离心泵水力设计相关理论与软件操作

1Concepts

NREC离心泵水力设计相关理论与软件操作一、

Pumpal一维设计2► 初始设计的思路:通过沿流线方向的一维计算获得效率最高的方案► 设计目标:流量扬程► 工作条件及约束进口总温、总压转速► 一维设计的结果:确定整体布局根据效率最优确定几何参数非设计点性能预测1.1

计算模型► Wilder-based

modelingtechnology:Concepts

ETI

两区模型► Woburn-based

modelingtechnology:NREC

单区模型► Stepanoff

model► Concepts

ETI

单区模型（轴流风扇、轴流泵）31.1.1

两区模型及其关键参数► 假设:主流区：射流、

等墒、

没有能量损失二次流区：尾迹、低动量流体在此集中、

所有损失发生在二次流区主流区和二次流区在叶轮出口立刻混合41.1.1

两区模型及其关键参数► DR2

,

扩散比,

进口叶尖相对速度和出口主流区相对速度的比值► Msec

M

or

二次流区质量分数► Delta

P

and

Delta

S

主流区和二次流区的落后角51.2

三种模式及其用法► 设计模式指定目标参数，如流量、扬程、转速调整几何参数，优化进口速度三角形、调整出口流动角等► 分析模式指定几何尺寸修改模型参数► 数据处理模式使用测试数据校准模型参数61.2

三种模式及其用法7► 设计模式输入扬程、

转速和必要的几何约束根据经验和流体力学理论输入模型参数输出几何参数及设计点的流动参数，如流动角、落后角等► 分析模式输入几何参数根据经验和流体力学理论输入模型参数输出设计点的流动参数或者其他流量点甚至其他转速下的流动参数► 数据处理模式输入几何参数和测试数据或者CFD数据输出模型参数1.3

计算工质► 可以计算真实气体► 预定义工质，如半经验气体► DBR

or

NIST可支持79种碳水化合物和27种制冷剂及其混合物► Mollier

table指定流体性质81.4

AEDS®无缝接口► 一维模式到三维模式可实现无缝连接► 三维模式提供的额外参数使一维结果更加完善91.5

Python®功能扩展► Concepts

NREC

提供Python

hooks

，包括收费和免费两种。► 用户补充script101.6

离心泵布局11► 进口导叶► 叶轮进口► 叶轮出口► 无叶扩压器► 导叶► 蜗壳► 回流通道► 泄漏槽和密封► 侧流► 进口导叶► 叶轮进口► 叶轮出口► 无叶扩压器► 导叶► 蜗壳► 回流通道1.6

离心泵布局势加透博（北京）科► 泄漏槽和密封► 侧流技有限公司 121.7

离心叶轮的流动形式► Eckardt,

1975►

进出口流动面积和方向等变化引起的流动分离不可避免►

叶片旋转和流道曲率增加使二次流更加严重►

二次流在叶尖-吸力面区域更加集中►

以上因素导致出口流动很不均匀131.8

损失模型► Diffusion

modelTEIS(Two-Elements-in-Series)

modelBackbonecurve/state-of-the-artcurve(1970,Imp.3DRef.

Band)Functionofspecific

speedHybrid

functionUser-fixed

value► Secondarymassflowfractionmodel(impellertip

model)Two-zone

frozen

variableFunctionofspecific

speedUser-specifiedETA

rotorNRECsingle-zone

model► Deviationmodel

slipfactor

model141.8.1

扩散模型TEIS

Model► TEIS--

Two-Elements-in-Series151.8.1

扩散模型TEIS

Model161.8.2

扩散模型Backbone

Curve171.8.3

叶尖模型Function

of

Specific

Speed181.8.4

滑移模型Preferred

Deviation

Model191.8.5

其他损失► 泄露损失► 圆盘摩擦损失► 回流损失201.9

设计模式下叶轮进口尺寸的计算► 压缩机：进口叶尖相对速度最小► 泵：必需汽蚀余量最小211.10

设计模式下叶轮出口尺寸的计算► 指定扬程和叶轮出口环量系数,

LAM2=CT2/CM2► 叶轮出口外径和宽度需反复调整221.11

其他流动部件的计算23► Database-basedmodeling(usedatabasetodetermine

LC,CP,

ALPHA):Returnchannel/180-degree

bendCascadediffuser(NACA

series)► Two-zonemodel:foil

diffuser► Predictivegeometry-based

modeling:Genericvaned

diffuserReturn

channelContinuous

crossoverIGV► UsingStanitz

model:Vaneless

diffuser90-/180-degree

bend1.12

出口部件24► Volute/NREC

scroll► Returnchannel/NREC

deswirl► Radial-Axial

bend► NRECspecifiedlossexit

element► Collector1.13

Pumpal菜单► Agile:

和三维模式连接► Standard

screens:

界面模版，用户可自定义► Setup:

设置单位、计算模型、模式等► Multistage:

增加、减少和修改级（数）► Components:

当前级的详细设置► Solver:

计算► Mechanical:

简单的应力/结构分析► Acoustics:

简单的噪声分析► Correlation:

经验曲线，显示设计点的位置251.13

Pumpal菜单26► Toolbar：工具条► Program

setup► 练习：StartCOMPAL/PUMPALandopenanyexamplefrominstallation

directoryExplorethemenusystemandcompletethefollowing(donotworrytoomuchaboutthedetails,wewillcoverthemlater):Basicprogramsetup,suchaspreferences,unitsystem,

etc.Viewcurrentdesignlayout,findoutsettingsfor

eachcomponentRunthesolver,viewtextreportanddisplaytip

velocitytriangleatimpeller

exitTrysomestandardscreen

views1.13.1

Pumpal菜单_File► 另存为分析模式：从设计模式从数据处理模式► 向导所有模式适用► 存放目录271.13.2

Pumpal菜单_View► 对比显示：设计模式不适用281.13.3

Pumpal菜单_Setup► 模式：不同模式间的切换► 布局：添加进口导叶并选择类型增加叶轮出口导叶级数并选择类型更改出口部件类型，如蜗壳改为导叶291.13.3

Pumpal菜单_Setup► 通用：多点分析考虑失速工质单位制► 模化：301.13.4

Pumpal菜单_Multistage► 添加下一级：克隆后修改参数311.13.5

Pumpal菜单_Components► 叶轮进口：速度比绝对流动角空化系数321.13.5

Pumpal菜单_Components► 叶轮出口：叶尖模型滑移模型扩散模型出口宽度模型331.13.5

Pumpal菜单_Components► 蜗壳：断面形状双出口蜗壳341.13.6

Pumpal菜单_Solve► 自动求解► 优化：效率最高功率最低几何尺寸最小► 保存计算结果351.13.7

Pumpal菜单_Standard

Screens► 软件自带界面► 用户创建界面361.13.8

Pumpal菜单_Mechanical► 预估应力和寿命► 预估重量和转动惯量371.13.9

Pumpal菜单_Agile► 切换到三维详细设计► Python功能扩展381.13.10

Pumpal菜单_Correlation► 经验参数391.13.11

Pumpal菜单_Windows► 过滤器► 速度三角形► 轴向力401.14

分析模式下性能预测► 设计点性能预测► 非设计点性能预测设计模式不能使用最多可预测12个流量点最多预测8个相关的变量► 简单的强度计算预测叶轮应力振动重量和转动惯量411.15

分析模式下查看计算结果42► 两种输出方式文本输出表格输出► 过滤后输出软件自带的过滤器用户自定义的过滤器► 速度三角形► 练习将已经设计完成的结果输出并检查

:；确认设计点的数据；检查级数和叶轮的几何形状；创建你需要的输出过滤器并保存、留待以后使用。1.16

练习43► Openthepump-example01.geocascadediffuserfile;adjustthemassflowrangetocoverfrom

15%to160%ofthedesignmassflow;runthecaseandsavethemap

file► Findthestallrangeofthe

pump► Nowchangethestagetoacompletelyvanelessdiffuserpumpandrerunthemap;overlaythecascadediffuserresultsonthevaneless

diffusermap► Whichhasthebetterpeak

performance?► Whichhasthebetterstall

range?1.17

练习——设计模式44► ChooseConceptstwo-zonemodel,

chooseappropriateunits

system► Operation

condition:Massflowrate:

0.2P00:

10.232m T00:300

Km3/minRotationalspeed:3,000

rpmWater► Designheadrise:totaldynamicheadrise=10

m,safetyfactor:

1.05► Select3Dwheeloption,minimum

NPHSR► Specifyhub/tipratioforimpellerinlettipand

hubradius

option1.17

练习——设计模式45► Geometry:R1H/R1TandPhi

as

default Phi2=

90Numberofvanes=5Sealradius

ratioInletincidenceangle(Tip,RMSandHub)=

2.0LEthicknessatshroud=0.5

mmUser-specifiedvalues:velocityratio=1.05(Rseal/R1t)=

1.03Coveredimpeller:clearancegap=0.127

mmSeallength:5.0

mmnopump-outvanesorbalancing

holesTEthickness=

3.0

mm Numberofvanes

=F-factor:

0.75Beta2b(mean)=255No

diffuserSelectcollectorasexit

element► WhatistheT-T

efficiency?1.18

练习——分析模式46► Openthedesignwesavedandsavethedesign

inanalysismode(ifitisnot

already)► Activatemultiple-pointanalysisinGeneral

menu► Multiple-point

analysisSelectspeedasthedependentvariableandchoose1

speedFlowtab:selectAsFractionofinletflow,8points,evenlyspacefrom0.7to1.1ofinlet

flowRun

solverCheckresultsthroughwindows/map

view► Stallandchokeflow

check► Checkperformanceatadditional

speeds1.18

练习——分析模式47► Runthe

solver► Analyzethedesign;adjustparametersif

necessary► Saveasanalysistochangetoanalysis

safely► Starttoworkondetailedbladegeometryand

flowfieldanalysisusing

AxCent► Otherhelpfulfeaturesin

COMPAL/PUMPALAccumulate

designAuto

solveUsingdesignhelper:multipleinputparameterstooptimizeasingleoutput

parameterUsingoverlayview(formultipledataruns

only)1.19

模化48► 模化前后保持恒定的变量:流量系数扬程系数► 离心叶轮模化公式：从方案b到方案a:几何尺寸:

Da

=

Db*SF转速:

Na

=

Nb/SF流量:

Ma

=

Mb*SF*SFSF

为模化系数► Next

step?AgilelinktoAxCentfordetailed

designAxCentwillgenerate3Dgeometryfrommeanline

design1.20

设计模式和分析模式回顾49► 分析模式给定几何尺寸预测整机、

单级或者某一零件的性能计算每个零件进出口的速度► 设计模式给定运行参数，确定布局在运行参数和约束条件下计算出几何尺寸1.21

数据处理模式50► 使用测试数据或者CFD数据校准模型参数► 使计算结果和测试结果吻合► 叶轮数据处理扩散比滑移系数和落后角回流损失进口堵塞► 扩压器/导叶数据处理► 出口处理1.21.1

多点模式下的数据处理► Needtobe“MultipleData”

mode► InputdataarestoredinaLAB

file511.21.2

从数据处理模式到分析模式► 手动转换► 手动调整模型参数►

为使分析模式的计算曲线和测试曲线尽可能地吻合，模型参数需要多次调整52二、AxCent

三维详细设计53► 多级泵详细设计► 三维造型► 流动分析离线曲率法（单流管、多流管计算）一键式CFD计算► 结构和应力分析2.1

AxCent

概述542.2

AxCent

菜单► Menu

system:Flow:fluidloadingcalculationand

analysisGeometry:bladegeometrydefinitionand

editingCFD:PushbuttonCFD®settings,preprocessorandpostprocessorMechanical:PushbuttonFEA,vibration,noise

analysisAgile:linkstootherAgileEngineeringDesignSystemprograms552.2.1

AxCent

菜单_File► 导入/导出:562.2.1

AxCent

菜单_File► 导入/导出:第三方软件读取格式572.2.2

AxCent

菜单_Edit► 编辑/修改控制曲线:子午面型线包角/安放角分布曲线厚度分布曲线► 返回到文件最初打开时的状态582.2.3

AxCent

菜单_View► 选择部件（叶轮/导叶）► 选择流面（前盖板/后盖板）► 选择X坐标变量（流线/轴向长度/半径/包角）► 对比显示► 有限元计算592.2.4

AxCent

菜单_Setup► 增加/删减部件► 修改端点坐标602.2.4

AxCent

菜单_Setup► 端点斜率/曲率控制2019-08-13612.2.4

AxCent

菜单_Setup► 克隆部件2019-08-13622.2.4

AxCent

菜单_Setup► 修改/编辑蜗壳参数2019-08-13632.2.5AxCent

菜单_Flow► 载荷分布:展向周向► 多流管计算结果2019-08-13642.2.6

AxCent

菜单_Geometry► 编辑前/后盖板型线► 选择控制曲线类型贝塞尔曲线样条曲线直线（双）圆弧直线多段线端点斜率/曲率控制贝塞尔曲线► 编辑/修改准正交线:► 间隙设置2019-08-13652.2.6

AxCent

菜单_Geometry► 编辑安放角分布曲线► 编辑包角分布曲线► 编辑叶片倾角分布曲线► 选择叶片生成方式直纹面自由曲面柱坐标下的轴流叶片► 修改叶片起始包角► 编辑叶片转角2019-08-13662.2.6

AxCent

菜单_Geometry► 选择/调节中间流面厚度变化规律► 沿流线方向厚度变化规律等比例缩放2019-08-13672.2.6

AxCent

菜单_Geometry► 手动调节轴流翼型控制点分布2019-08-13682.2.6

AxCent

菜单_Geometry► 直纹面Bowed2019-08-13692.2.6

AxCent

菜单_Geometry► 选择进口/出口积叠► 调节积叠线轴向/周向分布2019-08-13702.2.6

AxCent

菜单_Geometry► 选择进/出口边形状► 设置间隙2019-08-13712.2.6

AxCent

菜单_Geometry► 前/后盖板型线轴向/径向偏移/拉伸► 镜像► 改变旋转方向► 导入安放角/厚度分布曲线2019-08-13722.2.6

AxCent

菜单_Geometry► 添加副叶片起始准正交线厚度分布安放角分布2019-08-13732.2.6

AxCent

菜单_Geometry► 切割进/出口边2019-08-13742.2.6

AxCent

菜单_Geometry► 流量切割► 扬程切割2019-08-13752.2.7

AxCent

菜单_Standard

Screens► 软件自带界面► 创建界面► 蜗壳编辑界面2019-08-13762.2.8

AxCent

菜单_CFD► 网格► 边界► 计算模型等► 后处理► 第三方软件接口2019-08-13772.2.9

AxCent

菜单_Mechanical► 网格► 边界► 后处理► 第三方软件接口2019-08-13782.2.10AxCent

菜单_Agile► 一维模式接口► Python功能扩展2019-08-13792.3

AxCent

颜色含义► 橙色：动叶► 绿色：静叶► 浅蓝色：不含叶片► 含叶片部件上的黑线：进出口扫掠线、积叠线、流量切割线等► 含叶片部件上的绿线：进出口边2019-08-13802.4

AxCent

对比显示2019-08-1381► 二维窗口和三维窗口都可显示► 几何尺寸和流动计算结果都可显示2.5

AxCent

标准界面► 软件自带的界面► 用户创建界面2019-08-13822.6

AxCent

叶片造型方式► 轴流叶片:

积叠各截面► 离心叶片：中弧线加厚度2019-08-13832.6

AxCent

叶片造型方式► 轴流叶片:

压力面、吸力面、进出口边► 通过

Python®

输入自己的造型方法2019-08-13842019-08-13852.6

AxCent

叶片造型方式► 1-independenthuband

shroud► 3-explicitshroud,radialinlet,exit

rake► 4-fully

radial► 5-2DwheelwithBezierbeta

distribution► 6-2Dwheelwithstraightorcirculararc

blades► NACA65airfoil

blades► CETI

(patented)► Arbitrarynumberofmid-spansectionsandstacking

curve► Specifyshroudandlean

angle► Useaseparatebladegenerating

sheet► UsebladesectionsdefinedinZ,RTheta(axialblades

only)► 2Dwedge

diffuser► Usethetainsteadofbeta

curves2.6

AxCent

叶片造型方式2019-08-1386► Independenthubandshroud

(default)前后盖板型线分别定义根据准正交线生成叶片需要考虑加工因素► Explicitshroud,radialinlet,exit

rakeShroudβisauser-specified

curveRadialinletuptouser-specifiedzvalue

(zrad)HubβiscalculatedbyAxCenttomatchthe

following:√Continuousβanddβ/dmatz=

zrad√User-specifiedrake(exitlean

angle)√User-specifiedexit

β2.6

AxCent

叶片造型方式► Fullyradial

bladingUsedforradialinflowturbines,canbeusedfor

compressorsAtanyzlocation,θis

constantUserspecifiesβdistributiononcylinderatmaximumradiusofimpeller;βisprojectedontohubandshroudusingconstanttanβ

/(rcosφ)Bladegeneratinglinesareconstantz

linesUsercanspecifyazlocation(zrad)forthestartofβ=0blading2019-08-13872.6

AxCent

叶片造型方式► 2DwheelwithBezier

betadistributionNoinducer,canbemanufacturedonthree-axismillsOnanyconstantr

cylinder,θis

constantUserspecifiesβdistributiononaconstantzplane,bisprojectedontohubandshroudusingconstant

tanβ/(rsin(φ))Bladegeneratinglinesareconstantr

lines2019-08-13882.6

AxCent

叶片造型方式2019-08-1389► 2DwheelwithBezierbeta

distributionNoinducer,canbemanufacturedonthree-axis

mills► 2Dbladingwithstraightlineorcirculararc

bladesBladesarestraightlinesorcircular

arcsUserentersexitbandradiusof

curvature► NACA65airfoil

blades► CETI

(patented)PatentedmodificationofNACA65profilestodefineairfoildiffuser

vanes2.6

AxCent

叶片造型方式2019-08-1390► Arbitrarynumberofmid-spansectionsand

stackingcurve中间截面数量不受限制每一个截面有独立的流线、beta线和厚度分布曲线进口积叠线控制每一个截面在周向的起始位置积叠后各截面生成自由曲面2.6

AxCent

叶片造型方式2019-08-1391► Specifyshroudbladeangle(β)andlean

angleAxCentcalculatesthehubblade-angledistribution

automatically► Use

blade

sections

defined

in

Z

、

R

、

Theta

(axialblades

only)Definesthepressureandsuctionsurfacesofthe

bladeCanbeusedONLYforaxial

bladingNotautomaticallyfittedtothecurrentsegment

boundariesPossiblesectiontypesinclude:DCA,MCA,Bezier,NACA,modifiedPritchard,simpleairfoil,andconstant

passagePossibletoeditbladeangleandthicknessdistributiondirectly,liketheradial-type

blade► 2DWedge

Diffuser2.7

一维、三维相互转换注意事项2019-08-1392► 一维模式下的几何尺寸和流动信息可以准确传递到三维模式► 三维模式下关键尺寸改变后需要返回一维模式重新预估性能，检查运行范围等► 确保没有数据丢失2.8

AxCent

修改设计布局2019-08-1393► Add/insertnew

segment(s)► Copysegment(s)fromexisting

design► Bringin

modelReusegeometry

featuresCombineusefulgeometryfeaturesfromdifferent

designs► ShiftdesigninZ/R

direction► StretchinZ/R

direction► Mirroring► Flipdirectionof

rotation► Flipbladeangle

direction► Scaledesign(pure

geometry)2.8.1

分割、合并零部件2019-08-1394► Combinetwo

segments► Splita

segment► Movetheboundary

betweentwosegmentswithoutchangingtheoverallshapeoftheflow

path2.8.2

叶片切割► 由进出口扫掠线切割直纹面叶片► Dotsonthegeometryplotsgivetheusera

referencepointtodeterminecriticalvaluesontheactualLE/TE2019-08-13952.8.3

编辑副叶片► 根据准正交线确定起始位置► 可以单独控制厚度和安放角分布规律2019-08-13962.8.4

叶片展向bowed2019-08-1397► Definehub-to-shroudbowedbladingatuser-specified

locationsalong

blade2.8.5

叶尖间隙► Fivewaystospecifytip

clearance► 指定间隙值:等间隙从进口到出口间隙值线性变化► Specifytosetthetip

clearancegapusingacontrol

curve► Specifytosetthetip

clearancegapusinga

contour2019-08-13983

蜗壳三维设计2019-08-1399► Supportbothupstreamanddownstream

volute► Fourvolutetypes

available:Turbocharger

(overhung)Pump

(symmetric)Asymmetric:circulararcsandlines-basedcross

sectionAdvanced:Beziercurve-basedcross

section► Keyoverallgeometry

parameters► Editabletongue

geometry► Editablewrappipe

geometry► Editableexitdiffuser

geometry3

蜗壳三维设计2019-08-13100► Supportbothupstreamanddownstream

volute► Fourvolutetypes

available:Turbocharger

(overhung)Pump

(symmetric)Asymmetric:circulararcsandlines-basedcross

sectionAdvanced:Beziercurve-basedcross

section► Keyoverallgeometry

parameters► Editabletongue

geometry► Editablewrappipe

geometry► Editableexitdiffuser

geometry3

蜗壳三维设计► Fourvolutetypes

available:· Turbocharger

(overhung)2019-08-131013.1

蜗壳设计界面► Anewstandardscreen:voluteviewsavailableforusertoquicklyaccesskeygeometry

parameters► Tonguegeometry

plot► Axial

view► Area

plot2019-08-131023.2

截面非对称蜗壳► Editthroughlinelengthandcirculararc

table► Editshapeusingcontrol

points► Easycircularprofile

control2019-08-131033.3

D型非对称蜗壳2019-08-131043.4

截面多点控制的蜗壳► Bezier-curve

based► Editusing

controlpoints► Canbesetto

besymmetric2019-08-131053.5

蜗壳截面面积调节灵活2019-08-131063.6

蜗壳扩散段设计► Editpipe

cross-sectionshape:Ellipse

ratioTransition

control► Axis

shape:Straight

lineCurvecontrolledby3points► Exit

direction:Inplane(R-Theta

plane)Outofplane(R-Z

plane)2019-08-131073.7

蜗壳包角调节2019-08-131083.8

蜗壳扩散段轴向偏移► Newoptiontoshifttheexitpipeofthevoluteintheaxial

directionReducesinterferenceregion

betweenthescrollandexit

pipeAvailableforasymmetric

andturbochargervolute

types2019-08-131093.9

蜗壳隔舌设计2019-08-13110► LE

radius► LEellipseaspect

ratio► LEscallop

ratio► Usingcontrol

points2019-08-131113.10

调节蜗壳进口宽度3.11

双出口蜗壳► Independently-editableareascheduleanddiffuser

shapes► Non-symmetricoptionfordifferentflowratesfromeachpipe► Availableforpumpand“advanced”

volutetypes2019-08-131123.12

蜗壳隔板设计2019-08-131133.13

生成实体蜗壳2019-08-131143.13

生成实体蜗壳► 不等厚度加厚► 生成法兰和圆角2019-08-131154

流线曲率法2019-08-13116► Fluiddynamicloading

calculationFundamentallyinviscid

approachesIsentropicprimary

zoneTwo-zonemodel,withpossibilityofoverallloss

imposedQuasi-three-dimensionalSubsonicflows

only► Rapidloading(single-streamtube,

SST)Frazer,Howard,and

LennoxSingle

streamtubeInstantaneous

feedback► Multi-streamtube

(MST)KatzanisMultiple

streamtubesSolvesavelocitygradientequationalong

quasi-orthogonal4.1

输运方程2019-08-131174.2

流线曲率法原理► Velocitygradientequation

(forceequilibrium)► Continuityequation► Solve

forvelocity► Reverse

curvefittingtofindnewstreamlines2019-08-131184.3

单流管计算2019-08-13119► Themeanmeridionalcomponentofvelocity

iscalculatedfromthecontinuity

equation► Themeanrelativevelocity,W,iscalculated

usingtheflowdirectiononthemean

streamline► Theshroudandhubrelativevelocitiesaredeterminedbycalculatingthevelocitygradientnormaltomeanstreamlineattheintersectionof

thelocal

quasi-orthogonal►Theblade-to-bladevelocitygradientisgeneratedattheshroudandhubbycomputingtheblade

loadingtermatthese

locations4.3

单流管计算2019-08-13120► Themeridionalposition,m,atwhichthevaluesofWsuctionandWpressureoccur,iscalculatedbytracingthenormalstothepassagecenterlineto

findtheirintersectionwiththesuctionandpressuresurfacesofthe

passage► The

flow

direction,

isgenerallychosen

asthepassage

directionHowever

thetwo-zonemodelrequiresthatasecondaryzonebuildsupalongthesuctionsurface

modifyingtheeffectivemean

angle

Atthesametime,themassflowisreducedintheprimaryzone4.4

多流管计算2019-08-13121► Calculationsperformedinfifteensecondstotwominutes,dependingonnumberofstreamlines

andquasi-orthogonals► MSTcanbeperformedinoneormore

segments► MSTcalculationsareindependentlycarriedout

ineachsegment(withextendedquasi-orthogonalsused)► Optionsfornumberofstreamlinesandnumberofquasi-orthogonalsaddedupstreamand

downstream► Optionalinputofcontrolparametersto

avoidnumerical

instabilities4.5

多流管计算设置2019-08-13122► 1.Numberof

streamlinesDefault=7,Maximum#=13,Minimum#=

3► 2.Numberof

Quasi-Orthogonals,Defaults=3(upstream),2

(downstream)Nomaximumlimit,suggestedminimum=

4► 3.Maximumnumberof

iterationsDefault=15,nomaximumlimit,suggestedminimum=

25Forcontinuousmulti-segmentelements=

100–2004.5

多流管计算设置2019-08-13123► 4.Maximumnumberof

divergencesAllowsspecifiednumberoftotalstreamlineshiftincreases,default=

4,

no maximumlimit,forcontinuousmulti-segmentelementsneed

25–50► 5.Massflowaccuracy

(prop)Usedinsatisfyingcontinuityequationatmean

streamlineDefault=0.0005,suggestmaximumvalueof

0.0014.5

多流管计算设置2019-08-13124► 6.Dampingfactor

(damping)DampssubsequentstreamlineshiftstoensurenumericalstabilityDefault=0.15(suggested

value)Forcontinuousmulti-segmentelementuse0.10-

0.05Suggestminimum=0.1(needmoreiterationsforgoodaccuracy),largevalueswillleadtonumerical

instabilities►