Investigation of flow through centrifugal pump impellers 5

5.1 Model Impellers M1 and M2 5.1.1 Impeller Design Parameters Two identical but scaled radial flow pumps M1: 19235-BS; M2: impeller has five backswept blades, each of them being compo

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 2 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 two-phase (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

scheme

5.1 Model Impellers M1 and M2

5.1.1 Impeller Design Parameters

Two identical but scaled radial flow pumps (M1: 19235-BS; M2:

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

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

this model is used by most of the researchers in their numerical study of centrifugal

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

ε

−

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

steps for each run, the above criterions can be satisfied and the convergence is reached gradually

are defined as

2 2/)2

=

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

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 1 mm from the hub, mid-height of the blade and 1 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 mid-plane 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

d

Q and 0.25 Q for impeller M2 It is found that the reduction of flow rate decreases d

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

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

impeller was measured from suction surface (SS) to pressure surface (PS) with its

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

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

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

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

ε

−

believed that the adverse pressure gradient will probably occur However, since the

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

extremely difficult to be satified in the present model Therefore, the advantage of

ω

−

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

liquid phase and the algebraic turbulence model for the dispersed gas phase

Only model impeller M2 is selected to do 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

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

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

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

numerical results

Figure 5.16 compares the pump characteristic curves at two gas fractions with

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

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

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, 1 mm from the shroud and 1 mm from the hub at 5%

analysis of gas fraction distribution at the inlet and discharge of the impeller It can be seen that, from inlet to outlet, shroud to hub of impeller, the gas volume fraction distribution appears to be nonuniform Normally, the gas volume fraction on the pressure side of the blade at the discharge will be higher than on the other regions It indicates that the accumulation of gas near pressure surface can be qualitatively reproduced by the present simulation, which matches well with the photography taken

by Kosyna and Kecke (2002) using a high-speed camera Compared with gas volume fraction distribution among three different planes in Figure 5.20, it is found that the gas fraction in shroud surface is much higher than that in hub and mid-plane And the gas will be most likely to accumulate near inlet area of shroud surface This trend can

be seen more clearly when the gas fraction at inlet increases This is because the inlet recirculation will always occur on the leading edge of the shroud, and it will cause the gas concentration in this area It can also be found that as the gas fraction at inlet increases, the gas fraction in the impeller passage will also increase In some area near the shroud, the gas volume fraction is even near 100% when the gas fraction at inlet is set to be 10% So it is very important to make sure that the fraction of gas at inlet will not reach above 10% of the total volumetric flow rate when the pump is running Or the total breakdown of the flow may happen From the distribution of gas volume fraction, the regions that are easy to wear can always be conveniently found out and this can further guide the design of the impeller

The impact of gas fraction on the velocity distribution at the inlet and outlet of

impeller was measured from suction surface (SS) to pressure surface (PS) with its

accumulate at the inlet and outlet of the impeller as the volume fraction increases and thus diminish the areas there and increase the velocity value It is also found that the uneven distribution of gas fraction along circumferential direction at the discharge of the impeller makes the corresponding velocity distribution more complex and thus has

an adverse effect on the relative flow in the volute

Next, different flow rates are specified at impeller inlet to study the two-phase flow at off-design condition Figures 5.22a, 5.22b and 5.22c compare the gas volume fraction distribution near the planes of mid-plane, 1 mm from the shroud and 1 mm

Figures 5.23 and 5.24 show quantitative analysis of gas fraction distribution at the inlet and discharge of the impeller It is found that the gas fraction distribution through the impeller is non-uniform and the flow rate has a great influence on the distribution of gas volume fraction As the flow rate decreases, the accumulation of gas in the impeller passage will increase obviously In the area of the shroud, the gas volume fraction even reaches to 80-100% This means that the two-phase flow in the pump impeller will get worse at the part load flow Therefore, it is necessary to make sure the pump operates at design or near design condition, especially at the time that air may be entrained into the pump impellers

5.2 Model Impellers M3, M4 and M5

5.2.1 Impeller Design Parameters

Impellers M1 and M2 are selected from Kosyna and Kecke’s paper (2002) to validate the numerical results After carefully comparing with experimental and numerical data given by Kosyna and Kecke (2002), the numerical schemes used so far are fully validated and thus can be safely applied to the numerical simulation of our own model impellers M3, M4 and M5

Impellers M3, M4 and M5 have four straight vanes (M3) and six twisted vanes (M4 and M5) respectively For model impeller M3, the design point is n = 2900 rpm,

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

The unstructured triangular meshes are still used to do the simulation However, two grid systems are adopted this time for model impellers M3, M4 and M5 As shown in Figures 5.25-5.27, one kind of grid system has grid extension along the inlet and outlet, and the other one has not This is because the latter grid system

mesh independent check for model impeller M5 revealed that a coarse mesh is sufficient to accurately predict the pump’s important parameters such as pump head Table 5.3 presents the results for mesh independent check It is seen clearly that much CPU time can be saved and the numerical accuracy can also be guaranteed by using relatively coarse mesh

Throughout the surfaces of the blade, hub and casing, inflated (structured) volume mesh is created to avoid generating highly distorted tetrahedral elements at the surface In addition, for grid system without extension, relatively fine grids are adopted near inlet, outlet and wall surface whereas the grids in other regions are coarse This mesh distribution is helpful to capture velocity gradient along the wall, inlet and outlet of the impellers

5.2.3 Results and Discussions

Currently two design rotational speeds of 2900 rpm and 1450 rpm were used

in the computations for each impeller model At each rotational speed, several different flow rates are specified at inlet boundary to study pump design and off-

the simulation Therefore, most of computational results are based on

Figures 5.28-5.30 show the convergence histories for model impellers M3, M4

required for the computations of different impellers For straight vane impeller M3, it takes about 500 time steps to converge, whereas for twisted vane impellers M4 and M5, less time steps are needed for final convergence The convergence criterions for each run are set to be 1.0e-5 for RMS (root-mean-square) residuals of

clearly that after several hundreds of time steps for each run, the above criterions can

be satisfied and the convergence is reached gradually

Figures 5.31-5.33 make comparison of experimental and computational flow H-Q curve for model impellers M3, M4 and M5 It is found that a good agreement between numerical and experimental result is achieved over the entire flow range Compared with the experiments, the numerical result is a little higher This is because flow losses in the pipes and volute are neglected in the current calculations It

head-is also found that the deviation in low flow rate head-is a little bigger Thhead-is head-is because the flow field at low flow rate will be more complex and it will probably make numerical simulation less accurate

Figures 5.34-5.36 compare the computational and converted H-Q data for model impellers M3, M4 and M5 The solid line indicates computational data at a specified speed and the broken line is the converted data from other speed by using the similarity law The equations for speed law are:

2 1

2 1

n

n H

1

2 1 2

n

n Q

Q =

another rotational speed

predict pump head H and pump capacity Q at any rotational speed by using H and Q

value at a given rotational speed

Pp

P W

=

the experiment In addition, the maximum efficiency obtained from both curves also agrees well with the design value Table 5.4 makes comparison among these efficiency values and it is found that the numerical deviation between predicted and design value for model impellers M4 and M5 falls below 5% The deviation for impeller M3 is a little higher for the complex flow field inside the impeller but still not more than 10% Therefore, it can be concluded that the present efficiency prediction is relatively accurate The comparison also shows that the efficiencies of model impellers M4 and M5 are much higher than that of model impeller M3 It may suggest that efficiency of twisted blade pump will be higher than that of straight blade pump However, this conclusion may not be accurate because the vane numbers of

twisted vane impeller M5 is used Fig 5.40 shows geometry of this new impeller with six straight vanes The comparison of efficiency between impeller M5 and this new impeller is made in Fig 5.41 and it is found that the efficiency of the twisted blade pump is higher So it can be concluded that efficiency of twisted blade pump will be higher than that of straight blade pump

Figures 5.42-5.44 show the velocity vectors on vane-to-vane plane for model impellers M3, M4 and M5 at design point and two rotational speeds respectively It is found that a severe recirculation occurs in the impeller passage for model impeller M3, whereas for model impellers M4 and M5 the flow is much smoother The flow profile at two rotational speeds looks quite similar to each other except that the velocity vector at 1450 rpm will be smaller The existence of recirculation for impeller M3 means that the hydraulic loss in pump impeller M3 is higher and thus its efficiency is lower than that of model impellers M4 and M5 Our experimental data also prove this For model impellers M4 and M5, the maximum experimental efficiencies are around 76% and 74% at the rotational speed of 2900 rpm, whereas the maximum efficiency for model impeller M3 is only about 50% Therefore, some modifications to the profile of model impeller M3 may be required to improve the pump efficiency

Next, different flow rates were specified to study off-design conditions for twisted vane model impellers 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

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 turned radially from an axial direction, the relative velocity is found to be larger in the low pressure side When the flow rate decreases, the velocity value will be reduced but the flow pattern looks similar However, at the mid-chord and outlet section, the velocity near the suction side decreases considerably and the main flow is shifted to the pressure side at the low flow rate If the flow rate continues to drop, the reversal flow may occur near the suction side The reversal flow at off-design point may be 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 Similar observation of back flow was reported by Sun

and Tsukamoto (2001) It can also be seen from Figures 5.45-5.48 that similar

conclusions can be obtained for the case that pumps operates at different rotational speed

However, the above conclusion can not be applied to the model impeller M3 with straight vane design The present numerical effort working on the model impeller M3 finds that even when we reduce the flow rate to a very low level, the flow pattern has no notable changes The detailed reason for this phenomenon is not clear yet One possible explanation is that the four straight vanes of M3 are not enough to constrain the flow even at design point, and thus the severe recirculation happens in the

impeller passage This recirculation exists at various inflow 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 along the impeller passage In addition, a weak recirculation occurs near shroud 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 compare the pressure distribution on vane-to-vane planes at

can be seen clearly that the pressure increases gradually along streamwise direction and normally it has higher pressure on pressure surface than suction surface for each plane In addition, 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 almost parallel to the circumference near the impeller outlet For model impeller M3, the comparison of pressure profiles in Figure

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

longer perpendicular to the impeller suction surface at low flow rate Compared with the pressure distribution at two rotational speeds, it is found that the static pressure drops severely as impeller rotational speed decreases Therefore, we can easily change the pressure distribution across the impellers by adjusting pump rotational speed

Figures 5.61-5.63 compare the pressure distribution along the impeller blade at

2.0)Q for pump impellers M3, M4 and M5 running at the rotational speeds of 2900 d

2 2/)2

no pressure drop at low flow rate

5.3 Model Impeller M6

5.3.1 Impeller Design Parameters

Model impellers M1 and M2 are selected from Kosyna and Kecke’s paper (2002) The numerical results are validated by comparing with experimental and numerical data given by Kosyna and Kecke (2002) Model impellers M3, M4 and M5 are obtained from one local pump manufacturing company The numerical results are compared with the experimental data on pump performance curves and the good agreement is also achieved After a series of tests and verifications, the numerical schemes are fully validated and thus can be safely applied to the design of new model impeller M6

Model impeller M6 is a newly designed impeller which is not manufactured

presented in Table 5.1

5.3.2 Computational Grid

The three-dimensional geometry for model impeller M6 is shown in Figure 5.1 As a preliminary study, only three-dimensional water flow through pump impellers is considered at the present time

The unstructured triangular mesh for model impeller M6 is shown in Figure 5.64 The total element is 103791 As discussed in section 5.2.2, this kind of mesh is enough to get relatively accurate numerical results

were specified at inlet boundary to study pump design and off-design flow patterns In

present study shows that there are no apparent differences among different turbulence models

Figures 5.65 shows the convergence history for model impeller M6 running at design point and rotational speed of 1450 rpm The convergence criteria for each run

is set to be 1.0e-4 for RMS (root-mean-square) residuals of mass/momentum

time steps for each run, the above criteria can be satisfied and the convergence is reached gradually

The computational head-flow H-Q curve for model impeller M6 is shown in Figure 5.66 Since no experimental data are available now, the validation of computational results at off-design points is not possible However, the present study shows good prediction at pump design point As shown in Fig 5.66, the design point

is very close to predicted head-flow curve and the difference between them is below 8% The difference is because flow losses in the pipes and volute are neglected in the current calculations If the full pump stage is used in the numerical simulation, it will provide more accurate results However, due to the limitation of software application, the full stage simulation is not applicable at the current moment

Figure 5.67 makes comparison of computational and converted H-Q data for

speed and the thin line shows the converted data from other speed by using the speed law Again, the computational and converted lines at rotational speeds of 2900 rpm and 1450 rpm for model impeller M6 are found to be very close to each other and thus the similarity law can be well verified So it is reasonable to use the head-flow curve

at some rotational speed to predict the head-flow curve at other rotational speed

Figure 5.68 shows the velocity vector on this vane-to-vane mid-height plane for model impeller M6 at design point and rotational speeds of 2900 rpm and 1450 rpm respectively It is found that the vortex occurs near the pressure side of the blade This observation is similar to that for model impeller M3 in which a severe vortex is also found inside However, the flows for model impellers M4 and M5 are quite smooth and there is no relative vortex at the design point The explanation may be as follows: the flow in the impeller can be represented by a through-flow and a relative vortex caused by the irrotational nature of the flow For impeller M1, M2, M4 and M5, they have 5 and 6 vanes These vane numbers can constrain flow very well and thus make the through-flow strong So the relative vortex is weak and not obvious For impeller M3, it has four vanes So this vane number is not enough to constrain the flow and thus the relative vortex can be observed For impeller M6, although it has 5 twisted vanes, it runs at higher rotational speed, so the relative vortex is strong and observed in the impeller Therefore, the total vane number and pump rotational speed both have influence on the velocity distribution in the impellers

Next, different volume flow rates are specified at inlet boundary condition to study off-design points for model impeller M6 Figures 5.69 and 5.70 show velocity vectors on vane-to-vane plane at different volume flow rates and rotational speeds Figure 5.71 shows the quantitative analysis of the velocity distribution on the mid-

impeller as the flow rate decreases It thus suggests that the flow field at low flow rate will become more complicated and unstable, and the flow loss will increase accordingly So if possible, the pump station should operate at normal flow rate to assure high efficiency and low damage to the impeller of the pump Similar conclusion can be obtained for the cases that model impeller M6 runs at different rotational speeds

Figures 5.72 and 5.73 show pressure contours on vane-to-vane plane for model impeller M6 running at various volume flow rates and rotational speeds of

2900 rpm and 1450 rpm The shaded area represents the vane-to-vane mid-plane The pressure is seen to increase gradually along the streamwise direction The isobars are perpendicular to the impeller surface on the suction side of the blade at pump design operating point However, this perpendicularity will not be kept at pump off-design points On the pressure side of the blade, it is found that the isobars are not perpendicular to the impeller surface even at design point This is because the flow re-circulation occurs along this side In addition, the pressure lines are seen to be inclined in the circumferential direction The equipressure lines in low flow rate are greatly deformed in the blade pressure side In this region, the lines lie nearly in the circumferential direction and there is no increase in the pressure along that direction All these observations are similar to those obtained from model impeller M3, M4 and M5

Figure 5.74 shows the pressure distribution along the blade surface for model impeller M6 running at different flow rates and rotational speeds The pressure rise

model impellers M3, M4 and M5, it is found that the conclusions drawn from M3, M4 and M5 are also valid for M6, i.e., the pressure difference between pressure and suction surfaces will get large at higher flow rate, and the main pressure variation occurs on the suction side of blade surface Since these findings are observed among the centrifugal pumps studied so far, it can thus be concluded that they are applicable

to all the small and medium size centrifugal pumps

Table 5.2 Grid systems for each model impeller

Model Impeller Total Mesh Elements (with extension) Total Mesh Elements (without extension)

Outlet Pressure (Pa)

Calculated Pump Head (m)

CPU time (hours)

Table 5.4 Comparison of efficiency value for model impellers

(a) impeller M1 or M2

(b) impeller M3

(c) impeller M4

(d) impeller M5

(e) impeller M6

Figure 5.1 Three-dimensional geometries of model impellers M1-M6

Figure 5.2 Unstructured triangular grids for impeller M1

Figure 5.3 Convergence histories for pump M1 operating at design point

Figure 5.4 Convergence history for pump M2 operating at design point

Figure 5.5 Pump characteristic curves measured and calculated by using present

model and PHOENICS codes for impeller M2

ψ

ϕ

(a) Present study

(b) Results by Kosyna and Kecke (2002)

Figure 5.6 Comparison of Pressure contours at design point of impeller M2

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

imp radius (r-r1)/(r2-r1)

measured =0.08 measure =0.097 calculated =0.08 calculated =0.097

Figure 5.7 Pressure distribution measured and calculated by present model for

impeller M2

measured ϕ= 0.08 measured ϕ= 0.097 calculated ϕ= 0.08 calculated ϕ= 0.097

ψ

pressure side

suction side

near shroud plane mid-height plane near hub plane

Figure 5.8 Diagram of three cut planes

(a) 1 mm from the hub

(b) mid-plane of the blade height

(c) 1 mm from the shroud Figure 5.9 Relative velocity distributions in the planes of 1mm from the hub, mid-

(a) 1 mm from the hub

(b) mid-plane of the blade height

(c) 1 mm from the shroud Figure 5.10 Relative velocity distributions in the planes of 1mm from the hub, mid-

(a) 1mm from the hub

(b) mid-plane of the blade height