A novel wall heat flux partitioning model based on bubble merging behavior and evaporation zone
By introducing bubble merging and evaporation regions into the wall heat flux partitioning model and combining multiple heat transfer mechanisms, the problem of inaccurate predictions in existing models under high wall superheat is solved, and accurate predictions of critical heat flux density and transition boiling stage are achieved, thus improving the accuracy of flow boiling numerical simulation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HEFEI UNIV OF TECH
- Filing Date
- 2026-03-10
- Publication Date
- 2026-06-02
AI Technical Summary
Existing wall heat flux partitioning models struggle to accurately predict critical heat flux density and transition boiling stages under high wall superheat, failing to adequately consider bubble coalescence behavior and slip heat transfer mechanisms, resulting in an underestimation of heat transfer.
In the spatial dimension, the wall is divided into non-bubble-affected region, nucleation point region, bubble sliding region and evaporation region. In the temporal dimension, bubble nucleation period and sliding period are divided. Combining bubble merging behavior and evaporation region, a new wall heat flux partitioning model is established, including mechanisms such as quenching heat transfer, sliding bubble heat transfer, evaporation heat transfer, one-way convective heat transfer and steam heat transfer.
It can accurately predict the wall heat flux during the nucleation boiling stage and successfully predict the transition boiling stage after the critical heat flux density, providing a safety assessment tool for equipment under extreme conditions and improving the accuracy of flow boiling numerical simulation.
Smart Images
Figure CN122133342A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of heat flux technology, specifically to a novel wall heat flux partitioning model based on bubble merging behavior and evaporation zones. Background Technology
[0002] In numerical simulations of fluid boiling, accurately predicting the heat exchange between the wall and the fluid is crucial, which typically relies on wall heat flux partitioning models. Classical wall heat flux partitioning models, such as... The model decomposes the total heat flux of the wall into three parts: single-phase convective heat transfer, quenching heat transfer, and evaporative heat transfer. It can achieve good prediction results under medium and low heat flux density (nuclear boiling stage).
[0003] However, existing models have significant limitations in handling boiling heat transfer under high wall superheat: classical models struggle to accurately predict the critical heat flux density and cannot describe the transition boiling stage after the critical heat flux density, restricting their application in equipment safety analysis and extreme condition design. Existing models typically do not adequately consider the bubble coalescence behavior unique to flow boiling and the slip heat transfer mechanism after bubbles detach from their nucleation points. The disruption of the thermal boundary layer and the enhancement of heat transfer by bubble slip are crucial components of flow boiling; neglecting this mechanism leads to an underestimation of the total heat transfer, especially under high wall superheat, where prediction bias further increases. Therefore, a novel wall heat flux partitioning model based on bubble coalescence behavior and the evaporation zone is needed to address these issues. Summary of the Invention
[0004] In view of the shortcomings of the existing technology, the purpose of this invention is to provide a new wall heat flux partitioning model based on bubble merging behavior and evaporation zone, so as to solve the problems existing in the above-mentioned background technology.
[0005] This invention is implemented as follows: a novel wall heat flux partitioning model based on bubble merging behavior and evaporation regions. Spatially, the model divides the wall into a non-bubble-affected region, a nucleation point region, a bubble sliding region, and an evaporation region. Temporally, the bubble nucleation cycle is divided into bubble waiting time and bubble generation time, and the bubble sliding cycle is divided into transient heat transfer-dominated time and one-way relative heat transfer-dominated time. Based on the above spatiotemporal partitioning, the total wall heat flux... Cooling and heat transfer caused by bubbles leaving the nucleation point Transient heat transfer caused by sliding bubbles Evaporative heat transfer during bubble growth Single-phase heat transfer in non-bubble-affected regions And steam heat transfer in the drying zone Together, the total heat flow of the wall is expressed as: ,in, This represents the percentage of the area that has been evaporated.
[0006] As a further aspect of the present invention, the model is constructed based on the following bubble merging behavior: the distance between adjacent nucleation points follows a Poisson distribution; bubbles on the vaporization nucleus do not nucleate simultaneously; after merging, bubbles leave the wall directly and enter the mainstream; only pairwise lateral merging occurs between bubbles; after merging, the thickness of the superheated liquid layer near the bubble is greater than the bubble's detachment diameter, and no condensation heat transfer occurs at this point.
[0007] As a further aspect of the present invention, based on bubble growth time... and bubble detachment frequency This results in the distance between adjacent nucleation points considering that bubbles nucleate at different times being smaller than the bubble detachment diameter. probability distribution , , The original nucleation point density is obtained directly from the nucleation point density model, based on probability. Density of original nucleation sites After correction, the density of nucleation sites for independent growth is obtained. and the number of nucleation points after the merger Ultimately, an effective assembly nucleation point density is obtained. .
[0008] As a further aspect of the present invention, evaporative heat transfer... The computational model includes the evaporation heat transfer of independently growing bubbles and merged bubbles, and incorporates the top condensation mechanism during bubble growth. ,in , , , , , , These are, respectively, steam density, latent heat of vaporization, condensation heat transfer coefficient, liquid saturation temperature, mainstream temperature, area of contact between bubbles and subcooled liquid, and condensation initiation time.
[0009] As a further aspect of the present invention, the rapid cooling heat transfer... The calculation model comprehensively considers the difference in liquid volume carried away by bubbles when they leave the nucleation point. Different liquid volume carry-away models are established for independently growing bubbles and merged bubbles, and the calculation formula is as follows: ,in , , , These are the density, specific heat capacity, liquid volume carried away by independently growing bubbles, and liquid volume carried away by merged bubbles, respectively, of the heating surface material. , , The area of the bubble-affected region at the nucleation point can be expressed as: .
[0010] As a further aspect of the present invention, the transient heat transfer caused by the bubble sliding... The computational model divides the heat transfer process in the sliding bubble-affected region within a bubble nucleation cycle into two stages: transient heat transfer dominance and single-phase convective heat transfer dominance. The calculation formula is as follows: ,in: For the area of influence of the sliding bubble, the transient heat transfer dominance time is... , , , as well as These are the time for one bubble nucleation cycle, the liquid's thermal conductivity, the liquid's thermal diffusivity, and the convective heat transfer coefficient, respectively. ,in , , , These are, respectively, liquid density, liquid specific heat capacity at constant pressure, liquid friction velocity, and liquid dimensionless temperature.
[0011] As a further aspect of the present invention, the area of the sliding bubble-affected region... , Indicates the distance the bubble slides. This represents the average sliding diameter of the bubble; the bubble sliding distance combines the two processes of bubble growth through evaporation and merging with nucleation points along its path. , This indicates the number of nucleation points traversed by the sliding bubble. And a reduction factor was introduced. Nucleation point density of the sliding region Make corrections to obtain .
[0012] As a further aspect of the present invention, the proportion of the drying area is... It is a component of the average vapor volume fraction of the bubble layer. The relevant piecewise functions, ,in This represents the critical vapor volume fraction at the starting point of wall drying. , ,when At that time, the model determined that the flow boiling had transitioned from the nucleation boiling stage to the transition boiling stage.
[0013] As a further aspect of the present invention, the single-phase convective heat transfer... The calculations take place in the non-bubble-affected region, and its heat transfer coefficient is derived through the standard wall function, with the specific formula as follows: in, This represents the area of the bubble's influence region at the nucleation point.
[0014] As a further aspect of the present invention, the steam heat transfer in the drying zone... The calculation model is as follows: ,in , , , , , These are, respectively, steam density, steam specific heat capacity at isobaric pressure, steam friction velocity, steam dimensionless temperature, wall temperature, and steam temperature. This heat transfer mechanism is... Time relative to total wall heat flow Make a contribution.
[0015] Compared with the prior art, the beneficial effects of the present invention are: By introducing the drying zone and its steam heat transfer mechanism, and establishing a drying zone proportion model, it can not only accurately predict the wall heat flux during the nucleation boiling stage, but also successfully predict the occurrence of the critical heat flux density, and extend the prediction range to the transition boiling stage after the critical heat flux density, providing a powerful tool for the safety assessment of equipment under extreme operating conditions.
[0016] By incorporating bubble slip heat transfer as an independent and important component into the total heat flux calculation, and by performing a fine temporal and spatial degree of temperature control on its heat transfer process (divided into transient heat transfer dominance and single-phase flow dominance), the accuracy of flow boiling numerical simulation is improved. Attached Figure Description
[0017] Figure 1 This is a schematic diagram of a new wall heat flux partitioning model based on bubble merging behavior and the drying region.
[0018] Figure 2 This is a schematic diagram illustrating the random distribution and non-simultaneous growth of bubbles in an embodiment of the present invention.
[0019] Figure 3 This is a schematic diagram of the bubble growth process in an embodiment of the present invention.
[0020] Figure 4 This is a schematic diagram of rapid cooling heat transfer in an embodiment of the present invention.
[0021] Figure 5 This is a schematic diagram of bubble merging in an embodiment of the present invention.
[0022] Figure 6 This is a schematic diagram of the spacing between nucleation points in an embodiment of the present invention.
[0023] Figure 7This is a schematic diagram of the experimental channel and simulation boundary conditions in an embodiment of the present invention.
[0024] Figure 8 This is a schematic diagram illustrating the mesh independence verification in an embodiment of the present invention.
[0025] Figure 9 For the embodiments of the present invention in , , A schematic diagram of boiling data under operating conditions.
[0026] Figure 10 This is a model diagram for predicting the critical heat flux density in an embodiment of the present invention.
[0027] Figure 11 This is a comparative illustration of the critical heat flux density in embodiments of the present invention. Figure 1 .
[0028] Figure 12 This is a comparative illustration of the critical heat flux density in embodiments of the present invention. Figure 2 .
[0029] Figure 13 This is a comparative illustration of the critical heat flux density in embodiments of the present invention. Figure 3 .
[0030] Figure 14 This is a comparative illustration of the critical heat flux density in embodiments of the present invention. Figure 4 . Detailed Implementation
[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0032] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.
[0033] like Figure 1 As shown, this embodiment of the invention provides a novel wall heat flux partitioning model based on bubble merging behavior and evaporation regions. Spatially, the model divides the wall into a non-bubble-affected region, a nucleation point region, a bubble sliding region, and an evaporation region. Temporally, it divides the bubble nucleation cycle into bubble waiting time and bubble generation time, and the bubble sliding cycle into transient heat transfer-dominated time and one-way relative heat transfer-dominated time. Based on the above spatiotemporal partitioning, the total wall heat flux... Cooling and heat transfer caused by bubbles leaving the nucleation point Transient heat transfer caused by sliding bubbles Evaporative heat transfer during bubble growth Single-phase heat transfer in non-bubble-affected regions And steam heat transfer in the drying zone Together, the total heat flow of the wall is expressed as: ,in, The formula, which defines the percentage of the evaporation zone, couples the five independent heat transfer mechanisms using an area-weighted approach.
[0034] like Figure 2 As shown in this embodiment of the invention, the model is based on five basic assumptions: 1. The distance between adjacent nucleation points follows a Poisson distribution; 2. Bubbles on the vaporization nucleus do not nucleate simultaneously; 3. After merging, bubbles leave the wall and enter the mainstream directly; 4. Bubbles only merge laterally in pairs; 5. After merging, the thickness of the superheated liquid layer near the bubble is greater than the bubble's escape diameter, and no condensation heat transfer occurs at this point. Based on these assumptions, the distance between two adjacent nucleation points can be categorized as greater than or equal to the bubble's escape diameter. and smaller than the bubble detachment diameter Two scenarios. When the distance between adjacent nucleation points is less than... When, its probability distribution can be expressed as The influence of interactions caused by closely spaced bubbles on the density of the vaporization nucleus is considered. Based on this, the density of the original nucleation sites is... After correction, the density of nucleation sites for independent growth is obtained. and the number of nucleation points generated by the merger Ultimate effective assembly core density .in For bubble growth time, For bubble detachment frequency, The original nucleation point density directly obtained from the nucleation point density model. The diameter at which the bubble detaches. This represents the density of nucleation sites for independent bubble growth. This indicates the number of nucleation sites after two bubbles merge. It also introduces the bubble growth time. This can represent a bubble being in a continuous but not simultaneous nucleation state within a bubble nucleation cycle.
[0035] In this embodiment of the invention, to enable the wall heat flux partitioning model to predict critical heat flux and transitional boiling, bubble merging and vapor layer heat transfer phenomena are introduced. Spatially, the wall is divided into a non-bubble-affected region, a nucleation point region, a bubble sliding region, and a drying-out region. Temporally, the bubble nucleation point time is divided into bubble waiting time and bubble generation time, and the bubble sliding time is divided into transient heat transfer-dominated time and one-way relative heat transfer-dominated time. Finally, an improved wall heat flux partitioning model is proposed. This indicates the time during which transient heat transfer dominates in the sliding region, in terms of... This indicates the time during which single-phase flow dominates within the region of influence of the sliding bubble.
[0036] like Figure 3 As shown in the embodiment of the invention, after bubble nucleation, the bubble diameter increases rapidly in the initial stage of formation; this stage is the bubble inertial growth stage. In the early stage of bubble growth, there is a layer of liquid at the bottom of the bubble with a thickness of micrometers; this thin liquid layer is called the microliquid layer. As the microliquid layer evaporates, bubble growth gradually slows down; at this time, bubble growth mainly originates from the evaporation of the superheated layer. When the bubble height exceeds the thickness of the superheated layer, condensation occurs at the top of the bubble. Considering the impact of condensation at the top of the bubble on the bubble volume, evaporative heat transfer... It can be represented as: ,in , , , , , , , , , These are, respectively, vapor density, bubble departure frequency, latent heat of vaporization, bubble departure diameter, condensation heat transfer coefficient, liquid saturation temperature, mainstream temperature, area of contact between bubble and subcooled liquid, bubble growth time, and condensation start time. can be ,in For bubble growth model, The first part of the calculation formula represents the heat transfer of independently growing bubbles at the nucleation point; the second part represents the heat transfer from condensation at the top of the independently growing bubbles during growth; and the third part represents the heat transfer of bubbles after merging at the nucleation point. ,in Contact angle, This refers to the height of the overheating layer. ,in , , These are the liquid thermal conductivity, bubble Reynolds number, and Planck number, respectively.
[0037] like Figure 4 As shown in the embodiment of the present invention, when the bubble grows to a certain diameter (the bubble detaches from the diameter)... After detaching from its nucleation point, the supercooled liquid rapidly covers the dry spot where the bubble left the nucleation point, resulting in transient quenching heat transfer. This study hypothesizes that the bubble carries away a hemispherical vapor with a diameter half the diameter of the bubble as it leaves the nucleation point. The quenching heat transfer can be achieved by… It means that, among them , , , These are the density of the heating surface material, specific heat capacity, liquid volume carried away by independently growing bubbles, and liquid volume carried away by merged bubbles, respectively. , , Therefore, the area of the bubble-affected region at the nucleation point can be expressed as: .
[0038] like Figure 5 and Figure 6 As shown in this embodiment of the invention, during fluid boiling, bubbles leave the nucleation point and slide along the wall. This process is accompanied by the continuous disruption of the thermal boundary layer near the wall, while supercooled liquid continuously flows towards the thermal boundary layer. This process enhances wall heat transfer, and this heat transfer mechanism is called bubble slip heat transfer, which is an important component of fluid boiling heat transfer. To establish a transient quenching heat transfer model, this heat transfer process is simplified to a one-dimensional unsteady-state heat conduction problem of a semi-infinite flat plate. Within one bubble nucleation cycle, the transient heat transfer during the bubble sliding process dominates the influence region of the sliding bubble for a certain period of time. After this time, single-phase convective heat transfer becomes dominant. ,in: , , , as well as These represent the nucleation cycle time of a bubble, the thermal conductivity of the liquid, the thermal diffusivity of the liquid, and the convective heat transfer coefficient, respectively. Wherein: ,in , , , These are, respectively, liquid density, liquid specific heat capacity at constant pressure, liquid friction velocity, and liquid dimensionless temperature.
[0039] In this embodiment of the invention, the bubble sliding distance is a relatively complex parameter. Gilman proposed a bubble sliding distance... In his calculation method, Gilman divided bubble sliding into two parts: evaporative growth and merging. Bubbles slide after leaving the nucleation point. The distance, through evaporative heat transfer, reaches the diameter This growth was determined using the individual bubble correlation proposed by Maity in fluid boiling. ,in , , , , Bubble sliding time The following parameters are considered: bubble diameter, bubble detachment diameter, bubble sliding time, Jacobian number, and bubble Reynolds number. Bubbles merge as they pass through other nucleation points; the diameter of the merged bubble... , These represent the diameter of the merged bubble and the diameter of the bubble at the nucleation point, respectively. (The path of the sliding bubble is shown.) After one nucleation point, the diameter reaches Then continue sliding independently for a distance. Until the diameter grows to the diameter of the bubble buoyancy. Finally, it detaches from the wall. The distance the bubble slides. Bubble sliding time and the average diameter during bubble sliding It can be expressed by the following formula: , , ,in The speed at which the bubble slides. Let be the sliding average diameter of the bubble. Therefore, the area of the region affected by the sliding bubble is... After merging with bubbles at other nucleation points, no new bubbles will slide at that nucleation point for the remainder of the bubble cycle. Therefore, Gilman introduced a reduction factor. This yields a new nucleation point density. , , .
[0040] In this embodiment of the invention, in the spatial dimension, single-phase convective heat transfer occurs in the non-bubble-affected region. Within this region, only single-phase convective heat transfer occurs during the bubble nucleation cycle, and the liquid phase is in direct contact with the superheated wall. Therefore, the single-phase convective heat transfer coefficient is derived using the standard wall function. The single-phase convective heat transfer in the non-bubble-affected region can be expressed as: .
[0041] In this embodiment of the invention, as the wall superheat continuously increases, nucleation sites are continuously activated, and the number of bubbles formed on the wall gradually increases. When the vapor volume fraction near the wall increases to a certain level, the heat transfer mode changes to convective heat transfer between the vapor and the wall, and the flow boiling changes from nucleation boiling to transition boiling. The convective heat transfer between the wall and the vapor can be expressed as: ,in , , , , , These are, respectively, steam density, steam specific heat capacity at isobaric pressure, steam friction velocity, steam dimensionless temperature, wall temperature, and steam temperature. Steam convective heat transfer occurs in the drying region, and the percentage of this region can be expressed as: , The average vapor volume fraction over the entire bubble layer thickness. This represents the vapor volume fraction at the wall drying breakpoint or at the start of drying. When At this time, steam convection participates in the heat flow across the wall, typically The value is 0.82. It can be represented as: , ,when Once the temperature reaches 0.82, the region transitions from the nucleation boiling stage to the transition boiling stage.
[0042] like Figure 7 and Figure 8 As shown, the model is validated and the results are analyzed below: This study uses the Eulerian two-fluid method as a framework, where the gas-liquid interface between the two phases is calculated using a group equilibrium model. Regarding momentum exchange between the gas and liquid phases, the drag force adopts Tomiyama's improved drag model; the lift force adopts Tomiyama's proposed lift model; the turbulent dissipation force adopts the model of Burns et al.; the wall lubrication force adopts the model proposed by Antal et al.; and the virtual mass coefficient of the virtual mass force is a constant with a value of 0.5. Regarding interphase heat transfer, the vapor-side heat transfer coefficient is a constant, and the liquid-side heat transfer coefficient is calculated using the Ranz-Marshall method. The gas-liquid turbulent flow adopts the k-ε turbulence model, and near-wall heat transfer is embedded in both the new model and the RPI model, with model validation using Gilman's experimental data. The experimental section uses a rectangular channel with dimensions of 220mm × 30mm × 10mm, and a rectangular structure with a heating surface of 10mm × 20mm. The boundary conditions are as follows: a velocity inlet and a pressure outlet; constant heat flux heating on the heating surface; and all other surfaces are adiabatic walls. To verify mesh independence, a structured mesh was used, divided into three mesh numbers: 150216, 340110, and 965138. A new wall heat flux partitioning model was employed for simulation. Verification results show that, under the same superheat, the prediction of wall heat flux by this wall heat flux partitioning model is less affected by the mesh number. To ensure computational accuracy and reduce computational cost, this study uses a mesh number of 340110 for numerical simulation.
[0043] like Figure 9 As shown, boiling curves and heat transfer ratio analysis were performed. Figure 9 (a) shows the system pressure at 1.05 bar and the mass flow rate at 1000 kg / (m³). 2(s) Under a subcooling condition of 10K, the comparison between wall heat transfer predictions using the RPI model and the new wall heat flux partitioning model and experimental data is shown. It can be seen that at low wall superheat, the predictions of both the RPI model and the new wall heat flux partitioning model are close to the experimental values. However, at high wall superheat, the predicted values of the RPI model are significantly lower than the experimental values, while the predicted values of the new wall heat flux partitioning model are closer to the experimental values. Furthermore, the new wall heat flux partitioning model can further predict the critical heat flux density and wall heat flux under transition boiling conditions, while the RPI model's prediction deviation at high wall superheat will further increase, and may even result in calculation non-convergence.
[0044] To further analyze the reasons for the improved prediction accuracy of the new wall heat flux partitioning model, this paper studies the heat transfer ratio of each heat transfer mechanism, the area ratio of the wall heat transfer partitions, and the characteristic diameter of bubbles under this condition. The prediction results are shown in [reference needed]. Figure 9(b), (c), and (d). It can be seen that: 1) Convective heat transfer dominates at low wall superheat, gradually decreasing as wall superheat increases. This is because at low wall superheat, fewer nucleation sites are activated, the bubble-affected area is small, and the non-bubble-affected area occupies a larger area, thus single-phase convection dominates. As wall superheat increases, the non-bubble-affected area decreases, and the proportion of single-phase convection heat transfer in this area decreases, resulting in the phenomenon that the proportion of convective heat transfer decreases as wall superheat increases. 2) Bubble slip heat transfer still dominates in the nucleation boiling region, and its proportion first increases and then decreases with increasing wall superheat. This is because at lower wall superheat, the difference between the bubble rising diameter and the bubble detachment diameter increases with increasing wall superheat, resulting in a longer bubble slip distance and a larger slip influence area. Therefore, at low wall superheat, the proportion of bubble slip heat transfer shows an increasing trend. As the wall superheat further increases, although bubble slip heat transfer increases, the increase in other heat transfer mechanisms is more significant, resulting in a decreasing trend in the proportion of bubble slip heat transfer with increasing wall superheat. 3) The proportions of evaporative heat transfer and quenching heat transfer increase with increasing wall superheat. This is because as the wall superheat increases, both the bubble detachment diameter and the vaporization nucleus density increase, leading to an increasing trend in evaporative heat transfer and quenching heat transfer. 4) Steam convection heat transfer appears and rapidly increases near the critical heat flux density, becoming dominant. This is because at this point, the flow boiling transitions from nucleation boiling to transitional boiling, and the wall is covered by a vapor film, thus the proportion of steam heat transfer increases rapidly. The heat transfer proportions of each component under different operating conditions show roughly the same trend with wall superheat. The above analysis shows that the main reason for the low prediction of the RPI model is that it does not consider bubble slip heat transfer, a major heat transfer mechanism in flow boiling that plays a dominant role. It can also be seen that when the wall superheat exceeds the wall superheat corresponding to the critical heat flux density, steam convection heat transfer increases rapidly, while other heat transfer is suppressed, resulting in overall heat transfer deterioration. This process corresponds to... Figure 9 The decrease in the heat transfer curve in (a) is also the reason why the new wall heat flux partitioning model can predict the critical heat flux and part of the transition boiling state.
[0045] Figure 9(c) shows the change in the proportion of heat transfer zones for different heat transfer mechanisms with wall superheat under this operating condition. From this figure, we can see that: 1) At low wall superheat, the non-bubble-affected area is dominant. As the wall superheat increases, the non-bubble-affected area gradually decreases. This is because as the wall superheat increases, the vaporization nucleus density gradually increases, thus causing the bubble-affected area to expand. Therefore, the non-bubble-affected area gradually decreases with increasing wall superheat. 2) The bubble slip region increases rapidly with increasing wall superheat. This is because as the wall superheat increases, the vaporization nucleus density increases, and both the bubble detachment diameter and the buoyancy diameter increase, as does the difference between them. These combined factors lead to an increase in the proportion of the bubble slip area with increasing wall superheat. 3) The nucleation point region increases with increasing wall superheat. This is mainly because as the wall superheat increases, the bubble detachment diameter and the vaporization nucleus density gradually increase. 4) The evaporation zone expands rapidly after exceeding the critical heat flux density point. This is because the volume fraction of the gas phase near the wall increases rapidly after exceeding the critical heat flux density point, leading to a larger gas phase evaporation zone. This is also the key to the new wall heat flux partitioning model for predicting the critical heat flux density.
[0046] Figure 9 (d) illustrates the variations in bubble detachment diameter and bubble rise diameter with wall superheat. The figure shows that: 1) Both bubble detachment diameter and bubble rise diameter increase with increasing wall superheat. This is because as wall superheat increases, the superheated wall layer expands, the bubble growth rate changes, and the unsteady drag force on the bubble increases, leading to larger bubble detachment and rise diameters. 2) The bubble rise diameter is larger than the bubble detachment diameter. This means that after detaching from the nucleation point, the bubble slides along the wall, and evaporative heat transfer still occurs during this process, promoting continuous bubble growth. Bubble slippage disrupts the thermal boundary layer, causing cold fluid to contact the superheated wall, resulting in transient quenching heat transfer. This further explains why the RPI model's predictions are always underestimated. Because the RPI model does not consider bubble sliding heat transfer, it consistently underestimates the predicted boiling flow at high wall superheat. The new model, however, considers the influence of sliding bubbles during the bubble nucleation cycle and exhibits good prediction accuracy across a wider range of wall superheat.
[0047] like Figure 10 As shown, the critical heat flux density is predicted using a vertical water-cooled pipe with a diameter of 8 mm and a length of 1 m. To ensure sufficient fluid development and prevent backflow, an inlet extension and an outlet extension, both 0.2 m indiameter, are added to the 3D model. The boundary conditions are: a constant-temperature heating surface, a velocity inlet, a pressure outlet, and all other wall surfaces are adiabatic. The simulated fluid inlet subcooling is obtained through the inlet equilibrium mass, and the specific expression is as follows: ,in , , , , These are the vertical pipe diameter, fluid mass flow rate, latent heat of phase change, heating section length, and critical heat flux density measured under critical conditions (which can be estimated as 500 when unknown). Meanwhile, this study considers the flow boiling point to have been reached when the gas phase fraction at the wall reaches 0.82.
[0048] Figure 11 The system pressure was shown to be 1.0. The mass flow rate is 1000 The critical heat flux density predicted by the new model for vertical water-cooled pipes is compared with that obtained from the 2006 lookup table. The results show that the new model has good predictive ability for the critical heat flux density of fluid boiling under this operating condition. The red dashed line in the figure represents the critical heat flux density obtained from the 2006 critical heat flux lookup table for this operating condition. This demonstrates that the new model has a certain feasibility in predicting the critical heat flux density of fluid boiling. To further explore the accuracy of the new model in predicting the critical heat flux density of fluid boiling, this study tested the system pressure at 1.0... Up to 5.0 Mass flow rate 1000 By 2000 Numerical simulations were performed on nine sets of operating conditions within the range. The simulation results are shown in the table.
[0049]
[0050] Figure 12 This paper presents a comparison between the critical heat flux density (CHF) predicted by the new model and the CHF obtained from the 2006 lookup table. The results show that the error of the new model in predicting the CHF remains within 22%. This demonstrates that the new model has high accuracy in predicting CHF.
[0051] like Figure 13 As shown, to investigate the effects of different pressures and mass flow rates on the critical heat flux (CHF) of fluid boiling, and to analyze the variation of CHF under different operating conditions, this study compares and analyzes the CHF under different operating conditions. The changes in CHF with mass flow rate under different pressures are presented. The results show that under the same pressure conditions, the CHF of fluid boiling shifts to a later position with increasing mass flow rate. This is because as the fluid mass flow rate increases, the heat carried away from the wall by the fluid also increases. Therefore, under the same wall superheat, the wall heat flux at a higher mass flow rate is lower than that at a lower mass flow rate. This demonstrates that increasing the fluid mass flow rate is an effective means to improve the CHF of fluid boiling and prevent surface failure.
[0052] like Figure 14 The figure shows the variation of the critical heat flux (CHF) for flow boiling with system pressure at different mass flow rates. The results indicate that, at the same mass flow rate, the CHF for flow boiling also shifts later in the system with increasing system pressure. This is because the energy required for bubble growth increases with increasing system pressure, and at the same wall superheat, the bubble diameter decreases with increasing pressure. Therefore, at low wall superheat, the wall heat flux decreases with increasing pressure. At high wall superheat, the wall heat flux increases with increasing pressure. This phenomenon effectively broadens the nucleate boiling range of flow boiling; therefore, the CHF for flow boiling increases with increasing pressure, corresponding to a shift in the wall superheat. Thus, increasing the system pressure is also an effective means of increasing the CHF for flow boiling.
[0053] The above description only details the preferred embodiments of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
[0054] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the disclosure in the specification and embodiments. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the claims.
Claims
1. A novel wall heat flux partitioning model based on bubble merging behavior and evaporation zones, characterized in that, The model divides the wall into a non-bubble-affected region, a nucleation point region, a bubble sliding region, and an evaporation region in the spatial dimension; and divides the bubble nucleation cycle into bubble waiting time and bubble generation time in the temporal dimension, and divides the bubble sliding cycle into transient heat transfer-dominated time and one-way relative heat transfer-dominated time. Based on the above spatiotemporal division, the total heat flux of the wall Cooling and heat transfer caused by bubbles leaving the nucleation point Transient heat transfer caused by sliding bubbles Evaporative heat transfer during bubble growth Single-phase heat transfer in non-bubble-affected regions And steam heat transfer in the drying zone Together, the total heat flow of the wall is expressed as: ,in, This represents the percentage of the area that has been evaporated.
2. The novel wall heat flux partitioning model based on bubble merging behavior and evaporation zone as described in claim 1, characterized in that, The model is constructed based on the following bubble merging behavior: the distance between adjacent nucleation points follows a Poisson distribution; bubbles on the vaporization nucleus do not nucleate simultaneously; after merging, bubbles leave the wall and enter the mainstream directly; only pairwise lateral merging occurs between bubbles; after merging, the thickness of the superheated liquid layer near the bubble is greater than the bubble's detachment diameter, and no condensation heat transfer occurs at that point.
3. The novel wall heat flux partitioning model based on bubble merging behavior and evaporation zone as described in claim 2, characterized in that, Based on bubble growth time and bubble detachment frequency This results in the distance between adjacent nucleation points considering that bubbles nucleate at different times being smaller than the bubble detachment diameter. probability distribution , , The original nucleation point density is obtained directly from the nucleation point density model, based on probability. Density of original nucleation sites After correction, the density of nucleation sites for independent growth is obtained. and the number of nucleation points after the merger Ultimately, an effective assembly nucleation point density is obtained. .
4. The novel wall heat flux partitioning model based on bubble merging behavior and evaporation zone as described in claim 3, characterized in that, Evaporative heat transfer The computational model includes the evaporation heat transfer of independently growing bubbles and merged bubbles, and incorporates the top condensation mechanism during bubble growth. ,in , , , , , , These are, respectively, steam density, latent heat of vaporization, condensation heat transfer coefficient, liquid saturation temperature, mainstream temperature, area of contact between bubbles and subcooled liquid, and condensation initiation time.
5. The novel wall heat flux partitioning model based on bubble merging behavior and evaporation zone as described in claim 3, characterized in that, The quenching heat transfer The calculation model comprehensively considers the difference in liquid volume carried away by bubbles when they leave the nucleation point. Different liquid volume carry-away models are established for independently growing bubbles and merged bubbles, and the calculation formula is as follows: ,in , , , These are the density, specific heat capacity, liquid volume carried away by independently growing bubbles, and liquid volume carried away by merged bubbles, respectively, of the heating surface material. , , .
6. The novel wall heat flux partitioning model based on bubble merging behavior and evaporation zone as described in claim 3, characterized in that, The transient heat transfer caused by bubble sliding The computational model divides the heat transfer process in the sliding bubble-affected region within a bubble nucleation cycle into two stages: transient heat transfer dominance and single-phase convective heat transfer dominance. The calculation formula is as follows: ,in: For the area of influence of the sliding bubble, the transient heat transfer dominance time is... , , , as well as These are the time for one bubble nucleation cycle, the liquid's thermal conductivity, the liquid's thermal diffusivity, and the convective heat transfer coefficient, respectively. ,in , , , These are, respectively, liquid density, liquid specific heat capacity at constant pressure, liquid friction velocity, and liquid dimensionless temperature.
7. The novel wall heat flux partitioning model based on bubble merging behavior and evaporation zone as described in claim 6, characterized in that, The area of the sliding bubble's influence region , Indicates the distance the bubble slides. This represents the average sliding diameter of the bubble; the bubble sliding distance combines the two processes of bubble growth through evaporation and merging with nucleation points along its path. , This indicates the number of nucleation points traversed by the sliding bubble. And a reduction factor was introduced. Nucleation point density of the sliding region Make corrections to obtain .
8. The novel wall heat flux partitioning model based on bubble merging behavior and evaporation zone as described in claim 1, characterized in that, The proportion of the drying area It is a component of the average vapor volume fraction of the bubble layer. The relevant piecewise functions, ,in This represents the critical vapor volume fraction at the starting point of wall drying. , ,when At that time, the model determined that the flow boiling had transitioned from the nucleation boiling stage to the transition boiling stage.
9. The novel wall heat flux partitioning model based on bubble merging behavior and evaporation zone as described in claim 1, characterized in that, The single-phase heat transfer The calculations take place in the non-bubble-affected region, and its heat transfer coefficient is derived through the standard wall function, with the specific formula as follows: in, This represents the area of the bubble's influence region at the nucleation point.
10. The novel wall heat flux partitioning model based on bubble merging behavior and evaporation zone as described in claim 8, characterized in that, Steam heat transfer in the drying zone The calculation model is as follows: ,in , , , , These are, respectively, steam density, steam specific heat capacity at isobaric pressure, steam friction velocity, steam dimensionless temperature, wall temperature, and steam temperature. This heat transfer mechanism is... Time relative to total wall heat flow Make a contribution.