CN112464581A - Flow control method based on flow velocity slip and energy consumption coupling turbulence model - Google Patents

Flow control method based on flow velocity slip and energy consumption coupling turbulence model Download PDF

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CN112464581A
CN112464581A CN202011149199.6A CN202011149199A CN112464581A CN 112464581 A CN112464581 A CN 112464581A CN 202011149199 A CN202011149199 A CN 202011149199A CN 112464581 A CN112464581 A CN 112464581A
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energy consumption
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CN112464581B (en
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张金良
尹德文
吴昊
王攀科
李希
唐林
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Yellow River Engineering Consulting Co Ltd
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Abstract

The application belongs to the technical field of fluid dynamics, and particularly relates to a flow control method based on a flow velocity slip and energy consumption coupling turbulence model. The turbulence model is for a constant, incompressible viscous fluid; the turbulence model takes the flow velocity distribution of fluid in a flow area after generating certain flow velocity on a fixed boundary and sliding as an independent variable, takes a continuity equation, a motion equation, a limit shear strain, the fixed boundary and the flow boundary of fluid motion as constraint conditions, and takes the minimum flow energy consumption of the fluid as an objective function. The turbulence model has the advantages of being simple in model, convenient to solve, high in applicability and capable of obtaining flow elements such as flow velocity, pressure intensity and energy consumption of a flow field, providing basic technical parameters such as flow velocity and pressure intensity required by design for engineering design related to fluid movement, and verifying results show that calculation results of the turbulence model are in accordance with engineering practice and are suitable for solving general flow problems in engineering, so that the turbulence model has good practical value and popularization and application significance.

Description

Flow control method based on flow velocity slip and energy consumption coupling turbulence model
Technical Field
The application belongs to the technical field of fluid dynamics, and particularly relates to a flow control method based on a flow velocity slip and energy consumption coupling turbulence model.
Background
Flow is a natural phenomenon and technical problem that widely exists in the fields of nature and engineering. In nature, the air flows from the global motion of atmospheric circulation to the regions of rivers and lakes; in the engineering field, from traffic vehicles such as land, sea, air and the like to weapons such as submarines, ships and the like; from global weather forecast to regional water conservancy project design; from the traditional industries such as impeller machinery and oil and gas pipelines to the emerging industries such as medical instruments and nano device designs, the flow shadow exists, and the understanding of the flow rule and the reasonable utilization of the flow have important engineering application values.
It has been statistically believed that the flow problems encountered in nature and in engineering applications are, for the most part, complex turbulence problems. The core problem of turbulence is a turbulence model and numerical solution thereof, and based on the turbulence model, a technical foundation can be laid for solving the flow problem. In the prior art, turbulence models relied on to solve the turbulence problem mainly include: direct Numerical modeling (DNS), Reynolds Average Navier-Stokes (RANS), and Large Eddy modeling (LES). The models are briefly described below.
The direct numerical model does not directly establish a solution model for the turbulence problem, but directly solves the control equation by adopting a numerical method. However, due to the complexity of the turbulence scale, the spatial and temporal resolution requirements for obtaining information of all turbulence scales are extremely high, and huge computational memory and time are required. Therefore, direct numerical models generally solve only simple turbulence problems, and are often difficult to solve for complex turbulence problems.
When the Reynolds average model solves the turbulence problem, firstly, the flow field variable in the turbulence is assumed to be composed of a time average quantity and a pulsation quantity, and a Reynolds time mean square range is obtained, and the Boussinesq assumption is introduced to carry out statistical averaging on the control equation, so that the calculation of turbulence pulsation of each scale is not needed, and only the average motion needs to be calculated, thereby reducing the spatial and temporal resolution and reducing the calculation workload. However, the reynolds average model can only provide average information of turbulence, which is not enough for fast local natural environment prediction and engineering design in practical situations, and the model has no universality, so that the application range is limited.
The large vortex simulation model is an important numerical simulation method in fluid mechanics developed in recent decades, and the basic idea is that the motion of all turbulence scales above a certain scale is accurately solved, so that large scale effects and quasi-sequence structures which are generated in many unsteady and unbalanced processes and can not be realized by a Reynolds average model can be captured, and simultaneously the problem of huge calculation overhead required by directly solving all turbulence scales through numerical simulation is solved, but the actual calculation cost of the large vortex simulation model is still very high, and the large vortex simulation model is difficult to be widely applied to engineering at present.
Of course, there are many other flow models that actually address the flow or specific turbulence problem, but each has its advantages and disadvantages and corresponding applicability. However, in general, most of these flow models use only the model to solve for the flow core region, but the wall region is not directly solved, and only the semi-empirical formula is used to link the physical quantity on the wall surface with the solution variable in the core region, so as to obtain the node variable value of the control volume adjacent to the wall surface. Although the models have certain convenience for engineering application, the calculation theory is not strict enough, so that further verification is still needed when the solving method is applied and the actual engineering problem is solved to reduce the engineering risk as much as possible.
Disclosure of Invention
The flow control method based on the flow speed slippage and energy consumption coupling turbulence model is used for constant and incompressible viscous fluid, can obtain flow factors such as flow speed, pressure intensity and energy consumption of a flow field, and can provide basic technical parameters such as flow speed, pressure intensity and the like required by design for engineering design related to fluid movement, so that a foundation is laid for fluid control in the engineering design.
The technical solution adopted in the present application is detailed as follows.
A flow control method based on a flow velocity slip and energy consumption coupling turbulence model is suitable for a constant and incompressible viscous fluid; the turbulent flow model takes the flow velocity distribution of fluid in a flow area after the fluid generates a certain flow velocity on a fixed boundary and slides as an independent variable, takes a continuity equation, a motion equation, a limit shear strain, the fixed boundary and the flow boundary of fluid motion as constraint conditions, and takes the minimum flow energy consumption of the fluid as an objective function, and the specific method comprises the following steps:
determining physical parameters of fluid movement
Determining physical parameters required for solving the technical problem of fluid movement according to the practical engineering application;
in general, the physical parameters required to address the fluid movement problem include, but are not limited to: viscosity coefficient of fluid
Figure RE-RE-DEST_PATH_IMAGE001
Density, density
Figure RE-850349DEST_PATH_IMAGE002
Fixed boundary coefficient of energy consumption
Figure RE-RE-DEST_PATH_IMAGE003
And ultimate shear strain
Figure RE-578527DEST_PATH_IMAGE004
；
It should be noted that these parameters are determined by the physical and mechanical properties of the fluid or the boundary, and are generally regarded as constants in the specific solving of the solution problem;
construction of (II) constraint
Specifically, when solving and solving technical problems in engineering applications, the flow constraints include a continuity equation, a motion equation, a limit shear strain constraint, a fixed boundary constraint and a flow boundary constraint of fluid motion, specifically:
(2.1) continuous equation constraints
The fluid motion should satisfy the constraint of a continuity equation, specifically:
Figure RE-RE-DEST_PATH_IMAGE005
formula (1);
in the formula (1), the first and second groups,
Figure RE-540798DEST_PATH_IMAGE006
is a Hamiltonian, and is a Hamiltonian,
Figure RE-RE-DEST_PATH_IMAGE009
；
Figure RE-528848DEST_PATH_IMAGE010
in order to be able to distribute the flow rate of the fluid,
Figure RE-RE-DEST_PATH_IMAGE011
；
Figure RE-594893DEST_PATH_IMAGE012
in system coordinates for flow velocityx、y、zA component in direction;
Figure RE-RE-DEST_PATH_IMAGE013
presentation pairx、y、zCalculating a deviation derivative;
i、j、krepresenting along a coordinate axisx、y、zA unit vector in the direction;
(2.2) equation of motion constraint
The fluid motion satisfies the constraint of motion equation Navier-Stokes equation, which is specifically as follows:
Figure RE-831313DEST_PATH_IMAGE014
equation (2);
in the formula (2), the first and second groups,
Figure RE-RE-DEST_PATH_IMAGE015
is the unit physical strength,
Figure RE-100752DEST_PATH_IMAGE016
；
Figure RE-121798DEST_PATH_IMAGE002
is the fluid density;
Figure RE-RE-DEST_PATH_IMAGE017
in order to be the pressure of the fluid,
Figure RE-26037DEST_PATH_IMAGE018
；
Figure 100002_RE-RE-DEST_PATH_IMAGE019
is the fluid motion viscosity coefficient;
Figure RE-920175DEST_PATH_IMAGE020
in order to be the laplacian operator,
Figure 100002_RE-RE-DEST_PATH_IMAGE021
；
(2.3) Limit shear Strain restraint
The fluid motion should satisfy the limit shear strain constraint, specifically:
Figure RE-443954DEST_PATH_IMAGE022
equation (3);
in the formula (3), gamma is the flow shear strain of the fluid motion at any point and in any direction;
Figure RE-268690DEST_PATH_IMAGE004
is the fluid ultimate shear strain;
(2.4) fixed boundary constraint
The fixed boundary constraint is a known boundary of fluid motion, determined according to the specific engineering application, which is not affected by fluid motion that cannot cross the boundary, but can produce flow velocity slip on the boundary;
the fixed boundary constraint specifically comprises:
Figure 100002_RE-RE-DEST_PATH_IMAGE023
equation (4);
in the formula (4), β is a normal vector of a tangent plane of the fixed boundary at a certain point on the fixed boundary;
Figure RE-794481DEST_PATH_IMAGE024
for the flow velocity profile of the fluid motion at this point,
Figure 100002_RE-RE-DEST_PATH_IMAGE025
；
Figure RE-826897DEST_PATH_IMAGE026
a fixed boundary representing fluid motion;
(2.5) flow boundary constraint
Flow boundary constraints are constraints on fluid motion elements known on the boundary determined based on engineering practice, including but not limited to flow rate, flow or pressure, specifically:
the flow rate boundary constraint is:
Figure 100002_RE-RE-DEST_PATH_IMAGE027
equation (5);
in the formula (5), the first and second groups,
Figure RE-336506DEST_PATH_IMAGE028
is a boundary
Figure RE-699355DEST_PATH_IMAGE026
An upper flow velocity distribution;
Figure 100002_RE-RE-DEST_PATH_IMAGE029
is a known flow rate;
the flow boundary constraints are:
Figure RE-846696DEST_PATH_IMAGE030
equation (6);
in the formula (6), the first and second groups,
Figure RE-RE-DEST_PATH_IMAGE031
is a boundary
Figure RE-817057DEST_PATH_IMAGE026
The flow distribution of (2);
Figure RE-913DEST_PATH_IMAGE032
is a known flow rate;
the pressure boundary constraints are:
Figure RE-RE-DEST_PATH_IMAGE033
equation (7);
in the formula (7), the first and second groups,
Figure RE-213458DEST_PATH_IMAGE034
is a boundary
Figure RE-900791DEST_PATH_IMAGE026
Pressure distribution of (2);
Figure RE-510895DEST_PATH_IMAGE035
is a known pressure;
(III) independent variable
The independent variable in the present application is the flow velocity distribution of the fluid in the flow region after generating a certain flow velocity slip on a fixed boundary
Figure RE-916469DEST_PATH_IMAGE010
，
Figure RE-RE-DEST_PATH_IMAGE036
；
(IV) objective function
The objective function in the application is the flow energy consumption, and the practical engineering application problem is solved based on the solution of the flow energy consumption;
the flowing energy consumption
Figure RE-935634DEST_PATH_IMAGE037
Including flow boundary energy consumption
Figure RE-RE-DEST_PATH_IMAGE038
And internal friction and friction in the flow
Figure RE-539790DEST_PATH_IMAGE039
Two parts, specifically:
Figure RE-RE-DEST_PATH_IMAGE040
equation (8);
wherein the flow boundary consumes energy
Figure RE-851954DEST_PATH_IMAGE038
Refers to the energy consumption of the fluid due to the slippage of the flow velocity on a fixed boundary; if the boundary
Figure RE-259671DEST_PATH_IMAGE026
Has a flow velocity distribution of
Figure RE-768012DEST_PATH_IMAGE024
Then the flow boundary consumes energy
Figure RE-446249DEST_PATH_IMAGE038
Comprises the following steps:
Figure RE-381844DEST_PATH_IMAGE041
formula (9);
in the formula (9), the reaction mixture,
Figure RE-RE-DEST_PATH_IMAGE042
the flow rate boundary energy consumption coefficient;
internal friction and friction in flow
Figure RE-64806DEST_PATH_IMAGE043
Then, it is:
Figure RE-111259DEST_PATH_IMAGE044
equation (10);
(V) solving, analyzing and engineering application
Solving based on the formula, namely finding an objective function which meets constraint conditions
Figure RE-644003DEST_PATH_IMAGE045
Independent variable when taking minimum value
Figure RE-16078DEST_PATH_IMAGE010
Namely the flow velocity distribution when the fluid motion energy consumption is minimum;
for general problems, a numerical method can be adopted for solving; according to the obtained flow velocity distribution, other flow factors such as the pressure of fluid motion, energy consumption and the like can be obtained by further combining a motion equation and an energy consumption equation of the fluid, and after each flow factor is analyzed and combined with the reality, the flow factors can be used for solving the problem of specific engineering application.
Generally, the turbulence model provided by the application has the advantages of simple model, convenience in solving, strong applicability and capability of obtaining flow elements such as flow velocity, pressure intensity and energy consumption of a flow field, can provide basic technical parameters such as flow velocity, pressure intensity and the like required by design for engineering design related to fluid movement, and verification results show that the calculation result of the turbulence model is in accordance with engineering practice and is suitable for solving general flow problems in engineering, so that the turbulence model has good practical value and popularization and application significance.
Drawings
FIG. 1 shows the specific flow rate of 4.6 m passing through a long straight circular tube in the embodiment3A flow velocity profile at/s;
FIG. 2 is a graph comparing the energy consumption calculation results with the Chzy formula when different flow rates pass through the long straight circular tube in the embodiment.
Detailed Description
The present application is further explained with reference to the following examples so that those skilled in the art can more clearly understand the aspects of the present application.
Examples
By taking the water flow motion in a horizontally placed long straight circular tube as an example, the method of the application is adopted to establish a flow velocity slippage and energy consumption coupling turbulence model of the water flow motion and solve the model, thereby laying a foundation for fluid motion control. The details are as follows.
Flow velocity slip and energy consumption coupling turbulence model
(1) Determining physical parameters of fluid movement
Taking the water flow movement in a horizontally placed long straight round pipe as an example, the diameter of the long straight round pipe is setdIs 1.0m, and the physical parameters of each fluid movement have the following values:
viscosity coefficient of fluid
Figure 100002_RE-DEST_PATH_IMAGE044
=0.0000025m2/s，
Density of
Figure 174866DEST_PATH_IMAGE002
=1000kg/m3，
Fixed boundary coefficient of energy consumption
Figure 635935DEST_PATH_IMAGE003
=0.00305，
Ultimate shear strain
Figure 957457DEST_PATH_IMAGE004
=3.19s-1。
(2) Construction of constraints
The constraints include continuity equations of fluid motion, equations of motion, ultimate shear strain, fixed boundary, and flow boundary constraints, as follows.
(2.1) continuous equation constraints
The constraints of the continuity equation are:
Figure 185700DEST_PATH_IMAGE005
formula (1);
for the convenience of calculation, the present embodiment adopts a cylindrical coordinate system. The continuity equation constraint formula (1) has the corresponding expression in a cylindrical coordinate system as follows:
Figure DEST_PATH_IMAGE045
chinese character of 'pin' (11)
For the flow in the long straight round tube, there are
Figure DEST_PATH_IMAGE046
(ii) a Will be provided with
Figure DEST_PATH_IMAGE047
The continuity equation is naturally satisfied by substituting into the equation (11).
(2.2) equation of motion constraint
With a cylindrical coordinate system, the fluid motion satisfies the constraint of motion equation (Navier-Stokes equation), specifically:
Figure 481729DEST_PATH_IMAGE012
equation (2);
for the convenience of calculation, the present embodiment adopts a cylindrical coordinate system. The corresponding expression of the motion equation constraint formula (2) in a cylindrical coordinate system is as follows:
Figure DEST_PATH_IMAGE048
(ii) a Formula (12);
Figure DEST_PATH_IMAGE049
(ii) a Formula (13);
Figure DEST_PATH_IMAGE050
(ii) a Formula (14);
for the movement of fluid in a horizontally placed long straight circular tube,
Figure DEST_PATH_IMAGE051
；
further, it can be verified that the formula (12) and the formula (13) can be naturally satisfied;
and can be derived from equation (14):
Figure DEST_PATH_IMAGE052
(ii) a Formula (15);
further from equation (15) we can derive:
Figure DEST_PATH_IMAGE053
equation (16);
at the moment, the formula (16) is the motion equation constraint of the flow in the long straight circular tube; from the equation (16), it can be seen that the flow velocity of the fluid at the wall surface of the fixed bounding circular tube is not zero, but a flow velocity slip is generated
Figure DEST_PATH_IMAGE054
。
(2.3) Limit shear Strain restraint
Based on the above equation (16), it is rewritten into the form in the rectangular coordinate system:
Figure DEST_PATH_IMAGE055
formula (17);
the constitutive equation for incompressible Newtonian fluids is:
Figure DEST_PATH_IMAGE056
(ii) a Formula (18);
based on the above formula (17), formula (18) and
Figure DEST_PATH_IMAGE057
the stress of the flow at a certain point can be obtained as follows:
Figure DEST_PATH_IMAGE058
(ii) a Formula (19);
according to equation (19), the maximum and minimum principal stresses at this point can be found as:
Figure DEST_PATH_IMAGE059
(ii) a Formula (20);
from equation (20), the maximum flow shear at this point can be found as:
Figure 817811DEST_PATH_IMAGE060
equation (21);
as can be seen from equation (21), the flow shear strain takes a maximum value when r = r0 throughout the entire flow region:
Figure DEST_PATH_IMAGE061
equation (22);
from equation (22), satisfying the ultimate shear strain constraint
Figure DEST_PATH_IMAGE062
Equation (3)) the flow shear strain constraint is:
Figure DEST_PATH_IMAGE063
equation (23);
(2.4) fixed boundary constraint
Based on the aforementioned correlation settings, the fixed boundary constraint is known as:
Figure DEST_PATH_IMAGE064
equation (24);
for the present embodiment there are
Figure 347451DEST_PATH_IMAGE065
(ii) a It can be verified that equation (24) is naturally satisfied.
(2.5) flow boundary constraint
Setting the flow rate in the circular tube as
Figure DEST_PATH_IMAGE066
Then, the flow boundary constraint in this embodiment is only the flow constraint, and combining the foregoing equation (17), we can obtain:
Figure DEST_PATH_IMAGE067
equation (25);
the corresponding flow boundary constraint is therefore:
Figure DEST_PATH_IMAGE068
equation (26);
by combining the continuity equation constraint (2.1), the motion equation constraint (2.2), the ultimate shear strain constraint (2.3), the fixed boundary constraint (2.4) and the flow boundary constraint (2.5), the following results are obtained:
Figure DEST_PATH_IMAGE069
equation (27);
if order
Figure DEST_PATH_IMAGE070
Equation (27) is further developed to yield:
Figure DEST_PATH_IMAGE071
equation (28);
that is, at this time, the formula (28) is the constraint condition of the present embodiment.
(3) Independent variable
The independent variable being the flow velocity distribution of the fluid
Figure 421847DEST_PATH_IMAGE022
，
Figure 218770DEST_PATH_IMAGE035
；
Based on the above setting, for the present embodiment, there are
Figure DEST_PATH_IMAGE072
；
According to the above formula (27), while taking into account
Figure 906628DEST_PATH_IMAGE070
Whereby the flow passing through the long straight circular tube
Figure 130805DEST_PATH_IMAGE066
At a given time, the flow velocity distribution
Figure 864799DEST_PATH_IMAGE022
Can be composed of
Figure DEST_PATH_IMAGE073
Unique determination;
for ease of calculation, the argument is then equivalently chosen to be
Figure 248769DEST_PATH_IMAGE073
。
(4) Objective function
The motion equation constraint formula (16) and the flow boundary constraint formula (26) of the flow in the long straight circular tube can be obtained according to the following steps:
Figure RE-117839DEST_PATH_IMAGE077
formula (29);
thereby consuming energy at the flow boundary
Figure RE-130794DEST_PATH_IMAGE078
（
Figure RE-RE-DEST_PATH_IMAGE079
Equation (9)) is:
Figure RE-124551DEST_PATH_IMAGE080
equation (30);
the internal friction and internal friction loss in the flow are as follows:
Figure RE-273773DEST_PATH_IMAGE081
formula (31);
l in the formulas (30) and (31) is the length of the circular tube;
further, the flow energy consumption (30) and (31) can be obtained
Figure RE-763791DEST_PATH_IMAGE082
Equation (8)) is:
Figure RE-RE-DEST_PATH_IMAGE083
equation (32);
to be provided with
Figure RE-60780DEST_PATH_IMAGE084
Substituted and used for head loss in a pipe of unit length
Figure RE-DEST_PATH_IMAGE085
Representing the flow energy consumption, equation (32) can be transformed into:
Figure RE-589720DEST_PATH_IMAGE086
formula (33);
the equation (33) is the objective function of this embodiment.
(5) Solution and analysis
By combining the above (1), (2), (3) and (4), it is possible to obtain:
constraint conditions are as follows:
Figure DEST_PATH_IMAGE083
independent variable:
Figure 411645DEST_PATH_IMAGE073
an objective function:
Figure DEST_PATH_IMAGE084
；
the flow velocity distribution in the long straight circular tube can be conveniently obtained by adopting a numerical method for solving, and is shown in figure 1. As can be seen from figure 1, the flow generates flow velocity slippage on a fixed boundary, the flow velocity is distributed uniformly along the section, the flow velocity belongs to fully developed turbulent motion, and the flow velocity distribution rule of the turbulent motion in the engineering practice is relatively consistent. In comparison, it is difficult to obtain a flow velocity distribution of a turbulent motion that has sufficiently developed in a long straight circular tube by a numerical solution method using a DNS, RANS, or LES model.
Furthermore, through the model provided by the application, the flow energy consumption of the long straight circular pipe passing through different flow rates can be conveniently obtained, and compared with the calculation result of the Chuezy formula, which is an empirical formula widely adopted in the current engineering, the calculation result is shown in figure 2. As can be seen from fig. 2, the energy consumption calculation results of the two are more consistent. However, the empirical Ch zy formula can only calculate the flow energy consumption of the fluid in the pipeline, and cannot solve all flow elements, such as flow velocity distribution, and even solve the general flow problem in the engineering.
In summary, the present embodiment only takes the flow in the long straight circular tube as an example, and combines the established flow velocity slip and energy consumption coupled turbulence model to solve the parameters required for controlling the relevant flow process, and the relevant settings are also only to better explain the technical solutions adopted in the present application. It can be seen that the flow velocity slip and energy consumption coupling turbulence model provided by the application has the advantages of simple model, convenient solution, strong applicability, and capability of obtaining flow elements such as flow velocity, pressure intensity, energy consumption and the like of a flow field, can provide basic technical parameters such as flow velocity, pressure intensity and the like required by design for engineering design related to fluid movement, and the model solution result is in accordance with engineering practice, can obtain all flow elements, is more suitable for general flow problems in engineering, and therefore has better practical value and popularization and application significance.

Claims (3)

1. A flow control method based on a flow velocity slip and energy consumption coupled turbulence model is characterized in that the method is used for constant and incompressible viscous fluid;
the turbulent flow model takes the flow velocity distribution of fluid in a flow area after the fluid generates a certain flow velocity on a fixed boundary and slides as an independent variable, takes a continuity equation, a motion equation, a limit shear strain, the fixed boundary and the flow boundary of fluid motion as constraint conditions, and takes the minimum flow energy consumption of the fluid as an objective function, and the specific model construction steps are as follows:
determining physical parameters of fluid movement
Determining physical parameters required for solving the technical problem of fluid movement according to the practical engineering application;
construction of (II) constraint
Specifically, when solving and solving technical problems in engineering applications, the flow constraints include a continuity equation, a motion equation, a limit shear strain constraint, a fixed boundary constraint and a flow boundary constraint of fluid motion, specifically:
the fluid motion should satisfy the constraint of a continuity equation, specifically:
Figure RE-DEST_PATH_IMAGE001
formula (1);
in the formula (1), the first and second groups,
Figure RE-551062DEST_PATH_IMAGE002
is a Hamiltonian, and is a Hamiltonian,
Figure RE-DEST_PATH_IMAGE003
；
Figure RE-826317DEST_PATH_IMAGE004
in order to be able to distribute the flow rate of the fluid,
Figure RE-DEST_PATH_IMAGE005
；
Figure RE-984241DEST_PATH_IMAGE006
in system coordinates for flow velocityx、y、zA component in direction;
Figure RE-DEST_PATH_IMAGE007
presentation pairx、y、zCalculating a deviation derivative;
i、j、krepresenting along a coordinate axisx、y、zA unit vector in the direction;
the fluid motion should satisfy the motion equation constraint, specifically:
Figure RE-3144DEST_PATH_IMAGE008
equation (2);
in the formula (2), the first and second groups,
Figure RE-DEST_PATH_IMAGE009
is the unit physical strength,
Figure RE-933054DEST_PATH_IMAGE010
；
Figure RE-DEST_PATH_IMAGE011
is the fluid density;
Figure RE-518492DEST_PATH_IMAGE012
in order to be the pressure of the fluid,
Figure RE-DEST_PATH_IMAGE013
；
Figure RE-104325DEST_PATH_IMAGE014
is the fluid motion viscosity coefficient;
Figure RE-DEST_PATH_IMAGE015
in order to be the laplacian operator,
Figure RE-848290DEST_PATH_IMAGE016
；
the fluid motion should satisfy the limit shear strain constraint, specifically:
Figure RE-DEST_PATH_IMAGE017
equation (3);
in the formula (3), gamma is the flow shear strain of the fluid motion at any point and in any direction;
Figure RE-835969DEST_PATH_IMAGE018
is the fluid ultimate shear strain;
the fixed boundary constraint is a known boundary of fluid motion, determined according to the specific engineering application, which is not affected by fluid motion that cannot cross the boundary, but can produce flow velocity slip on the boundary;
the fixed boundary constraint specifically comprises:
Figure RE-RE-DEST_PATH_IMAGE019
equation (4);
in the formula (4), β is a normal vector of a tangent plane of the fixed boundary at a certain point on the fixed boundary;
Figure RE-374398DEST_PATH_IMAGE004
for the flow velocity profile of the fluid motion at this point,
Figure RE-306582DEST_PATH_IMAGE020
；
Figure RE-RE-DEST_PATH_IMAGE021
a fixed boundary representing fluid motion;
flow boundary constraints are constraints on fluid motion elements known on the boundary determined based on engineering practice, including but not limited to flow rate, flow or pressure, specifically:
the flow rate boundary constraint is:
Figure RE-726674DEST_PATH_IMAGE022
equation (5);
in the formula (5), the first and second groups,
Figure RE-RE-DEST_PATH_IMAGE023
is a boundary
Figure RE-693493DEST_PATH_IMAGE024
An upper flow velocity distribution;
Figure RE-RE-DEST_PATH_IMAGE025
is a known flow rate;
the flow boundary constraints are:
Figure RE-543769DEST_PATH_IMAGE026
equation (6);
in the formula (6), the first and second groups,
Figure RE-RE-DEST_PATH_IMAGE027
is a boundary
Figure RE-635353DEST_PATH_IMAGE021
The flow distribution of (2);
Figure RE-49016DEST_PATH_IMAGE028
is a known flow rate;
the pressure boundary constraints are:
Figure RE-RE-DEST_PATH_IMAGE029
equation (7);
in the formula (7), the first and second groups,
Figure RE-483059DEST_PATH_IMAGE030
is a boundary
Figure RE-628869DEST_PATH_IMAGE021
Pressure distribution of (2);
Figure RE-DEST_PATH_IMAGE031
is a known pressure;
(III) independent variable
The independent variable is the flow velocity distribution of the fluid in the flow area after generating a certain flow velocity slip on a fixed boundary
Figure RE-535645DEST_PATH_IMAGE004
，
Figure RE-893945DEST_PATH_IMAGE032
；
(IV) objective function
Taking the minimum value as the objective function as the flow energy consumption;
the flowing energy consumption
Figure RE-DEST_PATH_IMAGE033
Including flow boundary energy consumption
Figure RE-38619DEST_PATH_IMAGE034
And internal friction and friction in the flow
Figure RE-DEST_PATH_IMAGE035
Two parts, specifically:
Figure RE-293014DEST_PATH_IMAGE036
equation (8);
wherein the flow boundary consumes energy
Figure RE-359190DEST_PATH_IMAGE034
Refers to the energy consumption of the fluid due to the slippage of the flow velocity on a fixed boundary; if the boundary
Figure RE-DEST_PATH_IMAGE037
Has a flow velocity distribution of
Figure RE-49410DEST_PATH_IMAGE004
Then the flow boundary consumes energy
Figure RE-314169DEST_PATH_IMAGE038
Comprises the following steps:
Figure RE-739465DEST_PATH_IMAGE039
formula (9);
in the formula (9), the reaction mixture,
Figure RE-DEST_PATH_IMAGE040
the flow rate boundary energy consumption coefficient;
internal friction and friction in flow
Figure RE-292938DEST_PATH_IMAGE041
Then, it is:
Figure RE-DEST_PATH_IMAGE042
equation (10);
(V) solving, analyzing and engineering application
Solving based on the formula, namely finding an objective function which meets constraint conditions
Figure RE-789778DEST_PATH_IMAGE043
Independent variable when taking minimum value
Figure RE-DEST_PATH_IMAGE044
I.e. the flow velocity distribution at which the energy consumption of the fluid movement takes a minimum.
2. The flow control method based on the flow rate slip and energy consumption coupled turbulence model as claimed in claim 1, wherein in step (one), the physical parameters required for solving the fluid motion problem include but are not limited to: viscosity coefficient of fluid
Figure RE-315568DEST_PATH_IMAGE045
Density, density
Figure RE-770820DEST_PATH_IMAGE011
Fixed boundary coefficient of energy consumption
Figure RE-865117DEST_PATH_IMAGE046
And ultimate shear strain
Figure RE-572173DEST_PATH_IMAGE018
。
3. The flow control method based on the flow rate slip and energy consumption coupled turbulence model of claim 1, wherein the fluid is water flow.
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