CN112464581B - Flow control method based on flow velocity sliding and energy consumption coupling turbulence model - Google Patents

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

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CN112464581B
CN112464581B CN202011149199.6A CN202011149199A CN112464581B CN 112464581 B CN112464581 B CN 112464581B CN 202011149199 A CN202011149199 A CN 202011149199A CN 112464581 B CN112464581 B CN 112464581B
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energy consumption
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CN112464581A (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 sliding 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 a constant flow velocity sliding is generated on a fixed boundary 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 provided by the application has the advantages of simple model, convenient solution, strong applicability, capability of obtaining flow factors such as flow velocity, pressure intensity and energy consumption of a flow field, capability of providing basic technical parameters such as flow velocity, pressure intensity and the like required by design for engineering design related to fluid movement, verification results show that the calculation result is in accordance with engineering reality, and suitability for solving general flow problems in engineering, so that the application has good practical value and popularization and application significance.

Description

Flow control method based on flow velocity sliding 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 sliding and energy consumption coupling turbulence model.
Background
Flow is a natural phenomenon and technical problem that is widely present in the fields of nature and engineering. In nature, from the global motion of atmospheric circulation to regional flows of rivers and lakes; in the engineering field, from land, ocean, aerospace and other transportation vehicles to submarines, ships and other weapons; from global weather forecast to regional hydraulic engineering design; from traditional industries such as impeller machinery and oil gas pipelines to emerging industries such as medical equipment and nano device design, the flow body and shadow exists, and the flow law is known and the flow is reasonably utilized, so that the flow has important engineering application value.
Statistics have shown that the flow problems encountered in nature and 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, the turbulence model on which the problem of turbulence is dependent mainly comprises: direct numerical model (Direct Numerical Simulation, DNS), reynolds average model (Reynolds Average Navier-Stokes, RANS), and large vortex simulation model (Large eddy simulation, LES), etc. The following is a brief description of each model.
The direct numerical model does not directly build a solution model to the turbulence problem, but directly solves the control equation using a numerical method. However, due to the complexity of the turbulence scale, the resolution requirements for space and time are extremely high, requiring enormous computational memory and time to obtain information for all turbulence scales. Therefore, direct numerical models generally solve only simple turbulence problems, which tend to be 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 consist of a time average quantity and a fluctuation quantity, and the mean square distance of the Reynolds time is obtained, and the control equation is statistically averaged by combining with the Boussinesq assumption, so that the turbulence fluctuation of each scale is not required to be calculated, and only the average movement is required to be calculated, thereby reducing the space and time resolution and the calculation workload. However, the reynolds average model only provides the average information of turbulence, which is insufficient for rapid 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, the basic idea is that by accurately solving the motion of all turbulence scales above a certain scale, the large scale effect and the ordered structure which appear in a plurality of unsteady and unbalanced processes and cannot be achieved by the Reynolds average model can be captured, meanwhile, the problem of huge calculation cost 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 large, and the large vortex simulation model is difficult to widely apply in engineering at present.
Of course, there are many other flow models to actually solve the flow or specific turbulence problem, but each has its advantages and disadvantages and corresponding application range. However, in general, these flow models are mostly solved only for the core region of the flow using models, while the wall region is not directly solved, but only the semi-empirical formula is used directly to relate the physical quantity on the wall to the solution variable in the core region, resulting in a node variable value for the control volume adjacent to the wall. 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 solution method is applied and the actual engineering problem is solved, and the engineering risk is reduced as much as possible.
Disclosure of Invention
The flow control method based on the flow velocity sliding and energy consumption coupling turbulence model is used for constant incompressible viscous fluid, can obtain flow factors 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 motion, and lays a foundation for fluid control in engineering design.
The technical scheme adopted by the application is described in detail below.
A flow control method based on a flow rate slip and energy consumption coupled turbulence model, the turbulence model being suitable for constant, incompressible viscous fluids; the turbulence model takes the flow velocity distribution of fluid in a flow area after a constant flow velocity sliding is generated on a fixed boundary 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:
(one) determining a physical parameter of fluid movement
According to engineering application practice, determining physical parameters required for solving the technical problem of fluid movement;
in general, the physical parameters required to solve the fluid movement problem include, but are not limited to: viscosity coefficient of fluid
Figure 100002_DEST_PATH_IMAGE001
Density->
Figure 850349DEST_PATH_IMAGE002
Fixed boundary energy consumption coefficient->
Figure 100002_DEST_PATH_IMAGE003
And limit shear strain->
Figure 578527DEST_PATH_IMAGE004
；
It should be noted that, these parameters are determined by the physical and mechanical properties of the fluid or boundary, and are generally regarded as constants in the specific solution of the problem;
(II) construction of constraint conditions
When solving and solving technical problems in engineering applications, the flow constraints include continuity equations of fluid motion, motion equations, limit shear strain constraints, fixed boundary constraints, and flow boundary constraints, and specifically:
(2.1) continuity equation constraint
The fluid motion should satisfy the constraint of the continuity equation, specifically:
Figure 100002_DEST_PATH_IMAGE005
formula (1);
in the formula (1),
Figure 540798DEST_PATH_IMAGE006
QUOTE is Hamiltonian, +.>
Figure 100002_DEST_PATH_IMAGE009
；
Figure 528848DEST_PATH_IMAGE010
For the flow velocity distribution of the fluid->
Figure 100002_DEST_PATH_IMAGE011
；
Figure 594893DEST_PATH_IMAGE012
In system coordinates for flow ratex、y、zA component in the direction;
Figure 100002_DEST_PATH_IMAGE013
representation pairx、y、zObtaining a deflection guide;
i、j、krepresenting along the coordinate axisx、y、zA unit vector in the direction;
(2.2) equation of motion constraints
The fluid motion should satisfy the motion equation Navier-Stokes equation constraint, specifically:
Figure 831313DEST_PATH_IMAGE014
formula (2);
in the formula (2),
Figure 100002_DEST_PATH_IMAGE015
is the unit physical strength of->
Figure 100752DEST_PATH_IMAGE016
；
Figure 121798DEST_PATH_IMAGE002
Is the fluid density;
Figure 100002_DEST_PATH_IMAGE017
for fluid pressure +.>
Figure 26037DEST_PATH_IMAGE018
；
Figure 100002_DEST_PATH_IMAGE019
Is the fluid movement viscosity coefficient;
Figure 920175DEST_PATH_IMAGE020
for Laplace operator>
Figure 100002_DEST_PATH_IMAGE021
；
(2.3) Limit shear Strain constraint
The fluid motion should meet the limit shear strain constraint, specifically:
Figure 443954DEST_PATH_IMAGE022
formula (3);
in the formula (3), gamma is the flow shear strain of the fluid motion at any point and in any direction;
Figure 268690DEST_PATH_IMAGE004
is fluid limit shear strain;
(2.4) fixed boundary constraints
A fixed boundary constraint is a known boundary of fluid motion that is not affected by fluid motion, but across which fluid motion cannot cross, but on which flow velocity slip can occur, as determined by the particular engineering application;
the fixed boundary constraint is specifically:
Figure 100002_DEST_PATH_IMAGE023
formula (4);
in the formula (4), β is a normal vector of a fixed boundary tangential plane at a certain point on the fixed boundary;
Figure 794481DEST_PATH_IMAGE024
for the flow velocity distribution of the fluid movement at this point, < >>
Figure 100002_DEST_PATH_IMAGE025
；
Figure 826897DEST_PATH_IMAGE026
Representing a fixed boundary of fluid movement;
(2.5) flow boundary constraints
Flow boundary constraints are constraints based on engineering practices that determine fluid movement elements known at boundaries, including but not limited to flow rates, flows, or pressures, in particular:
the flow boundary constraint is:
Figure 100002_DEST_PATH_IMAGE027
equation (5);
in the formula (5) of the present invention,
Figure 336506DEST_PATH_IMAGE028
is boundary->
Figure 699355DEST_PATH_IMAGE026
Upper flow velocity profile; />
Figure 100002_DEST_PATH_IMAGE029
Is a known flow rate;
the traffic boundary constraint is:
Figure 846696DEST_PATH_IMAGE030
equation (6);
in the formula (6) of the present invention,
Figure 100002_DEST_PATH_IMAGE031
is boundary->
Figure 817057DEST_PATH_IMAGE026
Flow distribution over the network; />
Figure 913DEST_PATH_IMAGE032
Is a known flow rate;
the pressure boundary constraint is:
Figure 100002_DEST_PATH_IMAGE033
equation (7);
in the formula (7) of the present invention,
Figure 213458DEST_PATH_IMAGE034
is boundary->
Figure 900791DEST_PATH_IMAGE026
Pressure distribution over; />
Figure 510895DEST_PATH_IMAGE035
Is a known pressure;
(III) independent variable
The independent variable in the present application is the flow velocity distribution after the fluid in the flow area generates a constant flow velocity slip on a fixed boundary
Figure 916469DEST_PATH_IMAGE010
，
Figure DEST_PATH_IMAGE036
；
(IV) objective function
The objective function in the application is the flow energy consumption, and the actual engineering application problem is solved based on the solution of the flow energy consumption;
the flow energy consumption
Figure 935634DEST_PATH_IMAGE037
Comprising the flow boundary energy consumption->
Figure DEST_PATH_IMAGE038
And friction-in-flow consumption->
Figure 539790DEST_PATH_IMAGE039
Two parts, specifically:
Figure 100002_DEST_PATH_IMAGE040
equation (8);
wherein the flow boundary energy consumption
Figure 851954DEST_PATH_IMAGE038
Refers to the energy consumption of the fluid on a fixed boundary due to the sliding of the flow velocity; if the boundary is
Figure 259671DEST_PATH_IMAGE026
The flow velocity distribution is->
Figure 768012DEST_PATH_IMAGE024
Flow boundary energy consumption->
Figure 446249DEST_PATH_IMAGE038
The method comprises the following steps:
Figure 381844DEST_PATH_IMAGE041
equation (9);
in the formula (9) of the present invention,
Figure 100002_DEST_PATH_IMAGE042
the energy consumption coefficient is the boundary of the flow velocity;
friction and internal consumption in flow
Figure 64806DEST_PATH_IMAGE043
The method comprises the following steps:
Figure 111259DEST_PATH_IMAGE044
equation (10);
fifth, solving, analyzing and engineering application
Solving based on the formula, namely searching for the objective function meeting the constraint condition
Figure 644003DEST_PATH_IMAGE045
The argument +.>
Figure 16078DEST_PATH_IMAGE010
I.e. the flow velocity distribution when the fluid movement energy consumption takes the minimum value;
for general problems, a numerical method can be adopted to solve; according to the obtained flow velocity distribution, other flow elements such as pressure, energy consumption and the like of fluid movement can be obtained by further combining a motion equation and an energy consumption equation of the fluid, and after analysis and combination of the flow elements, the flow elements can be used for solving the application problem of specific engineering.
In general, the turbulence model provided by the application has the advantages of simple model, convenient solution, strong applicability, capability of obtaining flow factors such as flow velocity, pressure intensity, energy consumption and the like of a flow field, capability of providing basic technical parameters such as flow velocity, pressure intensity and the like required by design for engineering design related to fluid movement, verification results show that the calculation result is more in line with engineering reality, and is suitable for solving general flow problems in engineering, so that the application has better practical value and popularization and application significance.
Drawings
FIG. 1 shows that the flow rate in the long straight round tube is specifically 4.6. 4.6 m in the embodiment 3 Flow velocity profile at/s;
fig. 2 is a graph showing the comparison between the energy consumption calculation result of the chezy formula and the flow rate of the long straight round tube passing through the long straight round tube in the embodiment.
Detailed Description
The present application is further explained in conjunction with examples below so that those skilled in the art can more clearly understand the aspects of the present application.
Examples
Taking the water flow movement in a horizontally placed long straight circular tube as an example, by adopting the method, a flow velocity sliding and energy consumption coupling turbulence model of the water flow movement is established, and the model is solved, so that a foundation is laid for fluid movement control. The specific description is as follows.
Flow velocity sliding 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 tube as an example, the diameter of the long straight round tube is setdThe physical parameters of the movement of each fluid are as follows, at 1.0 m:
viscosity coefficient of fluid
Figure 883540DEST_PATH_IMAGE001
=0.0000025m 2 /s，
Density of
Figure 982952DEST_PATH_IMAGE002
=1000kg/m 3 ，
Fixed boundary energy consumption coefficient
Figure 619470DEST_PATH_IMAGE042
=0.00305，
Ultimate shear strain
Figure 647600DEST_PATH_IMAGE004
=3.19s -1 。
(2) Construction of constraints
Constraints include continuity equations of fluid motion, equations of motion, ultimate shear strain, fixed boundaries, and flow boundary constraints, as follows.
(2.1) continuity equation constraint
The constraints of the continuity equation are:
Figure DEST_PATH_IMAGE046
formula (1);
for ease of calculation, the present embodiment employs a cylindrical coordinate system. The continuity equation constraint formula (1) corresponds to the following expression in the cylindrical coordinate system:
Figure 533516DEST_PATH_IMAGE047
formula (11)
For the flow in a long straight round tube, there is
Figure DEST_PATH_IMAGE048
The method comprises the steps of carrying out a first treatment on the surface of the Will->
Figure 501865DEST_PATH_IMAGE049
Substituting into the formula (11) for verification shows that the continuity equation is naturally satisfied.
(2.2) equation of motion constraints
By adopting a cylindrical coordinate system, the fluid motion satisfies the constraint of a motion equation (Navier-Stokes equation), in particular:
Figure DEST_PATH_IMAGE050
formula (2);
for ease of calculation, the present embodiment employs a cylindrical coordinate system. The expression corresponding to the motion equation constraint formula (2) under the cylindrical coordinate system is as follows:
Figure 805939DEST_PATH_IMAGE051
the method comprises the steps of carrying out a first treatment on the surface of the Equation (12);
Figure DEST_PATH_IMAGE052
the method comprises the steps of carrying out a first treatment on the surface of the Equation (13);
Figure 300243DEST_PATH_IMAGE053
the method comprises the steps of carrying out a first treatment on the surface of the Equation (14);
for fluid movement within a horizontally placed long straight circular tube,
Figure DEST_PATH_IMAGE054
；
further, it can be verified that the formula (12) and the formula (13) can be satisfied naturally;
and is derived from equation (14):
Figure 689767DEST_PATH_IMAGE055
the method comprises the steps of carrying out a first treatment on the surface of the Equation (15);
further from equation (15):
Figure DEST_PATH_IMAGE056
equation (16);
at this time, the formula (16) is the constraint of the motion equation of the flow in the long straight circular tube; from equation (16), it is known that the flow velocity of the fluid is not zero at the wall surface of the fixed-boundary round tube, but flow velocity slip is generated
Figure 944031DEST_PATH_IMAGE057
。
(2.3) Limit shear Strain constraint
Based on the above formula (16), it is rewritten into a form in a rectangular coordinate system as follows:
Figure DEST_PATH_IMAGE058
equation (17);
the constitutive equation for an incompressible newtonian fluid is:
Figure 604076DEST_PATH_IMAGE059
the method comprises the steps of carrying out a first treatment on the surface of the Equation (18);
based on the above formula (17), formula (18)
Figure DEST_PATH_IMAGE060
The stresses that can give flow at a point are:
Figure 36325DEST_PATH_IMAGE061
the method comprises the steps of carrying out a first treatment on the surface of the Equation (19);
according to formula (19), the maximum and minimum principal stresses at this point can be found as:
Figure DEST_PATH_IMAGE062
the method comprises the steps of carrying out a first treatment on the surface of the Equation (20);
the maximum flow shear strain at this point can be found according to equation (20) as:
Figure 146102DEST_PATH_IMAGE063
equation (21);
as can be seen from equation (21), the flow shear strain takes a maximum value when r=r0 throughout the flow region:
Figure DEST_PATH_IMAGE064
equation (22);
the method is characterized in that the method is obtained by a formula (22) and meets the limit shear strain constraint
Figure 954789DEST_PATH_IMAGE065
Equation (3)) flow shear strain constraints are:
Figure 154826DEST_PATH_IMAGE066
equation (23);
(2.4) fixed boundary constraints
Based on the related setting, it can be known that the fixed boundary constraint is
Figure DEST_PATH_IMAGE067
Equation (4)) is:
Figure 525021DEST_PATH_IMAGE068
equation (24);
for the embodiment there are
Figure DEST_PATH_IMAGE069
The method comprises the steps of carrying out a first treatment on the surface of the It can be verified that the formula (24) is naturally satisfied.
(2.5) flow boundary constraints
Let the flow in the round tube be
Figure 623558DEST_PATH_IMAGE070
In this embodiment, the flow boundary constraint is only a flow constraint, and by combining the foregoing formula (17), it can be obtained:
Figure DEST_PATH_IMAGE071
equation (25);
the corresponding flow boundary constraints are therefore:
Figure 468892DEST_PATH_IMAGE072
equation (26);
combining the continuity equation constraint (2.1), the motion equation constraint (2.2), the limit shear strain constraint (2.3), the fixed boundary constraint (2.4) and the flow boundary constraint (2.5) to obtain the following components:
Figure DEST_PATH_IMAGE073
equation (27);
if order
Figure 585752DEST_PATH_IMAGE074
Further finishing of equation (27) may result:
Figure DEST_PATH_IMAGE075
equation (28);
that is, 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 625384DEST_PATH_IMAGE010
，/>
Figure 927663DEST_PATH_IMAGE036
；
Based on the above settings, for the present embodiment, there are
Figure 265103DEST_PATH_IMAGE048
；
According to the above formula (27) taking into account
Figure 705312DEST_PATH_IMAGE074
Thereby when the flow rate passing through the long straight round tube
Figure 587948DEST_PATH_IMAGE070
Given, flow distribution +.>
Figure 379187DEST_PATH_IMAGE010
Can be by->
Figure 504007DEST_PATH_IMAGE076
Uniquely determining;
for ease of calculation, the argument is equivalently chosen at this time as
Figure 798722DEST_PATH_IMAGE076
。
(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:
Figure 117839DEST_PATH_IMAGE077
equation (29);
thereby flow boundary energyConsumption of
Figure 130794DEST_PATH_IMAGE078
（/>
Figure DEST_PATH_IMAGE079
Equation (9)) is:
Figure 124551DEST_PATH_IMAGE080
equation (30);
the friction internal consumption in the flow is as follows:
Figure 273773DEST_PATH_IMAGE081
equation (31);
in the formulas (30) and (31), l is the length of a circular tube;
the flow energy consumption is further obtained by the formulas (30) and (31)
Figure 763791DEST_PATH_IMAGE082
Equation (8)) is:
Figure DEST_PATH_IMAGE083
equation (32);
to be used for
Figure 60780DEST_PATH_IMAGE084
Substitution and use of head loss in round tube of unit length +.>
Figure DEST_PATH_IMAGE085
Representing flow energy consumption, equation (32) may be transformed into:
Figure 589720DEST_PATH_IMAGE086
formula (33);
this equation (33) is the objective function of the present embodiment.
(5) Solution and analysis
By combining the above (1), (2), (3) and (4), it is possible to obtain:
constraint conditions:
Figure DEST_PATH_IMAGE087
independent variable:
Figure 406497DEST_PATH_IMAGE088
objective function:
Figure 51105DEST_PATH_IMAGE089
；
the flow velocity distribution in the long straight circular tube can be conveniently obtained by solving through a numerical method, and the flow velocity distribution is shown in figure 1. As can be seen from fig. 1, the flow generates flow velocity sliding on a fixed boundary, the flow velocity is distributed uniformly along the section, and the flow velocity belongs to fully developed turbulent motion, and is in accordance with the flow velocity distribution rule of the turbulent motion in engineering practice. By comparison, it is very difficult to obtain a flow velocity profile of a well developed turbulent motion in a long straight circular tube by a method of numerical solution by DNS, RANS or LES models.
Further, through the model provided by the application, the flow energy consumption of the long and straight circular pipe passing through different flow rates can be conveniently obtained, and compared with the calculation result of the empirical formula Chezy formula widely adopted in the current engineering, as shown in fig. 2. As can be seen from fig. 2, the energy consumption calculation results of the two are consistent. However, the experience-based chezy formula can only calculate the flow energy consumption of the fluid in the pipeline, but cannot calculate all flow elements such as flow velocity distribution and the like, and cannot solve general flow problems in engineering.
In summary, in this embodiment, only the flow in the long straight circular tube is taken as an example, and the parameters required for controlling the relevant flow process are solved by combining the established flow velocity sliding and energy consumption coupled turbulence model, and the relevant setting is only used for better explaining the technical scheme adopted in this application. It can be seen that the flow velocity sliding and energy consumption coupling turbulence model provided by the application has the advantages of simple model, convenient solution, strong applicability, capability of obtaining flow factors such as flow velocity, pressure, energy consumption and the like of a flow field, capability of providing basic technical parameters such as flow velocity, pressure and the like required by design for engineering design related to fluid motion, and relatively accords with engineering practice in model solution results, capability of obtaining all flow factors, and suitability for general flow problems in engineering, thereby having relatively good practical value and popularization and application significance.

Claims (3)

1. A flow control method based on a flow rate slip and energy consumption coupled turbulence model, characterized in that the method is used for constant incompressible viscous fluid;
the turbulence model takes the flow velocity distribution of fluid in a flow area after a constant flow velocity slip is generated on a fixed boundary 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:
(one) determining a physical parameter of fluid movement
According to engineering application practice, determining physical parameters required for solving the technical problem of fluid movement;
(II) construction of constraint conditions
When solving and solving technical problems in engineering applications, the flow constraints include continuity equations of fluid motion, motion equations, limit shear strain constraints, fixed boundary constraints, and flow boundary constraints, and specifically:
the fluid motion should satisfy the constraint of the continuity equation, specifically:
Figure DEST_PATH_IMAGE001
formula (1);
in the formula (1),
Figure 551062DEST_PATH_IMAGE002
is Hamiltonian, japan>
Figure DEST_PATH_IMAGE003
；
Figure 826317DEST_PATH_IMAGE004
For the flow velocity distribution of the fluid->
Figure DEST_PATH_IMAGE005
；
Figure 984241DEST_PATH_IMAGE006
In system coordinates for flow ratex、y、zA component in the direction;
Figure DEST_PATH_IMAGE007
representation pairx、y、zObtaining a deflection guide;
i、j、krepresenting along the coordinate axisx、y、zA unit vector in the direction;
the fluid motion should satisfy the motion equation constraint, specifically:
Figure 3144DEST_PATH_IMAGE008
formula (2);
in the formula (2),
Figure DEST_PATH_IMAGE009
is the unit physical strength of->
Figure 933054DEST_PATH_IMAGE010
；
Figure DEST_PATH_IMAGE011
Is the fluid density; />
Figure 518492DEST_PATH_IMAGE012
For fluid pressure +.>
Figure DEST_PATH_IMAGE013
；
Figure 104325DEST_PATH_IMAGE014
Is the fluid movement viscosity coefficient;
Figure DEST_PATH_IMAGE015
for Laplace operator>
Figure 848290DEST_PATH_IMAGE016
；
The fluid motion should meet the limit shear strain constraint, specifically:
Figure DEST_PATH_IMAGE017
formula (3);
in the formula (3), gamma is the flow shear strain of the fluid motion at any point and in any direction;
Figure 835969DEST_PATH_IMAGE018
is fluid limit shear strain;
a fixed boundary constraint is a known boundary of fluid motion that is not affected by fluid motion, but across which fluid motion cannot cross, but on which flow velocity slip can occur, as determined by the particular engineering application;
the fixed boundary constraint is specifically:
Figure DEST_PATH_IMAGE019
formula (4);
in the formula (4), β is a normal vector of a fixed boundary tangential plane at a certain point on the fixed boundary;
Figure 374398DEST_PATH_IMAGE004
for the flow velocity distribution of the fluid movement at this point, < >>
Figure 306582DEST_PATH_IMAGE020
；
Figure DEST_PATH_IMAGE021
Representing a fixed boundary of fluid movement;
flow boundary constraints are constraints based on engineering practices that determine fluid movement elements known at boundaries, including but not limited to flow rates, flows, or pressures, in particular:
the flow boundary constraint is:
Figure 726674DEST_PATH_IMAGE022
equation (5);
in the formula (5) of the present invention,
Figure DEST_PATH_IMAGE023
is boundary->
Figure 693493DEST_PATH_IMAGE024
Upper flow velocity profile; />
Figure DEST_PATH_IMAGE025
Is a known flow rate;
the traffic boundary constraint is:
Figure 543769DEST_PATH_IMAGE026
equation (6);
in the formula (6) of the present invention,
Figure DEST_PATH_IMAGE027
is boundary->
Figure 635353DEST_PATH_IMAGE021
Flow distribution over the network; />
Figure 49016DEST_PATH_IMAGE028
Is a known flow rate;
the pressure boundary constraint is:
Figure DEST_PATH_IMAGE029
equation (7);
in the formula (7) of the present invention,
Figure 483059DEST_PATH_IMAGE030
is boundary->
Figure 628869DEST_PATH_IMAGE021
Pressure distribution over; />
Figure DEST_PATH_IMAGE031
Is a known pressure;
(III) independent variable
The independent variable is a flow velocity distribution after the fluid in the flow area generates a constant flow velocity sliding on a fixed boundary
Figure 535645DEST_PATH_IMAGE004
，
Figure 893945DEST_PATH_IMAGE032
；
(IV) objective function
The objective function is the flow energy consumption, and the minimum value is taken;
the flow energy consumption
Figure DEST_PATH_IMAGE033
Bag(s)Include flow boundary energy consumption->
Figure 38619DEST_PATH_IMAGE034
And friction-in-flow consumption->
Figure DEST_PATH_IMAGE035
Two parts, specifically:
Figure 293014DEST_PATH_IMAGE036
equation (8);
wherein the flow boundary energy consumption
Figure 359190DEST_PATH_IMAGE034
Refers to the energy consumption of the fluid on a fixed boundary due to the sliding of the flow velocity; if the border->
Figure DEST_PATH_IMAGE037
The flow velocity distribution is->
Figure 49410DEST_PATH_IMAGE004
Flow boundary energy consumption->
Figure 314169DEST_PATH_IMAGE038
The method comprises the following steps:
Figure 739465DEST_PATH_IMAGE039
equation (9);
in the formula (9) of the present invention,
Figure DEST_PATH_IMAGE040
the energy consumption coefficient is the boundary of the flow velocity;
friction and internal consumption in flow
Figure 292938DEST_PATH_IMAGE041
The method comprises the following steps:
Figure DEST_PATH_IMAGE042
equation (10);
fifth, solving, analyzing and engineering application
Solving based on the formula, namely searching for the objective function meeting the constraint condition
Figure 789778DEST_PATH_IMAGE043
The argument +.>
Figure DEST_PATH_IMAGE044
I.e. the flow velocity profile at which the fluid movement energy consumption takes a minimum.
2. The flow control method based on a flow rate slip and energy consumption coupled turbulence model of claim 1, wherein in step (one), the physical parameters required to solve the fluid motion problem include, but are not limited to: viscosity coefficient of fluid
Figure 315568DEST_PATH_IMAGE045
Density of
Figure 770820DEST_PATH_IMAGE011
Fixed boundary energy consumption coefficient->
Figure 865117DEST_PATH_IMAGE046
And limit shear strain->
Figure 572173DEST_PATH_IMAGE018
。
3. The flow control method based on a flow rate slip and energy consumption coupled turbulence model of claim 1, wherein the fluid is a water flow.
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