CN105045987B - Method for calculating influence relation of pore plate thickness on pore plate energy loss coefficient - Google Patents
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Abstract
The invention relates to a method for calculating an influence relation of pore plate thickness on a pore plate energy loss coefficient. The method for calculating the influence relationship of the thickness of the pore plate on the energy loss coefficient of the pore plate can calculate the energy loss coefficient of the pore plate more accurately, so that the method is applied to engineering design.
Description
Technical Field
The invention relates to the technical field of hydraulic engineering, in particular to a method for calculating an influence relation of an orifice plate thickness on an orifice plate energy loss coefficient.
Background
With the rapid development of the hydropower industry, in the hydropower engineering project, high dams are used more and more, and according to the recorded content of the thesis of the current situation and the facing challenge of the sputtering of the high dams in China in journal 37(12) in journal 2006 of the journal, the dam heights of the first-level hydropower project and the double-river-mouth hydropower stations in the brocade screen in Sichuan province and the double-river-mouth hydropower stations respectively reach 305m and 315 m. The great dam has huge energy of the discharged water flow, and how to eliminate the huge energy of the high dam to protect the safety of the dam and the downstream river channel is always an important subject in front of vast hydropower workers.
As shown in figure 1, the orifice plate energy dissipation is characterized in that by means of the special body shape, water flow can be suddenly contracted and expanded when passing through the orifice plate, so that strong turbulence and strong shearing are formed, and the purpose of energy dissipation is achieved. The pore plate has the characteristics of simple structure, convenience in installation and high energy dissipation efficiency, and has important application prospect in future hydropower energy dissipation.
A large amount of research work is carried out at home and abroad around the hydraulics characteristic of the energy dissipation of the orifice plate, the research field of the orifice plate mainly focuses on the energy loss coefficient and the initial cavitation number of the orifice plate, the energy loss coefficient of the orifice plate reflects the energy dissipation efficiency of the orifice plate, and the initial cavitation number of the orifice plate reflects the cavitation erosion damage resistance of the orifice plate. The existing research shows that the larger the energy loss coefficient of the pore plate is, the better the energy dissipation effect of the pore plate is; the greater the number of incipient cavitations of the orifice plate, the more susceptible the orifice plate is to cavitation damage.
According to the content of the paper "Effects of cavitation and plate thickness on small diameter orientation meters" published in journal "Flow Measurement and Instrumentation" by Kim et al in 1998 8(2), and the content of Takahashi and Matsuda in the paper "Effects of geometry orientations", it can be known that the initial cavitation number and energy loss coefficient of an orifice plate are mainly closely related to the aperture ratio β (β ═ D/D, where D is the diameter of the orifice and D is the diameter of the flood hole), and the larger β is, the smaller the initial cavitation number of the orifice plate is, the stronger the cavitation damage resistance is, but the smaller the energy loss coefficient is, and the effect is also deteriorated.
According to the contents recorded in journal of Water conservancy and Power Generation journal, 1994 and 3, and the contents recorded in journal of section of paper of influence of body type of orifice plate energy dissipater on Tunnel flood discharge and energy dissipation, 1993 and 6, Multi-stage orifice plate energy dissipation coefficient problem discussion, it can be seen that when Reynolds number is less than 105In order of magnitude, the initial cavitation number and the energy loss coefficient of the orifice plate both have a small increase trend along with the increase of the Reynolds number. According to the contents recorded in journal of "numerical simulation of cavitation characteristics of energy dissipation orifice plate" in journal 33(3) in 2001 and the contents recorded in "experimental study on dissipation of orifice plate in pipe flow" in journal A2(3) in 1987, where Reynolds number is greater than 105At orders of magnitude, the Reynolds number has little effect on the energy loss coefficient and the nascent cavitation number of the orifice plate, at which point the effect of Reynolds number on energy loss can be ignored.
At present, the relation between the aperture plate aperture ratio and the energy loss system thereof is basically agreed, and the empirical expression of the aperture plate energy loss coefficient in the handbook of practical fluid resistance is generally accepted
(where D is the diameter of the orifice plate and D is the spillway tunnel diameter). However, the empirical expression of the energy loss coefficient of the orifice plate only considers the influence of the aperture ratio on the energy loss coefficient of the orifice plate, and does not fully consider the influence of the thickness of the orifice plate on the energy loss coefficient of the orifice plate. According to the content recorded in the publication "vertical simulation research on the length of the recirculation zone behind the orifice plate" in the publication of hydrodynamics research and development, 2010, 26(6), the thickness of the orifice plate is an important consideration factor for dividing the orifice plate and the orifice plug, and the thickness of the orifice plate directly influences the length of the recirculation zone of the orifice plate. According to the record of the book of Head load coeffficient of orifice energy disparities in Journal of hydropharic research of 2010 48(4), the large amount of rotation and shearing of water flow in the orifice plate backflow area are important sources of orifice plate energy dissipation, so the thickness of the orifice plate tends to influence the energy loss coefficient of the orifice plate. Neglecting the effect of thickness on the energy loss coefficient of the aperture plate is not scientific enough.
Disclosure of Invention
The invention aims to solve the technical problem of providing a method for calculating the influence relationship of the thickness of a pore plate on the energy loss coefficient of the pore plate, which is simple and accurate in calculation.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for calculating the influence relationship of the thickness of an orifice plate on the energy loss coefficient of the orifice plate is characterized by comprising the following steps:
the energy loss coefficient of the orifice plate is defined by the formula:
in the formula (1), xi is the energy loss coefficient of the orifice plate, p1The average pressure of the cross section of the flood discharge tunnel at 0.5D in front of the pore plate, D is the diameter of the flood discharge tunnel, p2The average pressure of the water flow recovery section behind the orifice plate is shown, rho is the water flow density, and u is the average flow velocity of the air interface section at the tail end of the orifice plate;
the empirical formula of the energy loss coefficient of the orifice plate is as follows:
in the formula (2), d is the diameter of the orifice plate;
step one, in a numerical value interval Re capable of neglecting the Reynolds number Re to the energy loss coefficient xi>Re0Under the condition of aperture ratio beta in the range of beta1<β<β2And the thickness-diameter ratio alpha range alpha1<α<α2Selecting a plurality of groups of working condition conditions with different aperture ratios and thickness ratios, respectively calculating the corresponding aperture plate energy loss coefficients under the plurality of groups of working condition conditions by utilizing an RNG k-calculation model according to a definition formula (1) of the aperture plate energy loss coefficients, thereby obtaining an aperture plate energy loss coefficient array;
wherein, alpha is T/D, beta is D/D, and T is the thickness of the pore plate;
re ═ sD/(mu/rho), s is the average flow velocity of the water flow in the spillway tunnel, mu is the dynamic viscosity of the water flow;
step two, drawing a relation curve of the energy loss coefficient of the pore plate, the aperture ratio and the thickness-diameter ratio according to the data in the energy loss coefficient array of the pore plate obtained in the step one;
and step three, fitting the relation curves of the energy loss coefficient of the pore plate, the aperture ratio and the thickness-diameter ratio in the step two on the basis of the empirical formula (2) of the energy loss coefficient of the pore plate, thereby obtaining an influence relation equation of the thickness of the pore plate on the energy loss coefficient of the pore plate:
the formula (3) is applicable within the range: beta is a1≤β≤β2，α1≤α≤α2And Re>Re0；
And step four, calculating the influence relation of the thickness of the pore plate on the energy loss coefficient of the pore plate according to the formula (3).
Beta is more than or equal to 0.4 and less than or equal to 0.8, alpha is more than or equal to 0.5 and less than or equal to 2.0, and Re>105Under the condition (2), the calculation formula of the influence relation of the thickness of the pore plate on the energy loss coefficient of the pore plate is as follows:
compared with the prior art, the invention has the advantages that: according to the method for calculating the influence relationship of the pore plate thickness on the pore plate energy loss coefficient, numerical simulation calculation is carried out on the pore plate energy loss coefficient by using an RNG k-calculation model, and on the basis, an empirical expression of the pore plate energy loss coefficient in a practical fluid resistance manual is corrected, so that a relational equation between the pore plate thickness and the pore plate energy loss coefficient is obtained, the influence of the pore plate thickness on the pore plate energy loss coefficient can be obtained according to the calculation of the relational equation, and meanwhile, a more accurate pore plate energy loss coefficient can be calculated by using the relational equation to determine the pore plate energy loss coefficient applied to engineering design.
Drawings
FIG. 1 is a schematic view of the water flow in a prior art flat head orifice plate.
Fig. 2 is a schematic coordinate diagram of an orifice plate in a spillway tunnel according to an embodiment of the present invention.
FIG. 3 is a fitting curve plotted according to the data in Table 1 in an embodiment of the present invention.
FIG. 4 is a comparative fit curve plotted from the data in Table 2 and Table 3 in accordance with an embodiment of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying examples.
The formula for calculating the energy loss coefficient of the orifice plate can adopt a definition formula commonly used in the prior art, and the definition formula is also described in a paper of Head load coefficient of orientation plant diseases in Journal of hydraulic research 2010 48 (4).
The energy loss coefficient of the orifice plate is defined by the formula:
in the formula (1), xi is the energy loss system of the orifice plateNumber, p1The average pressure of the cross section of the flood discharge tunnel at 0.5D in front of the pore plate, D is the diameter of the flood discharge tunnel, p2The average pressure of the cross section of the water flow behind the orifice plate is recovered, the normal flow state of the cross section water flow at the 3D position behind the orifice plate is generally considered to be recovered, rho is the water flow density, and u is the average flow velocity of the empty cross section at the tail end of the orifice plate.
The practical fluid resistance manual records that the empirical formula of the energy loss coefficient of the orifice plate is as follows:
in the formula (2), d is the orifice diameter. From the formula (2), it can be seen that the empirical formula of the energy loss coefficient of the orifice plate only considers the influence of the aperture ratio D/D on the energy loss coefficient of the orifice plate, and the relation between the thickness of the orifice plate and the energy loss coefficient of the orifice plate is not involved in the empirical formula.
The method for calculating the influence relationship of the thickness of the pore plate on the energy loss coefficient of the pore plate comprises the following specific steps:
step one, in a numerical value interval Re capable of neglecting the Reynolds number Re to the energy loss coefficient xi>Re0Under the condition of aperture ratio beta in the range of beta1<β<β2And the thickness-diameter ratio alpha range alpha1<α<α2Selecting a plurality of groups of working condition conditions with different aperture ratios and thickness ratios, and respectively calculating corresponding aperture plate energy loss coefficients under the plurality of groups of working condition conditions by using an RNG k-calculation model so as to obtain an aperture plate energy loss coefficient array;
wherein, alpha is T/D, beta is D/D, and T is the thickness of the pore plate;
and Re is sD/(mu/rho), s is the average flow velocity of the water flow in the flood discharge tunnel, and mu is the dynamic viscosity of the water flow.
Because the orifice plate spillway tunnel has strict axial symmetry, the three-dimensional numerical simulation problem of the orifice plate spillway tunnel can be simplified to be solved by two-dimensional numerical simulation. As shown in fig. 2, for the three-dimensional coordinate axis XYZ of the orifice plate spillway tunnel, in this embodiment, research may be performed on the hydraulic characteristics of the orifice plate spillway tunnel of the two-dimensional plane of the axial coordinate and the radial coordinate XZ of the orifice plate, and the hydraulic characteristics of the orifice plate spillway tunnel of the XZ two-dimensional plane represent the hydraulic characteristics of the entire orifice plate spillway tunnel.
The RNG k-model is one of the common models for solving the hydraulics problem, and specifically includes a mass conservation equation, a momentum conservation equation, a turbulent energy equation (k-equation), and a turbulent energy dissipation ratio equation (equation). The four equations together form a closed equation set, and the specific expression form is as follows:
(1) mass conservation equation (continuous equation):
(2) conservation of momentum equation:
(3) k-equation:
(4) -the equation:
the meanings of the parameters in the formulas (1-1) to (1-4) are as follows: x is the number ofi(x, y) represents the coordinates of the axial and radial directions; u. ofi(═ ux, uy) represents the water flow velocity in the axial and radial directions; ρ represents the density of the water flow; p represents pressure; v represents the dynamic viscosity of the water stream; v. oftIndicating the vortex viscosity, vt＝Cμ(k2V), k represents the turbulence energy, representing the dissipation rate of the turbulence energy, Cμ0.085. The values of the other parameters are as follows:
the computed boundary conditions include an inflow boundary, an outflow boundary, a symmetry-axis boundary, and a wall boundary. The boundary conditions are processed as follows:
(1) inflow boundary: the inflow boundary conditions include inflow average flow velocity, turbulent kinetic energy distribution, and distribution of turbulent kinetic energy dissipation rate. The mathematical expression is as follows: u. ofin＝u0；k＝0.0144u0 2；＝k1.5V (0.5R), wherein: u. of0Is the inlet average flow rate; and R is the radius of the flood discharge tunnel.
(2) Outflow boundary: assuming the outflow is fully developed, the mathematical expression is:
wherein: u is the axial flow velocity.
(3) Symmetry axis boundaries: assume that the radial velocity is 0 and the gradient of each variable along the radial direction is also 0. The mathematical expression is as follows:
wherein: u is the axial flow velocity and v is the radial flow velocity.
(4) Wall surface boundary: the non-slip assumption is adopted in the boundary layer flow, namely the velocity of the wall boundary is equal to the velocity component of the boundary node, and a wall function method is adopted.
According to the literature, when Reynolds number Re>105In the process, the influence of the Reynolds number on the energy loss coefficient of the hole plate can be ignored, so the Reynolds numbers used in the calculation in the embodiment are all larger than 105. Meanwhile, the diameter of the flood discharging tunnel for summarizing vertical simulation in the embodiment is set to be 0.21m, and the aperture ratio interval is 0.4<β<The aperture ratio beta values are selected to be 0.4, 0.5, 0.6, 0.7 and 0.8 in 0.8, and the thickness-diameter ratio interval is 0.05<α<The thickness-diameter ratio alpha values are respectively 0.05, 0.1, 0.15, 0.2 and 0.25 within 0.25, aiming at different aperture ratios and thickness diametersAnd (3) calculating by using an RNG k-model according to the definition formula (1) of the energy loss coefficient of the pore plate under the specific combined working condition so as to obtain the energy loss coefficient of the pore plate under each working condition to form a pore plate energy loss coefficient array, wherein the calculation result is shown in a table 1.
TABLE 1 Orifice plate energy loss coefficient array calculated by RNG k-model
And step two, drawing a relation curve of the energy loss coefficient of the pore plate, the aperture ratio and the thickness-diameter ratio according to the data in the energy loss coefficient array of the pore plate obtained in the step one, namely the data in the table 1, and referring to fig. 3.
And step three, fitting the relation curves of the energy loss coefficient of the pore plate, the aperture ratio and the thickness-diameter ratio in the step two on the basis of the empirical formula (2) of the energy loss coefficient of the pore plate, thereby obtaining an influence relation equation of the calculated thickness of the pore plate on the energy loss coefficient of the pore plate:
the formula (3) is applicable within the range: beta is more than or equal to 0.4 and less than or equal to 0.8, alpha is more than or equal to 0.5 and less than or equal to 2.0, and Re>105。
A physical model is established to perform experimental verification on the formula (2) and the formula (3), and the specific experimental conditions and experimental results in this embodiment are analyzed as follows.
1) Test conditions
A physical test model of the orifice plate pipeline is established, and main equipment of the test comprises a water tank for providing water level, a water pumping system, a pressure measuring pipe and the orifice plate pipeline. The designed diameter D of the spillway tunnel is 0.21m and is consistent with the diameter of the spillway tunnel analyzed by a numerical model. The total length of the spillway tunnel reaches 4.75 m. The maximum water level of the water tank may reach 10D. Arranging a pressure measuring pipe on the flood discharge tunnel within 0.5D behind the pore plate at intervals of 1cm, measuring the height of a water column of the pressure measuring pipe to obtain the pressure of each end face of the wall surface of the flood discharge tunnel, and further calculating and obtaining the energy loss coefficient of the pore plate according to the formula (1). The aperture ratio β of the selected aperture plate in this test was 0.7, and measurement calculations were performed for different water level heights under the condition that the thickness ratio α was 0.05, 0.15, 0.2, and 0.25, respectively, to obtain a data set shown in table 2.
Table 2 measurement calculation results of physical test model (β ═ 0.7)
In table 2, H represents the test water level height;
and (3) representing the average value of the energy loss coefficients of the pore plates obtained by calculation under different test water level heights under the test condition of the same thickness-diameter ratio alpha.
And (3) respectively calculating the energy loss coefficients of the pore plates under various working conditions in the table 2 by using the formula (2) and the formula (3), and calculating a result table 3.
Table 3 results of the orifice plate energy loss coefficients calculated by formula (2) and formula (3) (β is 0.7, Re)>105)
In Table 3, xi1Represents the result of the energy loss coefficient, ξ, of the orifice plate calculated according to equation (2)2Representing the results of the orifice plate energy loss coefficients calculated according to equation (3).
The data in tables 2 and 3 were plotted as a comparison curve as shown in fig. 4.
2) Analysis of test results
As can be seen from the comparison curve in fig. 4, the energy loss coefficient calculated using the empirical formula (2) in the manual of practical fluid resistance does not change with the change in the thickness of the orifice plate, and the energy loss coefficient calculated using the empirical formula in the manual of practical fluid resistance greatly differs from the physical model test data. The energy loss coefficients obtained by the physical model test all change along with the thickness of the pore plate, the energy loss coefficient result of the pore plate obtained by the test calculation is closer to the energy loss coefficient result of the pore plate obtained by the formula (3), the calculation result of the formula (3) is well matched with the actual result, and the energy loss coefficient of the pore plate obtained by the formula (3) is more accurate. That is, the equation (3) can accurately reflect the influence relationship of the thickness of the orifice plate on the energy loss coefficient of the orifice plate, and the energy loss coefficient of the orifice plate is influenced by the aperture ratio of the orifice plate, and the thickness of the orifice plate also has a non-negligible influence on the energy loss coefficient of the orifice plate. The energy loss coefficient of the orifice plate decreases with increasing thickness of the orifice plate.
Claims (1)
1. The method for calculating the influence relationship of the thickness of the pore plate on the energy loss coefficient of the pore plate is characterized by comprising the following steps of:
the energy loss coefficient of the orifice plate is defined by the formula:
in the formula (1), xi is the energy loss coefficient of the orifice plate, p1The average pressure of the cross section of the flood discharge tunnel at 0.5D in front of the pore plate, D is the diameter of the flood discharge tunnel, p2The average pressure of the water flow recovery section behind the orifice plate is shown, rho is the water flow density, and u is the average flow velocity of the air interface section at the tail end of the orifice plate;
the empirical formula of the energy loss coefficient of the orifice plate is as follows:
in the formula (2), d is the diameter of the orifice plate;
step one, in a numerical value interval Re capable of neglecting the Reynolds number Re to the energy loss coefficient xi>Re0Under the condition of aperture ratio beta in the range of beta1<β<β2And the thickness-diameter ratio alpha range alpha1<α<α2With different aperture ratiosAccording to a definition formula (1) of the energy loss coefficient of the pore plate, utilizing an RNG k-calculation model to respectively calculate the energy loss coefficients of the pore plate corresponding to the multiple groups of working conditions, thereby obtaining an energy loss coefficient array of the pore plate;
wherein, alpha is T/D, beta is D/D, and T is the thickness of the pore plate;
re ═ sD/(mu/rho), s is the average flow velocity of the water flow in the spillway tunnel, mu is the dynamic viscosity of the water flow;
step two, drawing a relation curve of the energy loss coefficient of the pore plate, the aperture ratio and the thickness-diameter ratio according to the data in the energy loss coefficient array of the pore plate obtained in the step one;
and step three, fitting the relation curves of the energy loss coefficient of the pore plate, the aperture ratio and the thickness-diameter ratio in the step two on the basis of the empirical formula (2) of the energy loss coefficient of the pore plate, thereby obtaining an influence relation equation of the calculated thickness of the pore plate on the energy loss coefficient of the pore plate:
the formula (3) is applicable within the range: beta is a1≤β≤β2，α1≤α≤α2And Re>Re0；
Beta is more than or equal to 0.4 and less than or equal to 0.8, alpha is more than or equal to 0.5 and less than or equal to 2.0, and Re>105Under the condition (2), the calculation formula of the influence relation of the thickness of the pore plate on the energy loss coefficient of the pore plate is as follows:
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| CN107895070A (en) * | 2017-11-01 | 2018-04-10 | 浙江海洋大学 | A kind of orifice plate based on numerical simulation and hole plug division methods |
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| CN103215932A (en) * | 2013-03-19 | 2013-07-24 | 浙江海洋学院 | Flood discharging tunnel pore plate building method |
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