A method for simulating a deep tunnel containing a stagnant air mass

Abstract

This invention discloses a simulation calculation method for deep tunnels containing trapped air masses, comprising: considering three known different trapped air mass formation mechanisms, constructing a model of air mass deformation, motion, and trapped air mass assumptions; based on the air mass deformation, motion, and trapped air mass assumption models, constructing models of air mass morphology, air mass pressure head, and control parameters in the deep tunnel; constructing parameterized assumption models of trapped air masses under different dimensions of calculation based on the air mass morphology, air mass pressure head, and control parameter models in the deep tunnel; and calculating the transient pressure caused by water flow impact in the deep tunnel containing trapped air masses based on the trapped air mass parameterized assumption models and the water-air two-phase flow simulation calculation model. This method can be used in modern information technology simulation calculations to solve the problem of trapped air masses that conforms to the layout and actual conditions of deep tunnel systems, thereby achieving real-time monitoring and simulation of the operation of deep tunnels containing trapped air masses.

Description

Technical Field

[0001] This invention belongs to the field of tunnel simulation technology, specifically relating to a method for simulating and calculating deep tunnels containing stagnant air masses. Background Technology

[0002] In response to the current characteristics of urban areas—low water surface ratio, high building density, complex underground pipelines, and dense population—frequent short-duration heavy rainfall, this paper explores the use of stormwater storage shafts as a means to mitigate overflow from existing large-scale combined sewer systems. These shafts, combined with deep tunnels to form a deep tunnel system, represent a relatively reliable and economical new option for urban stormwater management and renovation. Extensive engineering practice and research have shown that with multiple stormwater storage shafts inflowing, the presence of stagnant air masses within the deep tunnels is unavoidable, and the transient pressures caused by water flow impacts pose a potential safety hazard to the system.

[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). have made progress in the study of actual deep tunnel systems containing entrapped air pockets by directly referencing pipeline experience. However, the initial entrapped air-water interface, shape of a single entrapped air pocket, and state parameters used in different rapid filling backgrounds are worth discussing. (1) The assumptions made do not conform to the existing theoretical understanding of pipelines containing entrapped air pockets. Specifically, this manifests as: a. Vertical air-water interface. As previously mentioned (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.), this was the object initially proposed to define; b. 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 was concluded that the concept of a single trapped air mass within a pipe 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 initially used for pipeline test control. The specific formation principle is: a. Filling process. The volume of potential trapped air masses may be formed when the air initially present in the pipeline is discharged; b. Emptying process. Single or multiple trapped air masses located after 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 trapped air masses related to hydrostatic pressure. The statement about 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 under enclosed air in the pipe. However, the actual trapped air mass is developed from the system headline reaching the top of the deep tunnel, and its shape and state parameters are dynamically changing and independent of 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 given time using a normal distribution. The mathematical distribution description does not provide a theoretical basis or reasoning process, and it is inconsistent with the general understanding in existing experimental hydraulic theories that only the probability density statistics of flow random variables have functional characteristics. For a more recent mathematical application of this understanding, 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] To achieve real-time monitoring and simulation of deep tunnels containing trapped air masses, and thus better control and manage transient pressure changes caused by water flow impact, especially in the information-based assessment and processing of sudden events (such as tunnel rupture) in deep tunnels, a parametric assumption modeling method for trapped air masses needs to be proposed for further simulation calculations of deep tunnels containing trapped air masses. Summary of the Invention

[0005] Objective: To address the shortcomings of existing technologies, this invention provides a simulation calculation method for deep tunnels containing trapped air masses, which solves the problem of assuming trapped air masses that conform to the layout and actual conditions of deep tunnel systems in modern information technology simulation calculations, and obtains the transient pressure caused by water flow impact in deep tunnels containing trapped air masses.

[0006] Technical Solution: To solve the above-mentioned technical problems, this invention provides a method for simulating deep tunnels containing trapped air masses. The technical solution adopted is as follows:

[0007] This invention provides a method for simulating deep tunnels containing trapped air masses, comprising:

[0008] Step S1: Construct a hypothetical model of air mass deformation, motion, and retention;

[0009] Step S2: Based on the gas mass deformation, motion and retention assumption model, construct a model of gas mass morphology, gas mass pressure head and control parameters in deep tunnels;

[0010] Step S3: Construct parameterized hypothetical models of stagnant air masses under different dimensions of calculation based on the air mass morphology, air mass pressure head, and control parameter model in the deep tunnel.

[0011] Step S4: Based on the parameterized assumption model of the stagnant gas mass and the simulation calculation model of water-gas two-phase flow, calculate the transient pressure caused by water flow impact in the deep tunnel containing the stagnant gas mass.

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

[0013] In some embodiments, the construction of the hypothetical model of air mass deformation, motion, and retention specifically includes:

[0014] 1) Air mass deformation motion includes two types: volumetric oscillation and coupled migration;

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

[0016] Step S1: Construct a hypothetical model of air mass deformation, motion, and retention;

[0017] Step S2: Based on the gas mass deformation, motion and retention assumption model, construct a model of gas mass morphology, gas mass pressure head and control parameters in deep tunnels;

[0018] Step S3: Construct parameterized hypothetical models of stagnant air masses under different dimensions of calculation based on the air mass morphology, air mass pressure head, and control parameter model in the deep tunnel.

[0019] Step S4: Based on the parameterized assumption model of the stagnant gas mass and the simulation calculation model of water-gas two-phase flow, calculate the transient pressure caused by water flow impact in the deep tunnel containing the stagnant gas mass.

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

[0021] In some embodiments, the construction of the hypothetical model of air mass deformation, motion, and retention specifically includes:

[0022] 1) Air mass deformation motion includes two types: volumetric oscillation and coupled migration;

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

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

[0025] Using a point in a deep tunnel as the local coordinate origin o, the morphology of air masses under different formation mechanisms is represented as follows:

[0026]

[0027] In the formula: V a The volume of the trapped air mass is represented by x; x is the abscissa of the local coordinate system; y is the ordinate of the local coordinate system; z is the ordinate of the local coordinate system; f is a function; S is the cross-sectional area function; h a The height of the air mass; l a c is the length of the air mass. a The perimeter of the air mass.

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

[0029] The head loss of any stagnant air mass morphology is equal to the height h of the air mass formed between the nose and tail. a That is, the initial relative pressure head of the stagnant air mass:

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

[0031] Where: H aThe relative pressure head of the air mass; Z nose The water head at the nose of the air mass; Z tail The water head at the tail of the air mass; H nose The relative pressure head at the nose of the air mass; H tail The relative pressure head at the tail of the air mass; h a This represents the height of the air mass.

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

[0033] The morphology of the stagnant air mass, where the initial water level of the storage shaft is equal to the diameter of the deep tunnel, is selected as the research object. The corresponding relationship between the morphology and the head control parameters is as follows:

[0034]

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

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

[0037] In some embodiments, step S3, constructing a parameterized hypothesis model of the stagnant air mass under different dimensions of calculation, includes:

[0038] 1) The parameters assumed for modeling stagnant air masses for one-dimensional calculation are: (1) air mass height h a (2) Air mass porosity Where: V a V represents the volume of the retained air mass. tunnel The volume of the deep tunnel;

[0039] 2) The modeling parameters for stagnant air masses are: (1) air mass height h a (2) Air mass length l a (3) Air mass width h a .

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

[0041] Beneficial Effects: As a core technology for the intelligent operation and management of deep tunnel systems, this paper addresses the theoretical assumptions and application difficulties currently faced in the simulation calculation of deep tunnels containing trapped air masses. It proposes two key assumptions: 1) air mass deformation and movement assumptions under various formation mechanisms; and 2) a research object considering air mass pressure head values ​​and changes in water level in regulating shafts. Ultimately, a parametric assumption modeling method for trapped air masses is established, applicable to the simulation calculation of deep tunnels containing trapped air masses. Based on this method, the simulation calculation of deep tunnels containing trapped air masses is realized, yielding the transient pressure caused by water flow impact within the tunnel. This method solves the problem of assuming trapped air masses that conforms to the layout and actual conditions of deep tunnel systems in modern information technology simulation calculations, and can be used to obtain the transient pressure caused by water flow impact within deep tunnels containing trapped air masses. Attached Figure Description

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

[0043] Figure 2 This is a schematic diagram of the contact and contact path in an embodiment of the present invention;

[0044] Figure 3 This is a schematic diagram of the parameterization of the stagnant air mass in an embodiment of the present invention. Detailed Implementation

[0045] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit this application or its application or use. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0046] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of this application. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0047] In the description of this application, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only used to explain the relative positional relationship and movement between components in a specific orientation. If the specific orientation changes, the directional indication will also change accordingly. These terms are used only for the convenience of describing this application and for simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

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

[0049] In the description of this application, it should be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art will understand the specific meaning of the above terms in this application based on the specific circumstances.

[0050] It should be noted that in this application, firstly, three known different mechanisms for the formation of stagnant air masses are considered: (1) large interfacial bubble slugs formed during rapid filling (see Martin, CS (1976). Enrapped air in pipelines. Proc. 2nd Intl. Conf. Pressure Surges, 15-28, F2, BHRA, Bedford, UK.); (2) bubble accumulation in the water flow of a regulating 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) Separation of water columns in high-point filling bodies (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 key to the existence of gas masses with 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 emptying bottlenecking breaking and making of interacting interfaces. Physics of Fluids, 32(4).).

[0053] Example 1: This example provides a method for simulating deep tunnels containing trapped air masses, including:

[0054] Step S1: Construct a hypothetical model of air mass deformation, motion, and retention.

[0055] In some embodiments, step S1, which involves constructing a hypothetical model of air mass deformation, motion, and retention, specifically includes:

[0056] 1) Air mass deformation motion includes two types: volumetric oscillation and coupled migration;

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

[0058] (1) Deformation of air mass movement

[0059] The possible modes of motion of the air mass, derived from the continuity equation, are as follows:

[0060] a. Carried downstream by the current:

[0061] b. Remain relatively still:

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

[0063] In the formula: Q is the flow rate of the deep tunnel; g is the acceleration due to gravity; For deep tunnel longitudinal slope; r tunnel This refers to the inner diameter of a deep tunnel.

[0064] Its deformation during the hydraulic transient process is manifested 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 cross section, causing the water flow velocity at that cross section to increase and the pressure to decrease. The saturated water body is forced to release a small amount of bubbles that were originally dissolved in the water, further increasing the size of the air mass; (2) The process of decreasing the outer surface of the air mass. After the air mass occupies the entire tunnel cross section, the locally increased flow velocity in the deep tunnel causes the gas at that location to be easily dispersed and some small air masses to be discharged along the water flow direction.

[0065] (2) Hypothesis of air mass deformation and stagnation

[0066] Referring to Plateau's theorem regarding the stable bubble configuration that achieves the minimum surface area for a given volume, we assume a constant diameter cross-section for the convex polyhedral gas cloud after continuous deformation of its outer surface. Based on this assumption, it is necessary to prove that for any centrally symmetric convex polyhedron U, a ternary (semi-)positive definite quadratic form with a constant cross-section can be found whose outer surface j encloses the convex polyhedron. This allows us to achieve the key to satisfying the maximum saturation at the minimum outer surface area by controlling the unknown gas cloud morphology and volume. The reasoning process is as follows:

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

[0068]

[0069] In the formula: K is the set of all ternary positive definite quadratic forms; l is the set of outer surfaces; L is the set of positive rational numbers; x is the x / y coordinate of the iso-radius coordinate system; For each convex set U to uniquely correspond to N 3 The norm of ; N is the range of real numbers.

[0070] From equation (2), we can see that: (1) K is N 3*3 The subset in is a bounded closed set and has compactness; (2) if 0 ≤ l1(x, x), Then for any Where l1 and l2 are sets of different outer surfaces; λ is a linear parameter.

[0071] Let V(l) be the volume contained within the outer surface {l(x, x) ≤ 1}, then due to the compactness of K, there exists... Make The minimum value is obtained. If we assume there is another l′ such that V(l′) = V(l), then this is to illustrate... We need to introduce constructive equations Furthermore, considering the convexity of the exponential function, we can obtain:

[0072]

[0073] In the formula: f is a function; l is the set of outer surfaces; x is the x / y coordinate of the iso-radius coordinate system; A convex set U uniquely corresponds to N 3 The norm of ; (e) = exponential function.

[0074] From equation (3), we can see that the corresponding There exists a unique outer surface j such that the volume it encloses can be minimized, therefore this assumption holds.

[0075] Dynamic analysis of stagnant air masses under the assumption of constant cross-section reveals two key results: the compressibility of the stagnant air mass allows for accelerated flow of non-constant pressure water, causing its size and pressure to vary with the velocity of adjacent interfaces, resulting in volumetric oscillations similar to those defined in bubble dynamics; neglecting gas inertia and gravity, the oscillating air mass, due to the anisotropy of the surrounding flow, such as pressure gradients or gravitational fields caused by nearby boundaries, will further undergo coupled migration accompanied by water-filling collapse. At this point, the unfavorable location of the stagnant air mass and its subsequent pressurization behavior can be assessed by considering the basic characteristics of the deep tunnel system layout and the five stagnant air mass ventilation mechanisms employed. In particular, geometrically misaligned air mass emissions are more common when the system lacks sufficient ventilation. Related experimental observations also indicate that the generation of stagnant air between water bodies may lead to higher peak pressures than pure water. Therefore, a single stagnant air mass is assumed to preferentially be located at the midpoint of the flow segment and occupy a certain constant cross-section. Figure 1 This is a schematic diagram illustrating the assumption of air mass retention at the midpoint of any flow segment in an embodiment of the present invention; Figure 1 Chinese: (O) a )1、(O a )2、(O a )3、(O a )4 is a schematic diagram of the centers of different air masses; (r a )1、(r a )2、(r a 3. (r) a )4 represents the radius of the corresponding air mass; O tunnel r tunnel The center and radius of the deep tunnel.

[0076] Step S2: Based on the gas mass deformation, motion and retention assumption model, construct a model of gas mass morphology, gas mass pressure head and control parameters in deep tunnels;

[0077] Step S21, Air mass morphology:

[0078] Different morphologies of stagnant air masses are represented by investigating the volume changes that cause oscillations in the stagnant air mass. Using a point in a deep tunnel as the local coordinate origin o, the air mass morphologies under different formation mechanisms are represented as follows:

[0079]

[0080] In the formula: V aThe volume of the trapped air mass is represented by x; x is the abscissa of the local coordinate system; y is the ordinate of the local coordinate system; z is the ordinate of the local coordinate system; f is a function; S is the cross-sectional area function; h a The height of the air mass; l a c is the length of the air mass. a The perimeter of the air mass.

[0081] Step S22, air mass pressure head:

[0082] The head loss of any stagnant air mass morphology is equal to the height h of the air mass formed between the nose and tail. a That is, the initial relative pressure head of the stagnant air mass:

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

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

[0085] The proof is as follows:

[0086] a. The rate of change of pressure head under different air mass morphologies can be obtained from the Bernoulli equation;

[0087]

[0088] In the formula: P is the relative pressure; ρ = density; g is the gravitational acceleration; t is time, where subscripts 1 and 2 represent different times.

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

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

[0091] In the formula: V a V represents the volume of the retained air mass. a0 H represents the initial volume of the retained gas mass. a0H represents the initial relative pressure head of the air mass. a The relative pressure head of the air mass.

[0092] c. The comprehensive change rate of the morphology of the stagnant air mass is obtained by considering the synchronous change rate of the change rate of the expansion head of the air mass from t1 to t2 with respect to the change rate of the change rate of the pressure head of the air mass.

[0093]

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

[0095] d. As can be seen from the pressure-head relationship, the overall head change rate of the stagnant air mass volume is a function of the stagnant air mass volume height.

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

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

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

[0099] The morphology of the stagnant air mass, where the initial water level of the storage shaft is equal to the diameter of the deep tunnel, is selected as the research object. The corresponding relationship between the morphology and the head control parameters is as follows:

[0100]

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

[0102] The proof is as follows:

[0103] Given the formation height h of a certain stagnant air mass morphology a Simultaneously satisfying the following air mass volume relationship:

[0104]

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

[0106] Equations (9) and (10) show that the formation height of the stagnant air mass morphology is related to the lower tailwater depth h. d Closely related, that is, within a deep tunnel with a diameter of 2r tunnel Within a fixed range of values, the tailwater depth h d This will affect the formation height h of the stagnant air mass morphology. a This results in a loss of the initial driving head of the system. Since the system driving head is a representation of the continuously changing water level within the regulating shaft, the morphology of the stagnant air mass with the initial water level of the regulating shaft equal to the diameter of the deep tunnel is chosen as the research object, thus eliminating the influence of arbitrary calculated head references.

[0107] Corresponding to this selective change in the morphology of the stagnant air mass, by relating equation (4) with equations (1-a), (1-b), and (1-c), we obtain that the reason for the deformation and movement of the air mass morphology is due to the lower tailwater depth h. d The resulting cross-sectional gas volume V a Displacement. At this point, the initial head velocity under this selection is considered constant as 0, and the relationship between the selected object's shape and head control parameters is obtained as follows:

[0108]

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

[0110] The longitudinal section shape assumption used for model calculations is: the initial air mass longitudinal section shape is assumed to be elliptical.

[0111] The proof is as follows:

[0112] (1) Hypothesis on the morphology of the stagnant gas-water interface

[0113] Under a certain deep tunnel slope, the morphology of the stagnant air mass in equation (11) is related to the depth of the lower tailwater. The change in the lower tailwater depth causes the ratio of the cross-sectional area of ​​the stagnant air mass invading the water body to the cross-sectional area of ​​the tunnel to be ξ. It is known that when ξ is small, it has little effect on the inflow. Therefore, a certain length of stagnant air mass has volume adjustment under the influence of internal gas flow and external pressure changes when 0≤ξ≤1. Equation (4) generates two different stagnant-air-water interface morphologies, namely planar and curved surfaces.

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

[0115] If we consider the full-tunnel retained gas mass that maintains the gas-water interface and moves towards the storage shaft as the basic configuration without considering coupling migration effects, 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] In the formula: J system J represents the coordinate set of a deep tunnel system. tunnel J represents the coordinate set of a deep tunnel system. tunnel The coordinate set of the regulating shaft; x is the abscissa of the local coordinate system; y is the ordinate of the local coordinate system; N is the range of real numbers; r tunnel r is the inner diameter of the deep tunnel. deep To regulate the inner diameter of the vertical shaft.

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

[0121] (31) From L tunnel Move continuously to L deep At the same time, maintain L system Inside;

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

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

[0124] Using a dual-view longitudinal section shape reference system, connecting segment J tunnel ∪J shaft A longitudinal section shape can move within a connecting segment if it is translated and rotated in a reference frame while its position relative to the stationary longitudinal section remains unchanged, and the following conditions are met:

[0125]

[0126] In the formula: It satisfies σ(0)=(0,0) T The continuous path; t is both a time parameter and the rotation angle of the interior angle of the connecting segment, used to describe the motion of the interior angle (0, 0) of the connecting segment in the longitudinal section shape reference frame; M t S is the rotation matrix; S is the longitudinal cross-sectional area function; J tunnel J represents the coordinate set of a deep tunnel system. tunnel The coordinate set of the regulating shaft.

[0127] Let σ(t) be the rotation path. Then, under a given rotation path, equation (15) does not lose its generality by only considering the shape of the longitudinal section. Therefore, under strict containment conditions, a shape with a larger (or equal) area can be used to replace the shape:

[0128]

[0129] In the formula: It satisfies σ(0)=(0,0) T The continuous path; t is both a time parameter and the rotation angle of the interior angle of the connecting segment, used to describe the motion of the interior angle (0, 0) of the connecting segment in the longitudinal section shape reference frame; M t Represents the rotation matrix; S is the longitudinal cross-sectional area function; J tunnel J represents the coordinate set of a deep tunnel system. tunnel The coordinate set of the regulating shaft.

[0130] Equation (16) represents the set of shapes associated with the rotation path. A method for tracking possible contact points is used to map the relevant shapes to the effective portion of the rotation path. Relatedly, except for the rotational interior 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 denoted by A(t), B(t), C(t), and D(t). For any given value of t, 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 consider failure scenarios with complex multiple tangent points (e.g., Figure 2 As shown, Figure 2 In the diagram: A, B, C, and D are possible contact points; t is time.

[0131] Projecting the air mass motion onto 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] In the formula: σ(t) is the rotation path; M t Represents the rotation matrix; t is both a time parameter and the rotation angle of the interior angle of the connecting segment, used to describe the motion of the interior angle (0, 0) of the connecting segment in the longitudinal section shape reference frame.

[0137] When the contact points in equations (18) to (21) are defined, they are considered valid, meaning the contact path is continuous at point t and σ(t) is differentiable. In this case, 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 σIf the neighborhood of time t remains unchanged, then the set of contact points Γ at time t is... σ (t) has the following 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] In the formula: Γ σ (t) represents the set of possible contact points; t is both a time parameter and the rotation angle of the inner angle of the connecting segment, used to describe the motion of the inner angle (0, 0) of the connecting segment in the longitudinal section shape reference frame; A, B, C, D, and σ are possible contact points.

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

[0147] From equations (22-a) to (22-f), we obtain the set of contact points Γ in the direction of volume oscillation at t=0. σ (t) The number of elements is 2 or 4, and the relevant longitudinal cross-sectional shape and its porosity can be compared and statistically analyzed by the size of the connecting section (Table 1).

[0148] Table 1. Statistics of possible cross-sectional shapes under the assumptions of the morphology of the trapped gas-water interface.

[0149]

[0150] As shown in Table 1, the longitudinal cross-sectional shape of the combined air mass under the curved surface assumption is more varied than that under the planar assumption. However, the maximum porosity of the planar surface is greater than that of the curved surface under the same number of interface contact points. Furthermore, by comparing the longitudinal cross-sectional shapes of the combined air mass under different numbers of contact points, it can be seen that the porosity is the largest when the longitudinal cross-sectional shape of the combined air mass is elliptical, which is more likely to satisfy the maximum porosity characteristics of the air mass trapped in the tunnel under a certain degree of saturation.

[0151] Step S3: Construct parameterized hypothetical models of stagnant air masses under different dimensions of calculation based on the air mass morphology, air mass pressure head, and control parameter model in the deep tunnel. Figure 3 This is a schematic diagram of the parameterization of the stagnant air mass in an embodiment of the present invention. Figure 3 In the middle: 1# and 2# represent the regulating shafts at both ends of the deep tunnel, respectively; r tunnel r is the inner diameter of the deep tunnel. shafts To adjust the inner radius of the shaft; Longitudinal slope of deep tunnel; a h is the length of the air mass. a For air mass height; PL 12 PL 34 These represent the lengths of the water body before and after the air mass.

[0152] 1) The parameters assumed for modeling stagnant air masses for one-dimensional calculation are: (1) air mass height h a (2) Air mass porosity (Note: V) a V represents the volume of the retained air mass. tunnel (This refers to the volume of a deep tunnel.)

[0153] 2) The modeling parameters for stagnant air masses are: (1) air mass height h a (2) Air mass length l a (3) Air mass width h a (Note: Based on the constant-diameter cross-section retention assumption of the air mass in the air mass deformation, motion, and retention assumption model, the air mass width is related to the air mass height h.) a (Maintain consistency).

[0154] Step S4: Based on the parameterized assumption model of the stagnant gas mass and the simulation calculation model of water-gas two-phase flow, calculate the transient pressure caused by water flow impact in the deep tunnel containing the stagnant gas mass.

[0155] In this application, the gas mass pressure head is incorporated as a supplementary parameter into an existing water-gas two-phase flow simulation model. This model is then used in conjunction with modern information technology to obtain the transient pressure caused by water flow impact within a deep tunnel containing a trapped gas mass. The existing water-gas two-phase flow simulation models include: 1) a one-dimensional water-gas two-phase flow calculation model: a rigid column model (RC) or a model of characteristics (MOC); and 2) a three-dimensional computational fluid dynamics (CFD) model.

[0156] The technical means disclosed in this application are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. This application has been disclosed above with reference to preferred embodiments, but it is not intended to limit this application. All technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of this application.

Claims

1. A method for simulating a deep tunnel containing a stagnant air mass, characterized by, The application relates to a method for calculating the transient pressure of a deep tunnel containing a trapped air mass, comprising the following steps: Step S1, constructing an air mass deformation movement and trapped air mass assumption model, including: 1) the air mass deformation movement contains two types of volume oscillation and coupled migration; 2) a single trapped air mass assumption is preferentially located at the midpoint of a flow section and has a certain equal-diameter cross-section occupying form; Step S2, constructing an air mass form, air mass pressure head and control parameter model in a deep tunnel based on the air mass deformation movement and trapped air mass assumption model; The air mass form model comprises: taking a certain point in the deep tunnel as a local coordinate origin o, and expressing the air mass form under different formation mechanisms as: ； where: V a is the volume of the air mass; x is the horizontal coordinate in the local coordinate system; y is the vertical coordinate in the local coordinate system; z is the vertical coordinate in the local coordinate system; f is a function; S is a function of the vertical cross-sectional area; 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; The plume pressure head model includes that the head loss for any plume shape is equal to the height h of the plume formed between the nose and the tail of the plume a i.e. the initial relative pressure head of the plume: ； where: H a is the relative pressure head of the air mass; Z nose is the nose position head of the air mass; Z tail is the tail position head of the air mass; H nose is the relative pressure head of the nose of the air mass; H tail is the relative pressure head of the tail of the air mass; h a is the height of the air mass; The control parameter model comprises: selecting an initial storage shaft water level equal to the trapped air mass form under the diameter in the deep tunnel as a research object, and the corresponding form and head control parameter relationship is: ； where: V a is the volume of the stagnant air mass; H a0 is the initial relative pressure head of the air mass; f is a function; φ is the longitudinal slope of the deep tunnel; h d is the tail water depth; S is a function of the longitudinal cross-sectional area; h a is the height of the air mass; l a is the length of the air mass; c a is the perimeter of the air mass; Step S3, according to the deep tunnel air mass form, air mass pressure head and control parameter model, a parameterized assumption model of the trapped air mass under different dimensions is constructed, including: 1) the modeling assumption parameters of the trapped air mass for one-dimensional calculation are: (1) air mass height h a ; (2) air mass porosity , wherein: V a is the volume of the trapped air mass; V tunnel is the volume of the deep tunnel; 2) the modeling assumption parameters of the trapped air mass are: (1) air mass height h a ; (2) air mass length l a ; (3) air mass width h a ; Step S4, calculating the transient pressure caused by water flow impact in the deep tunnel containing a trapped air mass according to the trapped air mass parameterized assumption model and a water-air two-phase flow simulation calculation model.

2. The method of claim 1, wherein, The formation mechanism of the trapped air mass comprises: (1) an interface air bubble slug formed in a rapid filling process; (2) air bubbles accumulated in water flow in a storage shaft; and (3) water column separation of filling water at a high point.

3. The method of claim 1, wherein, The initial air mass longitudinal cross-section shape is constructed as an ellipse.

4. The method of claim 1, wherein, The water-air 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 visualized computational fluid model CFD.

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