EX2.2 Lab report PDF

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EX 2.2 Fan pressure report...

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E2.2 STUDY OF FAN PERFORMANCE USING DIMENSIONAL ANLYSIS

1. INTRODUCTION A turbo fan machine produces work energy to increase the total pressure of the fluids leaving the system. This energy is generated by driving rotors or impellers with an external source of power to move rows of blades. In this experiment, we will be focusing on the centrifugal fan. This fan consists of three main components, which are: inlet duct, impeller and a volute casing. The inlet duct allows the flow of fluid(air) to the impeller. The air then passes through the rows of rotating blades which results in an increase in velocity and pressure. The high exit velocity of the air is converted into additional pressure rise. The pressurized air is then expelled into the atmosphere or into a chamber through the outlet duct. Dimensional analysis is often used to characterize the fan performance and it represents data in terms of a few numbers of non-dimensional groups. Dimensional analysis also enables the prediction of turbo fan performance by conducting tests on a scale model at different operating variables such as fluid density and fan rotational speed.

2. OBJECTIVES The first aim of this experiment is to characterize the centrifugal fan performance with dimensional analysis by determining the relationship between pressure rise and the flow rate at different rotational speeds. Secondly, to use the dimensionless performance characteristic curves of the scale model to make estimations of physical quantities of a geometrically similar prototype fan unit.

3. THEORY The parameters used to describe fan performance are pressure rise, flow rate and input power. The fan performance is also influenced by fluid density, rotational speed, impeller diameter and fluid viscosity. These variables can be related by the expression below. f( w´ , ∆ p , Q , ω , D , ρ , μ ¿=o where,       

w=work ´ in put ∆ p= pressure rise Q=flow rate ω=rotational speed D=impeller diameter ρ=fluid density μ=fluid vicosity ¿

A set of dimensionless groups can be derived by using the above variables and applying Buckingham π -theorem. Each expression below relates one performance variable to other variables.

∆p ρ ω2 D 2

Pressure Coefficient: CP =

Q 3 ωD

Flow Coefficient: CQ = Power Coefficient: C w´ =

w ´ p ω 3 D5 ω D2 ρ μ

Reynolds Number: Re =

The effect of fan performance at high Reynolds number is not very significant, hence, it is not represented in similitude studies. The functional relationship of the dimensionless groups can be expressed as:

η=

∆p ρ ω2 D 2

= ∅

1

(

Q ) ω D3

w ´ p ω 3 D5

= ∅

(

Q

2

=

∅ 3(

∆ pQ w ´

=

CP CQ ´ Cw

ω D3

) Q ) ω D3

The above expressions show the relationships of a family of geometrically similar fans. The below two equations can be used unconditionally for geometrically similar machines of different sizes and high Reynolds number. (CP)1 = (CP)2 (CQ)1 = (CQ)2 The above expressions should not be used to derive efficiency and input power. The volume flow rate (Q) can be measured by a venturi meter and can be expressed by: 2 2

Q = Cd At [1−(

1

2 ∆ Pv 2 At ] ) ][ ρ A

and ∆ Pv =¿ (Pl - Pt) in N/ m 2 where, 

Cd = Coefficient of discharge (approximately 0.99)



At = Venturi Throat Area = 0.003848 m 2



A = Venturi Inlet Area = 0.008577 m 2



Pl = Inlet pressure in N / m 2

  

Pt = Throat pressure in N /m 2 ρ

= Density of air

D = Diameter of impeller = 0.14m

The fluid for this experiment is Air. Hence ideal gas law is used to estimate the density of air. Patm = ρ R T atm where 

Patm = Atmospheric pressure in N/ m 2



R = Gas constant = 287 J/kg K



Tatm = Absolute Temperature of atmospheric air in K

4. RESULTS AND DISCUSSION Graph plotting Done on excel. Calculation and discussion 1. The curves in graph 1 are separated from each other and the curves in graph 2 are almost touching. Q Qρω ∆p =∅1 ( ) , ∆ p=∅1 The expressions, , tell us that the increase in the 2 2 3 D ρω D ωD rotational speed of the fan, ω , will shift the curve to the right. For graph 1, the pressure rise of the curves is different since power used is different which results in the gap between the 2 curves plotted. As for graph 2, using the dimensional similarity relationships, the 2 curves plotted will be very close to each other. Both curves are similar in shape and travels downwards. The downward sloping curves can be explained using the Bernoulli’s equation where: 1 2 p+ ρV ∞ + ρgh=constant 2 This equation implies that as the flow rate increases, the pressure rise across the point will decrease. The advantages of using dimensionless coefficients are that firstly, it reduces the number of variables to a manageable number of dimensionless groups, allowing us to work with fewer variables while characterizing the fan performance. With this method, there will be fewer errors and the amount of time required to interpret data from the experiments will be reduced. This method also allows us to predict the consequences of changing one variable by determining the effect of varying its dimensionless group containing the individual variable. Lastly, it allows us to do our experiment in a scaled down model and allow the experiment data to be relevant to a geometrically similar full-scaled model. This allows engineers to save cost and time when working on this experiment.

2. i) Given that (CQ)1 = (CQ)2 = 0.2 at best efficiency point, and diameter of the impeller, D in terms of speed, to be

ω p , CQ

Q , expressing ω D3 and flowrate, Q p is given CQ =

√

Qp . Since we know Q p ,C Q ,∧ω p , we can solve for the diameter of the C Q ωp impeller and hence calculate the size of the prototype fan.

D=

3

ii) For graph 2 where Cp is plotted against CQ, the graphs nearly overlaps and hence it supports the argument in part (i). Because if (Cp)1 = (Cp)2 and (CQ)1 = (CQ)2, then regardless of how (Cp)1 changes with (CQ)1, (Cp)2 will also change with the same amount with (CQ)2. The graphs plotted do not directly overlap with each other and this could be due to inaccuracies from experimental error. For example, there are difficulties in determining the exact pressure readings due to the large intervals in the scale used to measure the pressure in the venturi and fan causing inaccurate readings. Hence, experimental errors will cause a difference between the 2 curves plotted in the Cp VS CQ graph. 3. ωmax = 3000 × 2π/60 = 314.16 rad/s, 75% of ωmax = 2250 x 2π/60 = 235.62 rad/s, Given that D = 0.14m, P atm 101498.34 And using Patm=ρR T atm , ρ = = = 1.204 R T atm 287 x 293.85 The maximum Cp for 3000 RPM curve is 0.1183 and the corresponding CQ = 0.0285 Q Using the equation CQ = , and ωmax = 314.16 rad/s, ω D3 Q is calculated to be = 0.0246 From graph 1, when Q = 0.0246, the 2100 RPM curve gives (∆P) actual = 275Pa Applying (CQ)1 = (CQ)2 = 0.0285 and using CQ =

Q 3 ωD

, where ωmax = 235.62 rad/s,

Q is calculated to be = 0.0184 From graph 1, when Q = 0.0184, the 2100 RPM curve gives (∆P) estimated = 270Pa Hence the deviation of the CP value is 1.852% This can be repeated for other values of CQ to estimate and compare the performance of the fan. From the calculations, it shows that the deviation between the actual pressure rise and estimated pressure rise is small. Hence, the predictions are relatively accurate. The inaccuracies that arises causing the slight deviation may be due to experimental errors such as the large intervals for scales and thick lines used to plot the graph. As such, it is difficult to read the exact value of the coefficients as well as the flowrate, Q, and the change in pressure, ∆P. Also, the actual pressure rise may be smaller than that of the estimated pressure rise due to factors such as dynamic and frictional pressure loss.

4. From the data collected thus far we can tell that the type of impeller used in the fan is a backwards curved impeller fan. The data corresponds to the theoretical graph as shown in figure 1 below.

Figure 1: Pressure vs Airflow 5. Specific speed is a dimensionless geometry-defining parameter which is the speed at which an air mover will deliver one unit of volume against one unit of pressure rise calculated at maximum efficiency. The formula below is the expression for specific speed. ω s= where,     

ω √Q ∆ P f 34 ρ

( )

ω s=specific speed ω=Operational speed Q = Flowrate ∆ Pf =Pressure rise ρ = Density of air

The specific speed of a fan can be used to determine the shape and efficiency of the fan. With this expression, we can also determine which type of fan (forward, backwards or radial) is the mist efficient and practical for applications....