# Numerical Simulation of Flow Field for a whole centrifugal fan and analysis of the Effects of Blade.pdf

VOLUME 11, NUMBER 2 HVAC accepted August 18, 2004Numerical simulation of the flow field was carried out for a whole centrifugal fan to considerthe interaction of three parts—inlet, impeller, and scroll. A modern optimum design method fora centrifugal fan has been presented using a computational fluid dynamics (CFD) technique toreplace the conventional method. A sample fan based on the optimum design was manufacturedand tested. The numerical prediction agrees well with the test data. The excellent performanceof the sample fan has proved the validity of the method adopted. Moreover, the effects of theblade inlet angle and the gap between impeller and inlet on the fan performance are quantita-tively analyzed. Particularly the energy loss in every passage, including the gap loss and theleakage flow rate in the gap, are discussed in detail in the paper. It is found that the blade inletangle and the impeller gap play an important role for fan performance. INTRODUCTIONThe aerodynamic design of a centrifugal fan has long followed the conventional method,which is based on the assumption of one- or two-dimensional ideal flow and some empiricalcoefficients. The three main parts, i.e., impeller, scroll type of housing (called scroll in the fol-lowing), and inlet ring (called inlet in the following), are designed, respectively, and their inter-actions are neglected (Eck 1973). Furthermore, the fan performance cannot be predicted at thedesign stage. In fact, there is a three-dimensional, complicated, and highly turbulent flow in acentrifugal fan, and the effect of interaction between the main parts on fan performance is seri-ous, which cannot be neglected. Thus, the existing simplified design method is insufficient todescribe the real flow situation, and the performance of a fan designed based on this method iscommonly not very good. Sometimes, in order to obtain an excellent performance, it takes a lotof time and cost to make several cycles of design-test-redesign. Therefore, the existing conven-tional design method needs to be improved.Computational fluid dynamics (CFD) has made great progress in calculating thethree-dimensional flow in centrifugal pumps and fans. Zhang et al. (1996) computed thethree-dimensional viscous flow in a blade passage of a backswept centrifugal impeller at thedesign point with the standard k-ε model. The comparison of computed and measured valuesshowed good agreement. The computation also successfully predicts the jet-wake structure,though slightly different in location and size from the measured ones. In recent years the k-εmodel has been more widely used in numerical simulation of flow fields in turbomachineryZhao Yu and Wenqi He are research assistants, Song Li is a lecturer, Weixiong Wang is a graduate student, and Dong-tao Huang and Zhichi Zhu are professors at the Fluid Acoustics Lab, Department of Engineering Mechanics, TsinghuaUniversity, Beijing, China.264 HVAC the latter is alsocalled impeller diameter. Φ is the flow rate coefficient, and ε and β1are the accelerationcoefficient and flow angle at the blade entry, respectively. In β1 = β1j– α, α is called attackangle. In our design, d2 = 0.8 m and Φ = 0.15 are given before the design, and ε =d1 / 4b1=0.68 and α = 0 (β1 = β1j) are selected optimally. Therfore, d1 is decreased monotonously withthe increase of β1j. In our design, both the diameters of the blade entry and the impeller entryare the same. Since d1 minus two times the radial gap between inlet and impeller is the exitdiameter of the inlet, the latter is also decreased monotonously with the increase of β1j. Thenthe flow velocity in the inlet and the inlet length are increased. Therefore, the inlet loss issharply increased with increase of β1j, as shown in Table 5.5. The effect of β1j on the fan performance is remarkable. It is seen from Table 5 that the benefitof the total pressure and its efficiency can be obtained up to 6% and 5%, respectively, at theoptimum β1j. Therefore, β1j is an important design parameter for improvement of fanperformance.Table 6. Energy Losses in Different Passages and Fan Performance at Different β1j(δ = 0)β1j (deg)Impeller Loss (1)(%)Impeller Loss (2)(%)Impeller Loss (3)(%)Total Impeller Loss(%)Scroll Loss(%)Inlet Loss (%)Total Efficiency(%)Total Pressure (Pa)24 1.9 7.5 1.0 10.4 7.3 0.5 81.8 121325 1.9 7.0 1.1 10.0 7.3 0.6 82.1 122226 1.9 6.3 0.9 9.1 7.1 0.7 83.1 123927 1.9 4.9 0.7 7.5 6.0 0.9 85.6 128329 2.1 5.0 0.5 7.6 6.7 1.2 84.5 126731 2.4 5.0 0.6 8.0 6.9 1.6 83.5 125233 2.8 5.0 0.6 8.4 7.2 2.1 82.3 123235 2.9 4.9 0.6 8.4 7.5 3.0 81.1 121836 3.2 5.0 0.9 9.1 7.8 3.4 79.7 1193Table 7. Total Pressure (Absolute Value) in Different Passages, Leakage Flow Rate and Shaft Power at Different δ (Q =11000 m3/h, β1j = 27)δ (mm) P1(Pa) P2(Pa) P3(Pa) P4(Pa) P5(Pa) P6(Pa) q (m3/h) q /Q (%) W (KW)0 -531 -544 842 752 170 -524 0 0 4.582 -524 -533 805 719 63 -121 307 2.79 4.502.5 -514 -524 812 721 105 -54 396 3.60 4.50d13d23-----Φtanβ1------------- ε× ,=VOLUME 11, NUMBER 2, APRIL 2005 2796. The total pressure and its efficiency at β1j = 27° is about 5% better than that at β1j = 35°.(Note β1 = β1jin the present case) so that the present method to optimally select β1j by use ofCFD technique is much better than Eck’s theory about the blade inlet angle. EFFECTS OF THE GAP AT IMPELLER ENTRY As described in the introduction above, the gap size should be as small as possible. For thedesigned fan, whose impeller diameter is 800 mm, considering its commercial application andmarket competition, the possible small size of δ is 2.5 or 2.0 mm. Therefore, in this section theeffect of δ is discussed using numerical simulation of the flow field for a whole fan only forthree cases of δ = 0, 2.0 mm, and 2.5 mm, and the mesh generation is based on the geometricmodel II.Effect of δ on the Flow Pattern in the PassagesFigure 9 shows two-dimensional streamlines in the meridian plane of the fan passage,especially near the front disc of the impeller and corresponding scroll passages, at δ = 0, 2.0mm, and 2.5 mm, respectively. Obviously the flow in both the impeller and the scroll isremarkably different if there is an impeller gap or not. Thus, it will affect the total pressure lossin both the impeller and the scroll. Effects of δ on the Energy Loss and Fan PerformanceTable 7 shows the original data obtained from the numerical results about the total pressure indifferent passages, leakage flow rate, and shaft power at different δ. Table 8 denotes the totalpressure rise (if plus sign) or loss (if minus sign) and energy loss in different passages and fanperformance at different δ. Following are some comments on Table 8: 1. The effect of on the fan performance is remarkable. The fan total efficiency is decreased by1.2% and 1.8% for δ = 2.0 mm and δ = 2.5 mm, respectively, mainly because of the gapenergy loss. Meanwhile, the total pressure of the fan is decreased by 40 Pa (3.1%) and 48 Pa(3.7%) for δ = 2.0 mm and δ = 2.5 mm, respectively. This is because the total efficiency isdecreased and the flow rate in the impeller is increased a little with the increase of the gapwidth when the flow rate of the fan remains the same as Q = 11000 m3/h. 2. As seen from Figure 9, a small fraction of the total volume discharged from the impeller intothe scroll will pass the channel between the scroll and the front disk and reenter the impellerthrough the gap to form a secondary flow. It is called the leakage flow rate, which could beestimated by Eck (1973) using a simplified formula as (4)Substituting the parameters of the designed fan for the formula (Equation 4), q is 425.8 m3/hand 532.2 m3/h for δ = 2.0 mm and δ = 2.5 mm, respectively. But according to the numericalsimulation results from Table 7, q is 300.9 m3/h and 396.2 m3/h for δ = 2.0 mm and δ =2.5 mm, respectively. Eck’s formula overestimates the leakage flow rate by about 42% and35% for δ = 2.0 mm and δ = 2.5 mm, respectively.3. The gap energy loss can be determined using the formula in Table 5, once the total pressurerise through the impeller and the leakage flow rate are obtained by CFD. They are 1.75% and2.12% for δ = 2.0 mm and δ = 2.5 mm, respectively. The distribution of gap loss in its twopassages for different δ is shown in Table 9. It is seen that the main loss occurs in the secondflow in the passage between the scroll and the front disk where a big vortex ring appears, asshown in the Figure 9b. More than 80% of the impeller total pressure exhausts in that region.Only less than 20% of the impeller total pressure exhausts in the gap flow itself, which wasnot expected before. q 3600πδd14P03ρ⁄ .=280 HVAC (b) δ = 2.5 mm;(c) near the gap, δ = 2.0 mm; and (d) near the gap, δ = 2.5 mm.(a) (b)(c) (d)VOLUME 11, NUMBER 2, APRIL 2005 2814. The existence of the gap can be helpful to improve the flow in the impeller and the inlet. Asseen in Table 8, the impeller loss and the inlet loss are decreased with the increase of the gapwidth. It can be explained that the reentering leakage flow could improve the main streamnear the impeller entry and the exit of the inlet. In fact, the flow channel transferred from theaxial to the centrifugal direction is designed as highly divergent for the sample fan, since thecoefficient of acceleration at the impeller entry is only 0.68. Meanwhile, the centrifugal forceat the impeller entry is smaller so that the retarded air in the main stream could accumulatenear the front disk at the impeller entry and the exit of the inlet, and, thus, the thickness of theboundary layer there will be increased even to form separation flow. The reentering leakageflow through the gap with high speed can supply additional energy of P6– P2, such as 412 Paand 470 Pa for δ = 2.0 mm and δ = 2.5mm, respectively, to the retarded air and carry it away,as seen in Figures 9c and Figure 9d; thus, the main flow in the impeller and the inlet can beimproved. It is very similar to the blowing technique used for a slotted wing, i.e., boundarylayer control technique, in aeronautical engineering to improve the separate flow at the rearedge of the wing (Schlichting 1968). Therefore, the total impeller loss and the inlet loss forδ =2.0 mm are 0.15% and 0.25% less than that without a gap and for δ = 2.5 mm are 0.19%and 0.32%, respectively.5. Someone considers the magnitude of gap effect on the fan efficiency just being the leakageflow rate percent. It means if the latter is 3%, the fan efficiency should decrease by 3%. Butnow from the numerical simulation for the sample fan, the leakage flow rate percent are2.79% (δ = 2.0 mm) and 3.60% (δ = 2.5 mm), but the reductions of the efficiency are only1.18% and 1.78%, respectively, mainly because the work done by the impeller for theleakage flow rate is much less than that for the main flow rate. For example, the total pressurerise for the former is 926 Pa (δ = 2.0 mm) and 966 Pa (δ = 2.5 mm), but the total pressure risefor the latter is 1338 Pa (δ = 2.0 mm) and 1322 Pa (δ = 2.5 mm), respectively. Another reasonis the energy loss of the impeller and inlet are decreased, owing to the gap, as indicatedabove. CONCLUSIONS1. The numerical computation of flow field for a whole centrifugal fan, including all threeparts—impeller, scroll, and inlet—and considering the impeller gap between the impeller andinlet is completed in order to consider the interaction of these three parts and the effect of theimpeller gap. Thus, the recent numerical simulation of flow field for a centrifugal fan is fur-ther improved. The computational results are validated by the data from the performanceTable 8. Total Pressure Rise and Energy Losses in Different Passages and Fan Performance at Different δ (Q = 11000 m3/h, β1j =27)δ(mm)Total Pressure Rise (Pa) Energy Loss or Fan Total Efficiency (%)Inlet Impeller Scroll Gap Fan Inlet Impeller Scroll Gap Fan0 -13 1386 -90 0 1283 0.86 7.54 6.01 0 85.592 -9 1338 -86 -926 1243 0.61 7.39 5.84 1.75 84.412.5 -10 1336 -91 -866 1235 0.67 7.22 6.18 2.12 83.81Table 9. Distribution of Gap Energy Loss in Two Passages (%)δ (mm) 5-6 (Gap) 3-5 (Scroll) 3-6 (Total)2.0 0.35 1.40 1.752.5 0.39 1.73 2.12282 HVAC&R RESEARCHexperiment of the sample fan described in this paper and other centrifugal fans. The errors ofthe numerical prediction for total pressure and total efficiency of the fan at the design opera-tion are within 3% and 2%, respectively. 2. A modern optimum design method for a centrifugal fan is presented in this paper, whichcombined a conventional aerodynamic design method with the numerical computation offlow field for a whole centrifugal fan and the optimum selection of some main design param-eters, such as the blade inlet angle, the ratio of entry and exit axial breadths of the impeller,and the coefficient of acceleration at the impeller entry, etc. This new method not only con-siders the three-dimensional complicated flow in a centrifugal fan but also considers theinteractions of its three main parts and the effect of the impeller gap on the flow. Further-more, it can predict the fan performance near design operation. In this paper, excellent per-formance of a sample fan designed by this method is achieved. Not only the performancecompletely satisfies the design request, but also the fan total pressure efficiency reaches85.3%, which is about 2% to 3% higher than that of other similar fans with high efficiencyavailable in the Chinese market.3. The effect of β1j on the fan performance is remarkable. Under the conditions described in thepaper, the benefit of the total pressure and its efficiency can be obtained up to 6% and 5%,respectively, at the optimum β1j, being 27°, if only β1jis changed ranging from 24° to 36°.Therefore, β1jis also an important design parameter for improvement of fan performance. 4. The total pressure and its efficiency at β1j= 27° is about 5% higher than that at β1j= 35°,which is the blade inlet angle suggested by Eck (Note: β1= β1jin the present case), so thepresented method to optimally select β1jby use of CFD technique is much better than Eck’stheory about the blade inlet angle.5. According to the numerical simulation results, the percentage of the leakage flow rate in theimpeller gap is 2.79% and 3.6% for δ = 2.0 mm and δ = 2.5 mm, respectively, which is about42% and 35% less than that from Eck’s formula for δ = 2.0 mm and δ = 2.5 mm, respectively.6. The effect of on the fan performance is also remarkable. The fan total efficiency is decreased1.2% and 1.8%, and the total pressure of the fan is decreased 40 Pa (3.1%) and 48 Pa (3.7%)for δ = 2.0 mm and δ = 2.5 mm, respectively. It is noted that the reduction of the fan totalefficiency owing to the gap is much less than the percent of leakage flow rate. The reasonsare explained in detail in the comments above. 7. It is very interesting that the total pressure and the energy loss in every passage, including thegap passage, for a centrifugal fan with excellent performance are given out and analyzed indetail, which is very useful for fan desi