Optimization Research of Centrifugal Fan with Different Blade Number and Outlet Blade Angle

Songling WANG, Lei ZHANG, Zhengren WU Hongwei QIAN Department of Power Engineering, North China Electric Power University, Baoding 071003, Hebei Province, P.R. China

Email: zl83828@163.com

Abstract—The characteristics of the three-dimension flow field of the G4-73 centrifugal fan were numerically simulated based on the k ε− turbulence model with the Fluent, and then verified the simulating result by experiment. Taking the efficiency ηmaximizing as a function goal, while the blade number and the angle of blade outlet as the variable quantities, the fan impeller parameters are optimized based on least squares method. The optimizing results showed that the performance of centrifugal fan was improved by lowering the energy loss which caused by the secondary flow vortex, the volute tongue, the wake-jet and the angle of attack. After the optimization, the total pressure and efficiency increased 3.7% and 0.5% respectively.

Keywords--thermal power engineering; centrifugal fan; numerical simulation; optimum design; least squares method

I. INTRODUCTION

In recent years, generating cost of power plants increases due to the shortage of coal. As important auxiliary equipments, fans consumed 30 percent of plant electrical consumption. So the study and optimization of centrifugal fan to improve the efficiency are important for the energy-saving of plant [1].

Total pressure and efficiency are important parameters of fan performance. In deduction of the energy equation for centrifugal fan, one of the assumption is that the impeller has unlimited blade. In fact, the blade number is always limited, which results in lower total pressure. Slip factor reflect the influence of limited blade on theoretical total pressure. The results show that the slip factor relate to the number of blade, the outlet blade angle, the ratio of inside diameter to outside diameter, the dynamic viscosity of the fluid and the runner’s surface roughness[2]. Therefore, the number of fan blades and the size of the outlet blade angle directly impact on the fan performance, but it is still difficult to calculate it by theoretical methods[3-4]. Cheng xinde studied the selection of the number of the forward-curved blade by experiments, and few papers did research on the impact of blade number and the size of the outlet blade angle on the performance of fan by numerical method. This paper will use the software of Fluent to calculate the total pressure and efficiency of centrifugal fans with different blade numbers and blade outlet angles, and optimize the fan for a higher efficiency based on the least square method.

II. NUMERICAL METHODS

A. Geometric Model G4-73-serie centrifugal fans are widely used as induced and

draft fans of the boiler which match to 200MW and 300MW power generating units. In this paper, G4-73No.8D centrifugal fan was studied, and it’s geometric model was shown in Figure 1. External diameter of the blade is

280cmD = , the blade angle

is 2 45yβ = the number of blade is 12, the blades style is airfoil, and the blades uniformly distributed along the circle, volute arbor’s width is 52cm and gap of tongue snail's is 8cm.

(Units:mm

Figure 1. Fan structure diagram

B. Equations and Boundary Conditions In the centrifugal fan, the three-dimensional motion of the

gas is thought to be the incompressible and steady flow, and calculated by using three-dimension Reynolds both conservation Navier-Stokes equations. As the fluid in a state of turbulence, the standard k ε− equation of the second model was selected as the turbulence model, and when near wall, the standard wall function was used. Calculating method was SEGREGATED implicit method, the pressure - speed coupled using the SIMPLE calculation method, and turbulent kinetic energy, dissipation of turbulence and the momentum equation all use second-order discrete upwind.

Equations include the continuity equation, the momentum equation and k ε− equation.

0i

i

ux

∂ =∂

(1)

21( ) ( )3

i

i j j i

ji i j

i i

uP uu uut x x x x x x

ρ ρ μ μ∂∂ ∂ ∂ ∂ ∂+ =− + +

∂ ∂ ∂ ∂ ∂ ∂ ∂ (2)

2

kj k j

kCD k GDt x x

με εμ εσ

∂ ∂= + + −∂ ∂

(3)

720

520

1400

1560

800

200

impeller

volu

te

978-1-4244-2487-0/09/$25.00 ©2009 IEEE

2

2

1 2kj j

kCD C G CDt x x k k

μ

ε εε

ε ε ε εεμσ

∂ ∂= + + −∂ ∂

(4)

Among them 1Cε =1.44 2Cε =1.92 Cμ =0.09

kσ =1.0 εσ =1.3[5].

C. Result Comparisons Figure 2 shows performance curves obtained through

numerical simulation and experiment. point A shows the status of the design points, It can be seen that the error of the total pressure of the fan which attained from numerical simulation is less than 3%, while the efficiency error in the design point is less than 2.3%, so it can be drawn conclusion that the calculation results derived by numerical simulation are accurate enough to predict the inner flow of the fan and the results could be used as the guide to optimize the impeller and verify the accuracy of numerical simulations.

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A

qv(m3/s)

exp sim

(a) Performance curves of (b) Performance curves of total pressure and flow efficiency and flow

Figure 2. Performance curves of numerical simulation and experimental results

III. THE OPTIMIZATION OF CENTRIFUGAL FAN IMPELLER

A. Optimum Model The factors that impact fan’s performance are coupled with

each other, various factors have a combined action together to the fan performance. This paper take the efficiency η as a maximizations goal, take the number of blade of Z and the angle of 2 yβ ∞ as the variable quantity, and construct the optimized mathematical model:

( )11 14

43 48

Max ,S.t

f x yxy

< <

< < (5)

In the model, ( , )f x y represents the objective function of efficiency η ,and parameters x and y separately represent the

number of blade and the angle of 2 yβ ∞ .

B. The least-squares Curved Fitting of Rectangular Domain

the function valuation ijz of curved face ( , )f x y on the n

× m net points of rectangular domain for ( , )i jx y is known,

and the curved face ( , )f x y is:

1 1

0 0( , )

N Mi j

iji j

f x y a x y− −

= =

= (6)

Its approximately parameters { }ij N Ma × can be looked for by least squares method. And N × M-order algebraic equations with regard to { }ija can be obtained as follow:

1 1 1 1

0 0 0 0( , ) ( , ) 0

n m N Mi j i j

s t s t ij s t s ts t i j

x y f x y a x y x yω− − − −

= = = =− ⋅ =

(7) The equations can be solved with programming by

software of MATLAB software, and get the curved surface fitting expression of efficiency η with regard to Z and 2 yβ ∞ .

And the values of Z and 2 yβ ∞ at maximum surface point are solved by search method. 4 × 4 high-order fitting is used to ensure the fit accuracy. The basic data for fitting obtained through numerical simulation is shown in table.1.

TABL EFFICIENCY VALUE OF DIFFERENT PARAMETERS IMPELLER

2yβ ∞

Z43° 44° 45° 46° 47° 48°

11 74.7 75.1 74.8 66.5 72.6 70.8 12 75.9 74.6 76.58 75 74.5 73.7 13 75.9 76.7 76.9 76.3 75.5 72 14 76.5 76.7 77 76.8 74.7 73.6

The optimization results are Z =14 and2 44.5yβ ∞ = .

C. Optimization and Analysis of the Results In order to verify the optimization results, the fan was

optimized by using the FLUENT software and compared with un-optimized for inner flow field and performance curve. Fig. 3 shows the distribution map for total and dynamic pressure of impeller channel. And large-scale spiral vortex is showed. Because of volute’s diffusing action, large-scale secondary flow vortex is formatted between the front end plate of impeller, volute and collector. Figures (a) (b) display that the scale, intensity and center of secondary flow vortex change as the increasing of the volute capacity in the different circumferential cross section of the volute.

Also Fig. 3 indicates that the intensity of secondary flow vortex is lower and the flow field distribution is more homogeneous after optimized. Then optimization reduced the energy degradation. And local outlet nearby the front end plate of impeller is blocked on the 0 cross-section of volute

channel before optimization because of rotating center closing with the outlet of impeller, inducing the deviation of air flow in the outlet and vortex low-energy air flow mixed, the energy degradation increased. Figures (a) and (c) present that the vortex intensity reduces and the vortex center moves to back plate of the volute far from impeller outlet so that the local block of fan outlet reduced and the energy loss that resulting from the mixing of low-energy air flow reduced after optimization. Based on charts (b) and (d), before optimization, there is a large scale vortex on the 180 cross-section, at the same time, a small one on the fore end plate of the volute near the anti-vortex ring. The energy loss caused by small vortex is lower but can’t be neglected because of the interaction with the big one. After optimization, the intensity of both big and small vortex is reduced, and the size of the latter one is only a half of the previous mode, which greatly reduced the energy loss caused by the interaction.

(a) 0°section/ before optimization (c) 0°section/ after optimization

(b) 180°section / before optimization (d) 180°section / after optimization

Figure3. Streamline of different flow passage section

Fig. 4 shows the distributions of the full pressure and dynamic pressure in cross-section of volute before and after optimization. In the picture (a), there is a low-energy field where full pressure is lower in 120 region of the original fan. The field continues to fan outlet and caused by diffusing action of volute and secondary flow vortex running along spiral direction, which have mentioned above. By means of increasing the number of leaves by 12 pieces to 14, the impeller working area added obviously and function strength enhanced. Then figure (c) shows that full pressure of fan enhanced after optimizing. In addition, exit setting angle 2 yβ ∞ has been reduced 0.5°, which reducing the full pressure, but the proper exit setting angle improves the inner flow field and the low-energy fluid regions vanishing on 120region. Energy losses reduced in volute and the distribution of full pressure is more homogeneous in the fan, making up the energy loss caused by reducing outlet setting angle.

By figures (a) and (b) it was known that tremendous pressure gradient appears on the volute tongue of fan and double obviously low-energy fluid regions turn up on the upstream surface of the volute tongue and fan outlet near it. Due to the sharp narrowing of the volute tongue channel, air flow nearby separated into two parts: a part of high-speed air

flow approaches to volute tongue’s upstream and mixes with the main air flowing out from impeller outlet around the volute tongue, which result in the direction offsetting of the main flow and energy losing on the upstream surface of the volute tongue; and another slow-speed part approaches to volute tongue’s downstream, which causes the stack of the low power fluid and the block of parts of outlet on account of the obviously velocity gradient near the fan outlet. Figures (c) and (d) reveal that optimization to outlet setting angle improves inner flow field of the fan, increasing the total pressure on the volute tongue upstream surface and the fan outlet nearing volute tongue significantly, reducing the low-energy fluid regions either.

(a) Total pressure/before optimization (c) Dynamic pressure/before optimization

(b)Total pressure / after optimization (d) Dynamic pressure /after optimization Figure 4. The total pressure and dynamic pressure distribution of volute section

Fig. 5 shows the distributions of full pressure and dynamic pressure of initial and optimized condition. According to the figures (a) and (c), the full pressure grows evenly along the circumferential direction before optimization. It can form a low pressure area at the front of the suction surface. And this indicates the existence of the positive attack angle, which causes the eddy-current in suction surface and the low energy region. After optimized, the full pressure of the flow grows evenly, and the area at the front of the suction surface decreases following the increase of the pressure. That thanks to the reduction of impeller outlet setting angle 2 yβ ∞ . Then the positive incidence angle and he eddy current loss of the suction surface reduced accordingly.

Figures (b) and (d) indicate the offset to pressure side of the dynamic pressure isoline in the middle flow channel. That caused by the different velocity between the pressure and suction surface in impeller channel, inducing uneven distribution of the dynamic pressure and current-jet flow structure in the channel outlet. After optimization the number of leaf blade increased, and enlarging the flow channel, narrowing the width and lengthen the acting time of vane to air current. At the same time, the reducing of the flow channel width cuts down the differential dynamic between the pressure and suction surface, bringing the dynamic pressure distribution more homogeneous and reducing energy loss caused by current-jet flow.

(a) Total pressure distribution before optimization

(b) Dynamic pressure distribution before optimization

(c) Total pressure distribution after optimization

(d) Dynamic pressure distribution after optimization Figure 5. The total pressure and dynamic pressure distribution of impeller passage

Fig. 6 is the performance curves before and after optimization. Through the comparison it is obtained that the fan’s performance has improved integrality and total pressure enhanced widely near the operating mode especially. Further more, full pressure and efficiency respectively enhanced by3.6% and 1.4% averagely during the full flow range. Under the design flow, the full pressure is 1912 Pa and the efficiency η =77.3%, and the initial values are only 1844 Pa and 76.8%, and the values respectively increased by 3.7% and 0.5%. The results reach to optimization purpose as remarkable effect.

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sim opt

(a) total pressure and flow (b) efficiency and flow

Figure 6. Performance curves before and after optimization

IV. CONCLUSIONS

(1) Numerical simulation can accurately predict the performance of centrifugal fan and the details of the flow field in the fan. And it also has the important guiding significance in researching interior losses of centrifugal fans, optimizing impeller and modifying fans.

(2) Impeller optimization weakened the vortex intensity of secondary flow in volute, and reduced the energy loss caused by the secondary flow vortex and volute tongue of fan. Through the optimization of blades number Z and impeller outlet setting angle 2 yβ ∞ , the energy loss in fan’s impeller channel caused by wake current-jet and positive incidence angle was reduced.

(3) Impeller structure optimization plan was derived by using the least squares method in the rectangular territory. After the optimization, the averages of full pressure and efficiency enhanced respectively by 3.6% and 1.4% through the full flow, while, the growth rates of them are 3.7% and 0.5% under the design operating mode.

REFERENCES

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