Simulation calculation method for deep tunnel containing retained air mass

Abstract

The invention discloses a retained air mass-containing deep tunnel simulation calculation method, which comprises the following steps of: considering three known different retained air mass forming mechanisms, and constructing an air mass deformation motion and retention hypothesis model; based on the air mass deformation motion and retention hypothesis model, constructing an air mass form, an air mass pressure water head and a control parameter model in the deep tunnel; according to the air mass form, the air mass pressure water head and the control parameter model in the deep tunnel, constructing a retention air mass parameterization hypothesis model under different dimension calculation; and according to the retention air mass parameterized assumption model and the water-gas two-phase flow simulation calculation model, calculating transient pressure caused by water flow impact in the deep tunnel containing the retention air mass. The method can be used for solving the problems of deep tunnel system arrangement type and actual retention air mass hypothesis in modern information technology simulation calculation so as to realize real-time monitoring and simulation of the operation of the deep tunnel containing the retention air mass.

Description

Technical Field

[0001] The invention belongs to the technical field of tunnel simulation, and in particular relates to a simulation calculation method for a deep tunnel containing a stagnant air mass. Background Art

[0002] In view of the current characteristics of low water surface rate, high building density, complicated underground pipelines and dense population in urban areas under the condition of frequent short-duration heavy rainfall, the attempt to use storage shafts as a facility to alleviate the overflow of the original large-scale combined sewer and form a deep tunnel system with deep tunnels is a relatively reliable and economical new option in the transformation of urbanized rainwater management. A large number of engineering practices and studies have shown that the existence of trapped air masses in deep tunnels is inevitable when multiple storage shafts flow in, and the transient pressure caused by water flow impact will bring potential dangers to system safety.

[0003] Recently (Wang, YR, Yu, XD, Qin, XH, Cheng, N., and Yu, C. (2022). Analysis of pressure surges for water filling in deep stormwater storage tunnels with entrapped air-pocket using a VOF model. AQUA—Water Infrastructure, Ecosystems and Society, 71(9), 992-1001.; Wang, YR, Yu, XD, Yu, C., Zhang, J., and Xu, H. (2024). Sensitivity analysis on transient pressure of entrapped air pocket in deep stormwater tunnel system. Physics of Fluids, 36(6).) made the first progress in the study of the actual deep tunnel system with trapped air masses by directly referring to pipeline experience. However, the assumptions about the initial trapped air-water interface, the shape of a single trapped air mass, and the state parameters used in different rapid filling backgrounds are worth discussing. (1) The assumptions made are not consistent with the existing theoretical understanding of pipelines with trapped air masses. Specifically, it is manifested as follows: a. Vertical trapped air-water interface. It was introduced in the previous article (Zhou, F., Hicks, FE, and Steffler, PM (2002). Observations of air-water interaction in a rapidly filling horizontal pipe. Journal of hydraulic engineering, 128 (6), 635-639.) as the object used by the original proposer to determine; b. The shape of a single trapped air mass. (Vasconcelos, JG, and Wright, SJ (2009). Investigation of rapid filling of poorly ventilated stormwater storage tunnels. Journal of hydraulic research, 47 (5), 547-558.) Through analysis, it is believed that the concept of a single trapped air mass in a pipeline is not applicable to deep tunnel applications. c. State parameters. The trapped air mass height and initial pressure parameters selected under this assumption exceed the state range corresponding to a. and b.(2) The assumptions made do not conform to the formation principle originally used for the control of the pipeline test. The specific formation principle is: a. Filling process. The volume of potential trapped air masses that may be formed when the air initially present in the pipeline is discharged; b. Emptying process. Single or multiple trapped air masses in a full tunnel located behind the pipeline gate valve or at the high point of an irregular pipeline. (3) The assumptions made do not conform to the objective physical reality of trapped air masses in deep tunnels. The specific objective reality is: a. The shape and state parameters of the trapped air masses related to the hydrostatic pressure. The statement of hydrostatic pressure can be found in (Huang, B., and Zhu, DZ (2021). Rigid-column model for rapid filling in apartially filled horizontal pipe. Journal of Hydraulic Engineering, 147 (2), 06020018.) Regarding the influence of water body under closed air in the pipeline, the actual trapped air mass is developed when the system head line reaches the top of the deep tunnel, and its shape and state parameters in dynamic change are not related to the hydrostatic pressure (Vasconcelos, JG, and Wright, SJ (2017). Anticipating transient problems during the rapid filling of deep stormwater storage tunnel systems. Journal of Hydraulic Engineering, 143 (3), 06016025.). b. The distribution of air mass state parameters at any moment is described by normal distribution. This mathematical distribution description does not provide a theoretical basis or reasoning process, and is inconsistent with the general understanding in existing experimental hydraulics theory that only the probability density statistics of flow random variables have functional characteristics. For newer mathematical applications of related understandings, see (Jiao, X., Zhao, LH, Wang, ZZ, et al (2022). Calculating Water Flow Rate with Measurement Errors of the Weir Considered. Journal of Irrigation and Drainage, 2022, 41(6): 105-112, 146.).

[0004] In order to realize the real-time monitoring and simulation of the operation of deep tunnels with trapped air masses, so as to better control and manage the transient pressure changes caused by water flow impact, especially in the information-based assessment and processing of sudden events in deep tunnels (such as tunnel rupture), it is necessary to propose a parameterized hypothesis modeling method of trapped air masses, which can be further used for simulation calculations of deep tunnels with trapped air masses. Summary of the invention

[0005] Objective: To address the deficiencies in the prior art, the present invention provides a simulation calculation method for a deep tunnel containing trapped air masses, which is used to solve the problem of trapped air mass assumptions that conform to the deep tunnel system layout type and reality in modern information technology simulation calculations, and obtain the transient pressure caused by water flow impact in a deep tunnel containing trapped air masses.

[0006] Technical solution: To solve the above technical problems, the present invention provides a simulation calculation method for a deep tunnel containing trapped air masses, and the technical solution adopted is:

[0007] The present invention provides a simulation calculation method for a deep tunnel containing a stagnant air mass, comprising:

[0008] Step S1, constructing an air mass deformation movement and retention hypothesis model;

[0009] Step S2, constructing a model of air mass morphology, air mass pressure head and control parameters in a deep tunnel based on the air mass deformation movement and retention hypothesis model;

[0010] Step S3, constructing a parameterized hypothetical model of trapped air masses under different dimensional calculations according to the air mass morphology, air mass pressure head and control parameter model in the deep tunnel;

[0011] Step S4, calculating the transient pressure caused by the water flow impact in the deep tunnel containing the trapped air mass based on the parameterized assumption model of the trapped air mass and the water-air two-phase flow simulation calculation model.

[0012] In some embodiments, the formation mechanism of the trapped air mass includes: (1) large bubble plugs formed at the interface during the rapid filling process; (2) bubble accumulation in the water flow of the storage shaft; and (3) separation of the water column at the high point of the filling water body.

[0013] In some embodiments, constructing the air mass deformation movement and retention hypothesis model specifically includes:

[0014] 1) The deformation movement of air masses includes two types: volume oscillation and coupled migration;

[0015] 2) A single stagnant air mass is assumed to be preferentially located at the midpoint of the flow segment and to occupy a certain equal-diameter cross-section.

[0016] Step S1, constructing an air mass deformation movement and retention hypothesis model;

[0017] Step S2, constructing a model of air mass morphology, air mass pressure head and control parameters in a deep tunnel based on the air mass deformation movement and retention hypothesis model;

[0018] Step S3, constructing a parameterized hypothetical model of trapped air masses under different dimensional calculations according to the air mass morphology, air mass pressure head and control parameter model in the deep tunnel;

[0019] Step S4, calculating the transient pressure caused by the water flow impact in the deep tunnel containing the trapped air mass based on the parameterized assumption model of the trapped air mass and the water-air two-phase flow simulation calculation model.

[0020] In some embodiments, the formation mechanism of the trapped air mass includes: (1) large bubble plugs formed at the interface during the rapid filling process; (2) bubble accumulation in the water flow of the storage shaft; and (3) separation of the water column at the high point of the filling water body.

[0021] In some embodiments, constructing the air mass deformation movement and retention hypothesis model specifically includes:

[0022] 1) The deformation movement of air masses includes two types: volume oscillation and coupled migration;

[0023] 2) A single stagnant air mass is assumed to be preferentially located at the midpoint of the flow segment and to occupy a certain equal-diameter cross-section.

[0024] In some embodiments, the air mass morphology model comprises:

[0025] Taking a point in the deep tunnel as the local coordinate origin o, the air mass morphology under different formation mechanisms is expressed as:

[0026]

[0027] Where: V a is the volume of the trapped air mass; x is the horizontal coordinate of the local coordinate system; y is the vertical coordinate of the local coordinate system; z is the vertical coordinate of the local coordinate system; f is a function; S is the longitudinal cross-sectional area function; h a is the height of the air mass; l a is the length of the air mass; c a is the circumference of the air mass.

[0028] In some embodiments, the air mass pressure head model includes:

[0029] The head loss of any stagnant air mass is equal to the height of the air mass formed from the nose to the tail h a , that is, the initial relative pressure head of the trapped air mass:

[0030] H a =Z nose +H nose -Z tail -H tail =h a ;

[0031] Where: H ais the relative pressure head of the air mass; Z nose Z is the water head at the nose of the air mass; tail H is the water head at the tail of the air mass; nose H is the relative pressure head at the nose of the air mass; tail is the relative pressure head at the tail of the air mass; h a is the air mass height.

[0032] In some embodiments, the control parameter model includes:

[0033] The morphology of trapped air mass when the initial water level of the storage shaft is equal to the inner diameter of the deep tunnel is selected as the research object, and the corresponding morphology and head control parameter relationship are as follows:

[0034]

[0035] Where: V a is the volume of the trapped air mass; H a0 is the initial relative pressure head of the air mass; f is a function; is the longitudinal slope of the deep tunnel; h d is the tailwater depth; S is the longitudinal cross-sectional area function; h a is the height of the air mass; l a is the length of the air mass; c a is the circumference of the air mass.

[0036] In some embodiments, the longitudinal cross-section of the initial air mass is constructed as an ellipse.

[0037] In some embodiments, step S3, constructing a parameterized hypothetical model of trapped air masses under different dimensional calculations, includes:

[0038] 1) The parameters of the trapped air mass modeling used for one-dimensional calculations are: (1) The air mass height h a ; (2) Air mass porosity Where: V a V is the volume of the trapped air mass; tunnel is the volume of deep tunnel;

[0039] 2) The parameters assumed for the modeling of the trapped air mass are: (1) The height of the air mass h a ; (2) Air mass length l a ; (3) Air mass width h a .

[0040] In some embodiments, the water-gas two-phase flow simulation computational model is selected from at least one of a rigid column model (RC), a characteristic line model (MOC), and a three-dimensional visualization computational fluid model (CFD).

[0041] Beneficial effects: As the core technology of intelligent operation and management of deep tunnel systems, in view of the theoretical assumptions and application difficulties faced by the current simulation calculation of deep tunnels with trapped air masses, 1) the deformation movement and retention assumptions of air masses under various formation mechanisms; 2) the research objects under the value of air mass pressure head and the change of water level in the regulating shaft are timely proposed, and finally a parameterized assumption modeling method of trapped air masses that can be used for the simulation calculation of deep tunnels with trapped air masses is established, and based on this, the simulation calculation of deep tunnels with trapped air masses is realized, and the transient pressure caused by the impact of water flow in deep tunnels with trapped air masses is obtained. This method solves the problem of trapped air mass assumptions that conform to the layout type and actual situation of deep tunnel systems in modern information technology simulation calculations, and can be used to obtain the transient pressure caused by the impact of water flow in deep tunnels with trapped air masses. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of the air mass retention assumption at the midpoint of any flow segment in an embodiment of the present invention;

[0043] Figure 2 Schematic diagram of contact and contact path in an embodiment of the present invention;

[0044] Figure 3 Schematic diagram of parameterization of the trapped air mass in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present application and its application or use. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0046] Unless otherwise specifically stated, the relative arrangement, numerical expressions and numerical values ​​of the parts and steps set forth in these embodiments do not limit the scope of the present application. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to those of ordinary skill in the relevant field may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be considered as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so that once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0047] In the description of the present application, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the drawings, and are only used to explain the relative position relationship, movement, etc. between the components in a certain posture. If the specific posture changes, the directional indication will also change accordingly. It is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present application.

[0048] In addition, the terms "first", "second", etc. are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first", "second", etc. may explicitly or implicitly include one or more of the feature. In the description of this application, unless otherwise specified, "plurality" means two or more.

[0049] In the description of this application, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood by specific circumstances.

[0050] It should be noted that, in the present application, first, three known different mechanisms of formation of trapped air masses are considered: (1) large bubble slugs formed at the interface during rapid filling (see Martin, CS (1976). Entrapped air in pipelines. Proc. 2nd Intl. Conf. Pressure Surges, 15-28, F2, BHRA, Bedford, UK.); (2) bubble accumulation in the water flow of the storage shaft (see Chanson, H.. (2003). Experimental investigation of dropshaft hydraulics-two-phase flow and acoustics. International Association of Hydraulic Engineering and Research (IAHR) Congress Theme B: Urban and Rural Water Systems for Sustrinable Development;

[0051] 20030824-20030829; AUTH; GR. Dept of Civil Engineering, The University of Queensland, Brisbane QLD 4072, Australia.); (3) Water column separation at high point filling water body (see Liou, CP, and Hunt, WA (1996). Filling of pipelines with undulating elevation profiles. Journal of Hydraulic Engineering, 122 (10), 534-539.).

[0052] Second, higher porosity and saturation are the key to the existence of gas clusters of different mechanisms that also originate from bubbles (see Wylie, EB, and Streeter, VL (1993). Fluid transients in systems, Prentice Hall, New York.; Rohilla, L., and Das, AK (2020). Fluidics in an emptyingbottleduring breaking and making of interacting interfaces. Physics of Fluids, 32(4).).

[0053] Embodiment 1: This embodiment provides a simulation calculation method for a deep tunnel containing a trapped air mass, comprising:

[0054] Step S1, constructing an air mass deformation movement and retention hypothesis model.

[0055] In some embodiments, step S1, constructing an air mass deformation movement and retention hypothesis model, specifically includes:

[0056] 1) The deformation movement of air masses includes two types: volume oscillation and coupled migration;

[0057] 2) A single stagnant air mass is assumed to be preferentially located at the midpoint of the flow segment and to occupy a certain equal-diameter cross-section.

[0058] (1) Air mass movement and deformation

[0059] The possible movement modes of air masses obtained from the continuity equation are:

[0060] a. Follow the current downstream:

[0061] b. Keep relatively still:

[0062] c.Move against the direction of water flow:

[0063] Where: Q is the deep tunnel flow; g is the gravitational acceleration; is the longitudinal slope of the deep tunnel; r tunnel The inner diameter of the deep tunnel.

[0064] Its deformation during hydraulic transients is reflected in the following two processes: (1) The process of increasing the outer surface of the air mass. Large and small air masses gather and occupy part of the tunnel section, causing the water flow velocity at the section to increase, the pressure to decrease, and the saturated water body to be forced to release a small amount of bubbles originally dissolved in the water, further increasing the air mass; (2) The process of shrinking the outer surface of the air mass. After the air mass occupies the entire tunnel section, the locally increased flow velocity in the deep tunnel causes the gas there to be easily dispersed, and some small air masses are discharged along the water flow direction.

[0065] (2) Air mass deformation, movement and retention hypothesis

[0066] Referring to the Plateau theorem about the stable bubble configuration with the minimum surface area under the same volume, the equal diameter assumption is made for the cross section of the convex polyhedron air mass after the outer surface is continuously deformed. Based on this assumption, it is necessary to prove that for any centrally symmetric convex polyhedron U, a ternary (semi) positive quadratic outer surface j with equal cross section can be found to wrap the convex body, so as to achieve the maximum saturation when the outer surface area is the minimum by controlling the volume of the unknown air mass shape. The reasoning process is as follows:

[0067] Let U be N 3 A non-empty bounded convex open set symmetric about the origin. 3 Let all ternary (semi) positive quadratic forms be L, and the corresponding (possibly degenerate) outer surface for l∈L be {e(x, x)≤1}. By The total number of ternary positive definite quadratic forms corresponding to the (possibly degenerate) outer surface j containing U is:

[0068]

[0069] Where: K is the set of all ternary positive definite quadratic forms; l is the set of external surfaces; L is the set of positive rational numbers; x is the horizontal / vertical coordinate of the isodiametric coordinate system; For a convex set U uniquely corresponding to N 3 The norm of ; N is the range of real numbers.

[0070] From formula (2), we can know that: (1) K as N 3*3 The subset in is a bounded closed set with compactness; (2) if 0≤l 1 (x, x), Then for any Among them l 1 , l 2 is a set of different external surfaces; λ is a linear parameter.

[0071] Let V(l) be the volume contained by the outer surface {l(x, x)≤1}, then from the compactness of K we know that there exists Make Take the minimum value. If we assume that there is another l' that also makes V(l') = V(l), then Need to introduce the construction equation Then, combining the convexity of the exponential function, we can get:

[0072]

[0073] Where: f is the function; l is the outer surface set; x is the horizontal / vertical coordinate of the equal diameter coordinate system; Convex set U uniquely corresponds to N 3norm; (e) = exponential function.

[0074] From formula (3), we can see that the corresponding There exists a unique outer surface j such that the volume it encloses can reach the minimum value, so the assumption holds.

[0075] The dynamic analysis of the air masses that produce stagnation behavior under the assumption of equal diameter cross section will be reflected in two aspects: the compressibility of the stagnation air mass allows the non-constant pressure water body to accelerate the flow, causing its size and pressure to change with the different movement speeds between adjacent interfaces, thus producing a volume oscillation phenomenon similar to that defined in bubble dynamics; ignoring the inertia and gravity of the gas, the oscillating air mass will further undergo coupled migration accompanied by water-filled collapse due to the anisotropy of the surrounding flow, such as the pressure gradient or gravity field caused by the nearby boundary. At this time, the unfavorable position of air mass stagnation and subsequent pressurization behavior can be evaluated through the basic characteristics of the deep tunnel system layout and the five ventilation mechanisms of the stagnation air mass adopted. In particular, when the system is not sufficiently ventilated, geometrically dislocated air mass emissions will be more common. At the same time, relevant experimental observations also pointed out that the generation of stagnation of air between water bodies may lead to higher peak pressures than pure water bodies. Therefore, a single stagnation air mass is assumed to be preferentially located at the midpoint of the flow segment and is a form with a certain equal diameter cross section. Figure 1 It is a schematic diagram of the air mass retention assumption at the midpoint of any flow segment in an embodiment of the present invention; Figure 1 In: (O a ) 1 , (O a ) 2 , (O a ) 3 , (O a ) 4 The centers of different air masses are shown; (r a ) 1 、(r a ) 2 、(r a ) 3 、(r a ) 4 is the radius of the corresponding air mass; O tunnel 、r tunnel is the center and radius of the deep tunnel.

[0076] Step S2, constructing a model of air mass morphology, air mass pressure head and control parameters in a deep tunnel based on the air mass deformation movement and retention hypothesis model;

[0077] Step S21, air mass morphology:

[0078] By investigating the volume changes of the trapped air mass oscillations, different trapped air mass forms are represented. Taking a point in the deep tunnel as the local coordinate origin o, the air mass forms under different formation mechanisms are represented as follows:

[0079]

[0080] Where: V a is the volume of the trapped air mass; x is the horizontal coordinate of the local coordinate system; y is the vertical coordinate of the local coordinate system; z is the vertical coordinate of the local coordinate system; f is a function; S is the longitudinal cross-sectional area function; h a is the height of the air mass; l a is the length of the air mass; c a is the circumference of the air mass.

[0081] Step S22, air mass pressure head:

[0082] The head loss of any stagnant air mass is equal to the height of the air mass formed from the nose to the tail h a , that is, the initial relative pressure head of the trapped air mass:

[0083] H a =Z nose +H nose -Z tail -H tail =h a ;

[0084] Where: H a is the relative pressure head of the air mass; Z nose Z is the water head at the nose of the air mass; tail H is the water head at the tail of the air mass; nose H is the relative pressure head at the nose of the air mass; tail is the relative pressure head at the tail of the air mass; h a is the air mass height.

[0085] The proof process is as follows:

[0086] a. The Bernoulli equation can be used to obtain the rate of change of the kinetic pressure head under different air mass forms;

[0087]

[0088] Where: P is relative pressure; ρ = density; g is the acceleration due to gravity; t is time, and angle codes 1 and 2 represent different moments.

[0089] b. Boyle's law is used to approximate the volume oscillation effect of local spatial changes on the trapped air mass, and the relative initial pressure head-volume correspondence at constant temperature is obtained;

[0090] H a Va =H a0 V a0 (6)

[0091] Where: V a V is the volume of the trapped air mass; a0 is the initial volume of the trapped air mass; H a0 is the initial relative pressure head of the air mass; H a is the relative pressure head of the air mass.

[0092] c. By t 1 to 2 The change rate of the air mass expansion head during the period takes into account the synchronous change of the movement pressure head change rate, and the comprehensive change rate of the retained air mass morphology is obtained;

[0093]

[0094] Where: H a is the relative pressure head of the air mass; t is the time; Vg0 is the initial air mass volume; s a is the cross-sectional area of ​​the air mass.

[0095] d. From the pressure-head relationship, we can see that the rate of change of the integrated head of the retained air mass volume is a function of the height of the retained air mass volume.

[0096] H a =Z nose +H nose -Z tail -H tail =h a (8)

[0097] Where: H a is the relative pressure head of the air mass; Z nose Z is the water head at the nose of the air mass; tail H is the water head at the tail of the air mass; nose H is the relative pressure head at the nose of the air mass; tail is the relative pressure head at the tail of the air mass; h a is the air mass height.

[0098] Step S23, research object under the change of water level in the storage shaft:

[0099] The morphology of trapped air mass when the initial water level of the storage shaft is equal to the inner diameter of the deep tunnel is selected as the research object, and the corresponding morphology and head control parameter relationship are as follows:

[0100]

[0101] Where: V a is the volume of the trapped air mass; H a0 is the initial relative pressure head of the air mass; f is a function; is the longitudinal slope of the deep tunnel; h d is the tailwater depth; S is the longitudinal cross-sectional area function; h a is the height of the air mass; l a is the length of the air mass; c a is the circumference of the air mass.

[0102] The proof process is as follows:

[0103] The formation height h of a certain stagnant air mass is known. a At the same time, the following air mass volume relationship is satisfied:

[0104]

[0105] h d =r tunnel -h d (10) Where: V a is the volume of the trapped air mass; t is the time; h a is the height of the air mass; s tunnel is the cross-sectional area of ​​the deep tunnel; s d is the cross-sectional area of ​​the tailwater depth; u L is the water flow rate.

[0106] Equations (9) and (10) show that the formation height of the trapped air mass is related to the lower tailwater depth h d Closely related, that is, in the deep tunnel, the diameter is 2r tunnel Within a fixed range of values, the tailwater depth h d The formation height h will be affected by the morphology of the stagnant air mass a The system driving head is a representation of the continuously changing water level in the storage shaft, so the trapped air mass morphology under the initial storage shaft water level equal to the inner diameter of the deep tunnel is selected as the research object, and the influence of arbitrary calculated head benchmark is eliminated.

[0107] Corresponding to the selective change of the retained air mass morphology, by linking equation (4) with equations (1-a), (1-b) and (1-c), we can get that the reason for the deformation of the air mass morphology is the depth of the lower tailwater h d The resulting cross-sectional gas volume V a At this time, the initial head velocity under this selection is always regarded as 0, and the relationship between the shape of the selected object and the head control parameter is obtained as follows:

[0108]

[0109] Where: V a is the volume of the trapped air mass; H a0 is the initial relative pressure head of the air mass; f is a function; is the longitudinal slope of the deep tunnel; h d is the tailwater depth; S is the longitudinal cross-sectional area function; h a is the height of the air mass; l a is the length of the air mass; c a is the circumference of the air mass.

[0110] Assumption of longitudinal section shape used for model calculation: The initial air mass longitudinal section shape is assumed to be an ellipse.

[0111] The proof process is as follows:

[0112] (1) Hypothesis of the morphology of the trapped air-water interface

[0113] Under a certain deep tunnel slope, the shape of the trapped air mass in formula (11) is related to the depth of the lower tailwater. When the lower tailwater depth changes, the ratio of the cross-sectional area of ​​the trapped air mass invading the water body to the cross-sectional area of ​​the tunnel is ξ. It is known that when ξ is small, the impact on the inflow is not significant. When the trapped air mass of a certain length is 0≤ξ≤1, there is internal gas flow and volume adjustment under external pressure changes. Formula (4) generates two different assumptions of the trapped-air-water interface shape: plane and curved surface.

[0114] (2) Coordinates of the connection section between the regulating shaft and the deep tunnel

[0115] If the full tunnel trapped air mass that maintains the trapped air-water interface and moves toward the storage shaft is taken as the basic configuration without considering the coupled migration effect, then:

[0116] J system =J tunel ∪J deep (12)

[0117] J tunel ={(x, y)∈N 2 :x≤2r tunnel , 0≤y≤2r deep} (13)

[0118] J tunel ={(x, y)∈N 2 :y≤2r tunnel , 0≤x≤2r deep} (14)

[0119] Where: J system is the coordinate set of the deep tunnel system; J tunnel is the coordinate set of the deep tunnel system; J tunnel is the coordinate set of the storage shaft; x is the horizontal coordinate of the local coordinate system; y is the vertical coordinate of the local coordinate system; N is the real number range; r tunnel is the inner diameter of the deep tunnel; r deep It is the inner diameter of the regulating shaft.

[0120] (3) Shape composition of longitudinal section motion sequence:

[0121] (31) From L tunnel Continuously move to L deep , while maintaining L system Inside;

[0122] (32) When translated, it rotates monotonically from 0 radians to radian angle;

[0123] (4) Longitudinal section shape under dual-view reference system:

[0124] Using the longitudinal section shape reference system under dual perspective, the connecting segment J tunnel ∪J shaft The longitudinal section shape can move within the connection segment if it is translated and rotated in the reference system while its position relative to the retained longitudinal section shape remains unchanged and satisfies the following conditions:

[0125]

[0126] Where: is that σ(0)=(0,0) T t is the time parameter and the rotation angle of the inner angle of the connecting segment, which is used to describe the movement of the inner angle (0, 0) of the connecting segment in the reference system of the longitudinal section shape; M t is the rotation matrix; S is the longitudinal cross-sectional area function; J tunnel is the coordinate set of the deep tunnel system; J tunnel It is the coordinate set of the storage shaft.

[0127] Let σ(t) be the rotation path. Then, Equation (15) does not lose generality by only considering the longitudinal cross-sectional shape under a given rotation path. Therefore, under strict inclusion conditions, the shape can be replaced by a shape with a larger (or equal) area:

[0128]

[0129] Where: is that σ(0)=(0,0) T t is the time parameter and the rotation angle of the inner angle of the connecting segment, which is used to describe the movement of the inner angle (0, 0) of the connecting segment in the reference system of the longitudinal section shape; M t represents the rotation matrix; S is the longitudinal cross-sectional area function; J tunnel is the coordinate set of the deep tunnel system; J tunnel It is the coordinate set of the storage shaft.

[0130] Formula (16) represents the shape set related to the rotation path. The method of tracking possible contact points is used to map the relevant shapes to the effective part of the rotation path. In addition to the rotational internal angle position (0, 0), the possible contact points refer to the tangent points A, B, C and D between the connecting segment and the shape, and the corresponding contact paths are represented by A(t), B(t), C(t) and D(t). For any given t value, the set of possible contact points of the related shape is Γ σ (t) = {σ, A, B, C, D}. Note that the selection of tangent points B and D does not take into account the failure of complex multi-tangent points (such as Figure 2 As shown, Figure 2 In: A, B, C, D are possible contact points; t is time).

[0131] Let the air mass motion projection be in the rotating standard orthogonal coordinate system μ t and v t The relationship between the possible contact paths A(t), B(t), C(t) and D(t) and the rotation path σ(t) is obtained as follows:

[0132] A(t)=σ(t)+<σ(t),M t {1, 0} T >M t {1, 0} T +M t {1, 0} T (17)

[0133] B(t)=σ(t)+σσ(t),M t {1, 0} T >M t {1, 0} T (18)

[0134] C(t)=σ(t)+<σ(t),M t {0, 1} T >M t {1, 0} T +M t {0, 1} T (19)

[0135] D(t)=σ(t)-<σ(t),M t {0, 1} T >M t {1, 0} T (20)

[0136] Where: σ(t) is the rotation path; M t Represents the rotation matrix; t is the time parameter and the rotation angle of the inner angle of the connecting segment, which is used to describe the movement of the inner angle (0, 0) of the connecting segment in the longitudinal section shape reference system.

[0137] When the contact points in equations (18) to (21) are defined, they are all considered valid, that is, the contact path is continuous at point t and σ(t) is differentiable. At this time, the polygonal transition limit of the relevant shape composed of the contact path can be determined based on the rotation path σ(t).

[0138] Assume Γ = Γ σ The neighborhood of t remains unchanged, then the contact point set Γ at time t σ (t) There are six possibilities:

[0139] Γ σ (t) = {σ, C, D} (21-a)

[0140] Γ σ (t) = {σ, A, C} (21-b)

[0141] Γ σ (t) = {A, B, C} (21-c)

[0142] Γ σ (t) = {σ, A, B, C} (21-d)

[0143] Γ σ (t) = {σ, A, C, D} (21-e)

[0144] Γ σ (t)={σ,A,B,C,D} (21-f)

[0145] Where: σ (t) is a set of possible contact points; t is a time parameter and also the rotation angle of the inner angle of the connecting segment, which is used to describe the movement of the inner angle (0, 0) of the connecting segment in the reference system of the longitudinal section shape; A, B, C, D, σ are possible contact points.

[0146] (5) Initial longitudinal section shape used for calculation

[0147] From equations (22-a) to (22-f), we can get the contact point set Γ in the direction of volume oscillation at t = 0: σ (t) The number of elements is 2 or 4, and the comparative statistics of the relevant longitudinal section shapes and their porosity can be obtained through the size of the connecting segment (Table 1).

[0148] Table 1 Statistics of possible cross-sectional shapes under the assumption of trapped air-water interface morphology

[0149]

[0150] It can be seen from Table 1 that the longitudinal section shape of the combined air mass at the contact point when the curved surface is assumed is richer than that of the plane, but the maximum porosity of the plane at the same number of interface contact points is larger than that of the curved surface. Furthermore, from the comparison of the longitudinal section shapes of the combined air mass at different numbers of contact points, it can be seen that the porosity is the largest when the longitudinal section shape of the combined air mass is an ellipse, which is easier to meet the maximum porosity characteristics of the trapped air mass in the tunnel under a certain saturation.

[0151] Step S3, constructing a parameterized hypothetical model of trapped air masses under different dimensional calculations according to the air mass morphology, air mass pressure head and control parameter model in the deep tunnel; Figure 3 Schematic diagram of parameterization of the trapped air mass in an embodiment of the present invention. Figure 3 Middle: 1# and 2# represent the storage shafts at both ends of the deep tunnel; tunnel is the inner diameter of the deep tunnel; r shafts It is the inner radius of the storage shaft; is the longitudinal slope of the deep tunnel; l a is the length of the air mass; h a is the air mass height; PL 12 , PL 34 are the lengths of the water body before and after the air mass, respectively.

[0152] 1) The parameters of the trapped air mass modeling used for one-dimensional calculations are: (1) The air mass height h a ; (2) Air mass porosity (Note: V a V is the volume of the trapped air mass; tunnel is the volume of the deep tunnel. )

[0153] 2) The parameters assumed for the modeling of the trapped air mass are: (1) The height of the air mass h a ; (2) Air mass length l a ; (3) Air mass width h a (Note: According to the assumption of air mass equal cross-section retention in the air mass deformation movement and retention hypothesis model, the air mass width is taken as the same value as the air mass height h a stay consistent).

[0154] Step S4, calculating the transient pressure caused by the water flow impact in the deep tunnel containing the trapped air mass based on the parameterized assumption model of the trapped air mass and the water-air two-phase flow simulation calculation model.

[0155] In this application, in combination with the air mass pressure head, the air mass control parameter is substituted into the existing water-air two-phase flow simulation calculation model as a supplementary parameter, and used to obtain the transient pressure caused by the water flow impact in the deep tunnel containing the trapped air mass in combination with modern information technology. The existing water-air two-phase flow simulation calculation model includes: 1) One-dimensional water and air two-phase flow calculation model: rigid column model (RC) or characteristic line model (MOC). 2) Three-dimensional visualization computational fluid model (CFD).

[0156] The technical means disclosed in the present application are not limited to the technical means disclosed in the above implementation mode, but also include technical solutions composed of any combination of the above technical features. The present application has been disclosed in the above preferred embodiments, but it is not used to limit the present application. Any technical solution obtained by equivalent replacement or equivalent transformation falls within the protection scope of the present application.

Claims

1. A simulation calculation method for a deep tunnel containing a trapped air mass, characterized in that: include: Step S1, constructing an air mass deformation movement and retention hypothesis model; Step S2, constructing a model of air mass morphology, air mass pressure head and control parameters in a deep tunnel based on the air mass deformation movement and retention hypothesis model; Step S3, constructing a parameterized hypothetical model of trapped air masses under different dimensional calculations according to the air mass morphology, air mass pressure head and control parameter model in the deep tunnel; Step S4, calculating the transient pressure caused by the water flow impact in the deep tunnel containing the trapped air mass based on the parameterized assumption model of the trapped air mass and the water-air two-phase flow simulation calculation model.

2. The deep tunnel simulation calculation method containing stagnant air masses according to claim 1 is characterized in that: The formation mechanisms of trapped air masses include: (1) large bubble plugs formed at the interface during the rapid filling process; (2) bubble accumulation in the water flow of the storage shaft; and (3) separation of the water column at the high point of the filling water body.

3. The deep tunnel simulation calculation method containing stagnant air masses according to claim 1 or 2 is characterized in that: The construction of the air mass deformation movement and retention hypothesis model specifically includes: 1) The deformation movement of air masses includes two types: volume oscillation and coupled migration; 2) A single stagnant air mass is assumed to be preferentially located at the midpoint of the flow segment and to occupy a certain equal-diameter cross-section.

4. The deep tunnel simulation calculation method containing stagnant air masses according to claim 1 is characterized in that: The air mass morphology model includes: Taking a point in the deep tunnel as the local coordinate origin o, the air mass morphology under different formation mechanisms is expressed as: Where: V a is the volume of the trapped air mass; x is the horizontal coordinate of the local coordinate system; y is the vertical coordinate of the local coordinate system; z is the vertical coordinate of the local coordinate system; f is a function; S is the longitudinal cross-sectional area function; h a is the height of the air mass; l a is the length of the air mass; c a is the circumference of the air mass.

5. The deep tunnel simulation calculation method containing stagnant air masses according to claim 1 is characterized in that: The air mass pressure head model includes: The head loss of any stagnant air mass is equal to the height of the air mass formed from the nose to the tail h a , that is, the initial relative pressure head of the trapped air mass: Ha=Znose+Hnose-Ztail-Htail=ha; Where: H a is the relative pressure head of the air mass; Z nose Z is the water head at the nose of the air mass; tail H is the water head at the tail of the air mass; nose H is the relative pressure head at the nose of the air mass; tail is the relative pressure head at the tail of the air mass; h a is the air mass height.

6. The deep tunnel simulation calculation method containing stagnant air masses according to claim 1 is characterized in that: The control parameter model includes: The morphology of trapped air mass when the initial water level of the storage shaft is equal to the inner diameter of the deep tunnel is selected as the research object, and the corresponding morphology and head control parameter relationship are as follows: Where: V a is the volume of the trapped air mass; H a0 is the initial relative pressure head of the air mass; f is a function; is the longitudinal slope of the deep tunnel; h d is the tailwater depth; S is the longitudinal cross-sectional area function; h a is the height of the air mass; l a is the length of the air mass; c a is the circumference of the air mass.

7. The deep tunnel simulation calculation method containing stagnant air masses according to claim 1 is characterized in that: The initial air mass longitudinal cross-section shape is constructed as an ellipse.

8. The deep tunnel simulation calculation method containing stagnant air masses according to claim 1 is characterized in that: Step S3, constructing a parameterized hypothetical model of trapped air masses under different dimensional calculations, including: 1) The parameters of the trapped air mass modeling used for one-dimensional calculations are: (1) The air mass height h a ; (2) Air mass porosity Where: V a V is the volume of the trapped air mass; tunnel is the volume of deep tunnel; 2) The parameters assumed for the modeling of the trapped air mass are: (1) The height of the air mass h a ; (2) Air mass length l a ; (3) Air mass width h a .

9. The deep tunnel simulation calculation method containing stagnant air masses according to claim 1 is characterized in that: The water-gas two-phase flow simulation calculation model is selected from at least one of a rigid column model RC, a characteristic line model MOC, and a three-dimensional visualization computational fluid model CFD.

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