Methods, systems and equipment for predicting bubble detachment volume and optimizing injection control in submerged non-isothermal gas injection systems

Abstract

This invention discloses a method, system, and equipment for predicting bubble detachment volume and optimizing gas injection control in an immersion non-isothermal gas injection system, belonging to the fields of multiphase flow control and chemical and metallurgical automation technology. By setting the hydrodynamic drag coefficient as a constant and introducing kinematic constraints, the cross-interference between momentum integral and heat source terms is isolated, obtaining a macroscopic thermodynamic closed term that conforms to physical laws, thus improving the prediction stability of the model under complex and variable operating conditions. The inherent spatial trajectory calculation deviation of the one-dimensional model in the prior art is transformed into a smaller time variance, effectively suppressing the propagation of prediction errors and improving the online prediction accuracy of detachment volume. Through real-time comparison and constraint adjustment of thermal expansion fraction and critical expansion threshold, bubbles are prevented from detaching before sufficient heat exchange, alleviating the phenomenon of near-field bubble aggregation and gas flow short-circuiting, improving the comprehensive utilization rate of gas while ensuring production capacity, and optimizing the global gas-liquid interphase mass transfer area.

Description

Technical Field

[0001] This invention belongs to the field of multiphase flow control and chemical metallurgical automation technology, and relates to a method, system and equipment for predicting bubble separation volume and optimizing gas injection control in an immersion non-isothermal gas injection system. Background Technology

[0002] In industrial applications such as metallurgical side-blowing, chemical bubble towers, and cryogenic fluid management, submerged gas injection processes under non-isothermal conditions are frequently involved. Under these conditions, sensible heat exchange between the gas and liquid phases causes dynamic changes in the gas density inside the bubble over time, and the transient volume evolution of the bubble is determined by both isothermal mass accumulation and sensible heat-driven expansion.

[0003] The existing technology has the following technical defects:

[0004] 1. Isothermal model prediction bias. Existing industrial control systems mostly use bottom-blowing isothermal models to predict bubble size. Under non-isothermal side-blowing conditions, using the isothermal model will lead to inaccurate prediction of bubble detachment volume, which in turn will cause the distributed control system (DCS) to have a bias in estimating the specific surface area between the gas and liquid phases, reducing the gas distribution accuracy of the reaction process.

[0005] 2. Multiple solutions and distortions in parameter identification. When establishing a non-isothermal coupled model, there is a nonlinear coupling between the thermodynamic volume expansion and the dynamic force motion of the bubble. If the parameters are directly inverted using macroscopic detached volume, it is easy to cause numerical cross-compensation between the source terms of the momentum equation and the energy equation, resulting in distortion of the identified heat transfer parameters and reducing the predictive reliability of the model under varying operating conditions.

[0006] 3. High-flow-rate gas injection leads to deterioration of the flow pattern. Under current high-flow-rate gas injection conditions, the rate of increase in convective heat transfer within the gas lags behind the rate of increase in the enthalpy flow of the cold gas. This often results in the gas detaching from the nozzle before it has fully absorbed heat and expanded. This phenomenon leads to an increased frequency of bubble formation, causing bubble aggregation and short-circuiting of the gas flow in the near-nozzle region. This reduces the macroscopic interphase mass transfer area and weakens the work done by the gas during in-situ expansion at the bottom of the reactor.

[0007] Therefore, a new technical solution is urgently needed to effectively solve the above-mentioned defects, improve the prediction accuracy of bubble detachment volume, and achieve optimal control of gas injection parameters. Summary of the Invention

[0008] This invention aims to provide a method, system, and equipment for predicting bubble release volume and optimizing gas injection control in an immersion non-isothermal gas injection system. It improves the prediction accuracy and stability of bubble release volume under complex operating conditions, optimizes the global gas-liquid interphase mass transfer area, and achieves optimal control of gas injection parameters. It enhances the comprehensive utilization rate of gas while ensuring production capacity and is applicable to immersion non-isothermal gas injection systems.

[0009] To achieve the above objectives, the technical solution adopted by this invention is: a method for predicting bubble detachment volume and optimizing gas injection in an immersion non-isothermal gas injection system, comprising:

[0010] S1. Obtain the gas mass flow rate of the submersible non-isothermal gas injection system. Injection orifice diameter Initial gas temperature Liquid ambient temperature and gas-liquid physical properties;

[0011] S2, using the gas mass flow rate The initial temperature of the gas and the ambient temperature of the liquid Using the bubble volume expansion equation, internal temperature evolution equation, centroid vertical motion equation, and centroid kinematic equation as input variables, a system of one-dimensional ordinary differential equations is constructed; wherein, the additional mass coefficient in the centroid vertical motion equation... and surface tension correction factor Let it be a constant;

[0012] S3. Obtain the effective convective heat transfer coefficient and substitute it into the aforementioned one-dimensional ordinary differential equation system to obtain an updated one-dimensional ordinary differential equation system; based on the orifice Froude number... And Bond Number Obtain the critical height ratio ;

[0013] S4. Perform forward time integration on the updated one-dimensional ordinary differential equation system to obtain the centroid height and equivalent diameter of the bubble; when the ratio of the centroid height to the equivalent diameter is not less than the critical height ratio The integration process ends at a certain point, and the actual time it takes for the bubble to detach is obtained. Output the predicted actual detachment volume ;

[0014] S5, Based on the initial temperature of the gas and the actual detachment time of the bubble Instantaneous absolute pressure, obtaining isothermal mass injection equivalent volume ;

[0015] S6. Maintain the gas mass flow rate Assuming the initial temperature of the injected gas remains constant at the same level as the ambient temperature of the liquid environment. Turn off the heat exchange; repeat steps S2 to S4 until the geometric separation criterion is met, and output the isothermal reference separation volume. ;

[0016] S7. Based on the predicted actual detachment volume and the equivalent volume of the isothermal mass injection Obtain the thermal expansion fraction ; based on the isothermal reference, the volume is separated and the equivalent volume of the isothermal mass injection Obtain the critical expansion threshold ;when At that time, reduce the gas mass flow rate. ;when At the same time, increase the gas mass flow rate. .

[0017] The solution provided by the present invention includes and By setting the hydrodynamic drag coefficient as a constant to introduce kinematic constraints, the cross-interference between momentum integral and heat source term is isolated, and a macroscopic thermodynamic closed term conforming to physical laws is obtained. This improves the predictive stability of the model under complex variable working conditions and eliminates the problem of multiple solutions in parameter identification.

[0018] The above solution transforms the inherent spatial trajectory calculation bias of the one-dimensional model in the existing technology into a smaller temporal variance, effectively suppressing the propagation of prediction errors and improving the online prediction accuracy of volume-detached models.

[0019] The solution provided by this invention also utilizes the fraction of thermal expansion. With critical expansion threshold Real-time comparison and constrained adjustment prevent bubbles from detaching before sufficient heat exchange, alleviate the phenomenon of near-field bubble aggregation and short-circuiting with airflow, improve the comprehensive utilization rate of gas while ensuring production capacity, and optimize the global gas-liquid phase mass transfer area.

[0020] According to embodiments of the present invention, the present invention can be further optimized, and the optimized technical solution is as follows:

[0021] In one preferred embodiment, in step S2, the formula for calculating the bubble volume expansion equation is:

[0022] ;

[0023] The formula for calculating the internal temperature evolution equation is as follows:

[0024] ;

[0025] The formula for calculating the vertical motion equation of the centroid is as follows:

[0026] ;

[0027] After expansion and merging, it looks like this:

[0028] ;

[0029] The formula for calculating the kinematic equations of the center of mass is as follows:

[0030] ;

[0031] in, Let the transient volume of the bubble be... The time variable is the independent variable within a single bubble formation cycle. The gas constant is... The internal temperature of the bubble. The absolute pressure of the bubble. For the transient mass of the bubble, The specific heat capacity of a gas at constant pressure. For an effective convective heat transfer coefficient, This represents the equivalent surface area of ​​the bubble. For the liquid ambient temperature, The initial temperature of the gas. Let V be the velocity vector of the bubble's center of mass. For the gas injection velocity vector, It is the buoyancy vector. It is the surface tension vector. For the additional quality coefficient, For the density of the liquid, It is the acceleration due to gravity. For the theoretical maximum surface tension, The height of the bubble's center of mass. Let the vertical upward velocity of the bubble's center of mass be denoted as . Let the bubble's equivalent radius be 1. Let be the sine of the elevation angle of the center of mass. This is the surface tension correction factor.

[0032] In one preferred embodiment, in step S3, the formula for calculating the effective convective heat transfer coefficient is:

[0033] ;

[0034] ;

[0035] ;

[0036] in, The effective convective heat transfer coefficient is... For an effective Stanton number, The specific heat capacity of a gas at constant pressure. For gas density, The gas injection rate at the orifice. For the gas phase Pecklet number, The thermal diffusivity of the gas;

[0037] The critical height ratio The calculation formula is:

[0038] ;

[0039] ;

[0040] ;

[0041] in, For the Froude number at the orifice, For Bond number, It is the acceleration due to gravity. For the density of the liquid, Liquid surface tension .

[0042] In one preferred embodiment, step S4 specifically includes:

[0043] S4.1, Settings Initial conditions at time: initial volume of the bubble initial temperature Initial centroid velocity Initial centroid height ;

[0044] S4.2. The fourth-order Runge-Kutta method is used to apply a fixed-step method to the system of one-dimensional ordinary differential equations. The time-forward integration is performed; at the end of each integration step, the following judgment is made:

[0045] S4.2.1 Obtain the transient volume obtained by integrating at the current time step. and center of mass height ;in, For the first Each integration step size. It is a positive integer;

[0046] S4.2.2. Based on the equivalent sphere assumption, obtain the equivalent diameter of the bubble at the current moment. ;

[0047] S4.2.3, The ratio of the centroid height to the equivalent diameter Ratio to the critical height Perform a comparison; if If so, proceed to the next integration step and repeat steps S4.2.1 to S4.2.3; if If the bubble escapes, the bubble escape check is triggered, the scoring loop terminates, and the current scoring time at the time the bubble escape check is triggered is recorded. The actual time of bubble release Output the bubble volume at the current moment. For the predicted actual detachment volume .

[0048] The above scheme utilizes the kinematic characteristic that the rising velocity of the centroid at the end of the bubble pinch-off is greater than the equivalent radial expansion velocity, transforming the inherent spatial trajectory calculation deviation of the one-dimensional model in the prior art into a smaller time variance, effectively suppressing the propagation of prediction errors, thereby improving the online prediction accuracy of the detached volume.

[0049] In one preferred embodiment, the formula for calculating the equivalent volume of the isothermal mass injection in step S5 is:

[0050] ;

[0051] in, To inject an equivalent volume into the isothermal mass at the moment the bubble detaches. The gas constant is... For the actual detachment time of the bubble Instantaneous absolute pressure.

[0052] In one preferred embodiment, in step S6, the geometric separation criterion is: The isothermal reference is separated from the volume. The transient volume obtained by integrating at the current time step ;in, The height of the centroid obtained by integration at the current moment. The equivalent diameter of the bubble at the current moment. For the first Each integration step size. It is a positive integer.

[0053] In the above scheme, the isothermal reference is separated from the volume. Characterizes the detachment volume that bubbles can achieve under ideal isothermal conditions that eliminate the influence of the initial high density of cold air.

[0054] In one preferred embodiment, in step S7, the thermal expansion fraction The calculation formula is: The critical expansion threshold The calculation formula is: .

[0055] In the above scheme, the isothermal reference volume is compared. Equivalent volume of the isothermal mass injection This allows for the quantification of the initial volume loss caused by cold gas injection, providing a dynamic critical threshold for assessing whether the sensible thermal expansion of the bubbles is sufficient.

[0056] In one preferred embodiment, in step S7, when At that time, reduce the gas mass flow rate. Simultaneously activate the backup nozzle to increase the number of working nozzles; and / or when At that time, a hill-climbing algorithm is used to increase the gas mass flow rate by a preset step size. Repeat S1 to S7 until... The preset safety margin boundary is reached. Preferably, .

[0057] The submerged non-isothermal gas injection system described in the above scheme is equipped with a multi-nozzle array. While maintaining the total gas injection volume, it extends the generation and sensible heat exchange time of a single bubble at the nozzle by reducing the single-hole injection flow rate and simultaneously increasing the number of working nozzles. This transforms the concentrated high-flow-rate gas injection into a multi-point distributed low-flow-rate gas injection, helping to alleviate the bubble aggregation and airflow short-circuiting phenomenon that easily occurs under single-hole high-flow-rate conditions. Thus, while ensuring the total gas injection capacity of the system, it improves the gas-liquid phase mass transfer area within the reactor. Based on the heat exchange margin of the submerged non-isothermal gas injection system, the above scheme gradually increases the gas injection capacity until it approaches the heat transfer limit, for example... This allows for the maximization of reactor gas injection volume and production efficiency while ensuring that the mass transfer area between the gas and liquid phases does not decrease.

[0058] Based on the same concept, the present invention also provides a bubble detachment volume prediction and gas injection optimization control system, comprising:

[0059] The parameter acquisition module is used to obtain the gas mass flow rate of the submersible non-isothermal gas injection system. Injection orifice diameter Initial gas temperature Liquid ambient temperature ;

[0060] The equation construction and regularization module is used to employ the gas mass flow rate. The initial temperature of the gas and the ambient temperature of the liquid Using the bubble volume expansion equation, internal temperature evolution equation, centroid vertical motion equation, and centroid kinematic equation as input variables, a system of one-dimensional ordinary differential equations is constructed; wherein, the additional mass coefficient in the centroid vertical motion equation... and surface tension correction factor Let it be a constant;

[0061] The closed-loop setting module is used to substitute the effective convective heat transfer coefficient into the one-dimensional ordinary differential equation system to obtain an updated one-dimensional ordinary differential equation system; based on the orifice Froude number... And Bond Number Obtain the critical height ratio ;

[0062] The forward integral prediction module is used to perform forward integration over time on the updated one-dimensional ordinary differential equation system to obtain the centroid height and equivalent diameter of the bubble; when the ratio of the centroid height to the equivalent diameter is not less than the critical height ratio... The integration process ends at a certain point, and the actual time it takes for the bubble to detach is obtained. Output the predicted actual detachment volume ;

[0063] The equivalent volume calculation module is used to calculate the volume based on the initial temperature of the gas. and the actual detachment time of the bubble Instantaneous absolute pressure, obtaining isothermal mass injection equivalent volume ;

[0064] The reference volume calculation module is used to maintain the gas mass flow rate. Assuming the initial temperature of the injected gas remains constant at the same level as the ambient temperature of the liquid environment. Turn off the heat exchange; repeat steps S2 to S4, perform forward integration of the reference one-dimensional ordinary differential equation system until the geometric separation criterion is met, and output the isothermal reference separation volume. ;

[0065] The optimization control module is used to determine the actual detachment volume based on the prediction. and the equivalent volume of the isothermal mass injection Obtain the thermal expansion fraction ; based on the isothermal reference, the volume is separated and the equivalent volume of the isothermal mass injection Obtain the critical expansion threshold ;when At that time, reduce the gas mass flow rate. ;when At the same time, increase the gas mass flow rate. .

[0066] Based on the same concept, the present invention also provides an electronic device, including a memory, a processor, and a computer program / instructions stored in the memory, wherein the processor executes the computer program / instructions to implement the bubble detachment volume prediction and gas injection optimization control method for the immersion non-isothermal gas injection system as described above.

[0067] Compared with the prior art, the beneficial effects of the present invention are:

[0068] This invention provides a method, system, and device for predicting bubble detachment volume and optimizing injection control in an immersion non-isothermal gas injection system. By introducing kinematic constraints to decouple thermodynamic and kinetic parameters, the prediction accuracy of bubble detachment volume is improved, and optimization control of injection parameters is achieved based on volume decoupling. By setting the hydrodynamic drag coefficient as a constant and introducing kinematic constraints, the cross-interference between momentum integral and heat source terms is isolated, obtaining a macroscopic thermodynamic closed term that conforms to physical laws, thus improving the model's prediction stability under complex variable operating conditions. The inherent spatial trajectory calculation deviation of the one-dimensional model in existing technologies is transformed into a smaller time variance, effectively suppressing the propagation of prediction errors and improving the online prediction accuracy of detachment volume. Through real-time comparison and constraint-based adjustment of the thermal expansion fraction and critical expansion threshold, bubbles are prevented from detaching before sufficient heat exchange, alleviating the phenomenon of near-field bubble aggregation and short-circuiting with the airflow, improving the comprehensive utilization rate of gas while ensuring production capacity, and optimizing the global gas-liquid interphase mass transfer area. Attached Figure Description

[0069] Figure 1 This is a flowchart of a method for predicting bubble detachment volume and optimizing gas injection in an immersion non-isothermal gas injection system according to an embodiment of the present invention.

[0070] Figure 2 This is a parametric flow pattern diagram of the expansion and contraction of bubble net volume according to an embodiment of the present invention;

[0071] Figure 3 This is a competition curve of thermal expansion fraction and critical expansion threshold according to an embodiment of the present invention; wherein, (a) is the nozzle orifice diameter. Operating conditions, the curve on the left shows Always higher The result on the right indicates that the bubble is in a net expansion state, which means that the bubble has a relatively sufficient sensible thermal expansion process under small aperture conditions; (b) is the nozzle orifice diameter. Operating conditions, the curve on the left shows the low gas mass flow rate. The corresponding result on the right indicates that the bubble is in a state of net expansion; as the mass flow rate increases, Exceed The bubbles enter a net shrinkage state, indicating that there is a critical condition for the transition from sufficient heat transfer to insufficient heat transfer at this orifice diameter; (c) is the nozzle orifice diameter. The right-hand side analysis shows that under this condition, the nozzle also exhibits a net expansion state at low mass flow rates and a net contraction state at higher mass flow rates. Furthermore, as the orifice diameter increases and the single-orifice flow rate increases, the ability of sensible thermal expansion to compensate for volume loss further weakens; (d) is the nozzle orifice diameter. Under operating conditions, except for the low gas mass flow rate point where it is still in a net expansion state, the medium and high gas mass flow rates show net contraction, indicating that the thermal expansion margin is more obvious under large aperture conditions, and the bubbles are more likely to detach before fully absorbing heat and expanding.

[0072] Figure 4 This is a comparison diagram of the kinematic characteristics at the end of bubble pinch-off according to an embodiment of the present invention. Detailed Implementation

[0073] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other.

[0074] Example 1

[0075] This invention provides a method for predicting bubble detachment volume and optimizing injection control in an immersion non-isothermal gas injection system. This method relies on the calculation module of an industrial distributed control system (DCS) or programmable logic controller (PLC) for execution. The flowchart is shown below. Figure 1 As shown, the specific steps are as follows:

[0076] S1. Obtain the gas mass flow rate of the submersible non-isothermal gas injection system. Injection orifice diameter Initial gas temperature Liquid ambient temperature and gas-liquid physical properties;

[0077] Real-time acquisition of current operating parameters via sensors, including: gas mass flow rate. Injection orifice diameter Initial gas temperature (e.g., cryogenic nitrogen, 210 Kelvin) and liquid ambient temperature (For example, a room-temperature aqueous solution, 298 Kelvin). Simultaneously, it retrieves pre-stored gas-liquid property parameters from the database, including: gas constant. Specific heat capacity of gas at constant pressure Gas thermal diffusivity Liquid density and surface tension .

[0078] S2, using the gas mass flow rate The initial temperature of the gas and the ambient temperature of the liquid Using the bubble volume expansion equation, internal temperature evolution equation, centroid vertical motion equation, and centroid kinematic equation as input variables, a system of one-dimensional ordinary differential equations is constructed; wherein, the additional mass coefficient in the centroid vertical motion equation... and surface tension correction factor Let it be a constant;

[0079] In the solution module, time is used as the basis for calculation. Using [variable name] as the independent variable, a system of one-dimensional ordinary differential equations describing the transient growth process of bubbles is constructed. Specifically, based on the quasi-isobaric approximation (ignoring the transient rate of change of pressure inside the bubble), the following equations are constructed:

[0080] Bubble volume expansion equation:

[0081] (1);

[0082] Internal temperature evolution equation:

[0083] (2);

[0084] Equation of vertical motion of the center of mass:

[0085] (3);

[0086] The expanded and combined equations of motion for the centroid perpendicular to the ground are as follows:

[0087] (4);

[0088] Kinematic equations of the center of mass:

[0089] (5);

[0090] in, Let the transient volume of the bubble be... The time variable is the independent variable within a single bubble formation cycle. The gas constant is... The internal temperature of the bubble. The absolute pressure of the bubble. For the transient mass of the bubble, The specific heat capacity of a gas at constant pressure. For an effective convective heat transfer coefficient, This represents the equivalent surface area of ​​the bubble. For the liquid ambient temperature, The initial temperature of the gas. Let V be the velocity vector of the bubble's center of mass. For the gas injection velocity vector, It is the buoyancy vector. It is the surface tension vector. For the additional quality coefficient, For the density of the liquid, It is the acceleration due to gravity. For the theoretical maximum surface tension, The height of the bubble's center of mass. Let the vertical upward velocity of the bubble's center of mass be denoted as . Let the bubble's equivalent radius be 1. The sine of the centroid elevation angle represents the geometrical substitution term characterizing the degree of asymmetric necking of the bubble. This is the surface tension correction factor.

[0091] In formula (4), the left side of the equation is the additional mass inertial force of the bubble displacing the liquid (ignoring the very small mass of the gas itself); the first term on the right side of the equation is the macroscopic net buoyancy force on the bubble; the second term on the right side of the equation is the vertical capillary retention force; and the third term on the right side of the equation is the expansion inertial reaction force caused by the rapid expansion of the bubble volume.

[0092] In this embodiment of the invention, parameter regularization is set as follows: to decouple thermodynamic and kinetic parameters, during the initialization phase, the hydrodynamic drag coefficient in the vertical motion equation of the center of mass is forcibly set to a constant, that is: the additional mass coefficient is set to... The surface tension correction factor is set to .

[0093] S3. Substitute the effective convective heat transfer coefficient into the aforementioned one-dimensional ordinary differential equation system to obtain an updated one-dimensional ordinary differential equation system; based on the orifice Froude number... And Bond Number Obtain the critical height ratio ;

[0094] The formula for calculating the effective convective heat transfer coefficient is as follows:

[0095] ; ; ;

[0096] in, The effective convective heat transfer coefficient is... For an effective Stanton number, The specific heat capacity of a gas at constant pressure. For gas density, The gas injection rate at the orifice. For the gas phase Pecklet number, denoted as the gas thermal diffusivity.

[0097] The effective convective heat transfer coefficient was obtained through calculation. Substitute the internal temperature evolution equation into the thermodynamic closure equation.

[0098] The critical height ratio The calculation formula is:

[0099] ; ; ;

[0100] in, For the Froude number at the orifice, For Bond number, It is the acceleration due to gravity. For the density of the liquid, Liquid surface tension Using the aforementioned critical height ratio This serves as the termination threshold for subsequent integration.

[0101] S4. Perform forward time integration on the updated one-dimensional ordinary differential equation system to obtain the centroid height and equivalent diameter of the bubble; when the ratio of the centroid height to the equivalent diameter is not less than the critical height ratio The integration process ends at a certain point, and the actual time it takes for the bubble to detach is obtained. Output the predicted actual detachment volume Specifically, this includes:

[0102] S4.1, Settings Initial conditions at time: initial volume of the bubble initial temperature Initial centroid velocity Initial centroid height ;

[0103] S4.2. The fourth-order Runge-Kutta method is used to apply a fixed-step method to the system of one-dimensional ordinary differential equations. The time-forward integration is performed; at the end of each integration step, the following judgment is made:

[0104] S4.2.1 Obtain the transient volume obtained by integrating at the current time step. and center of mass height ;in, For the first Each integration step size. It is a positive integer;

[0105] S4.2.2. Based on the equivalent sphere assumption, obtain the equivalent diameter of the bubble at the current moment. ;

[0106] S4.2.3, The ratio of the centroid height to the equivalent diameter Ratio to the critical height Perform a comparison; if If so, proceed to the next integration step and repeat steps S4.2.1 to S4.2.3; if If the bubble escapes, the bubble escape check is triggered, the scoring loop terminates, and the current scoring time at the time the bubble escape check is triggered is recorded. The actual time of bubble release Output the bubble volume at the current moment. For the predicted actual detachment volume .

[0107] S5, Based on the initial temperature of the gas and the actual detachment time of the bubble Instantaneous absolute pressure, obtaining isothermal mass injection equivalent volume ;

[0108] The formula for calculating the equivalent volume of the isothermal mass injection is as follows:

[0109] ;

[0110] in, To inject an equivalent volume into the isothermal mass at the moment the bubble detaches. For the actual detachment time of the bubble Instantaneous absolute pressure.

[0111] S6. Maintain the gas mass flow rate Assuming the initial temperature of the injected gas remains constant at the same level as the ambient temperature of the liquid environment. Turn off the heat exchange; repeat steps S2 to S4 until the geometric separation criterion is met, and output the isothermal reference separation volume. ;

[0112] Copy the system of equations from step S2 in the solution module, and keep it. Unchanged, forced setting of input parameters And assume Repeat the forward integration process in step S4 until the geometric separation criterion is satisfied. Record and output the isothermal reference separation volume The isothermal reference is separated from the volume. This characterizes the achievable detachment volume of bubbles under ideal isothermal conditions that eliminate the influence of the initial high density of cold air. By comparison... and This allows for the quantification of the initial volume loss resulting from cold gas injection, thus providing a dynamic critical threshold for subsequent evaluation of whether the sensible thermal expansion of the bubbles is sufficient.

[0113] S7. Based on the predicted actual detachment volume and the equivalent volume of the isothermal mass injection Obtain the thermal expansion fraction ; based on the isothermal reference, the volume is separated and the equivalent volume of the isothermal mass injection Obtain the critical expansion threshold ;when At that time, reduce the gas mass flow rate. ;when At the same time, increase the gas mass flow rate. .

[0114] In this embodiment of the invention, the thermal expansion fraction ( The actual volume of the bubble escaping is not an inherent physical property parameter of the gas, but a dimensionless process evaluation index used to characterize the degree of sensible heat-driven expansion of the bubble at the moment of escaping. ) isothermal mass injection into equivalent volume ( The thermal expansion fraction is composed of the thermally expanded volume and the actual volume separated. The thermal expansion fraction is defined as the proportion of the thermally expanded volume to the actual volume separated. The larger this value, the more heat the gas absorbs before it leaves the vent, and the more fully the work is done during in-situ expansion.

[0115] Similarly, the critical expansion threshold ( ) is defined as the isothermal reference separation volume ( ) and isothermal mass injection equivalent volume ( The difference between the two is a percentage of the actual detached volume. The proportion of ), that is This threshold characterizes the minimum volume deficit that the system must overcome to achieve macroscopic escape from force equilibrium due to the relatively high initial density of the injected cold gas.

[0116] In this embodiment of the invention, by comparing the two dimensionless indicators in real time, it is determined whether the current gas injection process is in a state of "net expansion (sufficient heat exchange)" or "net contraction (insufficient heat exchange)", thereby guiding the optimization control.

[0117] The adjustment logic of the optimization control is as follows:

[0118] Operating condition A (insufficient heat exchange): When the comparison result is Time (e.g.) Figure 2 The net contraction zone shown indicates that the gas detached before it could fully absorb heat and expand. The PLC controller outputs an adjustment command to the Mass Flow Controller (MFC), which reduces the gas mass flow rate per orifice by a preset step size. Alternatively, a switching signal can be output to the multi-channel nozzle switching valve group to close the current large-diameter nozzle and switch to a smaller-diameter standby nozzle to extend the bubble growth time. Extending the growth time promotes sufficient thermal expansion of the bubbles, increasing the macroscopic detachment volume of a single bubble, optimizing the contact surface area between the gas and liquid phases, and suppressing near-zone bubble aggregation and short-circuiting of the gas flow caused by the high-frequency detachment of unexpanded cold bubbles. This, in turn, improves the overall mass transfer efficiency and gas utilization rate of the reactor. In this embodiment of the invention, the operating condition A (insufficient heat transfer state) has a clear mathematical definition and macroscopic physical manifestation:

[0119] a1. Mathematical definition: The thermal expansion fraction calculated in real time by the system is strictly less than the critical expansion threshold, i.e., it satisfies the inequality. The inequality indicates that the thermal expansion volume generated by the bubble during its growth period through sensible heat exchange between the gas and liquid phases is insufficient to compensate for the initial isothermal volume loss caused by the injection of low-temperature, high-density gas.

[0120] a2. Macroscopic manifestations:

[0121] Net volume shrinkage: Under this operating condition, the actual volume of the bubble that escapes. Strictly less than the isothermal reference separation volume under the same mass flow rate (That is, a net contraction in macroscopic volume occurs).

[0122] Deteriorating flow pattern: Because bubbles prematurely meet the kinetic detachment conditions before reaching thermal equilibrium, the bubble detachment frequency increases abnormally. In industrial settings, this manifests as a dense cluster of small bubbles near the nozzle, which easily leads to violent coalescence or localized gas flow short-circuiting. This significantly reduces the effective gas-liquid mass transfer surface area within the reactor and decreases the efficiency of in-situ gas expansion at the bottom of the molten pool.

[0123] Operating Condition B (Capacity Optimization State): When the comparison result is Time (e.g.) Figure 2 The net expansion zone shown indicates that heat utilization is sufficient. While maintaining the total gas injection volume requirement, the PLC controller uses a hill-climbing algorithm, increasing the volume slightly by a preset step size. And reassess in the next control cycle. and The difference. When the difference narrows to a preset safety margin boundary (e.g. When ), lock the current The setpoint. Operating condition B (capacity optimization state) represents a state of efficient sensible heat utilization and net expansion. In this state, the actual volume of the bubble detachment is greater than the isothermal reference volume, the gas has fully absorbed heat and expanded before detachment, the flow near the nozzle is stable, and no airflow short circuit occurs. The purpose of the PLC controller using the hill-climbing algorithm to gradually increase the gas mass flow rate is to: based on utilizing the current system heat transfer margin, gradually increase the gas injection capacity until it approaches the heat transfer limit (i.e., ...). This allows for maximizing the gas injection rate and production efficiency of the reactor while ensuring that the mass transfer area between the gas and liquid phases does not decrease.

[0124] Multi-nozzle coordinated control: If the system is configured with an independently controllable multi-nozzle array, single-orifice adjustment is triggered under operating condition A. Simultaneously, the PLC controller outputs commands to activate additional backup nozzles to ensure a constant total gas injection capacity of the reactor, achieving optimal combined efficiency of single-hole mass transfer and overall capacity. This multi-nozzle collaborative control is essentially a flow regime adjustment strategy based on spatial flux dispersion. Its technical effect is that, while maintaining the total gas injection rate of the reactor, by reducing the single-hole injection flow rate and simultaneously increasing the number of working nozzles, the generation and sensible heat exchange time of a single bubble at the nozzle is extended. This control method transforms concentrated high-flow-rate gas injection into multi-point distributed low-flow-rate gas injection, helping to alleviate the bubble aggregation and short-circuiting phenomenon that easily occurs under single-hole high-flow-rate conditions, thereby improving the gas-liquid phase mass transfer area within the reactor while ensuring the total gas injection capacity of the system.

[0125] like Figure 2 The figure illustrates the change in the detachment volume of a non-isothermal bubble relative to an isothermal reference under different combinations of injection orifice diameters and single-orifice mass flow rates. Figure 2 The horizontal axis represents the gas mass flow rate per orifice, and the vertical axis represents the injection orifice diameter; the upward-pointing triangle indicates that the actual separation volume is greater than the isothermal reference separation volume, i.e. The net expansion state; the downward triangle indicates that the actual separation volume is less than the isothermal reference separation volume, i.e. The net shrinkage state. The percentages in the figure represent the relative deviation of the actual separation volume from the isothermal reference separation volume. (From...) Figure 2 It can be seen that under non-isothermal gas injection conditions, the volume of the bubble detachment does not increase monotonically with the extension of the generation time, but is controlled by the competition between the volume loss caused by the initial density of the cold gas and the expansion driven by sensible heat.

[0126] like Figure 3 As shown, this illustrates the fraction of thermal expansion in embodiments of the present invention. With critical expansion threshold The determination relationship. Figure 3 The curve on the left in the figure represents different nozzle orifice diameters. and The variation of gas mass flow rate with single-orifice flow rate; the symbols on the right indicate the volumetric state obtained by comparing the thermal expansion fraction with the critical expansion threshold. When When the sensible heat-driven expansion can compensate for the volume loss caused by the initial density of the cold air, it is determined to be a net expansion state; when When the sensible heat-driven expansion is insufficient to compensate for the volume loss, it is determined to be a net contraction state. The PLC controller can then determine whether the current injection parameters have sufficient thermal expansion margin and implement adjustment strategies such as reducing the single-orifice flow rate, increasing the number of working nozzles, or increasing the single-orifice flow rate.

[0127] like Figure 4 The diagram illustrates the kinematic basis for using the ratio of the center of mass height to the equivalent diameter as the criterion for geometric separation in embodiments of the present invention. The upper bar chart compares the vertical rising velocity of the bubble's center of mass with the equivalent radial expansion rate under various experimental conditions; the lower scatter plot shows the ratio of the two, represented by a rhombus. The results show that at the end of the pinch-off period, the rising velocity of the bubble's center of mass is usually greater than the equivalent radial expansion rate, with an average ratio of approximately 6.34. This kinematic difference causes the spatial deviation of the center of mass trajectory to be mainly converted into a smaller separation time deviation, thereby reducing the impact of the one-dimensional model spatial trajectory error on the separation volume prediction. Figure 4 This demonstrates the rationality of the forward integral termination criterion and the kinematic regularization settings.

[0128] Example 2

[0129] This invention provides a bubble detachment volume prediction and injection optimization control system, comprising:

[0130] The parameter acquisition module is used to obtain the gas mass flow rate of the submersible non-isothermal gas injection system. Injection orifice diameter Initial gas temperature Liquid ambient temperature and gas-liquid physical properties;

[0131] The equation construction and regularization module is used to employ the gas mass flow rate. The initial temperature of the gas and the ambient temperature of the liquid Using the bubble volume expansion equation, internal temperature evolution equation, centroid vertical motion equation, and centroid kinematic equation as input variables, a system of one-dimensional ordinary differential equations is constructed; wherein, the additional mass coefficient in the centroid vertical motion equation... and surface tension correction factor Let it be a constant;

[0132] The closed-loop setting module is used to substitute the effective convective heat transfer coefficient into the one-dimensional ordinary differential equation system to obtain an updated one-dimensional ordinary differential equation system; based on the orifice Froude number... And Bond Number Obtain the critical height ratio ;

[0133] The forward integral prediction module is used to perform forward integration over time on the updated one-dimensional ordinary differential equation system to obtain the centroid height and equivalent diameter of the bubble; when the ratio of the centroid height to the equivalent diameter is not less than the critical height ratio... The integration process ends at a certain point, and the actual time it takes for the bubble to detach is obtained. Output the predicted actual detachment volume ;

[0134] The equivalent volume calculation module is used to calculate the volume based on the initial temperature of the gas. and the actual detachment time of the bubble Instantaneous absolute pressure, obtaining isothermal mass injection equivalent volume ;

[0135] The reference volume calculation module is used to maintain the gas mass flow rate. Assuming the initial temperature of the injected gas remains constant at the same level as the ambient temperature of the liquid environment. Turn off the heat exchange; repeat steps S2 to S4 until the geometric separation criterion is met, and output the isothermal reference separation volume. ;

[0136] The optimization control module is used to determine the actual detachment volume based on the prediction. and the equivalent volume of the isothermal mass injection Obtain the thermal expansion fraction ; based on the isothermal reference, the volume is separated and the equivalent volume of the isothermal mass injection Obtain the critical expansion threshold ;when At that time, reduce the gas mass flow rate. ;when At the same time, increase the gas mass flow rate. .

[0137] This embodiment 2 also provides an electronic device, which includes: a memory, a processor, and a computer program or instructions stored in the memory. The processor executes the computer program or instructions to implement the bubble detachment volume prediction and gas injection optimization control method of the immersion non-isothermal gas injection system in embodiment 1.

[0138] Although not shown, the electronic device includes a processor that can perform various appropriate operations and processes based on programs and / or data stored in read-only memory (ROM) or loaded from a storage portion into random access memory (RAM). The processor can be a multi-core processor or may contain multiple processors. In some embodiments, the processor may include a general-purpose main processor and one or more specialized coprocessors, such as a central processing unit, graphics processing unit (GPU), neural network processor (NPU), digital signal processor (DSP), etc. Various programs and data required for device operation are also stored in RAM. The processor, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0139] Furthermore, in this embodiment of the invention, the initial gas temperature is acquired in real time via a thermocouple installed at the end of the gas injection pipeline, a temperature transmitter installed on the side wall of the reactor, and a pipeline pressure transmitter. Liquid ambient temperature and system pressure;

[0140] Furthermore, in this embodiment of the invention, an industrial-grade programmable logic controller (PLC) or an industrial control computer is used for calculation and control to realize the bubble separation volume prediction and gas injection optimization control method of the immersion non-isothermal gas injection system in Embodiment 1, including the solution steps of the one-dimensional ordinary differential equation system and the optimization control steps; periodically reading the data from the parameter acquisition module, performing forward integration and volume decoupling calculation, and generating analog or digital adjustment instructions;

[0141] Furthermore, in this embodiment of the invention, the adjustment command is received by a mass flow controller (MFC) connected in series with the main gas injection pipeline, and a multi-channel nozzle array and matching electromagnetic switching valve group installed at the bottom of the reactor, so as to dynamically adjust the single-hole inlet flow rate ṁ and the start / stop state of the nozzle.

[0142] The above embodiments should be understood as being used only to illustrate the present invention more clearly, and not to limit the scope of the present invention. After reading the present invention, any modifications of the present embodiments by those skilled in the art will fall within the scope defined by the appended claims.

Claims

1. A method for predicting bubble separation volume and optimizing injection control in an immersion non-isothermal gas injection system, characterized in that, include: S1. Obtain the gas mass flow rate of the submersible non-isothermal gas injection system. Injection orifice diameter Initial gas temperature Liquid ambient temperature and gas-liquid physical properties; S2, with the gas mass flow rate The initial temperature of the gas and the ambient temperature of the liquid Using the bubble volume expansion equation, internal temperature evolution equation, centroid vertical motion equation, and centroid kinematic equation as input variables, a system of one-dimensional ordinary differential equations is constructed; wherein, the additional mass coefficient in the centroid vertical motion equation... and surface tension correction factor Let it be a constant; S3. Substitute the effective convective heat transfer coefficient into the aforementioned one-dimensional ordinary differential equation system to obtain an updated one-dimensional ordinary differential equation system; based on the orifice Froude number... And Bond Number Obtain the critical height ratio ; S4. Perform forward time integration on the updated one-dimensional ordinary differential equation system to obtain the centroid height and equivalent diameter of the bubble; when the ratio of the centroid height to the equivalent diameter is not less than the critical height ratio The integration process ends at a certain point, and the actual time it takes for the bubble to detach is obtained. Output the predicted actual detachment volume ; S5, based on the initial temperature of the gas and the actual detachment time of the bubble Instantaneous absolute pressure, obtaining isothermal mass injection equivalent volume ; S6. Maintain the gas mass flow rate Assuming the initial temperature of the injected gas remains constant at the same level as the ambient temperature of the liquid environment. Turn off the heat exchange and repeat steps S2 to S4 until the geometric separation criterion is met, and output the isothermal reference separation volume. ; S7. Based on the predicted actual detachment volume and the equivalent volume of the isothermal mass injection Obtain the thermal expansion fraction ; based on the isothermal reference, the volume is removed and the equivalent volume of the isothermal mass injection Obtain the critical expansion threshold ;when At that time, reduce the gas mass flow rate. ;when At the same time, increase the gas mass flow rate. .

2. The method for predicting bubble separation volume and optimizing gas injection in an immersion non-isothermal gas injection system according to claim 1, characterized in that, In step S2, the formula for calculating the bubble volume expansion equation is as follows: ； The formula for calculating the internal temperature evolution equation is as follows: ； The formula for calculating the vertical motion equation of the centroid is as follows: ； After expansion and merging, it looks like this: ； The formula for calculating the kinematic equations of the center of mass is as follows: ； in, Let the transient volume of the bubble be... The time variable is the independent variable within a single bubble formation cycle. The gas constant is... The internal temperature of the bubble. The absolute pressure of the bubble. For the transient mass of the bubble, The specific heat capacity of a gas at constant pressure. For an effective convective heat transfer coefficient, This represents the equivalent surface area of ​​the bubble. For the liquid ambient temperature, The initial temperature of the gas. Let V be the velocity vector of the bubble's center of mass. For the gas injection velocity vector, It is the buoyancy vector. It is the surface tension vector. For the additional quality coefficient, For the density of the liquid, It is the acceleration due to gravity. For the theoretical maximum surface tension, The height of the bubble's center of mass. Let the vertical upward velocity of the bubble's center of mass be denoted as . Let the bubble's equivalent radius be 1. Let be the sine of the elevation angle of the center of mass. This is the surface tension correction factor.

3. The method for predicting bubble separation volume and optimizing gas injection in an immersion non-isothermal gas injection system according to claim 1, characterized in that, In step S3, the formula for calculating the effective convective heat transfer coefficient is: ； ； ； in, The effective convective heat transfer coefficient is... For an effective Stanton number, The specific heat capacity of a gas at constant pressure. For gas density, The gas injection rate at the orifice. For the gas phase Pecklet number, The thermal diffusivity of the gas; The critical height ratio The calculation formula is: ； ； ； in, For the Froude number of the orifice, For Bond number, It is the acceleration due to gravity. For the density of the liquid, is the surface tension of the liquid.

4. The method for predicting bubble separation volume and optimizing gas injection in an immersion non-isothermal gas injection system according to claim 1, characterized in that, Step S4 specifically includes: S4.1, Settings Initial conditions at time: initial volume of the bubble initial temperature Initial centroid velocity Initial centroid height ; S4.

2. The fourth-order Runge-Kutta method is used to apply a fixed-step method to the system of one-dimensional ordinary differential equations. The time-forward integration is performed; at the end of each integration step, the following judgment is made: S4.2.1 Obtain the transient volume obtained by integrating at the current time step. and center of mass height ;in, For the first Each integration step size. It is a positive integer; S4.2.

2. Based on the equivalent sphere assumption, obtain the equivalent diameter of the bubble at the current moment. ; S4.2.3, The ratio of the centroid height to the equivalent diameter Ratio to the critical height Perform a comparison; if If so, proceed to the next integration step and repeat steps S4.2.1 to S4.2.3; if If the bubble escapes, the bubble escape check is triggered, the scoring loop terminates, and the current scoring time at the time the bubble escape check is triggered is recorded. The actual time of bubble release Output the bubble volume at the current moment. For the predicted actual detachment volume .

5. The method for predicting bubble separation volume and optimizing gas injection in an immersion non-isothermal gas injection system according to claim 1, characterized in that, In step S5, the formula for calculating the equivalent volume of the isothermal mass injection is: ； in, To inject an equivalent volume into the isothermal mass at the moment the bubble detaches. The gas constant is... For the actual detachment time of the bubble Instantaneous absolute pressure.

6. The method for predicting bubble separation volume and optimizing gas injection in an immersion non-isothermal gas injection system according to claim 4, characterized in that, In step S6, the geometric separation criterion is: The isothermal reference is separated from the volume. The transient volume obtained by integrating at the current time step ;in, The height of the centroid obtained by integration at the current moment. The equivalent diameter of the bubble at the current moment. For the first Each integration step size. It is a positive integer.

7. The method for predicting bubble separation volume and optimizing gas injection in an immersion non-isothermal gas injection system according to claim 1, characterized in that, In step S7, the thermal expansion fraction The calculation formula is: The critical expansion threshold The calculation formula is: .

8. The method for predicting bubble separation volume and optimizing gas injection in an immersion non-isothermal gas injection system according to claim 1, characterized in that, The immersion non-isothermal gas injection system is configured with a multi-channel nozzle array; in step S7, when At that time, reduce the gas mass flow rate. Simultaneously activate the backup nozzle to increase the number of working nozzles; and / or when At that time, a hill-climbing algorithm is used to increase the gas mass flow rate by a preset step size. Repeat S1 to S7 until... The preset safety margin boundary has been reached.

9. A bubble detachment volume prediction and gas injection optimization control system, characterized in that, include: The parameter acquisition module is used to obtain the gas mass flow rate of the submersible non-isothermal gas injection system. Injection orifice diameter Initial gas temperature Liquid ambient temperature and gas-liquid physical properties; The equation construction and regularization module is used to employ the gas mass flow rate. The initial temperature of the gas and the ambient temperature of the liquid Using the bubble volume expansion equation, internal temperature evolution equation, centroid vertical motion equation, and centroid kinematic equation as input variables, a system of one-dimensional ordinary differential equations is constructed; wherein, the additional mass coefficient in the centroid vertical motion equation... and surface tension correction factor Let it be a constant; The closed-loop setting module is used to substitute the effective convective heat transfer coefficient into the one-dimensional ordinary differential equation system to obtain an updated one-dimensional ordinary differential equation system; based on the orifice Froude number... And Bond Number Obtain the critical height ratio ; The forward integral prediction module is used to perform forward integration over time on the updated one-dimensional ordinary differential equation system to obtain the centroid height and equivalent diameter of the bubble; when the ratio of the centroid height to the equivalent diameter is not less than the critical height ratio... The integration process ends at a certain point, and the actual time it takes for the bubble to detach is obtained. Output the predicted actual detachment volume ; The equivalent volume calculation module is used to calculate the volume based on the initial temperature of the gas. and the actual detachment time of the bubble Instantaneous absolute pressure, obtaining isothermal mass injection equivalent volume ; The reference volume calculation module is used to maintain the gas mass flow rate. Assuming the initial temperature of the injected gas remains constant at the same level as the ambient temperature of the liquid environment. Turn off the heat exchange; repeat steps S2 to S4 until the geometric separation criterion is met, and output the isothermal reference separation volume. ; The optimization control module is used to determine the actual detachment volume based on the prediction. and the equivalent volume of the isothermal mass injection Obtain the thermal expansion fraction ; based on the isothermal reference, the volume is removed and the equivalent volume of the isothermal mass injection Obtain the critical expansion threshold ;when At that time, reduce the gas mass flow rate. ;when At the same time, increase the gas mass flow rate. .

10. An electronic device comprising a memory, a processor, and a computer program / instructions stored in the memory, characterized in that, The processor executes the computer program / instructions to implement the bubble detachment volume prediction and gas injection optimization control method for the immersion non-isothermal gas injection system as described in any one of claims 1 to 8.

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