Student Research Paper Conference Vol-2, No-36, July 2015

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A Design Tecnique for a High Quantity Axial Flow

Pump Impeller using Voznisenki Mean Camber Line

Design Method

M.Hamza Khan

Department of Aeronautics and Astronautics

Institute of Space Technology

Islamabad, Pakistan

hamzakhanshamsi@yahoo.com

Abstract— Axial Flow Pumps or AFPs have numerous

applications in agriculture, sewage treatment, and domestic water

requirement fulfillment. For preliminary design purposes velocity

triangles are widely employed, but they are inadequate when it

comes to selecting design parameters such as the number of blades

required, the stagger angle, the twist angle and the mean camber

line of the impeller blade. In this paper a design technique is

explained, which upon employment not only gives the above

mentioned parameters but also caters for the anti-cavitation

characteristics of the blade. To elaborate the technique; the

researchers design problem is presented as an example in which

Voznisenki method design technique is used to design an impeller

which is then analyzed through ANSYS CFX software for

verification of agreement with the theoretical design calculations.

Keywords—Axial Flow Pumps; Camberline Design; Turbo

machines

I. INTRODUCTION

Axial Flow Pumps are those, in which the radial direction of the flow does not change. They have numerous applications in agriculture, sewage treatment, urban and rural water supply and etc. Using circulation, in 1966, Prof. Voznisenki of the Moscow Institute of Power, Russia devised a method for blade profile design by treating the mean camber line of the profile as circular arcs for which the radii are to be calculated [1]. The velocity triangle approach has been a popular tool for turbomachine design for the last two centuries. By using these two design tools a preliminary pump can be designed.

In this paper a non-trial and error design technique is developed which utilizes both the Voznisenki Mean Camber Line blade profile design approach and velocity triangles. With the input of flow rate, head requirement and the blade velocity; the blade design parameters: solidity, tip radius, hub radius, twist angle, stagger angle and blade profile camber line can be determined.

II. PRINCIPLES OF DESIGN

A. Pump Design Requirements

Suppose that a pump is to be designed for the following specified requirements 1) Total Head H 2) Flow Rate / Quantity Q 3) Blade Speed U.

For an idea of the required pump, the specific speed s is required, which is given by [1]:

√

⁄ (1)

For Axial Flow Pumps, the specific speed is of a high value from 700 to 3000.

On obtaining the specific speed from (1), the impeller eye velocity C0 can be obtained as [1]:

√ (2)

B. Selection of hub ratio and calculation of outer and hub

diameter

In 1951, the French engineer A. Cordier made a relation between the specific speed and hub ratio of high efficiency pumps. These results were graphically charted and are termed as Cordier Diagram [2], which can be viewed in Fig.1. Using

the diagram a value for hub ratio can be obtained.

The blade tip diameter or the outer diameter D0 can be calculated as [3]:

√

(3)

Now the hub diameter can simply be obtained by

multiplying D0 with .

(4)

C. Calculation of Unit Head and Unit Flow Rate

The unit head KH and unit flow rate KQ can be calculated as [1]:

(5)

(6)

Using these two parameters the hydraulic efficiency of the pump can be estimated using the universal performance charts created by Prof. Staritzky [5] in Fig. 2.

A Design Technique for a High Quantity Axial Flow Pump Impeller using Voznisenki Mean Camber Line Design Method

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D. Streamline Selection

For constant energy transfer over the entire blade span the blade must twist with increasing radius or blade span. To incorporate this twist automatically in the blade design calculations are done for different streamlines with increasing distance from the hub. As per Prof. Voznisenki’s method five streamlines are selected. The streamlines are termed in a successive order as rI, rII , rIII, rIV and rV. They are determined as follows:

(7)

E. Selection of Vane/Blade Solidity

After selecting the streamlines the blade solidity of the blade can be selected for each respective streamline by the following steps involving velocity triangle calculations:

Calculate the blade speed U by:

(8)

By velocity triangle calculation the relative flow inlet angle is calculated as:

(9)

The outlet tangential component of the absolute flow velocity is calculated by a simple derivation of the Euler’s turbo machinery equation:

(10)

The relative flow outlet angle is then calculated as

Fig. 1: Cordier Diagram

Fig. 2: Staritzky Diagram for unit head as a function of unit quantity,

hydraulic efficiency and specific speed

A Design Technique for a High Quantity Axial Flow Pump Impeller using Voznisenki Mean Camber Line Design Method

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Fig. 4 Papir Chart for Periphery Vane Solidity estimation

Fig. 3 Howell Chart for l/t estimation

Fig. 5 Stepanoff Chart

(11)

The difference between the outlet and inlet relative flow angles is then calculated as

(12)

The vane solidity l/t for the streamlines I to IV are selected per the Howell chart (Fig. 3) obtained from experimental results obtained by the Moscow Institute of Power. For the streamline closer to the periphery the solidity is selected from the results (Fig. 4) obtained by Papir [6]

F. Impeller Design

To begin the impeller design the numbers of blades required are needed for blade pitch calculation. Prof. Stepanoff has provided a novel way to calculate number of blades required for different specific speeds. Using the Stepanoff charts (Fig. 5) the number of blades required Z can be found out.

The blade pitch t can then be simply calculated as:

(13)

The blade span l is then found out as:

(14)

The circulation over the entire blade can be calculated by an application of the Kutta-Jowkovski Theorem for cascade blade system [8]:

(15)

For the individual streamline sections it is

A Design Technique for a High Quantity Axial Flow Pump Impeller using Voznisenki Mean Camber Line Design Method

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Fig. 7 𝒇 𝜹𝒎 calculation

Fig. 6 𝚪𝟏

𝑾∞ 𝒍𝜷 estimation

Fig. 7 𝜷 estimation

(16)

The average tangential component of relative velocity is calculated as:

(17)

The average relative flow angle is then calculated as:

∞ (18)

The relative flow velocity can then be calculated as

∞ (19)

Then

∞ (20)

From chart explained in Fig. 6 the parameter

∞ is

estimated. From these two parameters the curvature can be calculated.

Using the chart provided in Fig. 7, is calculated , from here an iterative procedure begins until the sum of and is equal to . Using the new value of the curvature is found out using Fig. 6.

The impeller blade thickness is selected as per wind tunnel test results which usually range from 6 to 4 millimeters. The value is selected such that there is a uniform variation from

hub to periphery usually about 0.5 millimeters to avoid

cavitation. The normalized thickness is then used to calculate the mean difference in relative curvature. The relative curvature f is given by

A Design Technique for a High Quantity Axial Flow Pump Impeller using Voznisenki Mean Camber Line Design Method

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(21)

The curvature difference per mean thickness is

found out using the chart in Fig. 8. Thus the curvature difference is obtained by the product of the normalized thickness and the curvature difference per mean thickness. The next value for the relative curvature f1 is calculated by the sum

of the curvature f and curvature difference .

The impeller curvature is calculated as

(22)

Finally the arc radius R for the mean camber line can then simply calculated as:

(23)

The camber line profile achieved can then be dressed with a thick profile after appropriate wind tunnel tests.

III. EXAMPLE

The researcher’s design problem was to design an axial

flow pump that can impart 1800 gpm/ 0.136 m3/sec for a 3.66

meter head.

A. Pump Specifications

The following design specifications were calculated for the

required head and flowrate:

√

⁄

√ = 4.6 m/sec

= 0.5 (Cordier Diagram)

√

= 0.226 m

= 0.113 m

B. Flow Coefficients

= 0.125

= 0.493

C. Streamline Selection

= 61 mm

= 73 mm

= 85 mm

= 97 mm

= 109 mm

D. Impeller Design

The results are presented in a tabular form, to save space

only the first two streamlines are presented.

Sr.No

Parameter

I

II

1 Radius (mm) 61 73

2 Impeller eye

Velocity

C0 (m/sec)

4.6

3 Tangential

Velocity

U (m/sec)

9.2 11.01

4 Relative inlet

Flow Angle

(deg)

26.6 22.68

5 Solidity (l/t) 2 1.43

6

2.36 1.97

7 Average

Tangential

Relative

Velocity (m/s)

6.84 9.04

8 Stagger Angle

(deg)

35.34 28.21

9 Average

Relative

Velocity(m/s)

8.4 10.26

10 Chapligin’s

Postulate

0.280 0.268

11

∞ 1.27 1.82

12 Curvature

(rad/deg)

0.223/

13.12

0.150/

8.6

13 1.67 0.666

14 + 37.01 28.88

A Design Technique for a High Quantity Axial Flow Pump Impeller using Voznisenki Mean Camber Line Design Method

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15

∞ 1.24 1.78

16 Curvature

(rad/deg)

0.229 0.150

17 Blade

Thickness(mm)

6 5.5

18 Normalized

Thickness

0.0313 0.0335

19 Relative

Curvature

0.0577 0.038

20 0.28 0.17

21 0.0087

7

0.005695

22 0.06647

0.043695

23

15.14 9.98

24

192 288

IV. CONCLUSION

A non trial-and-error method for designing an impeller blade for an axial flow pump is presented. The method utilizes the velocity triangle design approach and the Voznisenki mean camber line design technique. Using the head and flow rate required by the pump, an impeller blade can be designed by calculating the blade design parameters: solidity, tip radius, hub radius, twist angle, stagger angle and blade profile camber line. As seen from the example the CFD results are in agreement with theoretical design calculations, thus proving that the Voznisenki Method is an excellent choice for the preliminary impeller desigm.

V. REFERENCES

[1] Voznisenski, I.N. (1952). Life, action and selection of the work in the area of Hydraulic Machine development and automatic regulation. Moscow Pub. House.

[2] A Valan Arasu (2012). Turbo Machines (2nd ed.). Vikas Publishing House. p. 342.

[3] Rama S.R. Gorla, Aijaz A. Khan (2003). Turbomachinery Design and Theory (illustrated ed.). CRC Press. p. 59.

[4] Merle C. Potter, David C. Wiggert, and Bassem H. Ramadan (2011). Mechanics of Fluids (4th ed.). Cengage Learning. p. 609.

[5] S M Yahya (2005). Turbines Compressors and Fans (3 ed.). Tata McGraw-Hill Education

[6] Abromavich, S.F. (1950). Application of N.E Joukovski’s method and Research on flow over cascade of profiles with finite thickness

[7] Joukovski, N.E. (1960) Calculation of flow over cascades of Turbomachine, Moscow Publishing House.

[8] Papir, A.N. (1965). Axial flow Blades for ships (Fundamental theory andcalculation – Ship Building Publication, Leningrad

[9] Srinivasan, K.M. (1966). Comparative Analysis of Design of Axial Flow Pumps. Ph.D.Thesis Deptt. of Hydraulic Machines, Leningrad Polytechnic, Leningrad USSR

[10] Staritski, V.G (1955). Calculation of Interaction between Cascades of Impeller blades and diffuser blades in Axial flow Machines

Fig.8 The designed impeller

Fig.9 ANSYS-CFX CFD results for the impeller designed by Voznisenki Method