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Factors Impacting on Performance of Lobe Pumps: A Numerical
Evaluation
Y.-H. Kang, H.-H. Vu and C.-H. Hsu
Journal of Mechanics / Volume 28 / Issue 02 / June 2012, pp 229 - 238
DOI: 10.1017/jmech.2012.26, Published online: 08 May 2012
Link to this article: http://journals.cambridge.org/abstract_S1727719112000263
How to cite this article:
Y.-H. Kang, H.-H. Vu and C.-H. Hsu (2012). Factors Impacting on Performance of Lobe Pumps: A Numerical Evaluation.
Journal of Mechanics, 28, pp 229-238 doi:10.1017/jmech.2012.26
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FACTORS IMPACTING ON PERFORMANCE OF LOBE PUMPS:
A NUMERICAL EVALUATION
Y.-H. Kang *
H.-H. Vu
C.-H. Hsu
Department of Mechanical Engineering
National Kaohsiung University of Applied Sciences
Kaohsiung, Taiwan 80778, R.O.C.
Department of Mold and Die Engineering
National Kaohsiung University of Applied Sciences
Kaohsiung, Taiwan 80778, R.O.C.
ABSTRACT
The aim of current research is to investigate numerically the fluid dynamics of lobe pumps and typical
factors which could impact on performance of the pump including profile of rotor surface, number of
lobes, gap size between rotor and casing, and clearance between two rotors, etc. The circular and epicycloidal curves are used to generate profiles for rotor surface, while the complex flow phenomena inside
the pump are simulated by dynamic mesh technique. With wide range of investigated speed from 1000
to 5000rpm, the study produces significant information on flow pattern, velocity and pressure fields.
The advantage of epicycloidal pumps over circular ones has been demonstrated via characteristic curve
which performs pressure head versus rotational speed. Meanwhile the analysis has proved that multilobes, three and four lobes, do not increase performance of the pump but provide more stable output and
higher capacity compared with two-lobe pumps. The results confirm great impact of gap size between
rotor and casing wall on the pump efficiency. Decrease of the gap from 1.25mm down to 0.5mm produces about 425 increasing of pressure head. In addition, it has been also proved that the clearance
between two rotors could be varied from 0.12mm to 0.15mm without much effect on performance of the
pump.
Keywords: Epicycloidal curve, Lobe pump, Characteristic curve.
1.
INTRODUCTION
The lobe pump receives its name from the rounded
shape of the rotor radial surfaces that permits the rotors
to be continuously in contact with each other as they
rotate. Lobe pumps can be either single- or multiplelobe pumps, and carry fluid between their rotor lobes
much in the same way a gear pump does [1]. Lobe
pumps have wide range of applications in industry from
food, medicine to beverage, biotechnology, etc., from
very large scale to very small in micron size. Furthermore, the lobe pump is able to work with various
materials from low viscosity such as water to very high
viscosity such as oil, and even handle with solids [2].
Lobe pumps could be categorized to positive displacement rotary pumps which move fluid using the principles of rotation. Different from other kinds of pump,
saying kinetic pumps, the working domain of lobe
pump deforms continuously during every revolution of
rotors. Thus, to understand the physical phenomena of
compressed fluid in such a complex working domain is
not an easy work.
The most reliable information about physical phe*
nomena is usually given by experiment. In certain
situations, an experiment investigation involving fullscale equipment can be used to predict how the equipment would perform under given conditions. However,
in most practical engineering applications, such full
scale tests are either difficult or very expensive to perform, or not possible at all. A common alternative is
to perform experiments on small scale models. The
resulting information however, needs to be extrapolated
to the full scale and general rules for doing this are often unavailable. The small scale models do not usually simulate all the features of the full scale system.
This sometimes limits the usefulness of the test results.
In many situations, there are serious difficulties in
measurements and the measuring equipment can have
significant errors [3]. Meanwhile, computer simulation is more and more developed in both software and
hardware.
Computational Fluid Dynamics (CFD)
techniques are numerical methods which developed to
find out how the flow behaves in a given system for a
given set of inlet and outlet conditions. With the development of fast and validated numerical procedures,
and the continuous increase in computer speed and
Corresponding author (yhkang@cc.kuas.edu.tw)
Journal of Mechanics, Vol. 28, No. 2, June 2012
DOI : 10.1017/jmech.2012.26
Copyright © 2012 The Society of Theoretical and Applied Mechanics, R.O.C.
229
availability of cheap memory, larger and larger problems are being solved using CFD methods at cheaper
cost and quicker time. In comparisons with experimental procedures in most engineering applications,
CFD approaches offer a more complete set of information. CFD methods usually provide all relevant flow
information throughout the domain of interest which
could not be often accomplished by experimental procedures because of limitations from measuring equipments. CFD simulations also enable flow solutions at
the true scale of the engineering systems with the actual
operating conditions [3].
Many modern algorithms have been developed to
deal with very complicated problems in fluid mechanics,
even deformable domain of positive displacement rotary pump. Houzeaux et al. [4] has developed an innovative algorithm to simulate the fluid mechanics of
rotary pumps such as gear pump. On the other hand,
Voorde et al. [5] has applied fictitious domain method
to study three-blade lobe pump and tooth compressor.
Similarly, Huang and Liu [6] used the renormalization
group k- model, PISO algorithm, and second-order
upwind difference scheme to solve governing equations
of a involute-type three-lobe positive discharge blower.
However, most of above researches were applied to
only several strict cases within laboratorial limits.
Recently, the commercial computational fluid dynamics package FLUENT has been utilized widely to
study fluid dynamics such as flow behavior, heat transfer, multi phases, etc. in large number of complex geometries. FLUENT provides complete mesh flexibility, including the ability to solve flow problems using
unstructured meshes that can be generated about complex geometries with relative ease. Especially, FLUENT 6.2 possesses Moving Dynamic Mesh tool which
could be used to model flows where the shape of the
domain is changing with time due to motion on the domain boundaries. In addition, FLUENT allows user to
define input functions by User-Defined-Function (UDF)
which provides users more flexible options to setup the
problems [7]. Utilizing this advantage of FLUENT,
various studies related to deformable domain of rotary
pumps have been reported. For example, Kim et al. [8]
used FLUENT to conduct two-dimensional CFD analysis of a hydraulic gear pump, and found that the gap
size between rotors and casing wall was the most pertinent parameter affecting the pump capacity. Some
researches have reported to develop new algorithm to
deal with deformable domain of rotary pumps, but basically were still based on FLUENT dynamic mesh and
UDF [5,9]. According to our knowledge, numbers of
studies related to rotary pumps such as gear pumps have
been conducted, but none of them exposed an adequate
report about fluid dynamic of the lobe pump. In order
to research the impact factors on performance of lobe
pumps, two rotor profiles commonly used in lobe
pumps, circular-based rotor and epicycloidal-based rotor, are chosen to evaluate the effects of factors and
make comparison between them.
The aim of current research is to utilize advantages
of FLUENT, especially Moving Dynamic Mesh and
UDF, to study fluid dynamics of the lobe pump. A
230
comprehensive evaluation about fluid characteristics of
lobe pumps as well as factors that could affect the performance of the pump would be reported as major outcome for this research.
2.
2.1
GEOMETRIC DESIGN OF ROTOR PROFILE
Circular-Based Lobe Pump
In order to express the rotor profiles of circularbased and epicycloidal-based lobe pumps, coordinate
systems S1, S2 and Sf are applied to driving rotor and
driven rotor, respectively. As shown in Fig. 1, a fixed
coordinate system Sf (Xf Yf) is set with its origin coincide with center of driving rotor while two moving coordinate systems S1(x1 y1) and S2(x2 y2) are rigidly
connected to driving rotor and driven rotor, respectively.
The position vector of profile for driving rotor with
circular curve, R1, is expressed in S1 as follows
 X 1   cos   a 
R1   Y1     sin  
 1  

1
(1)
The relation between parameters of circular curve is
described as
2  r 2  a 2  2ar cos  / 2n
(2)
where  is the rotation angle of driving rotor, n is the
number of lobe, a is the distance from origin to the
center of circular arc, a  0.8rp, and , rp are the radii of
circular arc and pitch circle, respectively. The position vector of profile for driven rotor, R2, expressed in
coordinate system S2 is generated by applying theorem
of gearing [10] as follows
Fig. 1
Coordinate systems
Journal of Mechanics, Vol. 28, No. 2, June 2012
R 2  M 21 R1
 cos 2 sin 2 2rp cos   X 1 
   sin 2 cos 2 2rp sin    Y1 
 0
  1 
0
1
 cos(  2)  a cos 2  2rp cos 
   sin(  2)  a sin 2  2rp cos  


1
(3)
where M21 is the homogeneous coordinate transformation matrix from coordinate system S1 to coordinate
system S2. The geometric parameter  and motion
parameter  at the contact points must satisfies the
equation of meshing [10]
f (, )  r sin(  )  a sin   0
2.2
In general, procedure of generating lobe profile with
epicycloidal curve is similar to above steps for lobe
profile with circular curve. Coordinate systems S1, S2
and Sf are also applied to driving rotor and driven rotor
(Fig. 2). The epicycloidal curve traced by point P for
driving rotor in coordinate system S1 is described as
follows
Coordinate systems for generating
epicycloidal profile
Journal of Mechanics, Vol. 28, No. 2, June 2012
 rp  r

f (, )  rp sin(  )  rp sin 
   
 r

rp
rp
r sin   ( rp  r ) sin   0
r
r
(5)
(7)
It should be noted that set of Eqs. (1) ~ (4) and (5) ~
(7) is described family of circular and epicycloidal profiles for rotor which could be two, three or more lobes,
i.e. numbers of “teeth” of the rotor. In current research the simplest case, i.e. two-lobe rotor, is conducted for both circular and epicycloidal lobe pump, the
obtained rotor profiles based on Eq. (1) ~ (7) are shown
as Fig. 3.
2.3
where r is the radius of rolling circle for epicycloidal
curve. The profile for driven rotor can be obtained
like as Eq. (3)
Fig. 2
The equation of meshing at contact point of two
meshing rotors is
(4)
Epicycloidal-Based Lobe Pump
rp  r 


(rp  r ) cos   r cos
r


X
 1
rp  r 




R1   Y1    (rp  r ) sin   r sin
r


 1 
1






R 2  M 21 R1


 rp  r

  2   2rp cos  
 (rp  r ) cos(  2)  r cos 
 r





 rp  r

  (rp  r ) sin(  2)  r sin 
  2   2rp sin  


 r



1






(6)
Model of Lobe Pump for CFD
A simple model of lobe pump which consists of three
basic components, casing, driving rotor, and driven
rotor is selected to conduct fluid dynamics analysis in
this study. Following are the specifications of the
chosen lobe pump. Type: External lobe pump, dimensions: Inlet port: 20.0mm, outlet port: 20.0mm, distance
between rotors: 66.8mm, rotor width: 100.0069mm
Fig. 3
(On) Two-lobe circular rotor
(Under) Two-lobe epicycloidal rotor
231
3.
3.1
COMPUTATIONAL MODELING
Governing Equations
The governing equations in the Cartesian coordinate
system, with its origin at the center of driving rotor, can
be expressed as follows [8].
The continuity equation is

  . V  0
t
(8)
Two scalar equations of the Navier-Stokes equation
may be simplified as
  2u  2u 
 u
u
u 
P
  u
v   
  2  2 
x
y 
x
y 
 t
 x
(9)
 2v 2v 
 v
v
v 
P
  u  v   
  2  2 
x
y 
y
y 
 t
 x
(10)
3.3
Initial condition,
At time t  0: V  0
where  is the density, t is the time, x, y are the coordinates in the x, y directions, u, v are the velocities in the
x, y directions, V is the velocity.
The governing equations were numerically solved,
using standard k-ε turbulent model, SIMPLE algorithm,
and first-order upwind difference scheme. The standard k- model is a semi-empirical model based on
model transport equations for the turbulence kinetic
energy (k) and its dissipation rate (). The transport
equations are based on assumptions that the flow is
fully turbulent and the effect of the molecular viscosity
is negligible.
Transport equations for the standard k-ε model [8] is


  
(k )   (kV )      t  k 
t
k  

 Gk  Gb    YM  S k


(11)

where the turbulent viscosity, t Ck2/, and the
model constants are C11.44, C21.92, C0.09,
k 0.3 and 1.3.
Assumptions and Boundary Conditions
The present research is conducted with water whose
density of 998.2kg/m3 and viscosity of 0.001003kg/m-s
as fluidic sample and subjected to following assumptions: (1) the fluid is Newtonian and incompressible (2)
the fluid is initial stationary; the flow is two-dimensional; (3) the fluid is isothermal and has constant
232
Operating Conditions
The analysis performed for two different models
having circular and epicycloidal profiles. The simulation was conducted for 30 cases with different operating
conditions such as rotational speed, gap size, etc., as
shown in Table 1.
There is no universal regulation for judging convergence of solution. For most problems the default
convergence criterion in FLUENT is sufficient. The
convergence criterion for current analysis is 1e-6 for
residual and the size of time step is 1e-5 sec.
4.
4.1
3.2
Grid Generation
In order to generate grid system and define working
zones, model of the pump including rotor profiles generated in Matlab and casing sketched in AutoCAD is
imported to Gambit Package. Gambit is a preprocessing software package designed to import, build, and
mesh models for FLUENT and other scientific applications. Gambit performs fundamental steps of building,
meshing, and creating zone types in a model. In numerical simulation, success of the analysis including
convergence speed, computer working time, etc. largely
depends on mesh quality of the model. Thus, to reduce calculating time but maintain accuracy of the
analysis, mesh ratio is selected as 1.5 with triangular
element type. The whole numerical model consists of
4302 nodes, and 7874 elements (Fig. 4).
3.4


  
()   (V )      t   
t
k  


2
 C1 (Gk  C3 Gb )  C2   S
k
k
(12)

constant properties.
The mass flow inlet boundary conditions were applied at the inlet of the intake region; the outflow
boundary conditions were adopted at the outlet of the
discharge region; wall functions were introduced at the
solid wall.
In general, the working speed of rotor of lobe pump
could be varied from tens of revolutions to thousands of
revolutions depends on the viscosity of transport medium in the pump. In current study, it is assumed that
the pump operates continuously in the range of rotational speed from 1000rpm to 5000rpm. These angular velocities were specified to both driving and driven
lobes of the pump by user-defined function (UDF).
For the lobe pump, it is essential to use UDF to define
the motion of lobes as the geometry of fluid domain
changes with time. A UDF code was written in “C”
language, and then hooked into FLUENT to act as a
function of the software.
RESULTS AND DISCUSSIONS
Pressure Variation of Lobe Pump
As mentioned earlier, lobe pump is categorized as
positive displacement rotary pump. The principle motion of lobe pump is rotating, rather than reciprocating,
and the pump displaces a finite volume of fluid with
each shaft revolution. Pumping in lobe pump begins
with the rotating and stationary parts of the pump defining a given volume or cavity of fluid enclosure.
Journal of Mechanics, Vol. 28, No. 2, June 2012
Fig. 4
(Left) Circular lobe; (Right) Epicycloidal lobe
Table1
Lobe profile
Number
of lobes
Operating conditions
Speed
Gap size
between
casing and
lobe
 1000rpm
 2 lobes  2000rpm
 Circular
 1.25mm
 3 lobes  3000rpm
 Epicycloidal
 0.5mm
 4 lobes  4000rpm
 5000rpm
Clearance
between
lobes
 0.15mm
 0.12mm
This closure is initially open to the pump inlet but
sealed from the pump outlet and expands as the pump
rotates. As rotation continues, the volume progresses
through the pump to a point where it is no longer open
to the pump inlet but not yet open to the pump outlet.
It is in this intermediate stage where the pumping volume or cavity is completely formed. The fluid also
fills the clearances between the pumping elements and
pump body, forming a seal and lubricating the pumping
elements as they in turn pump the fluid. Rotation continues and the cavities progress, moving fluid along the
way. Soon a point is reached where the seal between
the captured fluid volume and outlet part of the pump is
breached. At this point the lobes force the volume of
captured fluid out of the pump. While this is happening, other cavities are simultaneously opening at the
inlet port to receive more fluid in a continual progression from suction to discharge ports [1]. This operating mechanism of lobe pump would lead to variation of
pressure inside the pump.
Figure 5 shows the pressure variation of circular lobe
pump in various stages from initial state to the moment
when rotors complete a half revolution with the rotational speed of 1000 rpm, and the gap between casing
and rotor is 1.25mm. At t 0 sec, since no loading
was assigned for this initial state, pressure distribution
is homogeneous in whole domain of the pump (Fig.
5(a)). When the pump starts to be active, the fluid
now moves due to the movement of the rotors. This
motion is expressed through increasing pressure in the
chamber trapped by two rotors, and high differential
pressure between inlet and outlet of the pump (Fig.
5(b)). At t  0.0105s, the differential pressure between two ports of the pump reaches maximum magnitude (namely peak point or discharge point), and the
pump is going to release the load at the outlet (Fig.
5(c)).
Journal of Mechanics, Vol. 28, No. 2, June 2012
Fig. 5
Circular lobe pump – Pressure distribution
Simultaneously with releasing load, low pressure at
inlet port forms by itself a suction force to attract more
fluid comes inside the pump. This phenomenon
causes the pressure distribution in whole the pump becomes almost like the initial state (named as mimic
state), i.e. homogeneous (Fig. 5(d)). Because of continual rotation of rotors, this process repeats, and the
pump gets the peak point again at t  0.024s (Fig. 5(f)).
At t  0.03s, the pump returned the mimic state, and be
ready for next suction-discharge process. In summary,
it is clear that this numerical analysis results totally
obey to literatures of pumping mentioned in the first
paragraph.
In addition, the analysis results also confirm the periodicity of output for lobe pump. In this case, parameter of pressure head is utilized to illustrate this
property of the pump. Pressure head is simply identified by differential pressure between outlet and inlet,
and then converted to mmHg. As shown in Fig. 6, the
pressure head as a function of time is in sinusoidal form.
One cycle of this sinusoidal function, i.e. from one peak
to next peak, is corresponding to a half revolution of the
rotor. However, it is obvious that the pressure variation is in unusually sinusoidal form with some abnormal points. For example, at t  0.0225s, pressure head
drops to lower value while it should be increasing according to theory of the pump. The appearance of
vortices in some areas inside the pumps could account
for this phenomenon.
A vortex is a spinning, often
233
Fig. 6
Circular lobe pump – Pressure head vs. time at
1000rpm
turbulent, flow of fluid, and often exhibits a very low
pressure at the center. As shown in Fig. 7(a), at t 
0.0225s, three vortices have occurred at area near inlet
port and two chambers formed by two rotors. Low
pressure at these vortices caused reversed flow from
discharge area back to suction area through the gaps
between casing and rotors, and even through clearance
between two rotors (Fig. 7(b), 7(c), 7(d)). In fact, the
vortices could be found earlier at t  0.021s. Thus, it
could be observed pressure drop at both these two
points.
Various reasons could explain for the formation of
vortex. In this case, the shape of rotor with many
curved surfaces is a noticeable reason. The fluid
flows from inlet port to the chamber formed by two
rotors, and then tends to bend to the curved surfaces of
rotors. Combined with continually rotational motion
of rotor, it created an ideal condition to form a vortex.
Interestingly, when rotational speed increases, output of
the pump becomes more stable. At speed of 5000rpm,
the pressure head is completely in sinusoidal form although vortices still exist (Fig. 8). This provides a
good suggestion to improve the performance of lobe
pump.
4.2 Circular Lobe Pump vs. Epicycloidal Lobe
Pump
As discussed above, the shape of rotor surface affects
on performance of the pump considerably. In order to
verify this issue, current research conducts analysis
with rotor profile generated from epicyloidal curve, and
then compares results with circular profile. The input
parameters for epicyloidal lobe are set similarly to case
of circular lobe, i.e. rotational speed is in range of
1000rpm to 5000rpm, and the gap between rotors and
casing is 1.25mm.
Figure 9 describes the pressure head variation with
time of circular lobe and epicycloidal lobe at rotational
speed of 2000rpm. In general, two graphs are similar,
and both in sinusoidal form. However, less pressure
drop points could be found in graph generated by epicycloidal lobe. The pressure variation from the fourth
peak point (t0.0027s) to fifth peak point (t  0.0345s)
could illustrate for this difference. As observed in
graph of circular lobe, pressure drops at t  0.033s, and
causes deformation of sinusoidal form. Whereas, the
234
Fig. 7 Circular lobe pump – Velocity distribution
Fig. 8
Circular lobe pump – Pressure head vs. time at
5000rpm
Fig. 9(a) Epicycloidal lobe pump – Pressure head vs.
time
Fig. 9(b) Circular lobe pump – Pressure head vs. time
Journal of Mechanics, Vol. 28, No. 2, June 2012
pressure variation from t  0.03s to t  0.035s is almost
linear in case of epicycloidal profile. This phenomenon could be explained by referring to velocity distribution of two profiles.
As shown in Fig. 10, at t  0.033s, there are three
vortices which formed at inlet area and two chambers
captured by two rotors in both circular and epicycloidal
lobe pumps. As discussed above, the existing of these
vortices, especially vortex-1 and vortex-3, causes pressure drop in the pump. However, as observed on the
figure, while the vortex-3 is fully developed, i.e. already appears spinning flow, in circular pump, that of
epicycloidal pump is being in forming state. In addition, maximum velocity which located at the gap between rotors and casing in epicycloidal lobe pump is
lower than that of circular lobe pump. According to
Bernoulli law, with the same dimension of the gap,
lower speed results in higher pressure. This higher
pressure has a part in preventing backward flow from
discharge area to suction area. Combination of less
vortex and lower speed helps epicycloidal lobe pump to
take an advantage to circular lobe pump.
In order to accomplish more comprehensive evaluation between circular and epicycloidal pumps, concept
of characteristic curve is utilized to compare these two
kinds of pump. Characteristic curve is a graph describes the relationship between some typical parameters of the pump such as flow rate vs. pressure head,
flow rate vs. efficiency, flow rate vs. power, etc. It
could evaluate performance of a pump through characteristic curve, thus it is also called performance curve.
Within limit of current research, characteristic curve
which expresses the variation of pressure head according to rotational speed of rotor, named as N-H chart, is
Fig. 10(a)
Fig. 10(b)
used to compare performance of circular and epicycloidal pumps.
In this case, the pressure head is calculated by average value for each rotational speed. Theoretically, this
curve should be linear. As shown in Fig. 11, characteristic curves of two pumps are almost linear with
slope ratio is around 20.7 for epicycloidal profile, and
about 19.6 for circular profile. Higher slope ratio of
characteristic curve results in higher efficiency of the
pump. Furthermore, the average value of pressure
head of epicycloidal pump is nearly 10 higher than
that of circular pump in all cases.
In summary, the lobe pump with rotor surface generated from epicycloidal curve is proved to take many
advantages to lobe pump with circular profile.
4.3
Effect of Gap Between Rotor and Casing
As discussed above, the back flow through gap between rotor and casing plays an important role in pressure drop phenomenon in the pump. It is evident that
adjustment of the gap could improve performance of
the pump. In a study about Waukesha (Universal Series) lobe pump, Prakash et al. [11] proved that an increase in the gap width could cause an unexpected decrease in the pump efficiency. The efficiency drops to
about 43 for the 2.0mm gap and as low as 24 for the
4.0mm gap in comparison with the 1.0mm gap case.
According to our viewpoint, the assumption of the gap
width of 2.0mm and 4.0mm is too far from real gap size
in practice. Our research proposes a gap size of
0.5mm for the pump with epicycloidal profile, and
conducts analysis with range of speed from 1000rpm to
5000rpm.
Circular lobe profile – Velocity distribution
Epicycloidal lobe profile – Velocity distribution
Journal of Mechanics, Vol. 28, No. 2, June 2012
235
Fig. 11 Characteristic curve - Epicycloidal vs. Circular
Fig. 12
As expected, pressure head of the pump increases
with finer gaps between rotors and casing. The
characteristic curve of the pump with gap size of
0.5mm is quasi-linear with slope ratio approximately
110, i.e. five times bigger than that of the pump with
gap size of 1.25mm (Fig. 12). Additionally, the
average pressure head in case of finer gap increase
nearly 425 compared with case of big gap size. The
astounding effect of finer gap could be explained
theoretically by low slip through the gap which
prevents the back flow from discharge area to suction
area.
Furthermore, the numerical analysis also
provides very interesting results suggesting an
explaination about the effect of finer gap in another
way.
Figure 13 depicts vector velocity distribution of the
pump with finer gap at t  0.033s under rotation speed
of 2000rpm. Similarly to case of 1.25mm gap size,
three vortices could be found at suction area including
inlet area (vortex-2), chambers formed by two rotors
(vortex-1, vortex-3).
Quantitatively, vortices in finer gap case seem to be
less immense than case of 1.25mm gap although the
maximum velocity in finer gap case increases
considerably. However, the most diffent in case of
0.5mm gap size is apparance of two vortices (vortex-4,
vortex-5) in discharge area. Low pressure at vortex-4
and vortex-5 trend to balance with effect of three
vortices at suction area. This prevents back flow
phenomenon, and therby increasing efficiency of the
pump.
4.4 Effect of Clearance Between Driving Rotor and
Driven Rotor
Literatures and practices stated that during operating
process, because of high rotational speed mechanical
interference may occur between various parts of lobe
pump such as interference between two rotors [12,13].
Therefore, an appropriate clearance must be provided
there in order to avoid such interference. The question
is what size of clearance should be. If the clearance is
large, the fluid being pump leaks from the clearance
during the rotation of the rotors. Consequently there
arises the problem of a drop in the volumetric efficiency
of the pump. The phenomenon of pressure drop mentioned at the section of pressure variation in current
236 of Mechanics, Vol. 27, No. 4, December 2011
Journal
Fig. 13
N-H Chart
Velocity ditribution – Gap 0.5mm
study could illustrate for this problem. The reverse
flow has been found at the clearance between driving
and driven rotors, and thus this took a part in causing
pressure drop, affecting on performance of the pump.
It should be noted that in this case and entire above
analyses, the clearance of 0.15mm has been setting.
The validation of this value has been proved by Fukagawa [12] in his patent. The author proposed that the
clearance between two rotors must be provided, and this
clearance would alter from 0.1mm to 0.16mm according to rotational angles of rotors. In order to verify the
effect of clearance between rotors on performance of
the lobe pump, the analysis with clearance of 0.12mm
at rotational angle of 0 degree has been conducted and
compared with clearance of 0.15mm.
Figure 14 describes characteristic curves of circular
lobe pump with clearance is 0.12mm and 0.15mm. As
predicted, smaller clearance provides higher pressure
head. The average value of pressure head produced by
0.12mm-clearance is around 3.9 bigger than that by
clearance of 0.15mm. This effect seems to be natural,
but it should be noted that 0.12mm and 0.15mm of
clearance are still in acceptable range proposed by
Fukagawa [12]. In order to balance between expense
of fabrication and assembly of increasing 20 in
precise, i.e. from 0.15mm down to 0.12mm, and
increasing only 3.9 of efficiency in return, bigger
clearance should be considered to use in pratice.
4.5
Effect of Number of Lobes
According to the analysis results of two-lobe pump,
the output of the pump shows unsteady at low rotational
Journal of Mechanics, Vol. 28, No. 2, June 2012
236
Fig. 14 N-H chart clearance 0.12mm vs. 0.15mm
speed (1000 ~ 3000rpm) and more stable at high speed,
saying 4000 to 5000rpm. However, working at such
high speed often leads to damage at the rotors’ surface,
and thereby reducing durability of the pump. It is
suggested that using multi-lobe pump, i.e. the number
of lobes are more than two, is more appropriate. In
order to verify the effect of number of lobes on the
performance of the pump, current study has conducted
analysis with three lobes and four lobes. For simplicity, the gap size between rotor and casing wall, and
clearance between rotors are kept at 1.25mm and
0.15mm, respectively. The simulation was performed
for 10 cases with different rotational speed (1000 ~
5000rpm).
It is obvious that multi-lobe improves capacity of the
pump significantly. As shown in Fig. 15, two-lobe
pump produces four peaks (Fig. 15(a)) at the outlet
during one rotational round of the rotor with speed of
1000rpm while three-lobe and four-lobe pump produces
six (Fig. 15(b)) and eight peaks (Fig. 15(c)), respectively. These results seem to be natural due to the
number of lobes of the pump. However, it can be also
observed from these figures that the output of multilobe pump is more stable than that of two-lobe pump.
The pressure drop points can be found in curve of twolobe pump whereas fewer points can be found from
three-lobe pump, and the pressure head variation of
four-lobe pump is in fully sinusoidal form.
On the other hand, the characteristic curves of multilobe pump have shown astonishing results. As illustrates in Fig. 16, it is obvious that multi lobes do not
improve performance of the pump, and the average
pressure head for each individual case is even smaller
than two-lobe pump. The slope ratio of performance
curve of three-lobe pump is approximately 18.6, i.e.
reducing around 10 compared with two-lobe pump.
The four-lobe pump generates even smaller efficiency
with slope ratio of 18. Theoretically, pressure head is
directly related to flow rate of the pump. In multi-lobe
pump, the fluid carried in each cycle of rotors is less, i.e.
the flow rate reduces, and thereby reducing the performance of the pump.
5.
Fig. 15(a) Two-lobe pump – Pressure head vs. time at
1000rpm
Fig. 15(b) Three-lobe pump – Pressure head vs. time
at 1000rpm
Fig. 15(c) Four-lobe pump – Pressure head vs. time at
1000rpm
CONCLUSIONS
The current study has utilized Dynamic Mesh Tool of
commercial CFD package FLUENT to accomplish a
Journal of Mechanics, Vol. 28, No. 2, June 2012
Fig. 16
N-H chart – Multi-lobe pump comparison
237
comprehensive knowledge about fluid mechanics of
lobe pump. With a wide range of rotational speed
from 1000rpm to 5000rpm, the research provides significant information on flow pattern, velocity and pressure field which could as well as could not be achieved
by any experimental approach. Such a simulation
offers a scope for visualizing the flow through the lobe
pump. The success of this work exposes an effective
method to analyze and test new designs of lobe pumps.
Furthermore, this approach could be also applied to
wide range of positive rotary pumps such as gear pumps
or vane pumps from micro to very large scale.
The analysis results in this study demonstrate that the
profile of rotors could affect considerably on performance of the pump. The analyses were conducted with
two-lobe rotor profiles generated by circular and epicycloidal curves. According to characteristic curve
which describes the relation between pressure head and
rotational speed, it could conclude that epicycloidal
lobe pump provided better performance than circular
lobe pump. However, in both two cases, at low rotational speeds, i.e. less than 3000rpm, pressure head was
in unstable state with many pressure drop points. Although it could be found less pressure drop points in the
pump with epicycloidal profile, an obvious effect is still
missed. Interestingly, when rotational speed of rotors
increases, the pressure head becomes more stable, and
was complete in sinusoidal form at speed of 5000rpm.
This suggested that working in high speed might be an
option for two-lobe pump. However, the lobe pumps
often work in low speeds in practice. It means that
using more-lobe rotors or modifying rotor profiles is
more appropriate option to improve performance of
lobe pump.
The results also confirmed strong effect of gap between rotors and casing on performance of the lobe
pump. The analyses started with gap size of 1.25mm,
and then decreased it down to 0.5mm. 0.75mm reducing in gap size resulted in 425 increasing of average pressure head. In practice, working with such
small gaps in normal pumps could cause increasing
expenses for manufacturing pump elements. Thus, the
users as well as manufacturers might prefer to work
with gap sizes bigger than 1mm. However, in precise
pumps which are often in small scale, finer gaps would
be considered as one of the most effective factors which
could impact performance of the pump.
Furthermore, the effect of clearance between driving
rotor and driven rotor has been approved. According
to analysis result, it might conclude that the clearance
can alter from 0.12mm to 0.15mm without affecting on
performance of the pump, and can be considered as a
“safe limit” for lobe pump in practical fabrication and
assembly.
Lastly, current research proves that number of lobes
of rotor do not improve performance of lobe pump
while provide higher capacity and more stable output.
Although the analysis has just conducted in three different models with two, three and four lobes, it might
predict that the more stable of output is needed, the
more lobes of rotor should be used, and the higher performance of the pump wanted to achieve, the less
238
number of lobes should be applied. However, this
prediction should be validated, and an optimization for
each case should be conducted in further studies.
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(Manuscript received January 14, 2011,
accepted for publication June 1, 2011.)
Journal of Mechanics, Vol. 28, No. 2, June 2012