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UNIVERSITY OF SALFORD School of Computing, Science and Engineering

Aerodynamics E3 Laboratory Experiment

Performance Characteristics of a Two-Stage Axial-Flow Compressor

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Abstract In this experiment the performance characteristics of a two-stage axial-flow compressor was investigated in terms of compressor efficiency, pressure ratio and mass flow rate. The surge stage of the compressor occurs at different points at different RPM inputs. Graphs and tables are produced to analyse the behaviour of the axial-compressor at 2000, 2500 and 3000 RPMs. These discussion and conclusion proves that the increase of the RPM, increases the efficiency of the compressor.

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Table of contents Abstract..............................................................................................................................2 1.

Introduction................................................................................................................4

2.

Aims and objectives...................................................................................................4

3.

Theory........................................................................................................................5

4.

Description of Apparatus............................................................................................7

5.

Project methodology..................................................................................................9 5.1

Experimental methodology.................................................................................9

5.2

Theoretical calculations......................................................................................9

6.

Results......................................................................................................................11

7.

Discussion................................................................................................................13

8.

Conclusion................................................................................................................14

References.......................................................................................................................15 Appendix – Data analysis................................................................................................16 Appendix – Results tables...............................................................................................17

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1. Introduction Air compressors are used nowadays in various industries having the aim to provide compressed and pressurized air for a large range of applications. The technology of the air compressors has developed through the history since 3000 B.C. when the first air compressors was used in metallurgy. Nowadays, there are several types of modern compressors. For example, in the aerospace industry, air compressors are used to pump the fuel into space shuttle engines. Gresh (2001) defines a compressor as a device that transfers energy to a gaseous fluid for the purpose of raising temperature of the fluid as in the case where the compressor is the prime mover of the fluid through the process. There are two types of compressors positive displacement and dynamic. An axial compressor is considered a dynamic one, depending on motion to transfer energy from the compressor rotor to the process gas. An axial compressor imparts momentum to a gas by means of a cascade of airfoils. The lift and drag coefficients of the airfoil shape determine the compressor characteristics (Gresh, 2001). The performance of an axial compressor is characterized by the pressure ratio across the compressor CPR, the rotational speed of the shaft necessary to produce the pressure increase, and an efficiency factor that indicates how much additional work is required relative to an ideal compressor. There are additional important compressor topics, like stall and surge, which can be further discussed. (Axial Compressor, 2017)

2. Aims and objectives The aim of this laboratory is to evaluate the performance characteristics of an axial-flow compressor power by an electric motor, in terms of stagnation pressure rise, mass flow-rate and isentropic efficiency of the compression process. The isentropic efficiency is determined by measuring the useful power transferred to the air flow through the compressor as a function of shaft power required to drive the compressor. A range of shaft rotational speeds (2000, 2500 and 3000RPM) and air mass-flow rates are considered to give a trend-line for isentropic efficiency that will pass through the optimal or peak value. Graphs and tables are produced to analyse the behaviour of the flow including surge conditions, mass-flow rates, pressure increase and compressor efficiency at different shaft rotational speeds.

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3. Theory A figure showing the schematic arrangement of the compressor is showed below.

Figure 3.1 – Schematic arrangement (Source: Laboratory Notes)

The theory covers the calculation of the mass flow rate across the tube, the stagnation pressure rise across compressor and the compressor isentropic efficiency. The theoretical calculation is based on some assumption such as the variation of the density is low and it can be neglected. Bernoulli’s equation is applied across the Venturi between two points; the flow is incompressible, so the conservation of massflow rate through the Venturi is applied. Rearranging these equations, gives equation (1) which represents the equation of mass-flow rate. 1 1 P2+ ρV 22 =p 3+ ρ v 23 2 2 m ´ air= ρV 2 A 2= ρV 3 A 3

m ´ air = A3

√[ ( ) ] 2 ρ Δ P23

A 1− 3 A2

2

(Eq .3 .1)

The stagnation pressure is constant downstream of the compressor. The Bernoulli’s Equation is used to calculate the total pressure increase. 1 Δ p0 =P 3+ ρV 23−P 01 2

( ρV 3 A 3 )

2

Δ P0 =P 3−P01 +

2 ρ A 32

=P3−P01 +

´ 2air m 2 ρ A32 5

(Eq .3.2)

Assuming that the flow passing through the compressor is isentropic, the compressor isentropic efficiency can be defined as the useful power transferred to the air flow divided by the shaft power input for the electric motor. ηc =

m ´ air C p ΔT 0 T qs ω

Applying isentropic relations across the compressor and inserting the specific heat ratio for the air (=1.4) gives:

(

T0 Δ P0 = +1 T 01 P01

)

γ−1 γ

−1

For the axial compressors, the stagnation pressure rise is small and the terms in the brackets can be expanded using the binomial theorem, therefore:

(( )

)

( )

( )

ΔT 0 γ −1 Δ P0 = 1+ +… −1 γ T 01 P01 ΔT 0=T 01

γ −1 Δ P 0 = RT 01 ΔP 0 1 Δ P 0 = P01 P01 C P ρ C P γ

Finally, the isentropic efficiency of the compressor becomes: ηc =

m ´ air ΔP 0 (Eq .3 .3) ρ T qs ω

The figure below illustrates a typical graph of an axial compressor in terms of increase in pressure ratio vs the mass flow rate. This can be either plotted in terms of x vs y, or y vs x. The surge line, lines of constant efficiency are showed on the graph. The design point represents the desired point that the axial compressor efficiency should achieve. This point increases with the rise in the pressure ratio.

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Figure 3.2 – Pressure ratio vs Mass Flow Rate (Shepherd, 1960) According to Yadav (2014), surging is the complete breakdown of steady through flow, affecting the whole machine, in other words, when stalling takes place on all the blades simultaneously. This leads to choking of the flow. Sometimes even reversal of the flow may take place. Heavy vibrations also occur.

4. Description of Apparatus A description of apparatus used in the experiment is listed below. The compressor used in this experiment is a Budworth two stage, axial flow compressor which is driven by an electric motor. The motor can be set at different speeds, but for this exercise it is set between 2000 to 3000RPM. A Venturi tube having six pressure tapings is used to measure the pressure of the mass-flow rate through the duct. Furthermore, the compressor is equipped with a butterfly valve which is placed downstream of the compressor which has the role of controlling the air which passes the duct. A figure with the axial compressor is showed below.

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Figure 4.1 – Budworth axial flow compressor

The pressure at different locations is measured using a multi tube water manometer. The values recorded are then converted into S.I. units to be able to calculate the mass-flow rate across the duct. Figure 4.2 shows the multi tube manometer with 13 stations to measure the pressure at a 90° angle.

Figure 4.2 – Multi tube water manometer

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In this experiment, a digital and analog shaft are used. The digital shaft shows an offset of the actual torque of the shaft which needs to be deducted from the final torque result. The shaft rotation is showed in RPM on the right-hand side of Figure 4.3.

Figure 4.3 – Experiment gauges The ambient temperature along with the laboratory pressure are recorded and measured using a thermometer and respectively, a barometer.

5. Project methodology The project methodology for this laboratory involves the experimental procedure in which the data is recorded from the apparatus and theoretical calculations which covers the analysis of the data recorded in the previous stage.

5.1 Experimental methodology Experimental procedure is done by following the steps listed below:       

The butterfly valve is opened completed in order to have a maximum flow rate. The compressor rotational speed is set firstly to 2000 r.p.m. From the tachometer, the shaft rotational speed is recorded (ω in r.p.m.). The torque input to the compressor is recorded (Tqs in kgf.ft). The water tube manometer is recorded (in inH2O). The butterfly valve control is turned one revolution and the above 3 measurements are repeated. The butterfly valve control is turned until the compressor goes into surge. The 3 measurements are repeated and recorded, as well.

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 

The whole process is redone at a compressor rotational speed of 2500 and nearly 3000 r.p.m. The laboratory temperature (To1 in °C) and pressure (Po1 in cmHg) is recorded.

5.2 Theoretical calculations The first step in order to start the data analysis is to convert the laboratory temperature and pressure in S.I. units, K and N/m2, respectively. Therefore, T ( K )=273.15+℃=273.15+ 20=293.15 K

Patm =ρmercury gh=13.530 x 9.80665 x 754=100043.72 Pa (

N ) m2

Using the Equation of State for a perfect gas, the air density is evaluated. P=RρT , therefore ρ=

100043.72 kg P = =1.1891 3 RT 287∗293.15 m

Water manometer readings are converted to gauge pressure (Pa or N/mm2) as shown below. The height is in meters and density is in S.I. units, kg/m 3. Therefore,1inch of H2O in the manometer tube is equal to 249.09 Pa. This conversion factor will be used in further calculations. Pmanometer =ρwater gh=1000 x 9.80665 x 0.0254=249.09 Pa (

N ) 2 m

To calculate the mass flow rate, the pressure drop across the Venturi tube needs evaluating. A generic example using the conversion factor found above is showed below. The tables with the results for all runs is attached to Appendix – Data Analysis. 1 ∆ P23 =P2− P3 =[ (h2+ h3 +h4 +h5)−h6 ]∗ρWater∗g 4

(needs to be S.I. units, Pa)

1 ∆ P23 =P2− P3 =[ (13 + 13 + 12.9+ 13.1)− 5.3 ]∗249.09=1917.9 Pa 4 Therefore, the mass flow rate (in kg/s) can be calculated. m air = A3

√

2 ρ ∆ P23 2

A 1−( 3 ) A2

Where, A2= πr2 = π (0.354/2)2 = 0.09842m2 and A3=0.03664m2. A generic calculation for a random run is showed below. The calculation for the three runs are attached to Appendix – Data Analysis.

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m air =0.03644

√

2∗1.1891∗1917.9 =2.67 kg / s 0.03644 2 1−( ) 0.09842

The total pressure increase is calculated by expressing the pressure in terms of the air mass-flow rate. Therefore,

[

2

]

m air 1 ∆ P0=P 3−P01 + , where P 3−P01 = h1− ( h2 + h3 +h 4 +h5) ρg ( Pa ) 2 4 2 ρ A3

[

]

1 2.67 2 ∆ P0= 7.8− ( 13 + 13 + 12.9 + 13.1 ) ∗249.09+ =931.32 Pa 4 2∗1.1891∗0.03664 2 In order to calculate the compressor isentropic efficiency, ηc, the compressor shaft power Tqs is converted to Nm using two conversion factors, while the shaft rotational speed is converted from rpm to rad/s. Therefore, 1ft= 0.3048m and 1kgfm = 9.80665 Nm. Actual Torque (Nm)= 12.19 * 0.3048 * 9.80665=36.44 Nm (where the residual torque was already subtracted -0.01) Shaft power (rad/s) = 2 *RPM *π /60 = 209.33 rad/s. Therefore, the isentropic m air ∆ P0 2.67∗931.32 ηc= =0.2738 . = ρT qs ω 1.1891∗36.44∗209.33

efficiency

is

The spreadsheet used for calculation of all values for the three runs (2000, 2500 and 3000 RPM) is attached to Appendix – Data analysis. These table are further used to plot the results graph in Section 6 which are further discussed and analysed.

6. Results The results section covers a set of graphs which are further used in analysing the behaviour of flow through the axial compressor. The tables used in creating the graphs are attached to Appendix – Results tables.

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Stagnation Pressure Rise vs Mass Flow rate 4.00 3.75

Mass Flow Rate (kg/s)

3.50 3.25 3.00 2000RPM 2500RPM 3000RPM

2.75 2.50 2.25 2.00 1.75 1.50 1.25 450.00

650.00

850.00 1050.00 1250.00 1450.00 1650.00 1850.00 2050.00

∆P0 (Pa or N/m^2)

Figure 6.1 – Stagnation Pressure Rise vs Mass Flow Rate

Compressor Efficiency vs Mass Flow Rate 4.00

Mass fow rate (kg/s)

3.50 3.00 2000RPM 2500RPM 300RPM

2.50 2.00 1.50 1.00 0.10

0.13

0.15

0.18

0.20

0.23

0.25

0.28

0.30

0.33

Compressor efficiency

Figure 6.2 – Compressor Efficiency vs Mass Flow rate

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∆P0/ω^2 vs Mair/ω 0.013 0.012 0.011

Mair/ω

0.010 0.009 0.008 0.007 0.006 0.010

0.012

0.014

0.016

0.018

0.020

0.022

∆P0/ω^2

Figure 6.3 - ∆P0/ω2 vs Mair/ω

Compressor efficiency vs Mair/ω 0.013 0.012 0.011

Mair/ω

0.010

2000RPM 2500RPM 3000RPM

0.009 0.008 0.007 0.006 0.10

0.13

0.15

0.18

0.20

0.23

0.25

0.28

Compressor efficiency

Figure 6.4 – Compressor efficiency vs Mair/ω

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0.30

0.33

7. Discussion The discussion section involves an analysis of the resulted graphs, a comparison of the reality process with the theoretical approach, a further discussion about the compressor surge and efficiency. The first graph showed in Figure 6.1 illustrates the rise in stagnation pressure ∆P0 against the mass flow rate. For each shaft speed the curves have the same trend. The highest mass-flow rate occurs at the highest shaft speed, respectively 3000RPM. By comparing the three lines, the surge for 2000RPM occurs at the last 3 points, while at higher RPM rates occurs at the last 2 points. Furthermore, the surge is also showed by a suddenly sharp drop in stagnation pressure. The Compressor Efficiency vs Mass Flow rate graph has the same pattern as the previous one. An increase in the shaft speed of the axial compressors translates into an increase of the isentropic compressor efficiency. However, the gradient of the graph is different being more linear than the previous one. Overall, this proves the theory of axial compressor which are more efficient at higher shaft rotational speeds. When the compressor hits the surge points, there is massive drop in efficiency from around 0.3 to 0.12. The graph of ∆P0/ω2 vs Mair/ω is non-dimensional having the data lying on a single trend line. The surge occurs relatively at the same points as the previous graphs. However, only there is a slightly difference between the 2000RPM line and the other two, 2500 and 3000RPM, which gently collapses over each other. This can come from an error of data recording or instrument error. The last graph showed in Figure 6.4 illustrated the compressor efficiency vs Mair/ ω. The graph is more linear in comparison with the previous ones. By analysis of the graph and the tables, the surge occurs at the last 3 points at 2000RPM, while at higher RPM occurs at the last 2 points. During the surge, Mair/ω has the same value for all rotational speeds, while in the compressor efficiency is difference of +, - 0.01. Due to this fact, the three rotational speeds do not lie completely on a single trend line. Surge has been traditionally defined as the lower limit of stable operation in a compressor, and it involves the reversal for flow. Compressors are usually operated at a working line, separated by some safety margin from the surge line (Boyce, 2006). A surge is mainly caused by a decrease in the mass flow rate, an increase in the rotational speed of the impeller or both, when basically the stators inside the compressors are stalling. Operating at a higher efficiency implies operation closer to surge. Basically, it can be said that the surge occurs when there is a breakdown of the flow through the compressor and it takes place when all the blades of the compressor have stalled simultaneously leading to a choked flow. On a given corrected speed line, as the corrected mass flow is reduced the pressure ratio increases until it reaches a limiting value on the surge line. For an operating point at or near the surge line the orderly flow in the compressor tends to break down and can become violently unsteady (Boyce, 2006). 14

According to Boyce (2006), the performance losses in an axial flow compressor can be divided into two groups, losses encountered in the rotor and loses encountered in the stator. These can be further described as disc friction and skin friction loss, incidence loss or wake and exist loss. The performance efficiency calculation can also have errors which has the source in the data measurement and apparatus. The assumption made at the beginning of the calculations, the flow being isentropic which means the change in density of the flow is negligible may be incorrect for some points along the ‘duct’ of the axial compressor as the measurements cannot be taken inside the compressor. Another source of error can be the tapings along the Venturi tube which proved to be unreliable, as one of them has fallen during the first stage of the laboratory experiment.

8. Conclusion The resulted graphs show that there is a slightly increase in the compressor efficiency with the increase of the input RPM, the most efficient stage being at 3000RPM. When the compressors blades enter the stall stage, the axial compressor gets into the surge stage showing a suddenly decrease in mass flow rate and pressure ratio and, respectively in compressor efficiency. It was found out that the surge points are different for each RPM input, therefore when designing an axial compressor this should be taken into consideration.

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References A...