Supersonic flow over a diamond shaped aerofoil Lab PDF

Preview

Summary

lab report...

Description

Supersonic flow over a Diamond shaped aerofoil. Adam Farley, @00541872 09/11/20

Module: Aerodynamics Lecturer: Dr Andreea Koreanschi

Contents Symbols and abbreviation list ............................................................................................................. 3 Abstract ................................................................................................................................................... 3 Aims and Objectives................................................................................................................................ 3 Introduction ............................................................................................................................................ 4 Equipment list ......................................................................................................................................... 4 Theory ..................................................................................................................................................... 6 Oblique Shock Wave Theory ............................................................................................................... 6 Expansion Wave Theory...................................................................................................................... 6 Experimental Procedure ......................................................................................................................... 7 Calculations ............................................................................................................................................. 8 Oblique Shock Wave ........................................................................................................................... 8 Expansion Wave .................................................................................................................................. 8 Pressure Graphs ................................................................................................................................ 12 Liner 1.4 ........................................................................................................................................ 12 Liner 1.8 ........................................................................................................................................ 13 Discussion.............................................................................................................................................. 14 Conclusion ............................................................................................................................................. 15 References ............................................................................................................................................ 16

Symbols and abbreviation list AoA (α) – Angle of Attack CL – lift coefficient CD – drag coefficient Θ – flow deflection angle

Abstract This report investigates the behaviour of supersonic flow within a normal shockwave over a diamond shaped aerofoil at different Mach and Angle of Attack. For this investigation, 2 different freestream flow Mach numbers were used, 1.4 Mach and 1.8 Mach. From the values recorded in the investigation, we will calculate the lift and drag coefficients.

Aims and Objectives The first objective of this report is to observe and analyse a Diamond shaped aerofoil under supersonic flow, and using geometric and linearized results to calculate the lift and drag coefficients. The second objective is to compare the lift and drag coefficients of 2 different Mach conditions, at 4 different angles of attack to see if a trend is produced, and identify what that trend is. The final objective is to process the data collected into a graph to see where along the aerofoil the different types of shock waves occur.

Introduction Supersonic flow applies to flow that has a Mach number above Mach 1.2 but below Mach 5. Supersonic flow is compressible which means the density varies according to temperature and pressure. [1] When supersonic flow goes over a diamond shaped aerofoil it creates 2 different types of shockwaves, Oblique shock waves and Expansions waves. Oblique shock waves are created when supersonic flow hits sharp pointed object, like a diamond shaped aerofoil. Expansion waves are waves that expand the medium through which they are transmitted. Diamond Shaped aerofoils are used for supersonic flight because the sharp point at the leading edge creates neat shockwaves coming off the aerofoil which causes less turbulent air to surround the aerofoil in flight. A rounded leading edge aerofoil wouldn’t be able to work properly at supersonic speed because of the turbulent air produced when the flow passes over the aerofoil.

Equipment list Diamond Shaped Aerofoil: • • • •

made from steel chord = 49mm span of 25mm Max thickness of 2.5mm

Mach Liners: • •

Mach 1.4 Liner Mach 1.8 Liner

Small Supersonic Wind Tunnel: • • • •

• • •

A manual control gauge connected to a high-pressure storage tank which allowed air to be introduced through an injector. A pressure gauge which indicated how much pressure was being introduced into the system via the injector. a cast iron injector block which introduced the injector pressure at the downstream end of the working section. A mixing chamber made of cast aluminium in which the jet of air from the injector transferred its momentum to the air flowing through the working section, causing a lower pressure. An aluminium diffuser and varnished mahogany plywood return duct to slow the flow and increase static pressure. Gauze screen to allow the injected air in the system to escape. Overhead duct containing wire mesh screens to cause the flow to be of a uniform velocity and low turbulence.

• • •

Fiberglass contraction cone to accelerate and further stabilise the flow containing a pressure taping for the datum. Working section in which the Mach liners are inserted and contains 25 pressure tapings. A graded ruler on the side and handle used to manually change the models angle of attack.

Incline Manometer

Multitube Mercury Manometer

Theory Oblique Shock Wave Theory Continuity equation:

𝜌1 𝑢1 = 𝜌2 𝑢2

𝑝1 + 𝜌1 𝑢12 = 𝑃2 + 𝜌2 𝑢22

Momentum equation:

ℎ1 +

Energy equation:

𝑣21 2

= ℎ2 +

𝑀𝑛1 = 𝑀1 𝑠𝑖𝑛 𝛽

Oblique shock relations:

𝑀𝑛22

𝑣22 2

𝛾−1 2 2 ) 𝑀𝑛1 = (𝛾 − 1) 𝛾𝑀𝑛21 − 2 1+(

(𝛾 + 1)𝑀𝑛21 𝜌2 𝑢1 = = 𝜌1 𝑢2 2 + (𝛾 − 1)𝑀𝑛21

2𝛾 𝑝2 =1+ (𝑀2 − 1) 𝑝1 𝛾 + 1 𝑛1 𝑇2 𝑃2 𝜌1 = 𝑇1 𝑝1 𝜌2

𝜃 – 𝛽 – M relation

𝑀2 =

𝑡𝑎𝑛 𝜃 = 2cotβ

Expansion Wave Theory The Prandtl-Meyer function 𝜈(𝑀) = √ [2].

𝛾+1

𝛾−1

𝑀𝑛2 𝑠𝑖𝑛(𝛽 − 𝜃)

𝑀12 𝑠𝑖𝑛2 𝛽 − 1

𝑀21(𝛾 + 𝑐𝑜𝑠2𝛽) + 2

𝑡𝑎𝑛 −1 √(𝑀2 − 1)

𝛾−1

𝛾+1

− 𝑡𝑎𝑛 −1√𝑀2 − 1

Experimental Procedure The experiment begins by recording the room pressure and temperature using the thermohygrometer barometer. Apparatus checks are then conducted, these checks are; The calibration of the incline manometer, make sure that the injector pressure gauge is set to 0, the external receiver tanks pressure exceed 10 Bar, the mercury manometer is clamped, the model is set to the correct angle of attack for the experiment and the correct liner has been installed into the system. Three participants are positioned at the inclined manometer, operating valve, and mercury manometer. To initiate the experiment, the wind tunnel is started by rotating the value until the gauge reads 8 bar, this value must be turned continuously to maintain the injector pressure, the mercury manometer is then unclamped and allowed to settle for a minute, once settled the inclined manometer can be read and recorded and at the same time the mercury manometer is clamped. Once this has been done, the valve can be closed and all the 28 measurements of the pressure readings from the multitube manometer are recorded. This procedure is conducted for angles of attack 0° 1°, 2° and 3° for both Mach liners 1.4 and 1.8 and all measurements are collated into a table.

Calculations Liner 1.4, AoA = 0:

Figure X, results recorded from experiment 1.4 Mach, 0 Angle of Attack.

Oblique Shock Wave Mn,2 = M2sinβ Β = 47 Mn,2 = 1.44sin47 = 1.053149

P3/P2 = 1 + 2γ/γ+1(Mn,2-1) P3/P2 = 1.127311 P3 = 1.127311 x 30138.12493 = 33975.03 Pa

Expansion Wave 𝛾−1

1+( 2 )𝑀𝑛,22 Mn,32 = 𝛾−1 𝛾𝑀𝑛,22 −( 2 )

Mn,32 = 0.90345

Mn,3 = 0.950368

Mn,32 =

1+0.2(1.0532 )

1.4(1.0532 )−0.2

𝑀𝑛,3 M3 = sin (𝛽−𝜃)

θ = 0, β = 47

M3 = 1.366135

T3/T2 =

𝜌2

𝑃3 𝜌2 𝑥 𝑃2 𝜌3

𝜌3

T3/T2 = 1.034883

=

ν(M3) = √𝛾 + 1 (𝛾 − 1)𝑡𝑎𝑛 −1 √(𝑀32 − 1)

(𝛾+1)𝑀𝑛,22

2+ 𝛾−1(𝑀𝑛,2 2 )

𝛾−1

𝛾+1

= 1.089312

- 𝑡𝑎𝑛−1 √𝑀32 − 1

ν(M3) = 8

θ = ν(M4) – ν(M3) ν(M4) = ν(M3) + θ

θ = 5.84

ν(M4) = 13.84

Use Trial and Error Method using the equation below to see what Mach number gives a value θ = 13.84. 𝑀2 𝑠𝑖𝑛2 𝛽−1 tanθ = 2cotβ 2 𝑀 (𝛾+𝑐𝑜𝑠2𝛽)+2

When θ = 13.84 M = 1.5656 P02/P2 = (1 + (

𝛾−1 2

𝛾

)𝑀22 )𝛾−1

P02/P2 = 3.367803 P02 = 101499.3 Pa

S3 – S2 = CpLn(T3/T2) – RLn(P3/P2) Cp = 1004.5

R = 287

S3 – S2 = 0.05038

𝑆3−𝑆2 𝑅

P03/P02 = 𝑒 P03/P02 = 1.000176 P03 = 101517.1 Pa

P03 = P04

P04/P4 = 4.03996 P4 = 25128.2 Pa

These are the pressure values obtained from the Oblique shock wave and expansion wave relations and the pressure values calculated from the α = 0ᵒ spreadsheet. Pressure’s (pa) 33963.97 21662.64 33963.97 21662.64

P3 P4 P5 P6

Due to the symmetry of the aerofoil P3=P5 and P4=P6. The pressures are then resolved in the x-axis and y-axis and then multiplied by the length of the area’s surface. AOA = 0 P3 P4 P5 P6

CL =

pressure forces (N/mm) X Y 42455.24 -832322.42 -27078.5 -530865.53 42455.24 832322.42 -27078.5 530865.53

2 𝑥 (832322.42−832322.42+530865.53−530865.53)

1.4 × 30138.12×(1.44)2 × 49

Therefore, for this angle of attack it has no CL.

CD =

2×𝐷

1.4× 31205.453×(1.392)2 × 49

= 0.01

=0

Repeat these calculations using the different values recorded from each experiment.

Figure X, Table of results for Cl and Cd.

Pressure Graphs Liner 1.4

Pressure distributon α=1

Pressure distributon α=0 90000 80000 70000 60000 50000 40000 30000 20000 10000 0

90000 80000 70000 60000 50000 40000 30000 20000 10000 0 0

5

10

15

20

25

0

30

5

10

15

20

25

Oblique Shock Waves between stations 18 – 19

Oblique Shock Waves between stations 17 – 18

Expansion Waves between stations 19 – 20

Expansion Waves between stations 19 – 20

Pressure distributon α=2

90000

Pressure distributon α=3

90000

80000

80000

70000

70000

60000

60000

50000

50000

40000

40000

30000

30000

20000

20000

10000

10000

0

30

0 0

5

10

15

20

25

30

0

5

10

15

20

25

Oblique Shock Waves between stations 17 – 19

Oblique Shock Waves between stations 16 – 19

Expansion Waves between stations 19 – 21

Expansion Waves between stations 19 – 22

30

Liner 1.8

Pressure distributon α=1

Pressure distributon α=0 100000 100000 90000 80000 70000 60000 50000 40000 30000 20000 10000 0

90000 80000 70000 60000 50000 40000 30000 20000

0

5

10

15

20

25

30

10000 0 0

Pressure distributon α=2

5

10

15

20

25

30

Pressure distributon α=3 100000

100000 90000 80000 70000 60000 50000 40000 30000 20000 10000 0

90000 80000 70000 60000 50000 40000 30000 20000

0

5

10

15

20

25

30

10000 0 0

5

10

15

20

25

30

Discussion The first aim of the experiment was to analyse the shockwaves created by the diamond shaped aerofoil in supersonic flow. The experiment shows that both oblique shock waves and expansion waves were created. We can tell this because of the graphical representation of the static pressure throughout the small supersonic wind tunnel. The oblique shock waves are identified on the graph because they show a steep increase in the static pressure. The expansion waves occur after the oblique shock waves and are identified by a decrease in the static pressure which begins to gradually increase after the shock.

The second aim was to calculate the lift and drag coefficients for each experimental condition and compare it with other results to see if the results show a trend and see if the trend they are showing is correct. My results show the trend that by increasing the angle of attack of the aerofoil we will also increase the lift and drag caused by the aerofoil. These results comply with the results from a separate paper [3], As well as what we expect to happen theoretically. For the report that was used to compare my results, I only compared my trend of lift and drag to theirs because the paper was observing other aspects of aerodynamics which didn’t apply to my experiment. One point that needs to be made for this experiment is that if the free stream velocity in front of the aerofoil M...