Investigation of flow through centrifugal pump impellers 5

CHAPTER RESULTS AND DISCUSSIONS In present work, six different types of centrifugal pump impellers are selected for the numerical simulation using the theoretical models developed in Chapter and Chapter 3. The first two which are named impellers M1 and M2 are radial flow pump impellers with five straight vanes that are also used by Kosyna and Kecke (2002) in their research work. The numerical results from these two pump impellers will be compared with their reported experimental and numerical data to validate our numerical model. The other four impellers are named as impellers M3-M6 accordingly. Their profiles are provided by a local pump company who is willing to support our research work. The results from these pump impellers will be validated by comparing with the experiment data. The comparison will mainly focused on the pump performance. The detailed specifications for model impellers M1-M6 are presented in Table 5.1. Figure 5.1 shows the built-up three-dimensional geometries for M1-M6. In this chapter, the results and discussions will be presented in three separate parts. First, a brief introduction will be given to the first two pump impellers M1 and M2, the numerical results from these two pump impellers will be presented and necessary analysis and discussion are also made. Both single-phase (water) and twophase (water/air) flow through centrifugal pump impellers will be considered and the numerical results will be compared with experimental and numerical data given by Kosyna and Kecke (2002) for validation. In the second part, a brief introduction will be given to another three pump impellers M3, M4 and M5, the numerical results from 58 Chapter Results and Discussions these pump impellers will be compared with the experimental data and the analysis and discussion will be made accordingly. In the last part, a newly designed impeller M6 will be introduced and numerically analysed by using the developed numerical scheme. 5.1 Model Impellers M1 and M2 5.1.1 Impeller Design Parameters Two identical but scaled radial flow pumps (M1: 2KB-19235-BS; M2: 2KB19235-MD) with a specific speed of approximately n s =27 are investigated. The impeller has five backswept blades, each of them being composed of two circular arcs, one with a smaller radius from inlet to nearly half of the chord and one with a larger radius up to the impeller outlet. The dimensions and specifications of the two scaled test impellers are shown in Table 5.1. 5.1.2 Computational Grid The built-up three-dimensional geometry of model impeller M1 is shown in Figure 5.1. The geometry of impeller M2 is similar to that of impeller M1 except in the scale. In the current study, only three-dimensional flow through impellers instead of the whole pump stage is considered. The unstructured triangular mesh between model impeller M1 is shown in Figure 5.2. The unstructured mesh is preferred here for the reason that the pump geometry is highly irregular and the applicability of structured grids is only limited to simple, regular geometries. The total elements for the entire computational domain are about 347980 for impeller M1 and 226606 for impeller M2. 59 Chapter Results and Discussions 5.1.3 Results and Discussions on Single-Phase Flow The numerical investigations are first applied to the single-phase (water) flow through model impellers M1 and M2. For each run, the above defined grid systems are adopted. The boundary conditions are also stipulated according to the description in Chapter 2. At the inlet boundary, several different flow rates are specified for the purpose of studying pump design and off-design flow patterns. In most of our run cases, the standard k − ε turbulence model is selected to the simulation because this model is used by most of the researchers in their numerical study of centrifugal pump impellers. However, as pointed out by Menter (1992), the standard k − ε model had accuracy problems in predicting adverse pressure gradient flows, which will usually occur under pump off-design conditions, and sometimes even under the design point. So to prevent the possible numerical errors brought by the standard k − ε model, several different turbulence models which are already proved to be more accurate in predicting adverse pressure gradient flows are included in our later runs and the numerical results from these turbulence models will be compared with each other to investigate the influence of different turbulence models on the pump performance. Figures 5.3 and 5.4 show the convergence histories for pump impeller running at design point. The convergence criterions for each run are set to be 10 −5 for RMS (root-mean-square) residuals of mass/momentum equations and 10 −4 for RMS residuals of k − ε equations. It is seen clearly that after about two hundreds of time steps for each run, the above criterions can be satisfied and the convergence is reached gradually. 60 Chapter Results and Discussions The predicted pressure rise coefficient ψ versus flow coefficient ϕ curve is compared with the experimental and numerical results presented by Kosyna and Kecke (2002) in Figure 5.5. The pressure rise coefficient ψ and flow coefficient ϕ are defined as ψ = (2 gH ) / u 22 ϕ = c m / u = Q /(πd bu ) (5.1) where H is pump head, u is the peripheral velocity at impeller outlet, Q is volumetric flow rate, d is the impeller outlet and b is the blade width. A good tendency is achieved over the entire flow range. Compared with the experiments, the present numerical results are a little higher. This is because flow losses in the pipes and volute are neglected in the current calculations. However, the present method still provides more accurate results than numerical ones of Kosyna and Kecke (2002). Figure 5.6 compares the computed pressure contour of the present study and that of Kosyna and Kecke (2002) at design operating point of impeller M2. The comparison shows good agreement. It can be seen that the pressure increases gradually along the streamwise direction. Normally, the pressure is higher on the pressure surface than on the suction surface. Especially on the pressure side of the blade, the isobars are not perpendicular to the impeller surface. This may be one possible reason for flow separation around this area. In addition, a low-pressure region is found near the inlet side of the blade suction surface. It may be deduced that cavitation will possibly occur around this region. Figure 5.7 compares the pressure distribution along the impeller blade numerically and experimentally for model impeller M2. The filled marks show 61 Chapter Results and Discussions measured data by Kosyna and Kecke (2002). One can observe that the conformity of the computed and measured pressure distribution is very good on the blade suction side. Even the pressure distribution discontinuity at the point where the two circular arcs intersect can be clearly seen. However, the computed pressure distribution on the blade pressure side is a little higher than the experimental data. To study the flow field in the pump impeller, three vane-to-vane planes are cut along the blade height as shown in Figure 5.8. These three planes are located at mm from the hub, mid-height of the blade and mm from the shroud respectively. Figure 5.9 and 5.10 show the relative velocity distributions in these three planes at the design flow rate for impellers M1 and M2. It is found that relative velocity on the suction side of inlet is higher than that on the pressure side of inlet at the design flow rate. However, with increasing radius, the relative velocity on the suction side is decreased while on the pressure side it is increased. This finding agrees well with the experimental results of Yang et. al (2002). It is also found that the flow in the midplane of the passage near the design point is quite smooth and follows the curvature of the blade with departure from blade curvature at inner radii close to the hub and a less regular flow close to the shroud. This phenomenon was also reported by Liu et al. (1994). Figure 5.11 shows the relative velocity distributions in the planes of 1mm from the hub, mid-plane and 1mm from the shroud at the off-design flow rates of 0.5 Qd and 0.25 Qd for impeller M2. It is found that the reduction of flow rate decreases the velocity vector and increases the flow angle (the angle between radius and relative velocity vector), and the flow tends to decelerate towards the suction side of the passage and to accelerate towards the pressure side. Figure 5.11 also shows the 62 Chapter Results and Discussions tendency for the velocity vectors to change direction and to form vortices at small radii and close to the shroud as the flow rate decreases. If the flow rate continues to drop to a very low level such as 0.25 Qd , the reversal flow will occur even in the mid-plane of the blade height. The reversal flow at off-design point is caused by the re-circulation near shroud side of inlet section and secondary flow from hub to shroud. But it may be also for the reason that the number of blades is not sufficient to constrain the flow in the impeller at low flow rate. The existence of the vortices in the passages at small flow rates will increase the loss of flow and thus reduce the efficiency of the centrifugal pump. Figure 5.12 shows the angle-resolved velocity distribution on the mid-plane of the impeller M2 passage at inlet and outlet. The relative angular coordinate β on the impeller was measured from suction surface (SS) to pressure surface (PS) with its origin at the center of the blade thickness. The velocity value V is normalized by the impeller tip velocity u2 . It can be seen that the velocity component increases from suction to pressure surface at the discharge of the impeller and it decreases from suction to pressure surface slightly at the inlet. As the flow rate decreases, the velocity component at the inlet and outlet will also be reduced. In addition, the gradient of velocity between blade surfaces at the discharge will be increased with decreasing flow rate, leading to flow reversal near the suction surface at very low flow rate. The pressure distribution in the mid-plane of the blade height at the flow rates of Q d and 0.25Q d for impeller M2 are compared in Figure 5.13. In both cases, the pressure lines are seen to be inclined in the circumferential direction. The angle of this inclination tends to be lower along the streamwise direction and the pressure lines are 63 Chapter Results and Discussions almost parallel to the circumference near the impeller outlet. However, at the low flow rate as shown in Fig. 5.13(b), the equipressure lines are deformed in the blade suction side. In this region, the lines lie nearly in the circumferential direction and there is no increase in the pressure along that direction. Another turbulence models named RNG k − ε model, the Wilcox k − ω model and the shear stress transport (SST) model are then added and a similar analysis procedure repeated by using these new turbulence models. The computational results show no apparent difference in the pump performance and velocity profile. Hence, the comparison between these turbulence models will focus on the pressure distributions along pressure and suction surfaces of the blade. Figure 5.14 shows comparison of pressure distribution along the blade with these turbulence models at the design flow rate for impeller M2. The pressure profiles for the standard k − ε model and RNG k − ε model are found almost the same. The results from the Wilcox k − ω model and the shear stress transport (SST) model are also quite close to that from the standard k − ε model except at outlet sections where it is always believed that the adverse pressure gradient will probably occur. However, since the difference is not obvious, it is hard to conclude whether the Wilcox k − ω model and the SST model are superior to k − ε model in predicting adverse pressure gradient flows in the centrifugal pump impeller. The reason for the lack of difference among the various turbulence models may be due to use the relatively coarse mesh near the wall in the present model. As discussed by Wilcox (1988), the boundary-layer program can use Eq. (2-17) for all points up to y + = 2.5 rather than attempting to solve the differential equation for ω directly. This procedure is very accurate, provided the mesh point closest to the surface lies below y + = and that at least 64 Chapter Results and Discussions mesh points lie between y + = and y + = 2.5 . However, this condition cannot be guaranteed in most of engineering applications. Since unstructured mesh is used for the reason that the pump geometry is highly irregular, this condition becomes extremely difficult to be satified in the present model. Therefore, the advantage of k − ω model cannot be fully revealed and thus the difference among the various turbulence models is not obvious. Further research work is required to draw a clearer conclusion on the influence of various turbulence models. 5.1.4 Results and Discussions on Two-Phase Flow For calculating the two-phase flow through the centrifugal pump impellers, the numerical model with the implemented Eulerian multiphase flow model is applied. The governing equations for both liquid phase and gas phase are given in Chapter 3. The interphase drag force is calculated by using the Schiller Naumann drag model for solid spherical particles. Thereby, the bubble diameter is assumed to be constant in the flow field. In addition, the turbulence dissipation force is also considered in the current two-phase fluid simulation, and the other forces such as lift force and pressure force are considered to be negligible. The calculations are done in a relative frame of reference, i.e., the entire flow field rotates with rotational speed Ω . The turbulent flow is approximated by using the standard k − ε turbulence model for the continuous liquid phase and the algebraic turbulence model for the dispersed gas phase. Only model impeller M2 is selected to two-phase flow simulation. This is because model impellers M1 and M2 are geometrically similar; therefore any conclusion drawn on impeller M2 will be also applicable to impeller M1. For each run, the grid system is built the same as what we used for calculating the single-phase 65 Chapter Results and Discussions flow and the pump rotational speeds are also set at 600 rpm. The boundary conditions are set up as discribed in Chapter 3. At the inlet boundary, the parameters such as inlet flow rate, air/water volume fractions and the diameter of bubble particle are input before the run starts. Figure 5.15 makes comparison of the pump head drops at the operation point ϕ =0.088 due to the increase of gas fraction with the experimental and numerical results given by Kosyna and Kecke (2002). The experimental curve was measured by keeping the total flow rate, the static pressure at the pump inlet, and the rotational speed of the impeller constant while the amount of gas was gradually increased. The relative pressure rise coefficient hr is defined as hr = ψ ψ0 (5.2) where ψ is the pressure rise coefficient at the zero gas fraction. Despite some of the simplifications made in the two-phase model, the present study successfully shows the similar trend in the pump head drop with the experimental and numerical results given by Kosyna and Kecke (2002). In the low gas fraction region, the present numerical results provide even better prediction than numerical ones from Kosyna and Kecke (2002) and match with the experimental results very well. The present study also indicates three states of pump performance, that is, when the gas fraction is increased from the state without gas loading, the pump decreases its head continuously in state 1. However, at a certain gas fraction the pump shows an abrupt change (state 2). In state 3, it depends on the operating point whether the pump is still able to operate or not. The discrepancy between numerical simulation and experiment in higher gas fraction may be explained by the simplications made for 66 Chapter Results and Discussions the simulation, such as calculating with a single bubble diameter for all gas contents and negligence of some interfacial forces like lift force. It may suggest that all these factors will need to be considered in the future study to obtain more accurate numerical results. Figure 5.16 compares the pump characteristic curves at two gas fractions with those presented by Kosyna and Kecke (2002). The pressure rise coefficient ψ and flow coefficient ϕ are defined in relation (5.1). It is found that the pump performance curves predicted by the two-phase model agree well with the results given by Kosyna and Kecke (2002). As the gas fraction increases, the magnitude of pressure rise coefficient ψ will be reduced and the characteristic curve appears to drop more abruptly. Therefore, controlling the gas volume fraction is very important to ensure the pump operating normally. Figure 5.17 compares the pressure distribution along the impeller blade surface at flow coefficient ϕ = 0.088 and 5% gas volume fraction experimentally and numerically. The solid line shows the calculated data from the present study and the filled marks show the experimental data given by Kosyna and Kecke (2002). It is found that the predicted pressure distribution by using two-phase model is less accurate than that by using single-phase model. This is because the two-phase model is more complicated and thus more assumption and simplication have been made so far in the two-phase model. However, the present study successfully predicts the trend of pressure distribution along the impeller blade surface. Figures 5.18a, 5.18b and 5.18c compare the gas volume fraction distribution near the planes of mid-plane, mm from the shroud and mm from the hub at 5% and 10% inlet gas fraction respectively. Figures 5.19 and 5.20 show quantitative 67 Chapter Results and Discussions Q=Qd Q=0.25Qd Q=1.25Qd 0.8 ψ 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 0.8 (r-r1)/(r2-r1) (a) n = 2900 rpm 1.4 Q=Qd Q=0.5Qd Q=1.25Qd 1.2 ψ 0.8 0.6 0.4 0.2 0.4 0.6 (r-r1)/(r2-r1) (b) n = 1450 rpm Figure 5.61 Comparison of pressure distribution along the blade for impeller M3 150 Chapter Results and Discussions Q=Qd Q=0.25Qd Q=1.5Qd 0.8 0.6 ψ 0.4 0.2 -0.2 0.2 0.4 0.6 0.8 0.8 (r-r1)/(r2-r1) (a) n = 2900 rpm 1.2 Q=Qd Q=0.25Qd Q=1.25Qd 0.8 ψ 0.6 0.4 0.2 0 0.2 0.4 0.6 (r-r1)/(r2-r1) (b) n = 1450 rpm Figure 5.62 Comparison of pressure distribution along the blade for impeller M4 151 Chapter Results and Discussions 1.2 Q=Qd Q=0.25Qd Q=2.0Qd 0.8 ψ 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 0.8 (r-r1)/(r2-r1) (a) n = 2900 rpm 1.4 1.2 Q=Qd Q=0.25Qd Q=1.5Qd ψ 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 (r-r1)/(r2-r1) (b) n = 1450 rpm Figure 5.63 Comparison of pressure distribution along the blade for impeller M5 152 Chapter Results and Discussions Figure 5.64 Computational mesh system for model impeller M6 153 Chapter Results and Discussions (a) RMS residuals for mass/momentum equations (b) RMS residuals for k − ε equations Figure 5.65 Convergence history for impeller M6 at design point (n = 1450 rpm) 154 Chapter Results and Discussions 300 250 H (m) 200 150 Computational data Design point Poly. (Computational data) 100 50 0 50 100 150 200 250 300 Q (m^3/hr) (a) n = 2900 rpm 80 70 60 H (m) 50 40 30 Computational data Design point Poly. (Computational data) 20 10 0 50 100 150 200 Q (m^3/hr) (b) n = 1450 rpm Figure 5.66 Computational head-flow curve for model impeller M6 155 Chapter Results and Discussions 300 250 H (m) 200 150 Computational data at n = 2900 rpm 100 Converted data from n = 1450 rpm 50 0 50 100 150 200 250 300 350 400 Q (m^3/hr) (a) n = 2900 rpm 80 70 60 H (m) 50 40 30 Computational data at n = 1450 rpm Converted data from n = 2900 rpm 20 10 0 50 100 150 200 Q (m^3/hr) (b) n = 1450 rpm Figure 5.67 Comparison of computational and converted data for model impeller M6 156 Chapter Results and Discussions (a) n = 2900 rpm (b) n = 1450 rpm Figure 5.68 Velocity vectors on vane-to-vane mid-height plane for model impeller M6 at design point 157 Chapter Results and Discussions (a) Q = 1.25Q d (c) Q = 0.5Q d (b) Q = Q d (d) Q = 0.25Q d Figure 5.69 Velocity vector on vane-to-vane plane for model impeller M6 at different volume flow rates (n = 2900 rpm) 158 Chapter Results and Discussions (a) Q = 1.25Q d (c) Q = 0.5Q d (b) Q = 0.75Q d (d) Q = 0.25Q d Figure 5.70 Velocity vector on vane-to-vane plane for model impeller M6 at different volume flow rates (n = 1450 rpm) 159 Chapter Results and Discussions 0.4 V/u2 0.3 0.2 Q = Qd 0.1 Q = 0.5Qd Q = 0.25Qd 0 12 24 36 48 60 β , deg SS 72 PS (a) outlet of the blade 0.5 Q = Qd 0.4 Q = 0.5Qd V/u2 0.3 Q = 0.25Qd 0.2 0.1 -0.1 -0.2 12 24 36 48 60 β , deg SS 72 PS (b) mid-chord of the blade 0.4 V/u2 0.3 0.2 Q = Qd 0.1 Q = 0.5Qd Q = 0.25Qd 0 12 SS 24 36 48 β , deg 60 72 PS (c) inlet of the blade Figure 5.71 Velocity distribution on the mid-plane of the impeller M6 160 Chapter Results and Discussions (a) Q = Q d (b) Q = 1.25Q d 161 Chapter Results and Discussions (c) Q = 0.5Q d (d) Q = 0.25Q d Figure 5.72 Pressure contours on vane-to-vane plane at various flow rates for model impeller M6 (n = 2900rpm) 162 Chapter Results and Discussions (a) Q = Q d (b) Q = 1.25Q d 163 Chapter Results and Discussions (c) Q = 0.5Q d (d) Q = 0.25Q d Figure 5.73 Pressure contours on vane-to-vane plane at various flow rates for model impeller M6 (n=1450rpm) 164 Chapter Results and Discussions Q=Qd Q=0.5Qd Q=1.25Qd 0.8 0.6 ψ 0.4 0.2 -0.2 0.2 0.4 0.6 0.8 0.8 (r-r1)/(r2-r1) (a) n = 2900 rpm 1.2 Q=Qd Q=0.5Qd Q=1.25Qd 0.8 ψ 0.6 0.4 0.2 0 0.2 0.4 0.6 (r-r1)/(r2-r1) (b) n = 1450 rpm Figure 5.74 Comparison of pressure distribution along the blade for impeller M6 165 [...]... Calculated Pump Head (m) CPU time (hours) 122616 74479.1 57 4318 80.21 6 34 759 8 74427.1 57 0938 79.34 17 51 4324 74416 .5 568764 78.67 33 84 Chapter 5 Results and Discussions Table 5. 4 Comparison of efficiency value for model impellers M3 Model Impeller M4 M5 Rotational speed (rpm) 2900 1 450 2900 1 450 2900 1 450 Design flow (m 3 /h) 27 14 270 180 70 45 Design efficiency (%) 55 48 76 81 74 .5 65 Calculated... distribution across the impellers by adjusting pump rotational speed Figures 5. 61 -5. 63 compare the pressure distribution along the impeller blade at the design flow rate Qd , low flow rates of (0. 25- 0 .5) Qd and high flow rates of (1. 252 .0) Qd for pump impellers M3, M4 and M5 running at the rotational speeds of 2900 rpm and 1 450 rpm The pressure rise coefficient ψ is defined as 2 ψ = (2 gp) / u2 (5. 3) where p... efficiency (%) 58 .68 52 .5 79. 25 84.86 76 .5 67.4 Expeimental efficiency (%) 55 .22 48.88 76.8 81. 15 73 .5 64.6 Numerical deviation (%) 6.69 9.3 75 4.28 4.77 2.68 3.69 85 Chapter 5 Results and Discussions (a) impeller M1 or M2 (b) impeller M3 (c) impeller M4 86 Chapter 5 Results and Discussions (d) impeller M5 (e) impeller M6 Figure 5. 1 Three-dimensional geometries of model impellers M1-M6 87 Chapter 5 Results... Discussions rates are above 25% of design flow rate, the flow pattern looks similar to each other But if flow rate continues to drop below 25% of design flow rate, the flow pattern will be changed A strong recirculation will occur near pressure surface as shown in Figure 5. 45- 5.48 (c) and (d) Figures 5. 49 and 5. 50 also show this trend At the inlet section of the impeller channel, where the flow has just been... 2900 1 450 2900 1 450 2900 1 450 2900 1 450 (rpm) Design flow 400 55 .5 27 14 270 180 70 45 220 140 (m 3 /h) Design head 3.27 1 96 24 148 36 66 14 220 24 (m) Specific speed 27 27 30 30 68 81 64 82 46 30 (n s ) Number of vane 5 5 4 6 6 5 (z) Vane Straight straight straight twisted twisted twisted type Outer width 46 23 6 21 14 15. 1 (mm) Inner diameter 260 130 46 106 70 1 15. 6 (mm) Outer diameter 55 6 278 269... M4 and M5 Figures 5. 45- 5.48 show velocity vectors for these cases at different rotational speeds Figures 5. 49 and 5. 50 show the quantitative analyses of the velocity distribution on the mid-height of the impellers M4 and M5 at rotational speed of 2900 rpm The relative velocity value V in Figures 5. 48 and 5. 49 is normalized by the impeller tip velocity u 2 It is found that when flow 74 Chapter 5 Results... M3, the comparison of pressure profiles in Figure 5. 55 and 5. 56 show no apparent difference at flow rate of Q d and 0.25Q d This is understandable since the velocity pattern for model impeller M3 has no notable change at different flow rate as we discussed before However, for model impellers M4 and M5, the pressure profile will change as the flow rate decrease As shown in 76 Chapter 5 Results and Discussions... rates and makes the flow field inside the impellers more complex The comparisons of velocity vectors along the meridional surface near the central plane at two rotational speeds for model impellers M4 and M5 are shown in Figures 5. 51 -5. 54 A secondary flow between hub and shroud is observed near inlet region at pump design flow rate And this secondary flow becomes more severe at low flow rate and extends... design point is n = 2900 rpm, Q = 70 m 3 /hr; n = 1 450 rpm, Q = 45 m 3 /hr The detailed specifications of model impellers M3, M4 and M5 are also presented in Table 5. 1 5. 2.2 Computational Grid The three-dimensional geometries for model impellers M3, M4 and M5 have been shown in Figure 5. 1 As a preliminary study, only three-dimensional water flow through pump impellers is considered at the present time The... side of inlet This may be caused by the rapid change of flow direction at the inlet section of the impeller channel The relative velocity is also found to decrease along the impeller passage And the velocity value at design flow rate will be higher than that at low flow rate All these findings suggest that the pump efficiency at design flow rate will be better than that at low flow rate Figures 5. 55- 5.60 . Chapter 5 Results and Discussions 75 rates are above 25% of design flow rate, the flow pattern looks similar to each other. But if flow rate continues to drop below 25% of design flow rate,. outlet. For model impeller M3, the comparison of pressure profiles in Figure 5. 55 and 5. 56 show no apparent difference at flow rate of Q d and 0.25Q d . This is understandable since the velocity. shown in Figures 5. 51 -5. 54. A secondary flow between hub and shroud is observed near inlet region at pump design flow rate. And this secondary flow becomes more severe at low flow rate and extends