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1 The 3 d Confeence of the Mechanical Engineeing Netwok of Thailand Novembe 4 7, 009, Chiang Mai Eos Compaison of aious Flow elocity Convesion Methods fo Tubulent Flow in Cicula Pipe Khajonsak Jeenkhajon 1,*, Nat oayos 1 and Sumpun Chaitep 1 1 Depatment of Mechanical Engineeing, Chiang Mai Univesity, Chiang Mai, Thailand * Coesponding autho: Tel , Jeenkhajon@hotmail.com Abstact Flow measuement in mechanical system is essential as it can signify the accuacy of key of designed systems such as ated efficiency and pefomance. Pimay objective of this pape focuses on the compaison of mean-velocities measuements obtained fom vaiety of convesion methods (e.g., point of maximum velocity to mean velocity) of Pitot tube applying to tubulent flow. All esults ae then veified them with those calculated fom computational fluid dynamics softwae. Discepancy is eventually justified. Nozzle flow mete is kept as a base efeence fo all compaisons. Reynolds Numbe of flow was between,800 to 1,000,000 inside 0.1m-diamete cicula pipe at oom tempeatue and studied section is position at 10% beyond a fully developed length downsteam the inlet of pipe. The esults showed that the best convesion method occued when the Pitot tube is located at 4.% fom pipe adius whee coesponding eo is lowe than 5% fo all focused Reynolds numbe. The eo tended to decease invesely popotional to Reynolds numbe. Eo of Tial & eo of Pai s equation method, Thee point tansvese method and Exponential n method ae also educe with espect to the inceasing of Reynolds numbe. Howeve, eo of Appoximation method and Nozzle flow mete is inceasing in popotional to Reynolds numbe. 1. Intoduction Fluid flow measuement is an eveyday event. Whethe filling up a ca with petol (gasoline) o wanting to know how much wate the gaden spinkle is consuming, a flow mete is equied. It can be expessed in tems of eithe volume flow ate o mass flow ate. Flow meteing is used in many applications, such as industial pocess contol, city wate systems, petoleum o natual-gas pipeline systems and iigation systems. The fluid involved in measuement may be a liquid, a gas o a mixtue of them (multiphase flow). Flow itself can be confined o closed (as in a pipe o conduit), semiconfined (as in a ive o open channel) o unconfined (as in the wake behide the jet). In each of paticula measuement, a suitable instument of flow measuement should be used, Those includes oifice, ventui, nozzle, vaiable aea, tubine flow mete, ultasonic flow mete, etc. In this cuent study ai flow in pipe and measuement by Pitot tube, is in focus.

2 The Pitot tube is moe commonly used as a eseach tool than commecial flow meteing device. Sometime a Pitot tube is used to measue ai velocities in a duct when eos in the detemination ae toleable. It can be used to establish the aveage velocity acoss the pipe fom measuement made at seveal edial locations. If the point of measuement is fa enough downsteam fom any intefeence, then a single measuement at the cente of pipe will give the maximum velocity (fully developed and unifom flow). Methods that ae used to convet fom maximum velocity to aveage velocity ae studied, fo example, Tial & Eo of Pai's equation, Thee-point tavese and Exponential n. Sometime Pitot tube is not located at the cente of pipe, it might be located at somewhee along a tansvese line of coss-section of pipe whee velocity equal to aveage velocity of pipe. Last method is the easiest way that is the velocity pofile appoximation, fo a tubulent flow the velocity at the cente being about 1. times the mean velocity [5]. Howeve, Pitot tube is not popula fo an industial measuement because it must be pefectly aligned with the velocity vecto. So ove 40% [5] of all liquid, gas, and steam measuements pacticed in industy ae nomally accomplished using diffeential pessue flow mete such as the oifice plate, ventui tube, and nozzle. Thus eos fom convesion methods to eo of nozzle flow mete need to be investigated fo clealy undestanding.. Measuement device.1 Pitot tube The Pitot tube (named afte Heni Pitot in 173) [] measues a fluid velocity by conveting the kinetic enegy of the flow into potential enegy. The convesion takes place at the stagnation point, located at the Pitot tube entance. A pessue at this point is highe than the feesteam (i.e., dynamic) pessue esulting fom the kinematics to potential convesion. This "static" pessue is measued by compaing it to the flow's dynamic pessue with a diffeential manomete Fig. 1 Coss-section of a typical Pitot tube [8] The velocity of the flow can be obtained [7] fom ( P t P s ) = (1) ρ. Nozzle flow mete Nozzle flow mete is one of diffeential pessue flow metes. It is moe expensive than oifice plate but less loss. The nozzle with a smooth guided enty and a shap exit is placed in the pipe to change the flow field and ceate a pessue dop that is used to calculate the flow velocity. A common fom of nozzle is the ASME s long adius nozzle with a thoat pessue tap fo moe accuacy. Fig. ASME long-adius nozzle with a thoat pessue tap [7]

3 The aveage velocity acoss a pipe can calculated fom [7] ( P 1) = β P K () 0 ρ a = (1 s) /( m 1) (6) m = ( )( NRe) (7) Also, the quantity s could be coelated with the Reynolds numbe, i.e. S = ( )( N Re ) (8) Fig.3 Flow coefficient fo an ASME long-adius nozzle with a thoat pessue tap [7] 3. Convesion Method 3.1 Pai s equation Pai developed the complete solution fo velocity distibution of incompessible flow in pipe flows fo tubulent and fully-developed flow [] as max 1 a1 0 a 0 m = (3) is velocity at adius of pipe (Fig 4). The aveage velocity was obtained by the integation of the velocity pofiles ove the pipe coss-section with espective to pipe adius (on du/d). ave (4) a1 a = 1 ( m max When, a1 and a wee uniquely detemined fom the bounday conditions, and m was a paamete which was expected to be a unique function of the Reynolds numbe. Bodkey [] indicated that the paamete m could be expessed as the closet intege to the values given by equations below; a = ( s m) /( m 1) (5) 1 1) 3. Thee-point tavese Thee-point tavese [] is common method which is based upon the Gauss method of integation. The thee points ae located at the cente and at ± The mean velocity is ( ) ave max o o = (9) and velocity at can be calculated fom equation (3) 3.3 Exponent n In fully developed tubulent flow in smooth cicula pipe, as shown in Fig.4. It can be shown that aveage velocity av is elated to the centeline velocity 0 by the expession n ave ( n 1)(n 1) = (10) max Fig. 4 elocity pofile of tubulent flow [3] Fig. 5 Exponent n and velocity atio as a function of Reynolds numbe [3]

4 3.4 Location of Pitot tube In Fig.6 the point of aveage velocity is shown fo powe-law and Pai pofiles fo pipe nomally used in flow measuement. The fixed location fo Pitot tube ecommended by ISO/DIS 7145(1981) fo ±3 pecent accuacy is shown on this cuve. Fig. 6 Location of mean velocity fom pipe wall [4] 3.5 elocity pofile appoximation The tubulent flow with in a pipe is dominated by inetia. Pipe wall effects ae less in significance such that velocity pofile is flatte than that of lamina flow, with the velocity at the cente at 1. times the mean velocity [5]. The exact flow pofile of tubulent flow depends on pipe wall oughness and Reynolds numbe. Fig. 7 shows the fully developed flow pofiles fo tubulent flow. These is the flow pofiles that would be obtained at the end of a vey long pipe, thus ensuing that any changes to the flow pofile due to pipe bends and settings ae no longe in pesence. Fig. 7 elocity pofiles in tubulent flow [5] 4. Methodology The case focused in this wok is on fully developed tubulent flow inside 0.1 m-diamete of cicula pipe. Inne pipe wall is smooth and measuement takes place at 10% of pipe length fa fom the inlet whee fully developed flow is anticipated. All convesion methods ae coelated with a ange of Reynolds numbe stating fom,800 to 1,000,000 and measuements ae taken fo 15 samples. 4.1 Convesion scheme selection Convesion of maximum velocity at cente line of the cicula pipe that get fom Pitot tube to a mean velocity in this wok includes 4 appoaches, i.e., Tial & eo of Pai's equation, Thee-point tavese, Exponential n and elocity pofile appoximation. 4. Location selection fo measuement As seen fom Fig.6, the standadized ISO/DIS7145 (1981) ecommends the fixed location fo measuement at a distance 4.% fom pipe adius. It can be used to establish the aveage velocity acoss the pipe fom measuement made at this location. 4.3 Computational fluid dynamics Computational fluid dynamics is used fo efeence to obtained eo fom each compaison. Additionally it can show a pessue diffeent acoss the nozzle flow mete nomally used in industial. The initial flow condition that was set in CFD was aveage velocity at inlet of pipe and than measued the maximum velocity whee the fluid was fully-develop flow and finally compae both values and find an eo of each method.

5 5. Results and discussion Figue 8 shows eos obtained fom velocity convesion methods compaed fo initial inlet velocity. The best convesion method is achieved when Pitot tube is placed at the distance 4.% fom pipe adius. Coesponding eo is almost steady and lowe than 5% though the ange of study (,800 Re 1,000,000) and the egession of eo value decease invesely with Reynolds numbe. Eo calculated fom of Tial & eo of Pai s equation method, Thee-point tansvese method and the Exponential n method showed simila tendency. On the othe hand, a egession of eo value of Appoximation method and nozzle flow mete is popotional to Reynolds numbe. Tendlines of eo that ae analyzed fom 15 samples of expeiment data fom each method (,800 Re 1,000,000) ae epesented by solid lines while dotted lines ae used to foecast eo value of each method pojected to Reynolds numbe of,000,000 This extapolation is caied out using the egession analysis on equation of each method as compiled in Table 1. Fig. 8 Eo of velocity convesion method Eo of appoximation and location method may be inceased when oughness of pipe diffes since both methods do not use this facto to calculate an aveage velocity. Eo of nozzle flow mete method might change if diffeent geomety of nozzle is selected as inside diamete of nozzle, nozzle adius and length of nozzle can be alteed. Table 1 Equation of velocity convesion methods Method Equation R Type Tial & Eo of Pai's equation (-0.057) y = 19.9x (-0.18) Thee-point tavese y = x (-0.087) Exponential n y = x (0.07) Appoximation y = x Pitot tube 4.% adius y = X Nozzle flow mete y = X Conclusion Fom the esult of all convesion methods which ae used fo convet a maximum velocity value of fluid flow in cicula pipe to mean velocity value. Pitot tube located at a distance 4.% fom a pipe adius is the best convesion method of this study as the coesponding eo is nealy steady and tend to deceases with inceasing Reynolds numbe. All methods in this pape show effective measuement at wide ange of Reynolds numbe sufficient in vaiety of applications. Howeve selection of method of measuement has to be based on not only accuacy but also the consideation of othe factos such as cost, maintenance and installation which is the best fit fo paticula application. 7. Acknowledgement The authos gatefully acknowledge the contibution of Populsion and Aeodynamics Reseach and Application, (PARA) laboatoy,

6 Depatment of Mechanical Engineeing, Faculty of Engineeing, Chiang Mai Univesity, Chiang Mai, Thailand. Thanks also to the suppoting fund fom the Design and Development of Gas tubine poject, the Institute fo Science & Technology Reseach & Development, Chiang Mai Univesity. 8. Nomenclatue = fluid velocity (m/s) P = pessue (Pa) ρ = density (kg/m 3 ) β = atio the nozzle diamete to the pipe diamete K 0 = flow coefficient NRe = Reynolds numbe = pipe adius (m) Subscipt = elated to adius t = total s = static ave = aveage value max = maximum value x,y,z = axis 0 = centeline 1, = position of measuement [4] Richad W. Mille, Flow Measuement Engineeing Handbook (3 d ed.), McGaw-hill, 1996 [5] John G. Webste, Measuement Instumentation and Sensos Handbook, CRC Pess, 1999 [6] Sandy Polak and Caoline Pande, Engineeing Measuements: Methods and Intinsic Eos, Pofessional Engineeing Publishing, 1999 [7] Richad S. Figliola and Donald E. Beasley, Theoy and Design fo Mechanical Measuement (3 d ed.), John Wiley & Sons, 000 [8] Pitot Tube, See also 9. Refeence [1] Fluid Metes, Theoy and Applications (6 th ed.), Ameican Society of Mechanical Enginees, New Yok, 1971 [] Robet S. Bodkey and Hay C. Heshey Tanspot Phenomena: A Unified Appoach, McGaw-hill, 1989 [3] James W. Dally, William F. Riley and Kenneth G. McConnell, Instumentation fo Engineeing Measuement ( nd ed.), John Wiley & Sons, 1993