Numerical Simulation and Experimental Verification of Air Flow through a Heated Pipe

Transcription

1 International Journal of Mechanical & Mechatronic Engineering IJMME-IJENS Vol:0 No:02 7 Numerical Simulation and Exerimental Verification of Air Flow through a Heated Pie Qaier Abba, M. Mahabat Khan, Rizwan Sabir, Yair Mehmood Khan, Zafar Ullah Korehi Abtract The henomenon of forced convection with turbulent flow i chaotic, comlex and hard to develo analytically. Only key to the roblem i exerimental correlation and numerical olution. The goal of our roject i to validate the Dittu-Boelter euation, a correlation ued to find the value of heat tranfer coefficient h for turbulent flow in many fluid tranfer ytem. Heat tranfer coefficient h and friction factor are very imortant arameter becaue they determine rate of heat tranfer and the reure dro reectively. Thi aer ue three method to determine thee arameter, Correlation, CFD imulation and exeriment. Thi aer will dicu how the Dittu-Boelter euation i alied to the roblem of circular ie. Index Term Pie Flow, Dittu Boelter, CFD, Fluent, Nuelt I. INTRODUCTION Dittu Boelter relation The conventional exreion for calculating the heat tranfer coefficient in fully develoed turbulent flow in mooth ie i the Dittu Boelter []. Nu m n C Re Pr () where C, m and n are contant determined exerimentally. We will ue thee value - C=0.023, m=0.8 and n 0.4 for heating of the fluid n 0.3 for cooling of the fluid Dittu Boelter relation arameter are defined in [2]. The roertie of thi relation have been calculated at the average fluid bulk temerature. Euation () i valid for ingle hae heat tranfer in fully develoed turbulent flow in Manucrit received: March 0, 200. Thi work wa uorted in art by the Deartment of Mechatronic Engineering, Air Univerity, Ilamabad, Pakitan Qaier Abba i with the Air Univerity, E-9, PAF Comlex, Ilamabad, Pakitan ( aier.abba@mail.au.edu.k) Dr. Zafar Ullah Korehi i the Dean of Engineering, Air Univerity ( zafar@mail.au.edu.k) mooth ie for fluid with Prandtl number ranging from 0.6 to 00 at low heat fluxe. At high fluxe the fluid roertie change reulting in higher error. At higher heat fluxe the Sieder-Tate euation i ued to reduce the error. For a detailed comarion between the Dittu Boelter euation and the Sieder Tate euation one may refer to [3]. The work reented i about deigning and acuiring data from an exerimental etu to verify the Dittu -Boelter emirical relation by finding the heat tranfer coefficient. The value of the heat tranfer coefficient ha been calculated from theory, exeriment and CFD imulation to comare the reult. Thi reearch work ue different aroache to calculate two very imortant erformance conideration, heat tranfer rate and reure dro in turbulent duct flow, uing Re, Pr and Nu. Thi work i not only baed on thermal fluid but a major art of the roject i the deign of the comlete hardware and oftware of a data acuiition ytem. It comrie the integration of different field of knowledge uch a intrumentation, microroceor, C++, Viual Baic, electronic, ignal conditioning, etc. It comrie of the undertanding of different temerature and reure enor, their ue and comuter interfacing and analyzing techniue. II. MATHEMATICAL MODELING For laminar flow in ie the heat tranfer coefficient ( h ) and the friction factor ( f ) can be found by olving the governed differential euation analytically. But in the cae of turbulent flow thing become chaotic and it i imoible to olve differential euation analytically. For turbulent flow we rely on exeriment and develo correlation. One uch correlation i Dittu-Boelter euation. A. Dittu-Boelter euation It i ued to find out overall convective heat tranfer coefficient. The euation i Nu 0.023Re Pr (2) where D Re (3)

2 International Journal of Mechanical & Mechatronic Engineering IJMME-IJENS Vol:0 No:02 8 and C k Pr (4) Nuelt number i alo hd Nu (5) k Subtituting euation (3), (4) and (5) in (2) and olving for h, we get h k D D 0.8 C k Thi i one method ued to calculate the heat tranfer coefficient; there are two more method- energy balance and comuter imulation. B. Preure Dro The reure dro i of vital imortance ince we can determine the reure to utain the flow uing a um or a fan (blower in our cae). P 2 f 2D x 2 x where i the length of the flow region. The value of the reure dro deend on the friction factor of the ie ln Re.64 2 f (8) for 3000 Re 50 6 The value of the friction factor can alo be determined by uing the Moody Chart for fully develoed terbulent flow in tube [4]. C. Energy Balance Energy balance i alied to the air flowing in the ie. The energy which i roduced by the heater i carried away by the air flowing inide the ie and only a mall ortion of the heat roduced i lot by natural convection from the outer urface of the ie. We will make the following aumtion for alying the energy balance rincile:. Ma flow rate i contant. 2. Heat tranfer occur at the inner urface of the ie only. 3. No haft work i done by the fluid. 4. Contant heat flux i alied at the urface. 0.4 (6) (7) Then we can ay that convection heat tranfer to the fluid i eual to the rate at which thermal energy of the fluid increae for an ideal ga. Therefore we can write: conv m m2 mc T T (9) Where T m and T m2 are the mean temerature at the inlet and at the outlet reectively. Furthermore conv i the total heat tranferred to air by forced convection and i given by: conv Where T m m ha T T (0) urface temerature. i the average mean temerature and T i the Comaring (9) and (0), we get mc T h A T We can write conv where m T T Pdx m m2 conv a: (2) () // the contant urface heat flux and P i the erimeter of the ie. Hence the temerature rofile come out to be: T m x P Tm x (3) mc Thi relationhi i linear and how that mean temerature of the air increae a it move through the ie and i lotted in the reult ection. D. Heat Lo Heat lo can be mot imortant factor to be conidered for large error. Hence uitable inulating material ha been ued to minimize the heat lo radially. lo T ha m2 T t k A in (4) Euation (4) can be ued to calculate the heat lo radially, in our cae the heat lo i 3.04 (5) lo

3 International Journal of Mechanical & Mechatronic Engineering IJMME-IJENS Vol:0 No:02 9 III. CFD SIMULATION IN FLUENT The third method i the CFD imulation. All of our work i done in GAMBIT and FLUENT 6.. Thee are very owerful tool with many advanced feature. We have created the geometry and meh in GAMBIT. In mehing we have ued edge mehing techniue with high meh concentration where the gradient are large. The boundarie are alo ecified in the GAMBIT. A from the fig. it i clear that the ytem i ymmetric, hence we ue ymmetry to horten our comutational time. There are two art of the ie one i unheated ection wall and other i heated ection wall2. IV. EXPERIMENT In the exeriment, a coer ie wa ued which i heated along it circumference with contant heat flux. Air i blown through the ie and the wall temerature i noted at different interval uing enor. The reure and centerline temerature of the fluid i alo noted at the beginning and at the end of the ie uing enor (ee fig. 2). The data i then analyzed in the comuter and the heat tranfer coefficient i calculated. Fig.. Contant heat flux on ie Boundary tye are ecified in GAMBIT are given a Boundarie Inlet Outlet Centerline T ABLE I BOUNDARY TYPES Tye Velocity inlet Preure outlet Axi Fig. 2. Exerimental Layout The coer ie i uorted on tand and connected to a blower fixed on a table. All the intrumentation and interfacing circuitry reide on the table. The ie i heated externally by mean of electric reitance heater. Air i blown through one end of the ie and remove heat by forced convection while the other ide of the ie i oen. Heater and the ie are well inulated uing gla wool to make ure that maximum heat flux hould go inide the ie intead of convected away. Temerature enor are attached at the outer urface of the ie between the heater and one temerature enor i attached to meaure the centerline temerature of the fluid at the outut. Similarly two reure enor are alo attached at the inlet and outlet of the ie to meaure the reure difference. The actual exerimental etu i hown in fig. 3. Wall Wall Wall2 Wall The olver and the boundary condition are ecified in FLUENT 6.. We have ued egregated olver with axymmetric ace and k-eilon (2 en) for turbulent modeling. The working condition are given below in table II. T ABLE II WORKING CONDITIONS Inlet velocity 30 (m/) Contant heat flux on Wall2 Inlet temerature (W/ ) 33 (k) The Convergence criteria are choen to be *e-6. Reidual lot tell u about the minimum error we allow. Fig. 3. The exerimental etu The ie ued i made of ure coer and the ecification are given in table III.

4 International Journal of Mechanical & Mechatronic Engineering IJMME-IJENS Vol:0 No:02 0 Length of the ie O uter diameter Wall thickne Inner diameter T ABLE III PIPE SPECIFICATIONS 3.38 m ( feet) 0.38 m m 0.34 m Cutom made heater were ued which are band tye heater (Fig. 4) wraed around the ie on a length of.8 meter. Heater are made uing Nichrome wire which rovide heat when electric current i aed through it. V. RESULTS After the meh indeendence ha been achieved the velocity rofile for the terbulent flow in the ie i hown in fig. 5 where a vicou ub layer or film i formed along the inner wall of the ie. In thi cae a mooth ie i conidered with the friction factor found from the knowledge of Reynold Number and develoed by Petukhov e. (8). According to [6] the terbulent boundary ha three layer, vicou layer or laminar ublayer where the laminar hear tree are dominant, overla region where a tranition i in effect and the outer layer where the terbulent hear tre i more dominant. Fig. 4. Cutom made band tye heater The ecification of the heater are hown in table IV. T ABLE IV SPECIFICATIONS OF THE HEATER Number of heater attached 8 Length of each heater 0.85 m Power of each heater 98.5 watt Length of heated ection.8 m Total heat flux 788 watt Length of Nichrome wire in m each heater Reitance er meter of 64 ohm Nichrome wire Thickne of mica heet m The blower we have ued i an ordinary dut blower. It ha a converging nozzle outlet which i inerted in the ie and the blower itelf i fixed on the table. Number aociated with blower are given in the table V. T ABLE V SPECIFICATIONS OF THE BLOWER Ma flow rate.8 kg/min Air eed Nozzle diameter Power 30 m/ 0.03 m 550 (W) 5 u v* where Fig. 5. Terbulent boundary layer 2 * u w (6) and w DP 4l (7) From the known arameter, the hear tre i calculated w 2. 43a (8) and hence the vicou ublayer i 6mm (9)

5 International Journal of Mechanical & Mechatronic Engineering IJMME-IJENS Vol:0 No:02 The urface wall temerature for the heated ection of the ie (outer urface) i hown below (fig. 6). The curve how a linear reone once the thermal boundary layer ha develoed. Fig. 8. Centerline velocity rofile of the fluid The comarion of the wall temerature ditribution of the outer urface between the CFD reult and exerimental reult are hown in fig. 9. Fig. 6. Pie outer urface temerature rofile of the heated ection The temerature ditribution along the centerline of the fluid i hown in fig. 7. The temerature remain contant in the unheated ortion and tart riing linearly in the heated ection of the ie. Fig. 9. Comarion of the ie wall urface temerature of the CFD and exerimental reult Fig. 7. Centerline temerature rofile of fluid Fig. 8 how the centerline velocity rofile of the fluid. It i clearly een that the grah i aroximately contant beyond the entrance length. The reult calculated from all three method are comared and given in the table VI. T ABLE VI COMPARISON OF THEORETICAL, CFD AND EXPERIMENTAL RESULTS Method h Correlation CFD Exeriment The value calculated from CFD and Exeriment i comared with the theoretical reult and ha following error. T ABLE VII ERRORS Method Error in h Error in CFD 7.04%.5% Exeriment.4% 3.% VI. CONCLUSION After carrying out exeriment, imulation and calculation we conclude that thee correlation give an error well with in the

6 International Journal of Mechanical & Mechatronic Engineering IJMME-IJENS Vol:0 No:02 2 range 25% and uually le in reciely controlled environment. Thee reult are good enough to make an engineering ene rather to have nothing at all (in the cae of analytical olution which i not oible). The reult clearly validate the ue of Dittu-Boelter correlation in many indutrial alication. There are many reaon which contribute to the error. The heat lo doe account for error, but the value of heat lo i negligible a comared to total heat flux. The heater are local made and do not rovide contant urface heat flux although we have tried to control wattage of each heater. Secondly all enor (temerature and reure enor) are attached in a cloe roximity of 220 V AC line coming from heater. Therefore ignal from enor are ditorted and give an error. If omehow thee roblem are overcome reult may imrove. REFERENCES [] Dittu, F. W., and L. M. K. Boelter. Univerity of California (Berkley) Pub. Eng., vol. 2.,. 443, 930. [2] Holman, J. P., Heat Tranfer, 9 th edition, Mc Graw Hill, [3] Diane L. Linne, Michael L. Meyer, Tim Edward, and David A. Eitman. Evaluation of Heat Tranfer and Thermal Stability of Suercritical JP 7 Fuel. NASA Technical Memorandum [4] Incroera, Fundamental of Heat and Ma Tranfer, 5th edition, John Wiley and Son [5] J. R. Lamarh & Anthony B., Intro to Nuclear Engineering, 3 rd edition, Wiley [6] Munon, Young, Okihi, Fundamental of Fluid Dynamic, 4 th edition, Wiley [7] Tichakorn, Forced Convection, reearch aer, Cornell Univerity, Nov 2004 [8] Mechanical and Aeroace Engineering Laboratory, Forced Convection Heat Tranfer, State Univerity of New Jerey [9] Alication note, Active Filter Deign, Texa intrument [0] Alication note, AN699, AN823, AN990, AN682, AN685, AN687, AN684 Microchi Technology Inc..