Interphase resistance calculation method for different flow patterns of vertical circular pipe

Abstract

The invention discloses an inter-phase resistance calculation method for different flow patterns of a vertical circular tube, and is applied to the technical field of gas-liquid two-phase flow analysis. Comprising the following steps: carrying out an air-water two-phase flow experiment based on a vertical circular tube, and collecting experiment parameters in the experiment process; the flow pattern of the vertical circular pipe is divided into bubble flow, slug flow, annular flow and mist flow; respectively setting drag force calculation models of different flow patterns to obtain inter-phase resistance calculation schemes of different flow patterns; the flow pattern is recognized, and the inter-phase resistance of the vertical circular pipe is calculated through the inter-phase resistance calculation scheme of the corresponding flow pattern. According to the method, the characteristics of different flow patterns of the vertical circular pipe are considered, the corresponding drag force calculation models are designed to serve as calculation models of the interphase resistance, and the interphase resistance calculation precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of gas-liquid two-phase flow analysis, and more specifically, to a method for calculating the interfacial resistance of different flow patterns in a vertical circular tube. Background Art

[0002] In a vertical circular tube channel, the liquid phase and the gas phase flow together to form a flow system with an interfacial boundary, which is the most common two-phase flow scenario. Since the gas-liquid interface is prone to deformation and continuously changes along the way under the action of wall friction and interfacial resistance, different stages of flow pattern evolution occur. The interfacial resistance in two-phase flow specifically includes drag force, lift force, virtual mass force, Basset force, wall lubrication force, and turbulent dissipation force. In basic experiments and model applications, the interfacial drag force plays a major role. Existing interfacial resistance models are based on the drift-flux model and the two-fluid model to describe the interaction between the two phases. In the prior art, Ishii proposed using the drift velocity and distribution parameter in the drift-flux model to express the relative velocity between the phases, and then solving the interfacial resistance coefficient through the balance of buoyancy and interfacial drag force. This method only considers the influence of phase distribution characteristics on the cross-sectional average slip velocity and does not consider the local slip characteristics and force characteristics. Therefore, it cannot reflect the physical essence of the interfacial resistance. Therefore, how to provide a method for calculating the interfacial resistance of different flow patterns in a vertical circular tube is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0003] In view of this, the present invention provides a method for calculating the interfacial resistance of different flow patterns in a vertical circular tube, using the drag force model as the interfacial resistance calculation scheme, and respectively designing corresponding drag force calculation models for different flow patterns in the vertical circular tube.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A method for calculating the interfacial resistance of different flow patterns in a vertical circular tube, comprising the following steps:

[0006] S1. Conduct an air-water two-phase flow experiment based on a vertical circular tube, and collect experimental parameters during the experiment for subsequent flow pattern identification and interfacial resistance calculation;

[0007] S2. Divide the flow patterns of the vertical circular tube into bubbly flow, slug flow, annular flow, and mist flow;

[0008] S3. Respectively set drag force calculation models for different flow patterns to obtain interfacial resistance calculation schemes for different flow patterns;

[0009] S4. Identify the flow pattern and calculate the interfacial resistance of the vertical circular tube through the interfacial resistance calculation scheme corresponding to the flow pattern.

[0010] Optionally, the drag force calculation model for slug flow is specifically as follows:

[0011] The drag coefficient C under slug flow is obtained through calculation D and the interfacial area concentration a i , and the interphase resistance model is closed:

[0012]

[0013] In the formula, F1 is the drag force of slug flow, ρ f is the liquid phase density, v r is the interphase velocity, S F is the shape factor, d0 is the average bubble chord length, g is the acceleration due to gravity, Δρ is the two-phase density difference, σ is the surface tension, α is the void fraction, d max is the maximum bubble chord length, a i is the interfacial area concentration, C D is the drag coefficient, j f is the apparent liquid velocity, D h is the hydraulic diameter, We crt is the critical Weber number.

[0014] Optionally, the drag force calculation model for slug flow is specifically as follows:

[0015] The slug flow structure consists of two parts: Taylor gas slugs and wake liquid slugs. Therefore, the interphase drag force of slug flow consists of two parts. The drag coefficients are calculated separately for the two parts of Taylor gas slugs and wake liquid slugs, and only the interfacial area concentration on the side of Taylor gas slugs is considered:

[0016] F2 = F 2t + F 2s

[0017]

[0018] In the formula, F2 is the drag force of slug flow, F 2t is the drag force of the Taylor gas slug part, F 2s is the drag force of the wake liquid slug part, C Dt is the drag coefficient of the Taylor gas slug part, v rt is the interphase velocity of the Taylor gas slug part, C Ds is the drag coefficient of the wake liquid slug part, v rs is the interphase velocity of the wake liquid slug part, a it is the interfacial area concentration of the Taylor gas slug part, a is is the interfacial area concentration of the wake liquid slug part, D h is the hydraulic diameter, α T is the average ratio of the Taylor gas slug cross-section to the flow channel cross-section, αt is the void fraction of Taylor slug flow, α gs is the void fraction of the wake liquid slug part, α bs is the void fraction at the bubbly - slug flow transition point, α sa is the void fraction at the slug - annular flow transition point.

[0019] Optionally, the drag force calculation model for annular flow is specifically:

[0020] Annular flow is composed of a liquid film near the pipe wall and a gas core. For the annular flow in a vertical circular pipe, all the liquid phase is distributed in the liquid film, and there are no entrained liquid droplets in the gas core. The interfacial friction coefficient f i is used to replace the drag coefficient C D as the closure condition:

[0021]

[0022] In the formula, F3 is the drag force of annular flow, ρ f is the liquid phase density, v r is the interfacial velocity, S F is the shape factor, a i is the interfacial area concentration, α ff is the liquid phase fraction of the liquid film, Re i is the interfacial Reynolds number.

[0023] Optionally, the drag force calculation model for mist flow is specifically:

[0024] Mist flow is composed of entrained liquid droplets and a continuous gas core, and the drag force model is used for closure:

[0025]

[0026] In the formula, F4 is the drag force of mist flow, ρ c is the gas phase density, v r is the interfacial velocity, S F is the shape factor, C D is the drag coefficient, a i is the interfacial area concentration, α w is the void fraction of mist flow, d0 is the average bubble chord length, and Re is the droplet Reynolds number.

[0027] Optionally, the following form is used to calculate the interfacial resistance in the transition region between slug flow and annular flow:

[0028]

[0029] In the formula, F5 is the drag force of bubbly flow, ρ f is the liquid phase density, v r is the interfacial velocity, S Fis the shape factor, α is the void fraction, a i is the interfacial area concentration, C i is the drag coefficient in the transition region, α crt_h and α crt_l respectively represent the upper limit and lower limit of the void fraction in the transition region, C i_slug and C i_ann respectively represent the drag coefficients in the slug flow and annular flow regions.

[0030] As can be seen from the above technical solutions, compared with the prior art, the present invention provides a method for calculating the interfacial resistance of different flow patterns in a vertical circular tube, and has the following beneficial effects: The present invention considers the characteristics of different flow patterns in a vertical circular tube, and respectively designs corresponding drag calculation models as the calculation models for the interfacial resistance, improving the accuracy of the interfacial resistance calculation; The present invention sets up a flow pattern identification model for quickly identifying the flow pattern types of the vertical circular tube, and improves the calculation rate of the interfacial resistance on the premise of ensuring the accuracy. Description of the Drawings

[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0032] Figure 1 is the flow chart of the method for calculating the interfacial resistance of different flow patterns in a vertical circular tube according to the present invention. Detailed Embodiments

[0033] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0034] The embodiment of the present invention discloses a method for calculating the interfacial resistance of different flow patterns in a vertical circular tube, as Figure 1 shown, including the following steps:

[0035] S1. Conduct an air-water two-phase flow experiment based on a vertical circular tube, and collect experimental parameters during the experiment for subsequent flow pattern identification and interfacial resistance calculation;

[0036] S2. Divide the flow patterns of the vertical circular tube into bubble flow, slug flow, annular flow, and mist flow;

[0037] S3. Set drag calculation models for different flow patterns respectively to obtain the calculation schemes for the interfacial resistance of different flow patterns;

[0038] S4. Identify the flow pattern and calculate the interfacial resistance of the vertical circular tube through the calculation scheme for the interfacial resistance of the corresponding flow pattern.

[0039] Furthermore, the drag calculation model for bubbly flow is specifically:

[0040] Obtain the drag coefficient C under bubbly flow through calculation D and the interfacial area concentration a i , and close the interfacial resistance model:

[0041]

[0042] In the formula, F1 is the drag of bubbly flow, ρ f is the liquid phase density, v r is the interfacial velocity, S F is the shape factor, d0 is the average bubble chord length, g is the acceleration due to gravity, Δρ is the two-phase density difference, σ is the surface tension, α is the void fraction, d max is the maximum bubble chord length, a i is the interfacial area concentration, C D is the drag coefficient, j f is the apparent liquid velocity, D h is the hydraulic diameter, We crt is the critical Weber number.

[0043] In the embodiment of the present invention, the average bubble diameter is obtained by calculating the critical Weber number We crt and then the interfacial area concentration a is calculated i ; the shape factor measures the deviation of the dispersed phase from the sphere and takes different values in different flow patterns, and the value in the embodiment of the present invention is 1.

[0044] Furthermore, the drag calculation model for slug flow is specifically:

[0045] The slug flow structure consists of two parts: Taylor gas slug and wake liquid slug. Therefore, the interfacial drag of slug flow consists of two parts. The drag coefficients are calculated separately for the two parts of Taylor gas slug and wake liquid slug, and only the interfacial area concentration on the side of Taylor gas slug is considered:

[0046] F2 = F 2t + F 2s

[0047]

[0048]

[0049] Wherein, F2 is the drag force of slug flow, F 2t is the drag force of the Taylor gas slug part, F 2s is the drag force of the wake liquid slug part, C Dt is the drag coefficient of the Taylor gas slug part, v rt is the inter-phase velocity of the Taylor gas slug part, C Ds is the drag coefficient of the wake liquid slug part, v rs is the inter-phase velocity of the wake liquid slug part, a it is the interfacial area concentration of the Taylor gas slug part, a is is the interfacial area concentration of the wake liquid slug part, D h is the hydraulic diameter, α T is the average ratio of the Taylor gas slug cross-section to the flow channel cross-section, α t is the void fraction of the Taylor gas slug, α gs is the void fraction of the wake liquid slug part, α bs is the void fraction at the bubble flow - slug flow transition point, α sa is the void fraction at the slug flow - annular flow transition point.

[0050] Furthermore, the drag force calculation model for annular flow is specifically as follows:

[0051] Annular flow is composed of a liquid film near the pipe wall and a gas core. For the annular flow in a vertical circular pipe, all the liquid phase is distributed in the liquid film, and there are no entrained liquid droplets in the gas core. The inter-phase friction coefficient f i is used to replace the drag coefficient C D as the closure condition:

[0052]

[0053] Wherein, F3 is the drag force of annular flow, ρ f is the liquid phase density, v r is the inter-phase velocity, S F is the shape factor, a i is the interfacial area concentration, α ff is the liquid phase fraction of the liquid film, Re i is the interfacial Reynolds number.

[0054] In the embodiment of the present invention, the liquid phase fraction of the liquid film is calculated by the following formula:

[0055]

[0056] Wherein, α f is the overall liquid phase fraction, C f is the correction coefficient, α g is the overall void fraction, v g is the gas phase velocity, vεrt is the critical entrainment velocity, ρ g is the gas-phase density;

[0057] The interfacial Reynolds number Re i is calculated by the following formula:

[0058]

[0059] In the formula, μ g is the gas-phase dynamic viscosity, v f is the liquid-phase velocity, D is the inner diameter of the circular tube, D i is the gas-core diameter;

[0060] In the drag force calculation model of annular flow, the interfacial area concentration of the annular liquid film and the gas core is:

[0061]

[0062] In the formula, C ann is the correction factor considering the ripples on the liquid film surface, α fd is the liquid-phase fraction in the gas core part, and d0 is the average diameter of the entrained droplets.

[0063] Furthermore, the drag force calculation model of mist flow is specifically:

[0064] Mist flow is composed of entrained droplets and a continuous gas core, and a drag force model is used for closure:

[0065]

[0066] In the formula, F4 is the drag force of mist flow, ρ c is the gas-phase density, v r is the interfacial velocity, S F is the shape factor, C D is the drag coefficient, a i is the interfacial area concentration, α w is the void fraction of mist flow, d0 is the average chord length of bubbles, and Re is the droplet Reynolds number.

[0067] In the embodiments of the present invention, the calculation of the droplet Reynolds number Re is specifically:

[0068]

[0069] In the formula, ρ c is the density of the continuous phase, which is the gas-phase density in mist flow, μ m is the dynamic viscosity of the mixed phase, μ g is the gas-phase dynamic viscosity, α g is the void fraction.

[0070] Furthermore, due to the order-of-magnitude difference in the interfacial drag coefficient between slug flow and annular flow, simply using a linear transition cannot meet the requirements of numerical calculations, and it is necessary to add a transition region. The following formula is used to calculate the interfacial drag in the transition region between slug flow and annular flow:

[0071]

[0072] In the formula, F5 is the drag force of bubbly flow, ρ f is the liquid-phase density, v r is the interfacial velocity, S F is the shape factor, α is the void fraction, a i is the interfacial area concentration, C i is the drag coefficient in the transition region, α crt_h and α crt_l respectively represent the upper limit and lower limit of the void fraction in the transition region, C i_slug and C i_ann respectively represent the drag coefficients in the slug flow and annular flow regions;

[0073] The size of the transition interval is jointly determined by experimental data and the numerical stability of the model, and is taken as 0.05 in the embodiments of the present invention.

[0074] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The same or similar parts among the various embodiments can be referred to each other.

[0075] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating the phase resistance of different flow patterns in a vertical circular tube, characterized in that: The following steps are involved: S1. Conduct air-water two-phase flow experiments based on vertical circular tubes, and collect experimental parameters during the experiment for subsequent flow pattern identification and interphase resistance calculation; S2. Classify the flow patterns of the vertical circular tube into bubbly flow, slug flow, annular flow and mist flow; S3, respectively setting drag calculation models of different flow types to obtain interphase resistance calculation schemes of different flow types; S4. Identify the flow pattern and calculate the interphase resistance of the vertical circular tube using the interphase resistance calculation scheme corresponding to the flow pattern.

2. A method for calculating phase resistance of different flow patterns in a vertical circular pipe according to claim 1, characterized in that: The drag calculation model of bubbly flow is as follows: The drag coefficient C under bubbly flow is obtained by calculation D and the interface area concentration a i , close the interphase resistance model: Where F1 is the drag force of the bubbly flow, ρ f is the liquid density, v r is the phase speed, S F is the shape factor, d0 is the average bubble chord length, g is the gravitational acceleration, Δρ is the density difference between the two phases, σ is the surface tension, α is the cavitation fraction, and d max is the maximum bubble chord length, a i is the interfacial area concentration, C D is the drag coefficient, j f is the liquid phase superficial velocity, D h is the hydraulic diameter, We crt is the critical Weber number.

3. A method for calculating phase resistance of different flow patterns in a vertical circular pipe according to claim 1, characterized in that: The drag calculation model of slug flow is as follows: The slug flow structure consists of two parts: the Taylor air bomb and the wake liquid block. Therefore, the interphase drag of the slug flow consists of two parts. The drag coefficients are calculated for the Taylor air bomb and the wake liquid block respectively, and only the interface area concentration on the Taylor air bomb side is considered: F2=F 2t +F 2s Where F2 is the drag force of the slug flow, F 2t is the drag force of the Taylor air bomb, F 2s is the drag of the wake fluid block, C Dt is the drag coefficient of the Taylor air-elastic part, v rt is the phase velocity of the Taylor air-elastic part, C Ds is the drag coefficient of the wake fluid block, v rs is the phase velocity of the tail flow block, a it is the interfacial area concentration of the Taylor gas bomb part, α is is the interfacial area concentration of the tail flow block, D h is the hydraulic diameter, α T is the average ratio of Taylor aeroelastic cross section to flow channel surface, α t is the cavitation fraction of the Taylor bomb, α gs is the cavitation fraction of the wake mass, α bs is the cavitation fraction at the transition point from bubbly flow to slug flow, α sa is the cavitation fraction at the slug-annular flow transition point.

4. A method for calculating phase resistance of different flow patterns in a vertical circular pipe according to claim 1, characterized in that: The drag calculation model of annular flow is as follows: The annular flow is composed of the liquid film near the tube wall and the gas core. For the annular flow of the vertical circular tube, all the liquid phases are distributed in the liquid film, and there are no entrained droplets in the gas core. The interphase friction coefficient f is used. i Instead of drag coefficient C D As a closing condition: Where F3 is the drag of the annular flow, ρ f is the liquid density, v r is the phase speed, S F is the shape factor, a i is the interfacial area concentration, α ff is the liquid phase fraction of the liquid film, Re i is the interface Reynolds number.

5. A method for calculating phase resistance of different flow patterns in a vertical circular pipe according to claim 1, characterized in that: The drag calculation model of mist flow is as follows: The mist flow consists of entrained droplets and a continuous gas core, which is closed using the drag model: Where F4 is the drag force of the mist flow, ρ c is the gas phase density, v r is the phase speed, S F is the shape factor, C D is the drag coefficient, a i is the interfacial area concentration, α w is the cavitation fraction of the mist flow, d0 is the average bubble chord length, and Re is the droplet Reynolds number.

6. A method for calculating phase resistance of different flow patterns in a vertical circular pipe according to claim 1, characterized in that: The interphase drag in the transition region between slug flow and annular flow is calculated using the following form: Where F5 is the drag force of the bubbly flow, ρ f is the liquid density, v r is the phase speed, S F is the shape factor, α is the cavitation fraction, a i is the interfacial area concentration, C i is the drag coefficient in the transition zone, α crt_h and α crt_l They represent the upper and lower limits of the cavitation fraction in the transition region, respectively, and C i_slug and C i_ann denote the drag coefficients in the slug flow and annular flow regions, respectively.

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