Modeling and simulation of ducted axial fan for one dimensional flow no restriction

International Journal of Advanced Research in Engineering and Technology RESEARCH IN–
INTERNATIONAL JOURNAL OF ADVANCED (IJARET), ISSN 0976
6480(Print), ISSN 0976 – 6499(Online) Volume 3, Number 1, January - June (2012), © IAEME
ENGINEERING AND TECHNOLOGY (IJARET)

ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online) IJARET
Volume 3, Issue 1, January- June (2012), pp. 97-106
© IAEME: www.iaeme.com/ijaret.html ©IAEME
Journal Impact Factor (2011): 0.7315 (Calculated by GISI)
www.jifactor.com

MODELING AND SIMULATION OF DUCTED AXIAL FAN FOR
ONE DIMENSIONAL FLOW
Manikandapirapu P.K.1 Srinivasa G.R.2 Sudhakar K.G.3 Madhu D. 4
1
Ph.D Candidate, Mechanical Department, Dayananda Sagar College of Engineering, Bangalore.
2
Professor and Principal Investigator, Dayananda Sagar College of Engineering, Bangalore.
3
Dean (Research and Development), CDGI, Indore, Madhya Pradesh .
4
Professor and Head, Mechanical Department, Government Engg. College, KRPET-571426.

ABSTRACT

The paper presents to develop the analogy for modeling and simulation of ducted
Axial Fan by using the one dimensional flow equation of axial turbo machines. Main
objective of this paper is to derive the flow model from radial equilibrium concepts and
compute the pressure rise for varying the functional parameters of inlet velocity, whirl
velocity, rotor speed and diameter of blade from hub to tip in ducted axial fan by using
simulink software for one dimensional flow. In this main phase of paper, the analogies
for modeling and simulation has been investigated for optimize the parameter of pressure
rise in ducted axial flow fan.

Keywords: Pressure rise, Whirl velocity, Pressure Ratio, Flow ratio, Rotor speed,
Simulink, Axial Fan.

1.INTRODUCTION
Mining fans and cooling tower fans normally employ axial blades and or required to
work under adverse environmental conditions. They have to operate in a narrow band of
speed and throttle positions in order to give best performance in terms of pressure rise,
high efficiency and also stable condition. Since the range in which the fan has to operate
under stable condition is very narrow, clear knowledge has to be obtained about the
whole range of operating conditions if the fan has to be operated using active adaptive
control devices. The performance of axial fan can be graphically represented as shown in
figure 1.

97

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –

Fig: 1 Graphical representation of Axial Fan performance curve
2. TEST FACILITY AND INSTRUMENTATION
Experimental setup, fabricated to create stall conditions and to introduce unstall
conditions in an industrial ducted axial fan is as shown in figure 2.

Fig: 2 Ducted Axial Fan Rig
A 2 HP Variable frequency 3 phase induction electrical drive is coupled to
3-phase
the electrical motor to derive variable speed ranges. Schematic representation of
ducted fan setup is shown in figure 3.

98


Fig: 3 Ducted Axial Fan - Schematic
The flow enters the test duct through a bell mouth entry of cubic profile. The bell mouth
performs two functions: it provides a smooth undisturbed flow into the duct and also
serves the purpose of metering the flow rate. The bell mouth is made of fiber reinforced
polyester with a smooth internal finish. The motor is positioned inside a 381 mm
diameter x 457 mm length of fan casing. The aspect (L/D) ratio of the casing is 1.2. The
hub with blades, set at the required angle is mounted on the extended shaft of the electric
motor. The fan hub is made of two identical halves. The surface of the hub is made
spherical so that the blade root portion with the same contour could be seated perfectly on
this, thus avoiding any gap between these two mating parts. An outlet duct identical in
every way with that at inlet is used at the downstream of the fan. A flow throttle is placed
at the exit, having sufficient movement to present an exit area greater than that of the
duct.
3.0 GOVERNING EQUATION
3.1 Continuity Equation
A continuity equation in physics is a differential equation that describes the transport
of some kind of conserved quantity. Since mass, energy, momentum, electric charge and
other natural quantities are conserved.
Continuity equation
ߩଵ × ‫ܣ‬ଵ × ܸଵ ߩଶ × ‫ܣ‬ଶ × ܸଶ (3.1)

3.2 Momentum Equation
A body of mass m subject to a net force F undergoes an acceleration that has the same
direction as the force and a magnitude that is directly proportional to the force and
inversely proportional to the mass. Alternatively, the total force applied on a body is
equal to the time derivative of linear momentum of the body.
Momentum equation

99


డ ଶ
ሺߩ௠ ߭௠ ) + ∇. ሺߩ௠ ߭௠ ) =
డ௧

∆p + ∇. [μ୫ (∆߭௠ + Δ߭௠ )]+ ߩ௠ ݃ + ‫ + ܨ‬Δ. ൫∑௡ ߙ௞ ߩ௞ ߭ௗ௥,௞ ߭ௗ௥.௞ ൯ (3.2)
்
௞ୀଵ
3.3 Energy Equation
Energy may be stored in systems without being present as matter, or as kinetic or
electromagnetic energy. The law of conservation of energy is a law of physics. It states
that the total amount of energy in an system remains constant over time (is said to be
conserved over time). A consequence of this law is that energy can neither be created nor
destroyed: it can only be transformed from one state to another
Energy equation
డ
∑௡ ሺߙ௞ ߩ௞ ‫ܧ‬௞ ) + ∆. ሺ∑௡ ሺߙ௞ ߭௞ ሺߩ௞ ‫ܧ‬௞ + ܲ)) = ∆. ൫݇௘௙௙ ∇ܶ൯ + ܵா (3.3)
௞ୀଵ ௞ୀଵ
డ௧

4.0 FLOW MODELING FOR ONE DIMENSIONAL FLOW
4.1 Radial Equilibrium Concepts and evaluation
Consider a small element of fluid of mass dm as shown in fig.4 and fig.5 of unit depth
and subtending an angle dθ at the axis and rotating about the axis with tangential velocity
and ܿ௾ at radius r.

C
asing p+dp Mass/Unit depth
Streamlines dr = ρrdθdr
Velocity = c θ
p+1/2 dp p+1/2 dp

p
r dθ

Hub

Axis

Fig: 4 Radial equilibrium flow through a rotor blade row Fig: 5 A fluid element in radial equilibrium ( Cr = 0)

The general three dimensional momentum equation of inviscid fluid in a radial
direction expressed in a cylindrical coordinate system can be written as follows:

ଵ ப୮ ப୚୰ ୚୳ ப୚౨ ப୚౨ ୴మ
− ቀ ஡ ப୰ ቁ = Vr ቀ ப୰ ቁ + ቀ ப஘ ቁ + Va − ౭
(4.1)
୰ ப୸ ୰

100


Assuming axisymmetric flow and imposing a zero radial flow velocity, it can be
simplified to
ଵ ப୮ ୴మ
=
஡ ப୰
౭
୰
(4.2)

The equation 4.2 is consider as the governing equation of axial flow fan for 1-
Dimensional flow

୴మ
dp = ࣋ ౭
୰
dr (4.3)
ந
v୵ = v୧ × ౬౟ (4.4)
ଶ
౫

ந ×୳ ந × ஠ୈ୒
v୵ = ଶ
= ଺଴×ଶ
(4.5)
ந ×ଷ.ଵସ ×ଶ ×୒×୰
v୵ = (4.6)
଺଴ ×ଶ
࣒ ×ଷ.ଵସ ×ே
‫ݒ‬௪ = ቀ ଺଴
ቁ‫ݎ‬ (4.7)

࣒ ×૜.૚૝ ×ࡺ ૛
Pressure Rise = ∆p =࣋ ቀ ቁ × ‫ݎ݀ ݎ ׬‬
૟૙
்௜௣
ట ×ଷ.ଵସ ×ே ଶ ௥మ
Pressure Rise = ∆p = ࣋ ቀ ቁ × ቀ ଶ ቁ (4.8)
଺଴ ு௨௕

The aim of the flow modeling is to measure the pressure rise as a function of
whirl velocity and rotor speed for different diameter of blade from hub to tip in ducted
axial flow fan. In this flow modeling equation helps to optimize the parameter of pressure
rise for different whirl velocity in a ducted axial fan.
5.0 SIMULINK
Simulink is a software package for modeling, simulating and analyzing dynamic
systems. It supports linear and nonlinear systems, modeled in continuous time, sampled
time, or a hybrid of the two. For modeling simulink provides a graphical user interface
for building models as block diagrams, using click and drag mouse operations. Simulink
includes a comprehensive block library of source, sink of linear and nonlinear
components and connectors.
5.1 SIMULINK MODEL FOR ONE DIMENSIONAL FLOW
The one dimensional flow model is considered for simulation study. The
governing parameters of the fan considered are density of the fluid, diameter of blade
from hub to tip, inlet velocity, pressure ratio, rotor speed and the effects of variation of

101


these parameters are testified through simulink simulation model. Constant block, gain
block, Math function, Sum block, inverse block, and display block are the typical blocks
used for simulink mathematical model in one dimensional flow is shown in fig.6.

Fig: 6 Simulink Flow Simulation Model for One Dimensional Flow in Ducted Axial Fan
6.0 RESULTS AND DISCUSSION
The aim of the flow modeling and simulation is to compute the pressure rise as a
function of whirl velocity and rotor speed for different diameter of blade from hub to tip
in ducted axial flow fan. Flow modeling and simulation of one dimensional flow helps to
optimize the parameter of pressure rise for different whirl velocity in a ducted axial fan.

35
Rotor Speed 3000 Rpm
30
Pressure Raise in N/m2

25 Rotor Speed 3300 Rpm

15

10

5

0
0.0575 0.072 0.08625 0.115 0.23
Pressure Ratio

Fig.7 Pressure Raise Variations for fixed diameter of Blade Rotor at 0.381 m

102


Analysis of one dimensional flow modeling and their governing parameters were
made as a function of whirl velocity, diameter of hub from tip to hub and rotor speed for
ducted axial fan. The variations in pressure rise for different pressure ratio at a constant
diameter of blade of 0.381m is shown in fig.7. Maximum pressure magnitude is found to
be 32 N/ m2 for the pressure ratio of 0.23. Further, it varies from 1 to 10 N/ m2 when the
rotor speed is incremented by 300 rpm.
8
Pressure Ratio 0.115
7 Pressure Ratio 0.0575

5
4
3
2
1
0
2400 2600 2800 3000 3200 3400 3600
Rotor Speed ( Rpm )

Fig.8 Pressure Raise Variations for fixed diameter of Blade Rotor at 0.381 m

The variations in pressure rise for different rotor speed from 2400 rpm to 3600 rpm
for fixed diameter of blade of 0.381 m is shown in fig.8. Maximum pressure magnitude is
found to be 8 N/ m2 for the pressure ratio of 0.115. Further, it varies from 1 to 5 N/ m2
when the rotor speed is incremented by 200 rpm.

250


100

50

0
0.0131 0.0714 0.01651 0.381 0.881 2.04
Blade Diameter in m

Fig.9 Pressure Raise Variations for fixed Pressure Ratio of 0.115

103


The variations in pressure rise for different diameter of blade from 0.0131m to 2.04
m at a constant pressure ratio of 0.115 is shown in fig.9. Maximum pressure magnitude is
found to be 210 N/ m2 for the blade diameter of 2.04 m. Further, it varies from 0 to 45 N/
m2 when the rotor speed is incremented by 300 rpm.

160
140
Pressure Rise in N/m2

80

60

40

20

0
0.0131 0.0714 0.01651 0.381 0.881 2.04
Blade Diameter in m

Fig.10 Pressure Raise Variations at constant Rotor Speed of 3000 Rpm

The variations in pressure rise for different diameter of blade from 0.0131m to 2.04
m at constant rotor speed of 3000 rpm is shown in fig.10. Maximum pressure magnitude
is found to be 160 N/ m2 for the pressure ratio of 0.115. Further, Pressure magnitude is
found to be varying from 0 to 160 N/ m2 for every double increment of rotor diameter.

7.0 CONCLUSION
In this paper, an attempt has been made to develop the flow modeling and
simulation for one dimensional flow in ducted axial fan by using theory of radial
equilibrium equation. It is useful to design the operating condition of axial fan to measure
the parameters of pressure rise as a function of pressure ratio, rotor speed, and diameter
of blade from hub to tip in ducted axial fan. Further, this work can be extended by
working on the modeling and simulation of characteristic study in stall control. The
results so far discussed, indicate that flow modeling and simulation of one dimensional
flow in ducted axial fan is very promising.

ACKNOWLEDGEMENT
The authors gratefully thank AICTE (rps) Grant. for the financial support of present
work.

104


NOMENCLATURE
cx = Axial velocity in m/s
ܿఏ = Whirl velocity in m/s
r2 = Radius of blade tip in m
r1 = Radius of blade hub in m
N = Tip speed of the blades in rpm
va = Axial velocity in m/s
dp= P2 - P1 = Pressure rise in N/m2
d = Diameter of the blade in m
ρair = Density of air in kg/m3
vw = Whirl velocity in m/s
η = Efficiency of fan

REFERENCES

[1] Day I J,”Active Suppression of Rotating Stall and Surge in Axial Compressors”,
ASME Journal of Turbo machinery, vol 115, P 40-47, 1993
[2] Patrick B Lawlees,”Active Control of Rotating Stall in a Low Speed Centrifugal
Compressors”, Journal of Propulsion and Power, vol 15, No 1, P 38-44, 1999
[3]C A Poensgen ,”Rotating Stall in a Single-Stage Axial Compressor”, Journal of
Turbo machinery, vol.118, P 189-196, 1996
[4] J D Paduano,” Modeling for Control of Rotating stall in High Speed Multistage
Axial Compressor” ASME Journal of Turbo machinery, vol 118, P 1-10, 1996
[5] Chang Sik Kang,”Unsteady Pressure Measurements around Rotor of an Axial
Flow Fan Under Stable and Unstable Operating Conditions”, JSME International
Journal, Series B, vol 48, No 1, P 56-64, 2005
[6] A H Epstein,”Active Suppression of Aerodynamic instabilities in turbo machines”,
Journal of Propulsion, vol 5, No 2, P 204-211, 1989
[7] Bram de Jager,”Rotating stall and surge control: A survey”, IEEE Proceedings of 34th
Conference on Decision and control, 1993
[8] S Ramamurthy,”Design, Testing and Analysis of Axial Flow Fan,” M E Thesis,
Mechanical Engineering Dept, Indian Institute of Science, 1975
[9] S L Dixon, Fluid Mechanics and Thermodynamics of Turbo machinery, 5th
edition, Pergamon, Oxford, 1998
[10] William W Peng, Fundamentals of Turbo machinery, John Wiley & sons.Inc,
2008
AUTHORS

Manikandapirapu P.K. received his B.E degree from Mepco Schlenk
Engineering college, M.Tech from P.S.G College of Technology,Anna
University,and now is pursuing Ph.D degree in Dayananda Sagar College of
Engineering, Bangalore under VTU University. His Research interest include:
Turbomachinery, fluid mechanics, Heat transfer and CFD.

105


Srinivasa G.R. received his Ph.D degree from Indian Institute of Science,
Bangalore. He is currently working as a professor in mechanical engineering
department, Dayananda Sagar College of Engineering, Bangalore. His Research
interest include: Turbomachinery, Aerodynamics, Fluid Mechanics, Gas turbines
and Heat transfer.

Sudhakar K.G received his Ph.D degree from Indian Institute of Science,
Bangalore. He is currently working as a Dean (Research and Development) in
CDGI, Indore, Madhyapradesh. His Research interest include: Surface
Engineering, Metallurgy, Composite Materials, MEMS and Foundry
Technology.

Madhu D received his Ph.D degree from Indian Institute of Technology (New
Delhi). He is currently working as a Professor and Head in Government
Engineering college, KRPET-571426, Karnataka. His Research interest include:
Refrigeration and Air Conditioning, Advanced Heat Transfer Studies, Multi
phase flow and IC Engines.

106

Modeling and simulation of ducted axial fan for one dimensional flow no restriction

Recomendados

Recomendados

Mais conteúdo relacionado

Mais procurados

Mais procurados (17)

Destaque

Destaque (9)

Semelhante a Modeling and simulation of ducted axial fan for one dimensional flow no restriction

Semelhante a Modeling and simulation of ducted axial fan for one dimensional flow no restriction (20)

Mais de iaemedu

Mais de iaemedu (20)

Modeling and simulation of ducted axial fan for one dimensional flow no restriction