The air then passes through a rotating row of blades resulting in the increase in pressure and velocity. The high velocity of the air in the exit of the impeller is converted into additional pressure rise by velocity reduction in the volute which acts basically as a fluid collection channel. The air at higher pressure is then delivered through the outlet duct and is finally discharged into a chamber or the atmosphere. (About a centrifugal fan and the volute: please see the illustrating figures at the appendix. ) A large number Of variables are usually involved in heartrending the fan performance.
Dimensional analysis is often used to reduce the number of variables to manageable number Of dimensionless groups. This method offers an economy in characterization of the performance of turbo- machine (e. G. A fan) in terms off few numbers of non-dimensional groups. In addition to this, dimensional analysis (applied through the concepts of similitude and modeling) also enables the prediction of the performance of turbo-machine by conducting tests on a scaled model at different operating variables e. G. Rotational speed and fluid density. Objectives
To determine the relationship between pressure rise and flow rate to characterize the performance of a centrifugal tan at different rotational speed using dimensional analysis, To use the dimensionless performance characteristic curves of the scale model to make estimates of physical quantities relevant to a geometrically similar prototype fan unit. Scope This experiment is conducted to show only some basic applications and advantages of the dimensional analysis on a centrifugal fond,vary curved impeller. Deeper understanding of both this analysis method and Other turbo-machines are not required.
THEORY REVIEW Application Of dimensional analysis to characterize fan performance The important parameters which describe the performance characteristics of a fan are the pressure rise, flow rate and input power. The fan performance is also determined by the following geometrical and operating variables: fluid density, rotational speed, impeller diameter and viscosity of the fluid. The functional relationship can be express as: Using OZ, p, D as repeating variables and applying Bucking n-theorem (see the appendix), a set of dimensionless groups can be derived.
Each group relates en performance parameter to other variables, For fans running at high Reynolds number (see appendix), the effect of Reynolds number is less significant and usually not directly represented in similitude studies. The functional relationships of dimensionless groups are traditionally expressed as The above three equations provide the desired complete similarity relationships among a family of geometrically similar fans However, only two equations can be used unconditionally for geometrically similar machines of different sizes at high Re number. The last one still relates to others efficiencies of the turbo-machine. Efficiency and input power should not be derived using similarity laws. Granular for Processing Fan Performance Parameters from Measured Data Estimation of Volume Vivo Rate For each setting of the volume flow rate control, the volume flow rate, Q mm/s, can be measured by a Venture meter and is given by The working fluid for this experiment is air. Hence the ideal gas law can be applied to estimate the density of air as follows: Pat = Pratt Where Pat Atmospheric pressure in Whim Gas constant – 287 J/keg.
K for air Temperature of atmospheric air in K ATM DESIGN OF REPORT The equipment provided to carry out the experiment consists of a model centrifugal tan, a venture meter and a flow regulator mounted on a bench top. Manometers and instruments to record current and voltage are provided to decapitate the necessary measurements. Note that the manometers are calibrated to give the direct reading of pressure change in N/mm. PROCEDURES 1. Record the atmospheric pressure and the temperature of the air in the laboratory so as to estimate the density of air, 2.
Switch on the power supply to the fan unit to start the experiment. 3. The rotational speed of the fan will automatically be set to the maximum of 2100 PRM. Record this maximum speed. 4. For this maximum rotational speed, record readings for the pressure developed across the fan and the pressure drop across the venture meter for different volume flow rates by adjusting the flow control damper (located at the fan exit) between 00 (fully opened) and 900 (fully closed). You may take about 10 readings between these limits. They are O, 5, 10 15, 20, 30, 40, 50, 70, 90 degrees. . Repeat the test at 75% Of maximum rotational speed. RESULTS After measuring all necessary data, we have 2 tables and 2 graph attached. We just write measured data into blank in MS Excel file, all necessary variables will be automatically calculated based on formulae in the “theorem review’ section. It is not necessary to calculate them by hand. DISCUSSION 1. Comparing 2 graphs plotted, we can see the main differences: a. On the Fig. 1, there are 2 distinct curves while on the Fig. 2, 2 curves coincide into the almost unique line. B. Distribution of data: On the Fig. , values gained at the same degree Of the flow control damper of 2 RPM regimes are quite different at both flow rate and pressure rise except tort the general curves’ shape. Meanwhile on he Fig. 2, respective pressure coefficient and flow coefficient are almost the same at different degree of the flow control damper. Based on what we see, we can deduce the advantage of dimensionless coefficients: using dimensionless coefficient can help gaining general views about problems, we do not need conducting the exactly conditions experiment, instead of that, we conduct the scaled model.
This reduces both difficulty and economic burden. 2. We have ICQ = Q (wad) In addition, based on data collected on the table, we can see that the nearest one to the ICQ = 0. 2 at the best efficiency point is 0. 935 (PRM = 2103) and 0. 1945 (RPM = 1500). In each case, it is easily to find out respective Q and w. Sows can easily calculate the diameter Of the fan is almost the same D = 0. 144 m (1st case) and D = 0. 1385 m (2nd case) Conclusion, D – 0. Mm. In our dimensionless graph, When ICQ = 0. 2, Cd = 0. 25, Which supports our calculation. 3.
Based on the test result achieved using RPM = 2103, we can predict the fan performance at RPM = 1500: a, GRAM=ISO 0. 75 x GRAM Max Calculating and comparing with the second table data, this guess is accurate. B, Shutoff head happens at the same position Q 0 , The best efficiency still occurs at the same position in the dimensionless graph ICQ 0. 2, cap -2. 25. 4. Comparing with typical performance curve off types of fan: forward, backward and radial (the technician in charge provides), we can conclude that in this experiment, we use forward curved fan. . Specific speed Ins, essentially, Ins = ICQ/2/ cap,’4 Where ha = ( pixie – Pinole) / (pig) the actual head rise. Normally, specific speed varies with flow coefficient just as other coefficients and efficiency discussed earlier do. However, when talking about specific speed, it implies to specific peed at highest efficiency point, In this case, ICQ at the peak of efficiency, Approximated, we see that at fan RPM= 2103, the nearest one to the peak efficiency ICQ = 0. 1935, cap = 0 2519, so Ins 1. 371 at fan RPM- of the Max one, the nearest one to the peak efficiency ICQ = 0. 1345, Cap = 0. 2553, so Ins = 1. 2258 (k) and are almost equal, INS – 1. 23. The significance Of Ins: Ins is dimensionless, therefore it is independent of the system of units used in its evaluation as long as the system is consistent. The concept Of specific speed makes it possible to choose the most appropriate pump for specific using, cause it contains information Of head, flow rate, and speed required.