solid flow and orifice plate and flow nozzle -ali fahem

Orifice Plate and Flow Nozzle

Otriectives

creati'g the soiidworks part for the orifice plateSetting up Flow Simulation projects for internal flowInserting boundary conditionsCreating point goals

Running the calculations

lJsing cut plots, XY plots and flow trajectories to visualize the resulti'g flow fieldsDetermine discharge coefficients for orifice plate and flow nozzle

Problem Description

We will use Flow Simulation to study the flow through an orifice plate and a long radius flownozzle' obstrl"rction flow meters are comfiIonly in use to rneasure flow rates i' pipes. Both theorificc and nozzle are modeled insicle a pipe with an inner diameter of 50 mm and a le'gth of Im' water in the pipe flows with a mean velocity of I m/s corresponding to a Reynolds number fte:50'000' The opening in the orifice is 20 mm in diameter. The long radius nozzle has a length of33'5 mm and the opening is 2l mm in diameter. we will study how the centerline velocity variesalong the length of the pipe for both cases and plot both pressure and velocity fields. Thedischarge coefficients will be determined and compared with experimental values.

i

I

i

Figure 10.0a) SolidWorks model of orifice plate

a

a

a

c

a

a

o

I

f't.!t

Figure I 0.0b) SolidWorks mode I of nozzle


Creating the Orifice Plate in a Pipe

1. Start by creating a new part in SolidWorks: select File>>New, select Part and click on the OKbutton in the New SolidWorks Document window. Click on Front Plane in the

FeatureManager design tree and select Front from the View Orientation drop down menu in

.. i ,___-_._r /r ; 1ts, !\t tl ._

+ ;1 ! Anrir:t*tir=ri*J - --{; I't$eriii inr,i ::f!Fi!iiF:j -

'.rl-:m,:_=,,., Tg,p F!.=rr*

:,'.:. Fli,lhl Fl,=rr=

J* ,_rr.i.Jlr,

Figure 10.la) Selection of front plane Figure l0.lb) Selection of fi'ont view

2. Click on Circle from the Sketch tools tab. Draw a circle with a 25.00mm radius. Close the

Circle dialog box by clicking on '''ir'

Figure 10.2a) Selecting the circle sketch tool

ir'i':tir

I

'fl

:J.E=

;= aJ+

i',:i.Jr,r, :i .,i.-r ir,: li;: :.r.. j-'i,_i l: ': ,i 1.- . .; ;_:: rPi ,i :i t.. i :

Cirrl*SF-slcF*= a rLrk, 5*leil the rerrtr,r rri lhecir**, th*n dr*g t* s*t ils r*dius,

Figure 10.2b) Sketch of a circle

il?=sa#€-+*= =+

*;, -


3' Select the Features tab and Extruded Boss/Base. set the Depth of the extrusion to 500.00mm inboth directions' check the Thin Feature box and enter a Thickness value of 5.00mm. check thecap ends box and enter 5.00 mm for the thickness. close the Boss-Extrude dialog box byclicking on OK t+$

.

Figure 10.3a) Selecting extruded boss/base feature

qF.#*t'-

;i;

s ._,' . _, .,,,"

g ifr [r.r**jg6 a*or.tur*

Et*trrded E*rrJB**eE,*Lril,J*c .l sk*trh *r. selait*d si.*tchcryfrtrjrs in *n* or tr** rjirsrtifins t,ltr*ate e +*ftd f**tir*"

Figure 10.3b) Settings for extrusion

il*a*€er =*

- S -

Orifice Flate and Flow Nozzle

4" Select Front view from View Orientation in the graphics winCow. Click on Front Flane in theFeaturemanager design tree and select Circle from the Sketch tools. Draw a circle with a 25

mm radius, see figure 10.4a). Close the Circle dialog box by clicking on OK *'' . Select theFeatures tab and Extruded Boss/Base. Set the Depth of the extmsion to 0.50mm in both

directions. Close the Boss-Extrude dialog box by clicking on OK

*dd*=**tasts

,lf rrx

*pt**n*

| ] Frt r.r,.lr r." ::i ':,

i P*f*r*fttEf=

. r.- ft t-tft_x

Direttian I

' * , Elind

t, f .,,

, ' :::' :

*'_f tr 1 rJ ,S[rrirrn

i{ I''!*-l,l= r+:i:i!

,lb r

[i] *:rrr*i** E

E!ind

*=+F; U,SUmrir

:= *- - fr. frfrY - _-

fa -,r nf,E -! a!r'ur-r

Figure 10.4a) Parameter settings for a circle Figure 10.4b) Settings fbr extrusion

5. Click on Front Plane in the Featuremanager design tree and select Circle frorn the Sketchtools. Draw a circle with a 10 mm radius, see figure 10.5a). Close the Circle dialog box by

clicking on OK ''' . Sclcct the Features tab and Extruded Cut. Set the Depth of the cut to

0.50mm in both directions. Click on the Draft L=t bl'r,,"n for Direction 2 and enter 45.00deg.

Check the Draft outward box, see figure 10.5b). Exit '":'" the cut-extrude window.

tdd Re**ticnq :-i

. E :ri*

@fbnsl-_i r,-', ' r ,r r{i * ril'r-r.

lli

Figure 10.5a) Circle parameters

-:\_=Ed:;J1q;:: E:-j r + r

Orifice Plate and Fiow Nozzle

:_-.!r, { ; ntin'i

..I: . :]:i

E1x::,: l

+fnf U,llrmn]

l

f_l =irr. =r,J*

lir rut

1E **gfggeElind

, tl, 5[trnrrr

*5, rlrJrJrq

f, [,r art *utr,'.,*;:J

Figure 10"5b) Directions setting for extrusion

6' select Left view f,rom view orientation in the graphics window. Select wireframe displaystyle fi'om the drop down lnenu in the graphics window. Select Zoomlpan/Rotate >>Zoam taArea and zoom in on the middle section of the pipe, right click in the graphics window and seiectzoamlPan/Rotate>>Rotate view. Rotate the view a little bit to get figure 10.6b). you have nowcompleted your orifice plate inside a pipe. Save the part as Orifice plate.

-'=

ffi

r=A I

LJJ

iln :

F.*-,.,tr

itu:

1*irrfr**:*i":;.:,i=t i ri. ; "r,{T., :-,r i!rF ll,r ,dgl

Figure 10.6a) Wireframe display style Figure 10.6b) Orifice plate

i'i:a*:er ii,:-5-


Settins up the Flow Simulation Proiect for the Orifice Plate

7" If Flow Simulation is not available in the menu, you have to add it fi'om SolidWorks menu:

Toolp>Add Ins... and check the conesponding SolidWorks Flow Simulation box. Setrect

Flow Simulation>>Project>>Wizard to create a new Flow Simulation project. Create a newfiguration named "Orifice Plate Study". Click on the Next > button. Select the default SI (m-kg-s) unit system and click on the Next> button once again. Use the defaunt trnternal Analysis type.Click on the Next > button.

Fr*irct

r -.--.'-,.ts

n.E

8.

Figure 10.7a) Starting a new Flow Sirnulation project

Figure 10.7b) Creating a name for the project

Add Water from Liquids as the Project Fluid. Click on the Next > button. Use the default WallConditions. Click on the Next > button. Use the default Initital Conditions. Click on the Next >

button. Set the Result resolution to 5. Check the box Manual specification of the rninirnumgap size and set the Minimum gap size: to 0"02 m. Check the box Manual specification of theminimum wall thickness and set Minimum wall thickness: to 0.001 m. This is done in order toresolve the opening of the orifice and the thickness of the orifice plate. Click on the Finishbutton.

Fkii#=

;fr Gnses

i:l Liquid*

' Anetane

:-. Ammonia

: Argon. Ethane

: fthanc,l, .. Ethl4ene

;' lulethane

h4ethqnol

hlrtrnqen

F*llr

Fre-Defined

Fre-Detined

Fre-Defin;d

PrE-[rElinEd

Fre-Definecl

Pre-Definrd

Fre'[lelined

Pre-Defin*d

Fre-Definer:i

Figure 10.8a) Adding air as the project fluid

ll"rnf iilr-ti,:irr ;r! **ii'!i

Fr-*j** Ft#d=

trr#*- i Li*i*,=:. j

il?:za;:la.*=^ e{a-4-


l.t*unllrrrr +ip *i:*

f, F,i*ri**l :{i*eiir**ti-rl"i *i ll:r i**tr-iiiirr-*-ri laF -+.f:r

I Flrtir,,rr,rni '].1!, :.ii* r*tet 1,3 tl,rr irtsrur* dtrrr*n.-r.:,r.r

l.lf rtffrt-llrr E,=Ir r:::Z*.

U.Uf nr

iil ri rr'ir-r*j l+,=ll ll clr:rl,r.:*:-- :,;

pl id,=r,il.t; =t,e*ritcalrr,ri *l lir= t-iin;rir+_:rrr r+*l! llrr,li.=rr*::;,

ill l=,!lrrrn:,-,r,r ++*il flir,:l.r"r+:-. rel*i: tr:r if ,r: i*.*1,lr* ,Jtreir:,l,fr,

Fl H't'rr,,.1,', rry.ill |ntl*l.rtf : ;

u.Llul nr

Figure l0'8b) Setting the result resolution, minimum gap size and minimum wall thickness

9' Select Left view from View Orientation in the graphics window. SelectzoomlPan/Rotate>>zoom to Area and zoom in on the left end of the pipe, right click in thegraphics window and sclecr ZoomlPan/Rotate>>Rotate view. Rotate the view a little bit, seefigure l0'9a)' click on the plus sign next to the Input Data folder in the FIow simulationanalysis tree' Right click on computational Domain and select Hide. Right click on HBoundary conditions and select Insert Boundary condition.... Right click on the end of thepipe and select select other. Select the irurer surface of the end cap. Select Inlet velocity in theType portion of the boundary condition window. Set the inlet velocity to I m/s and check the boxfor Fully developed flow, see figure 10.9a). click oK ar to exit the Boundary conditionwindow' Red arrows will appear showing the inlet velocity boundary conditio', see figure 10.9b)

{1.F*!;EitE.ti Zz.z *7 *


i iltii, ,:.rl_FEi -'.

inh,t l'l.rss Fl':r,\,

Inlel fr'lunrr Fl,:ru

,'f, ullet lt4s5s FIL-rrrr'

' ftullel: Uolurire Fl':r'\,t.l'utl et li'elucil:,;l

L' I ffrrts

ffi r*-:1t1. d*'.rei*i,*d ii*r.,,

Figure Figure 10.9b) Inlet velocity

10. Select Left view from View Orientation in the graphics window. Select

ZoomlPan/Rotate>zZoom to Area and zoom in on the right end of the pipe, right click in thegraphics window and select ZoomlPan/Rotate>>Rotate View. Rotate the view a litttre bit, see

figure 10.10a). Right click on E$ Boundary Conditions and select Insert BoundaryCondition.... Right click on the end of the pipe and setrect Select Other. Select the inner surface

of the pipe outflow cap. Select i;':' Pressure Openings in the Type poftion of the BoundaryCondition window. Select Static Pressure. Click OK 'r-" to exit the Boundary Conditionwindow.

Tutal Pressure

ii

t-

nfl10.9a) Selection of i ow boundary condition

t.Tk* crEdrF&fe ttr*F .tiirizs F;

r :is:i i 1..

Figure 10.10a) Selection of outflow boundary condition Figure l0.l0b) Static pressure

{. i=:apceE: E ii - Fi -

Orifice Plate and Nozzle

Insertins Goals

1 I " Right click on Goals in the Flow Sirnulation analysis tree and select Insert point Goals....

click on thc Poi't coordinates . --'

b.ttton and enter the coordi'ates as shown i' figurc 10.I I a).

check the static Pressure box as a point goal for the coordinate. click on the = Add pointbutton to add this point to the table. Add another point to the table of point goals and make surethat the static Pressure box is checked, see figure l0.l lb). click oK -,'" to exit the point Goalswindow.

,;r'}{lX r{

i: Unr

i l_l.UJl rn ^

'J 'lj,L-15 m*

Ftrsfiff.er .:.

Jr'urd';,ar r'; t"l,.r' j'. io,

i:il.,:iiL Fres;ur* EGLI

Figure 10. I I a) Selection of first point

trglrl* tts* f+r

Gs€l_tL

b) Selection of second point

';i I nr

'r Lr.UlE m

r U.Uil, ni

'F:*ii:retEr

:F=' E{It+!Fl

iit.rti': Fressure

Figure l0.l I

12' Select Flow Simulation>>solve>>Run to staft calculations. Click on the Run button i' the Runwindow.fr

Click on F-t Insert Goals Table to view the static pressure goals in a table. Click on .i":Insert Goals Plot to view a graph of the pressure goals. Click on the Add An button in theAddlRemove Goals window and click on the oK button to exit the window.

f'i -F, t

i.it+rir#::{

:f , irt,r: :-iil-,tFJi.. -

i.j. I i:Eii;irtll;it'-;.!+i fr{ii!'!.:j.! .

;ff lrrr,r FI*:i,(t*

!S : i*f!.-irrFn.--=1FJ. :

-i :_ 3i..rl,tri,-,: ::r.iin...,[ i.,1ri

:'*: r- i:r.,,_

Figure 1A )2a) Starting calculations Figure 10.12b) Run window

=ffs3f i:csiid++, c*b #ij-*i-f

:, l'i +.0,' i,=ii:.-:i+t,=r

i:=:r*ie= El: - !:


File {elrul*iior:=iir

i .sfgplafrirl

!,-'

Figure 10.12c) Inserting goals table

i:= ':: : '' " "

Figure 10.12d) Inserting goals graptr

Figure 10.12e) to the goals plot

1 :::

l_ ijf tl-:tll

.1 Eli.

Sbeolute $cale[Au{o MioAfio Maxl

iele*t g+a!:

*':+!\r F,ri Et;rti'_: Fre*er-tr* 1

.v F{_+ 51911a F',rEssutE f

I/Hl0{l r

', arru, l13300r i130000127006l2im0[1 2r 00111t00t11508[1 1200il10s08010600[10t00[1s1000gru00

s{00ss0ss5.2

Figure 10.120 Variation of static pressure goals before and after orifice plate

E*Eidi=.:E,{i :!-i h :=r


=-ig :,: i::: :::: il::!l:ai: :l:::::::::i:.: ::rl

ir{riy,sgt

I'lesh gener;l:i'-rn slartedh{*:h,leneralion nc,rrnellir,' FinishedFreparing data tc'r ralrul,llianfalculatir-rn startedilalrul;tirn has rnnuerged sint t,,,

EE.lls,rr* rOn,ier'ledrlaliulal:i':n Finish*d

fllrrirriurn Uair_:e : l'.lai;rn"iuni ,/alu* -_.*sEq::*iFG Slatir: prersure f :jt:iiir,EFl r-r:-i5'17,1FE i1li31[t,ilFa r--{f,I1-:i,i-t Fn

Figure 10.129) solver r.vincrow for orifice plate flow

lnserting Cut Plots

ti13' Right click on -{l{ cut Plots in the * Flow simulation analysis tree and :t:.Iy::l*

iSelect the Right Plane from the "'l'$- FeatureManager design tree. click on i -!Ii:4Et[., f

Slide the Number of colors: slide bar to 101. Sele ct z-component of velocity f,rom the

Parameter: dropdown menu. Click "r,

i-=-ijl--_=-J. Click oK ==i to exit the Cut plotwindow" Rename the cut plot to Z-velocity.

click on the Flow Simulation tab and the *it

Lighting butto' to apply lighting to thc c't plot.Select Left view from view orientation in the graphics window, see figure 10.l3b). Repeat thisstep but this time click o_n view Settings and select Pressure from the parameter: dropdown

mcnlr' click on i * fllt l . ctrrt oK '= to exit thc cut plot wi'dow, see figure r 0.l3c).Rename the cut plot to pressure.

*ruiFgiFi*.r.,' 5tr*rri*=Ir*:-i fjt=. , , -

Figure 10.13a) Lighting butron in Flow simuration

Il-*r*tiun= L.,,Jt r :

I Ir l4E: i;l E

lll{E,:{EI rli+El48I -1:48r541 lt :5:_r : ,:iE ;

1-+:5i-i:4f,i

I

q?

Flrglitrlgg

Fluid cell:Fartial cellsIlerationsLast iter,:lir:n iini, . ,

fFU lirne per la:L,,,Tra'rrl:;Iteralir'ns per I t, , ,

{pu tirri*t:Ehul,:linn lirrie l*il!ilatus

i'yi-or

l1+Il-ll t_-tt1"-i

t:-r

1i;51:lt,r_Lr_r:li0lrl4

1,IJrl45]Et:l :5:Sfill;tl:ISnlver is Finished,

-t=== =:{}:-:!-Jir i ji = !

=*.::{*;-:;_:}: E:: - ; :

Orifice Plate and Flow Nozzic

t- ii {.:+E:

-i-* * .!-fdr-r

- 1:'r._ ,' ; !{ t I

_ *i=?*5, r +L:i+

-- -q{ =

4

_ j :t'i**

=i: = ri € -'A'-= ?iL

ft .r ;.:.i..-.I .* +.I{:tr*rl*r;I ';f ?*l{'tr?*;

Figure 10.13b) Z-veloctty distribution before and after the orifice plate

1 i7451#FF.;::'''_

1 3t-li{l Ei

_ 1 141r5

_ 117835

* 111i!{4

_ 1tr4l5:1

- !Er'1i'.i

_ l.l1 FjIi

_ rt51il.4

,i;;=_ IESFI iffi* r'rntr r

Fre:r=ure [F a]

Figure 10.13c) Pressure distribution before and after the orifice plate

Determining Discharge Coefficient for Orifice Plate

14. From a rrlass balance and from Bernoulli equation we can derive an expression f,or the velocity at

the orifice 7o

where A,P - Pt -Pz is the pressure difference between the pressure F, before and P2 after the

orifice, p is the density of the fluid and B - d/D is the ratio of the orifice diameter d andtheinner pipe diameter D. Due to frictional effects and the vena contracta, we have to incorporate a

correction factor known as the discharge coefficient C6 in order to determine the volume flowrate V in the pipe

V = CaAoVo

where Ao is the area of the orifiee hole. The diseharge coefficient has been experimentailydetermined for orifiee flow meters as

7

(l)

(2)

2AP

pG-n

*ilE':g:::9.+i =i:

- E?


ca = 0'5959 + 0.0312p2't - o-Ll4p' + gL.7+"*+ 0.09.4 # - 0.0gzrB p3 (3)

where the Reynolds number Re = vtD /v is based on the approach velocity vland,kinematicviscosity v of the fluid. The constants A and B arezero for corner taps (pipe wall taps, one oneach side adjacent to the orifice plate) that have the value s A:0.4333 and -B :0.47 for pipe walltaps located the distance D upstream from the orifice and Dl2 downstrearn. Equatio' (3) is validin the region 104 < Re 1I0r,0.ZS < p < 0.T5.

0.635

cD

0.63

0.625

0.62

0.615

0.61

0.605

0.6

100000 Re 1000000 10000000

Figure l0'l4a) Discharge coefficient versus Reynolds number for three differe't p ratios, pipewall taps located distance D upstream and Dl2 dowrastream from orifice plate

The diameter ratio B :20mm/50mm :0.4 in the Flow Simulation calculations and the Reynoldsnumber is

Re=ry=ffi=5o,ooo(4)

The pressure difference can be determined from data in figure 10.12g)as Ap = I37,1.04 pa -93'310'9 = 43,793-1' Pa. The discharge coefficient from Flow Simulation is

{i=ap:er }S - i3 -


/- v Atvt.-6--=-u AoVo Ao

p(1-F4) -

v7

zAP P2

eegkg /m3(7-0.44) _ 0.6592.43,793.1Pa

(s)

The corresponding value from experiments, equation (3), is 0.603, a 9 o/o difference.

We would now like to see the velocity and pressure variation along the pipe. Click on the

Featuremanager design tree tab and select the Right Plane. Select Line from the Sketch tools.

Draw a horizontal 990.00 mm long line along the pipe wall, see figure 10.14b). Exit the LineProperties window and the Insert Line window. Rename the sketch and call it ooWall". Click on

FRu Rebuild from the SolidWorks rnenu. Repeat this step and sketch another horizontal line with

the same length along the centerline of the pipe, see figure 10.14c) and name the sketch"Centerline".

Fr. E!..*t #*, - - - --i'..' j'-JLl.UU

l:, tfrj.tli.r'

Figure l0.l4b) Drawing of a

F-a+s:lfil-l!

+ ;ffili: lfiu,rrr-'c

Figure 10.14c) Drawing of a

horizontal lines along the pipe wall

horizontal lines along the pipe centerline

Inserting XY Plots

Click on the Flow Simulation analysis tree tab and right click on XY Plots and select Insert....Click on the Featuremanager design tree tab and select the sketch named "Centerline". Choose

Model Zfromthe Abscissa: drop down menu. Check the Velocity box in the Parametersportion of the XY Plot window. Slide the Resolution to the maximum value and set the number

of evenly distributed output points to 200. Open the Options portion of the XY Ptot window and

select the template xy-plots.xlt, see figure 10.14d). Exit the XY PIot. An Excel file will open.

The maximum velocity along the centerline is around eight times higher than the approachvelocity, see figure 10.14e). Rename the XY Plot to in the Florv Simulation analysis tree toVelocity along Centerline. Repeat this step but select the sketch named "\l'all" and check the

box for Pressure. Rename the XY Plot to Pressure along \\'all. \\/e can see in figure l0.l4f) thatthere is a partial recovery in pressure after the orifice.

*l.lFr;e;:er,.r j ile - tc *


kg*i5q;.., ..: ...: :: ..:,:. ..i.,. ...,.,. e. ;#_d_*'---* -'+tl *j_l e++SE. H='t r rt::;-:1 !!.fq{+.Fq.*4rJrf] F;;;ii E-r"':*f,'

I A*'i ' -"- -"' a

:; !."'"-F-*F-." ;.

r t lI .:"-&A*F=^.

a L*+

,t _f#.Fi i'.:*"r-irt r ;*l :.;*r.

: l F=L+! e'e ;'* +- ci ,: i"-" !.- + _+ i i,

;i.ier flfr J"ai*+ i-! Lid fF-f,:

* r irF inz.

fl''= r ; __E*** ;i+-l'i,*;+.::

ilin*lerto+."d*-vkps": I

*J r,'^f*-{s iQ-0.5 -0.3 -0.1 0.1

ry,a.,

Figure 10.14d) Settings for Xy plot Figure 10.14e) Velocity along the centerline

-0.6 -0.4 -0.2 o o.2 0.4 0.6ModelZ (m)

Figure 10.140 Pressure variation along the pipe wail

oM3oa"tz (,gf

Chapter l{} - 15 -


Creatinq Sketch for XY Plots

Next, we want to see the variation of the velocity profile at different positions upstream and

downstream of tlie orifice. Click on the Featuremanager design tree tab and select the RightPlane. Select Line from the Sketch tools. Draw vertical lines across the pipe at different model

positions Z: -50,50, 100, 150, 200mm. These positions are coffesponding to x : 50, -50, -I00, -150, and -200mm, see figure 10. 1 ag) for the first vertical trine at Z : -50rnm (x : 50mm). Exit the

Line Properties window when you have completed all five vertical lines, see figure 10.14h).

Name the sketch "Velocity profiles". Clict on F Rebuild from the SolidWorks menlr.

Fare*t€*ry-+ : :

jt_i_f Stt,Lrti

FE ,1l- qfi.tlrts

J+-Jd*ic**i P*r*n ret *r;,t_. !-,t Lt il Idt

,f-. -:5,fitlEF

f, Fn.r-ir-rF€

FJ= 35'fitl

_.alr I t:t,llLl

*,= FlJ,tifi

Figure 10.lag) First line across the pipe with local parameter values

Figure 10.14h) Five lines across the pipe for velocity profiles

Click on the Flow Simulation analysis tree tab and right click on XY Plots and select Insert....Click on the Featuremanager design tree tab and select the sketch "Velocity profiles". Choose

Model Y from the Abscissa: drop down menu. Check the 7-Component of Velocity box in the

Parameters portion of the XY Plot window. Slide the Resolution to the maximum value and set

the number of evenly distributed output points to 200. Open the Options portion of the XY Plotwindow and select the template xy-plots.xlt. Exit the XY Plot. Rename the XY Plot to Z-veloeityProfiles. An Excel file will open, see figure 10.14i).

ilhaa-1-tter Ii; - iii -


th

E.

.t ,.-(JooI

Ni

-0.'03

Figure 10.14i) Velocity profiles atlevel 5 and refinernent of the mesh

-0.01 o 0.0L 0.03

different streamwise positions, results obtained for initial rneshis disabled

Flow Traiectories

Flow trajectories show the streamlines of the flow and we will now insert them for the orificeplate flow' Right click on the Pressure cut plot in the Flow Simulation analysis tree and selectHide' Right click on the z-velocity cttt plot in the Flow Simulation analysis tree and select Hide.Right click on FIow Trajectories in the Flow Sirnulation analysis tree and select Insert.... Go tothe FeatureManager design tree and click on the F'ront Plane. The front pla'e will now bc listedas the Reference: plane in the Flow Trajectories window. Set the Number of trajectories: to100' click on the view Settings..' button and select velocity from the parameter: drop downmenu' click on the oK button to exit the view Settings window. click on thc oK button to exitthe Flow Trajectories window.

+ 4;ri+r* s+39:a !.1..

- . r{ r i i

- iJ !':.E b i

- s:.*5 E*r a! 1'.-_ r i I ifi

,. I #Fj:!,* ;::

ai ++=*L+

+-,+l'1r,r.. t€;at. :,r-r ::t t'. !-.--iI

Figure 10.14j) Flow trajectories for orifice plate flow

i'4,-*-n-=. i,- i -:!.::<:i-!r!f, I r: - | ,


Running the Calculations for Lons Radius l\ozzle

15. Next, we will study the long radius flow nozzle meter. Open the fiie "Long Radius Nozzle".Select Flow Simulation>>Solve>>Run.... Check the Mesh box in the Run window and alsocheck New calculation in the same window. Click on the Run button. Insert cut plots of Z-velocity and pressure in the same way as was shown in step 13. The cut plots for the long radiusnozzle are shown in figures 10.15b) and 10.15c). Insert an XY-Plot of centerline velocity as wasshown in step 14, see figure 10.15e) for the result. Also, copy plot data and include centerlinevelocity for the orifice plate in the same graph. We see that the maximum velocity is 70 "/ohrgherfor the orifice plate as compared with the long radius nozzle.

Fil* i*kulati*rr 'rlieru Inl*r! il'iinduw H*lr'

:{:* ESFr=l:l

F

s, I''11=r*1tr

' t','l*rh gen*rafi,:n ttiti*':: I''tresh generel:i':n nornralll' Finishedi FreparinB dal,: t'-rr

':alculati'-rn, fahulalir-'n starl*d: 'lahulatinn h,:s r:r,n','erqr'l sinre 1,,,

' 6nals flrE r:LrrrverEEd

i-,:lrul,=tic'n Firrirh*d

it*raLiern;

r:r

lnr1[:tl tt+

L';l* ,i

1{:5I:5:r;itr{;5-1:14 i

l4:5:{i1E:,l4:5-:rrli r

15:[tr:3i i

l

l5:ttll:{4 :

F,93111*!=t

Fluid rell=

Fartial rxllEIteratinnrLast it*r,:Li':n Fini, , ,

CFU lirnr prr last,,,TrsuxlsIterali,:ns p*r I t,,,,IF u tinrerlahul':tinn tirnr leFt

5laLus

:;:i:',"r.JiJ. Iii--t I J.

1fl4

15:tlt-l::lfr-tD lillt : tl4

1,3r,-rr+i-iE

t-tlE:ilil: l.t : tl

5nl'rer is FiniEhed,

{urrenl: V.:lu*

_ ,ltizgn i_i= _ - :i,i+sr,rli_F,

Figure 10.l5a) Solver window for long radius nozzle calculation

Figure 10.15b) Z-velocrty distribution along long-radius flow nozzle

_ .{ :J*4=r

::::::: L*-: :;: :,:

=Jica+se=" -g+ - E& -

Orifice Plate and Flou, Nozzle

-l't I 844

I l:5534

: rr**:31 nC'.{ tr

: s44*lll_lj1*!J

I [ir_=ril*.:i

!{5;lii:

=;:e i 'J

Figure 10. 15c)

The discharge coefficient for the long radius nozzle is give'by

cd - 0.9975 - 6.53

,': Pi-lr.:-;t+ [F=i

Pressure distrib'tion arong long-radius flow nozzre

(6)

tcD

0.99

0.98

0.97

0.96

0.95

10000 100000 1000000 10000000Re

Figure l0' t 5d) Discharge coefficient versus Reynolds number for three different B ratios

The diameter ratio F :21mml50mm:0.42in the Flow Simulation calculations and the ReynoldsRe number is 50'000, see equation (a). The pressure difference can be determined from data infigure 10'15a) as AP - L1'1',2Lg Pa - 97,446.6 - L3,T52.4 pa.The discharge coefficient fromFlow Simulation is

cD-L063

The corresponding value from experiments, equation (6), is 0.g7g, a difference of g.6 %.

ggAkg /m3 (t-0.+Z+12.13752"4pa (7)

pRe

v A.v.

-=

f a-

Aovo Ao

il=:re=eei ;+ - =-G


-0.5 -0.3 -0.1 0.1 0.3

tn

E

E(.,oo

l,'lril-l.l

II

\

0.5

Model Z (m)

Figure 10.15e) A comparison of centerline velocity for orifice flow F = 0.4 (full line) and long-radius flow nozzle F : 0,42 (dashed line) at Re: 50,000

Reference

[1] White, F. M., Fluid Mechanics, 4th Edition, McGraw-Hill, 1999.

{lr*iepe*c' T-* - 2# -


Exercises

l ' change the mesh resolution in flow simulations and see how the mesh size affects thedischarge coefficient in comparison with experimental values for the orifice plate and longradius nozzle.

2' Determine the pressure difference between comer taps (where the orifice plate meets the pipewall)' determine the discharge coefficient using equation (5), and compare with equation (3)using values fot A: B : 0. The thickness of the orifice is I mrn. Use coordi'ates (*,y,r) :(0,0.025,0.00r ) rn and (0,0.025,-0.001) m for conler taps.

3' use Solidworks Flow Simulation to detennine the discharge coefficient for differentReynolds numbers and compare in graphs with figure l0.l4a) for the orifice plate and figure10' l5d) for the long-radius nozzle. use Re : 10,000; 25,000; 50,000, and 100,000. plotgraphs including both SolidWorks and experimental data in the sarne graphs.

4' use SolidWorks Flow Simulation to keep the Reynolds number constant at Re:50,000 anddetermine the discharge coefficient for different B ratios and compare with figure 10.14a) forthe orifice plate and figure 10.15d) for the long-radius nozzle.Use f : 0.3, 0.4,0.s,0.6, and0'7' Remember to change the minimum gap size for each case. plot graphs including bothSolidworks and experimentar datain the salne graphs.

ili=a::rei I* - 2;


Notes:

solid flow and orifice plate and flow nozzle -ali fahem

Documents

featuremanager

minimum gap

box manual

extrude dialog

static pressure

minimum wall

circle dialog

static pressure