Pressure Loss Analysis of the Perforated Tube Attenuator

Transcription

1 Purdue Universiy Purdue e-pubs Inernaional Refrigeraion and Air Condiioning Conference chool of Mechanical Engineering 014 Pressure Loss Analysis of he Perforaed Tube Aenuaor Zhan Liu Xi'an Jiaoong universiy, China, People's Republic of, Qin Tan Xi'an Jiaoong universiy, China, People's Republic of, Jming Cheng Xi'an Jiaoong universiy, China, People's Republic of, Xling Yu Xi'an Jiaoong universiy, China, People's Republic of, Quanke Feng Xi'an Jiaoong universiy, China, People's Republic of, Follow his and addiional works a: hp://docs.lib.purdue.edu/iracc Liu, Zhan; Tan, Qin; Cheng, Jming; Yu, Xling; and Feng, Quanke, "Pressure Loss Analysis of he Perforaed Tube Aenuaor" (014). Inernaional Refrigeraion and Air Condiioning Conference. Paper hp://docs.lib.purdue.edu/iracc/1379 This documen has been made available hrough Purdue e-pubs, a service of he Purdue Universiy Libraries. Please conac epubs@purdue.edu for addiional informaion. Complee proceedings may be acquired in prin and on CD-ROM direcly from he Ray W. Herrick Laboraories a hps://engineering.purdue.edu/ Herrick/Evens/orderli.hml

2 160, Page 1 Pressure Loss Analysis of he Perforaed Tube Aenuaor Used in he Reciprocaing Compressor Zhan LIU 1, Qin TAN, Jming CHENG 3, Quanke FENG 4, Xling YU* chool of Energy and Power, Xi an Jiaoong Universiy, Xi an , China *Tel(Fax): xlingyu@mail.xiu.edu.cn * Xling YU ABTRACT Oversize resisance loss of gas pulsaion aenuaor will cause he compressor exhaus back pressure higher, increase he compressor power consumpion and increase he exhaus emperaure, which leads o he deerioraion of he compressor operaion. Therefore, proper conrol he pressure loss of he aenuaor used in reciprocaing compressor is especially imporan. This paper presens an invesigaion of he pressure loss of he Perforaed Tube Aenuaor (PTA). Three-dimensional compuaional fluid dynamics (CFD) has been used o invesigae he influence of porosiy, flow velociy, diameer of he holes on he pressure loss. The resuls showed ha he pressure loss of PTA decreases wih porosiy increasing following nearly a hyperbolic rend, ascens according o a parabola law wih he inle velociy increasing and descens lile wih he hole diameer rising. 1. INTRODUCTION The reciprocaing compressor plays an imporan role in refineries and perochemical plans. Excessive vibraion in he reciprocaing compressor piping no only degrades he compressor performance bu also causes piping severe faigue, pipe damage, high-pressure gas leakage and even explosion. Vibraion of he reciprocaing compressor piping is mosly caused by gas pulsaion in he piping (Dang and Chen,1984). Therefore, reasonable analysis and proper conrol of he gas pulsaion and hen he piping vibraion become significan in engineering. Various pulsaion aenuaors used for decreasing gas pulsaion have been researched and developed worldwide for decades. Among hem he perforaed ube aenuaor (PTA) is pracical and commonly used because of is wide silencing frequency band and high amoun of noise eliminaion. Brablik(1976) proposed a PTA o reduce gas pulsaion in he pipe beween he valve chamber and he surge ank, and he experimens resuls showed ha PTA was able o damp he gas pulsaion in a very wide frequency range. Wang(1995) developed a numerical scheme for he aenuaion analysis of he perforaed inruding ube aenuaor and found ha he porosiy is an imporan facor which should be aken ino accoun in he aenuaor design. Luo e al.(1995) presened a new approach for modeling concenric parially perforaed inruding ube aenuaions.for acousic impedance in he linear regime, a closed form soluion of he parially perforaed inruding ube aenuaion ransmission loss was firs obained. The disribued parameer mehod is exended for he analysis of aenuaors employing concenric muliple pipes and i is seen ha increasing he diameer of he co-axial pipe improves he noise reducion for he higher frequencies, while decreasing i ends o improve i for he lower frequencies(dokumaci,001). iano(011) employed onedimensional and hree-dimensional approaches o predic he acousic behavior of a hree-pass perforaed ube muffler wih an end resonaor. For he aenuaor design, pressure loss and ransmission loss are he wo equally significan parameers characerizing is performance. Even if an aenuaor can grealy reduce he compressor pressure pulsaion, bu cause large pressure loss, i will no be used ye. o i s necessary o pursue he aenuaor wih low pressure loss as well as low pressure pulsaion. The radiional mehod of calculaing pressure loss of he aenuaor is according o empirical formulas, which only fi for simple srucures(hu,007). Bu for PTA, generally consising of hundreds of small holes disribued along a pipe, boh he srucure and he flow in i are complex, and he curren empirical formulas are no available o calculae he pressure loss.

3 160, Page o his paper predics pressure loss of he PTA wih various geomery parameers using hree dimensional CFD.. THEORETICAL ANALYI.1 Physical Model rucure of PTA sudied in his paper is shown in Figure 1. I is a concenric perforaed ube wih a radial baffler a he end of he inner ube in he aenuaor. Air flows hrough he holes on he inner ube ino he chamber, and hen flows ou of he expor of conainer. The basic dimensions of he physical model are as follows: L1 = 500mm, L = 60mm, D1 = 50mm, D 54mm =.. Governing equaion and numerical mehod A hree-dimensional CFD model of he PTA was esablished under he following assumpions: (1) The physical parameers of he solid and fluid domain of he aenuaor are consan; () The flow is seady urbulen flow; (3) The influence of he graviy is ignored; (4) The inle velociy of he PTA is homogeneous wihou pulsaion. The sandard k -ε model is used o describe he urbulen flow in he PTA. The flow in he PTA follows he law of mass conservaion, momenum conservaion and energy conservaion. The general equaion can be expressed as Equaion (1). ( rφ ) + div( rνφ) = div( Γ grad φ) + (1) Where φ is he general variable which represens differen physical variables. and Γ are respecively he generalized source iem and generalized diffuse coefficien according o φ. r is he air densiy and ν is he velociy vecor. The corresponding relaions are shown as Table 1, where u, v, w are he velociy in hree direcions x, y, z ; T is he absolue emperaure; k is urbulen dynamic and ε is he dissipaion raio of urbulen dynamic; Figure 1 Physical model of PTA and measuremen poins

4 160, Page 3 µ is he viscosiy coefficien and µ is he viscosiy coefficien of urbulence; G is he sress of urbulence. C µ, C 1, C, σ ε, σ T and σ k are all consans. Pr is Prandl number; u direcions x, y, z, respecively. µ and G can be expressed as Equaions.()and(3). µ C k µ r / ε, v, w are he source iem of hree = () µ u v w u v G = r x y z y x µ u w v w r z x z y Table 1 Values of φ and relaed equaions Equaion General variable Diffuse coefficien ource iem φ Γ Mass x u µ + µ u y v µ + µ v z w µ + µ w Energy T µ / Pr + µ / σ 0 T k equaion k µ + µ / σ pg ρε k ε equaion ε µ + µ / σ ε ε ( C1ρG Cρε ) k The values of he consans are se as: C µ =0.09, C 1 =1.44, C =1.9, σ ε =1.3, σ T =0.95, σ k =1.0. The soluion of he model was implemened wih he finie volume mehod. (3) Figure Grids in he PTA

5 160, Page 4.3 Grids and Boundary condiions The grids meshed for he calculaion domain was deermined by compromising he calculaion ime and he soluion precision, so he ype of mixed-mesh composed of erahedron and hexahedron was chosen, as shown in Figure. The gas column mm around he pipe was meshed wih he ype of erahedron, he oher par of he aenuaor is meshed wih he hexahedron elemen. The soluion independency of he grid number was validaed in he calculaion. The grid number in he model was 457,31 and he relaive error for he calculaed pressure loss was less han 1% compared o a case wih 503,561 grids. A he inle of PTA, velociy of gas flow was given. A he oule of he PTA, 450K Pa absolue pressure was given as he boundary condiion according an operaing compressor..5 Pressure loss calculaion of PTA As shown in Figure 1, 13 uniformly disribued poins were seleced o calculae he average pressure a he inle/oule of he aenuaor. The modifying facor used o calculae he dynamic pressure is expressed as Equaion (4) 1 α= ν / ν N N i m (4) i= 1 Where N is he number of he poins seleced in he cross-secions of he duc, ν i is he velociy of each poin which he uni is m/s, ν is he velociy a he cener of he cross-secion wih he uni of m/s. m The calculaion formula for he mean dynamic pressure is expressed as follows: pν α p vm = (5) p vm is he dynamic pressure a he cener of he cross- Where α is he facor obained from Equaion (4) and secion wih he uni of Pa. The mean oal pressure can be obained wih Equaion (6) p = pv + ps (6) Where p, p s are he mean oal pressure and he saic pressure wih he uni of Pa, respecively. Thus he pressure loss of he PTA can be expressed as follows: p = p p (7) 1 Where p is he pressure loss of he PTA and p 1, p are he inle/oule mean oal pressure a he cross-secion of he duc, respecively. 3. REULT AND DICUION

6 160, Page 5 Figure 3 Pressure loss of PTA wih differen hole diameers Figure 4 Pressure loss of PTA wih differen porosiies 3.1 Influence of he hole diameer on pressure loss Transmission loss of PTA is associaed wih he drilling hole diameer, he smaller he diameer, he beer aenuaion effec. Aenuaors used in reciprocaing compressors are normally for aenuaion of low frequency sound waves, so he drilling hole diameer is generally greaer han mm. The hole diameers sudied in his paper were: mm, 3mm, 4mm, 5mm, 6mm, 8mm, 10mm, 1mm, 14mm, and 16mm. The porosiy was 8.7% and he inpu velociy was 10m/s. Figure 3 shows he relaionship beween he pressure loss and he hole diameer. The pressure loss changed genly when he hole diameers were mm o 6mm, and declined sharply when he diameers increases from 6mm o 10mm, and changed lile when he hole diameers were 10mm o 16mm. For PTA used in he reciprocaing compressor, he hole diameers are generally from mm o 5mm, so he hole diameer has lile influence on he pressure loss according o Figure 3.

7 160, Page 6 3. Influence of he porosiy on pressure loss The porosiy of PTA is he area raio of holes drilled in he pipe. The inersecion area of gas-flow beween he chamber and he perforaed duc increases wih he porosiy growing, causing gas-flow more smoohly and lowering he pressure loss of aenuaor. The porosiies chosen in his paper were: %, 3%, 4%, 5%, 6%, 7%, 8.7%, 10%, 1%, 14%, 16%. Air velociy of he inle is 10 m/s and he hole diameer: d = 4mm. Figure 4 shows he relaionship beween he pressure loss and he porosiy. The pressure loss decreased wih he increasing of porosiy, in line wih a hyperbolic curve. The pressure loss rises very quickly wih he porosiy descen when he porosiy is smaller han 5%, bu goes up genly when he porosiy is higher han 10%. The resuls sugges ha he porosiy has wo hreshold values for PTA design. The pressure loss increases sharply as he porosiy decreases when he porosiy is smaller han he low hreshold and rises gradually wih he porosiy reducion when he porosiy is greaer han he high hreshold. 3.3 Influence of he inpu velociy on pressure loss When he porosiy is 8.7% and he drilling hole diameer is 4mm, he relaionship beween he pressure loss and he inpu velociy was shown in Figure 5. The velociies are 8m/s, 10m/s, 1m/s, 14m/s, 16m/s, 18m/s, 0m/s, m/s, 4m/s, 6m/s, and 8m/s. The pressure loss increases wih he inpu velociy ascen according o he form of parabola. And he relaionship beween he pressure loss and he inpu velociy has been fied o be a parabola equaion wih he mehod of he leas square fiing, which is depiced as Equaion (8) p = 6.64v 8.38v+ 08 (8) Where p is he pressure loss wih he uni of Pa, and v is he inpu air velociy m/s. These resuls indicae ha he inpu velociy is an imporan influencing facor of he pressure loss for he PTA design since he pressure loss rises wih velociy following a parabola rend. The higher gas velociy may bring much more addiional pressure loss. o he diameer of he inpu duc should be compued o be a proper value o ensure he velociy is limied o an allowable value. Figure 5 Pressure loss of PTA wih differen inpu velociies

8 160, Page 7 Figure 4 Velociy profile of PTA cener plane Figure 5 aic pressure profile of PTA cener plane 3.4 Analysis of he velociy field and saic pressure filed Figure 4 and Figure 5 respecively show he inernal velociy profile and inernal pressure profile in he PTA. Air passed hrough impor ino he perforaed pipe, punched ino he caviy and flowed ou of he expor. Velociy decreased and saic pressure increased in a cascaded mode along he cenerline of PTA. Velociy filed and saic pressure field is relaively uniform in he caviy. In he oule, fluid urbulence was relaively severe, which resuled in large flowing velociy and saic pressure change. 4. CONCLUION

9 160, Page 8 Based on he analyical invesigaion on pressure loss of PTA presened in his paper, he following conclusions may be drawn: Compared o he porosiy and he inpu velociy, he drilling hole diameer from mm o 5 mm has smaller impac on he pressure loss of PTA used in he reciprocaing compressor. Relaionship beween he porosiy and he pressure loss generally follows a hyperbolic curve. There are wo hreshold values of porosiy for each PTA. Pressure loss increases sharply when he porosiy is less han he low hreshold value, and changed smoohly when he porosiy is greaer han he high hreshold value. Inpu velociy of PTA links wih he pressure loss following a parabolic curve, and he polynomial equaion were fied from he invesigaed resuls. NOMENCLATURE L ube lengh (mm) D ube diameer (mm) r air densiy (kg/m 3 ) φ physical variables (-) ν velociy vecor (m/s) generalized source iem (-) Γ generalized diffuse coefficien (-) T absolue emperaure (K) u velociy a x direcion (m/s) v velociy a y direcion (m/s) w velociy a z direcion (m/s) k urbulen dynamic (m /s ) ε dissipaion raio of urbulen dynamic (m /s 3 ) µ viscosiy coefficien (Pa s) µ viscosiy coefficien of urbulence (Pa s) G sress of urbulence. (Pa/s) Pr Prandl number (-) u source iem a x direcion (-) v source iem a y direcion (-) source iem a z direcion (-) w N he number of he poins seleced (-) in he cross-secions of he duc ν velociy of each poin (m/s) i ν m velociy a he cener of he cross-secion (m/s) α modifying facor (-) p dynamic pressure (Pa) vm p mean oal pressure (Pa) p s mean saic pressure (Pa) p pressure loss of he PTA (Pa)

10 160, Page 9 REFERENCE Dang X, Chen., 1984, Flow pulsaion and pipe vibraion in pison compressor[m]. Xi an Jiao Tong Universiy Press Brablik, J., 1976, Aenuaion of Gas Pulsaion Using a Perforaed Tube. Proceedings of he 1976 Purdue compressor echnology Conference, Wes Lafayee, Indiana, pp Chao-Nan Wang., 1995, A Numerical cheme for he Analysis of Perforaed Inruding Tube Muffler componens. Applied Acousics, 44 (3):75-86 Luo H, Tse CC, Chen YN., 1995, Modeling and Applicaions of Parially Perforaed Inruding Tube Mufflers. Applied Acousics, 44(): Dokumaci E., 001, ound Transmission in Mufflers wih Muliple Perforaed Co-axial Pipes. Journal of ound and Vibraion, 47(3): D. iano., 011, Three-dimensional/one-dimensional numerical correlaion sudy of a hree-pass perforaed ube. imulaion Modelling Pracice and Theory 19 (011) Hu X., 007, Research of he resisan aenuaion based on he CFD simulaion and experimen[d]. handong Universiy ACKNOWLEDGEMENT This work is suppored by he Naional Naural cience Foundaion of China [NO ].