CN114611321B - Submerged vegetation area water flow vertical line flow velocity prediction method based on layered mixing length - Google Patents
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Abstract
The invention discloses a submerged vegetation area water flow vertical line flow velocity prediction method based on layered mixing length, which is characterized in that completely developed submerged vegetation water flow is divided into vegetation layers and surface water flow layers, and a submerged vegetation area water flow vertical line flow velocity distribution analysis solution is obtained by respectively solving momentum equations of all layers; the surface water flow layer provides a layered mixed length model from a submerged vegetation water flow turbulent diffusion mechanism. The analysis is subjected to model calibration and verification through a large number of water tank measured data, so that the model has extremely strong universality for data from different sources while the prediction accuracy is improved. The required determination constants are common calculation variables in the field, can be determined according to water flow conditions, vegetation conditions and river channel conditions, do not need to be unfolded for flow velocity measurement, reduce research cost, and have wide universality in the field.
Description
Technical Field
The invention belongs to the field of submerged vegetation area water flow velocity prediction, and particularly relates to a submerged vegetation area water flow vertical line flow velocity prediction method and system based on layered mixing length.
Background
The interaction of aquatic vegetation with the surrounding water environment has a significant impact on various aspects from nature to engineering. The submerged vegetation exerts resistance to water flow, which often reduces the carrying capacity of water flow to suspended sand, thereby affecting the water quality and the evolution of the beach morphology. Ecologically, vegetation provides shelter and slow flow areas for species, facilitating species diversity. As a friction resistance medium layer, vegetation can increase river resistance, so that water level rises, and finally flood risk is increased. Meanwhile, the concentration of the submerged vegetation water flow suspended sand has a layered distribution characteristic, and the selection of the water intake position is affected. Thus, in the last twenty years, research on the response of water flow structures to underwater vegetation has been one of the hot spots of water environment resource research.
The vertical distribution of flow rates predicted based on numerical modeling and analytical models is a very practical means in engineering applications compared to measurements. Numerical simulation can solve most of flow problems by means of a numerical method, has good adaptability to boundaries, but is complex in operation mode and relatively time-consuming. On the basis of the analytical model for solving the fluid motion control equation, the problem of simplifying the boundary can be solved, but once the analytical solution exists, the prediction is very convenient. Aiming at the complete development of water flow movement under the condition of submerged vegetation canopy, the vegetation canopy can be divided into a vegetation layer and a surface water flow layer according to the geometric characteristics of the vegetation canopy, and the water flows of all the layers are balanced under different stress conditions due to the medium. In the vegetation layer, water flow is mainly subjected to vegetation resistance, component force of gravity in the flow direction and Reynolds shearing force generated by turbulence; and for the surface water layer, the vegetation resistance disappears. The vegetation canopy interface flow velocity gradient increases to induce large-scale vortex generation, so that two layers of water bodies are fully mixed, and the vertical flow velocity distribution is changed.
Although the former has conducted many researches on the theoretical analytical solution of the flow velocity distribution of submerged vegetation, the current proposed solution model has larger limitation due to insufficient knowledge on the adjustment of the vegetation canopy scale vortex induced water flow structure, and the prediction applicability under different boundaries and water flow vegetation conditions is low.
Disclosure of Invention
The invention aims to solve the technical problems in the background art, and aims to provide a submerged vegetation area water flow vertical velocity prediction method and a submerged vegetation area water flow vertical velocity prediction system based on a layered mixing length, and provide a universal analytic solution under a wider range of vegetation canopy water flow conditions by considering a vegetation canopy scale vortex effect based on a mixing length model, so that the submerged vegetation water flow vertical velocity distribution prediction under a general condition is solved.
In order to solve the technical problems, the technical scheme of the invention is as follows:
A submerged vegetation area water flow vertical line flow velocity prediction method based on layered mixing length comprises the following steps:
Dividing a submerged vegetation area into a vegetation layer and a surface water flow layer along the depth direction of water by taking the top of the vegetation canopy as a boundary;
Establishing a vegetation layer momentum control equation and a surface water flow layer momentum control equation by using preset basic parameters;
simulating and calculating the vortex-viscosity coefficient of the vegetation layer by utilizing the characteristic length scale parameter and the pre-acquired flow velocity parameter to obtain the vortex-viscosity coefficient of the vegetation layer;
Simulating and calculating the vortex-viscosity coefficient of the surface water flow layer by using a preset layered mixed length model; obtaining the vortex viscosity coefficient of the surface water flow layer;
Inputting the eddy current viscosity coefficient of the vegetation layer into the vegetation layer momentum control equation, and solving the vegetation layer momentum control equation to obtain a vegetation layer prediction model;
Inputting the vortex-viscosity coefficient of the surface water flow layer into the surface water flow layer momentum control equation, and solving the surface water flow layer momentum control equation to obtain a surface water flow layer prediction model;
and predicting the flow velocity of the water flow vertical line of the submerged vegetation area by using the vegetation layer prediction model and the surface water flow layer prediction model.
It can be understood that: dividing completely developed submerged vegetation water flow into a vegetation layer and a surface water flow layer, and obtaining a flow vertical line flow velocity distribution analysis solution of the submerged vegetation area by respectively solving momentum equations of all the layers; the surface water flow layer provides a layered mixed length model from a submerged vegetation water flow turbulent diffusion mechanism. The analysis is subjected to model calibration and verification through a large number of water tank measured data, so that the model has extremely strong universality for data from different sources while the prediction accuracy is improved. The required determination constants are common calculation variables in the field, can be determined according to water flow conditions, vegetation conditions and river channel conditions, do not need to be unfolded for flow velocity measurement, reduce research cost, and have wide universality in the field.
Further, the base parameters include: the former person records the submerged vegetation water flow velocity distribution data, the flow velocity data, the water depth data, the vegetation height data and the water surface ratio drop data.
Further, the vegetation layer momentum control equation is specifically:
wherein z is the water depth position coordinate, U is the time average flow velocity, v t is the vortex viscosity coefficient, a is the vegetation density, C d is the drag coefficient, S is the water surface ratio drop, and g is the gravity acceleration.
Further, the table rivers layer momentum control equation specifically is:
Wherein z is a certain water depth position coordinate, U is an average flow velocity, v t is a vortex viscosity coefficient, S is water surface ratio drop, and g is gravity acceleration.
Further, by using a preset mixed length model, the simulation calculation of the vortex viscosity coefficient of the surface water flow layer specifically comprises the following steps:
Using a predetermined mixed length model And ls is corrected, i.e. l s＝κs z+r is substituted into a mixed length model, and the vortex-viscosity coefficient of the surface water flow layer is simulated and calculated, wherein l s is the mixed length, kappa s is the mixed length proportionality coefficient, z is a certain water depth position coordinate, r is the mixed length correction constant, kappa s and r are model parameters, and based on the mixed length model, the vegetation canopy scale vortex effect is considered, and a universal analytic solution is provided under the vegetation canopy water flow condition in a wider range, so that the prediction of the vertical flow velocity distribution of submerged vegetation water flow under the general condition is solved
Further, solving the vegetation layer momentum control equation to obtain a vegetation layer prediction model, which specifically comprises:
Wherein:
P 1 is the transform coefficient; p 2 is the transform coefficient; p 3 is the transform coefficient; c 1、c2 is the integration constant.
Further, the apparent water flow layer momentum control equation is solved to obtain an apparent water flow layer prediction model, which specifically comprises the following steps:
wherein: a=r/κ s -H;
Wherein y is a transformation variable, A is a transformation coefficient, H is water depth, y h is a transformation coefficient, c 3 is an integration constant, and U h is a vegetation canopy top flow rate.
Further, the eddy current viscosity coefficient v t＝cplvU;cplv of the vegetation layer is a model parameter;
Further, r= (1.02 κ s+0.067)h+0.015κs -0.028; where κ s, r are model parameters, H is water depth, H is vegetation height, k s =0.35.
Further comprises: a submerged vegetation area water flow plumb line flow rate prediction system based on a layered mixing length, the system comprising:
one or more processors;
A memory for storing one or more programs;
The one or more programs, when executed by the one or more processors, cause the one or more processors to perform any of the above-described submerged vegetation zone water flow plumb flow velocity prediction methods based on a layered blend length.
Compared with the prior art, the invention has the advantages that:
1. based on theoretical analysis of interaction mechanism of submerged vegetation surface water flow and vegetation layer, the invention develops a traditional mixed length model, introduces the developed model into a water flow control equation, and obtains theoretical analysis solution considering interaction of vegetation layer and water flow surface layer;
2. The invention carries out strict mathematical description on the water flow problem based on a mathematical physical method, thereby ensuring the reliability, the accuracy and the universality of analytic solutions;
3. The variable used by the invention is simple, the number is small, the variable is convenient to obtain, the variable is determined according to the most basic water flow condition and vegetation condition, and the invention has the advantages of low operation cost, convenient calculation and the like.
Drawings
FIG. 1, a schematic diagram of a fully developed submerged vegetation water flow velocity profile and vortex configuration;
FIG. 2, correlation diagram of model parameters c plv and H;
FIG. 3, correlation of model parameters r and h;
FIG. 4 is a graph showing a comparison between predicted values of published water tank data and actual measured values of water tank tests.
Detailed Description
The following describes specific embodiments of the present invention with reference to examples:
It should be noted that the structures, proportions, sizes and the like illustrated in the present specification are used for being understood and read by those skilled in the art in combination with the disclosure of the present invention, and are not intended to limit the applicable limitations of the present invention, and any structural modifications, proportional changes or size adjustments should still fall within the scope of the disclosure of the present invention without affecting the efficacy and achievement of the present invention.
Also, the terms such as "upper," "lower," "left," "right," "middle," and "a" and the like recited in the present specification are merely for descriptive purposes and are not intended to limit the scope of the invention, but are intended to provide relative positional changes or modifications without materially altering the technical context in which the invention may be practiced.
Example 1:
The invention provides a submerged vegetation area water flow vertical line flow velocity prediction method based on layered mixing length, which comprises the following steps:
(1) Considering the fully developed submerged vegetation canopy water flow, the entire water depth can be divided into vegetation layers and surface water flow layers. Therefore, only the flow velocity distribution of the two layers of areas is needed to be obtained respectively, and the theoretical analysis solution of the vertical flow velocity distribution of the whole water depth is obtained.
For vegetation layer (0<z. Ltoreq.h), the water flow motion is balanced under the action of the self gravity along the river bed component, vegetation drag force and Reynolds shear stress, the control equation can be expressed as,
For surface water flow, the water flow motion is balanced under the action of own gravity along the river bed component and Reynolds shear stress, and a control equation is expressed as follows.
Where U is the time average flow rate, z is the position coordinate of a certain water depth, v t is the vortex-viscosity coefficient, a is the vegetation density, C d is the drag coefficient, S is the water surface ratio drop (the average flow is similar to the bed surface gradient), and g is the gravitational acceleration.
The analysis finds that if the analytic solutions of the two ordinary differential equations are required, a mathematical model of the vortex viscosity coefficient v t needs to be found.
From dimensional analysis, v t can be expressed as the product of the characteristic velocity and the characteristic length, and reference ：(Klopstra D,Barneveld H,Van Noortwijk J,Van Velzen E.Analytical model for hydraulic roughness of submerged vegetation.Proceedings of the congress-international association for hydraulic research.LOCAL ORGANIZING COMMITTEE OF THE XXV CONGRESS,1996,pp.775-780.), is defined as v t＝cplv U. The eddy current viscosity coefficient expression is introduced into a vegetation layer control equation, and the solution can be obtained:
U h is the vegetation canopy top flow rate.
The vortex-viscosity coefficient of the upper surface flow is similar to that of the wall flow, and can be described by adopting a mixed length model, namelyWall conditions were l s = kz (k = 0.4 is karman constant). However, the existence of the vegetation porous medium generates large-scale vortex, and enhances the momentum exchange between the vegetation layer and the surface water flow layer, so that the traditional mixed length theory needs to be developed.
For the surface water flow layer, the invention provides that the corrected l s is represented as l s＝κsz+r(κs and r is represented as a coefficient, the corrected mixed length is brought into a surface water flow layer control equation, a differential equation is solved,
Wherein a=r/κ s -H,
Therefore, the vertical flow velocity distribution of the submerged vegetation canopy can be predicted by using the formulas (2) and (3), namely the submerged vegetation area water flow vertical flow velocity prediction method based on the layered mixing length.
The new model inclusion model parameters c plv、κs and r are determined using the following fitting equation:
Where H is water depth, H is vegetation height, and k s =0.35.
The vegetation layer and the surface water flow layer simultaneously meet the following boundary conditions:
U(z＝h)＝Uh
Where U h represents the vegetation canopy top flow rate.
Example 2:
as shown in fig. 1, fig. 1 is a schematic diagram of a fully developed submerged vegetation water flow velocity profile and vortex configuration. The whole water depth can be divided into a vegetation water flow layer and a surface free water flow layer, and vortex is formed at the top interface of a vegetation canopy to drive momentum exchange of the vegetation layer and the surface water flow layer and strengthen diffusion effect. z m represents the lowest position of the vegetation layer that can be reached due to vortex diffusion.
As shown in fig. 2, the correlation of the model parameters c plv and H of fig. 2. Filled circles represent calculated values and solid lines represent fitted straight lines. The calculation process includes all of the published sink conditions listed in Table 1.
As shown in fig. 3, the correlation of the model parameters r and h of fig. 3. Open circles represent calculated values, and solid lines represent fitted straight lines. The calculation process includes all of the published sink conditions listed in Table 1.
As shown in FIG. 4, FIG. 4 is a graph showing a comparison of predicted values of published sink data with measured values of sink tests. Wherein the filled circles represent test values, the solid lines represent predicted values, and the dotted lines represent the positions of the tops of the vegetation canopies.
The embodiment is used for describing in detail a model prediction result obtained through a published flume experiment and based on a layered mixing length theory for predicting the flow velocity distribution of the vertical water flow of the submerged vegetation area.
In this embodiment, as shown in fig. 1, the current vertical distribution data (corresponding data of U, z) of submerged vegetation in the water tank test at home and abroad and relevant important test variables (water tank geometric parameters, vegetation canopy geometric parameters, water depth, water surface ratio drop, etc.) are collected first. Through statistics, 32 groups of working conditions are collected, and the total data of 6 groups of water tanks are shown in table 1.
Table 1 test parameters in published literature and calculated parameters of the present method
In the table: working conditions 1-6 from literature (King A,Tinoco R,Cowen E.2012.A k–εturbulence model based on the scales of vertical shear and stem wakes valid for emergent and submerged vegetated flows.Journal of Fluid Mechanics.701:1-39.); working conditions 7-9 from literature (Ghisalberti M,Nepf H.2004.The limited growth of vegetated shear layers.Water Resources Research.40.); working conditions 10 from literature (Nepf HM,Vivoni E.2000.Flow structure in depth-limited,vegetated flow.Journal of Geophysical Research:Oceans.105:28547-28557.) working conditions 12-19 from literature (Nguyen HT.2012.Characteristics of hydraulic resistance and velocity profile in vegetated open-channel flows.PhD,School of Civil and Environmental Engineering,Nanyang Technological University.) working conditions 20-21 from literature (Dunn C.1996.Experimental determination of drag coefficients in open channel with simulated vegetation.MS Thesis,University of Illinois at Urbana-Champaign.) working conditions 22-24 from literature (Zhao H,Yan J,Yuan S,Liu J,Zheng J.2019.Effects of submerged vegetation density on turbulent flow characteristics in anopen channel.Water.11:2154.) working conditions 25-32 from literature (Kubrak E,Kubrak J,Rowiński P.2008.Vertical velocity distributions through and above submerged,flexible vegetation.Hydrological sciences journal.53:905-920.)
By solving the control equation of the upper and lower layers of different media of submerged vegetation, the corresponding interval flow velocity distribution analytic solutions (3) and (4) are obtained. The model contains three parameters c plv、κs and r that require calibration solutions using existing sink data. The invention adopts matlab programming to carry out iterative optimization so as to determine parameter values. It was found that when κ s =0.35, the 32 sets of water tank data predictors can reach the optimal solution, i.e. the calculation error is minimum, while c plv and r change with the change of working conditions, and the calculated values are shown in table 1. And (3) carrying out correlation analysis on the calculated c plv and r and the test water flow-vegetation related parameters to obtain the highest correlation of c plv and the water depth (H), and the highest correlation of r and the vegetation height H. The correlation is obtained by establishing a linear relationship as shown in fig. 2 and 3:
The obtained relational expression is obtained through fitting and optimizing a large number of existing water tank data, and has universality and accuracy, so that the calculation result has very wide applicability to water flow vegetation conditions. Specifically, the average flow velocity U m =0.029 to 0.609m/s, the water depth h=0.15 to 0.467m, the vegetation density C da＝1.5～31.35m-1, and the water surface ratio drop gs=0.00013 to 0.1368m/s 2.
Analysis of test results:
By analyzing the test data in the published papers, the predicted values of the 6 water tank materials are compared with the actual measured values of the water tank tests, and the adopted working conditions comprise working conditions 4, 7, 12, 20, 23 and 27 respectively correspond to all 6 literature researches. Solving a theoretical solution of flow velocity distribution of water flow of the upper layer and the lower layer according to the obtained theoretical solution:
And calculating relevant parameters of the working conditions respectively as shown in table 1, so as to obtain the vertical flow velocity distribution of the submerged vegetation under each working condition. The calculation result is shown in fig. 4, wherein the filled circles represent test values, the solid lines represent predicted values, and the dotted lines represent positions of the tops of the vegetation canopies. It can be seen that all predicted values and measured values are better matched, and only the individual working condition (working condition 2) is slightly insufficient in predicting the surface water flow. However, compared with the prediction model proposed by the prior art, the model prediction accuracy proposed by the invention is greatly improved.
While the preferred embodiments of the present invention have been described in detail, the present invention is not limited to the above embodiments, and various changes may be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Many other changes and modifications may be made without departing from the spirit and scope of the invention. It is to be understood that the invention is not to be limited to the specific embodiments, but only by the scope of the appended claims.
Claims (4)
1. The method for predicting the vertical flow velocity of the water flow in the submerged vegetation area based on the layered mixing length is characterized by comprising the following steps:
Dividing a submerged vegetation area into a vegetation layer and a surface water flow layer along the depth direction of water by taking the top of the vegetation canopy as a boundary;
Establishing a vegetation layer momentum control equation and a surface water flow layer momentum control equation by using preset basic parameters;
simulating and calculating the vortex-viscosity coefficient of the vegetation layer by utilizing the characteristic length scale parameter and the pre-acquired flow velocity parameter to obtain the vortex-viscosity coefficient of the vegetation layer;
Simulating and calculating the vortex-viscosity coefficient of the surface water flow layer by using a preset layered mixed length model; obtaining the vortex viscosity coefficient of the surface water flow layer;
Inputting the eddy current viscosity coefficient of the vegetation layer into the vegetation layer momentum control equation, and solving the vegetation layer momentum control equation to obtain a vegetation layer prediction model;
Inputting the vortex-viscosity coefficient of the surface water flow layer into the surface water flow layer momentum control equation, and solving the surface water flow layer momentum control equation to obtain a surface water flow layer prediction model;
Predicting the flow velocity of the water flow vertical line of the submerged vegetation area by using a vegetation layer prediction model and a surface water flow layer prediction model;
the vegetation layer momentum control equation specifically comprises:
Wherein z is a water depth position coordinate, U is a time average flow velocity, v t is a vortex viscosity coefficient, a is a vegetation density, C d is a drag coefficient, S is a water surface ratio drop, and g is a gravity acceleration;
the flow layer momentum control equation of the surface water specifically comprises the following steps:
the simulation calculation of the vortex viscosity coefficient of the surface water flow layer is carried out by utilizing a preset mixed length model, and the simulation calculation specifically comprises the following steps:
Using a predetermined mixed length model And correcting ls, substituting l s＝κs z+r into a mixed length model, and performing simulation calculation on vortex-viscosity coefficients of a surface water flow layer, wherein l s is a mixed length, kappa s is a mixed length proportionality coefficient, r is a mixed length correction constant, and kappa s and r are model parameters;
the eddy current viscosity coefficient v t＝cplvU;cplv of the vegetation layer is a model parameter;
Wherein c plv = 0.013H-0.001;
r= (1.02 kappa s+0.067)h+0.015κs -0.028; h is water depth and h is vegetation height.
2. The submerged vegetation area water flow plumb line flow velocity prediction method based on the layered mixing length of claim 1, wherein the base parameters comprise: flow velocity data, water depth data, vegetation height data, and water surface ratio drop data.
3. The method for predicting the vertical water flow velocity of a submerged vegetation area based on the layered mixed length according to claim 1, wherein solving the vegetation layer momentum control equation to obtain a vegetation layer prediction model specifically comprises:
Wherein:
P 1 is the transform coefficient; p 2 is the transform coefficient; p 3 is the transform coefficient; c 1、c2 is the integration constant.
4. The submerged vegetation area water flow vertical line flow velocity prediction method based on the layered mixing length according to claim 1, wherein the method is characterized by solving the surface water flow layer momentum control equation to obtain a surface water flow layer prediction model, and specifically comprises the following steps:
wherein: a=r/κ s -H;
Wherein y is a transformation variable, A is a transformation coefficient, y h is a transformation coefficient, c 3 is an integration constant, and U h is a vegetation canopy top flow rate.
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