o Compare results with theory and empiric al data ChapterT-1- Flow across a Tube Bank Problem Description

Transcription

1 Obiectives o Creating the SolidWorks model of the tube bank. Setting up Flow Simulation projects for extemal flow o Inserting boundary condition. Running the calculations ' Using cut plots and Xy prots to visualize the resulting flow field o Compare results with theory and empiric al data Problem Description In this chapter, we will use Flow Simulation to study the two-dimensional flow across a tube bank' we will use a total of twelve 20 mm diametercylinders in an in-line arrangement. The cylinders will have a temperature of 373.2K and the free stream velocity of the air will be 4 m/s. Thc temperature and velocity fields will be shown inside the tube bank and the development of both temperature and velocity profiles after the tube bank. The exit temperature of the fluid from Flow simulation calculations will be compared with theoretical and empirical results. Figure 7.0 SolidWorks model of in-linc tube bank ChapterT-1-

2 ttizard - lnitial and Ambient fonditionl )0 1t) t) Parametet Psrameter Definition Thermodynamic Parameters Farameters: Fressure Temperature Veloci$r Parameters Fararneter: Velocity in X direction Velocity in Y direrrtion Velocity in Z direclisn Value User Delined Pressure, temperature Pa t Velocity 4 m/s 0 mrs 0 mis Figure 7.8b) Setting the velocity in the X-direction 5 E f o Figure 7.8c) Setting the result resolution Modifvinq the Computational Domain and Mesh 9. Select Flow Simulation>>Computational Domain... Click on the Boundary Condition tab and select XY - Plane Flow from the 2D plane flow: drop down menu. Click on the OK button to exit the Computational Domain window. Select Flow Simulation>>Initial Mesh... Uncheck thc Automatic setting box at the bottom of the window. Change the Number of cells per X: to 198 and set Number of cells per Y: to 300 and Number of cells per Zz to l. Click on the OK button to exit the Initial Mesh window. Flouc Snulatitn i bvn&+, H Proie':t Insert pt' eeneral Settirrgs... EJ Unts,,. computational Dcrnain,,. Figure 7.9a) Modiffing the computational domain Chapter7-6-

3 Flord S{adatxn I urgow tk Proiect Si=e BoundaryCondition Color Setting 2D plane flow: Figure 7.9b) Selecting2D plane flow Insert ff Generalsetthgs.,, Units,.. Q Comput"tionalDomain... ffi rnmatmesh,,, Figure 7.9c) Modifiing initial mesh Easrc Mesh Solid/FliJ lrrerface Eahirg Cels Nurorer Chamab Number o[ ceil' Nurnber of cells perx: Number of cells per!': Number ol cels per Z: 198 Ior: I l-c"*"r_l i- H+-l Figure 7.9d) Setting the number of cells lnsertin g Boundarv Conditions l0' Select lsometric view from the view orientation drop down menu in the graphics window. Select Flow Simulation>>Insert>>Boundary condition... Select,t ",*"1u. cylindrical surfaces' click on the * wall button in the Type portion of the Boundary condition window and select Real wall' Adjust the wall remperature 3 b 373.2K by clicking on the button and enter the numerical value in the wall Parameters window. click ok v2 to exit the Boundary Condition lg \-- ' I lroretric E El I not*es ard zonr Ere m#l to the ism-etric viee{ riertetidn Figure 7.10a) Selecting an isometric view Figure 7.10b) Selection of cylindrical surfaces Chapter 7-7 -

4 7.13a) shows the pressure gradient along the tube bank. distribution in the same cross section and figure 7.13c) Figure 7.13b) is showing the velocity is showing the temperature distribution. Flilir; Lu,rrn -,r,,tn l;lll,l l.lx:t: hx:l: Figure 7.13a) Pressure distribution along the tube bank Figure 7.13b) Velocity distribution along the tube bank Figure 7.13c) Temperaturc distribution along the tube bank Creatins Sketch for XY Plots 14. Click on the I FeatureManager design tree and select the tr'ront Plane. Click on the Sketch tools tab and select Line. Draw a 50 mm long vertical line starting at (X,Y) : (275 mm, 0), see figure 7.l4a). Exit the Line Properties window and draw two more vertical lines with the same length starting at (X,Y): (300 mm, 0) and (X,n: Q25 mm, 0). Close the Insert Line window and select I *.Oorrd from the SolidWorks Menu. Rename the new sketch to the name x:275, 300, 325 mm as shown in figure 7.14d). Chapter 7-1{1-

5 Place the files "xy-prot figure 7.14f)" and..xy-plot figure 7Ja$,, into the Locar Disk (c:)/program f iles/soridworks corp/soridworks Frow simuration /lang/english/templated(y-plots folder to make it available in the Template list. click on the =';' Flow Simulation analysis tree tab. Right click Xy plot and select Insert... check the Temperature box. open the Resolution portion of the Xy plot window and slide the Geometry Resolution as far as it gocs to the right. open the options portion of the Xy plot window and selcct the template xy-plot figure 7.14f) from the template drop down menu. click on the 9 FeatureManager design tree and select the sketch x:27s,300, 325 mm. click ok */ to exitthe XY Plot window. An Excel file will open with a graph of the temperahre across the exit of the tube bank, see figure 7.!4t).Repeat this step once again but choose to check the X - component of velocity box and select the xy-prot figure 7 Jagtemplate. Puun.tEr$ ', sr-i,do A n!r:r,ud', Adffiiond porarnctctr./, E7E,oo.4 Lr'ol'l ', / t Ji5,UU : A 5r-r.r-rrr Figure 7.14a) Drawing a vertical line for the Xy_plot i Re$utld [-n"uru, the prnt. assenb,yl, or drav+rng Figure 7.14b) Rebuilding the new sketch Figure 7.14c) Sketch with three lines for temperature profiles ChapterT-tt-

6 qi E ($ fntine tube bank. (In-Line tube Banlr 5tudy) ':-.1 Sensors + A I Annotations + gl 5olid Bodies(lZ) $] material <not specified> (i Front Phre $ {2 Top Plar'e Rigtrt etan" [. origin * le Extrudel E t I *: ris,3oo, szsmm Figure 7.l4d) Rename the new sketch Figure 7.l4e) Different settings for XY Plot T (K) 300..]li' "r x =275mm x=300mm -x=325mm 295 '07,,/ - thsery Y (m) Figure 7.14D Exit temperatures for the tube bank from Flow Simulation compared with calculations (full line) Chapter7-l2-

7 x=275mm -'---- x=300mm - ---x=325mm v (m) 7.149) Exit vclocities for the tube bank from Flow Simulation Theorv and Empirical Data 15' The Reynolds number for a tube bank is defined based on the maximum velocity u,,". (m/s) in the bank: R D,^o, --!-^g'!- (l) where D (m) is the diameter of the tubes and u (m/s) is the kinematic viscosity of the fluid. t il_+ Figure 7.15a) Geometry of in_line tube bank For the in-line tube arrangement, see figure 7.1Sa),the maximum velocity is related to the approach velocity U: vmax tr - fi - Sru (2) Chapter7-13-

8 For the staggered tube arrangement, see figure 7.15b), the maximum velocity is determined by equation (2) if 2AD> Ar.If 2AD< A7,the maximum velocity is determined by (3) U-+ i: Figure 7.15b) Geometry of staggered tube bank The pressure drop across the tube bank is given by the following equation: ^ n _ NiXpItkM tlr -- ) (4) where llr is the number of rows of tubes in the flow direction,./ is the friction factor, T is a correction factor and p (kg/m^3) is the density of the fluid. The friction factor for in-line and staggered tube banks can be determined from figures 7.l5c) and 7.15d), respectively. ij B".t * 6 4 6sl0l I * 6lt16P I { 6110"3 I r ot11/ 3 { 6r1g'r 1 ft*on*. 6 r+l# Figure 7.15c) Friction factors for in-line tube bank, from Cengel (2003) Chapter7-14-