CN106570263A - Double-volute hydraulic design method based on RSM model - Google Patents

Abstract

The invention discloses a double-volute hydraulic design method based on an RSM model. The design method comprises the steps of 1) solving double-volute initial hydraulic geometric parameters based on a velocity coefficient method; 2) performing optimization solving on double-volute key geometric parameters by adopting an RSM-based adaptive sequence algorithm; 3) performing parameterization automatic modeling based on a CATIA macroprogram, and outputting to obtain a three-dimensional double-volute model; 4) by adopting a GridPro script file to output a grid file used for numerical value calculation; 5) automatically completing grid loading and boundary condition setting based on a CFX CCL language drive program to complete calculation of related data, and outputting a calculation result; 6) repeatedly executing the steps 3) to 5) to obtain a double-volute scheme with the minimum total pressure loss coefficient; and 7) taking the data obtained in the steps 1) to 6) as the double-volute design parameters to manufacture a double-volute centrifugal pump. By adoption of the double-volute hydraulic design method, the double-volute hydraulic optimization design can be realized.

Description

A kind of double volute Hydraulic Design Method based on RSM models

Technical field

The invention belongs to fluid machinery (centrifugal pump, the hydraulic turbine, blower fan etc.) Hydraulic Design Method field, and in particular to a kind of Based on the double volute Hydraulic Design Method of RSM models, be mainly used in fast and effectively carrying out double volute model the Hydraulic Design and Optimization, under the premise of regulation conveyance capacity is ensured, to reduce the hydraulic loss in spiral case, further lifts the effect of hydraulic model Rate, realizes the purpose of energy-saving and emission-reduction.

Background technology

Double volute has two runners being arranged symmetrically, and compared with traditional single spiral case, it can the non-design work of active balance Radial force under condition on centrifugal impeller, it is ensured that pump even running, while it possesses higher efficiency, therefore it is widely used In the large centrifugal pump (such as large-scale middle-opening pump) higher to stability requirement.Current traditional double Volute Design method and single spiral case It is close, it is main to spiral case based on empirical coefficient method by calculating volute throat area using constant velocity method or uniform velocity moments method Geometric parameter (base circle diameter (BCD) D₃, entrance width b₃, cut water laying angle θ₀, cut water pitch angle alpha₀, dividing plate initial angle φ, dividing plate diffusion Segment length z) is calculated.The Hydraulic Design Method is more traditional, mainly rule of thumb spiral case is designed and type is painted, not Have and design is optimized to double volute model using related optimized algorithm, therefore its internal hydraulic loss is often larger.At present, pin Research to double volute Hydraulic Design Method is concentrated mainly on：1) sternly respect in its paper《A kind of external centrifugal pump double volute design The introduction and analysis of method》The method for designing based on velocity-coefficient method of middle proposition and the numeral product based on velocity moment conserva-tion principle Divide method for designing；Thank to the septuagenarian grade of work(on this basis in its paper《The parameter of double volute is calculated and paints shape and inner flew field》In enter one Step has developed the velocity coeffficient design method of double volute, while being calculated spiral case interior flow field using numerical computation method；2) In terms of double volute Optimization Design, Xiao Ruofu etc. is in its paper《Double volute double entry pump diaphragm structure is to impeller radial force Affect》In employ numerical computation method design be optimized to double volute diaphragm structure, the method adopts mathematical calculation model, The scheme of different parameters combination is calculated, more excellent scheme is drawn by relative analyses, to improve the efficiency of hydraulic model；But The method still has certain limitation, and its last scheme chosen is not necessarily optimal solution；3) it is public with regard to double volute method for designing The patent opened mainly includes " product that a kind of optimization method of double volute formula double entry pump dividing plate and the method make " (patent No.： CN102032217 A), the patent is optimized design mainly for the diaphragm structure of double volute, but not to spiral case its He carries out overall optimization design by geometric parameter；A kind of " pump shell structure of high-efficiency centrifugal pump " (patent No.：CN 201934387U)、 " Double suction single stage volute pump " (patent No.：US 4563124) and " Centrifugal Pump with double volute the casing " (patent No.s：US 4406583) etc., above patent mostly provides double volute pump The version of body, does not provide the Hydraulic Optimizing Design method of double volute.

For above-mentioned problem, this patent using based on RSM (Response Surface Method) model from Sequential optimization algorithm is adapted to, Average total pressure loss coefficient carries out excellent as target variable to double volute main geometric parameters with spiral case Change design, the method can carry out global traversal, ask by iterating by Optimized model to double volute geometric parameter variable Solution, realizes the acquisition to optimal objective value, to reach the purpose of the fluid flow state in stable spiral case and raising efficiency.Cause This, the method has important academic and engineering application value.

Jing retrieve, so far there is not yet with regard to the method document and declare patent.

The content of the invention

The technical problem to be solved is that existing double volute Hydraulic Design Method has following a few class shortcomings：1) Design parameter too relies on the selection of the experience of designer and correlation experience coefficient；2) stagnation pressure cannot fast and effectively be obtained The hydraulic model of loss reduction；3) double volute geometric model quickly cannot accurately be built.It is an object of the invention to provide a kind of Based on the double volute the Hydraulic Design new method of RSM models, by setting up a kind of self adaptation sequential optimization algorithm based on RSM models Realize the Hydraulic Optimizing Design to double volute.

To reach above-mentioned purpose, the technical scheme is that：

A kind of double volute Hydraulic Design Method based on RSM models, described double volute hydraulic structure includes spiral section, expands Scattered section and this three part of dividing plate；The design procedure of three described part water conservancy structures is：1) according to given flow, lift, turn Speed value and known impeller the Hydraulic Design parameter, based on velocity-coefficient method the initial waterpower geometric parameter of double volute is solved；2) by step 1) numerical range for obtaining that double volute key geometric parameter is determined in initial waterpower geometric parameter is solved；With the total crushing in spiral case Coefficient is lost as optimization aim variable, double volute key geometric parameter is carried out most using the self adaptation sequence algorithm based on RSM Optimization Solution；3) based on CATIA macroprograms to step 2) required by the crucial geometric parameter that obtains of solution carry out parametrization automatic modeling, The area and coordinate control point of spiral case different section is calculated using mathematical model, is realized to different spiral case parameter combinations Rapid automatic modeling and output obtain three-dimensional double volute model；4) using GridPro script files to step 3) obtain three Dimension double volute model carries out rapid structure stress and strain model, exports the grid file for numerical computations；5) based on CFX CCL languages Speech driver is to step 4) network file that obtains is automatically performed grid loading and boundary condition is arranged, and completes correlation values meter Calculate, export result of calculation；6) repeat the above steps 3) -5), by continuous iterative, obtain the double of total pressure loss coefficient minimum Spiral case scheme；7) according to above-mentioned steps 1) -6) in resulting data as double volute design parameter, making meets given Flow, lift, the double volute centrifugal pump of the efficiency of pump and tachometer value.

Described step 1) in known impeller the Hydraulic Design parameter be according to design requirement, purposes, casting require and intensity, The empirical value that pump housing installation dimension is required and artificially determined in advance, including impeller outer diameter D₂, blade exit width b₂, forward and backward cover plate Thickness, specific speed n_s, blade exit fluid flow angle β_2F, actual installation pipeline diameter, volute throat section is relative to cut water section Laying angle θ_t, the flow Q under Centrifugal Pump Design operating mode_n, impeller outlet absolute velocity circumferential components v_2u；Described double volute is initial Waterpower geometric parameter includes：Spiral case base circle diameter (BCD) D₃；Spiral case inlet width b₃；Cut water laying angle θ₀；Cut water pitch angle alpha₀；Spiral case Throat cross-sectional area A_t；Volute outlet diameter D₄；Cut water radius R₀；Diffuser height H₀；Diffuser centre-to-centre spacing L₀；Dividing plate initial angle；Dividing plate spreads segment length z；Block board thickness t；

It is described double volute waterpower geometric parameter is solved based on velocity-coefficient method method be：

Described spiral case base circle diameter (BCD) D₃According to known impeller outer diameter D₂It is determined that, shown in computing formula such as formula (1)：

D₃=(1.05～1.2) D₂(1)；

Entrance width b of described spiral case₃By known blade exit width b₂And front/rear cover plate thickness determines, computing formula As shown in formula (2)：b₃=(1.6～2) b₂(2)；

Described cut water laying angle θ₀According to specific speed n_sIt is determined that；Specific speed n_sIt is higher, cut water laying angle θ₀It is bigger；When than Rotating speed n_sBetween=40～60, cut water laying angleSpecific speed n_sBetween=60～130, cut water laying angleSpecific speed n_sBetween=130～220, cut water laying angleSpecific speed n_sBetween=220～360, every Tongue laying angle

Described cut water pitch angle alpha₀According to blade exit fluid flow angle β_2FIt is determined that；Cut water pitch angle alpha₀For cut water helix Angle between tangent line and basic circle tangent line, in order to meet flowing law, reduces impact loss of the liquid stream to cut water, usual cut water spiral Angle is designed to be equal to the fluid flow angle β that impeller outlet is located after a while_2F；

Described volute throat cross-sectional area A_tDetermined according to velocity moment equal principle；Specially：It is disconnected according to volute throat Face velocity and the product and the impeller outlet absolute velocity peripheral compoent of velocity of volute throat cross sectional radii and the product phase of impeller outlet radius Determine volute throat cross-sectional area, i.e. v etc. principle_tu·R_t=v_2u·R₂=constant；Calculating process such as formula (3)-(6)：

In formula：θ_tFor volute throat section relative to cut water section laying angle, its value is set toD_tIt is straight for throat's section Footpath, mm；R_tFor throat's cross sectional radii, mm；Q_nFor the flow under Centrifugal Pump Design operating mode, m³/s；v_2uFor impeller outlet absolute velocity Circumferential components, m/s；v_tuFor volute throat section speed, m/s.

Described volute outlet diameter D₄It is the empirical value artificially determined in advance according to standard pipeline diameter, working standard pipe The specification of road diameter adopts DN150, DN200, DN250, DN300, DN350, DN400, DN450, DN500, DN600, DN800, One kind in DN1000, DN1200；

Described cut water radius R₀Intensity requirement is cast according to cut water to determine, generally according to the volute outlet that double volute is selected Diameter D₄Bond strength requires determination cut water radius, works as D₄During less than or equal to DN200, R is taken₀=6mm；Work as D₄It is more than DN200 and little When equal to DN350, R is taken₀=8mm；Work as D₄During more than DN350 and less than or equal to DN600, R is taken₀=10mm；Work as D₄It is more than DN600 and during less than or equal to DN1200, takes R₀=12mm；

Described diffuser height H₀For the artificial empirical value for determining in advance；

Described diffuser centre-to-centre spacing L₀For the artificial empirical value for determining in advance；

Described dividing plate initial angleBy the above-mentioned cut water laying angle θ having determined₀, determine further according to symmetrical principle, Shown in computing formula such as formula (7)；

Described dividing plate diffusion segment length z is according to occupying diffuser height H₀30% -80% percentage ratio carry out really It is fixed；

Block board thickness t is required according to casting and intensity requirement determines, generally according to the volute outlet diameter that double volute is selected D₄Bond strength requires determination block board thickness, works as D₄During less than or equal to DN200, t=6mm is taken；D₄More than DN200 and it is less than or equal to During DN350, t=8mm is taken；D₄During more than DN350 and less than or equal to DN600, t=10mm is taken；D₄More than DN600 and it is less than or equal to During DN1200, t=12mm is taken.

Described step 2) in the selection of crucial geometric parameter be, based on spiral case waterpower flow mechanism, to affect double volute stagnation pressure Lose is principle from step 1) in initial waterpower geometric parameter in select following 6 parameters：Spiral case base circle diameter (BCD) D₃；Spiral case enters Mouth width b₃；Cut water laying angle θ₀；Volute throat cross-sectional area A_t；Dividing plate initial angle；Dividing plate spreads segment length z；Described base Carrying out optimization step to double volute key geometric parameter in the self adaptation sequence algorithm of RSM is：It is adaptive according to RSM first Sequence optimisation model is answered to set up double volute key geometric parameter numerical range table, as shown in table 1；

Then with total pressure loss coefficient δ in spiral case as optimization object function, the object function is by spiral case inlet mass flow Average total pressureWith volute outlet mass flow average total pressureDifference divided by spiral case inlet dynamic pressureCalculate Arrive, wherein spiral case inlet mass flow average total pressureBy step 5) in the physical model leaf that carries out acquired in CFD numerical computations Stagnation pressure value on wheel and spiral case interface；Volute outlet mass flow average total pressureBy step 5) in physical model carry out CFD Stagnation pressure value on volute outlet acquired in numerical computations；Spiral case inlet mass flow average static pressureBy step 5) in physics mould Type carries out the static pressure on impeller and spiral case interface acquired in CFD numerical computations.Shown in computing formula such as formula (8)；Simultaneously The functional relationship of total pressure loss coefficient δ and spiral case key geometric parameter is set up, shown in computing formula such as formula (9)：

In formula：For mass flow average static pressure；For mass flow average total pressure；In represents spiral case inlet；Out is represented Volute outlet；

By continuing to optimize each crucial geometric parameter so that total pressure loss coefficient reaches minima.Wherein RSM sequences are excellent Change algorithm basic procedure as shown in figure 4, wherein response surface design method for designing (Response Surface Methodology, RSM it is) to obtain certain data using rational test design method and by experiment, is fitted using polynary quadratic regression equation Functional relationship between factor and response value, optimal design parameters are sought by the analysis to regression equation, solve multivariate A kind of statistical method of problem.And then the process of continuous improvement RSM precision of forecasting model, because RSM models have unbiased esti-mator Characteristic, with the increase of sample points in design space, RSM models are improved constantly to the precision of true response prediction, Jin Ertong Cross accurate solution of the model realization to object function.

Described step 3) in, the Secondary Development Module that CATIA macroprograms are carried for CATIA Three-dimensional Design Software, user Can be programmed on this basis to realize the automatic parameter model to actual part.Based on CATIA macroprograms to step The rapid crucial geometric parameter 2) tried to achieve carries out parametrization automatic modeling, using mathematical model to the area of spiral case different section and Coordinate control point is calculated, and realizes the rapid automatic modeling to different spiral case parameter combinations；Concretely comprise the following steps：

A) during spiral case model construction, (the 12nd breaks with volute throat section for setting spiral case cut water section (the 0th section) Face) same profile coordinate system is in, the laying angle of cut water section is θ₀, as shown in Figure 5；It is right using left and right for cut water section 13 points for claiming are controlled, here first according to the geometric properties of cut water section, 7 points (pA0_0 to pA0_6) to the right Mathematical modeling is carried out, the mathematic(al) representation at each control point of pA0_0 to pA0_6 is obtained；

B) secondly, for cut water cross-sectional area according to cut water cross-section structure equation, it is divided into 4 regions, as shown in fig. 6, every Shown in the computing formula such as formula (10) of tongue cross-sectional area (the 0th section)：

Wherein AreaTri, AreaCir and AreaElli are tried to achieve by formula (11)-(13)；Based on each control of pA0_0 to pA0_6 The mathematic(al) representation of system point, for a triangle, it is known that three point coordinates A (r₀,z₀), B (r₁,z₁), C (r₂,z₂), solve three Angular areal calculation formula is as shown in Equation 11：

For one section of circular arc, it is known that the radius r of circle and the angle, θ of circular arc span, (the intrinsic parameter of circular arc) then justifies The area formula of segmental arc is as shown in Equation 12：

For an ellipse, it is known that the seat of oval major axis radius radR, minor axis radius radZ and upper 2 points of ellipse Mark A (r₀,z₀), B (r₁,z₁), (oval intrinsic parameter) then the area formula of point-to-point transmission ellipse section is as shown in Equation 13：

C) again, according to given throat opening area A_t, the control point pA12_0 to pA12_9 on throat's section is calculated, Control point is as shown in Figure 5；

Due to known throat opening area A_t, according to using iterative approach Algorithm for Solving point pA12_1, pA12_2, pA12_3, PA12_4 and pA12_5；Connected using straight line between its midpoint pA12_0 and pA12_1；Point pA12_1, pA12_2, pA12_3 are adopted Use circular sliding slopes；Point pA12_3, pA12_4, pA12_5 adopt circular sliding slopes；Connected mode is similar with cut water section；

Spiral case other control of section equations are tried to achieve based on above-mentioned similar method；

The original position of double volute dividing plate is to, using arc transition, arc transition adopts log spiral between final position Equation, as shown in Equation 14：

In formula, D₃For spiral case base circle diameter (BCD)；E is natural logrithm；β is, with the center of circle of basic circle as summit, to be located with cut water and cut The angle that arbitrary section is made up of side in face and spiral case；α₃For the absolute velocity angle of impeller outlet；Q_n For design discharge；b₂For the exit width of impeller；G is acceleration of gravity；H_tFor theoretical head；ω is impeller angular velocity；

D) it is last, above-mentioned computation model is compiled by the macros that CATIA is carried, to double volute geometric model reality Existing parametric modeling.

Described step 4) in, using GridPro script files to step 3) the three-dimensional double volute model that obtains carries out soon Fast structured grid is divided, and exports the grid file for numerical computations：

Quick gridding division is carried out to three-dimensional double volute model using the stress and strain model software GridPro of business, is passed through Set up double volute topological structure；For different spiral case geometric models, automatically Topological Mapping to high-quality multi-block technique On；Finally the output of ready-portioned structuring double volute grid file is carried out into numerical value in Fluid Mechanics Computation analysis software CFX Analysis.

Described step 5) in, based on CFX CCL Language-Driven programs to step 4) grid file that obtains is automatically performed Grid is loaded and boundary condition is arranged, and completes correlation values calculating, exports result of calculation；Concretely comprise the following steps：

The loading of grid and the setting of boundary condition are completed using CFX CCL Language-Driven Automatic Program, by design Spiral case internal flow under operating mode is calculated, and is obtained spiral case and is imported and exported stagnation pressure value and static pressure, according to stagnation pressure value and static pressure Total pressure loss coefficient δ is calculated, and then obtains total pressure loss coefficient value corresponding under different spiral case geometrical conditions；Then base In Optimizing operator, by continuous iterative, the minimum spiral case model of total pressure loss coefficient is obtained, be finally completed design process.

The invention has the beneficial effects as follows：1) centrifugal pump double volute can be carried out according to specified design operating mode quickly accurately setting Meter；2) spiral case different section area can be automatically adjusted according to design requirement, and is distributed to snail based on new cross-sectional area Shell carries out automatic modeling, in order to the optimization design of spiral case cross-sectional area；3) can more accurately to centrifugal pump spiral casing dimensioning Very little and cross-sectional area is controlled, and reduces the hydraulic loss that physical dimension and cross-sectional area error band come；4) using RSM models Self adaptation sequential optimization algorithm, Average total pressure loss coefficient improves the flow of fluid in spiral case as target variable with spiral case State and efficiency is improved, reduce the operation energy consumption of equipment；5) the double volute design reduction centrifugal pump double volute of automatization sets Meter difficulty, shortens double volute and designs and develops the cycle.

Description of the drawings

Fig. 1 is the waterpower geometric parameter figure of double volute；

Fig. 2 is the A-A sectional views of Fig. 1；

Fig. 3 is the B-B sectional views of Fig. 1；

Fig. 4 is the basic flow sheet of RSM sequential optimization algorithms；

Fig. 5 is double volute cut water section and throat's section geometry control parameter figure；

Fig. 6 is that spiral case cut water cross-sectional area calculates schematic diagram；

Fig. 7 is double volute Automatic Optimal Design system flow chart；

Fig. 8 is volute throat area distribution plot before and after optimization；(abscissa is spiral case circumference angle, and vertical coordinate is spiral case mistake Flow cross-sectional area is distributed).

Specific embodiment

Embodiment 1

Below in conjunction with drawings and Examples, the present invention is described in further detail.The present embodiment empirical coefficient and push away Recommending value is obtained by substantial amounts of test statistics data correction, that is, conventional those skilled in the art are in the experience for using Value；Final design load need to be checked by numerical result.

With reference to shown in Fig. 1-Fig. 8, a kind of double volute Hydraulic Design Method based on RSM models, described double volute waterpower Structure includes this three part of spiral section 1, diffuser 2 and dividing plate 3；As shown in Figure 1, 2, 3；Described three part water conservancy structures set Counting step is：1) according to given flow, lift, tachometer value and known impeller the Hydraulic Design parameter, asked based on velocity-coefficient method The initial waterpower geometric parameter of solution double volute；Wherein described the step of 1) in known impeller the Hydraulic Design parameter be according to demand, use On the way, the empirical value that casting is required and intensity, pump housing installation dimension are required and artificially determined in advance, including impeller outer diameter D₂, blade Exit width b₂, front/rear cover plate thickness, specific speed n_s, blade exit fluid flow angle β_2F, actual installation pipeline diameter；Volute throat Laying angle θ of the section relative to cut water section_t, the flow Q under Centrifugal Pump Design operating mode_n, impeller outlet absolute velocity circumferential components v_2u；The given flow 1800m of the present embodiment³/ h, lift 135m, the efficiency of pump 85% and tachometer value 1480r/min, the present embodiment is The geometric parameter for knowing impeller is：Impeller outer diameter D₂For 665mm, impeller outlet width b₂For 50mm, specific speed n_sGo out for 96, blade Oral fluid stream angle beta_2FFor 22 °；Front and rear cover plate thickness is 20mm；Actual installation pipeline diameter be DN300, volute throat section relative to The laying angle θ of cut water section_tForFlow Q under Centrifugal Pump Design operating mode_nFor 1800m³/ s, impeller outlet absolute velocity circle All component v_2uFor 24m/s；The initial waterpower geometric parameter of described double volute includes：Spiral case base circle diameter (BCD) D₃；Spiral case inlet width b₃；Cut water laying angle θ₀；Cut water pitch angle alpha₀；Volute throat cross-sectional area A_t；Volute outlet diameter D₄；Cut water radius R₀；Diffusion Duan Gaodu H₀；Diffuser centre-to-centre spacing L₀；Dividing plate initial angle；Dividing plate spreads segment length z；Block board thickness t；

Based on traditional design experience, D₃、b₃Selection can be determined according to following empirical formula：

Described spiral case base circle diameter (BCD) D₃According to impeller outer diameter D₂It is determined that, shown in computing formula such as formula (1)：

D₃=(1.05～1.2) D₂(1)；

The present embodiment takes D₃=1.05D₂=700

Entrance width b of described spiral case₃By blade exit width b₂And front/rear cover plate thickness determines, computing formula such as formula (2) shown in：b₃=(1.6～2) b₂(2)；

The present embodiment takes b₃=2b₂=100

Cut water laying angle θ₀With specific speed n_sIt is relevant, usual specific speed n_sIt is higher, cut water laying angle θ₀It is bigger.According to tradition Design experiences, specific speed n_sBetween=40～60, the cut water laying angle of recommendationSpecific speed n_sBetween=60～130, push away The cut water laying angle recommendedSpecific speed n_sBetween=130～220, the cut water laying angle of recommendationSpecific speed n_sBetween=220～360, the cut water laying angle of recommendationDue to the specific speed n in embodiment 1_sFor 96, therefore θ₀= 20°。

Cut water pitch angle alpha₀The angle between tangent line and basic circle tangent line for cut water helix, in order to meet flowing law, subtracts Impact loss of the little liquid stream to cut water, usual cut water pitch angle alpha₀It is designed to be equal to the fluid flow angle β that impeller outlet is located after a while_2F.Therefore Cut water pitch angle alpha₀=22 °.

According to the product and impeller outlet absolute velocity circumference point speed of volute throat section speed and volute throat cross sectional radii Degree determines volute throat cross-sectional area A with the product equal principle of impeller outlet radius_t, i.e. v_tu·R_t=v_2u·R₂= constant.Concrete calculating process is as follows：

In formula：θ_tFor volute throat section relative to cut water section laying angle, its value is set toD_tIt is straight for throat's section Footpath, mm；R_tFor throat's cross sectional radii, mm；Q_nFor the flow under Centrifugal Pump Design operating mode, its value is 1800m³/s；v_2uGo out for impeller Mouth absolute velocity circumferential components, its value is 24m/s；v_tuFor volute throat section speed, m/s.Obtain volute throat cross-sectional area A_tFor 29500mm²。

Dividing plate initial angleDetermined according to following empirical formula：

Other geometric parameters can require to be determined based on experience value according to actual design specification and casting, respectively spiral case Outlet diameter D₄=300mm；Cut water radius R₀=8mm；Diffuser height H₀=650mm；Diffuser centre-to-centre spacing L₀=400mm；Every Plate spreads segment length z=300mm；Block board thickness t=8mm.

2) numerical range of double volute key geometric parameter is given, based on spiral case waterpower flow mechanism, affects double volute total The crucial geometric parameter that crushing loses is respectively：Volute throat area A_t, spiral case base circle diameter (BCD) D₃, spiral case inlet width b₃, cut water peace Put angle θ₀, dividing plate initial angle φ, dividing plate diffusion 6 variables such as segment length z；Using the total pressure loss coefficient in spiral case as optimization mesh Mark variable, optimization is carried out using the self adaptation sequence algorithm based on RSM to double volute key geometric parameter.Such as Fig. 4 institutes Show.Double volute key geometric parameter numerical range table, the present embodiment key geometry are set up according to RSM self adaptation sequence optimisation models Parameter values range table is as shown in table 2.Wherein response surface design method for designing (Response Surface Methodology, RSM it is) to obtain certain data using rational test design method and by experiment, is fitted using polynary quadratic regression equation Functional relationship between factor and response value, optimal design parameters are sought by the analysis to regression equation, solve multivariate A kind of statistical method of problem.

The total pressure loss coefficient δ with spiral case is as optimization object function, and the object function is average by spiral case inlet mass flow Stagnation pressureWith volute outlet mass flow average total pressureDifference divided by spiral case inlet dynamic pressureIt is calculated, its Middle spiral case inlet mass flow average total pressureBy step 5) in physical model carry out the impeller acquired in CFD numerical computations and snail Stagnation pressure value on shell interface；Volute outlet mass flow average total pressureBy step 5) in physical model carry out CFD numerical value meters Calculate the stagnation pressure value on acquired volute outlet；Spiral case inlet mass flow average static pressureBy step 5) in physical model carry out The static pressure on impeller and spiral case interface acquired in CFD numerical computations.Its definition is as shown in formula (8)；Set up stagnation pressure simultaneously The functional relationship of loss coefficient δ and spiral case key geometric parameter, as shown in formula (9).

In formula：For mass flow average static pressure；For mass flow average total pressure；In represents spiral case inlet；Out is represented Volute outlet.

By continuing to optimize each crucial geometric parameter so that total pressure loss coefficient reaches minima.Wherein RSM sequences are excellent Change algorithm basic procedure as shown in figure 4, this be one continuous improvement RSM precision of forecasting model process, because RSM models have The characteristic of unbiased esti-mator, with the increase of sample points in design space, RSM models are constantly carried to the precision of true response prediction Height, and then the accurate solution to object function can be realized by the model.

3) parametrization automatic modeling is carried out to double volute model based on CATIA macroprograms, using mathematical model to spiral case not Calculated with the area and coordinate control point of section, realized the rapid automatic modeling to different spiral case parameter combinations.As schemed 5th, shown in 6.CATIA macroprograms are the Secondary Development Module that CATIA Three-dimensional Design Software is carried, and user can enter on this basis Row programs to realize the automatic parameter model to actual part.

Described step 3) in, parametrization automatic modeling is carried out to double volute model based on CATIA macroprograms, using mathematics Model is calculated the area and coordinate control point of spiral case different section, realize to different spiral case parameter combinations it is rapid from Dynamic modeling：

During spiral case model construction, it is assumed that (the 12nd breaks spiral case cut water section (the 0th section) with volute throat section Face) same profile coordinate system is in, the laying angle of cut water section is θ₀, as shown in Figure 5.It is right using left and right for cut water section 13 points for claiming are controlled, here first according to the geometric properties of cut water section, 7 points (pA0_0 to pA0_6) to the right Mathematical modeling is carried out, the mathematic(al) representation at each control point of pA0_0 to pA0_6 is obtained；

Secondly, for cut water cross-sectional area according to cut water cross-section structure equation, 4 regions are segmented into, as shown in fig. 6, The computing formula such as formula (10) of cut water cross-sectional area (the 0th section)：

Wherein AreaTri, AreaCir and AreaElli are tried to achieve by formula (11)-(13).Based on each control of pA0_0 to pA0_6 The mathematic(al) representation of system point, for a triangle, it is known that three point coordinates A (r₀,z₀), B (r₁,z₁), C (r₂,z₂), solve three Angular areal calculation formula is as shown in Equation 11

For one section of circular arc, it is known that circular radius r and the angle, θ of circular arc span, then the area formula of arc section is such as Shown in formula 12.

For an ellipse, it is known that the seat of oval major axis radius radR, minor axis radius radZ and upper 2 points of ellipse Mark A (r₀,z₀), B (r₁,z₁), then the area formula of point-to-point transmission ellipse section is as shown in Equation 13.

Again, according to given throat opening area A_t, volute throat control of section point is as shown in figure 5, to the control on throat's section System point pA12_0 to pA12_9 is calculated.

Due to known throat opening area A_t, according to using calculating throat opening area A_{t_c}With given throat opening area A_tContinuous iterative approach Algorithm for Solving point pA12_1, pA12_2, pA12_3, pA12_4 and pA12_5.Adopt between its midpoint pA12_0 and pA12_1 Straight line connects；Point pA12_1, pA12_2, pA12_3 adopt circular sliding slopes；Point pA12_3, pA12_4, pA12_5 are connected using circular arc Connect；Connected mode is similar with cut water section.

Spiral case other control of section equations can be tried to achieve based on above-mentioned similar method.

The original position of double volute dividing plate is to, using arc transition, arc transition adopts log spiral between final position Equation：

In formula, D₃For spiral case base circle diameter (BCD)；E is natural logrithm；β is, with the center of circle of basic circle as summit, to be located with cut water and cut The angle that arbitrary section is made up of side in face and spiral case；α₃For the absolute velocity angle of impeller outlet；Q_n For design discharge；b₂For the exit width of impeller；G is acceleration of gravity；H_tFor theoretical head；ω is impeller angular velocity.

Finally, above-mentioned computation model is compiled by the macros that CATIA is carried, double volute geometric model is realized Parametric modeling.

4) the three-dimensional double volute model exported to CATIA using GridPro script files carries out rapid structure grid stroke Point, output can be used for the grid file of numerical computations；As shown in Figure 7.

Described step 4) in, three-dimensional double volute model is carried out quickly using the stress and strain model software GridPro of business Gridding is divided, by setting up double volute topological structure, for different spiral case geometric models, and can automatically Topological Mapping To on high-quality multi-block technique.Finally by the output of ready-portioned structuring double volute grid file to Fluid Mechanics Computation analysis Numerical analysis is carried out in software CFX.

5) grid loading is completed based on CFX CCL Language-Driven Automatic Program and boundary condition is arranged, complete correlation values Calculate, export result of calculation；As shown in Figure 7.

Described step 5) in, loading and the boundary condition of grid are completed using CFX CCL Language-Driven Automatic Program Arrange, by calculating the spiral case internal flow under design conditions, obtain spiral case and import and export stagnation pressure value and static pressure, according to Stagnation pressure value and static pressure calculate total pressure loss coefficient δ, and then obtain total crushing corresponding under different spiral case geometrical conditions Lose coefficient value；Optimizing operator is then based on, by continuous iterative, the minimum spiral case model of total pressure loss coefficient is obtained, most Whole complete design process.

6) according to above-mentioned steps 3)-continuous iterative 5), the minimum double volute scheme of total pressure loss coefficient is obtained, The throat opening area distribution of the double volute scheme after optimization is as shown in Figure 8；By the spiral case geometric parameters corresponding to pitot loss minima Number solution makes the double volute centrifugation for meeting given flow, lift, the efficiency of pump and tachometer value as the design parameter of double volute Pump.Jing Numerical Validations, after optimization double volute conceptual internal flowing be improved significantly, the whirlpool at spiral case diffuser is pressed down System, effectively eliminates the hydraulic loss that whirlpool is carried, while experiment proves that, it is optimized after double volute with optimize before it is original Scheme is compared, and efficiency improves 3%, greatly reduces the energy consumption of centrifugation pump operation.Resulting final spiral case geometric parameter data It is shown in Table 3.

The present embodiment 1) quick careful design can be carried out to centrifugal pump double volute according to specified design operating mode；2) energy basis sets Meter requires to be automatically adjusted spiral case different section area, and spiral case is built automatically based on new cross-sectional area distribution Mould, in order to the optimization design of spiral case cross-sectional area；3) can more accurately to centrifugal pump spiral casing physical dimension and cross-sectional area It is controlled, reduces the hydraulic loss that physical dimension and cross-sectional area error band come；4) the self adaptation sequence using RSM models is excellent Change algorithm, Average total pressure loss coefficient improves the fluid flow state in spiral case and improve as target variable with spiral case Efficiency, reduces the operation energy consumption of equipment；5) the double volute design of automatization reduces centrifugal pump double volute design difficulty, shortens double The Volute Design construction cycle.

Table 1

Table 2

Table 3

Claims (6)

1. a kind of double volute Hydraulic Design Method based on RSM models, it is characterised in that described double volute hydraulic structure includes Spiral section (1), diffuser (2) and this three part of dividing plate (3)；The design procedure of three described part water conservancy structures is：1) basis Given flow, lift, tachometer value and known impeller hydraulic engineering design parameter, based on velocity-coefficient method the initial waterpower of double volute is solved Geometric parameter；2) by step 1) solve the numerical value model for obtaining that double volute key geometric parameter is determined in initial waterpower geometric parameter Enclose；Using the total pressure loss coefficient in spiral case as optimization aim variable, using the self adaptation sequence algorithm based on RSM to double volute Crucial geometric parameter carries out optimization；3) based on CATIA macroprograms to step 2) required by the crucial geometric parameter that obtains of solution Parametrization automatic modeling is carried out, the area and coordinate control point of spiral case different section is calculated using mathematical model, realized Rapid automatic modeling to different spiral case parameter combinations and output obtains three-dimensional double volute model；4) using GridPro scripts File is to step 3) the three-dimensional double volute model that obtains carries out rapid structure stress and strain model, exports the grid for numerical computations File；5) based on CFX CCL Language-Driven programs to step 4) network file that obtains is automatically performed grid loading and perimeter strip Part is arranged, and completes correlation values calculating, exports result of calculation；6) repeat the above steps 3) -5), by continuous iterative, obtain To the double volute scheme that total pressure loss coefficient is minimum；7) according to above-mentioned steps 1) -6) in resulting data as double volute Design parameter, making meets the double volute centrifugal pump of given flow, lift, the efficiency of pump and tachometer value.

2. a kind of double volute Hydraulic Design Method based on RSM models as claimed in claim 1, it is characterised in that：Described Step 1) in known impeller the Hydraulic Design parameter be according to design requirement, purposes, casting require and intensity, pump housing installation dimension will The empirical value asked and artificially determine in advance, including impeller outer diameter D₂, blade exit width b₂, front/rear cover plate thickness, specific speed n_s, Blade exit fluid flow angle β_2F, actual installation pipeline diameter, laying angle of the volute throat section relative to cut water sectionCentrifugal pump Flow Q under design conditions_n, impeller outlet absolute velocity circumferential components v_2u；The initial waterpower geometric parameter bag of described double volute Include：Spiral case base circle diameter (BCD) D₃；Spiral case inlet width b₃；Cut water laying angleCut water pitch angle alpha₀；Volute throat cross-sectional area A_t； Volute outlet diameter D₄；Cut water radius R₀；Diffuser height H₀；Diffuser centre-to-centre spacing L₀；Dividing plate initial angleDividing plate spreads segment length Degree z；Block board thickness t；It is described double volute waterpower geometric parameter is solved based on velocity-coefficient method method be：

Described spiral case base circle diameter (BCD) D₃According to impeller outer diameter D₂It is determined that, shown in computing formula such as formula (1)：

D₃=(1.05～1.2) D₂(1)；

Entrance width b of described spiral case₃By blade exit width b₂And front/rear cover plate thickness determines, computing formula such as formula (2) It is shown：b₃=(1.6～2) b₂(2)；

Described cut water laying angleAccording to specific speed n_sIt is determined that；Specific speed n_sIt is higher, cut water laying angleIt is bigger；As specific speed n_s Between=40～60, cut water laying angleSpecific speed n_sBetween=60～130, cut water laying angleThan turning Fast n_sBetween=130～220, cut water laying angleSpecific speed n_sBetween=220～360, cut water laying angle

Described cut water pitch angle alpha₀According to blade exit fluid flow angle β_2FIt is determined that；Cut water pitch angle alpha₀For the tangent line of cut water helix With the angle between basic circle tangent line, in order to meet flowing law, reduce impact loss of the liquid stream to cut water, usual cut water helical angle sets Count into the fluid flow angle β located after a while equal to impeller outlet_2F；

Described volute throat cross-sectional area A_tDetermined according to velocity moment equal principle；Specially：According to volute throat section speed With the product and the impeller outlet absolute velocity peripheral compoent of velocity and the product equal principle of impeller outlet radius of volute throat cross sectional radii Determine volute throat cross-sectional area, i.e. v_tu·R_t=v_2u·R₂=constant；Calculating process such as formula (3)-(6)：

$D_t=\frac{2{\mathrm{\θ}}_t{Q}_n}{360{\mathrm{\πv}}_{2u}{D}_2}+\sqrt{\frac{2D_3{\mathrm{\θ}}_t{Q}_n}{180{\mathrm{\πv}}_{2u}{D}_2}+{\left(\frac{{\mathrm{\θ}}_t{Q}_n}{360{\mathrm{\πv}}_{2u}{D}_2}\right)}^2}---\left(3\right)$

$R_t=\frac{D_3}{2}+\frac{D_t}{2}---\left(4\right)$

$A_t=\frac{{\mathrm{\πD}}_t^2}{4}---\left(5\right)$

$v_{tu}=\frac{{\mathrm{\θ}}_t{Q}_n}{360A_t}---\left(6\right)$

In formula：For volute throat section relative to cut water section laying angle, its value is set toD_tFor throat's cross section diameter, mm；R_tFor throat's cross sectional radii, mm；Q_nFor the flow under Centrifugal Pump Design operating mode, m³/s；v_2uFor impeller outlet absolute velocity circle All components, m/s；v_tuFor volute throat section speed, m/s.

Described volute outlet diameter D₄It is the empirical value artificially determined in advance according to standard pipeline diameter, working standard pipeline is straight The specification in footpath adopts DN150, DN200, DN250, DN300, DN350, DN400, DN450, DN500, DN600, DN800, One kind in DN1000, DN1200；

Described cut water radius R₀Intensity requirement is cast according to cut water to determine, generally according to the volute outlet diameter that double volute is selected D₄Bond strength requires determination cut water radius, works as D₄During less than or equal to DN200, R is taken₀=6mm；Work as D₄More than DN200 and less than etc. When DN350, R is taken₀=8mm；Work as D₄During more than DN350 and less than or equal to DN600, R is taken₀=10mm；Work as D₄More than DN600 and During less than or equal to DN1200, R is taken₀=12mm；

Described diffuser height H₀For the artificial empirical value for determining in advance；

Described diffuser centre-to-centre spacing L₀For the artificial empirical value for determining in advance；

Described dividing plate initial angleBy the above-mentioned cut water laying angle having determinedDetermine further according to symmetrical principle, calculate Shown in formula such as formula (7)；

Described dividing plate diffusion segment length z is according to occupying diffuser height H₀30% -80% percentage ratio be determined；

Block board thickness t is required according to casting and intensity requirement determines, generally according to the volute outlet diameter D that double volute is selected₄With reference to Intensity requirement determines block board thickness, works as D₄During less than or equal to DN200, t=6mm is taken；D₄More than DN200 and less than or equal to DN350 When, take t=8mm；D₄During more than DN350 and less than or equal to DN600, t=10mm is taken；D₄More than DN600 and less than or equal to DN1200 When, take t=12mm.

3. a kind of double volute Hydraulic Design Method based on RSM models as claimed in claim 1, it is characterised in that：Described Step 2) in the selection of crucial geometric parameter be, based on spiral case waterpower flow mechanism, to affect double volute pitot loss to be principle from step It is rapid 1) in initial waterpower geometric parameter in select following 6 parameters：Spiral case base circle diameter (BCD) D₃；Spiral case inlet width b₃；Cut water is pacified Put angleVolute throat cross-sectional area A_t；Dividing plate initial angleDividing plate spreads segment length z；The described self adaptation sequence based on RSM Row algorithm carries out optimization step to double volute key geometric parameter：First according to RSM self adaptation sequence optimisation models Set up double volute key geometric parameter numerical range；

Then with total pressure loss coefficient δ in spiral case as optimization object function, shown in computing formula such as formula (8)；Set up stagnation pressure simultaneously The functional relationship of loss coefficient δ and spiral case key geometric parameter, shown in computing formula such as formula (9)：

$\mathrm{\δ}=\frac{{\stackrel{\‾}{p}}_{in}^0-{\stackrel{\‾}{p}}_{out}^0}{{\stackrel{\‾}{p}}_{in}^0-{\stackrel{\‾}{p}}_{in}}---\left(8\right)$

In formula：For mass flow average static pressure；For mass flow average total pressure；In represents spiral case inlet；Out represents spiral case Outlet；

By continuing to optimize each crucial geometric parameter so that total pressure loss coefficient reaches minima.And then it is pre- to improve constantly RSM The process of model accuracy is surveyed, because RSM models have the characteristic of unbiased esti-mator, with the increase of sample points in design space, RSM Model is improved constantly to the precision of true response prediction, and then the accurate solution by the model realization to object function.

4. a kind of double volute Hydraulic Design Method based on RSM models as claimed in claim 1, it is characterised in that：Described Step 3) in, based on CATIA macroprograms to step 2) the crucial geometric parameter tried to achieve carries out parametrization automatic modeling, using number Learn model to calculate the area and coordinate control point of spiral case different section, realize to the rapid of different spiral case parameter combinations Automatic modeling；Concretely comprise the following steps：

A) during spiral case model construction, setting spiral case cut water section is in same profile coordinate system with volute throat section, The laying angle of cut water section is θ 0；For cut water section, be controlled using symmetrical 13 points, here first according to every 7 points (pA0_0 to pA0_6) on the right are carried out mathematical modeling by the geometric properties of tongue section；Obtain pA0_0 to pA0_6 each The mathematic(al) representation at control point；

B) secondly, for cut water cross-sectional area according to cut water cross-section structure equation, it is divided into 4 regions, the meter of cut water cross-sectional area Calculate shown in formula such as formula (10)：

$\begin{array}{c}{A}_0=2({\mathrm{AreaTri}}_{0\_1}-{\mathrm{AreaElli}}_{0\_1}+{\mathrm{AreaTri}}_{0\_2}+{\mathrm{AreaTri}}_{0\_3}+{\mathrm{AreaCir}}_{0\_3}\\ +{\mathrm{AreaTri}}_{0\_4}+{\mathrm{AreaCir}}_{0\_4})\end{array}---\left(10\right)$

Wherein AreaTri, AreaCir and AreaElli are tried to achieve by formula (11)-(13)；Based on each control point of pA0_0 to pA0_6 Mathematic(al) representation, for a triangle, it is known that three point coordinates A (r₀,z₀), B (r₁,z₁), C (r₂,z₂), solve triangle Areal calculation formula it is as shown in Equation 11：

$AreaTri=\left|\frac{(r_1-r_0)(z_2-z_0)-(r_2-r_0)(z_1-z_0)}{2}\right|---\left(11\right)$

For one section of circular arc, it is known that the radius r of circle and the angle of circular arc spanThe then area formula of the arc section such as institute of formula 12 Show：

$AreaCir=\left|\frac{r^2(\mathrm{\θ}-sin\mathrm{\θ})}{2}\right|---\left(12\right)$

For an ellipse, it is known that the coordinate A of oval major axis radius radR, minor axis radius radZ and upper 2 points of ellipse (r₀,z₀), B (r₁,z₁), then the area formula of point-to-point transmission ellipse section is as shown in Equation 13：

$AreaElli=0.5|radR\·radZ\left(\frac{\mathrm{\π}}{2}+act\sin \frac{D}{ranZ}\right)+\frac{radR\·D\sqrt{{\mathrm{radZ}}^2-D^2}}{radZ}|-\left|\frac{\left(r_1-r_0\right)\left(z_1-z_0\right)}{2}\right|---\left(13\right)$

C) again, according to given throat opening area A_t, volute throat control of section point, to the control point pA12_0 on throat's section extremely PA12_9 is calculated；

Due to known throat opening area A_t, according to using calculating throat opening area A_{t_c}With given throat opening area A_tThe constantly calculation of iterative approach Method solution point pA12_1, pA12_2, pA12_3, pA12_4 and pA12_5；Straight line is adopted between its midpoint pA12_0 and pA12_1 Connection；Point pA12_1, pA12_2, pA12_3 adopt circular sliding slopes；Point pA12_3, pA12_4, pA12_5 adopt circular sliding slopes；Even Connect mode similar with cut water section；

Spiral case other control of section equations are tried to achieve based on above-mentioned similar method；

, to arc transition is adopted between final position, arc transition is using log spiral side for the original position of double volute dividing plate Journey, as shown in Equation 14：

$R=\frac{D_3}{2}{e}^{{\mathrm{\βtan\α}}_3}---\left(14\right)$

In formula, D₃For spiral case base circle diameter (BCD)；E is natural logrithm；β is with the center of circle of basic circle as summit, with cut water place section and snail The angle that arbitrary section is made up of side in shell；α₃For the absolute velocity angle of impeller outlet；Q_nFor design Flow；b₂For the exit width of impeller；G is acceleration of gravity；H_tFor theoretical head；ω is impeller angular velocity；

D) it is last, above-mentioned computation model is compiled by the macros that CATIA is carried, double volute geometric model is realized to join Numberization is modeled.

5. a kind of double volute Hydraulic Design Method based on RSM models as claimed in claim 1, it is characterised in that：Described Step 4) in, using GridPro script files to step 3) the three-dimensional double volute model that obtains carries out rapid structure grid and draws Point, export the grid file for numerical computations：

Quick gridding division is carried out to three-dimensional double volute model using the stress and strain model software GridPro of business, by setting up Double volute topological structure, while the reuse of topology is realized based on dynamic boundary adaptive technique, for different spiral case geometric models, Automatically in Topological Mapping to high-quality multi-block technique；Finally the output of ready-portioned structuring double volute grid file is arrived Numerical analysis is carried out in Fluid Mechanics Computation analysis software CFX.

6. a kind of double volute Hydraulic Design Method based on RSM models as claimed in claim 1, it is characterised in that：Described Step 5) in, based on CFX CCL Language-Driven programs to step 4) grid file that obtains is automatically performed grid loading and border Condition setting, completes correlation values calculating, exports result of calculation；Concretely comprise the following steps：

The loading of grid and the setting of boundary condition are completed using CFX CCL Language-Driven Automatic Program, by design conditions Under spiral case internal flow calculated, obtain spiral case and import and export stagnation pressure value and static pressure, calculated according to stagnation pressure value and static pressure Total pressure loss coefficient δ, and then obtain total pressure loss coefficient value corresponding under different spiral case geometrical conditions；It is then based on excellent Change operator, by continuous iterative, obtain the minimum spiral case model of total pressure loss coefficient, be finally completed design process.