# CFD Analysis on the Effect of Radial Gap on Impeller-Diffuser Flow Interaction as well as on the Flow Characteristics of a Centrifugal Fan

Authors: K. Vasudeva Karanth; N. Yagnesh Sharma
Journal: International Journal of Rotating Machinery
 (2009)

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## Abstract

The flow between the impeller exit and the diffuser entry (i.e., in the radial gap is generally considered to be complex). With the development of PIV and CFD tools such as moving mesh techniques, it is now possible to arrive at a prudent solution compatible with the physical nature of flow. In this work, numerical methodology involving moving mesh technique is used in predicting the real flow behavior, as exhibited when a target blade of the impeller is made to move past corresponding vane on the diffuser. Many research works have been undertaken using experimental and numerical methods on the impeller-diffuser interactive phenomenon. It is found from the literature that the effect of radial gap between impeller and diffuser on the interaction and on the performance of the fan has not been the focus of attention. Hence numerical analysis is undertaken in this work to explore and predict the flow behavior due to the radial gap. This has revealed the presence of an optimum radial gap which could provide better design characteristics or lower loss coefficient. It is found that there is a better energy conversion by the impeller and enhanced energy transformation by the diffuser, corresponding to optimum radial gap. The overall efficiency also found to increase for relatively larger gap.


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## Body

## 1. Introduction

A host of articles [1–16] is available
which explicitly explore the impeller diffuser interactive phenomenon by both
experimental and numerical methods.Ubaldi
et al. [1] attributed principal cause of the high loss levels observed in the
diffuser due to the strong spanwise distortion in swirl angle at inlet, which
initiates a strong hub/corner stall. Qin and Tsukamoto [2] has calculated the unsteady
flow caused by the interaction between impeller and diffuser vanes in a
diffuser pump by using the singularity method.According to Justen et al. [3], the
time-dependent pressure distribution on the diffuser front wall and on the
suction and pressure surfaces of the diffuser vanes reveal that the semivaned
space mainly the region near the vane suction side is influenced by the
unsteady impeller-diffuser interaction and that the pressure fluctuations
appear to be distinctly higher than the pressure fluctuations in the vaneless
space. Shi and Tsukamoto [4] in their study have shown that the Navier-Stokes
code with the k-ε model is found to be capable of predicting pressure
fluctuations in the diffuser.Sinha
et al. [5, 6] have carried out quantitative visualization of centrifugal pump
with diffuser vanes. The article by Meakhail et al. [7] deals with PIV applied
to the study of unsteady impeller-vaneless diffuser interaction in centrifugal
fan where measurements were applied to extract the unsteady flow at the exit
part of the impeller. In another study by Meakhail et al. [8] an attempt to
help understanding
the complex unsteady flow associated with the interaction between the impeller
and its vaned diffuser has been made. In their two-part paper, Ziegler et al. [9] have
presented an experimental investigation of the effect of impeller-diffuser
interaction on the unsteady flow and the time-averaged flow field in the
interactive region of impeller and diffuser. Akinori and Hisasada [10] have investigated the
pressure fluctuations in the downstream of the vaned diffuser of a centrifugal
pump impeller where they found the potential interaction between the impeller
and the diffuser blades more strongly than the impeller-wake interaction.
Cui [11] has carried out a comparative study of unsteady flow in a
transonic centrifugal compressor with vaneless and vaned diffusers.  A part of the current work is validated with
the results obtained by Meakhail
and Park [12], in which they explore the study of impeller—diffuser—volute
interaction in a centrifugal fan. These authors report measurement data in the region between the impeller and vaned diffuser
and have obtained results of numerical flow simulation of the whole machine. Feng et al. [13] have carried out numerical
simulations on impeller-diffuser interactions in radial diffuser pumps to
investigate the unsteady flow and pressure fluctuations on the blade and vane
surfaces. Different operating points, different blade number configurations,
and different radial gaps between the impeller and diffuser have been examined
to study their effects on the unsteady flow. They have found that flow rate,
blade number configuration, and radial gap influence significantly the pressure
fluctuation and associated unsteady effects in the diffuser pumps. Khelladi et al. [14] have
carried out the numerical unsteady flow analysis in a vaned centrifugal fan. Majidi [15] has used a CFD code with sliding mesh technique on a centrifugal
pump to consider the impeller/volute interaction. The results obtained by him show that the flow in the
impeller and volute casing is periodically unsteady and confirm the
circumferential distortion of the pressure distribution at the impeller outlet
and in the volute casing. Ibaraki
et al. [16] in their work have found that a complex three-dimensional flow with
distortion between the shroud and the hub is observed.It is clear
from the above literature survey that the effect of radial gap on the system performance
as well as on the impeller-diffuser interaction in a centrifugal fan has not
been explored well so far. Hence a numerical modeling of the flow domain which
includes a portion of the inlet to the impeller as well as the diffuser with
volute casing has been carried out, and moving mesh technique has been adopted
for unsteady flow simulation of the centrifugal fan in this analysis.


## 2. Numerical Modeling

### 2.1. Geometry and Grid Generation

The centrifugal fan stage consists of an
inlet region, an impeller, a vaned diffuser, and a volute casing (Figure1). The
impeller consists of thirteen 2-D backward swept blades with an exit angle of
76° relative to the tangential direction. The radial gap between the
impeller outlet and the diffuser inlet is 15% of the impeller outlet radius.
The diffuser ring has also the same number of vanes as that of the impeller.
All the blades are of 5 mm thickness. The specifications of the fan stage are
illustrated in Table 1.Table 1
Specifications of the
centrifugal fan.
Centrifugal fan specificationsImpeller
inlet radius,r1120 mmImpeller
outlet radius,r2200 mmDiffuser
inlet radius,r3230 mmDiffuser
outlet radius,r4300 mmVolute
exit flange width450 mmWidth
of diffuser blade35 mmWidth
of volute casing90 mmImpeller
inlet vane angle30°Impeller
outlet vane angle76°Diffuser
inlet vane angle23°Diffuser
outlet vane angle38°Number
of impeller vanes13Number
diffuser vanes13Speed
of the fan (RPM)1000 rrpmFigure 1
Model of the centrifugal fan used in the
analysis.The technical paper by Meakhail and Park [12] forms the basis
for geometric modeling in the present work. The model of the fan consists of
four parts: the inlet, the impeller, the diffuser, and the volute region. Unstructured
meshing technique is adopted for establishing sliding mesh configuration as the
analysis is unsteady as per CFD code [17].The grid for the volute part of the
domain has 163 590 nodes and 162 113 elements. The diffuser has 163 213 nodes
and 155 106 elements. The impeller has 80 971 nodes and 74 143 elements. The
inlet part of the domain has 5536 and 5190 nodes and elements, respectively.
The maximum size of the element is limited to elements having an edge length of
2 mm. However, to establish grid independency a finer model having an element
edge length of maximum of 1 mm is carried out and the variation in the results was found to be less than
2.5% and hence to save the computational time, elements edge length of maximum
2 mm size is adopted. Figure2 shows the meshed domain and it can be observed
that a finer mesh is adopted near the surface of the impeller and diffuser
vanes to capture the boundary layer effects using a suitable sizing algorithm as
in CFD code [17].Figure 2
A view of the meshed portion between the
impeller and diffuser of the centrifugal fan.


### 2.2. Unsteady Calculations Setup

Two-dimensional,
unsteady Reynolds-averaged Navier-Stokes equations set to polar coordinate system
are solved by the CFD code [17]. To obtain the flow characteristic and
efficiency curves of the fan, total pressure (gage) is applied at the inlet,
and static pressure (gage) is applied at the flange exit as the boundary
condition. However, for comparing the configurations with different radial gap,
an absolute velocity of 5 m/s which corresponds to the design point mass flow
rate of the optimal configuration is imposed at the inlet and a zero-gradient
outflow condition of all flow properties is applied at the flange exit of the
fan, assuming fully developed flow conditions.A no-slip wall condition is specified for the
flow at the wall boundaries of the blades, the vanes, and also the volute
casing. The turbulence is simulated using a standardk-ε model [17]. Turbulence
intensity of 5% and a turbulent length scale of 0.5 m which is the cube root of
the domain volume are adopted in the study. The unsteady formulation used is a
second-order implicit velocity formulation, and the solver is pressure based [17].
The pressure-velocity coupling is done using SIMPLE algorithm, and
discretization is carried out using the power law scheme. The interface between
the impeller and the diffuser is set to sliding mesh in which the relative
position between the rotor and the stator is updated with each time step. The
time step Δt is set to 0.0001 second, corresponding to the advance of
the impeller by Δγ=0.61° per time step for a rated speed of 1000 RPM to establish stability criterion.
The maximum number of iterations for each time step is set to 30 in order to
reduce all maximum residuals to a value below 10−5.
Since the nature of flow is unsteady,
it is required to carry out the numerical analysis until the transient
fluctuations of the flow field become time periodic as judged by the
pressure fluctuations at salient locations in the domain of the flow. In the
present analysis this has been achieved after two complete rotations of the
impeller. The salient locations chosen
are the surfaces corresponding to inlet to the impeller, impeller exit,
diffuser exit, impeller vanes, diffuser vanes, and the exit flange of the
volute casing. The time- and area-weighted averages for the pressure and
velocity fluctuations at each salient location in the computational domain are
recorded corresponding to each rotation of the impeller by time step
advancement. The static pressure recovery
coefficient and the total pressure loss coefficient for the diffusing domains
of the fan are calculated based on the weighted averages [17] and are plotted
with respect to time steps.


### 2.3. Validation of the Model

The numerical model for the
whole field flow calculations is validated by calibrating the results of the
current numerical work with the experimental work carried out by Meakhail and
Park [12].The graph shown in Figure3
captures the validation results for the current work with the work cited above.Figure 3
Validation
characteristics curve of head coefficient with flow coefficient.The validation curve is a
head coefficient versus flow coefficient curve which shows a decrease in the
head coefficient as the flow coefficient increases as is required for a
backward swept impeller blade. The validation shows a close agreement between
the present numerical model and the experimental model of Meakhail and Park [12].


### 2.4. Geometric Configurations for Impeller-Diffuser Radial Gap

A
total of six different configurations are generated by varying the radial gap
between the impeller and the diffuser. The outer radii of the impeller and the
diffuser are kept constant at 200 mm and 300 mm, respectively. However, the
inlet radius of the diffuser is changed to achieve the radial gap variation.Configurations A, B, C, D, E, and F are having a radial
gap ratio “Rgr” of 0.05,
0.1, 0.15, 0.2, 0.25, and 0.30, respectively.


## 2.1. Geometry and Grid Generation

The centrifugal fan stage consists of an
inlet region, an impeller, a vaned diffuser, and a volute casing (Figure1). The
impeller consists of thirteen 2-D backward swept blades with an exit angle of
76° relative to the tangential direction. The radial gap between the
impeller outlet and the diffuser inlet is 15% of the impeller outlet radius.
The diffuser ring has also the same number of vanes as that of the impeller.
All the blades are of 5 mm thickness. The specifications of the fan stage are
illustrated in Table 1.Table 1
Specifications of the
centrifugal fan.
Centrifugal fan specificationsImpeller
inlet radius,r1120 mmImpeller
outlet radius,r2200 mmDiffuser
inlet radius,r3230 mmDiffuser
outlet radius,r4300 mmVolute
exit flange width450 mmWidth
of diffuser blade35 mmWidth
of volute casing90 mmImpeller
inlet vane angle30°Impeller
outlet vane angle76°Diffuser
inlet vane angle23°Diffuser
outlet vane angle38°Number
of impeller vanes13Number
diffuser vanes13Speed
of the fan (RPM)1000 rrpmFigure 1
Model of the centrifugal fan used in the
analysis.The technical paper by Meakhail and Park [12] forms the basis
for geometric modeling in the present work. The model of the fan consists of
four parts: the inlet, the impeller, the diffuser, and the volute region. Unstructured
meshing technique is adopted for establishing sliding mesh configuration as the
analysis is unsteady as per CFD code [17].The grid for the volute part of the
domain has 163 590 nodes and 162 113 elements. The diffuser has 163 213 nodes
and 155 106 elements. The impeller has 80 971 nodes and 74 143 elements. The
inlet part of the domain has 5536 and 5190 nodes and elements, respectively.
The maximum size of the element is limited to elements having an edge length of
2 mm. However, to establish grid independency a finer model having an element
edge length of maximum of 1 mm is carried out and the variation in the results was found to be less than
2.5% and hence to save the computational time, elements edge length of maximum
2 mm size is adopted. Figure2 shows the meshed domain and it can be observed
that a finer mesh is adopted near the surface of the impeller and diffuser
vanes to capture the boundary layer effects using a suitable sizing algorithm as
in CFD code [17].Figure 2
A view of the meshed portion between the
impeller and diffuser of the centrifugal fan.


## 2.2. Unsteady Calculations Setup

Two-dimensional,
unsteady Reynolds-averaged Navier-Stokes equations set to polar coordinate system
are solved by the CFD code [17]. To obtain the flow characteristic and
efficiency curves of the fan, total pressure (gage) is applied at the inlet,
and static pressure (gage) is applied at the flange exit as the boundary
condition. However, for comparing the configurations with different radial gap,
an absolute velocity of 5 m/s which corresponds to the design point mass flow
rate of the optimal configuration is imposed at the inlet and a zero-gradient
outflow condition of all flow properties is applied at the flange exit of the
fan, assuming fully developed flow conditions.A no-slip wall condition is specified for the
flow at the wall boundaries of the blades, the vanes, and also the volute
casing. The turbulence is simulated using a standardk-ε model [17]. Turbulence
intensity of 5% and a turbulent length scale of 0.5 m which is the cube root of
the domain volume are adopted in the study. The unsteady formulation used is a
second-order implicit velocity formulation, and the solver is pressure based [17].
The pressure-velocity coupling is done using SIMPLE algorithm, and
discretization is carried out using the power law scheme. The interface between
the impeller and the diffuser is set to sliding mesh in which the relative
position between the rotor and the stator is updated with each time step. The
time step Δt is set to 0.0001 second, corresponding to the advance of
the impeller by Δγ=0.61° per time step for a rated speed of 1000 RPM to establish stability criterion.
The maximum number of iterations for each time step is set to 30 in order to
reduce all maximum residuals to a value below 10−5.
Since the nature of flow is unsteady,
it is required to carry out the numerical analysis until the transient
fluctuations of the flow field become time periodic as judged by the
pressure fluctuations at salient locations in the domain of the flow. In the
present analysis this has been achieved after two complete rotations of the
impeller. The salient locations chosen
are the surfaces corresponding to inlet to the impeller, impeller exit,
diffuser exit, impeller vanes, diffuser vanes, and the exit flange of the
volute casing. The time- and area-weighted averages for the pressure and
velocity fluctuations at each salient location in the computational domain are
recorded corresponding to each rotation of the impeller by time step
advancement. The static pressure recovery
coefficient and the total pressure loss coefficient for the diffusing domains
of the fan are calculated based on the weighted averages [17] and are plotted
with respect to time steps.


## 2.3. Validation of the Model

The numerical model for the
whole field flow calculations is validated by calibrating the results of the
current numerical work with the experimental work carried out by Meakhail and
Park [12].The graph shown in Figure3
captures the validation results for the current work with the work cited above.Figure 3
Validation
characteristics curve of head coefficient with flow coefficient.The validation curve is a
head coefficient versus flow coefficient curve which shows a decrease in the
head coefficient as the flow coefficient increases as is required for a
backward swept impeller blade. The validation shows a close agreement between
the present numerical model and the experimental model of Meakhail and Park [12].


## 2.4. Geometric Configurations for Impeller-Diffuser Radial Gap

A
total of six different configurations are generated by varying the radial gap
between the impeller and the diffuser. The outer radii of the impeller and the
diffuser are kept constant at 200 mm and 300 mm, respectively. However, the
inlet radius of the diffuser is changed to achieve the radial gap variation.Configurations A, B, C, D, E, and F are having a radial
gap ratio “Rgr” of 0.05,
0.1, 0.15, 0.2, 0.25, and 0.30, respectively.


## 3. Results and Discussion

The
head coefficient versus flow coefficient characteristic curves for all the six
configurations is plotted
after capturing the area weighted average values of the pressure coefficients
and mass averaged flow rates. It is seen from Figures3 and 4 that the design point operation as
well as efficiency seems to change with change in radial gap.Figure 4
Performance of centrifugal fan (efficiency versus flow coefficient).From Table2 and Figure 4
it is observed that the smaller radial gap ratio of 0.05 (configuration A) and
for the larger radial gap ratio of 0.3 (configuration F), the design point mass
flow rate is relatively higher than that of configuration C which has a radial
gap ratio of 0.15. More importantly, the efficiency corresponding to design
point operation is found to be higher for configuration C.Table 2
Computed flow parameters at design point operation of the fan.
Configuration
typeRadial
gap ratioRgrFlow
coefficient (Φ)Max.
efficiencyη(%)Head
coefficient(Ψ)A0.050.08522.840.235B0.100.07324.590.304C0.150.06627.370.360D0.200.07422.630.333E0.250.07822.020.3324F0.300.07620.990.372Radial
gap is required to avoid steep velocity gradients at the diffuser entry region
according to Yahya [18]. This allows nonuniform flow to mix out and enter the
diffuser with lower velocities. Also the flow emanating from the impeller has
jets and wakes as clearly seen in the relative velocity vector plots shown in
Figures 6, 7, 8, 9, and 10. When such a flow enters diffusing flow passages, the quality
of flow differs widely and some of the blades of the diffuser may experience
flow separation leading to rotating stall and poor performance.At
smaller radial gap, the flow enters the stationary diffuser almost at the same
velocity profile as it leaves the impeller and jets and wakes related to the
impeller exit flow do not have a chance to even out.  This causes lower diffusion leading to lower diffuser
static pressure recovery coefficient and lower overall static pressure recovery
coefficient across the fan as shown in
Figure11 as well as lower fan efficiency as shown in Figure 4.The
shifting of the design point operation at lower radial gap ratio of 0.05 may be
attributed to the fact that the energetic fluid jetting from the impeller
enters the diffuser and decelerates over the diffuser. As a result a large
recirculation zone is formed in many of the diffuser blade passages as seen in
Figure6.  This will block the flow and
hence for peak point operation a higher mass flow rate is required. Hence there
is a perceptible shift in the design point operation for radial gap ratio of
0.05.However,
when the radial gap is relatively larger, even though the jets and wakes
related to the exit flow from the impeller gets evened out, the flow tends to
stall in some of the vanes of the diffuser due to change in angle of incidence, as can be seen in Figure10.
This will have detrimental effect on the static pressure rise across the fan
leading to poorer efficiency.It is seen in a contrasting manner that
there is a higher mass flow rate corresponding to the design point operation for
the case of larger radial gap ratio of 0.25 from Figure4. This can be
attributed to stalling process occurring over some of the diffuser vanes due to
relatively larger radial gap (Figure 10) which requires a higher mass flow rate
to achieve peak point operation.The static pressure recovery
coefficients and total pressure loss coefficients for various configurations
are presented in the form of bar charts in Figures11 and 12, respectively.It
is seen from Figure12 that total pressure loss coefficient is higher for the
smaller radial gap but for larger radial gap it tends to decrease. This is
because of the fact that at larger radial gap, the diffusion passage gets
reduced and hence friction losses are lower compared to lower radial gap
configuration. Also it is clear from Figure 12 that for configuration C the total
pressure loss coefficient is least compared to configurations D and E. This is
due to the fact that at relatively larger radial gap, the fluid guidance is
decreased and hence there is a marginal rise in total pressure loss
coefficient.Hence
it can be stated that there must be an optimum radial gap which could provide
relatively higher efficiency and also lower mass flow rates to achieve the higher
static pressure rise.It can be seen from Figure11 that the
overall static pressure recovery coefficient increases with the increase in radial
gap while the diffuser static pressure recovery coefficient increases up to radial
gap ratio of 0.15 (configuration C) and then it decreases. This is also
reflected in Figure 12 in which the total pressure loss coefficient for the configuration
C is the lowest. The reason why there is an increase in overall static pressure
recovery for larger radial gap corresponding to configurations E and F is due
to the fact that the slope of the characteristic for these configurations
becomes slightly positive for lower mass flow rate as seen in Figure 5. Hence
there is an increase in head coefficient, resulting in increase in overall
static pressure recovery coefficient. But this can lead to the possibility of unstable
surge condition. So a larger radial gap ratio above Rgr=0.15 is not preferable. Figure 13 shows the dynamic
head coefficient at the design point mass flow rate for various configurations.
It is clear from Figure 13 that corresponding to Rgr=0.15, the dynamic head is found to be the maximum.
This shows that it is possible to have better energy transfer corresponding to
this radial gap ratio of Rgr=0.15.Figure 5
Performance characteristics
curves for all configurations.Figure 6
Relative velocity plot for configuration A (radial gap ratio = 0.05).Figure 7
Relative velocity plot for configuration B (radial gap ratio = 0.1).Figure 8
Relative velocity plot for configuration C (radial gap ratio = 0.15).Figure 9
Relative velocity plot for configuration D (radial gap ratio = 0.20).Figure 10
Relative velocity plot for configuration E (radial gap ratio = 0.25).Figure 11
Static pressure recovery coefficient.Figure 12
Total pressure loss coefficient.Figure 13
Dynamic head coefficient at the design
point mass flow rate of configuration C (inlet velocity of 5 m/s).Figure14 shows the impeller static pressure
coefficient for different configurations. It is seen from the figure that the
configuration C experiences the maximum static pressure rise. This also can be
verified from Figure 8 which shows a marginal reduction in the wake regions in
the impeller blade passages. The wake in the impellers for configurations D and
E is seen to increase indicating that a larger radial gap will tend to increase
the wake. Hence it becomes quite obvious from the stated facts in the last two
paragraphs that there is an optimum radial gap corresponding to Rgr=0.15 which provides highest
total energy transfer for the impeller blade.Figure 14
Impeller exit
static pressure coefficient for the various configurations.Figure15 shows the diffuser exit static pressure coefficient for the various
configurations. It is seen that for optimum radial gap ratio of 0.15 there is a
better static pressure conversion which tallies with the physical explanations
earlier given. Figure 16 depicts the amplitude of pressure fluctuations
captured at different time steps, at the exit flange of the fan. The
fluctuations die down with the increase in radial gap as the fluid particles
jetting out at the impeller exit tend to get evened out before the flow enters
the vaned diffusers and this agrees with the result obtained by Feng et al. [13]. It can,
therefore, be conclusively stated that there is an optimum radial gap which
could help providing
maximum energy transfer by the impeller blades as well as maximum
energy conversion by diffuser vanes.Figure 15
Diffuser exit
static pressure coefficient for the various configurations.Figure 16
Static
pressure coefficient at the exit flange of the fan versus time steps.


## 4. Conclusion

The
following conclusions can be drawn from the above study.(1)
As
a major inference from the above analysis, it is found that there is an optimum
radial gap at which better dynamic and static heads are developed by the impeller
blades as well as better energy conversion by diffuser vanes.(2)
The
above-mentioned facts lead to maximum efficiency of the centrifugal fan as
observed in the study.(3)
There
appears to be greater degree of stalling of the flow above or below the
optimum radial gap.(4)
The
static pressure recovery and total pressure loss for the diffusing
components of the fan change with the radial gap.(5)
The larger is
the radial gap, the
smaller are the
pressure fluctuations at the exit flange of the fan.(6)
The
jet and wake phenomena as seen in all the impeller passages are influenced
by the radial gap between impeller and diffuser.



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*Source: 293508-2009-04-27.xml*