CN112597714B - Resistance-reducing and heat-insulating integrated optimization method for labyrinth seal gap circulation - Google Patents
Resistance-reducing and heat-insulating integrated optimization method for labyrinth seal gap circulation Download PDFInfo
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- G06F30/28—Design optimisation, verification or simulation using fluid dynamics, e.g. using Navier-Stokes equations or computational fluid dynamics [CFD]
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- G06—COMPUTING; CALCULATING OR COUNTING
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Abstract
The invention discloses a resistance-reducing and heat-insulating integrated optimization method for labyrinth seal clearance circulation, and particularly relates to the field of labyrinth seal structure slotting size optimization design. According to an actual labyrinth seal structure, a CFD simulation software is used for establishing a labyrinth seal model to calculate a flow field and a temperature field of the labyrinth seal model, the groove depth, the groove width and the groove interval of an annular seal ring are used as design variables, the display function relation of the maximum temperature and the gap fluid resistance about the design variables is determined by surface fitting and subjected to dimensionless, the total seal length of the annular seal ring is used as a constraint condition, an objective function is established, an annular seal ring groove parameter optimization model is established, the annular seal ring groove parameter is optimized based on a moving asymptote method, and the optimal value of the annular seal ring groove parameter is determined. According to the invention, by solving the convex sub problem to continuously approach the solution of the original problem, the parameters of the groove body of the annular sealing ring are optimized, the solving speed is high, and an effective basis is provided for the industrial design of the labyrinth sealing structure.
Description
Technical Field
The invention relates to the field of labyrinth seal structure slotting size optimization design, in particular to a resistance-reducing and heat-insulating integrated optimization method for labyrinth seal clearance circulation.
Background
The sealing system is widely applied to turbomachines such as a gas turbine, a pump and a compressor, a common clearance in the sealing system circulates, a transmission shaft penetrates through the inside and outside of equipment, a circumferential clearance exists between the inside and the outside of the equipment and the equipment, media in the equipment leak outwards through the clearance, and labyrinth sealing is adopted at present to prevent the media inside the equipment from leaking.
The fluid in the labyrinth seal clearance forms the swirl when getting into the cavity, has reduced the flowing pressure of fluid, has better preventing leaking the effect, nevertheless because of the kinetic energy converts heat energy into in-process for the fluid temperature rises. Because liquid can not absorb heat through expansion like gas, the axial flow speed is the same, the friction generated by the liquid is much larger than that of the gas, the friction causes the temperature of the solid wall surfaces of the fluid and the rotor to rise, especially under the environment with high parameters (high temperature, high pressure and high rotating speed), the rotor and the stator generate mechanical and thermal deformation, the mechanical and thermal deformation can adversely affect the liquid flow between the end surfaces, and the mutual influence process is very complex.
Therefore, the size of the groove of the labyrinth seal structure needs to be optimized, the lease reduction and heat insulation performance of the labyrinth seal structure is improved, and the influence of a high-parameter environment on the labyrinth seal structure is relieved.
Disclosure of Invention
The invention aims to solve the problems and provides a resistance-reducing and heat-insulating integrated optimization method for labyrinth seal clearance circulation, which optimizes parameters of an annular seal ring of a labyrinth seal structure based on a moving asymptote method and provides a reference basis for industrial design of the labyrinth seal structure.
The invention specifically adopts the following technical scheme:
a resistance-reducing and heat-insulating integrated optimization method for labyrinth seal gap circulation specifically comprises the following steps:
step 2, defining the groove depth, the groove width and the groove space of the annular sealing ring as groove parameters of the annular sealing ring, and respectively obtaining a display function relation of the maximum temperature of the labyrinth seal model on the groove parameters of the labyrinth sealing ring and a display function relation of the clearance fluid resistance of the labyrinth seal model on the groove parameters of the labyrinth sealing ring by utilizing surface fitting according to the flow field distribution and the temperature field distribution of the labyrinth seal model;
step 3, carrying out non-dimensionalization treatment on a display function relation of the maximum temperature of the labyrinth seal model on parameters of the groove body of the labyrinth seal ring and a display function relation of the clearance fluid resistance of the labyrinth seal model on the parameters of the groove body of the labyrinth seal ring to obtain a non-dimensionalized function relation of the maximum temperature of the labyrinth seal model on the parameters of the groove body of the labyrinth seal ring and a non-dimensionalized function relation of the clearance fluid resistance of the labyrinth seal model on the parameters of the groove body of the labyrinth seal ring;
step 4, taking the parameters of the annular sealing ring groove body of the labyrinth seal model as design variables, taking the total sealing length of the annular sealing ring as a constraint condition, constructing a target function, and establishing an annular sealing ring groove body parameter optimization model, as shown in formula (1):
wherein x represents the parameters of the groove body of the annular sealing ring, and x 1 Indicating the depth of the channel, x 2 Denotes the width of the tank, x 3 Denotes the tank spacing, x 1 、x 2 、x 3 The units are all mm; phi (x) represents an objective function integrating the resistance reduction performance and the heat insulation performance, T (x) represents a non-dimensionalized functional relation of the maximum temperature of the labyrinth seal model with respect to parameters of a groove body of a labyrinth seal ring, and f (x) represents a non-dimensionalized functional relation of the clearance fluid resistance of the labyrinth seal model with respect to parameters of the groove body of the labyrinth seal ring; alpha represents a drag reduction performance weighting parameter, and beta represents a heat insulation performance weighting coefficient; g (x) represents a constraint; z is a radical of land The length of the flat ground at the inlet of the annular sealing ring is expressed in mm; nn represents the number of groove bodies in the annular sealing ring; l represents the total sealing length of the annular sealing ring, and the unit is mm;
step 5, optimizing parameters of the annular sealing ring groove body based on a moving asymptote method, and determining the optimal value of the parameters of the annular sealing ring groove body, wherein the method specifically comprises the following steps:
step 5.1, setting the parameters of the groove body of the annular sealing ring as follows
Including the depth of the groove body
Width of the tank
Space between the grooves
k is iteration number, when the iteration number k is 0, initial values of groove depth, groove width and groove interval in parameters of the annular sealing ring groove body and a convergence condition epsilon are input e And the threshold value range of the parameters of each annular sealing ring groove body;
step 5.2, calculating an objective function phi (x) by using the depth of the groove body, the width of the groove body and the distance between the groove bodies (k) ) And an objective function phi (x) (k) ) Sensitivity to groove depth, groove width and groove spacing
Calculating a constraint function g (x) by using the depth, width and distance of the groove body (k) ) And a constraint function g (x) (k) ) Sensitivity to groove depth, groove width and groove spacing
Step 5.3, moving up the asymptote by setting
And lower moving asymptote
Establishing a strict convex approximation subproblem, as shown in formula (2):
wherein the content of the first and second substances,
in the formula, n is the parameter total number of the annular sealing ring groove body,
for summing the positive first derivative quantities,
for summing the negative first derivative quantities;
first derivative aiming at groove body parameters of each annular sealing ring
According to first derivative
Is divided into moving asymptotes
And lower moving asymptote
Before entering the next iteration loop, moving an asymptote upwards
And lower moving asymptote
The modification is made as follows:
when k is 0 or 1,
when k is more than or equal to 2,
if it is
When the temperature of the water is higher than the set temperature,
if it is
When the temperature of the water is higher than the set temperature,
in the formula (I), the compound is shown in the specification,
expressing the parameter x of the groove body of the annular sealing ring i Maximum value of threshold, x i Expressing the parameter x of the groove body of the annular sealing ring i A threshold minimum value of (d); gamma ray 1 、γ 2 、γ 3 The moving progressive coefficient is represented, and the value range is as follows:
step 5.4, setting a Lagrangian multiplier lambda according to the Kuhn-Tucker condition, and constructing a Lagrangian function
Converting the solution to the convex approximation subproblem in the step 5.3 into a solution of the Lagrangian function
According to the Lagrangian function
Extreme condition of
Updating parameters of the groove body of the annular sealing ring and determining the new parametersAnnular seal ring groove body parameter x (k+1) ；
Step 5.5, judging the parameter x of the groove body of the annular sealing ring (k+1) Whether or not the convergence condition max | x is satisfied (k+1) -x (k) |≤ε e (ii) a If the convergence condition is not met, returning to the step 5.2, and utilizing the newly determined groove body parameter x of the annular sealing ring (k+1) Continuing to simulate to carry out iterative calculation, if the convergence condition is met, ending the optimization of the parameters of the groove body of the annular sealing ring, and obtaining the optimal value x of the parameters of the groove body of the annular sealing ring (k+1) Determining the optimal values of the depth of the groove body of the annular sealing ring, the width of the groove body and the distance between the groove bodies;
and 6, outputting optimal values of the depth of the groove body of the annular sealing ring, the width of the groove body and the distance between the groove bodies.
Preferably, in step 1, the computational fluid dynamics CFD simulation software is ANSYS simulation software or CFX simulation software.
Preferably, in step 1, the labyrinth seal structure parameters include the radius of the ring seal ring, the radius of the rotating shaft, the eccentricity, the rotating shaft rotating speed, the number of the groove bodies, the depth of the groove bodies, the width of the groove bodies, the distance between the groove bodies and the total length of the ring seal ring, and the boundary conditions of the labyrinth seal structure include the flow rate of a gap fluid at an inlet of the labyrinth seal structure, the outlet pressure of the labyrinth seal structure and the contact temperature of the gap fluid with the surface of the rotating shaft and the surface of the ring seal ring.
Preferably, in the step 2, the labyrinth seal model gap fluid resistance is calculated according to the gap fluid flow rate and the pressure of the labyrinth seal model, as shown in formula (8):
f＝∑h f ·A f +∑h j ·A j (8)
in the formula, f represents the fluid resistance of the clearance of the labyrinth seal model, and the unit is N; h is f Represents frictional resistance in units of N; h is j Represents the local resistance loss in units of N; a. the f Representing the area of action of frictional resistance; a. the j The expression represents the local resistance acting area;
wherein the frictional resistance h f The calculation formula is shown in formula (9):
in the formula (f) f Representing the coefficient of on-way resistance; l represents the acting length of the on-way resistance; w represents the interstitial circulation axial horizontal flow rate; g represents the gravitational acceleration; h represents the interstitial circulating current thickness;
local drag loss h j The calculation formula is shown in formula (10):
where ρ represents the interstitial fluid density; ξ represents the local drag coefficient, and is generally determined through experimental measurements, the calculation formula is shown as equation (11):
in the formula,. DELTA. A ＝A 2 /A 1 ，A 1 Cross-sectional area before change, A 2 Denotes the cross-sectional area after change, A 1 、A 2 Determined by experimental measurements.
Preferably, in said step 5.1, the convergence condition is set to ε e ＝1e-4。
The invention has the following beneficial effects:
the method takes the groove depth, the groove width and the groove interval of the annular sealing ring as design variables, sets the whole annular sealing ring structure as a constraint condition, constructs a target function integrating the resistance reduction performance and the heat insulation performance, establishes an annular sealing ring groove parameter optimization model, performs parameter optimization by using the annular sealing ring groove parameter optimization model, and determines the annular sealing ring groove parameters meeting the resistance reduction performance and the heat insulation performance at the same time; the method is based on a moving asymptote method to solve the parameters of the annular sealing ring groove body, based on Taylor series linear expansion and iterative approximation, a convex subproblem is established to approximate the original problem by using function and derivative information in the iterative process, a dual method or an initial dual interior point algorithm is used to solve the subproblem, and the solution of the original problem is continuously approximated by solving the moving asymptotic subproblem, so that the optimal value of the parameters of the annular sealing ring groove body is determined, the solution speed is high, the parameter optimization of the labyrinth sealing structure is facilitated, and effective reference is provided for designing the labyrinth sealing structure.
Drawings
FIG. 1 is a schematic view of a labyrinth seal.
FIG. 2 is a schematic view of a labyrinth seal model; wherein, B is the groove depth of the ring-shaped sealing ring, Lg is the groove width of the ring-shaped sealing ring, Ln is the groove space of the ring-shaped sealing ring, and z land The length of the land at the inlet and the outlet of the annular sealing ring, and L is the total sealing length of the annular sealing ring.
FIG. 3 is a flow chart for optimizing parameters of a groove body of an annular sealing ring based on a moving asymptote.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings:
a resistance-reducing and heat-insulating integrated optimization method for labyrinth seal gap circulation specifically comprises the following steps:
TABLE 1 labyrinth seal model structural parameter dimensions
Setting the flow rate of gap fluid at an inlet of a labyrinth seal model to be 5m/s, setting the static pressure at an outlet, setting the wall surface temperature of a contact part of the gap fluid in the labyrinth seal model and a rotating shaft to be 90 ℃, setting the wall surface temperature of a contact part of the gap fluid in the labyrinth seal model and an annular sealing ring to be 5 ℃, and calculating by using ANSYS simulation software to obtain the flow field distribution and the temperature field distribution of the labyrinth seal model.
Step 2, defining the groove depth, the groove width and the groove interval of the annular sealing ring as groove parameters of the annular sealing ring, and respectively obtaining a display function relation formula of the maximum temperature of the labyrinth seal model and the fluid resistance of the clearance of the labyrinth seal model relative to the groove parameters of the labyrinth seal ring by utilizing surface fitting according to the flow field distribution and the temperature field distribution of the labyrinth seal model;
and calculating the fluid resistance of the clearance of the labyrinth seal model according to the flow rate and the pressure of the clearance fluid of the labyrinth seal model, as shown in a formula (8):
f＝∑h f ·A f +∑h j ·A j (8)
in the formula, f represents the fluid resistance of the clearance of the labyrinth seal model, and the unit is N; h is f Represents frictional resistance in units of N; h is j Represents the local resistance loss in units of N; a. the f Representing the area of action of frictional resistance; a. the j The expression represents the local resistance acting area;
in the formula (8), frictional resistance h f The calculation formula is shown in formula (9):
in the formula (f) f Representing the coefficient of on-way resistance; l represents the on-way resistance acting length; w represents the interstitial circulation axial horizontal flow rate; g represents the gravitational acceleration; h represents the interstitial circulating current thickness;
local drag loss h j The calculation formula is shown in formula (10):
where ρ represents the interstitial fluid density; ξ represents the local drag coefficient, and is generally determined through experimental measurements, the calculation formula is shown as equation (11):
in the formula,. DELTA. A ＝A 2 /A 1 ，A 1 Cross-sectional area before change, A 2 Denotes the cross-sectional area after change, A 1 、A 2 Determined by experimental measurements.
And 3, carrying out non-dimensionalization on a display function relation of the maximum temperature of the labyrinth seal model on parameters of the groove body of the labyrinth seal and a display function relation of the clearance fluid resistance of the labyrinth seal model on the parameters of the groove body of the labyrinth seal, wherein in the non-dimensionalization process, the maximum temperature of the labyrinth seal model is divided by the initial temperature of the labyrinth seal model to obtain the non-dimensionalized maximum temperature, and the clearance fluid resistance of the labyrinth seal model is divided by the initial resistance of the clearance fluid to obtain the non-dimensionalized clearance fluid resistance, so that a non-dimensionalization function relation T (x) of the maximum temperature of the labyrinth seal model on the parameters of the groove body of the labyrinth seal and a non-dimensionalization function relation f (x) of the clearance fluid resistance of the labyrinth seal model on the parameters of the groove body of the labyrinth seal are determined.
Step 4, taking the groove depth, the groove width and the groove interval of the annular sealing ring of the labyrinth seal model as design variables, taking the total sealing length of the annular sealing ring as a constraint condition, constructing a target function phi (x) of comprehensive resistance reduction performance and heat insulation performance, and establishing an annular sealing ring groove parameter optimization model, wherein the formula (1) is as follows:
wherein x represents the parameters of the groove body of the annular sealing ring, and x 1 Indicating the depth of the channel, x 2 Denotes the width of the tank, x 3 Denotes the tank spacing, x 1 、x 2 、x 3 The units are all mm; phi (x) represents an objective function integrating the resistance reduction performance and the heat insulation performance, and T (x) represents a non-dimensionalized functional relation of the maximum temperature of the labyrinth seal model on the parameters of the groove body of the labyrinth seal ring(x) a non-dimensionalized functional relation of the labyrinth seal model clearance fluid resistance with respect to parameters of a groove body of the labyrinth seal ring; α represents a drag reduction performance weighting parameter, β represents a thermal insulation performance weighting coefficient, and α ═ β ═ 0.5 in the present embodiment; g (x) represents a constraint; z is a radical of land The length of the flat ground at the inlet of the annular sealing ring is expressed in mm; nn represents the number of grooves in the annular sealing ring, and in the embodiment, nn is 10; l represents the total sealing length of the ring seal, and in the embodiment, L is 35.2 mm.
Step 5, optimizing the parameters of the annular sealing ring groove body based on a moving asymptote method, and determining the optimal value of the parameters of the annular sealing ring groove body, as shown in fig. 3, the method specifically comprises the following steps:
step 5.1, setting the parameters of the groove body of the annular sealing ring as follows
Including the depth of the groove body
Width of the tank
Space between the grooves
k is the number of iterations;
in this embodiment, when the iteration number k is equal to 0, the groove depth in the parameters of the annular seal ring groove is 4.6mm, the groove width is 1.6mm, and the groove interval is 1.6mm, and the convergence condition ∈ is set e 1e-4, groove depth x 1 The threshold value range of (2 mm) is not less than x 1 Less than or equal to 10mm, and the width x of the groove body 2 The threshold value range of is not less than 0.5mm and not more than x 2 Not more than 2mm and the space x between the grooves 3 The threshold value range of (1.0 mm) is less than or equal to x 3 ≤3.0mm。
Step 5.2, calculating an objective function phi (x) by using the depth of the groove body, the width of the groove body and the distance between the groove bodies (k) ) And an objective function phi (x) (k) ) Sensitivity to groove depth, groove width and groove spacing respectively
Calculating a constraint function g (x) by using the depth, width and distance of the groove body (k) ) And a constraint function g (x) (k) ) Sensitivity to groove depth, groove width and groove spacing respectively
Wherein, i represents the serial number of the parameters of the annular sealing ring groove body, i is 1 the depth of the groove body, i is 2 the width of the groove body, and i is 3 the distance between the groove bodies.
Step 5.3, moving up the asymptote by setting
And lower moving asymptote
Establishing a strict convex approximation subproblem, as shown in formula (2):
wherein the content of the first and second substances,
in the formula, n is the parameter total number of the annular sealing ring groove body,
for summing the positive first derivative quantities,
for summing the negative first derivative quantities;
first derivative aiming at groove body parameters of each annular sealing ring
According to first derivative
Is divided into moving asymptotes
And lower moving asymptote
Moving an asymptote upwards before entering the next iterative loop
And lower moving asymptote
The modification is made as follows:
when k is 0 or 1,
when k is more than or equal to 2,
if it is
When the temperature of the water is higher than the set temperature,
if it is
When the utility model is used, the water is discharged,
in the formula (I), the compound is shown in the specification,
indicating a ring sealSeal ring groove parameter x i Of the threshold maximum value, x i Expressing the parameter x of the groove body of the annular sealing ring i Wherein, when the groove body parameter of the annular sealing ring is the groove body depth
x i 4.2, when the parameter of the annular sealing ring groove body is the width of the groove body
x i When the parameter of the annular sealing ring groove body is equal to 0.5, the groove body space is the groove body space
x i ＝1；γ 1 、γ 2 、γ 3 Representing the motion progression factor, gamma in this example 1 ＝0.5、γ 2 ＝1.2、γ 3 ＝0.7。
Step 5.4, setting a Lagrangian multiplier lambda according to the Kuhn-Tucker condition, and constructing a Lagrangian function
Converting the solution to the convex approximation subproblem in the step 5.3 into a solution of the Lagrangian function
According to the Lagrangian function
Extreme condition of
Updating parameters of the groove body of the annular sealing ring and determining new parameters x of the groove body of the annular sealing ring (k+1) 。
Step 5.5, judging the parameter x of the groove body of the annular sealing ring (k+1) Whether or not the convergence condition max | x is satisfied (k+1) -x (k) Less than or equal to 1 e-4; if the convergence condition is not satisfied, the procedure returns to step 5.2, and the newly determined condition is utilizedAnnular seal ring groove body parameter x (k+1) Continuing to simulate to carry out iterative calculation, if the convergence condition is met, ending the optimization of the parameters of the groove body of the annular sealing ring, and obtaining the optimal value x of the parameters of the groove body of the annular sealing ring (k+1) And determining the optimal values of the depth of the groove body of the annular sealing ring, the width of the groove body and the distance between the groove bodies.
And 6, outputting optimal values of the depth of the groove body of the annular sealing ring, the width of the groove body and the distance between the groove bodies.
Verifying the accuracy of the optimization method of the invention, establishing a labyrinth seal model according to the optimal values of the depth of the groove body of the annular seal ring, the width of the groove body and the distance between the groove bodies, calculating the flow field and the temperature field of the labyrinth seal model by using ANSYS simulation software, determining the highest temperature and the gap fluid resistance value of the labyrinth seal model, changing the values of the depth of the groove body, the width of the groove body and the distance between the groove bodies, taking the groove body depth as an example, increasing the optimal groove body depth by 0.02mm, keeping the width of the groove body and the distance between the groove bodies unchanged, calculating by using the ANSYS simulation software to obtain the maximum temperature value and the gap fluid resistance value of the labyrinth seal model at the moment, then reducing the optimal groove body depth by 0.02mm, calculating by using the ANSYS simulation software to obtain the maximum temperature value and the gap fluid resistance value of the labyrinth seal model at the moment, sequentially changing the width of the groove body and the distance between the groove bodies according to obtain the maximum temperature values and the gap fluid resistance values under different parameters of the annular seal ring groove bodies, after comparison, the parameters of the annular sealing ring groove body obtained by the optimized design of the invention have both resistance reduction performance and heat insulation performance, and are the optimal size of the parameters of the annular sealing ring groove body.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.
Claims (4)
1. A resistance-reducing and heat-insulating integrated optimization method for labyrinth seal gap circulation is characterized by specifically comprising the following steps of:
step 1, according to an actual labyrinth seal structure, establishing a labyrinth seal model consisting of a labyrinth seal ring, a rotating shaft and clearance fluid by using Computational Fluid Dynamics (CFD) simulation software, wherein a groove body is arranged on one side, close to the rotating shaft, of the labyrinth seal ring, structural parameters and boundary conditions of the labyrinth seal model are set, and the flow field distribution and the temperature field distribution of the labyrinth seal model are obtained through calculation;
step 2, defining the groove depth, the groove width and the groove space of the annular sealing ring as groove parameters of the annular sealing ring, and respectively obtaining a display function relation of the maximum temperature of the labyrinth seal model on the groove parameters of the labyrinth sealing ring and a display function relation of the clearance fluid resistance of the labyrinth seal model on the groove parameters of the labyrinth sealing ring by utilizing surface fitting according to the flow field distribution and the temperature field distribution of the labyrinth seal model;
step 3, carrying out non-dimensionalization treatment on a display function relation of the maximum temperature of the labyrinth seal model on parameters of the groove body of the labyrinth seal ring and a display function relation of the clearance fluid resistance of the labyrinth seal model on the parameters of the groove body of the labyrinth seal ring to obtain a non-dimensionalized function relation of the maximum temperature of the labyrinth seal model on the parameters of the groove body of the labyrinth seal ring and a non-dimensionalized function relation of the clearance fluid resistance of the labyrinth seal model on the parameters of the groove body of the labyrinth seal ring;
step 4, taking the parameters of the annular sealing ring groove body of the labyrinth seal model as design variables, taking the total sealing length of the annular sealing ring as a constraint condition, constructing a target function, and establishing an annular sealing ring groove body parameter optimization model, as shown in formula (1):
wherein x represents the parameters of the groove body of the annular sealing ring, and x 1 Indicating the depth of the channel, x 2 Denotes the width of the tank, x 3 Denotes the tank spacing, x 1 、x 2 、x 3 The units are all mm; phi (x) represents an objective function integrating the resistance reduction performance and the heat insulation performance, and T (x) represents the dimensionless method of the maximum temperature of the labyrinth seal model relative to the parameters of the groove body of the labyrinth seal ringA functional relation, f (x), which represents a non-dimensionalized functional relation of the labyrinth seal model clearance fluid resistance with respect to parameters of a groove body of the labyrinth seal ring; alpha represents a drag reduction performance weighting parameter, and beta represents a heat insulation performance weighting coefficient; g (x) represents a constraint; z is a radical of land The length of the flat ground at the inlet of the annular sealing ring is expressed in mm; nn represents the number of groove bodies in the annular sealing ring; l represents the total sealing length of the annular sealing ring, and the unit is mm;
step 5, optimizing parameters of the annular sealing ring groove body based on a moving asymptote method, and determining the optimal value of the parameters of the annular sealing ring groove body, wherein the method specifically comprises the following steps:
step 5.1, setting the parameters of the groove body of the annular sealing ring as follows
Including the depth of the groove body
Width of the tank
Space between the grooves
k is iteration number, when the iteration number k is 0, initial values of groove depth, groove width and groove interval in parameters of the annular sealing ring groove body and a convergence condition epsilon are input e And the threshold value range of the parameters of each annular sealing ring groove body;
step 5.2, calculating an objective function phi (x) by using the depth of the groove body, the width of the groove body and the distance between the groove bodies (k) ) And an objective function phi (x) (k) ) Sensitivity to groove depth, groove width and groove spacing
Calculating a constraint function g (x) by using the depth, width and distance of the groove body (k) ) And a constraint function g (x) (k) ) The depth, width and distance between the groove bodiesSensitivity of (2)
Step 5.3, moving up the asymptote by setting
And lower moving asymptote
Establishing a strict convex approximation subproblem, as shown in formula (2):
wherein the content of the first and second substances,
in the formula, n is the parameter total number of the annular sealing ring groove body,
for summing the positive first derivative quantities,
for summing the negative first derivative quantities;
first derivative aiming at groove body parameters of each annular sealing ring
According to first derivative
Is divided into moving asymptotes
And lower moving asymptote
Before entering the next iteration loop, moving an asymptote upwards
And lower moving asymptote
The modification is made as follows:
when k is 0 or 1,
when k is more than or equal to 2,
if it is
When the temperature of the water is higher than the set temperature,
if it is
When the temperature of the water is higher than the set temperature,
in the formula (I), the compound is shown in the specification,
expressing the parameter x of the groove body of the annular sealing ring i The maximum value of the threshold value of (c),x i expressing the parameter x of the groove body of the annular sealing ring i Threshold minimum of；γ 1 、γ 2 、γ 3 The moving progressive coefficient is represented, and the value range is as follows:
step 5.4, setting a Lagrangian multiplier lambda according to the Kuhn-Tucker condition, and constructing a Lagrangian function
Converting the solution to the convex approximation subproblem in the step 5.3 into a solution of the Lagrangian function
According to the Lagrangian function
Extreme condition of
Updating parameters of the groove body of the annular sealing ring and determining new parameters x of the groove body of the annular sealing ring (k+1) ；
Step 5.5, judging the parameter x of the groove body of the annular sealing ring (k+1) Whether or not the convergence condition max | x is satisfied (k+1) -x (k) |≤ε e (ii) a If the convergence condition is not met, returning to the step 5.2, and utilizing the newly determined groove body parameter x of the annular sealing ring (k+1) Continuing to simulate to carry out iterative calculation, if the convergence condition is met, ending the optimization of the parameters of the groove body of the annular sealing ring, and obtaining the optimal value x of the parameters of the groove body of the annular sealing ring (k+1) Determining the optimal values of the depth of the groove body of the annular sealing ring, the width of the groove body and the distance between the groove bodies;
step 6, outputting optimal values of the depth of the groove body of the annular sealing ring, the width of the groove body and the distance between the groove bodies;
in the step 2, the fluid resistance of the clearance of the labyrinth seal model is calculated according to the flow rate and the pressure of the clearance fluid of the labyrinth seal model, as shown in a formula (8):
f＝∑h f ·A f +∑h j ·A j (8)
in the formula, f represents the fluid resistance of the clearance of the labyrinth seal model, and the unit is N; h is f Represents frictional resistance in units of N; h is j Represents the local resistance loss in units of N; a. the f Representing the area of action of frictional resistance; a. the j The expression represents the local resistance acting area;
wherein the frictional resistance h f The calculation formula is shown in formula (9):
in the formula (f) f Representing the coefficient of on-way resistance; l represents the acting length of the on-way resistance; w represents the interstitial circulation axial horizontal flow rate; g represents the gravitational acceleration; h represents the interstitial circulating current thickness;
local drag loss h j The calculation formula is shown in formula (10):
where ρ represents the interstitial fluid density; ξ represents the local drag coefficient, and is generally determined through experimental measurements, the calculation formula is shown as equation (11):
in the formula,. DELTA. A ＝A 2 /A 1 ，A 1 Cross-sectional area before change, A 2 Denotes the cross-sectional area after change, A 1 、A 2 Determined by experimental measurements.
2. A drag reduction and thermal insulation integrated optimization method for labyrinth seal clearance circulation as claimed in claim 1, wherein in step 1, the computational fluid dynamics CFD simulation software is ANSYS simulation software or CFX simulation software.
3. A resistance-reducing and heat-insulating integrated optimization method for labyrinth seal clearance circulation as claimed in claim 1, wherein in step 1, labyrinth seal structure parameters include the radius of the annular seal ring, the radius of the rotating shaft, the eccentricity, the rotating speed of the rotating shaft, the number of the grooves, the depth of the grooves, the width of the grooves, the distance between the grooves and the total length of the annular seal ring, and labyrinth seal structure boundary conditions include the flow rate of the clearance fluid at the inlet of the labyrinth seal structure, the outlet pressure of the labyrinth seal structure and the contact temperature of the clearance fluid with the surface of the rotating shaft and the surface of the annular seal ring.
4. A drag reduction and thermal insulation integrated optimization method for labyrinth seal gap circulation as claimed in claim 1, wherein in step 5.1, the convergence condition is set to be e e ＝1e-4。
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