Narasimha Marakala 1, Appu Kuttan K K 2 and Ravikiran Kadoli 2

Transcription

1 IOSR Journal o Mechanical and Civil Engineering (IOSR-JMCE) ISSN: , PP: Exerimental and Theoretical Invetigation o Combined Eect o Fluid and Thermal Induced Vibration on Vertical Thin Slender Tube Naraimha Marakala 1, Au uttan and Ravikiran adoli 1( Deartment o Mechanical Engineering, NMAM Intitute o Technology, Nitte ) ( Deartment o Mechanical Engineering, National Intitute o Technology arnataka Srinivanagar-57505, Mangalore, India). Abtract: The aer reent an exerimental and theoretical analyi on the tudy o dynamic reone o a thin lender cantilever ie conveying air at dierent reure and. A dynamic characteritic o a ie line conveying internal luid exerience mechanical load due to inertia eect o luid, corioli orce, luid rotation kinetic orce due to luid low velocity, dynamic load due to inertia eect and thermal load due to hot air on the ie. One dimenional beam inite element i ued or invetigating the dynamic behavior o the thin lender ie with aroriate numerical comutational method or analyi. The undamental natural requency o vibration i correlated with exerimental and numerical method. eyword- Fluid and thermal induced vibration, inite element method, natural requency, lender tube I Introduction Thin walled tube are widely ound in variou tructural engineering alication. Static and dynamic reone o ie tructure to luid load and thermal load i very imortant or ae deign and oeration. Fluid lowing through a ie can imoe reure on the ie wall which delect the ie, lead to luid induced vibration. Non uniorm heat traner due to dierence in convective heat traner over the urace o the tube lead to thermal induced vibration. Many reearcher have tudied thermal and luid induced vibration. Studie have been conducted to ae the relationhi between luid low velocity, reure o the luid and it inluence on the ree vibration. Among the aer available in the literature, Paidoui et al. [1] and Rouelet and Herrmann [] reented a aer on analytical tudie to invetigate dynamic tability o a lender and long tube conveying luid. Numerical invetigation on the vibration behavior o the ie conveying luid wa reented by Lin and Tai [3] and Lee and Oh [4]. Bar-Avi [5] ha conducted an exerimental and analytical tudy on the dynamic reone o a vertical cantilever ie conveying luid which i ubjected to ea wave orce. uier and Metrikine [6] invetigated dynamic tability o a ubmerged vertical cantilever ie. Paidoui and Semler [7] examined the lanar dynamic o a luid conveying cantilever ie with a mall ma attached at the ree end by theoretically and exerimentally. Sinha et al. [8] tudied the reult o a modal exeriment on an oen ended cantilever ie conveying luid and their numerical imulation uing inite element method. Zou et al. [9] tudied analytically luid induced vibration o comoite natural ga ieline and invetigated the inluence o luid velocity, internal reure and initial tenion on ieline vibration requency. Tran et al. [10] analyed the tructural intenity attern o thin ientroic and laminated comoite late which are ubjected to thermally induced vibration. idawa-ukla [11] ha roved the requency o the thermally induced beam vibration i a multile o harmonic motion requency o the heat ource and then reonance can occur in the ytem. Hong [1] analyed the thermally induced vibration o a thermal leeve uing comutational Generalized Dierential Quadrature(GDQ) method or calculating the natural requency, dilacement and thermal tree. ukla [13] analyed the ditribution and tranvere vibration o beam induced by uing the roerty o the Green unction. Blandino and Thornton [14] carried out the detailed tudy o a thermally induced vibration caued by internal heating. From the literature review it i oberved that not much work ha been reorted on the reone o tructure due to combined loading o thermal, luid, luid inertia and tructure inertia. Hence the reent work ocuing on thi toic et out the ollowing objective. To viualize the roblem, an exerimental and theoretical analyi i contemlated. (a) An exerimental etu i abricated in the laboratory to imulate luid a well thermal load or the thin tube. (b) Exeriment were conducted or variou luid and reure (c)obervation on the tranient and teady tate reone o thin ie due to thee load will be analyzed. Second International Conerence on Emerging Trend in Engineering (SICETE) Dr.J.J.Magdum College o Engineering, Jayingur 63 Page

2 Exerimental and Theoretical Invetigation o Combined Eect o Fluid and Thermal Induced (d)exerimental and numerically obtained natural requency i comared. II Exerimental etu An exerimental etu i abricated in the laboratory to demontrate the luid thermal interaction in a thin lender tube. The etu conit o two narrow tube o diameter 3 mm. The tube are connected through an oriice aembly. The oriice aembly roduce an additional load due to luid exanion. The oriice ize can be changed to obtain dierent hole diameter. Exeriment were conducted or 1 mm and 1.5 mm oriice hole ize. The one end o the irt tube i or the entry o the comreed air. The other end o thi tube i connected to another tube through oriice aembly. The other end o the econd tube i exoed to atmohere. Thee two tube aemblie are in uch away that one end i ixed and other end i ree with oriice aembly. The etu i mounted inide a tet tand. The tet tand act a a mean to hold the two end o the tube a hown in Figure 1. The uly reure i controlled by the reure regulator. The air i aed through tainle teel heating box o cylindrical hae o diameter 00 mm and the arrangement i uitable or generating reurized air at required. The tainle teel heating box contain 00 watt heating coil connected through 0 V, 5 am AC ource with a voltage regulator. The voltage regulator i required to vary the ower uly to the heating coil in order to vary the uly air. A the air low, the heat rom the comreed air i lot by conduction through the tube and by convection rom the tube urace to atmohere. A thermocoule wa mounted inide the tet box to meaure the ambient which wa recorded by mean o digital thermometer. The data acquiition rogram in LabVIEW through a cloed loo controlled the acquiition o dilacement data rom the tet ecimen. Due to conveying o comreed air reurized air, luid load on the tructure and an additional load due to udden exanion o the air through an oriice i reent. The air enter into one chamber o the udden exanion aembly and low through an oriice late having mall hole. Thu, low reult in udden exanion o air and hence additional load at the tube ti. From the econd chamber, air exit through the econd tube to atmohere. To obtain the tranient and teady tate reone o the tube, a iezoelectric accelerometer AD11 N605 with enitivity 10 mv/g i ued. In order to acquire the ignal NIPXI 1050 chai containing NIPXI 447 DAQ with 4 bit having 8 analog inut channel and analog outut channel i ued a hown in Figure 1. Then, intrument i connected to CPU and monitor to dilay o the outut. The rogramming wa done to acquire reone ignal through LabVIEW 8.0. III Finite element ormulation Conider a hot luid element and ie element with variou orce and moment acting on it due to low o hot luid through ie a hown in igure 3 and 4. The luid element i ubjected to reure orce, reaction orce o the ie on the luid normal to the luid element F, and tangential to it i q S, Second International Conerence on Emerging Trend in Engineering (SICETE) Dr.J.J.Magdum College o Engineering, Jayingur 64 Page

3 Exerimental and Theoretical Invetigation o Combined Eect o Fluid and Thermal Induced aociated with the wall-hear treq and gravity orce m g. The ie element i ubjected to the longitudinal tenion T o, tranvere hear orce Q T, bending moment M and daming due to riction with the w urrounding luid a B. Heat traner rom hot luid to ie i h A t T T, heat traner rom hot ie T T, where h i heat to atmohere at comreed ide i 1 and at elongated ide i traner coeicient, T i o hot luid, T i o ie and T i ambient. The thermal moment due to change in rate o heat traner i M T. The baic equation o motion conveying luid [15] can be modiied to include the thermal load [14] and hence the governing equation or ie conveying hot luid could be derived a: 4 E I w m 4 U T A1 w m w ( ) w w 0, U m m E T x x x t t x (1) where E i the modulu o elaticity o the ie, I the area moment o inertia o the ie, A the luid low area o the ie, the denity o luid, m i the luid ma er unit length, and m i the ie ma er unit length, U i the low velocity o luid i the average reure,t i the alied tenion, i thermal coeicient o exanion o material and T i. The lat term, thermal moment w MT E T conider deormation due to thermal load (Blandino and Thornton, 001) which include x conduction and convection through the tube. Uing the Galerkin aroach or the equation (1), the inite element equation o motion can be obtained a: t th ( e) ( e) ( e) ( e) ( e) ( e) ( e) ( e) e ( e) M w G w w 0, () where, Stine matrix 1 6l 1 6l e EI 6l 4l 6l l 3 l 1 6l 1 6l 6l l 6l 4l Fluid element matrix 3 6 3l 3 6 3l e MU 3l 4l 3l l 3 6 3l 3 6 3l 3l l 3l 4l Pie tenion matrix 3 6 3l 3 6 3l e T 3l 4l 3l l t 3 6 3l 3 6 3l 3l l 3l 4l Fluid reure matrix Second International Conerence on Emerging Trend in Engineering (SICETE) Dr.J.J.Magdum College o Engineering, Jayingur 65 Page

4 Exerimental and Theoretical Invetigation o Combined Eect o Fluid and Thermal Induced 3 6 3l 3 6 3l e A1 3l 4l 3l l 3 6 3l 3 6 3l 3l l 3l 4l Fluid daming matrix 3 0 6l 3 0 6l e MU 6l 0 6l l G l 3 0 6l 6l l 6l 0 Element ma matrix l l e M ml l 4l 1 3l 3l M l l 1 3l 3l l 4l Element thermal matrix 3 6 3l 3 6 3l e 3l 4l 3l l E T th 3 6 3l 3 6 3l 3l l 3l 4l Aemble the element matrice o tine, daming, and ma matrice and rereent in a tate ace orm (Zou et.al, 005) a:. Θ Ψ where 0 0 M 0,, 0 G Eigenvalue are comuted uing matlab or the equation (3), e e e e e. t th (3) M T w B t M T Q T T 0 qs m g F o Q QT Fig. Hot luid element 1 T T M M T o M MT T F A T qs A( ) m g Fig.3 Pie element T Second International Conerence on Emerging Trend in Engineering (SICETE) Dr.J.J.Magdum College o Engineering, Jayingur 66 Page

5 Amlitude in meter Magnitude Exerimental and Theoretical Invetigation o Combined Eect o Fluid and Thermal Induced IV Reult and dicuion Figure 4 and 5 indicate the tranient reone o the tube and undamental natural requency at uly air reure o bar and at ambient 31 0 C. Exeriment were reeated or 1 bar, 3 bar, 4 bar and 5 bar with o air being 58 0 C and 78 0 C. Table 1 how the exerimental dilacement o the tube or variou reure and. Table how the exerimental and theoretical undamental requencie o the ie conveying hot air with variou reure and. From the reone analyi it i oberved that dilacement varie rom. mm to 5.3 mm a the reure increae rom bar to 5 bar at ambient o air lowing internally. When the o the air being conveyed through the tube i at 78 0 C and 1 bar reure the dilacement o the tube variou rom. mm to 4.0 mm. The requency o vibration or a tube o 800mm length increae rom.614 Hz to 6.17 Hz or an increae in reure rom 1 bar to 5 bar. Similarly requency o vibration varie rom.614 Hz to Hz or an increae in air rom ambient to 78 0 C. Thi how that a the reure increae the reone become more ocillatory and take more time to attain teady tate. Frequency o tube increae with reure and it decreae with. Thi may be due to the internal reure o air being tranlated into a tenile load along the ie, hence the natural requency increae. With the hot air being conveyed, there would likely be the otening eect that can caue the requency to decreae Time in econd Fig.4 Time reone Frequency Fig. 5 Frequency reone Table 1 Exerimental Dilacement o tube or variou reure and Preure in bar Ambient (31 o C) 58 0 C 78 0 C Preure in bar Table Exerimental and theoretical natural requency or variou and reure Fundamental natural requency (Hz) Exerimental reult Theoretical reult Ambient 31 0 C o the air 58 0 C o the air 78 0 C Ambient 31 0 C o the air 58 0 C o the air 78 0 C Second International Conerence on Emerging Trend in Engineering (SICETE) Dr.J.J.Magdum College o Engineering, Jayingur 67 Page

6 Exerimental and Theoretical Invetigation o Combined Eect o Fluid and Thermal Induced V Concluion Table how the concluding remark obtained exerimentally and theoretically on the undamental requencie o the ie conveying hot air. It i oberved that the requency o vibration increae with the increae in reure and decreae with increae in. The increae in reure increae the velocity o the luid low and reduce the daming eect. Temerature ha an eect on dilacement a well a requency, ince thermal contraction and exanion increae due to high heat traner rate at high velocity. A the o the luid increae, the requency decreae due to otening eect o tube. REFERENCES [1] Paidoui M.P.,Luu T.P. and Laithier B.E., Dynamic o inite length tubular beam conveying luid, Journal o Sound and Vibration, 106, 1986, [] Rouelt J. and Herrmann G., Dynamic behavior o continuou cantilever ie conveying luid near the critical velocity, Journal o Alied Mechanic, 48, 1981, [3] Yih-Hwang Lin and Yau-un Tai, Nonlinear vibration o thimohenko ie conveying luid, Journal o Solid and Structure, 34, 1997, [4] Uik Lee and Hyuckjin Oh,, The ectral element model or ieline conveying internal teady low, Journal o Engineering Structure, 5, 003, [5] Patrick Bar-Avi,, Dynamic reone o rier conveying luid, Journal o Ohore Mechanic and Arctic Engineering, 1, 000, [6] uier G.L. and Metrikine A.V., Exerimental invetigation o dynamic tability o a cantilever ie airating luid, Journal o Fluid and Structure, 4, 008, [7] Paidoui M.P. and Semler C., Non-linear dynamic o a luid conveying cantilever ie with a mall ma attached at the ree end, International Journal o Non-linear Mechanic, 33,1998, [8] Sinha J.., Singh S. and Rama Rao A., Finite element imulation o dynamic behavior o an oen ended cantilever ie conveying luid, Journal o Sound and Vibration, 40(1), 001, [9] Zou G.P.,Cheraghi N.,and Taheri F., Fluid induced vibration o comoite natural ga ieline, Journal o Solid and Structure, 4, 005, [10] Tran T.Q.N, Lee H.P. and Lim S.S., Structural intenity analyi o thin laminated comoite late ubjected thermally induced vibration, Journal o Comoite Structure, 78, 007, [11] idawa-ukla, Vibration o a beam induced by harmonic motion o a heat ource, Journal o Sound and Vibration, 05(), 1997, 13-. [1] Hong C. C., Liao H. W., Lee L. T., e J. B. and Jane. C., Thermally induced vibration o a thermal leeve with the GDQ method, International Journal o Mechanical Science, 47, 005, [13] idawa-ukla J., Alication o green unction to the roblem o thermally induced vibration o a beam, Journal o Sound and Vibration, 6, 003, [14 Blandino J. R and Thornton E. A., Thermally induced vibration o an internally heated beam, Journal o vibration and acoutic, 13, 001, [15] PaidouiM.P., Fluid-Structure interaction ( Academic re, Caliornia,USA, 1998). Second International Conerence on Emerging Trend in Engineering (SICETE) Dr.J.J.Magdum College o Engineering, Jayingur 68 Page