid in range, specifically refer to shown in Fig. 4 b.
Wherein, four source items are calculated by following formula respectively:
In formula: m is the quality of drop,For the acceleration of drop, VcellFor the volume of grid, FGFor the gravity of drop；Its
In, component source item SiWith quality source item SmIt is identical.
It is easily understood that since previous traditional Euler-Lagrange method can only add the source item of two Coupling Between Phases
Be loaded in the single calculating grid of the gas phase flow field of drop (assuming that drop be particle) position (as is shown in fig. 4 a) or
In several grids that person is located next to around it, the source item numerical value on other grids is then 0, be thus easy to cause carry out it is next
When walking gas phase flow field calculating, because the source item numerical value of the gas phase flow field grid of drop position is excessive, gas phase in grid is caused
Quality, momentum and Energy distribution Severe distortion, and then the gas phase flow field parameter in iterative process is caused to dissipate, it does not receive
It holds back.At this time, it is desirable to which size of mesh opening is more much greater than drop size, and Luo Kun et al. (publishes thesis and " drop evaporation model and its tests
Card ") it analyzes and points out: the size of grid at least needs to reach 10 times of liquid-drop diameter or more.But size of mesh opening becomes larger, and meeting
Computational accuracy is caused to reduce.
In order to solve this problem, it uses in the embodiment of the present invention by quality source item Sm, component source item Si, momentum source term
Energy source item SEIt is loaded on the grid within the scope of the domain of influence according to distance weighting mode, to make quality source item Sm, component source item
Si, momentum source termEnergy source item SEDisperse in the multiple grids being loaded into the domain of influence (as shown in fig 4b).
Specifically, referring at the position closer apart from drop apart from inverse ratio weight mode, add in gas phase flow field grid
The source item numerical value that the drop of load influences gas phase is bigger, more far from the drop loaded in gas phase flow field grid is to gas
The source item numerical value mutually influenced is smaller, and when grid distance droplet position is as far as a certain size, source item numerical value is 0.The present invention uses
Drop source item is loaded apart from inverse ratio weight mode, compared to traditional loading method, more conducively drop source item is added evenly dispersedly
In multiple grids around to drop, connect the source item size variation loaded on the gas phase flow field grid within the scope of the domain of influence more
Continuous, gentle, i.e. drop evaporation is more continuous to the influence of gas phase flow field Parameters variation around, uniformly, so as to avoid because
Source item is excessive in single grid and source item is 0 in other grids around it, causes gas phase quality, momentum and Energy distribution in grid
Severe distortion, or even there is the phenomenon that singular point, to ensure that the iterative process of each time step is easier to restrain, reach several
It is worth that computational stability is good, result more accurately and reliably purpose.In particular, compared with prior art, the present invention is more suitable for dense liquid
Drip or the temperature difference are larger, evaporation is more violent, the calculating between gas-liquid two-phase under the larger working condition of movement velocity difference, should add
Load mode also can effectively solve the problem that two is alternate since the source item of bidirectional couple is larger, cause to calculate the problem of being not easy convergence, tool
Have the characteristics that applied widely, computational accuracy is high.
In step s 6, calculation procedure can be according to the quality source item S of updated dropm, component source item Si, momentum source termEnergy source item SE, based on the computation model (i.e. gas-phase governing equations) in the step S2, with corrected Calculation subsequent time
Gas phase flow field parameter information then continues revised gas phase flow field parameter information to be iterated solution in generation time step S3,
Step S3~S6 is repeated to constantly update the movement phase transition parameter of gas phase flow field parameter and drop, until all iterative steps are complete
At.
In the present invention, by iterative process each time (in i.e. each calculating time step) all to influence domain radius
RifAnd quality source item Sm, component source item Si, momentum source termEnergy source item SEReal-time update is carried out, and by quality source item Sm, group
Divide source item Si, momentum source termEnergy source item SEIt is loaded into influence domain radius RifIn range, with the gas phase flow field to subsequent time
Parameter information carries out calculating amendment, and the gas phase flow field parametric results generation of subsequent time is returned liquid drop movement phase transition model, continues
The liquid drop movement phase transition parameter for updating subsequent time is calculated as a result, substantially increasing gas phase-drop phase Flow Field Distribution numerical value meter
The accuracy and reliability for calculating result, makes numerical simulation result more closing to reality operating condition, convenient for the details of drop evaporation behavior
Analysis, to instruct the prioritization scheme of container spray performance.
It is with the numerical simulation application process of containment spray system (TOSQAN spray condensation benchmarks device) below
Example describes to implementation process of the invention in detail.As shown in Figure 1, implementation process of the invention specifically includes following step
It is rapid:
S101, first according to geometric dimension (such as Fig. 2 a of object construction (i.e. TOSQAN spray condensation benchmarks device)
It is shown), utilize the two-dimensional axial symmetric geometrical model (as shown in Figure 2 b) of Solidworks Software on Drawing object construction.
As shown in Figure 2 a, TOSQAN sprays the overall structure size of experimental provision are as follows: volume is about 7m3, internal diameter 1.5m, always
Height 4.8m.Wherein, top is nozzle, i.e. injection droplet inlet, and eject position is apart from top 0.65m；Lower part enters for water vapour
Mouthful, steam entry positional distance bottom 2.1m, the nozzle diameter for spraying droplet inlet and steam entry is 0.41m；Bottom
Portion is sink, and sink height 0.87m, sink internal diameter is 0.68m；Middle and upper part container side has the cyclic annular condensation of one section of a height of 2m
Area, other positions are non-condensing area.
S102, using ICEM software to geometrical model grid division；And it is attached for the wall surface of the container close to geometrical model
Near field carries out mesh refinement processing (refined net structure is as shown in Figure 8)；Export grid file.
Specifically, the grid amount that geometrical model is selected in network is 28222, and the time step of selected gas phase flow field is
0.01s, the time step of drop phase are 10-6~10-5The specific time step of s, drop phase are related with the size of drop, drop
The smaller time step of radius also should accordingly reduce, and droplet radius, which gets over large time step, suitably to be increased.Pass through Local grid
Encryption, the size of mesh opening of refinement, to reduce flow field gradient corresponding to subdivided meshes in the regional area as much as possible, into
And guarantee that the gas phase flow field parameter in the region is more fine, accurate, reduce because the calculating that the distortion of gas phase flow field parameter introduces misses
Difference.
S201, starting FLUENT software for calculation read in grid file, setting containment spray system boundary condition, gas phase and
Drop primary condition selects the computation model of suitable gas phase flow field parameter (to herein refer to gas-phase governing equations, including continuity side
Journey, momentum conservation equation, energy conservation equation and diffusion of components equation), discrete method for solving and other related solution parameters.
The parameter setting of specific injection drop and environment gas phase (gaseous mixture for herein referring to air and water vapour) is as shown in Figure 9.
S202: gas-phase governing equations are solved, the gas phase flow field parameter information at current time, calculated result packet is calculated
It includes: the spatial position coordinate of each grid node, the temperature T of water vapour corresponding to each grid nodeg, speed u, pressure pg, density
ρg, viscosity, mugEqual gas phase flow fields parameter information.
S3: adding the UDF calculation procedure independently write in FLUENT software, reads gas phase flow field parameter information file,
It selects liquid drop movement phase transition model (such as formula 1), and obtains the gas phase flow field parameter (packet at the position drop nr at current time
Include the space seat for getting M grid node nearest around at the position drop nr with quick positioning by KD searching algorithm
Mark and using the gas phase flow field information for obtaining target location apart from inverse ratio interpolation algorithm), it substitutes into liquid drop movement phase transition model,
Solve the movement phase transition parameter of the drop at current time.
S4: the movement phase transition parameter and gas phase flow field parameter of the drop based on current time, according to influence domain radius RifTable
Up to formula (such as formula 2), the influence domain radius R of drop evaporation is calculatedif；
S501: the movement phase transition parameter and gas phase flow field parameter of the drop based on current time, again according to 3~formula of formula 6
Calculate the quality source item S that drop acts on gas phase flow field aroundm, component source item Si, momentum source termEnergy source item SE。
S502: by above-mentioned updated quality source item Sm, component source item Si, momentum source termEnergy source item SEAccording to distance
Weight mode is loaded on the grid within the scope of the domain of influence, make above-mentioned four source items disperse to be loaded into respectively it is multiple in the domain of influence
In grid.
S6: calculation procedure calls updated four source item to calculate the revised gas phase flow field parameter of subsequent time letter
Breath.
S7: revised gas phase flow field parameter information is continued into generation and is returned in step S3, the drop of subsequent time is solved
Move phase transition parameter.
The iterative process of step S3~S6 is repeated, to constantly update gas phase-drop phase Flow Field Distribution of subsequent time, until
All iterative steps are completed.
The embodiment of the present invention, which simulates, sprays drop spray movement in container in containment spray system benchmarks operating condition
Evaporation process is coincide preferably with experimental result, and relative error demonstrates the confined space established in the present invention within ± 15%
The correctness of the interior liquid drop movement phase transformation tow-way coupling model for considering the domain of influence, and the bidirectional couple numerical simulation established herein
Application method shows that the calculation method established herein can be more with using the analogy method comparison between calculation results of infinity parameter
Accurately reflection drop moves the local parameter situation of change of evaporation process in gas phase flow field.
Specifically, water vapour quality point in the gas phase temperature, gaseous pressure and gas phase during the spray being calculated
Versus time curve is counted respectively as shown in Fig. 5, Fig. 6, Fig. 7, gas phase temperature herein, gaseous pressure and quality of steam
Score refers both to average value.It can see from Fig. 5~Fig. 7, gas phase temperature in the container that " the present embodiment calculation method " is calculated
Degree, pressure and quality of steam score are less than that " infinity parameter " method is calculated as a result, this is mainly due to using nothing
When poor remote parameter, it is believed that the gas phase temperature, gaseous pressure at all positions around drop are identical with quality of steam score, are gas phase
The average value in flow field；And the air parameter in " the present embodiment calculation method " around drop is surrounding local parameter, drop
Around part gas phase temperature can due to low temperature drop cooling effect and be lower than gas phase flow field mean temperature, local steam
Mass fraction can be greater than the average value of gas phase flow field due to the evaporation of drop, and the present embodiment is using local parameter around drop
During being calculated, drop and the quality of steam score difference in surrounding gas phase flow field are less than normal, keep droplet evaporation rate less than normal,
Then cause quality of steam score relatively low, gas phase integral pressure is lower.General performance is that " the present embodiment calculation method " calculates
To container in gas phase temperature, pressure and quality of steam score it is relatively low.
Compared with prior art, the present invention make around drop local, real-time gas phase flow field parameter it is more accurate, can
It leans on, numerical simulation result is made to be more in line with reality；All real-time update calculates amendment to the present invention in iterative process each time,
The accuracy and reliability for improving result, makes numerical simulation result more closing to reality operating condition；Drop source item is pressed in the present invention
Range is loaded on the gas phase flow field grid in the domain of influence from the inverse ratio method of weighting, is made on the gas phase flow field grid within the scope of the domain of influence
The source item size variation of load is more continuous, gentle, avoid due to source item is excessive in single grid and other grids around it
Interior source item causes the Severe distortion of gas phase quality in grid, momentum and Energy distribution for 0, or even the phenomenon that singular point occurs, makes to change
Generation calculating more easily restrains, numerical value computational stability is good, result is more accurate and reliable；Present invention is particularly suitable for dense drops
The stream or temperature difference is larger, the numerical simulation calculation under the evaporation operating conditions such as more acutely, between gas-liquid two-phase movement velocity difference is larger,
It can effectively solve the problem that two is alternate since the source item of bidirectional couple is larger, causes to calculate the problem of being not easy convergence, have and be applicable in model
Enclose feature wide, that computational accuracy is high；The present invention combines local mesh reflnement with nearest point interpolation method, reduces grid computing
While amount, computational accuracy ensure that；The present invention is using grid nearest around KD searching algorithm quick obtaining to target position
Node coordinate is not only mentioned significantly by obtaining the gas phase flow field parameter information at object droplet position apart from inverse ratio interpolation method
High grid computing speed and guarantee computational accuracy, can be widely applied to containment spray system, steam-water separator, fuel spray
In the numerical simulation of drop evaporation behavior in the equipment running process such as system, spray scrubber.
To sum up, the present invention provides a kind of gas phase-drop phase bidirectional couple numerical computation methods, including S1, construct geometry
Model and grid division；S2, starting fluid calculation software read in grid file, select computation model, calculate the gas at current time
Phase flow field parameter；S3 establishes calculation procedure to obtain the gas phase flow field parameter at the position drop nr at current time, solves
The liquid drop movement phase transition parameter at current time；S4 calculates the influence domain radius of drop evaporation；S5 recalculates the quality of drop
Source item, component source item, momentum source term, energy source item, and updated source item is loaded on the grid within the scope of the domain of influence；
S6 calculates the revised gas phase flow field parameter of subsequent time；The iterative process of step S3~S6 is repeated, to constantly update lower a period of time
The gas phase at quarter-drop phase Flow Field Distribution, until all iterative steps are completed.The present invention establishes more reasonable gas phase-drop
Phase tow-way coupling model can get more accurate, reliable numerical simulation result.
Claims (8)
1. a kind of gas phase-drop phase bidirectional couple numerical computation method, it is characterised in that: comprise the following steps:
Step (1): the geometrical model and grid division of object construction are constructed, geometry mould is also directed to during grid division
The wall area of type and geometry change more violent texture surface area and carry out local mesh reflnement, then export grid
File；
Step (2): starting fluid calculation software reads in grid file, selects computation model, calculate the gas phase flow field at current time
Parameter information generates gas phase flow field parameter information file；
Step (3): establish calculation procedure read gas phase flow field parameter information file, and obtain current time apart from drop centered
Gas phase flow field parameter at the position nr, n are positive integers, and r is the radius of drop, select liquid drop movement phase transition model, are calculated current
The movement phase transition parameter of the drop at moment；
Step (4): the movement phase transition parameter and gas phase flow field parameter of the drop based on current time calculate the influence of drop evaporation
Domain radius Rif；
Step (5): the movement phase transition parameter and gas phase flow field parameter of the drop based on current time recalculate and update drop
Act on the quality source item S of gas phase flow field aroundm, component source item Si, momentum source term F and energy source item SE, and will be after above-mentioned update
Quality source item Sm, component source item Si, momentum source term F and energy source item SEIt is loaded into the domain of influence respectively according to distance weighting mode
Radius RifOn grid in range, make quality source item Sm, component source item Si, momentum source term F and energy source item SEDispersion is loaded into shadow
It rings in multiple grids in domain；
Step (6): the gas phase flow field parameter information of subsequent time is calculated based on the computation model adjustment selected in step (2)；
Step (7): repeating step (3) to step (6), constantly update gas phase-drop phase Flow Field Distribution of subsequent time, until institute
There is iterative step completion.
2. a kind of gas phase according to claim 1-drop phase bidirectional couple numerical computation method, it is characterised in that: described
The step of (2) in gas phase flow field parameter information include: density of gas phase ρg, gas phase flowing velocity u, the temperature T of gas phaseg, gas phase
Pressure Pg, fluid kinematic viscosity μg, flow field curl Ω, calculation expression is Ω=▽ × u, the diffusion coefficient D of steamv。
3. a kind of gas phase according to claim 1-drop phase bidirectional couple numerical computation method, it is characterised in that: described
The step of (3) in current time drop movement phase transition parameter include: drop acceleration a, the speed v of drop, drop
Position coordinates, the temperature T of dropd, the pressure P of dropd, the density p of dropd, the viscosity, mu of dropd, the specific heat at constant pressure of drop
Hold cp, the latent heat of vaporization γ of drop, the molal weight M of drop, the density p of the mixed gas in droplet surface liquid films, drop table
The temperature in face and the gas phase temperature at drop centered correspond to TrAnd Tnr。
4. a kind of gas phase according to claim 1-drop phase bidirectional couple numerical computation method, it is characterised in that: described
The step of (3) in acquisition current time the gas phase flow field parameter at the position drop centered nr process further include: build
Vertical KD searching algorithm obtains distance objective drop xiThe space coordinate of M grid node at position within the scope of (n-1) r to nr；
Using the gas phase flow field parameter information F obtained apart from inverse ratio interpolation method at the position drop centered nri；Interpolation scheme are as follows:
In above formula, ljIndicate the position vector x of i-th of dropiEuclidean distance between the space coordinate of j-th of grid node；
M is any integer in 1 to 8.
5. a kind of gas phase according to claim 1-drop phase bidirectional couple numerical computation method, it is characterised in that: described
The step of (3) in liquid drop movement phase transition model are as follows:
In above formula, x is the position vector of drop, and ω is the rotation speed of drop, and v is the speed of drop, and T is the temperature of drop；g
It is acceleration of gravity, R is gas constant；H is convection transfer rate, CMIt is torque coefficient, CDIt is Yi force coefficient, CMaIt is that mug(unit of measure) is exerted
This lift coefficient, CSaIt is Sa Fuman lift coefficient, BM=(Ys-Y∞)/(1-Ys) it is mass transfer number, Sh=2.0+0.6Re0.5Sc1/3It is
Sherwood number, Re=2 ρsvr/μgIt is Reynolds number, Sc=ν/DvIt is Schmidt number；λ1、λ2、λ3、λ4And λ5It is normalization coefficient, and
λ1=-15 ρg/16πρd；
λ2=3 ρf/(8ρdr+4ρgr)；
λ3=3 ρg(4ρd+2ρg)；
λ4=[1.615 (μd+2μg/3)2/(μd+μg)2(μgρg)0.5]/(ρdπr/3+ρgπr/6)；
λ5=2 (ρd-ρg)/(2ρd+ρg)。
6. a kind of gas phase according to claim 1-drop phase bidirectional couple numerical computation method, it is characterised in that: described
The step of (4) in influence domain radius RifCalculation formula:
In above formula, the temperature difference of the Δ T between drop phase and surrounding gas phase, t is time, Y∞For water vapour mass fraction, P in gas phase
For operating pressure, ξtIt is the correction factor of time, ξYIt is the correction factor of water vapour mass fraction, ξPIt is the amendment of operating pressure
Coefficient.
7. a kind of gas phase according to claim 1-drop phase bidirectional couple numerical computation method, it is characterised in that: described
The step of (5) in quality source item Sm:
Component source item Si:
Energy source item SE:
Momentum source term F:
F=- ∑ (ma-FG)/Vcell；
In above formula, m is the quality of drop, VcellFor the volume of grid, FGFor the gravity of drop.
8. a kind of gas phase according to claim 1-drop phase bidirectional couple numerical computation method, it is characterised in that: described
The step of (7) in gas phase-drop phase Flow Field Distribution include the temperature field of gas phase, gaseous pressure field, the velocity field of gas phase, gas phase
In water vapor concentration field, drop spatial position distribution, the radius distribution of drop, the velocity field of drop and drop temperature field
At least one of.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112685976A (en) * | 2021-01-05 | 2021-04-20 | 西安交通大学 | Numerical simulation method of natural circulation system under motion condition |
| CN113283187A (en) * | 2021-04-27 | 2021-08-20 | 福建省中科生物股份有限公司 | Flow field calculation method of plant factory under action of jet flow pipeline |
| CN113283187B (en) * | 2021-04-27 | 2023-08-11 | 福建省中科生物股份有限公司 | Flow field calculation method for plant factory under action of jet flow pipeline |
| CN113984394A (en) * | 2021-10-28 | 2022-01-28 | 中国人民解放军国防科技大学 | Liquid drop wall-collision simulation method for liquid transverse jet flow in supersonic velocity air flow |
| CN113984394B (en) * | 2021-10-28 | 2024-09-17 | 中国人民解放军国防科技大学 | Liquid drop wall collision simulation method for liquid transverse jet flow in supersonic airflow |
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