Experiment Study on the Interior Sound Field of Water Filled Pipe with Elastic Wall

Transcription

1 Interntion Indutri Informti nd Computer Engineering Conferene (IIICEC 5 Experiment Stud on the Interior Sound Fied of Wter Fied Pipe with Eti W Lu Xueong,, Li Qi,b, Liu Jun, Aouti Siene nd Tehnoog Lbortor, Hrbin Engineering Univerit, Hrbin, Chin 5; uxueong@hrbeu.edu.n, beehi@hrbeu.edu.n, 39537@qq.om Keword: Eti tube w, wter fied pipe, ound fied Abtrt. Thi pper reerhed on the wter fied pipe with eti w whih i wide ued in di ife. Conidering the exiting of the P-wve nd S-wve in the pipe w, the thin he mode nd iquid w mode re not ppibe. In thi pper, the ound fied in the wter fied pipe with eti w wi be ned nd oved. At the me time, the experiment tud on the ound fied wi be tken, nd the inertion o of different kind of pipe wi be got. Introdution The fuid fied pipe i wide ued in petrohemi indutr, hip nd erorft indutr, nd other. In hip indutr, the wter fied pipe tem, for exmpe the wter for ife pipeine nd the ooing wter pipeine, i ommon ued in ever kind of hip. So, the reerh of wter fied pipeine h exited interet of the reerher t erier. The outi trnmiion o through the ir pipeine w tudied b J. Y. Chung in 98[]. Lmb reerhed the infuene of the eti w for the ound pred in the fuid in the pipe[]. Fuer nd Fh diued the wve propgtion in wter fied pipe nd energ ditribution in the wter nd the w[3]. Conidering the infuene of the Poion rtio, Thomon uted the energ ditribution in the w nd wter[4]. Thi pper wi ove the ound fied eqution of the wter fied pipe with eti w, in order to ni the hrteriti of the outi propgtion in the pipe. At the me time, the experiment of different kind of pipe wi be tken, nd the inertion o of different kind of pipe wi be got. The ound fied in the pipe Fig. The mode of the pipe Suppoe tht the inner rdiu of the pipe i b, the outer rdiu i, the denit of the iquid in the tube i ρ, the ound veoit i, the denit of the pipe w i ρ, S-wve veoit i, P-wve veoit i, outide the pipe i the free boundr. The veoit potenti funtion of the pipe w nd the ound fied in the pipe houd tif the Hemho eqution: Φ (r, ϕ, + k Φ (r, ϕ, =, r < b, b r Φ (r, ϕ, + k Φ (r, ϕ, = ΦΦΦ ΦΦΦ, b r Ψ (r, ϕ, + k Ψ (r, ϕ, = 5. The uthor - Pubihed b Atnti Pre 569

2 Where, Φ Φ Ψ repetive re veoit potenti funtion of the iquid ound fied in the tube veoit potenti funtion of P-wve in the tube w nd veoit potenti funtion of S-wve in the tube w, k = ω, k = ω, ω k = The gener oution of ( i: o Φ ( r, j, t, = AJ m m( xr exp j ( k ωt m= in o Φ ( r, j, t, = BP m m exp j( k ωt ( m= in o ( r, j, t, = Qm exp j( k ωt m in Where, Pm = Jm( ξ Nm( ξr Jm( ξr Nm( ξ, Qm = Jm( ξ Nm( ξr Jm( ξr Nm( ξ, C C C k + ξ = k, k + ξ = k, k + ξ = k.proved Y= CmX+ DY m i tified with (,where X = ψ e, Y = M. So there i: o jk ( ωt m in C Cm Qm + DmjkQ m e er r o in ΦΦ o m in ΦΦ jk ( ωt Ψ= + CmQ m + Dmjk Qm e ej m= in r o m o C jk ( ωt + Dm Q m Q m e e r in Whereb, we C n obtin ΦΦC the tot ound veoit in the eti w, whih i : v = Φ + Ψ o o BmP m + CmjkQ mo in in ΦC jk ( ωt e er 3 in m m m Dm ( k Q 3 m Q + + m r r r o m in m in Bm Pm + Cm jk Qm r o r o ΦΦC jk ( ωt = + e ej m m o m + Dm Q ( 3 m + k Q m + Ψ r r in o m o BmjkPm + Cm Q m Q m in r in ΦC jk ( ωt + e e m in Dmjk Q m r o The boundr ondition n be expreed : ( When b,prtie veoit i ontinuou in the verti diretion: (3 (4 57

3 Φ (, ϕ, ΦΦ r = v r b ( When b, ound preure i ontinou in the verti diretion between iquid medium nd eti medium: P T (6 = b rr b r r = b (3 When, tngenti tre T rϕ in eti medium i ero: T rϕ µ vϕ v v r ϕ = ( + = r r ϕ r (4 When, tngenti tre T r in eti medium i ero: vr v Tr = µ( + = (8 r So we n obtin the eigenvue eqution nd intrini vue of the ound fied in the tube. Whereb, the Cut-off frequen of the ound fied in the eti tube i n be obtined. The outi wve of whih frequen i beow the ut-off frequen n not propgte in the pipe. Experiment tud of the ound fied of the wter fied pipe with eti w Seet two different mteri pipe, one i the tee pipe, of whih the outer dimeter i 6m, the inner dimeter i 3m, nd the tube ength i 4m, nother mteri i the PPR (penttrio-peptide-repet,of whih the outer dimeter i.4m, the inner dimeter i 9.8m,nd the tube ength i m. During the experiment the trnmitting trnduer nd the reeiving trnduer repetive re 85 hdrophone nd 83 hdrophone of B & K ompn. Keep the trnmitting trnduer enoed in one end of pipe, nd onnet the other end of the pipe with the reverb tnk. Then ue the reverbertion method to meure the ound rdition power of the ound wve rdited b trnmitting trnduer fter whih go through the pipe. When the pipe diret i rigid onneted to the reverb tnk, the ound rdition power of the ound wve whih i obtined in the reverb tnk i foow: The rdited ound power of the hdrophone No.85 (5 (7 SPL/dB(Pref=*e- P f/kh Fig. trnduer going through the pipe ontrt with the ound rdition power of the ound wve in the reverb tnk The upper urve in Fig i the ound rdition power of the trnduer meured in reverb tnk, the foowing urve i the bkground noie, nd the midde urve i the ound rdition power of the ound wve whih go through the pipe. You n find ever ine petrum ign exit between 5KH-5KH.A of now, Thee ign i reonne ign of the pipeine motivted b the trnduer. Owing to the tube whoe dimeter i mer thn it ength, nd tube w i thik, we n 57

4 ue bem mode to ne. So we n get onuion: When one end of the pipe i fixed, the other i free, the vibrtion frequenie of the bem i hown in eqution[3]: f = (n, ( n=,, 3 (9 4 In word, the reonnt frequen of the tee pipe n be uted. Through ontrting with the frequen of the ine petrum ign, we n get the tbe : Tbe : The reonnt frequen of the tee pipe nd the meured n The reonnt frequen (theoreti vue The reonnt frequen (meurement vue n The reonnt frequen (theoreti vue The reonnt frequen (meurement vue You n find the ine petrum ign i the reonnt frequen of the tee pipe. In order to prevent vibrtion of the tee pipe from ffeting the outome of ound fied meurement in the reverb tnk, pte the tee pipe to the reverb tnk through oft rubber. Equivent to dd hort-oft- onneted devie between tee pipe nd reverb tnk. Re-meured, we n get the reut fow in the figure 3. B omprion of figure nd 3, Tht ine petrum ign i ued b reonne of the tee pipe i one gin proved. In ddition, it n be een tht the tee pipe h good effet on utting off the ound wve whoe frequen i beow 5kH in Figure 3. Uing the PPR to re-meure, the reut hown in the figure 4. Cn be found the ut-off frequen of ound wve ontnt move to ower frequen, with the inree of the inner dimeter of the pipe. Menwhie, due to the different ie of the different pipe, the ound fied of the pipe h different effet on ound oure, Whih ed to different rdition impedne, when the ound oure i in the different pipe. o the ound fied of rdition effet fter the ut-off frequen i o different. Aording to figure 3 nd figure 4, we m o obtin the inertion o of the different pipe in figure 5 nd 6. The rdited ound power of the hdrophone No.85 SPL/dB(Pref=*e- P f/kh Fig 3. trnduer going through the pipe ontrt with the ound rdition power of the ound wve in the reverb tnk. 57

5 The rdited ound power of the hdrophone No.85 SPL/dB(Pref=*e- P f/kh Fig 4. trnduer going through the pipe ontrt with the ound rdition power of the ound wve in the reverb tnk.. Inertion o of the pti pipe. Inertion o of the tee pipe.8.8 inerto.6.4 inerto f/kh Fig 5. Inertion o of the pti pipe f/kh Fig 6. Inertion o of the tee pipe Conuion Due to the different truture nd prmeter of the pipe, the ut-off frequen of ound wve i not the me in the different pipe. At the me time, the me ound oure h different rdition in the pipe, owing to the ound fied in the pipe hving effet on the urfe of the ound oure. Thi pper give inertion o of two different pipe. The ound fied in the pipe infuene the rdition of the ound oure, whih i the fou of the next work. Referene [] J. Y. Chung nd D. A. Mer. Trnfer funtion method of meuring in-dut outi propertie[j]. Journ of the Aouti Soiet of Ameri. Vo. 68-3(98,p. 97. [] Lmb, A., On the veoit of ound in tube, ffeted b the etiit of the w,. Mnheter Literr nd phioophi Soiet-Memoir nd Proeeding, 898,4(9. [3] Fuer, Fh. Chrteriti of wve propgtion nd energ ditribution in indri eti he fied with fuid. J. Sound Vib., 98; 8:5-58 [4] W. T. Thomon. Trnmiion of preure wve in iquid fied tube, Proeeding of the firt U.S. Ntion Congre on Appied Mehni, Chigo, 953:9-933 [5] H. L. Zhng. Theoreti Aouti. ;