De Montfort University

Design of a rotor blade for axial flow turbomachine
ENGD3036 Plant Analysis and Sustainability

Student number: P15235891
Student name:

Haotian, Wu

10th of January, 2016
Lecturer: Professor Udai Singh

Contents
Abstract
1.0 Introduction ........................................................................................1
2.0 The plot of the blade ..........................................................................2
2.1 Data ..............................................................................................2
2.2procedure .......................................................................................3
3.0 The leading edge and trailing edge .....................................................5
4.0 Calculation of stagger angle at mid-height .........................................7
5.0 Discussion about calculation errors in design ....................................9
6.0 Realistic representation of the stage ..................................................12
7.0 Discussion about generation and effects of ‘shock’ ..........................14
7.1 The generation of the ‘shock’ ......................................................14
7.2 The effect of the ‘shock’ ..............................................................15
8.0 Stress pattern with a tangential load ..................................................16
8.1 3-D model creating ......................................................................16
8.2 Autodesk algor Simulation ..........................................................19
9.0 Conclusion .........................................................................................23
10.0 References .......................................................................................24

List of figures
Figure 1 shows different kinds of blades ........................................................................................................................................................1
Figure 2 shows the cooling design of a blade ...........................................................................................1
Figure 3 The extension of the coordinates ................................................................................................3
Figure 4 Open the txt file with Solidworks2016 .........................................................................................3
Figure 5 shows the curve of blade in Solidworks2016 ..............................................................................4
Figure 6 The save type of blade curve in Solidworks2016 ........................................................................4
Figure 7 shows the leading edge and trailing edge of a blade ..................................................................5
Figure 8 shows the blade with inscribed circles inside ..............................................................................5
Figure 9 shows the leading edge angle of the blade .................................................................................6
Figure 10 shows the trailing angle angle measured ..................................................................................6
Figure 11 The calculation results of mid-height stagger angle from the excel ...........................................9
Figure 12 shows the different results if the temperature was increased 10% ............................................9
Figure 13 shows the effect of the whole blade if the temperature was increased 10% ............................10
Figure 14 shows the effect of the whole blade if the temperature was decreased 10% ...........................10
Figure 15 shows the effect of the whole blade if the Mach number was increased 10% ..........................11
Figure 16 shows the effect of the whole blade if the leading edge angle was increased 10% ..................11
Figure 17 Import the blade diagram into PTC Creo .................................................................................12
Figure 18 The rotation of imported blade diagram in PTC Creo ...............................................................12
Figure 19 shows the diagram after using the mirror in the PTC Creo ......................................................13
Figure 20 shows the position of the stater at a design value of 50% degree of reaction ..........................13
Figure 21 shows the stage at a design value of 50% degree of reaction .................................................13
Figure 22 The Pressure-time diagram observed when the shock wave happens ....................................14
Figure 23 The layer interference because of the shock waves ................................................................15
Figure24 The diagram of shock waves happened in the rotors ................................................................15
Figure 25 The calculations of stagger angles for mid, tip and hub by excel .............................................16
Figure 26 Import the diagram of blade into PTC Creo ..............................................................................16
Figure 27 Creation of three basic planes based on the blade image .......................................................17
Figure 28 Creation of tip and hub sketch planes ......................................................................................17
Figure 29 The sketch of tip, mid and hub of the blade .............................................................................17
Figure 30 The diagrams of tip, mid and hub of the blade .........................................................................18
Figure 31 The solidifying processes of the designed blade .....................................................................18
Figure 32 The solidified blade ..................................................................................................................19
Figure 33 The chosen material for the simulation of rotor blade ..............................................................19
Figure 34 shows the load and constraints on the blade in Algor simulation .............................................20
Figure 35 The displacement of the blade in Algor simulation ...................................................................20
Figure 36 The factor of safety of the blade in Algor simulation .................................................................21
Figure 37 shows the stress pattern on the blade of the obverse of blade ................................................21
Figure 38 shows the stress pattern on the blade of the reverse of blade .................................................22

Abstract

This report mainly focus on the design of a rotor blade. The calculations based on the assumptions were made to carry of the stagger angles and base on the stagger angles, a 3-D model of blade was successfully created. In addition, the Algor simulation was used to analyze the pressure pattern on the blade. On the other hand, the defect of the popular designs such as ‘shock’ loss was also elaborated in this report.
Keywords: Blade; Compressor; Turbine; Shock wave; FEA.

1.0 Introduction
Rotor blades, like the wings of the aircraft, are the essentially cantilevered beams with lift-generating surfaces. The early blades were made of wood which is unstable and quick-wear. More recently, in order to increase the quality of the blades, the fiberglass and epoxy resins were used in manufacturing with complex processes. In general, the request for the greater power means the demand for longer blades. In that case, carbon fibres were added to make the blade lighter and increase the fatigue life. [1]

Figure 1 shows different kinds of blades

A rotor blade is an individual component in the compressor or turbine machine which are already wildly used in many fields from the hairdryer to the airspace engine.
The function of compressor is to compress the low pressure air into high pressure air which can increase the combustion efficiency and the difference of pressure is a method to store up the internal energy.The main function of the turbine is transferring the air or steam internal energy into mechanical energy of the rotating rotor dynamic organization. Because the rotor blades mainly be used in the high speed rotating machines in mechanical engineering such as turbine and compressor, the high temperature working condition is inevitable. Therefore, the cooling for the blades is necessary.
Otherwise, the high temperature will damage the turbine and the blades as the blades are under large centrifugal stresses and materials are weaker at high temperature.
In general, liquid cooling process is more attractive because of high specific heat capacity and chances of evaporative cooling but there are some problems of leakage,corrosion,choking,etc. That works against this method. On the other hand, air cooling allows the discharged air into main flow without any problem. Only 1-3% of main flow can help the blades reduce by 200-300 °C which is a quite high efficiency.
That is why many models of blades were designed hollow or with little holes on it more recently.

Figure 2 shows the cooling design of a blade

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2.0 The plot of the blade
The diagram of this generated blade can be plotted in different methods and in this report, software Solidworks2015 was used to plot the diagram.

2.1 Data
The X and Y co-ordinates around the blade profile (rotor) were given below:

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2.2procedure
In order to draw this diagram, firstly, the dimension was fixed with extending the
Z-axis values as zeros in the notepad.

Figure 3 The extension of the coordinates

Then, saved the text file as .txt and the ANSI coding pattern was be chose in order to be recognized and opened by the Solidworks2015.

Figure 4 Open the txt file with Solidworks2016

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As a result, a 2-dimension diagram was shown up in the Solidworks2015 by inserting curve through X,Y,Z.

Figure 5 shows the curve of blade in Solidworks2016

Finally, the curve was saved as type IGES for next steps.

Figure 6 The save type of blade curve in Solidworks2016

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3.0 The leading edge and trailing edge
In general, the leading edges is the part that contact the air firstly, alternatively it is the foremost edge of an blade.[3]On the other hand, the trailing edge is the edge that the air leave the blade. In addition,the line joining the leading and trailing edges of the blade is defined as its chord.

Figure 7 shows the leading edge and trailing edge of a blade [7]

The blade angles at leading and trailing edge can be worked out by drawing the inscribed circles in the blade and then connect the centers circles with a line in the
PTC Creo. The blade angle at the leading edge is the angle between extension of the line to the outside of the leading edge side and the horizontal line.

Figure 8 shows the blade with inscribed circles inside

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Figure 9 shows the leading edge angle of the blade

In the same way, the blade angle at the trailing edge is the angle between extension of the line to the outside of the trailing edge side and the horizontal line.

Figure 10 shows the trailing angle angle measured

Therefore, from the figures the blade angles at the leading and trailing edges can be seen as 15.64°and 16.57°respectively.

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4.0 Calculation of stagger angle at mid-height
The Mach number is given as M=0.793.
M 

v a (1)

Therefore v  Ma

a  γRT

(2)
(3)

 (12  7  273)  [(12  7  273)  0.263  210]  1.333
 334.11 m/s

Hence v  0.793  334.11  264.95 m/s

Where a is the velocity of axial incoming flow. v is the velocity of the sound in air.

The tangential velocity u can be calculated by the following equation: u 

2N
r
60

(4)

2  3.14  3000
 0.5  157.08 m/s
60

Where:
N is the rotational speed of the blade which is given as 3000rpm. r is the radius from the hub to the mid-height of the blade which is given as 500mm.

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The air incoming angle can be calculated with using of axial incoming speed and the tangential velocity by the equation (5) u Air income angle   tan 1 ( )
(5)
v
157.08
 tan 1 (
)  30.66 °
264.95

In order to achieve the value of stagger angle, the blade angle at leading edge β measured need to be used in the following equation.
Stagger angle i    

(6)

 30.66 - 15.64  15.02

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5.0 Discussion about calculation errors in design
In order to analyze how the results changes if some values changed, an excel sheet was created to finish numerous repeated calculations simply and fast. The equations and results been checked with the calculation part.

Figure 11 The calculation results of mid-height stagger angle from the excel

5.1Assumption 1.
The temperature was increased 10% by mistake from 292K to 321.2 K.
The figure below shows the values changed and the percentage of difference with the values before changed.

Figure 12 shows the different results if the temperature was increased 10%

As can be seen in the figure 12, the change rate of stagger angle is the same as the change rate of the temperature of air and the other values changed less in percentage from 0% to 6%. This 10% error happened on the value of temperature will lead to a
10% error in model design at the mid-height stagger angle.

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For the whole blade, because the stagger angle at tip and hub also change with the change of temperature, the effect of that error to the whole blade is not as much as the effect to the stagger angle of the mid-height of the blade. The figure below shows the error effect to the whole blade:

Figure 13 shows the effect of the whole blade if the temperature was increased 10%

According to the figure 13, the greatest difference is 13.6%. But the mid and hub also changed 10.03% and 8.24% separately. Hence the difference for the design of the whole blade is 9.7345°*13.6% - 15.02°*8.24% ≈ 0.09°

Assumption 2.
The temperature was decreased 10% by mistake from 292K to 262.8 K.
In this assumption, the analysis of the change at mid-height will not be discussed separately but analyze in the whole blade model. The following figure shows the results and differences from the excel.

Figure 14 shows the effect of the whole blade if the temperature was decreased 10%

From the figure 14, it is not hard to find that the greatest difference is 15.41%.
Because the results of stagger angles at mid-height, tip and hub changed together which reduced the effect of this error. The overall difference of stagger angle is
9.7345°*15.41% - 15.02°*9.15% ≈ 0.13°

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Assumption 3.
The mach number taken into calculation has an error of 10% from 0.793 to 0.8723.
The figure 15 shows the results before and after the change and the percentage of difference also shows in the figure.

Figure 15 shows the effect of the whole blade if the Mach number was increased 10%

This figure shows that if the Mach number has 10% error, only three values will change will the it. The three values are Axial velocity, Air income angle and stagger angle. In the overall design, the difference of stagger angle from tip to hub is
9.7345°*21.06% －15.02°*12.82% ≈ 0.12°

Assumption 4.
This assumption mainly focus on what is the effect of different leading edge angles.
If the leading edge angle which is also defined as blade angle increased 10%. The results can easy obtain from the excel. The figure of the results are as follows:

Figure 16 shows the effect of the whole blade if the leading edge angle was increased 10%

Based on the figure 15, the difference of stagger angle from tip to hub can be calculated as 9.7345 ° *16.07% － 15.02 ° *10.41% = 0 ° . That also means the difference of the blade angle has no effect on the whole model in design.

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6.0 Realistic representation of the stage
Procedure
Firstly, the igs file of the 2-D blade diagram was opened in the PTC Creo parametric which can edit the diagram easily.

Figure 17 Import the blade diagram into PTC Creo

When the blade diagram was inputted into the Creo, the original diagram was rotated a same angle as the stagger angle at mid-height of the blade because the rotor mid section is operating at a design value of 50% reaction. The size of the inputted diagram was kept same as the original one.

Figure 18 The rotation of imported blade diagram in PTC Creo

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The function Mirror was used to create a basic figure of stater

Figure 19 shows the diagram after using the mirror in the PTC Creo

Because the axial gap between rotor and stater was assumed as 15% chord and the value of the chord is 100 mm. So the axial gap between rotor and stater is 15 mm which can be located easily by drawing a 15 mm horizontal line. The position of the stater can be fixed at the end of the line.

Figure 20 shows the position of the stater at a design value of 50% degree of reaction

Therefore, the figure of the stage is shown as follows:

Figure 21 shows the stage at a design value of 50% degree of reaction
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7.0 Discussion about generation and effects of ‘shock’
With the rapid development of Aero engine, the improvement of pressure ratio in the compressor is becoming more and more urgent and the modern compressor designer prefer a high tip Mach number more recently. However, the ‘shock’ loss of energy is inevitable. This discussion mainly focus on the generation and effects of ‘shock’ on the performance of a compressor blade passage.

7.1 The generation of the ‘shock’
The ‘shock’ happens when an object (or disturbance) moves faster than the information about it can be propagated into the surrounding fluid. As a result, fluid near the disturbance cannot react or "get out of the way" before the disturbance arrives. In the compressor machine, when the velocity of air is greater than the speed of sound, ‘ shock ’ happens[4].At the region where this occurs, sound waves travailing against the flow reach a point where they cannot travel any further upstream and the pressure progressively builds in that region; a high pressure shock wave rapidly forms. Figure 22 The Pressure-time diagram observed when the shock wave happens.[8]

This figure was observed at an external observation point for the case of a supersonic object propagating past the observer.The leading edge of the object causes a shock
(left, in red) and the trailing edge of the object causes an expansion. This diagram also shows that the ‘shock’ forms in a very short time.

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7.2 The effect of the ‘shock’
The shock wave is relative to the rotating speed. If the shock wave intensity is too large, the total pressure loss of the shock wave itself and the shock wave boundary layer interference are serious, so that the efficiency of the moving blade decreases sharply. Figure 23 The layer interference because of the shock waves [10]

To be specific, if shock waves happen the effects are as follows:
 The air flow will become disturbed and the speed of flow will decrease.
 The incident air flow will be deflected through large angles for the stater.
 The airflow will be easy to be separated.
 The shock will be a loss to the energy and the efficiency of the compressor will drop. Figure24 The diagram of shock waves happened in the rotors [10]

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8.0 Stress pattern with a tangential load
In order to analyze the stress pattern when a tangential load at the tip mid chord, a 3-D model must be created firstly. In addition, the 3-D model is based on the stagger angles that calculated in the excel which is shown as follows:

Figure 25 The calculations of stagger angles for mid, tip and hub by excel

8.1 3-D model creating
Firstly, open the igs file in the PTC Creo.

Figure 26 Import the diagram of blade into PTC Creo

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Then, the 2-D image has already been inserted into the Creo. However, what should be created is a 3-D diagram. So, create 3 planes based on the 2-D diagram.

Figure 27 Creation of three basic planes based on the blade image

Because the 3-D diagram of the rotor blade is based on the stagger angles of mid, tip and hub, the other two planes should be created to sketch the 2-D rotated blades according to the stagger angles.

Figure 28 Creation of tip and hub sketch planes

Then insert the rotated blade images into the other two planes.

Figure 29 The sketch of tip, mid and hub of the blade

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After these steps, the figure of three sketches is shown as follows:

Figure 30 The diagrams of tip, mid and hub of the blade

Finally, use the Boundary Blend, fill and merge functions in the PTC Creo to solidify the designed blade. The figures below show these processes.

Figure 31 The solidifying processes of the designed blade

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The final solidified blade is shown as follows:

Figure 32 The solidified blade

8.2 Autodesk algor Simulation
After 3-D model creation of the design rotor blade, Algor simulation was used to analyze the stress pattern on the blade if the rotor blade is rigidly fixed at the root and a tangential load is applied at the tip mid chord.
Firstly, the blade was opened by the Autodesk simulation 2016. The material was chosen as Titanium alloy which is a popular material used in the manufacturing of blades. Figure 33 The chosen material for the simulation of rotor blade
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The load 1200N was added at the tip mid chord and the blade is rigidly fixed at the root by using the constraints.

Figure 34 shows the load and constraints on the blade in Algor simulation

Then, the analysis was ran and the results were inquired as follows:

Figure 35 The displacement of the blade in Algor simulation

From the figure, it is easy to find that the deformation of the blade is well arranged and the more distance from the fixed root, the more displacement. The maximum displacement happened at the tip mid chord.

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To make sure the stress is less than the yield stress that the blade works normally without broken, The factor of safety was inquired as follows:

Figure 36 The factor of safety of the blade in Algor simulation

According to the figure 36, the least factor of safety of this blade is approximately
2.881 which means the maximum stress on the blade is less than the yield stress.

Figure 37 shows the stress pattern on the blade of the obverse of blade
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Figure 38 shows the stress pattern on the blade of the reverse of blade

Figure 37 and 38 shows the stress pattern if the rotor blade is rigidly fixed at the root and a tangential load is applied at the tip mid chord. From the figures, it is not hard to find that the maximum stress happens at the point where the load applied.
On the obverse of the blade, the stress mainly concentrate near the root mid chord area and reduce generally from the center of root mid chord to other places on the blade. On the reverse of blade, the leading and trailing edge areas near the root are under greater stresses and reduce generally from the leading and trailing edges near the root to the other areas on the reverse of designed blade.
The pattern of stress on the obverse of the blade is almost opposite to the stress pattern of stress in the reverse of blade near the root area.

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9.0 Conclusion
During this design and analysis, different applications in the computer were used to curry out the assumptions made in the calculations, representation of the stage at a value of 50% degree of reaction and analysis of the stress pattern on the blade,etc. In the discussion part, different assumptions of calculation errors were made to observe the effect on the design of the blade. As can be seen, a little error in the calculation can lead to a large difference of stagger angle in design but the relation between these stagger angles of different parts of the blade fortunately reduces the effect on the final design. In the representation parts, the diagrams of the blade, blade angles , the stage of 50% degree of reaction and the 3-D model of this designed blade were successfully done. The stress pattern of the blade also vividly shown in the Algor simulation and through the simulation.

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10.0 References
[1] http://www.windpowerengineering.com/design/mechanical/blades/blades-101/
[2] Yahya, S M (2011). Turbines Compressors and Fans. New delhi: Tata McGraw-Hill Education, 2010. pp. 430–433. ISBN 9780070707023.

[3]Kumar, Bharat (2005). An Illustrated Dictionary of Aviation. New York: McGraw Hill.
[4]Settles, Gary S. (2006), High-speed Imaging of Shock Wave, Explosions and Gunshots 94 (1),
American Scientist, pp.22-31
[5]https://en.wikipedia.org/wiki/Turbine_blade
[6]Lesley M. Wright, Je-Chin Han. "Enhanced Internal Coolingof Turbine Blades and Vanes" (PDF).
4.2.2.2 Enhanced Internal Coolingof Turbine Blades and Vanes. Retrieved 27 May 2013.
[7]https://www.researchgate.net/post/What_is_the_main_characteristics_for_the_airfoils_whic
h_used_in_wind_turbine_blades_Megawatt
[8]https://en.wikipedia.org/wiki/Shock_wave
[9]Wu ZN,Xu YZ,etc (2013), Review of shock wave detection method in CFD post-processing 26 (3),
Chinese Journal of Aeronautics, pp.501-513
[10]Zetan Peng, Liu Gang(2000) “Principle of rotor Blade”Chapter 3，
Beihang University in
China.
[11] National Aeronautics and Space Administration website page "Mach Number", NASA.

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