Square Duct Experiment - Research Paper Example

AIR DUCT Table of contents 1.0 Introduction 1 1.1 Objectives of this study were 1 2.0 Theory 2 2.1 Pitot-static tube 2 2.2 Coefficient of discharge: 3 2.3 Turndown ratio 4 2.4 Fan Characteristic 5 3.0 Operating procedure 7 3.1 Starting up 7 3.2 Experimental Operation 7 3.2.1 Experiment 7 3.2.2 Experiment 2: 7 3.3 Shut Down 7 4.0 Results 9 4.1 Velocity profiles 9 4.2 Velocity profile for This section we look at the velocity profiles when the flowrate from the flow meter was 94.23 kg/hr. 4.2.1Velocity profile for  QUOTE

9 4.2.1Velocity profile for  QUOTE

9 4.2.2 Velocity profile for  QUOTE

10 4.2.3 Velocity profile for  QUOTE

11 4.2.4 Flow rate calculation for  QUOTE

11 4.3 Velocity profile for =187.39kg/hr 12 4.3.1 Velocity profile for  QUOTE

12 4.3.2 Velocity profile for  QUOTE

13 4.3.3 Velocity profile for  QUOTE

14 4.3.4 Flow rate calculation for  QUOTE

14 4.4 Velocity profile for  QUOTE

15 4.4.1 Velocity profile for  QUOTE

15 4.4.2 Velocity profile for  QUOTE

16 4.4.3 Velocity profile for  QUOTE

17 4.4.4 Flow rate calculation for  QUOTE

18 4.5 Comparison of calculated and flowmeter values 18 4.6 Discharge coefficients against Reynolds number 19 4.7 Fan characteristics 20 4.8 Turndown ration 21 5.0 Discussion and conclusion 22 5.1 Discussion 22 5.2 Conclusion 23 References 24 ABSTRACT This report is about air duct that consist a square section that is linked to the fan. The square section culminates to a circular section partly made of steel and other section made of Perspex section. The duct has installation of the three flow measuring devices: venturi, orifice and pitot tube. In the theory section the principles behind the working of the devices have been given where in both devices change in pressure is used in the calculation. For the venturi and orifice the drop considered involves the entire cross section of the system and thus resulting to flowrate duct system being obtained. For the case of the pitot tube velocities were obtained for various points in the square section using the difference between  and  and then the average velocities was used to calculate flow rate. The velocities in the section were also found to fluctuate along the x-axis which was a clear indication that the flow was turbulent in the duct. As expected the velocities calculated from the tube were found to be higher as the flowmeter flow rate was increased. The existent of turbulent flow was also seen to exist from the Reynold number plots where it was found that in all the flow considered Reynold number was over 20 000. The Cd values calculated were found to be higher in the venturi than in the orifice. The turn down ratio was found to be 4.612 for venturi and 7.202 in orifice. It was concluded that this experiment managed to successfully highlight the principles behind the working of the venturi, orifice and pitite tube. 1.0 Introduction The air duct construction consists of a section that is circular and made of stainless steel and the other section having Perspex section. In the duct there is installation of a venturi, orifice and pitot tube and there are associated pressure tapping and also we have Enfress & Hauser t-mass flowmeter. The generation of airflow is achieved by use of fan and the discharge rate is adjusted by use of throttle dumper located at the end of the duct. 1.1 Objectives of this study were 1. To plot illustrative velocity profiles in the square duct by means of pitot traverses, and hence use this to calculate the air flowrate in the duct. 2. To understand the principle of measuring over different flow measuring devices. 3. To calibrate the venturi and orifice meters by measuring the pressure drop across the meter versus flowrate. The discharge coefficients for each flowrate tested may then be calculated. 4. To plot the discharge coefficients against Reynolds number and compare the plots with published data. 5. To estimate the turndown ratio of the venturi and orifice meters. 6. To obtain the fan characteristic by plotting the pressure head produced by the fan against the flow rate delivered. 2.0 Theory 2.1 Pitot-static tube: A pitot static tube is an instrument consisting of two concentric tubes, the inner pitot tube and the outer static tube (Coulson and Richardson, 1999). The diagram of the tube is as shown Figure 1.1 considering a particle of the air stream as it approaches the pitot tube along the axis of tube with velocity u, the particle will stagnate as it approaches the nose of the tube with the result being the lose of kinetic energy. With conservation of energy principle put into consideration, the kinetic energy will be converted to pressure energy. This means that the impact pressure  that is experienced at the nose of tube is above the static or hydrostatic pressure  in the duct. The difference in pressure  corresponds to loss in kinetic energy and is referred to as dynamic pressure. The dynamic pressure is therefore expressed as Where  representing density of air in the duct. This density of air calculation involves assumption that air is an ideal gas, and having the knowledge that 22.4 m3 will be occupied by 1 kmol of an ideal gas at STP (1 atm and temperature 273) and using the temperature and pressure measurements at the lab. 2.2 Coefficient of discharge: The coefficient of discharge Cd for a venturi or orifice plate is derived from the discharge equation through the devices given by Coulson and Richardson (1999) and is given by With Q representing volume flow rate,  is the density of fluid (air) that is passing through the meter,  gives the pressure drop in the meter  with being the entry pressure while  is the vena contracta pressure  and being the cross sectional area of the pipe and vena contracta respectively. When dealing with an orifice as opposed to the venturi there is replacement of  with  where the later is larger than the former. As a result of this difference in areas we have the coefficient of discharge for the orifice being smaller than that of the venturi for same . The equation giving the coefficient of discharge is only applicable when dealing with fluids that are not compressible (Herschel, 1898). In the equation we have the constant Cd that acts as a correctional factor that carter for friction in fluids and the flow patterns as the fluid is approaching the vena contracta or orifice. 2.3 Turndown ratio Any flow meter will only serve satisfactorily in a certain range of flowrates. The turndown is the term given to the ratio between maximum to minimum flow rates. The ratio serves as a very important criterion when it comes to the selection of type of flow meter that is to be used in a specific situation. Generally rotameters have higher turndown ratio than orifice or venturi. Qmax, which is the maximum flowrate in the Air Duct that can be handled by a venturi and orifice meters, is fixed by the equipment as a whole. On the other hand Qmin is the minimum measurable flowrate that can be measured with desired precision. The precision, which can be proportional or percentage error, for the measurement being made will deteriorate with decreasing flowrate. Letting  to be the reading registered on a venturi or orifice meter manometer which corresponds to a flow rate Q , the we can have Turndown ration   (5) Now there can be determination of turndown ratio using the equation (5) (Pentz and Shott, 1988). Determining of  is achieved through setting the baffle aperture to a position that there is no  even when the baffle position is changed further. On the other hand  assessment is through the accuracy of the manometer that is put to use in measuring. 2.4 Fan Characteristic The characteristic curve of a fan, compressor or pump is a plot of the pressure head produced by the fan against the flow rate delivered. This curve important when making choice of the device for specific pumping duty. The pressure head is given by the difference between the discharge pressure and suction pressures of the fan, which is expressed as a head. The suction pressure point has pressure atmospheric level, i.e. zero gauge pressure, and the discharge pressure is the static pressure in the duct near the fan exit (Adrian, 1993). The two pressures must be expressed on a consistent basis, i.e. both absolute or both gauge pressures. Fans are single-stage centrifugal- or axial-flow units used to deliver a large flow of gas at a small pressure head. For a fan the pressure ratios achieved does not exceed 1.03. 3.0 Operating procedure 3.1 Starting up To start the damper was opened at the end of the duct to approximately 50mm. the mains was then turned on, followed by pressing the fan start button on the power panel. The damper was then adjusted according to the flow rate depending on what was needed. 3.2 Experimental Operation 3.2.1 Experiment This involved producing vertical and horizontal and vertical velocity over the square duct through traversing of the pitot tube vertically and horizontally as can be seen in figure 2.2. There was use of FE1 in comparing the experimentally determined flowrate. 3.2.2 Experiment 2: Measurements of flowrates of air were taken at for 10 runs,. For the 10 runs flow rate was measured using FE1, there was measurement of Δp of the in-line devices (venturi and orifice plate), also pressure recovery was measured was measured downstream the devices. The other measurement taken was the static pressure in the duct (for the fan characteristic). 3.3 Shut Down Shutting down the system involved switching of the mains supply Figure 2.1 4.0 Results 4.1 Velocity profiles This section gives the plots of velocity profiles in 5 different x positions at at y=9.5; y=8.5 and at y=7.5. The velocity profiles by applying the equation Velocity  4.2 Velocity profile for =94.23kg/hr This section we look at the velocity profiles when the flowrate from the flow meter was 94.23 kg/hr. 4.2.1Velocity profile for =94.23kg/hr at y=9.5 Figure 4.1 gives the velocity profiles along the x-axis at y=9.5. It can be seen that the highest velocity points were x=3 and x=6 with calculated velocities of about 3.9m/s for both points. It can also be observed that x=4.5 had the lowest velocity. Figure 4.1 4.2.2 Velocity profile for =94.23kg/hr at y=8.5 Figure 4.2 gives the velocity profiles along the x-axis at y=8.5. It can be seen that the positions with highest velocity we at x=6 and x=7.5 with calculated velocities of about 3.9 and 3.8 respectively. Position x=4.5 has the list value of 3.44. Figure 4.2 4.2.3 Velocity profile for =94.23kg/hr at y=7.5 Figure 4.3 gives the velocity profiles along the x-axis at y=7.5. It can be seen from the graph that the velocity was highest at x=1.5 dropped at a small rate to the lowest in the next 3 positions but the last point along the axis is seen to have a higher velocity than that its predecessor. The velocity ranged between 4m/s to 3.1m/s. Figure 4.3 4.2.4 Flow rate calculation for =94.23kg/hr velocity profiles Table 3.1 gives a summary of all the velocity profiles and positions. Using excel the average velocity profiles was calculated by summing up of the velocities and dividing by the number of locations. The average velocity was obtained as 3.468249 as can be seen from table 3.3. The other quantities were calculated as illustrated in the table with the calculated mass flow rate being found to be 139.2112kg/hr. Table 3.1 u 3.560847 3.900712 3.440105 3.900712 3.790811 u 3.560847 3.900712 3.440105 3.900712 3.790811 u 4.002529 3.55634 3.310772 3.180887 3.435751 Table 3.2 Average velocity v 3.468249 Volumetric flowrate =(vxA) 0.032688 Mass flowrate kg/s 0.03867 Mass flowrate kg/hr 139.2112 4.3 Velocity profile for =187.39kg/hr This section we look at the velocity profiles when the flowrate from the flow meter was 187.39kg/hr. 4.3.1 Velocity profile for =187.39kg/hr at y=9.5 From the figure 4.4 it can be seen that the velocity started at lowest and then rose to a maximum before coming down. It can be seen the velocity just dropped slightly below 5m/s , but the rest of the points had velocity of more than 5m/s with the highest velocity being about 5.8m/s. Figure 4.4 4.3.2 Velocity profile for =187.39kg/hr at y=8.5 From figure 4.5 it can be seen that the velocity along the x-axis was increasing with the lowest velocity at 1.5 being about 5m/s and the maximum velocity rising to go beyond 6m/s for the last to points. Figure 4.5 4.3.3 Velocity profile for =187.39kg/hr at y=7.5 The velocity along the x-axis at y=7.5 was as shown in figure 4.6 where it can be seen there was fluctuation in velocity along the axis. The velocity ranged between 5m/s to about 5.8m/s with the first point having lowest velocity and the last having the highest velocity level. Figure 4.6 4.3.4 Flow rate calculation for =187.39kg/hr velocity profiles Table 3.3 gives a summary of all the velocity profiles when the flowmeter reading was187.39kg/hr. Using excel the average velocity profiles was calculated by summing up of the velocities and dividing by the number of locations. A can be seen from table 3.4 the average velocity for all the 15 points was obtained as 5.503193m/s. The other quantities were calculated as illustrated in the table with the calculated mass flow being 220.8914kg/hr. Table 3.3 u 4.942807 5.351975 5.73201 5.73201 5.272682 u 5.027305 5.351975 5.583101 6.225204 6.225204 u 5.025189 5.270463 5.655664 5.349722 5.802589 14.9953 15.97441 16.97078 17.30694 17.30047 Table 3.4 Average velocity v 5.503193 Volumetric flowrate =(vxA) 0.051867 Mass flowrate kg/s 0.061359 Mass flowrate kg/hr 220.8914 4.4 Velocity profile for =234.116kg/hr In this sub-section we look at the velocity profiles when the flowrate from the flow meter was 234.116kg/hr 4.4.1 Velocity profile for =234.116kg/hr at y=9.5 In figure 4.7 it can be observed that there was fluctuation of velocity moving along the x-axis for y=9.5 but the velocity were generally high with only one point being slightly below 6.9 with the rest having velocity of more than 7m/s. Figure 4.7 4.4.2 Velocity profile for =234.116kg/hr at y=8.5 From figure 4.8 it can be seen that the velocity steadily to a maximum then dropped along the x-axis. The velocity ranged between 6.5m/s to just above 7.2m/s where the highest velocity was at x=4.5 Figure 4.8 4.4.3 Velocity profile for =234.116kg/hr at y=7.5 From figure 4.8 it can be seen there was fluctuation in velocity a long the x-axis with the highest velocity attained being just above 7.3m/s and with the lowest velocity being 6.95 at x=7.5 Figure 4.9 4.4.4 Flow rate calculation for =94.23kg/hr velocity profiles The summary of all the velocity profiles for flowmeter reading at 234.116kg/hr are as shown in table 4.5. Using excel the average velocity profiles was calculated by summing up of the velocities and dividing by the number of locations. In table 4.6 it can be seen that the average velocity for all the 15 points was obtained as 7.019953m/s. The other quantities were calculated as illustrated in the table with the calculated mass flow being 281.7722kg/hr. Table 4.5 X1 X2 X3 X4 X5 u 6.88895 7.13074 7.13074 7.010887 7.071068 u 6.509446 6.827164 7.248612 7.071068 6.764814 u 7.010887 7.306835 7.071068 7.306835 6.950186 Table 4.6 Average velocity v 7.019953 Volumetric flowrate =(vxA) 0.066162 Mass flowrate kg/s 0.07827 Mass flowrate kg/hr 281.7722 4.5 Comparison of calculated and flowmeter values Table 4.7 gives a comparison of the flowrates as read from flow meters along side the calculated flow rates. The errors in the values have also been calculated with the flowmeter reading being used as the base for calculating the errors. From the table it can be seen that the calculated values were all above flow meter values. Figure 4.10 clearly shows how the figures compare. Table 4.7 Calculated value Flowmeter value Error 134.7301 94.23 40.99 220.8914 187.39 17.87 281.7722 234.116 20.36 Figure 4.10 4.6 Discharge coefficients against Reynolds number Figure 4.11 shows the relationship between Cd and Reynold numbers for the venturi and the orifice. From the figure it can be seen that Cd values were higher in the ventruri than in the orifice at the same Reynold number points. It can also be seen that as the velocity increased, as signified by the increasing Reynold number, there was a decrease in Cd. Although according to theory the value of Cd , cannot go beyond 1 it can be seen that at a number of points in the venturi surpassed the 1 mark. From the graph it can also be seen that the flow was entirely turbulent with Reynold number well over 4000. Figure 4.11 4.7 Fan characteristics Figure shows a fan characteristic curve where change in level of pressure for different level of flowrates are shown. From the graph it can be seen that the fan shows almost linear relationship between pressure and flow rate, up to 250m3/hr discharge. Figure 4.12 4.8 Turndown ration The turn down ration is found by applying the formula   For venturi the ration was obtained at  = (941.5-622.5)PA and  Turn down ration for venturi =    For orifice the ration was obtained at  =(898-120)PA and  Turn down ration for orifice =  5.0 Discussion and conclusion 5.1 Discussion In the first part the pitote was used to obtain static pressure and dynamic pressure which were then used in calculation of velocity at different points in the square section of the system. It was seen that there was fluctuation of velocity along the x-axis. This could be attributed to the fact that the flow of air in the system was at a very high speed and this resulted to turbulent flow. With turbulent flow it is possible to have points which are towards the centre of the section area having lover velocity than the points which are close to the wall, even though under laminar flow this would not be the case. The existence of turbulent flow was seen with the high Reynold numbers that were associated with the different flow rates. The velocity profiles were found to increase with the increase in the rate of flow. This was as expected because of the fact that increasing flow rate in the system it means the air has to move much faster. There was calculation of velocity at 15 different points for each flow rate the results were present for five points along the x-axis at a time. The approximated velocity of air in the duct was obtained by averaging the velocity for the 15 points and then the average velocity was used in calculating the flow rate across the system. All the three discharges obtained through calculation were found to be above the flow meter flow rates. The discrepancy between the calculated and the flow meter flowrate was found to be highest in the smallest flow rate. This could be attributed to the fact that at a lower discharge the instrument was less accurate. This can be seen in the graphs of change pressure of the fan against flow rate where it could be seen that low flow rate had results that did not show consistency with some points being seen as outliers. The general high values for calculated flow rates can be attributed to the fact that the pitote results into increased turbulence and considering the high velocity in the system this would to high pressure difference which in turn results to high velocity being obtained. When Cd was plotted against Reynold number for both the venturi and the orifice, it was found that the Cd value in the former were higher than in the later in all flow rates as represented by the Reynold numbers. It was noted that the Cd values for the venturi were going beyond 1. This is not supposed to be the case as can be seen from the theory in deriving the equation of calculating Cd. A venturi that is well designed to minimize energy losses will have a Cd of about 0.98. With the possible Cd value being very close to 1 the Cd values slightly above I obtained in this experiment can be attributed to experimental errors. The calculation of Cd involves use a number of quantities which are taken by instruments that are likely to have errors. For flow rate used in calculation is obtained by flowmeters which are erroneous, also the pressure measurements may be erroneous. When these quantities are used in calculation, they increase errors and thus may results to a larger than expected value. Even with errors the results for this experiment were consistent with what was expected. 5.2 Conclusion From this experiment we have seen the principles flow measuring devices such as venturi, pitote tube have been enumerated. It has been seen that the venturi has higher efficiency with it Cd value being higher than that of an orifice. Even though the pitote gave results that were different from the results which were different from flow meter results, it was seen that it was superior in terms of its ability to give velocity at different points of cross section. References Adrian, R. J., editor (1993); Selected on Laser Doppler Velocimetry, S.P.I.E. Milestone Series, ISBN 978-0-8194-1297-3 Boljanovic, V. Applied Mathematical and Physical Formulas, 2nd ed. [Online]; Industrial Press: South Norwalk, CT, 2016; pp 351.http://app.knovel.com/hotlink/toc/id:kpAMPFE001/applied-mathematical/applied-mathematical (accessed March 14, 2017). Coulson, J.M. and Richardson, J.F. (1999), Chapter 6: Flow and Pressure Measurement, In: Chemical Engineering Volume 1, 6th Edition, Butterworth-Heinemann, Oxford, ISBN 0 7506 4444 3. Herschel, Clemens. (1898). Measuring Water. Providence, RI:Builders Iron Foundry. Kahn, M. K. Fluid Mechanics and Machinery [Online]; Oxford University Press: New York, NY, 2015; pp 508. http://app.knovel.com/hotlink/toc/id:kpFMM00004/fluid-mechanicsmachinery/fluid-mechanics-machinery (accessed March 14, 2017). Pentz, M. and Shott, M. (1988), Handling Experimental Data, Open University Press. Read More