Method for calculating flow pressure loss of flexible hose

Abstract

The application discloses a flexible hose flow pressure loss calculation method, comprising the following steps: (1) determining the relationship between the hose wall tensile stress and the internal pressure based on material mechanics; (2) determining the along-the-way pressure loss under the deformation of the hose based on the Lerbensong water head loss theory, the iterative calculation method and the material and fluid coupling relationship; (3) determining the local pressure loss under the deformation of the hose based on the deformation characteristics of the hose; (4) predicting the lowest point position of the hose in use based on the fluid momentum theorem, so as to avoid the collision of the hose; and (5) calculating the total pressure loss of the hose, and the application has the advantages of accurate and comprehensive prediction results.

Description

Technical Field

[0001] This invention relates to the field of pipeline flow pressure loss calculation technology, and specifically to a method for calculating flow pressure loss of a flexible hose. Background Technology

[0002] In practical engineering, pressurized pipe flow is divided into non-deformable pressurized pipe flow and deformable pressurized pipe flow. Non-deformable pressurized pipe flow is characterized by pipes made of rigid materials, resulting in minimal pipe deformation during fluid flow, with pressure losses along the pipe and at local points unrelated to material deformation. Deformable pressurized pipe flow, on the other hand, refers to pipes made of flexible or other easily deformable materials, which are prone to deformation under external forces or fluid impacts, thus affecting fluid flow. Because traditional rigid pipes have a very high elastic modulus, pipe diameter deformation is generally not considered when high-pressure fluids are introduced, and the conventional Reynolds formula can be used for relatively accurate calculations. However, for more flexible hoses, the pipe diameter changes significantly with the magnitude of the internal pressure of the fluid acting on it; therefore, the material properties of the hose must be considered.

[0003] Using the computational approach that couples materials mechanics and fluid mechanics is a common method for determining the energy loss of hoses. However, so far, the fluid pressure loss determined by this method is limited to ultra-long pipe flows, i.e., pipe flows whose length is much greater than their diameter. Based on this, traditional calculation methods only consider the friction loss along the pipe flow. However, for shorter pipes, in addition to friction loss, local pressure loss also has a significant impact on the overall pressure loss. Therefore, traditional hose pressure calculation methods are difficult to accurately estimate the pressure loss of shorter hoses and have obvious shortcomings. Summary of the Invention

[0004] To address the aforementioned technical shortcomings, the purpose of this invention is to provide a method for calculating the flow pressure loss of flexible hoses.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] This invention provides a method for calculating the flow pressure loss of a flexible hose, comprising the following steps:

[0007] (1) Determine the relationship between the tensile stress of the hose wall and the internal pressure based on the mechanics of materials;

[0008] (2) Based on the Repinzon head loss theory, iterative calculation method and material-fluid coupling relationship, and combined with step (1), determine the pressure loss along the hose considering the deformation of the hose;

[0009] (3) Based on the characteristics of hose deformation and combined with step (2), determine the local pressure loss when the hose is deformed;

[0010] (4) Based on the fluid momentum theorem and combined with step (2), predict the lowest point of the hose when it is put into use to avoid the hose from touching.

[0011] (5) Based on avoiding contact between the hose and the hose, calculate the total pressure loss of the hose in steps (2) and (3).

[0012] Preferably, the relationship between tensile stress and internal pressure determined in step (1) is determined by combining the following formulas:

[0013]

[0014]

[0015] 2π(r i +dr i )=(S i +dS i )

[0016] In the formula: i represents the i-th infinitesimal ring, Let S represent the strain along the circumference of the infinitesimal element, where S represents the circumference of the infinitesimal element. dS represents the stress along the circumference of the infinitesimal ring, E is the elastic modulus of the hose, and dS i For the deformation along the circumference of the infinitesimal ring, S i Let P be the perimeter of the i-th infinitesimal ring. i Let r be the pressure exerted on the infinitesimal ring, θ be the angle parameter used for integration, and r be the angle parameter used for integration. i Let dL be the radius of the i-th infinitesimal element, dL be the axial length of the selected infinitesimal element, dr be the total length of the hose, δ be the hose wall thickness, and dr be the radius of the ith infinitesimal element. i This indicates the magnitude of the radial deformation of the infinitesimal ring;

[0017] The dr determined by combining the formulas i With P i The relationship is as follows:

[0018]

[0019] Preferably, in step (2), based on the Repinzon head loss theory, iterative calculation method, and the coupling relationship between materials and fluids, the determination of the friction loss considering hose deformation specifically includes:

[0020] (21) The Repinzon head loss theory applicable to each i-th infinitesimal ring is determined as follows:

[0021]

[0022] ΔP ia =ρgh ia

[0023] In the formula: i represents the i-th infinitesimal ring, h ia ΔP represents the head loss along the friction path. ia The pressure loss along the flow path is represented by q, the velocity-flow rate is υ, and the kinematic viscosity of the fluid is d. i The diameter of the micro-ring;

[0024] β and m are Repinzantine parameters, determined by the following method:

[0025]

[0026] d i =d i-1 -2dr i

[0027] In the formula, the magnitude of the radial deformation of the infinitesimal ring is represented;

[0028] (22) Combining d i The modified Repinzon head loss theory, derived from the formulas β and m, is as follows:

[0029]

[0030] Where, ΔL i The iterative parameter is the axial length dL of the selected micro-element ring;

[0031]

[0032] In the formula, n is the preset number of iteration steps.

[0033] Preferably, step (3) of determining the local pressure loss under hose deformation based on the hose deformation characteristics specifically includes:

[0034] (31) Determine the pipe angle α at the lowest point of the hose under fluid action as:

[0035]

[0036] Among them, H max This is the vertical distance between the lowest point of the hose and the end of the hose;

[0037] (32) From the formula for calculating the local pressure loss of pressurized pipe flow at the rotation angle in fluid mechanics, we can see that:

[0038] ΔP y =ρgh y

[0039]

[0040]

[0041] In the formula, ΔP yh represents the local pressure loss within the pipeline. y For local head loss, is the local loss coefficient, v is the velocity of the fluid before the turning point, and g is the gravitational acceleration.

[0042] Preferably, step (4), which predicts the lowest point of the hose when it is put into use based on the fluid momentum theorem, specifically includes:

[0043] (41) Solve for L1, L2, θ, and η using the following formulas:

[0044] L = L1 + L2

[0045] L1sinθ+L2sinη=B

[0046] θ+η=α

[0047] L1cosθ=L2cosη

[0048] In the formula: L1 represents the length of the hose to the left of the lowest point, L2 represents the length of the hose to the right of the lowest point, θ represents the angle between the hose to the left of the lowest point and the vertical direction, η represents the angle between the hose to the right of the lowest point and the vertical direction, and B represents the horizontal distance between the two ends of the hose.

[0049] (42) Establish a coordinate system and determine the impact force on the pipe using the momentum theorem of fluid mechanics as follows:

[0050] ρq(v 2x -v 1x ) = F x +[P1A1-P2A2·cos(π-α)]

[0051] in:

[0052] v 2x =v2cosθ

[0053] v 1x =v1

[0054] In the formula: ρ is the fluid density, v1 is the inlet velocity, v2 is the outlet velocity, and v 1x Let v1 be the projection of v1 in the x-direction, v 2x F is the size of the projection of v2 in the x-direction. x Let P1 be the external force acting on the pipe in the x direction, P2 be the pressure at the fluid inlet, A1 be the cross-sectional area at the fluid inlet, and P2 be the pressure at the fluid outlet, A2 be the cross-sectional area at the fluid outlet.

[0055] (43) Determine the magnitude of the impact force on the hose at different locations using the formula in step (42), calculate the extreme value of the impact force, and determine the impact resistance strength of the selected hose based on the extreme value of the impact force to ensure that the hose works safely and without damage; use the following formula to calculate the vertical distance from the lowest point of the hose to the fixed point under the action of the extreme value of the impact force:

[0056]

[0057] (dL2+L2)·cosη=H av

[0058] Where: H av This represents the vertical distance from the lowest point of the hose to the fixed point under the extreme value of the impact force.

[0059] Preferably, the total pressure loss of the hose is calculated in step (5) using the following formula:

[0060]

[0061] In the formula, ΔP all This represents the pressure difference between the two ends of the hose, which is the total pressure loss of the hose during fluid flow.

[0062] The beneficial effects of this invention are as follows:

[0063] This invention uses the coupling concept of materials and fluid mechanics to derive the deformation of the hose and introduces the momentum theorem to determine the maximum allowable fluid velocity when the pipeline is put into use. Compared with the shortcomings of traditional calculation methods in predicting hose deformation, this invention has the advantages of accurate and comprehensive prediction results. This invention fully considers hose deformation, prediction of the lowest point position when the hose is put into use, and nonlinear friction loss iterative calculation method. The calculation method is more reasonable and accurate and can be better applied to engineering design. Attached Figure Description

[0064] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0065] Figure 1 This is a schematic diagram of the micro-rings cut from a whole flexible tube and their stress in an embodiment of the present invention;

[0066] Figure 2(a) shows the deformation of the hose when no fluid is introduced;

[0067] Figure 2(b) shows the deformation of the hose with fluid introduced;

[0068] Figure 3 A schematic diagram of rectangular coordinates established for calculating fluid impact force in an embodiment of the present invention;

[0069] Figure 4 This is a flowchart illustrating the implementation of an embodiment of the present invention. Detailed Implementation

[0070] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] like Figures 1 to 4 As shown, this embodiment provides a method for calculating the flow pressure loss of a flexible hose, including the following steps:

[0072] (1) Determine the relationship between the tensile stress of the hose wall and the internal pressure based on the mechanics of materials;

[0073] Because traditional rigid pipes have a very high elastic modulus, pipe diameter deformation is generally not considered when high-pressure fluids are introduced, and relatively accurate calculations can be performed using the conventional Reynolds formula. However, for more flexible hoses, the pipe diameter changes significantly with the magnitude of the internal pressure of the fluid acting at that point; therefore, the material properties of the hose need to be considered. A micro-ring of axial length dL is cut from the hose along its axial direction, named the i-th micro-ring taken from the hose. The shape and stress of the micro-ring are as follows... Figure 1 As shown; combining the stress-strain relationship in mechanics of materials, the relationship between the tensile stress in the guide tube wall and the internal pressure is as follows:

[0074]

[0075]

[0076] 2π(r i +dr i )=(S i +dS i )

[0077] In the formula: on the i-th infinitesimal ring, This represents the strain along the perimeter, where the subscript S indicates the perimeter. dS represents the stress along the circumference, E is the elastic modulus of the hose, and dS i For deformation along the perimeter, S i Let P be the perimeter. i The pressure exerted on the infinitesimal ring is given by θ, which is an angle parameter used for integration and has no real meaning.i For this micro-element radius, due to the expandable nature of the hose under internal pressure, this parameter varies at different positions on the hose. dL is the axial length of the selected micro-element, where L represents the total length of the hose, δ represents the hose wall thickness, and dr... i This indicates the magnitude of the radial deformation of the infinitesimal ring;

[0078] Combining the above three equations, we can obtain dr i With P i The relationship is as follows:

[0079]

[0080] (2) Based on the Repinzon head loss theory, iterative calculation method and material-fluid coupling relationship, and combined with step (1), determine the pressure loss along the hose considering the deformation of the hose;

[0081] Repinzon's head loss theory is one of the most accurate theories for calculating fluid pressure loss today. It has good accuracy for calculating deformable pipes. The modified Repinzon head loss theory, applicable to the i-th micro-element ring, is as follows:

[0082]

[0083] ΔP ia =ρgh ia

[0084] In the formula: in the i-th infinitesimal ring, h ia ΔP represents the head loss along the friction path. ia The pressure loss along the flow path is represented by q, the velocity-flow rate is υ, and the kinematic viscosity of the fluid is d. i Let β be the diameter of the infinitesimal ring, and m be Repinzan parameters, which can be determined by the following method:

[0085]

[0086] Among them, fluid state regions such as laminar flow region can be judged according to conventional fluid dynamics judgment methods known to those skilled in the art;

[0087] In the above formula, d i You can follow step (1) dr i The relationship between the two is derived as follows:

[0088] d i =d i-1 -2dr i

[0089] Combining the above equations, we can obtain the modified Repinzon head loss theory as follows:

[0090]

[0091] To facilitate iterative calculations, the parameter dL representing the infinitesimal element is replaced with the parameter ΔL representing the iteration. i Both represent the same meaning; the above formula can be iteratively calculated using existing tools well known to those skilled in the art, wherein:

[0092]

[0093] In the formula, n is the preset number of iteration steps. The larger the number of steps, the more accurate the iteration result. Those skilled in the art can select n according to the actual situation, provided that the amount of computation is controllable.

[0094] (3) Based on the characteristics of hose deformation and combined with step (2), determine the local pressure loss when the hose is deformed;

[0095] When using hoses for long-distance fluid transport, the local pressure loss is negligible compared to the pressure loss along the hose and is generally not considered. Only the pressure loss along the hose can be calculated using the method described in step (2). However, in short-distance transmission, the local pressure loss is significant and needs to be taken into account. In particular, for flexible hoses, under the action of external forces such as fluid impact and gravity, the pipe is more prone to large deformation, resulting in wrinkles and large curvature bends in local areas. Under this premise, the deformation characteristics of the hose are considered, and the pressure loss of the hose under local pressure deformation is determined.

[0096] like Figures 2(a)-2(b) As shown, Figure 2(a) shows the natural state of the hose under gravity when no fluid is introduced, and Figure 2(b) shows the deformation of the hose under multiple forces when fluid is introduced from the arrow end with a certain initial velocity. Assuming that the hose only undergoes small radial deformation, we can assume that the total length L of the hose remains constant. According to the relevant theories of mathematical geometric deformation, the angles between the lowest points of the hose in both figures are approximately equal. Therefore, the angle α between the lowest points of the hose under the action of fluid is:

[0097]

[0098] Among them, H max The vertical distance between the lowest point of the hose and the end of the hose in Figure (a);

[0099] From the formula for calculating the local pressure loss at the rotation angle in pressurized pipe flow in fluid mechanics, we can see that:

[0100] ΔP y =ρgh y

[0101]

[0102]

[0103] In the formula, ΔP y h represents the local pressure loss within the pipeline. y For local head loss, Here, v is the local loss coefficient, v is the velocity of the fluid before the turning point, and g is the acceleration due to gravity.

[0104] (4) Based on the fluid momentum theorem and combined with step (2), predict the lowest point of the hose when it is put into use to avoid the hose from touching.

[0105] Solve the following four equations simultaneously to find the four unknowns: L1, L2, θ, and η.

[0106] L = L1 + L2

[0107] L1sinθ+L2sinη=B

[0108] θ+η=α

[0109] L1cosθ=L2cosη

[0110] In the formula: L1 represents the length of the hose to the left of the lowest point, L2 represents the length of the hose to the right of the lowest point, θ represents the angle between the hose to the left of the lowest point and the vertical direction, as shown in Figure 2(b), η represents the angle between the hose to the right of the lowest point and the vertical direction, and B represents the horizontal distance between the two ends of the hose.

[0111] Because hoses undergo slight deformation under fluid impact, in order to determine the fluid impact force and the range of pipe deformation, a system is established as follows: Figure 3 The impact force on the pipe can be determined using the momentum theorem of fluid mechanics, as well as is well known to those skilled in the art, in the coordinate system shown below:

[0112] ρq(v 2x -v 1x ) = F x +[P1A1-P2A2·cos(π-α)]

[0113] in:

[0114] v 2x =v2cosθ

[0115] v 1x =v1

[0116] In the formula: ρ is the fluid density, v1 is the inlet velocity, v2 is the outlet velocity, and v 1x Let v1 be the projection of v1 in the x-direction, v 2x F is the size of the projection of v2 in the x-direction. xP1 is the pressure at the fluid inlet, A1 is the cross-sectional area at the fluid inlet, P2 is the pressure at the fluid outlet, and A2 is the cross-sectional area at the fluid outlet. P2 and A2 can be calculated using the flexible hose cross-section calculation method described in step (2).

[0117] The above formula can be used to determine the magnitude of the impact force on the hose at different locations; calculating the extreme value of this impact force can determine the impact resistance strength of the selected hose, ensuring that the hose operates safely and without damage; in addition, the deformation of the pipeline under this impact force is:

[0118]

[0119] (dL2+L2)·cosη=H av

[0120] Where: H av This indicates the vertical distance between the lowest point of the hose and the fixed point under this impact force. Calculating this distance can ensure that the hose will not deform significantly when it is put into use, thus preventing it from coming into contact with other structures. This avoids the hose from touching other structures, which would shorten its service life, and also maintains a safe distance from the structure to a certain extent.

[0121] (5) While avoiding contact between the hose and the other hose, calculate the total pressure loss of the hose by combining steps (2) and (3); the following formula is used for the calculation:

[0122]

[0123] In the formula, ΔP all Let ΔP be the pressure difference between the two ends of the hose, i.e., the total pressure loss of the hose under fluid flow. For ultra-long hoses, the pressure loss ΔP caused by local deformation of the hose can be neglected. y For shorter hoses, both friction loss and local pressure loss need to be calculated. The number of iteration steps should be determined before calculating friction loss, and the calculation should be performed with a convergent, accurate and convenient number of iteration steps.

[0124] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for calculating the flow pressure loss of a flexible hose, characterized in that, Includes the following steps: (1) Determine the relationship between the tensile stress of the hose wall and the internal pressure based on the mechanics of materials; (2) Based on the Repinzon head loss theory, iterative calculation method and material-fluid coupling relationship, and combined with step (1), determine the pressure loss along the hose considering the deformation of the hose; (3) Based on the characteristics of hose deformation and combined with step (2), determine the local pressure loss when the hose is deformed; (4) Based on the fluid momentum theorem and combined with step (2), predict the lowest point of the hose when it is put into use to avoid the hose from touching. (5) Based on avoiding contact between the hose and the hose, calculate the total pressure loss of the hose in combination with steps (2) and (3); Specifically, step (3) involves determining the local pressure loss under hose deformation based on the hose deformation characteristics, including: (31) Determine the pipe angle at the lowest point of the hose under fluid action. for: in, This is the vertical distance between the lowest point of the hose and the end of the hose; (32) From the formula for calculating the local pressure loss of pressurized pipe flow in fluid mechanics, we can see that: In the formula, This refers to localized pressure loss within the pipeline. For local head loss, This is the local loss coefficient. The velocity of the fluid before the turning point. It is the acceleration due to gravity; Step (4) predicting the lowest point of the hose when it is put into use based on the fluid momentum theorem specifically includes: (41) Solve using the following formula , , , : In the formula: This indicates the length of the hose to the left of the lowest point. This indicates the length of the hose to the right of the lowest point. This indicates the angle between the flexible tube to the left of the lowest point and the vertical direction. This indicates the angle between the hose to the right of the lowest point and the vertical direction. Indicates the horizontal distance between the two ends of the hose; (42) Establish a coordinate system and determine the impact force on the pipe using the momentum theorem of fluid mechanics as follows: in: In the formula: For fluid density, For the inlet speed, For export speed, for The size of the projection in the x-direction, for The size of the projection in the x-direction, Let x be the external force acting on the pipe in the x-direction. This refers to the pressure at the fluid inlet. The cross-sectional area at the fluid inlet end is... This refers to the pressure at the fluid outlet. The cross-sectional area at the fluid outlet end; (43) Determine the magnitude of the impact force on the hose at different locations using the formula in step (42), calculate the extreme value of the impact force, and determine the impact resistance strength of the selected hose based on the extreme value of the impact force to ensure that the hose works safely and without damage; use the following formula to calculate the vertical distance from the lowest point of the hose to the fixed point under the action of the extreme value of the impact force: In the formula: This represents the vertical distance from the lowest point of the hose to the fixed point under the extreme value of the impact force.

2. The method for calculating the flow pressure loss of a flexible hose as described in claim 1, characterized in that, The relationship between tensile stress and internal pressure determined in step (1) is determined by the following formulas: In the formula: i represents the i-th infinitesimal ring, Let S represent the strain along the circumference of the infinitesimal element, where S represents the circumference of the infinitesimal element. This represents the stress along the circumference of the infinitesimal ring. The elastic modulus of the hose. The deformation is along the circumference of the infinitesimal ring. Let be the perimeter of the i-th infinitesimal ring. The pressure exerted on the micro-ring The angle parameter used for integration. Let be the radius of the i-th infinitesimal ring. Let be the axial length of the selected micro-element ring, and represent the total length of the hose. Indicates the wall thickness of the flexible hose. This indicates the magnitude of the radial deformation of the infinitesimal ring; Determined by combining the formulas and The relationship is as follows: 。 3. The method for calculating the flow pressure loss of a flexible hose as described in claim 1, characterized in that, In step (2), based on Repinzon's head loss theory, iterative calculation methods, and the coupling relationship between materials and fluids, the specific pressure loss along the hose considering hose deformation is determined to include: (21) The Repinzon head loss theory applicable to each i-th infinitesimal ring is determined as follows: In the formula: i represents the i-th infinitesimal ring, Indicates head loss along the route, Indicates pressure loss along the process. For speed and flow rate, The kinematic viscosity of the fluid. The diameter of the micro-ring; , The Repinzon parameter is determined by the following method: In the formula This indicates the magnitude of the radial deformation of the infinitesimal ring; (22) Combination , , The modified Repinzon head loss theory derived from the formula is as follows: in, The axial length of the selected micro-element ring The iteration parameters; In the formula, This is the preset number of iterations.

4. The method for calculating the flow pressure loss of a flexible hose as described in claim 1, characterized in that, In step (5), the total pressure loss of the hose is calculated using the following formula: In the formula, This represents the pressure difference between the two ends of the hose, which is the total pressure loss of the hose under fluid flow.

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