M'PENDIX Do MATI.u1B M·FILES

% This io called internally bv make_opsom%function [D]=d_oper(n,etahat,muhat):k=n+4:etahat=otahat(l:k,l:k):muhat=muhat(l:lt,l:k) :D=etahat*(etahat*muhat-eye(k,k»*muhat~2:0=0(1 :n,l :n) :

D.5.6 makeus om

%% makeuo conotructs the polynomjoal ohift matricoo :forU and U 0 L%% [poly .•U,poly_T.u]"makeuo(n,U,Ll) j%% The l'eoulto of thio function lre panccd 0.0 argumonno to ooxl.m%function [poly_U,poly_LU]=makouo(n,U,L1)jk"nj[x,y]=oizt3(U):U(k)=O:poly_U=polyr(k,U):poly_LU=polyr(k,U*Ll):

D.u.7 bc .n

%Y. function (bc_o]=bc (n , eto.hat)'/.function [a]=bc(n,otahnt)amzoroo(n,n);otahatuotahnt(1:n,1:n)i~l~chobvoc(l,n);vO=chebv9c(O,n):bi"vO;b'2"'vlib3.:s(otnhat) *vO;b4'" (otnhat) *vl;bS-(otnho.t.~:)*vO:0.(: ,l)tJb2 in.(:,2)cb4j

% phi(O)"'O% phi(l)cO% 0 phi(O)=O% D phi (1)

i\PPBNDIX D, MNl'LAlJ ,'I-FILES

D.5.3 lLoper .m

%% Ll_OPER calculates the oporator L=D~2-1/r,D for the Sexl% equation, ill the transforrr,ad domain,%% This function is called internally by make_ops,m%'/.[L1J=l1_opor(n, otahat ,muhat) ;'/.function [Ll]cll_oper(n.etahat,muhat);k==n+4jotahat"'etaltat(1:k.l: k) jmuht'.t=muhat(1: It, 1:k) ;Ll"'otaha'~*(otahat*muhat+3*oye (k, It)) , , ,

*muhat"2jLl=Ll(l:n,l:n);

D.5.4 12_opor,m

'/.'/.L2_0PER calcul~cos the operator L"2=(D"2-1/r,D)"2 for the Sexl% oqul).tion,in tl10 transformed domain,%'/,Thio function is called internally by make_opo,m%'/.[L2]=12_opor(n,etahat,muhat)i'/.function CL2]=12_opor(n,otahat,muhat)jk"'I1+4jetaho:t:..otahat (1:k ,1:k) imuhat=muhat(1:1t.l:k) j

L2~otahat*( etnhnt"3*muhat"3+6*otahat "2*muhat "2+3>t

APl'BNDIX D. MATLMJ !lI·PILES

% shift right 2 places%%%%%%%%%%%'1.'1.'1.%%%%%%'1.%'1.%'1.'1.%%%%%%%%%%'1.%%%%%% preform eigenvalue calculation %%%'I.%'I.'I.%%'I.%%%'I.%'I.%%%%%%'I.%%%%'I.%%%~%%%%%%%%%%%

CAA,BB,Q,Z,VJ=qz(A,13)jAA=diag(AA)jBB=diag(BB) jI::::find(BB"=O)jAA=AA(I)iBB=BB(I)jV=V(J, :) iC;::,M./BBj[Y •IJ "'flort(imag(C)) j[r.,y]=size(I) ;J:"'I(l:x-j,,:)jeigval=C(I)jeigvoc"'V(:,J.)j

D.5.2 ma.ltG.ops.1n

'I.% mako_ops constructs tho oporo.tors L, L~2,mu,ota,lnu"3,p%% [Ll,L2,muhat,otahat,M,D]=mako_ops(n)j%'I. Thoso oporators are passod as arguments to sexl.m%:function [L1,L2,muhat,otahat,M,DJ=mako_ops(n)jIt"'n+20jmuhat=makomuhat (k) jetaho.t..makeetaho.t (It) jM-muho,t'"3 jL1",ll_opel'(n,etahat,muhat) jL2=12_opor (n ,otahat ,muhat) jnlt'ld_oper(n,otahat,muhat) jj'Jl",r.l(l:n,l:n)jL2=L2 (1m, 1:n) jn"'n(1 :n ,1 :n) jM=M(l:n,l:n)j

551

Al'I'BNDIX D, MAT1.AIJ M·FII.BS Gl'jO

rvur=poly2d(V,rur.C.Cinv)iend;N~ruux(: .1:n)*Ipluoint+rvur(: .1m) i

D.5 The Sox! stability equation

'l'lWH(1 1\1'(' t11('Matlah Iuuctlous and H('l'iptH l1H(I(1 t () caleulato t lJ(l Ht ahil! ty p1'Op·(lrtll'14of pipe wlodty profiles. Tho muin Iunctlou is ooxl, m, which «vnluntos (hI'Hll\hility of It HllJlllJi!'(1 wlol'ity prufllo, B!'f!ll'(' ('ulliug thiH function tIll' Iuncrtousmake.cpu .m nud makoua .m Ill\lst l){' invoked to Hllpply tlH' ('Ol'l'P('t lll'glllllPutH (0ooxl.tn,Two higJt('1' I(lwh; of Iunctiou wldc'lt Ilfoi(' ocxl .m art' HII[lpli('d, uumclv findro .mand gotnooo, m: Tho Iormor linds, fhr II parti0.m1111(1makeus .m. Th« Iunerloumukcuu.m tHill'lLill turn \)(1 HUJlpli(I(1 with It v(liol'ity prolll«, giwll H:-la row \'(I('lorof CIH'hYI11H'v ('()(IIIit

ml=makomuhat(n+2);cml"'ohml;c:l"collder(m)i% cl=ding(onoo(n-l,l) ,l)-diag(onoo(n-l,l) ,-1);% c1=c1/(~*(n-l»);Iint=oyc(n~2,n+2)-4 .*intmat(n+2)*vec*ml;ol"'ol(l:n,l:n)jo2r::e:G(1:n,l:n):ml;.;m1(1:n,l:n);eml=em1(1:n,l:n);rint=Iin~(l:n,"n)j

D.4.7 nonlini. m

1.1. nonlini c:o.lculo.teothe valueo of the non-linear tcrmo% for the integral fo~mulation.%Yo [N]=nonlini(n,U,V,otal,muOl,ctalmul,coll,Ipluoint{,C,Cinv})jYo

% n 10 tho crdor, and U,V are the matricoo of axial, radinl% velociUeo reopoctivcly. otal, o'tnlmul, coll, IpluointYo nro tho cencuane matricoo gonerated Ly tho £uncdo.\% mo.kcmatint.mYo

:function (N]-nonlini(n,U,V,otal,muOl,ota1mul.voll,Ipluoint, ..•C,Cinv);

%,; calculato tho te\'m r.u.u_x ..."1.ru..U*muOl;u_x-coll*Ujif (nargin=.8),

ruuxnpoly2d(ru,u_x);01013,

ruux=poly2d (ru,u_x, C.Cim') jcnd;%% Now tho term r.v.u_r ...Yorur",U*otn.1muliif (nnrginOQ8),

rvurcpoly2d(V,rur)j0100,

Al'J>BNDIX]) AIATLAB AI-FIDES

D.4.4 kopint.m

%% kopint dotormines tho C011Gto.nt Inatrix% KcooInoga.r% for tho RHS of the equation%% (K]"'ltopint(m,n,omega);%function [K)okopinc(m,n,omegu);muOl"makomuho.t(n);Ke.:zzoroo(m,n);K(:,l)aonoo(m,l)*omoga/2jK(:,2)Qonoo(m.t)~omoga/2:

D.4.5 linopiat.m

'/.% linopint calculatoo tho linear oporator:% -omcga.r-S+D+rDft2%% function [L]=l:'1opint(n,omoga):%function [L]~linopint(n,omogo.);muOl·lnakolnuhat(n):otal·maltootnhat(n);It_O''zcroo(l,n):It_O(l,l)-2:S·onoo(n,l)*R_O;L= -omoga .*muOl -eto.hS*mu01 + oto.l + otnl"'2*muOl:

D.4.0 makematd .m

%% mo.ltomo.tigonora'coo tho c;onotant matricl)o otal, otn2, otalmul,% coll, and Ipluoin'h for uno by the ocl'ipt,%% [otul, ota.2,muOl, otalmul, coli, Iplusint] cmo.Jtomo.ti(n,m) j%function [ol,02,ml,oml,cl,Iint]omo.ltomatl(n,m):vocczoroo(l,n+2)jvot:(l).,l;olomukootahn~(n+2):02001"2;

APPENDIX D, Mr1TLAI hI·FILES

diop(malt~milx(abn(diff (hulf+l :m, :»») ;urocoef2pto(u,C,Cinv);dr=coef2pto(diff,C,Cinv);ur=ur(:,1:6:3*n/2);dr=dr(:,1:6:3*n/2);Durf(Yplot,Xplot,dr,ur);view( (50,30J) ;drawnow;totartccputime;

end;end;

D.4.2 contint.m

%% contint roturnD tho radial velocity, V, whon paDDed% the axial velocity, U. T.no mo.triceo RHS and coll arc% gonero.tod by tho function CONTMATI.M%% CV)-contint(U,RHS,co11)j%function [V]acontint(U,RHS,coll);V"-coll*U*RHSj

D.4.3 contmati.m

'I.% contmati gonorateD tho conoto.nt matricoo lleeded by contint%% [RHS]=contmati(n,m);%:function [HilS) "'con'tmo.ti(n,m) ;Inul"'makemuho.t(n) iotnl=makootahn:c (n);divioor"(ota1*muHeyo(n»*rnu(n)~2jdivioor(:,l)=chebvoc(l,n);divioor(:,2)cchebvoc(0,n)j[l,u]=lu(divioor);RHS=mul*mu(n)~2*inv(u)*inv(1);

APPENDIX D. AlflTI,AB AI·FILBS

u(: ,1:n)=R*inv._N;if (tN",1) ,

u(l,:)cu_p(l,:); % the inlet Beond;v(:.l:n)=contint(u,RHS,coll)iv(l,:)=zeros(l,n);if (dt(dtmark.l)dtmarlt),

diap('changing discretisation');dtmark=dtmark+l ;if n>dt(dtmark,8),

n"'dt(dtm"rk,8);output=oprintf('n is now = %g',n);diop(output);InuOl=makemuhat (n~4) ;mu02=muOl~2jeto.i=makeetahat (n) jmuOl=muOl(l:n.l:n)jm1102ar:muQ2(1:n,l:n) ;Lt:linoptint(l1,omoga);

ondjKckopint(m,n,omeg~).*dt(dtmark,2)jN=(muOl- (dt(demark, 3) *dt (dtmarlc,2» *L) ;N"N*mu(n)~2;N(:,l)·chebv~c(lJn) .!n~2jN(:,2)=atal(1:n,1:n)*chebvec(O,n) .!n~2;[ll,uu]=lu(N) ;inv_N=mu(n)~2*inv(uu)*inv(ll)i

M~(dt(dtmark.2)*dt(dtmark,4» .*L+muOl;disp('end of lOOp');

andi

u=inv(diag(maosflow(u»)*u:if rem(t,Gavo)==O I ta=l,

disp('saving to filo');fnnmo=sprintf( ...

'save .!ncc.%02g!U%02g%g.mat u v dt t 10ngthC', ...omogo.,omega, t) iovo.l(fnnmo)ifnnmo=sprintf(laave u%02g_60 u v dt t longthC',omoga);eval(fname)

ondi

if rem(t,Show)==O,diffcll-u_p;half=m!4;disp(max(max(abo(diff(l:ho.lf,:»»);

Apr'r;NDIX D. l\IATLAB M-FII,ES 5-15

N=(u,uOl-(dt(dtmark, 2)*dt (dtmark ,3» .*L) jN=~,*mu(n)~2: % shift the tlatrix right 2 to augment BC I eoN(:,l)=chebv6c(l,n)./n~2;N(:,2)=etal*chebvec(O,n)./n~2:[ll.uu]=lu(N):inv_N=mu(n)~2*inv(uu)*inv(11):

%Uinit=[l 0 OJ:%[x,y)=size(Uinit)j%for i=l:m,% u(i,l:y)=Uinitj%endj%v=zeros(m,n)j

Nlin_p=zcros(~,n);Nlin_pp=zeros(m,n)jNlin=zeros(m,n)ju_PP"zeros(m,n);u_p"'zeroEl(m,n)j[x,y]t:size(u):if y >= n,

u=u(: ,1:n):else,

u(x,n)=Ojend:M=(dt(dtmark,2)*dt(dtmark,4».*L+muOl:%% start the loop%totartacputime::for t=?:tn,

% shift the last time matricos to provious r.imes..Nlin_pp=Nlin_PiNlin_p"'Nlin:Nlina-nonlini(n,u,v,otal,muOl,otalmul,coll,Iplusint,C,Cinv)ju_pp=u_PjU_p"Ujif t==i,

R=u_p(:,l:n)*M+I

APPENDIX D. MATLA13 P,J-FILES

D.4 The two dimensional base flow equation

D.4.1 base2d.m

%base2d.m%% this scr.iptgenerates the 2D entrance base flow model% using the pressure-integral approach.% Before implementing, specify the global matrices u, v.%% set pazamet era%%dt= [ti dt aO ai a2 bO bi n(140) ...clgi % 4e-7dt= [100000 7e-6 1 0 0 1 0 60l

100000 1e-4 100 1 0 32J;[dtoize,y]=size(dt)l11"'dt(1,8)lFirstN=n;me60ldtmark=liomega=60;tn=10000;lengthC=60i % axial domain is [O,l!lengthC]Save=20iFilt=20iShow=10i%% set global matrices%

Xplot:::(-lobgrid(m)+l)!(lengthC)jYplot=(lobgrid(3*n!2)-1)!2iYplot=Yplot(1:6:3*n!2)i[RHS]=contmati(n,m)i[etal,eta2,muOl,etalmul,coll,Iplusint]=makemati(n,m)icoll=··coJ.l'.*lengthC;filt=rcosfilt(m);

%% genernte operator matrices%L=linopint(n,omega)iK=kopint(m,n,omega).*dt(dtmark,2)j[C,Cinv]=transops(3*n!2)i

APPENDIX Do MA.TLAB M-FILES 543

D.3.5 smat 0 m

% smat calculates the shape matrix%% [S]=smat(n,eta,mu);%% Used by l_oper.m%function [S]=smat(n,eta,mu);k=n;onemat=zeros(k,k);onemat(:,l)=ones(k,l);8=-2 .* (eta(l:k,l:k)*onemat*mu(l:k,l:k»:S=S(l:n,l:n);

D.3.6 nmat.m

% nmat calculates the spatial operator for the l-D% pressure integral formulation%% Used by l_operom%% [N]=nmat(n,eta,mu);function [N]cnmat(n,eta,mu);k=n+4;N=eta(l:k,l:k)*(eye(k,k)+eta(l:k,l:k)*mu(l:k,l:k»;N=N(l:n,l:n):

D.3.7 omegamat.m

%% omegamat calculates the omega premultiplier onto u%% Used by l_operom%% [O]=omegamat(n,omega,mu);function [O]=omegamat(n,omega,mn);k=n;O=omega .* mu(l:k,l:k);O=O(l:n,l:n):

APPENDIX D. IvIATLAB lvI-FILES

endjendisave U u dt

D.3.2 etamu.m

%% etamu creates the matrices eta and mu%% A convenience function used by baseld.m%% [eta,mu]=etamu(n)j%function [eta,mu]cetamu(n)ieta=makeetahat(n)imu=makemuhat (n)i

D3.3 kmt.m

%% kmnt calculates the constant RHS matrix;%% Used by baseld.m%% [K]~kmat(m,n,omega,mu);functio,1 [K]=kmat (m,ll,omega,mu);vec=zei-cs Oa.n) ivec(:,l)=ones(m,l)*omegaiK=vec*mu(l:n,l:n)i

D.3.4 Loper.m

%% l_oper calculates the implicit spatial operator%% Used by baseld.m%% [L)=l_opElr(n,omega,eta,mu);function [LJ=l_oper(n,ome~

ilPPENDIX E, TIlE MMN CONTROl, SOFTH:,\RE 5(ii!

couvonlonro, and discussion of til(' flow ltsolf ill lutor dmlJt!'l'S 11H('1"> tll!' moreconvontioual nuliul cn-ordinato ~wst('ll1 with origin Oil tho plp« !lxis,

Tho origiu of tho axis systom ill tho lJo:; plano (tItl' plan» Pl'l'!H'I11lklllal' III th!'pip!' axis) was taken as h!'iu(.'; Oil till' iuner wall of II!!' plpo, OU tho horlzoutulllllt,iOl' llxis, This was nlso the most eonvoniont locntion Ior tIll' origin I b('('aus!'it. corrospouded to tho point w11('1'(,tho laHPl' would be initially nllgnod IH'fol'!'traversing into tIl(' flow, Dellnitlon of tl\(' pip!' axis as til!' origin would not luwohoen useful, \)(I('ltIlHl' this point was not paHY to Iind, All oxporhneutal data wasnliguod to IhP 1111>1'1'usual ('Plltr(I.lms!'1control t ho !ll'l·HKurhiill!'. of t.ltl' t auk.merely tho mnlntcunnco of It Hl'!. 1>l'I':i:I\I1'I',

Tho lll'(IHH1ll'(1 control WII" It sluiplo 'IHtllg ..llItug' control HYHt(lllIj hHHieally thoblood solenoid could olthor hI' switched Oil or (,It'. 'ro control ]>1'(,HH\11'(" tlt(· tankWIIH allowed to \)('('OIlW Hlil~htly ovor-prossurisod hy HPtting tho -uuuual l'l'gllllltol'Il('('ol'(lingly, This oxtru Pl'C'SH\ll'(' was thou hll'(l oll' through tho small solouokl,IItI' Iluo Irom which ('0111(11)('slil~htly !hrott-h'(1 to 1'('(1\1('1' Ilowrato.

Tho ohj('('t. lmplom-ntod a shnplo cnutrol svstom, WhNl(IV(Il'!t \\oil:; (,!tIl(I(1hy nu'main loop it would (']lI'('k tho jll'('HHIl1'C', If til(' value WIIS nhovo tIll' s('t point (plusn siuull (\t'nd·hnlllll'('!l;iou). rho valve wouhl bo opou 10 1'('dl1(,(11.11('prossur«, If ou111(' otlwt' hand fht' pressure 1'('(111('('

APPENDIX B, TlIE !lIMN CONTIWL S()PTlV;'Um 5G4

E.4.3 Limit object

This oneapsulatod tltO bohavlour of till' limit l'iwitcll(% 'I'lio ohjP('t. containod Itroferonco to the 1>('14 to allow til!' limit (lata to he road, Tho bench ohj('('[: usedt.1l

M'I)ENDIX E, TIlE MMN CONTROL SOFTniWE IiG3

polymorphic handling of tho trunsformatiou P1'()('('SH, Other more complicatedtrausfonnntious inherited from this basp class, TIl(,I"actuntor 1\11jl'cI ill ordor to rounuunlcato to 11)(1stopper-motor drive down tho sorlnl link, It contninod Iuuctlous to move the stopper-motors and chango 1)11111111('t·I'1':;. which mount that 11)(1USN' of tho Iunction» didnot huvo to bother with till' (\i'i:i('lllhly of counnaud Ht.l'illgl'l hut could cull highI(lV0IIllOVl.'IlH'nt Iunctious. Thus in till' splrl] of ohjl'ct orieutatiou, tll(' stI'Plll'l'-motor ohjl'('1 truly omulatod tho boluwlour of l~ S0t of stoppor-motors, COlIl-l11

;lPl'ENlJiX E, TIIB MAIN CONTltOlJ SOFTmU?B .')G2

E.2.6 Serial I/O object

This (lhj(,(,t coutnluod all till' log it' for !{t.l'C'lUuiug strings tn and f1om 1111'sorinlport, It diIf

M)PENDIX E. THB MMN CONTIWI. S()F'Tn~iRB 5Ul

E.2.2 Port control object

Tlli!'! was n Hiugh' glounl pi .: ('I in th« systl'lll, owned hy t he main ohj(,(·t. ItHt{)l'I'(1a list. of por! "I), '.'11"113 nnd tholr \lS('S. Thus ('·11It ('1'\1(1('level it Pl"Vl'ut('(\dHl'l'l'l'ut ohjl'('(s from .\ltl'lIlptiur, to lllilisp 1lip saui« 110l't acldl','s:-l('H. It didhowever have' It Inr 11101'(' important Iuuction, nud that was preventing ('ollflkts1)('IWI'(,11oiljl'('ts utilising a SillAI(' card for dHf(,l'Put purposes,

To oxpluln (.lIb, it iH ]\('st, to (,()llsh\l'l' tIll' ('ohl.g\\mt.iol\ of tJI

APPENDIX B. TIlE .MAIN CONTROl" SOFTn·:'WE [jUO

loop docs not. 1H'('('S~1 this object. so it should ronlly 1)('eucapsulated within somesub-object, HOW('V(,l" it is wklclv used, and b('('alllw it l'PPl'(,H(lutS It Hinp;i(> iteru(tho physical card itself), uot 1ll00'!, t hall ou« ('opy of t 11('objl'('t should 1)(' ill('xist(lll('p, Thus the ('II1'l'

APPENDIX E. THE !lIMN CONTROL SOFTWARE 55!)

1'11(' goncml rostrlctions, behaviour nnd conditious of the V1tl'iOIlH intorrolatinn-ships are outlined below.

lil.1.2 Containment

All objects must Ionn part of a containment hi -rarchy, Thus all tho I-\('ll('ricor mnltl-purposo oiJj('l'ts t hat an' not directly (lWIH'

,iPPENDIX E, TIlE AlAIN CONTROl. SOFTWilRE 558

... ",,'(roll conUol)"- __ '

Figure b,l: Tho top-level object relationships ill the system: -, inheritnnco: .,coutninuiont; 0, r('r('l'('llc(',

Cram tho object pointed to, Ilowover tho 0111' object d()('H not own tho other: itis just nwnro of it.. A good illustration of this rolationshlp is ill tho closed-loopcontrol of tb(' Ilowrate. Hero tht' closed-loop object 11('('('l'('uc(, to tho Ilowmotor object, The ('los('

Appendix E

The main control software

This appendix presents r. (h,tniled rlosr ription of the structure of tho controland acquisition softwaro TIl(' design is presented ill an objeet-orioutod 1I11UUH'l',with the Iunctional description of the various components boing in terma oftho interaction botwoon these objects. 'rhiH description nssumos that tllo renderhas sonic basic knowledge of the concepts of object-oriented design, although (h('fundamental structure of tile design should be evident despite this, The reader isreferred to Rumbauch (1991) for further reading on the object-oriented method,

The overall design is host Illustrated by au object diagram (figul'e E,l), showingthe functional relationships between the components.

E.l General design principles

E.!.1 The elements of the figure

This figure follows roughly the notation of Booch (19011), concerning the repro-scntation of object rolatiouships in Object-Oriented Programming (001'), al-though in a much simplified form, The various symbols ou tho interconnretiuglluos indicate the type of relationship l>('tW('

APPENDIX D. MATLAB M-FII.ES 556

alb..alp+dalp:curve=zeros(3.3):curve(1.1)=ala:curve(2.1)=alp:curve(3.1)=alb;

[curve (1.3: •curve Ct , 2)]=findre(n. C\ ••,_.,. .1) ,0 ,L1,L2.M,U,UL •...bc,rea,reb,remax,tol,k);

[curve(2,3),curve(2,2)]=findre(n,curve(2.1),o,L1,L2,M,U,UL •...bc,rea,reb,remax,tol.k):

[curva(3.3) ,curve(3,2)]=findre(n,curve(3,1) ,o,L1,L2,M,U ,UL,...bc,rea,reb,remax,tol.k);

%initial guesses for alpha bracket the given valuewhile (abs(cuxve(3,3)-curve(1,3» >alptol),

[aa,i]=sort(curvo(:,l»;curvo=curvo(i,:);% cu~ve is sortod in increasing alphafit=polyfit(curve(:,1),curve(:,3),2);root=-fit(2)/(2*fit(1»jcurve(4,1)=root

[curvo(4,3) ,curve(4,2)]=findre(n,curve(4,1) ,o,Ll,L2,M,U,UL, ...bc,rea,reb,remax,tol.k)j[aa,i]=sort(curve(:,3»jsave __temp;% curve is sorted in increasing Rocurve=curve(i,:);curve=curve(1:3,:)j% the smallest 3 elements of curve are retainedA=curve(l,l);R=cu2:ve(J.,3);E"curve(1,2);

end:

APPENDIX D. MATLAB lVI·FILES 555

eigc=s~xl(n,alp,rec,0,L1,L2,M,U,UL,bc);[I]:::fint1(real(eigc)60),

error (,Iteration overflow (niter>50) ,)endif (reb>remax),

error('Max Reynolds number exceeded');end

endrey=rec;

[Y,IJ=sort(imag(dJgc));I=flipud(I);eigc=eigc(I);eigval=eigc(1);

D.5.9 gatnose.m

%% This :functlon finds the nose of the stability curve :forpipe% :flow by using a polynominl iteration on findre% function% [alpha,rey,eig]=getnose(n,alp,rey,L1,L2,M,U,UL,% bc,tol,alptol,omGg~);function [A,R,E]=getnose(n,alp,rey,L1,L2,M,U,UL,bc,tol,alptol,0);

remax~1e12; %If above this Re, flow deemed stablek=O.5; % eigenvalue real component search cutoffdo.lp=O.OOOl\~:rea=rflYireb=rey+200;

o.lac:alp-dalp;

APPEND[\ D. l\JflTLAB M-FILES 554

D.S.S findre.m

y,% this function takes n (order), Ll,L2,M,D, two initial guesses% for ray, and a toler(ence), and then finds the neu.ral% stability curve crossing for that alpha by using ne.ton% iteration on the function genpois. A maximum Re is supplied to% terminate the search.%% [:rey,eigJ=fil1dre(n,alp,omega,Ll,L2,M,U,UL,bc,rea,reb,remax, ...% tol,k)%function [rey,eigvalJ=findre(n,~lp,o,Ll,L2,M,U,UL,bc,rea,reb, ...remax, toler ,k)

counter=l;eiga=sexl(n,alp,rea,o,Ll,L2,M,U,UL,bc);eigb=sexl(n,alp,reb,o,Ll,L2,M,U,UL,bc);(IJ~find(real(~iga)

Jll'PENl)[X B. TIlB M.,UN ('ONTIWL SOF1'H:·Um

Flow varlutlon

Tho l'Ollst ants ill the above t ahl« dollned fill' required flow ratt' variatlnn for (hi'f(,(·tlhal'!, control. For tll!' various choson flow vnrlutions, tbl' dl'sit'l'd Ilow wasgivon by:

(J(f)pob' -- (Jmilx [1.'0 + ~'I x f + k~ X f2] ,(J(t)t.ri~ :::: (JlllIlX [1"0+ 1.', Hill(I.'2 x t)j ,(J(t)

APPENDIX B, THB !lIMN ('ON nWL ,'iOFTmUm

E.) 1.1 Command-Ilne and macro syntax

All cununauds i~!'ll1'd at Iho ruuuunnd prompt. or included within 1\ mucro, uroof till' form

{xx}lJCOMMANj);{argJi1rg.(lr~.",}All itvms wit hln hnu'PH ,11'1' (I(,Pl'll1i(,111 OU I hI' context, 01' opl ionnl, Tho xx h~ Itnumeric luhol, llH(,['1I1oulv in t h .. ('1\:-;(' of 1\ maero, ",111'1'('it is 111'11'(1illit GOTO:I'ItatC'111l'llt. The portio II COMMAND: iH any rnnunand from tahl

ilPI'ENDlX B. TIIB ALUN ('ONTIWI, SOFTH:Um ~-..i)(i)and tho rest of t II(' progmm lH'j',wjolll' WIIS Implicit in tho ohjort lutoracfions,

E.1O.3 Data display sub-system

TIll' Iunctlon of this nhjC'{'1 was siluply to display t he LDV. Ilowuiotor and ot her,WI[11ir{'d data f(raphi('11tit!' tnp-lovel oh.i(l(,t d('sigu of tho syst('Ill, Thisl'C'('tioll suuunnriso» tho counuauds 11:;('

it} "BNlJIX B, TIlB MMN CONTROl, ,r.,'OFl'H',WB .'i74

(1) 'I 11(' [4tdll~ "l\1OVE:Y,200" WaH strlppod of loading aut! tl'ailill~~ [41HU'!'}'l, andconvort«] to 1l1111Pl'"('llS(' h'tt('I'[4, It was (11(111 [4(>ill'dwcl from til(> IH'giuuinguntil the colon was oucountored. TIll' dUtl'H('lt'l's lH'flll'

'1'11('mnin conunnud locp Hilllply ('OllHiHI.('

\VIWll it rounuand was l'!'(,!'iVP(1 within till' coutrol lcop fot' tIlt' S!C'JlIH'l' to 1110\'1',a movomout command W!\~ ,(,Ilt directly to tho S(!'PIH'l' oiljP(,t lbYl>!lHHihg t he'clnxed loop control of 1'11('1)('l('h), TIt(' Hh'llIWl' w011Id 1'11 WlIHnovel .uul yleldod lntorostlng global illsigittH ill to th« Ilowt1('wl01111ll'llt, ill tIl

APPENDIX E, TIlE MAIN CONTIWI, SOFTHiWB

('lr(,('tH. A rnhh('l' liN'liou wali iUH('l't('(\ dowustrr-rnu of tl\(' flOwllwtl'l' to try toditlliuish any Pl'C',:SIll'1' WIWPS l'!'HIlItil1P; Irom start-up, hut it was rlecklod to tala'Iurthnr ll!('aHIll'l'S on rig shutdown, to avokl duugorous impulsiv« clP('C'!('rat.iollIIllcl('r 1)1'('SH111'!',

Controlled shutdown was implcmontod t hrough n stundard Iunetion. When IhetrHtillp; torminnt rrl for whatever renson, I}I(' nhort Iuuctiou controlled t he rip;until it was dcomod safe' to simply closo all valves,

011 h('illg culled, tIl

E.g Auto traversing sub-system

'1'11('bench contrcl cll's('rihl'I11('1I1 was 1'I'stl'i

..lPPBNDIX E, THE MMN CONTROl, SOFTH:'lRE 571

Tho position of t ho pis tou or tho oct-nrroure of Il'aknl~(I wore moultorod by thisunit with «nrh loop, If tho piston position ('xr'ppdC'd its limits or water was cI('-('('I('d behind tho diaphrngm (implying It rupture) then tIl(' tpst was inunodintclystopped,

Pressure control was also impleiuontod Oll a constant hasis durlug operation ofIh(' rig, Tho prossurr-coutrol object was descrihcd earlier

As 1\ Ilnal Haf(·!y cousidoratlou, tho key hoard was polled for any keystroke duringtpsting, mal Ill!' dotoction of a k('y I>l'I'SS resulted ill lunnodiat« ondlug of til(' test,

E.S.4 Analogue acquisition & interrupts

TIl(' aualogn« nrquisidon did not ('()Jl('PI'Il itsPlfwith the arqnisitiou loup. Ratherau intorrupt sorvieo was iustantint pel at tho l)('ginlling of tho test and tonuinntodOIl complotlou. 'flip PCaD har] It hardwaro int errupt Sl'l'vi('(' that could 1)(·s('t togonorato interrupts at a pnrtlculnr Iroquoncy, All interrupt handler was writtento ncquiro till' Ilowuictor und other analogue datn from tI1

ilPPENDIX E. THE MAIN CONTROL SOFTWARE 570

E.S.2 Command execution

If tho return value was Hot Z(,1'O thou tho appropriato rouunund was C'x('(·Il{('(1.Within tho loop was 11case statement. Depending on till' rommand numbor (.11('appropriatv conunand waH executed, All eonuuauds had to bo (Illicit to (';{('('U({,.and any action roquirhu; extensive processing had to 11('avoided. The avnilnhloconuunnds wore:

Control the solenoid valve. TIl(' downstrenm solenoid valve could 11('switchedon or off, dependent on tho value of the returned paramotcr.

Slave machine, A Bip;nal could 1)(' sent to tho slavo 1111\('l1i11l1, tolling it tooithor start 01' stop a('OV(· conunnuds wore 'optional' ilia HC'IlS('· it, was Ih('\ls

APPEI\DIX E, THE AlAIN CONTROL SOFTWARE lim)

It contained 1'(,{'(,1'(,lI(,(,S to all the controllable or measurabl« clements of t he rig:t.he slrvo, solenoid. tank pressure, tank control, valves, closed loop control, anw('11 as the' auto-traversing object, which is described below,

Tho object executed a tight acqulsition loop, controlled by commands from t.h('run-Iilo execution object, This loop rend the time value' from tho system timorobject, and theu executed tilt' counnand from the run-file structure when thotime was correct. Dopoudeut on tile couunnnds it receivod, tho appropriateaotlous wore thou implemented. TIl!' gonoral structure of this loop is shown illfigure E,3

End

Figur« E,3: The data ncquisition & control loop.

The basic components of the 1)001 wore thus the' interrupt service, (,lw flowcontrol and tho command execution, Considering the execution of the connnnndIlrst, the structure of tho nm-filo ohjort must be ('o11si

APPENDIX E. THE MAIN CONTROL SOFTH'f\.RE GG8

needed for this study. It. was used only by tho moro gouoral cont '01 sub-system,described in section E.8 below.

The control of Ilowrnto was a classic control theory problem. A measured flow(Irom tho flowmeter) had to 1)('controlled to follow a ('hOS('l1 varintiou in flowrateby moviug a controllable valve, A gonoral-purpose control object was built,which implemented proportional, integral, rlerivatlvc and pscudo-dorivativc con-trol mechunisms. 'I'ho values for the various control constants wore given ill the~;ett.ingHohjoct, and components could 1)(' doaetivated simply by setting all ap-propriate constaut to zero,

TIl(' object contnined relerences to tho Ilowrate and pneumatic valve object IUHlobtained its thuo haso from the acquisitiou object, TIl(' mnin control functionof tho object WIlS lmplomeutod as a 'fail-through' Iunction; that, is tlIP controlfunction was ('a11('11within tho data ucqulsitlon loop, uud kept running totals oftho various relevant control parametors (running iutegral, \'11.111(' of Inst point)without delaying the loop, By this means appropriat« values could he sell! tothe valve oarh time t he Iuuctlou was rnllcd, based on calculations usillg thostored numbers,

The desired Iuuction WIW supplied to till' object as It serlos of constants. \limited impleuientatlon was dovolopod. whereby a qnndrntic, sinusoidal or ex-ponontlal flow variation could be specified. Foul' constants were pnssod to thoohjrctj the llrst dotenuined the typ(' of acrolomtlon (qundratlc, oxpcnontinl,otc.) while the other three, dependent 011 the value of t.he fil'Ht ronstant, definedthe desired How variation ill thno. These constants could bo set 'on-tho-fly'during control, so that piece-wise ('0I1t,iI11l0tlS or oven dlscontinuous functionsassembled from the throo bnsic typl'S of vnnatiou could he assembled,

J3eCI1.URC of tIll' nat me' of dynamic control, no calibmtlon of the valve was 11(,1'-ossnry, Duly adjustment of the parameters. Tho final conflgurntion only utilis«!tho illt('~rfll and pscudo-donvative mochanisms, ou the advice of Coustuntcnu(19!H), and nchlovod a suitably responsive and accurate system, However thoextreme rauge' of tho flow variatlou coupled with tIt!' nou-linenrity of I,ho valve,resulted in I~ control system that Wits not fl111~'opthuum over the ontiro l'ItlW·of opernciou. A suitable Improvement to tho control systrm, such as all arlnp-tivo control procedure would correct thls potential problem, although 11OU(' wasimplemented,

E.8 Acquisition control sub-system

This object was a primary compouout of tho sysll'lll, It wa» fully rosponsiblo forall dl\ia acquisition and rontrol during the ruuuing of tho test, Tho main loophaudod full control to this object during testing, thus nllowing for hip;h spoodcontrol and ncquisitiun.

flPPENDIX E, THE MMN CONTROL SOFTHJ.l.RE 5G7

data object. This was achiovod by passing a reference to this data object tothe acquire fuuction, as Sl:.we,acquire (~RawdataArray), Tho function thenreturned data in this array (or an error in tIt(l ('nRr of failure). Thus tho slaveobject did not contain it reference to the

APPENDIX E. TIlE !lIMN CONTROL SOFTn0tRE :JGG

controlsignAl tobleedvalve

pressurevnrlntlcn

time

Figure E.2: Tho principle of controlling the tank pressure,

other smL7Y'(! code, This is ill stark contrast to couveutlonal npproarhea, whoremany functions, all over the codo, would have to he modified to implement sucha change,

E.5.2 Tank control

The tank control object was merely for acquisition. It measured tank position(and any loalmge status), and was thus useful to both the acquisition and mainsub-systems, both described later.

E.6 The slave control, data transfer and processingsub-system

This sub-system WIIS really composed of two cliffl'l'!'nt components. Til!' slavecontrol and datn Lrallsfl'l' was due to tIll' slnvo iuachlne object, while' tlU' pro-cosslug wns done by till' data itsolf They are grouped together hero !W('ltU:iC'they formed part of n. routiguons process in t ho running of tho program,

E.G,! Slave control & data j,ransfer

As montiou«] this wns achieved by the slave machiue objoct. It. contalnod itroforon« to the 1'(,1:1 port .md ('0111

Gas!!'!' 1\1. HoIH'!'!s.1 B. (Wiil Tlu: »prrlml I'Jlt/I",'18 of IIlT1rl1l7ll/1I MI7IIpil'lll'l'I,'lI't/8Iil/ a direct In:lIQ/.J1'1>' l'J'()f'. Hoy. SOC'. A. 35·1 :!7-1iS

G!'l'stilll~ .T.!\I. (l!)1'-, NlI7IIrI'lI'lll 1111 ilu»!» fill' (,1!II'1I811sl(,//I,~" Tiu: ()rl',SOlllll1l'1:(('lti111'11lJ/(,7n C!8 (11/ illil/("'IJaiul' 111'II/l/c'1II ('Olllp. awl MatIH~.with .'.,IIlS. {I 107-17,1

(alh!'rt N. (1Ot{1{) NII1l11'1'/.rrht' simulnliou dl'!' 11'I11/,~ilitJ71 (11171 ilcr lumius n'lI illdic' iurbulrn! I' ktl7l1ll,\11'IJ1IIltll!1 Dbs('!'t at inu, F niv. Kurlsruhe

Gill A.E. (HJCiri) Oil llu: IlI'lltllliolt.l' IIf MIIII.Il cli,'lllrllll1ll'I"~ /0 l'oiscuill« jlolll in IIrirculiu: 111111'.1. Flllicl1\I('('lt 21 Uri·172

Gl('~.,·rA. Katz Y. Wygllallski 1. (l!ll'!l) On ilu. brl'llkclou'lI of llu: 11'111'1' lU1ch'dlmilill!/ a tlt!'bllll~lIf spot 111 II luuutuu: IlIIltllc/m'!/ill,ll('I'.T. Fluid Mcrh. 198 1·2G

Golc\stl'ill S. (wan) (.'III11C'l'lIi7l!l 801111'sulution» IIf the IIlJlwrlnl'!IiIl1l1'7' cquution»in h!ltlmci!lllllmi("q Pror. Camhr. Phil. SOC'. 20 1-aO

Golcbtl'iu !'oLE. (l!IH!i) Hmlil'l'ill,ll oj (/IIJ/I.,\til' 1II1t11('.~ tultl 1hll,/I('ill.Sd,zil'illill!11II(/.'IIC'8 bll Mllnll 811'1'1I111'1l1i,~I'oarialunt» ill slt/jau' !IC't.1IIl'i7'1I .J. Flnkl r.1('C'h. J 0,1riOD-52!)

Graehol W.P. (lUiO) The 8tllbili/!I o] 1111)(' flou: Pari 1. IlsJj1ll1)/lIli(' 1l111111lSi8 J(W811/ntl 'Wlt1w-71,1t1ll11l'7's .J. Fluid :o.1('C'h.-13 part 2 2iU-2UO

nl'(lC'llhlat.t D. (l!l!)Oa) kIJ('1'Il!lill!l 117111 ft'11I1)()1'Il1 !/I'lulil'nt bia» pmblr-11/'\ in 111/-,~1(,(/l11lturbulent U)V 711I'((8l!1'I'71I1'lI/,~ Fin 11 Iut, Svmp, Las!'!' T('('ltlli

Eilobachor G. Ilussnln! 1\[.Y. Sp(·7.ialt, C. Zang '1',A, (101-\7) 1'oWltrti8 tlu: lilme.ecZdy simulation oj c'(mIJl1'l'8,~i1il(' Illl'illlicllt .flow WASE Ht'l>. No, S7·20 (NASALnngloy H(I!'i('lil'(·!t CPU!!'!', Hampton, VA)

FURl'! II. Kouzohuanu V. (WOO) N07l.pllmlld sln/lilitll oj a ./lllt-pintc' /wuUclal'lIInlllT Ilsing till' complut» Ncwil'1'·,i'to!.;c'_\ rquations ,J. Fluitt Merh, 221 :H1··a,17

FhW'l'HOll L,M. Adrian ILl. Kaufman S,L. (WS!)) /'(18('1' dopple1' v!'[cwillH'tl'lI,'I'll ('(})',II, Cl1/]llit'll/iou iuu! 1('('ll1liqlL('8 TSI LDV (,OIU'S!' text,

Fox L. (1!J02) Ch(,1I118h('1I mdlllllis fcl1' IInli7ltL1'1I riilT('7'('nliail'(]I!(liion,q C'Olll}lU{!'l'.T. r1 :31s·:3:nFox I" Parker LB. (l!l(iH) (,'hl'l1!18hc'lI Pobmomials i,lI mmll~I'i(,(ll Analllst8 OxfordUniv('l'sity Pl'l'!'i!'i,London

Fraz(Il' H.A .JOlH'~ W.P. Skan S.W. (Wa7) All111'(uimnliol1 to Functions nndlo thoSo/ltt'ion oj Di.lTc'7'I'lllia/ Bqllalio1l8 H & M 1iUD Al'l'otmllti('al H(I~(lllr('h Cuuurll,Loudou

Gm'g V.K (10tH) SluMliill of rl('lIdclJlill!l .flow in a. lli111· III1?Hl:fl811mnwll'iC' ([i8-tll7'ban('('.~ ,J. Fluit! 1\1('('11. 110 20!)·21G

Gal'g \'.1\. Rouleau w:r. (1!J;'2) Liuron: spaHn I silt/lili/il oj II it/(: Paiscnille flow.T.Flnill :M('(')l. l:i4 par! 1 113-12i

Gary .1. II(I}g!lHOll n. (1U71) 11 mnt'l'i,v md/lOll Jc)!' cmlinn7',11 rli.lT!'I'cnlinl l'i!ll'rwullU']lmblrms .1. Comp. PhYH. {j IOU·1S7

Ga:-;t('l' M. (WG2) II nott: on tlu: ,dation iw/w('('1! !r:mp()1'lIllll-inc'/'('(!silll/ a:llrl81Iai.inllll·inel'C'rt8inl/ (li8In1'l1lL7Il'('8 in hyil1'Ocl!lllnmic 8taltilil" J. Flukl. Moch, 14222..224

Gm,j.(ll' M. (100G) Tlu. I'lIlt, oj 81mtiallll !,!'Owi'll!l W(W('8 ill the 111mI'll oj ""tim(ly-ntl.1I!i(' slaililitll Prog, /\(11'01

HEFEm~NCBS

Constantrou (" (1001) PC1'8011Cz{ C'01111Jl1l7liC'Clti(lll School of' Mech, EllP;, Univ. oft.IH'Wltwatorsmnd Sout It Afd('lI

('Ol'('OS (tM, Lin S ..I. (HHH) Tlu. maill!llllye'?'; deterministi: model» oj IL 1111'-/miront fll'lII, jlul'l:], Th« ori!lin of ilu: th",'C'·climc'1l8itlllClI wolion 1aU !ii·Dil

('or('os (j,M, S..llurs J.R, (l!l1i!)) On lilt' 8/nl!ilif:!II.f /lIl1,11 dC'11f'iflJlI'd }lolll ill It fl1lw.), Fluid Merh, 5 !Ji-1l2

Crnik ~vI.D,D, (10tl5) Wcw€, illtl'ral'iioll,' aiul flltulflows Call1hl'it\gp Univ. P1'('HS

Crau« eM, Blll'l{'Y n,M, (lDiO) .J. Comp. App!. l\fal hs, 2 111i

Cuunuins II.Z, Knnbl« N, Y('l1Y, (W(H) (}/18C'7'lIniw11 o] cli.fJU8i07! 1J1(lIuit'llill!l o]fl;~1Jlci!lh .~('(J,ltC7('rlli!lhl Phys, Rev. Lett, 12 l1i()·l1i:3

l'inl'il11c'8 tuul 117111'111', (If lClSC'1'dopp/I'l' t!lIC'HW711l'il'!I 'i('W Ycrk: A{'ac\('].Iit- Pr('Ht:

E{IWltl'tl H.V, D~'hhsA, (!!IIH) Rc:(mdil'c' intlc» IIIffll'hill!/ ,(m 1'1 InC'll,!! 1//('11811.1'1"11/('1It8 i7) C(l7111'/c',r !i"fI'I1Il'il'it'8 TSI quurtorlv X il'Klll' 'J

Ekman \',W, (1!llO) (in llu: I'hll71f/l' [nun ,~1(,(1I1,ll1(1 iurbulvu! motion (}llil}ltirl.~Ark. f, Mat. AHtl'OIl. orh FYH 0 No. 12

IlEFERENC'ES

Bouthlor 1\1 (lU72) StllbiJilil' liueairr dr'.~rcoulcmeut» ptrsqtu: 1Iltmlll'II·.~ .1. M(·-chnuiquo 11 5!l!l-111. Phys, 55 ,137-·WO

Brklgos '1'..1. Morris P .•I, (lUtH!» S]lI'('/1'1l1 cnlculaiion« of tlu: 8J1I1Ual stllbility ofNon-parallc! /lolLnril!1'IJ 1l!11t'1'8AIAA Pap. No. ~,l-().1:'1i

Bl'icl~('s '1' ..1. Morris P ..1. (1U~7) lloll71riUl',IJ 1111/1'1' .~i(lbilily calculations Phvs. Flu-his 30 Part 11 :1351·;]3ril{

Buchhavo P. G('Ol'g

References

Abbot A.II. Moss B.A. (lfl!1·1) The t'J'I.~tr'1I(·t' of critical Rt·JJ1Iold.9 numlm» l!I pi1J1'1!11.tntU{,(! jlows .~ltbj('dc'd to iujinitl'.mlllllu'i8!11IIml'll'i;c 1li.~/ItI'(Ja1I1'I·S Phys, Flnhl:;6 part 10 aaa5·33·10

A1>1>olA.II. ~Ioss E.A, Olivil't· (.:.II. (19!J2) A 1(l8t'l' t1Y£tIt'7Wlll!l tcclmiqtu: jlJ1' lilt'1II(,(!8Ul'1'mClIt of 11('lociill I1mjilc'8 in lL118lmd!J lliJl(' j10wB Proc, (jth Int. Sympo.slum Oil Appllcn! ions of Lnser Tochulquos to Fluid :vI(lC'lvmks 2.3

Ajmnlli D.B.S. Roberts ,1.B. (lOUD) b1111711l1l'1l .~lll'dml ostimnlinn. [or i7'1't'!lttitll'11l8pa('('d tlaia 'Using rli!lllal jiltt'T·.9 Mechanical SySI

Appendix G

Raw data on CD-ROM

TIH' CD-HOM cnutnlnod ill tho sloovc below routnins the' rnw data aH('Olllpr('HSl'dASCII fUI'H, arruugod ill a sulxllreetorv strurture lu [\('('ordnu('(' with tIl(' t(·S!llal\lNl, 'I'ho CD·HOM iHSl'lf·(ltH'11llH'lltNl: tho road-me lilt, ill thl' root (lil'(l('t.tll'~'H(,l'VI'HIlH It 'road-map" !LIllI point» t () moro SIl('('Hit' lnfonuatlon Illes (,(lIl!aill(l(1ill 111('Iurt her Hllhclh'('('(Ori('H, Till' modla was cronted uslug tIl(' stnndard (,DIt'SiiII' system, and Ill' It result should 1)(' rondablo fro III both DOS/WINDOWSruul UNIX HJ'sh'llls, Datn rmnprossion is vln tIl!' Pk:-lip Il(.i!it.y, which is [1'('(llynvailubl« as shnreware (Lc. Itt most Illtornet F'l'P sites).

APPENDlX F. TIlE uiv COMPONENTS 583

Model 9169-460 focusing lens: This unit (m'us(ls tho widely spared bemusonmunting from the bomn expander, aud (O('lISC'S them at 1\ single point in tilt'now. R('frnrt('(l light from this measuring volume is roll('('t('t\ hy this IN},'! andtransmittod hark through tho Hold-stop systom, and into tho phcto-dotortors.H had a Coral length of 450 nun,

M'PBNDlX F, TIIB u»: COMPONENTS 5~2

Model 9176 mounting ring: This unit serves as n support for tho ('OIllPO-ueuts, Several monuting adapters were spaced eveulv down t.h« length of thooptical barrel.

Model 9180A frequency shift unit: Two of thC's(' units WI'1'{' inrurporatedinto tho system. Two model Dl!:!2Brag c('lIs W(,1'(, placed ill the optical barrel- OIl closer lop;ptiI('l',to allow tlu-m to pas:- pl'op

jlPl'J~NDIXF. TIlE usv COMPONENTS 581

Model 9108 hr arn colllmatori This unit collin; the IOU1HI unit" whose primarytask is to sopnrnto th« inrirlont laser boum into its spectral ('01l11HlUPll(:S, and t.JH'11to transmit two of these components (blue at 'lSt-I.O 11111 and groon at. 514.5 mu).ItH Internal (,01111>01l(,l1tsare: model 92011attenuntor: model !)10(l dispersionprism; one model 910G and two model 910i mirrors; and a model 913HenclosureIn! e, Th(1 rut ire set of cmupoueuts is enclosed by tho model 013G (lUdOSUl'('over, The two dlOSC'1l colour laser 1H'lUllS leave tho enclosure and pass into till'optical barrel, the eoinponeuts of which arc doscrihod below.

The optlcn! hnrrol lucorporatos nil tho trawHuitt.illg and rocoivlug optlcs. Till'greon and bluo lnsor boamn I'nt,('l' tho unit Itt tho 1'('(\1' - OUl' on-axis I1.U

Appendix F

The LDV components

Thi» appendix coutnins 11 (lptail('cllistillg of the components rmuprising I ho twodll111111'1 9100 srrirs 'IS! Laser Doppler Volorhuctor lIHPd In till' current study.Thil4 HYHtC'1ll is n four beam-two channel dovir« All model 111ll11b

APPENDIX E, THE MAIN CONTROL SOFTWARE 57D

Table E,2: The C'uhau('('d progralll ('Dutrol counuunds [DI'macro HS('.(,Olllll1lUHl' I parametors Illleauiug ------~

int N, string 8 Display the string '8" if Ihe user pressps - --=DECISION:the 'Y' key jump to the label N.

END: UOlIt' The hu~t.lino of tll(' macro. Donoros tho end,FOR: char C, int 1,,1 St'! variable CE[I,.1,Kj to each value botwoon

I and .1I execute conunands below until NEXT:counuand is rcnchorl.

GOTO: int N .1limp to the label N -----r-:rnr.o; string S First line of mnero. A d('h('riptiVC' title. ---INPUT: striug 5, var V Display S, n'nd keyboard input into

,_

,- tho variable' VElVAIn,VAnS.VAnnjlsp(' below). -,NEXT: dllll'C SC'C' FOR:, rot urn program control to tho matching

FOR: loop. l:C: [1,.1,KJ,VARI NjA -;r'1iC;-illtl'gC'l' svstom varinhlo, Most ronuuauds (lX])('('tillg

uu illtC'grt' parauicter will (tc('('pt VARI as arjnnuent,VARR N/A Ali above, hilt for real number argumontaVARS NjA As above, hilt for string arguments

PTY Sot tho tYP(l of flow variation doslrodo =polynominl, l:=;trigouolllPtl'i('al,2=oxpouontial~Sii\!'~.Jr ::lIn}} LDV IW{l\1iHitioll (l=sll\1't,)OjH'uj"rYos(' t he dow list l'Plllll SOI(lIlOid (l-O!lI'll)-!'IIo\'(' th!' pnoumutic valve to posit ion N-:-'I'G;-mug(' of N ('Ol'l'(lSI)(lll

APPENDIX E. TIlE !lIAIN CONTROL SOFTn:ARE 5itl

[{·i)mUHlIIlI I parumnters I moaningTable E.1: TI1

5!)!)

Wygllltusld .I.H, Ilurltnnidls J.Il, Kaplun H .E, (1!liO) Ou It Tollmirn • .

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Author Abbot Anthony Hailey.Name of thesis The transition to turbulence in strongly accelerated pipe flows.

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