Journal of Thermal Science Vol.24, No.4 (2015) 323333

DOI: 10.1007/s11630-015-0791-1

Article ID: 1003-2169(2015)04-0323-11

Numerical Investigation of Rotating Stall in Centrifugal Compressor with Vaned and Vaneless Diffuser Taher Halawa1, Mohamed Alqaradawi2, Mohamed S. Gadala3, Ibrahim Shahin4, Osama Badr5 1. Mechanical Engineering Department, UBC-University of British Columbia, Vancouver, B.C., Canada Mechanical Engineering Department, Cairo University, Giza, Egypt 2. Mechanical & Industrial Engineering Department, Qatar University, Doha, Qatar 3. Mechanical Engineering Department, UBC-University of British Columbia, Vancouver, B.C., Canada Mechanical Engineering Department, Abu Dhabi University, Abu Dhabi, UAE 4. Mechanical and Industrial Engineering Department, Qatar University, Doha, Qatar Mechanical Engineering Department, Benha University, Egypt 5. Mechanical Engineering Department, British University, Cairo, Egypt © Science Press and Institute of Engineering Thermophysics, CAS and Springer-Verlag Berlin Heidelberg 2015

This study presents a numerical simulation of the stall and surge in a centrifugal compressor and presents a description of the stall development in two different cases. The first case is for a compressor with vaneless diffuser and the second is for a compressor with vaned diffuser of the vane island shape. The main aim of this study is to compare the flow characteristics and behavior for the two compressors near the surge operating condition and provide further understanding of the diffuser role when back flow occurs at surge. Results showed that for a location near the diffuser entrance, the amplitude of the static pressure fluctuations for the vaneless diffuser case is higher than that for the vaned diffuser case near surge condition. These pressure fluctuations in the case of the vaneless diffuser appear with a gradual decrease of the mean pressure value as a part of the surge cycle. While for the case of the vaned diffuser, the pressure drop during surge occurs faster than the case of the vaneless diffuser. Also, results indicated that during surge in the case of vaneless diffuser, there is a region with low velocity and back flow that appears as a layer connecting all impeller passages near shroud surface and this layer develops in size with time. On the other hand, for the case of vaned diffuser during surge, the low velocity regions appear in random locations in some passages and these regions expand with time towards the shroud surface. Results showed that during stall, the impeller passages are exposed to identical impact from stall cells in the case of vaneless diffuser while the stall effect varies from passage to another in the case of the vaned diffuser.

Keywords: centrifugal compressors, rotating stall, surge, vaneless diffuser, vaned diffuser

Introduction Compressor surge is one of the most important problems that can occur during compressor operation because

Received: March 2015

it can lead to a complete damage to the compressor blades. If the compressor operating condition is close to the surge line, the difference between the flow angle and the blade angle increases and the stall cells start to occur.

Taher Halawa: University of British Columbia. www.springerlink.com

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Nomenclature k Turbulence kinetic energy per unit mass (m2/s2)  s The source term of  t Time [s] Time step [s] t U Blade velocity [m/s] u Flow velocity vector [m/s] ug Mesh velocity of the moving mesh [m/s] V Mesh volume [m3] v Fluid absolute velocity [m/s] z The axial direction Abbreviations CFD Computational fluid dynamics NASA National Aeronautics and Space Administration The formation of the stall cells near the impeller shroud surface causes flow disturbance at the vaneless region and weakness of the flow at the diffuser throat. The stall cells may grow with time specially when the reversed flow appears at the diffuser inlet and this can develop to surge. Vo et al. [1] demonstrated that there are two conditions associated with stall phenomenon. The first condition is the appearance of the tip leakage flow where the flow moves from one impeller passage to another through the tip clearance. The second condition is the back flow impingement where the flow exits from some passage and turns back and enters the adjacent passage in a reverse direction hitting the blades surface and forming stagnation area. When the tip leakage flow appears during stall, the main flow interacts and impacts the tip leakage flow. Due to the difference between the main flow and the secondary flow in terms of the magnitude and direction, the interface forms as a result of this kind of interaction between the main and tip leakage flows. When the stall cells develop with time, the interface moves toward the impeller inlet leading edge [2]. Geng et al. [3] found that the tip leakage flow can move against the main flow and exits from the impeller entrance close to the impeller blades leading edge if the phase shift between the tip leakage flow and its tangential dispersal is developed with time. Huang et al. [4] performed a numerical simulation about stall development from a normal condition, and related the frequency of the tip leakage vortices to the blades passing frequency. Ramakrishna and Govardhan [5] found that the sweeping of the impeller blades may result in decreasing of the stalled area near the shroud surface. It was also found that the losses in the total pressure ratio can be decreased by sweeping the blades and by increasing the tip clearance slightly.  Ciorciari et al. [6] studied the effect of using different tip

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RMS Greek letters

Root Mean Square



Symbol for general flow variable Turbulence dissipation rate (m2/s3) Fluid density [kg/m3] Diffusion coefficient The gradient of a value

ε

  

Subscripts a Superscripts g n

axial Grid Equivalent to the current time step

clearance values on the compressor surge margin. Results confirmed that by decreasing the tip clearance thickness, the tip clearance flow strength decreases. Many experimental studies focusing on stall control using air injection were performed on the NASA CC3 compressor which was selected to be studied in the current paper. The idea of the air injection is that the air is injected at specific location at the compressor shroud surface in order to increase the stall margin of the compressor and in the same time to avoid making any modification on the casing geometry that can decrease the efficiency due to increased interaction between the main and the secondary flows. Benhegouga and Ce [7] studied the variation of air injection parameters on the air injection performance and the compressor surge margin. It was found that when the injector is close to the blades tip leading edge, the compressor surge margin is relatively high but the pressure losses are high too. When the injector is moved away from the impeller blades leading edge, the pressure losses are decreased but the surge margin is decreased also.  Nie et al. [8] made an experimental investigation about using air injection in a high speed centrifugal compressor. Results showed that the best location to inject air is at the upstream of the impeller blades tip because the flow separation is better controlled and minimized at the impeller inlet. Skoch [9] examined experimentally the effect of injecting air at the hub surface of the vaneless space of the CC3 transonic compressor. It was found that the injection at the angle of 8◦ is the best in terms of increasing the surge margin because there is a better interaction with the main flow compared to the other injection angles. Halawa et al. [10] made a numerical investigation for stall control using air injection in a high speed centrifugal compressor. Results showed that using air injection with angle of 30◦ at injection mass flow rate of 1.5% of the inlet mass flow rate

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Numerical Investigation of Rotating Stall in Centrifugal Compressor with Vaned and Vaneless Diffuser

shifted the stall onset to a mass flow rate of 3.8 kg/s. The mentioned air injection studies concerning centrifugal compressors confirmed that the weakest location in the compressor with vaned diffuser is the vaneless region. So, the diffuser plays an important role during stall and the comparison between vaneless and vaned diffuser needs to be studied in terms of stall initiation and development. The present study focuses on simulating surge in a compressor with vaneless and vaned diffusers. The main aim is to provide better understanding of the way that the stall is developed into surge and the factors associated with surge initiation for the compressor with vaneless and vaned diffusers by comparing the unsteady flow parameters and flow behavior at different operating conditions. This work marks new developments and enhancements of the initial work done by the authors for each compressor separately [10-12].

CASE STUDY The selected case study is the NASA CC3 high speed centrifugal compressor. Figure 1 shows the shape of the CC3 compressor with vaned diffuser.

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both the spatial and temporal discretization. The simulation was performed using DELL server with 4 AMD Opteron processor “48 core” and 64 GB of RAM. For each rotor revolution, the computational time is 10 hours by using a time step of 6×10-6 second. The k-ε realizable model was used for the turbulence modeling because it was designed to simulate the high speed compressible flow with high accuracy especially when strong flow separations take place. The sliding mesh model was applied because of its ability to simulate the unsteady transonic flow at high rotational speeds. The rotating zone containing the impeller slides on the fixed zone containing the diffuser and the inlet pipe through interface surfaces. The governing equation used in the sliding mesh method is similar to the general form of fluid governing equations but the velocity is modified to be relative to the moving mesh grid velocity at each mesh cell. Equation 1 describes this governing equation for a general flow variable . d  dV    u  u g  dA dt V V (1)     dA   S  dV



V



V

Where V is the cell mesh volume and  is the fluid density. While u and ug are the fluid velocity vector and the velocity of the moving grid mesh. Also, S is the source term of  and  is the diffusion coefficient. The rate of change of the volume with time was calculated with a second order accuracy as described in equation 2.

Fig. 1 [13].

NASA CC3 centrifugal compressor with vaned diffuser

The impeller contains 15 main blades and 15 splitter blades while the diffuser composed of 24 vane island passages and the tip clearance is 0.2 mm. The design operating conditions are corresponding to a mass flow rate of 4.5 kg/s (10 lbm/sec) with a rotational speed of 21,789 r/min and a pressure ratio of 4:1. The impeller inlet tip radius is 105 mm while the diffuser exit radius is 362 mm. McKain and Holbrook [14] reported the complete dimensions with the design specifications of the NASA CC3 compressor. This compressor is commonly used for simulating surge and stall as can be found in several studies [9, 15-20].

NUMERICAL METHOD The CFD numerical solver FLUENT [21] was used for solving the flow governing equations using the finite volume method with second order upwind scheme for

3  V  d  dV   dt V

n 1

 4  V    V  2 t n

n 1

(2)

Where n is an index represents the current time step. The rate of change of the volume with time (dV/dt) is calculated by making a summation of the dot product of the velocity vector and area vector at each mesh cell face. The Numerical Models The numerical model of the compressor with vaneless diffuser is composed of three main parts; the inlet pipe with a bell mouth attached to its exit, the impeller and the vaneless diffuser with impeller hub cavity followed by a shaft seal as shown in Fig.2. The straight pipe part was added at the inlet in order to ensure that the flow is fully developed at the impeller inlet, and the length of this pipe is 1.5 m. Also, there is a radial to axial bend added after the vaneless diffuser part in order to redirect the flow in the axial direction. The axial part of the bend was extended to be more than its actual size to reduce the effect of the outlet boundary condition on the flow distribution inside the vaneless diffuser. The numerical model of the compressor with vaned diffuser is similar to the previously described model but

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with replacing the vaneless diffuser part with a vaned diffuser as indicated in Fig.3. The vaned diffuser contains 24 vane island passages with vane angle of 13.5° at the diffuser inlet.

mesh growth rate, several mesh sets were generated with a selected total mesh elements range starting from 5 million up to 16 million cells. More details about the mesh sensitivity analysis can be found in a previous published article [10]. Figure 4 shows the mesh of the numerical model of the compressor with vaned diffuser for the final mesh level of 15 million cells.

Fig. 4

Meshing of the vaned diffuser numerical model.

Results Fig. 2 The numerical model of the compressor with vaneless diffuser.

Fig. 3

The numerical model of the compressor with vaned diffuser.

At the compressor inlet, the pressure inlet boundary condition was specified with a total pressure value of 101,325 Pascal, total temperature of 288K. At the compressor exit, the pressure outlet boundary condition was used with a pressure value depends on the required simulated operating condition. These types of boundary conditions were used for better convergence since the total pressure ratio is fixed and the unknown is the mass flow rate which can be determined with minimum number of iterations if the initial conditions are set close to the predicted values. Mesh Sensitivity Analysis The mesh accuracy test was performed by making a comparison between the results when using different mesh sets in order to find the proper mesh set which can achieve acceptable accuracy level. By changing the minimum and maximum mesh element sizes and the

In this section, the results for compressor with vaneless and vaned diffusers are compared at design condition and close to surge and also at surge condition are discussed in details. For the time averaged data part, the sampling time was chosen to be between 0.025 sec and 0.11 sec and this is equivalent to 18 rotor revolutions from the start of sampling at time of 0.025 sec. The reason for this choice is to ensure the convergence of the solution before sampling. There are several operating conditions used in the simulations in order to test the compressor from design condition up to surge. Figure 5 shows the location of six different operating conditions; half of them for the vaneless diffuser case and the other half for the vaned diffuser case. Operating conditions 1, 2, 3 represent the design condition, close to surge and at surge for the vaneless diffuser case, while the operating conditions 4, 5, 6 represent the design condition, close to surge and at surge for the vaned diffuser case.

Fig. 5

Location of the operating conditions used for simulations for the vaneless and the vaned diffuser cases.

Validation The numerical results were compared to measure-

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Numerical Investigation of Rotating Stall in Centrifugal Compressor with Vaned and Vaneless Diffuser

ments in order to validate the model and its accuracy. Figure 6 (a) and Figure 6 (b) show the compressor pressure map for vaneless and vaned diffuser cases, respectively for the numerical results against measurements [17].

the impeller tip exit velocity which has a value of 490 m/s. It may be concluded from Fig.7 that the numerical model predicted the velocity profile trend correctly with a relatively small error comparing with measurements. The validation test verified that the numerical model has a good accuracy and can be used for further numerical analysis.

Fig. 7

Fig. 6 Compressor pressure map for the numerical results and for measurements [17].

The validation results were performed at the compressor design speed which is 21,789 r/min. Each point on the numerical curve represents a complete computational run at a specified pressure ratio and its corresponding predicted mass flow rate inside the steady state margin between surge limit and choke limit. It may be concluded from Fig.6 (a) and Fig.6 (b) that the numerical results are very close to measurements at the mid-range of the mass flow rate and this difference error increases when approaching the surge condition or the choking condition. In order to make more verification for the numerical model accuracy in predicting the instantaneous flow parameter values, the velocity profile comparisons at a radius ratio of 1.1 relative to the impeller tip exit radius were performed as shown in Fig. 7 for the vaneless diffuser case for the numerical results against measurements [17]. The velocity values are normalized by referring to

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Velocity profile at radius ratio of 1.1 for the vaneless diffuser case for both of numerical results and measurements [17].

For validating unsteady flow variations, the velocity distribution inside the diffuser during surge cycle were compared to measurements [20] as shown in Fig.8. There are four points shown on the surge cycle graph on the top of Fig.8 representing the main stages before and during surge. The points A, B, C, D are for conditions before surge, at the maximum pressure, at intermediate pressure and at the minimum pressure. Fig.8 (b) shows that the numerical results for point B predicted a back flow appearance with a maximum velocity value around 220 m/s at the diffuser throat, and this result is close to the experimental result of 225 m/s as indicated in Fig.8 (a). At Point D, the measurements (Fig.8 (c)) shows that there is a small region with a corrected flow direction appears at the diffuser throat, while the numerical results (Fig.8 (d)) proves the same result but with a wider corrected flow region. It may be concluded from Fig.8 that the CFD code can capture the unsteady flow variations during surge accurately. Monitoring Parameters Fluctuating with Time during Surge Mass flow rate monitoring The mass flow rate monitoring can give an indication for the degree of flow unsteadiness and also the reversed flow in case of stall development. The mass flow rate

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averaged over the area at the diffuser exit was monitored with time near surge condition as shown in Fig.9. For the vaneless diffuser case shown in Fig.9 (a), there are

Fig. 8 Velocity at the diffuser at different times of the surge cycle (CFD results versus measurements [20]).

Fig. 9

Area weighted average of the mass flow rate at compressor exit near surge condition for the vaneless and vaned diffuser cases.

strong fluctuations with high amplitudes appear, and after some time the averaged mass flow rate value changes rapidly with smaller fluctuations. On the other hand, for the vaned diffuser case shown in Fig.9 (b), similar behavior appears but with amplitudes lower than those for the vaneless diffuser case and also each pulse takes more time relative to the vaneless diffuser case. For the vaneless diffuser case, there is no guide for the flow motion at the diffuser as the flow is not forced to move in a specified path, so, the flow moves randomly at the diffuser exit and this random motion results in the rapid mass flow rate fluctuations during stall. For the vaned diffuser case, during stall, there are some diffuser passages affected by stall in the vaneless region, and also there are some passages not affected by stall. So, the flow direction at the diffuser exit from all passages is not the same in the circumferential direction and there is a weak flow at the affected passages only, so, the mass flow rate fluctuations are relatively small because of the localized reversed flow at the affected diffuser passages during stall. Static pressure monitoring at the area between the impeller and the diffuser The stall initiates inside the impeller due to the formation of the secondary flow and the tip leakage flow but the stall development starts at the diffuser entrance. The chance of stall development is at the vaneless region between the impeller and diffuser for the vaned diffuser case, and at any position in the diffuser especially close to the impeller exit for the vaneless diffuser case. For that reason, it is very important to study the pressure variation of the flow after leaving the impeller. The static pressure was monitored with time at a location with a radius ratio of 1.1 near the surge condition as shown in Fig.10 in order to identify the characteristics of the stage before surge. For the vaneless diffuser case, the pressure decreases gradually from 305 kpa to 20 kpa accompanied with high pressure fluctuations. For the vaned diffuser case, the pressure varies in a periodic repeats around an average value of 325 kpa for some time and then drops suddenly to 100 kpa and then starts to rise again gradually and this is a part of the surge cycle which is supposed to be repeated continuously during surge. Figure 11 shows the pressure surge cycle for the vaned diffuser case according to accurate measurements [20]. The numerical results described in Fig.10 (b) match well with the measurements shown in Fig.11. The dotted rectangle shown in Fig.11 highlights one of the surge cycles obtained experimentally and it is clear that the pressure curve from numerical results in Fig.10 (b) has nearly the same trend as measurements except for the moment before the pressure drop appearance where the pressure does not reach exactly 400 kpa level but reaches 380 kpa instead. There is a very interesting point about the difference between the pressure variation during stall for the

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Fig. 10

Numerical Investigation of Rotating Stall in Centrifugal Compressor with Vaned and Vaneless Diffuser

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Static pressure at radius ratio of 1.1 near surge condition for the vaneless and vaned diffuser cases.

vaned and vaneless diffuser cases. The main difference is that the pressure decreases gradually with time during stall for the vaneless diffuser case but decreases suddenly and sharply for the vaned diffuser case, and this is due to the difference in the way of how the stall cells develop for the two cases. During stall, the flow leaves the impeller with an angle deviated from the design angle and then the flow passes through the vaneless region for the case of vaned diffuser and at some locations, the flow fails to enter the diffuser passages and the stall cells are formed at these locations. After some time, some stall cells are merged to form a large one causing a weak flow inside a large number of diffuser passages and at this moment, the reversed flow at diffuser exit appears strongly as a part of a surge cycle with a sharp rise and drop of the pressure value for the case of the vaned diffuser. When stall occurs in the case of vaneless diffuser, there is some kind of symmetry in the tangential direction when the stagnant flow starts to appear because there are no diffuser vanes and the flow does not impact with these vanes as in the vaned diffuser case. This can be the reason for the gradual pressure drop at the beginning of the surge cycle for the case of vaneless diffuser as the stall develops more uniformly than for the other case.

pressure signal is indicated in Fig.13. It may be noted that the pressure fluctuations in the case of vaneless diffuser (Fig.12 (a)) are similar to those for the vaned diffuser case (Fig.12 (b)) but the number of pulses in the case of vaneless diffuser is larger in the same time frame. The spectral analysis of the vaneless diffuser case (Fig.13 (a)) shows that there are 2 major peaks and several minor peaks while the spectral analysis of the vaned diffuser case (Fig.13 (b)) indicates that there are more than 2 major peaks and with higher magnitude values. This means that the impact of the dynamic fluctuations in the case of vaned diffuser is stronger than the impact for the vaneless diffuser case because as the number of frequency pulses increases, this means that there are stall cells formed and move with a specific speed.

Fig. 11

Fig. 12

Pressure surge cycle for the vaned diffuser case according to measurements [20].

Dynamic pressure monitoring at the area between the impeller and the diffuser The dynamic pressure was also monitored with time as shown in Fig.12 and the spectral analysis of the dynamic

Dynamic pressure at radius ratio of 1.1 near surge condition for the vaneless and vaned diffuser cases.

Velocity Contours Comparison It is also important to study the velocity variation near the impeller entrance as this can indicate the degree of severity of the stalled area formed at the impeller shroud

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during stall. Figure 14 shows the normalized axial velocity contours at a plane located upstream of the impeller inlet for the vaneless and vaned diffuser cases at three different operating conditions; design, near surge and at surge. The axial velocity is normalized by relating it to the tip velocity at the impeller exit. The unsteady results shown in Fig.14 (b) and Fig.14 (e) are the averaged values over 15 rotor revolutions from the start of the unsteady fluctuations while the results presented in Fig.14 (c) and Fig.14 (f) are at the time corresponding to the maximum pressure of the surge cycle.

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can be seen from Fig.14 (e). Figure 14 (f) indicates that at surge, the stall areas appeared earlier are merged forming larger areas, and these areas extend from the shroud surface toward the hub surface.

Fig. 14 Axial velocity contours upstream of the impeller inlet at different operating conditions for the vaneless and the vaned diffuser cases. Fig. 13 Spectral analysis of the convergence history of the dynamic pressure at radius ratio of 1.1 near surge condition for the vaneless and vaned diffuser cases.

For the vaneless diffuser case, it may be noted from Fig.14 (a) that the velocity distribution is nearly uniform without stall cells at the design condition. At the near surge condition, the velocity decreases in the radial direction from the hub surface towards the shroud surface as shown in Fig.14 (b). Also, near surge, there is a very low velocity region formed near the shroud surface and there are some small spots with negative values. Figure 14 (c) indicates the situation at surge, the low velocity area is increased and the overall axial velocity values are decreased compared to the results of the near surge condition. For the vaned diffuser case, the velocity distribution is uniform at the design condition except for very small part with slightly lower velocity value as shown in Fig.14 (d). When the compressor operates near surge, some stall areas are formed randomly with different size and intensity and they are localized close to the shroud surface as

It may be noted from this comparison that the stall cells appear near shroud surface in the form of one continuous layer developing with time in the case of compressor with vaneless diffuser. On the other hand, the stall cells appear at random locations and some of them merge together causing stall area to be enlarged and reach the hub surface. Pressure Contours Comparison In order to show the degree of unsteadiness during stall, the RMS of the static pressure at the impeller blades and hub surfaces are shown in Fig.15 for the vaneless and the vaned diffuser cases for the design, near surge and at surge conditions. The high values of pressure indicate high unsteadiness or relatively strong change with time. The unsteady results shown in Fig.15 are presented in the same way as mentioned before for the results in Fig.14 where the near surge results are averaged over 15 rotor revolutions time period while the results at the surge condition are shown at the time of the pressure peak of the surge cycle.

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Numerical Investigation of Rotating Stall in Centrifugal Compressor with Vaned and Vaneless Diffuser

For the vaneless diffuser case, the high pressure values are concentrated at the impeller blades leading edge and blades tip at the design condition as shown in Fig.15 (a). Near surge, the areas of high pressure values are increased specially at the blades tip near inlet and exit of the impeller as indicated in Fig.15 (b). At surge, the most affected area with pressure fluctuations is at the impeller passage exit while the pressure values are increased slightly compared with the case of near surge condition as can be seen from Fig.15 (c). For the vaned diffuser case, at the design operating condition, the pressure values are low at most of the locations inside the impeller except near the impeller exit as shown in Fig.15 (d). Near surge, there are some impeller passages with high pressure values from inlet to exit while there are also whole passages with relatively low pressure values as indicated in Fig.15 (e). Figure 15 (f) describes the strong pressure instability at the impeller tip exit area at surge condition with high pressure values formed at the splitter blades leading edge up to the impeller exit where the pressure values are maximized. The pressure contours comparison shows that the maximum pressure fluctuations are at the impeller tip exit, and the pressure distribution is nearly symmetric for the vaneless diffuser case while in the case of vaned diffuser, every passage has different pressure distribution from the other. This means that the most dangerous

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location is at the impeller tip exit in both cases because the strong pressure fluctuations causes high stresses on the blades and the blades tip may deform in the tip clearance gap which is 0.2 mm in a way to be close to the impeller shroud surface. Velocity Vectors Comparison Figure 16 describes the velocity vectors comparison between the vaneless and vaned diffuser cases at a plane located at 98% of the span length when the compressor works at surge condition. For the vaneless diffuser case, the flow inside the diffuser is nearly tangential and turns back toward the impeller at some locations and there is also a very low velocity region near the diffuser exit with stagnant areas as can be seen from the left hand side of Fig.16 at the zoomed in views. It may be noted also that the velocity distribution is identical at impeller exit for all passages. For the vaned diffuser case, the zoomed in views in Fig.16 at the right hand side shows that some impeller passages exposed to back flow from diffuser due to the failure of the flow to enter the diffuser as a result of weak flow and low velocity angle at the impeller exit. Also, this back flow causes stalling of the corresponding diffuser passages and a completely stagnant flow appears inside these passages.

Fig. 16

Velocity vectors at 98% of span for the vaneless and vaned diffuser cases during surge.

Conclusions

Fig. 15

RMS of the static pressure at the impeller hub and blades surfaces at different operating conditions for the vaneless and the vaned diffuser cases.

For the vaneless diffuser case, the stall region starts to appear close to the impeller shroud surface with low velocity values in the form of one layer extends all over the blades tip with nearly the same thickness. As the stall develops, the thickness of this layer grows slowly in the radial direction towards the hub surface and in the same

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time, the velocity values inside this layer decreases with time leading to the appearance of back flow and development of surge. For the vaned diffuser case, the stall cells form in some impeller passages near impeller exit and these regions vary in size and intensity from impeller passage to another. During stall development, the stall regions expand with time until it covers large part of some impeller passages and these regions merge together with time and cover group of impeller passages causing instability. During surge, the pressure fluctuations at the diffuser entrance in the case of vaneless diffuser are stronger than those for the vaned diffuser case in terms of amplitude fluctuation. Also, for the surge cycle, the time taken for the pressure to drop from its maximum value to its minimum value for the case of vaned diffuser is less than that time for the vaneless diffuser case and this may be an indication that the surge develops faster in the case of vaned diffuser. The stall region distribution is nearly identical for all impeller passages for the vaneless diffuser case while this distribution is completely different from one passage to another in the case of vaned diffuser. The compressor with vaneless diffuser is more balanced during surge than the vaned diffuser case because the pressure distribution on each blade is nearly the same for all blades for the vaneless diffuser case. This may be considered as evidence that the sum of the unbalance forces acting on blades due to the formation of stall cells for the vaneless diffuser case is expected to be lower than that for the vaned diffuser case.

Acknowledgments This publication was made possible by NPRP grant No. 4-651- 2-242 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.

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