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The increasing trend of high stage pressure ratio with increased aerodynamic loading has led to reduction in stable operating range of centrifugal compressors with stall and surge initiating at relatively higher mass flow rates. The casing treatment technique of stall control is found to be effective in axial compressors, but very limited research work is published on the application of this technique in centrifugal compressors. Present research was aimed to investigate the effect of casing treatment on the performance and stall margin of a high speed, 4 : 1 pressure ratio centrifugal compressor through numerical simulations using ANSYS CFX software. Three casing treatment configurations were developed and incorporated in the shroud over the inducer of the impeller. The predicted performance of baseline compressor (without casing treatment) was in good agreement with published experimental data. The compressor with different inducer casing treatment geometries showed varying levels of stall margin improvement, up to a maximum of 18%. While the peak efficiency of the compressor with casing treatment dropped by 0.8%–1% compared to the baseline compressor, the choke mass flow rate was improved by 9.5%, thus enhancing the total stable operating range. The inlet configuration of the casing treatment was found to play an important role in stall margin improvement.

Centrifugal compressors are widely used in various industries like oil and gas, aviation, refrigeration, and turbochargers. They require fewer stages to achieve a given pressure ratio and have relatively wider operating range compared to the axial compressors. The demand for compact compression systems in the recent years has led to increased pressure ratio per stage with increased aerodynamic blade loading and reduced stable operating range. Hence, there is a need to improve the compressor stability/stall margin using either active or passive techniques. The active stall control techniques, like air jets and oscillating inlet guide vanes, require activation mechanisms adding weight to the machine and reducing the operational reliability. On the other hand, the passive techniques operate independently without any aid of external controls. The casing treatment is one of the passive stall control techniques, used effectively in axial compressors. However, in most cases, an increase in compressor stall margin is accompanied by a reduction in compressor isentropic efficiency.

Casing treatment involves placing a porous casing around the compressor rotor tip, and in effect, it is a technique to control the casing or shroud boundary layer. Pioneering work on this technique was done by NASA [

The first ever attempt to study the fluid dynamic mechanism of flow through casing treatment was made by Boyce et al. [

There have been relatively few attempts to investigate the casing treatment technique in centrifugal compressors for improving the stall/surge margin. The first successful application of casing treatment technique in a centrifugal compressor was reported by Jansen et al. [

It may be noted that the inducer in a centrifugal compressor impeller behaves like an axial compressor rotor. It is, therefore, hypothesized that casing treatment with slotted casing/shroud around the inducer tip region may also be effective in controlling the suction surface and shroud boundary layers at low mass flow rate, thus delaying flow separation and consequently delaying the onset of rotating stall, with resulting improvement in stall margin. In the present studies, a high speed centrifugal compressor impeller has been numerically investigated with three configurations of slotted casing treatment at the inducer shroud. The streamwise shape of the treatment slots was designed to match with the aerofoil contour of inducer tip section. The treatment slot geometry was varied in terms of different upstream lengths and inlet configurations. The simulation results are presented in the form of global compressor performance and detailed flow behavior through impeller blade passages and casing treatment slots.

A back-swept centrifugal impeller [

Design specification of centrifugal impeller.

Parameter | Value |
---|---|

Total pressure ratio | 4 : 1 |

Rotational speed | 30,000 rpm |

Corrected mass flow rate | 2 kg/s |

Isentropic efficiency | 90% |

Number of impeller blades | 19 |

Inducer tip diameter | 160 mm |

Inducer hub diameter | 80 mm |

Impeller tip diameter | 300 mm |

Impeller blade width at tip | 6.94 mm |

Impeller blade tip clearance | 0.5 mm |

Impeller back sweep angle | 30 degrees (from radial direction) |

CAD model of centrifugal compressor impeller with shroud removed.

The geometrical details of the three casing treatment (CT) configurations in meridional plane are shown in Figure

Geometry details of casing treatment configurations.

S. number | Parameter | Geometric details | |
---|---|---|---|

1 | Number of slots | 76 (4 slots per blade passage) | |

2 | Slot thickness | 3.9 mm | |

3 | Gap between two adjacent slots | 2.7 mm | |

4 | Slot profile in radial direction | Linearly extended in spanwise direction of impeller blade | |

5 | Slot radial depth | 20 mm (25% of leading edge blade height) | |

6 | Slot profile in streamwise direction |
Following the impeller blade angle distribution at inducer tip section from leading edge | |

7 | Slot extension downstream of the inducer leading edge (over impeller blade tip) | 30% of impeller blade chord at shroud | |

8 | Slot extension upstream of inducer leading edge | CT-1: 20 mm |
Note: CT-1 and CT-2 differ in slot leading edge geometry |

Casing treatment configurations in meridional plane.

CT-1

CT-2

CT-3

The motivation for the present study was derived from Barton et al. [

CAD models of impellers with CT-1 and CT-2 highlighting the difference in shape of casing around the inducer.

Impeller with CT-1

Impeller with CT-2

CAD models of single impeller blade with CT-1 and CT-2, highlighting the position and proportions of casing treatment vane/slot. (For impeller with CT-3, the upstream length is 100% of leading edge height.)

Impeller with CT-1

Impeller with CT-2

It was hypothesized that the shape of treatment slots matching with the inducer tip profile will have better flow recirculation dynamics leading to improvement in compressor performance, especially the stability margin. With this concept in mind, the three variants of CT were chosen to investigate the effect of the geometric changes. It may be noted that, unlike casing treatment studies in axial compressors, the application of casing treatment in centrifugal compressors is not reported much in open literature. The present investigations may be regarded as leading steps in this area to provide motivation for further parametric studies.

The CAD models of the baseline centrifugal impeller (Figure

Figures

Computational domain of baseline impeller with one blade passage and inlet and exit domain extensions.

Computational domain of impeller with casing treatment CT-1 showing one blade passage and four treatment slots along with inlet and exit domain extensions.

Two computational fluid domains were created: (1) a rotating domain for impeller passage and (2) a stationary domain for casing treatment slots. These domains were discretized with structured grids having hexahedral elements using ICEM CFD software and multiblocking technique. The H-O-H mesh topology was employed for impeller flow domain. The O-grid topology was employed around the impeller to capture flow behavior accurately. Typical grids for impeller alone and the casing treatment slots are shown in Figures

Computational grid for baseline impeller.

Computational grid for casing treatment slots.

Boundary conditions applied to the impeller.

Steady state CFD simulations on the baseline impeller and the impellers with inducer casing treatment were carried out using ANSYS CFX software. The discretized form of Reynolds Averaged Navier-Stokes (RANS) equations was iteratively solved for all cases of baseline and treated impellers. The turbulence model used was SST

The stage interface (mixing plane interface) was used between impeller and casing treatment domains. As the impeller rotates, the circumferential position of the impeller blades changes with respect to casing treatment slots; hence, stage interface is a more appropriate condition in this situation. The interface was created at the middle of the impeller-shroud tip gap.

All simulations, except the one for experimental validation, were carried out at 100% design speed. Air as ideal gas and with standard properties was used as working fluid in the compressor. The total pressure and total temperature, both at sea level conditions, were prescribed at domain inlet, while a variable static pressure was specified at domain exit. The flow was treated as compressible and it entered the impeller axially. To obtain the compressor performance characteristic from choke to stall mass flow rate, the exit static pressure (back pressure) was varied in discrete steps, allowing the solution to converge at each back pressure. All simulations were converged to a RMS residual value of 10^{−5}. The numerical stall point was identified when, at a certain back pressure, the solution diverged. The stall point was resolved with a back pressure differential of 50 Pa between two consecutive values. The criterion for fixing the occurrence of numerical stall is quite well established. As the back pressure (static) is gradually increased from a low value in the choke region to higher values, the compressor performance moves towards design point and then towards stall. At some high back pressure, the CFD simulation does not converge and the solution diverges. This is termed as numerical stall. In the present studies, the numerical stall point was resolved with a difference in exit static pressure value of 50 Pa between last converged solution and the following diverged solution.

All the flow parameters were mass averaged at inlet and exit. The compressor total pressure ratio and adiabatic efficiency were calculated using the following equations:

Also, the corrected mass flow rate and corrected impeller rotational speed are defined as

The results of CFD simulations on the compressor without and with casing treatment are presented and discussed in this section. Initially, the grid independence and validation studies were carried out to select an appropriate grid density and also to confirm the accuracy level of the predicted data. Subsequently, the effects of casing treatment on compressor overall performance and on the flow development through the impeller blade passages are discussed.

Grid size plays an important role in both convergence and accuracy of the solution. Hence, a grid independence study was performed at 50% design speed to ensure that the numerical solutions were grid independent. CFD simulations on the baseline impeller were performed with different grid sizes, having 316800 elements (Grid-1), 397824 elements (Grid-2), 435200 elements (Grid-3), and 516864 elements (Grid-4), using ANSYS CFX software. The first element height was kept constant at 0.02 mm for all the grid sizes to avoid the influence of

Grid independence study.

The experimental results for baseline compressor impeller were available at 50% design speed. Hence, the impeller performance from CFD simulation is validated at this speed only. The impeller performance was then computed at 100% design speed and used as the baseline performance for casing treatment studies. Figure

Validation study. Comparison of experimental and predicted performance of compressor without casing treatment at 50% design speed.

Overall performance characteristics of the compressor at 100% design speed without and with three casing treatment configurations,

Overall performance characteristics of compressor without and with inducer casing treatment.

The isentropic efficiencies (Figure

The variations of circumferentially averaged relative Mach number through the blade passage of the baseline impeller at near-design and stall mass flow rate are shown in Figure

Circumferentially mass averaged relative Mach number distribution in impeller blade passage.

Near-design mass flow rate

Stall mass flow rate

At near-design mass flow rate (Figure

Figure

Impeller blade loading at three spanwise locations of 20%, 50%, and 90% from hub wall at near-design and stall mass flow rate.

Blade loading at near-design mass flow rate (2 kg/s)

Blade loading at stall mass flow rate (1.43 kg/s)

The relative effectiveness of different inducer casing treatment configurations CT-1, CT-2, and CT-3 can be better explained with the help of (i) absolute velocity vectors through the inducer flow passage (see observation plane in Figure

Location of periodic plane for plotting velocity vectors.

Absolute velocity vectors in the inducer channel and in the casing treatment slots.

Baseline impeller

Impeller with CT-1

Impeller with CT-2

Impeller with CT-3

Circumferentially mass averaged relative Mach number distribution in the meridional plane for impellers without and with three casing treatment geometries at stall mass flow rate of baseline compressor.

Baseline impeller

Impeller with CT-1

Impeller with CT-2

Impeller with CT-3

In the presence of casing treatment CT-1 (Figures

In case of treatment configurations CT-2 and CT-3, the scenario is quite different (Figures

From the above discussion, it is evident that among the three casing treatment configurations, the CT-1 configuration produces the largest gain in stall margin. Hence, the subsequent discussions are restricted to the comparison of flow behavior in baseline and CT-1 impellers.

The variations of static pressure on the suction and pressure surfaces of the blades of baseline and CT-1 impellers at 90% span are shown in Figure

Comparison of blade loading of baseline impeller and impeller with CT-1 casing treatment at respective stall mass flow rates.

It is interesting to examine the flow development along the impeller blade passages of baseline compressor and the one with CT-1 casing treatment. Figure

Observation planes in streamwise direction from inducer inlet to impeller exit.

Figure

Relative Mach number distribution on streamwise planes of baseline and CT-1 impeller at stall mass flow rate of baseline compressor.

Baseline impeller

Impeller with CT-1

The flow behavior within the impeller passage drastically changes in the presence of casing treatment CT-1, as shown in Figure

Even at stall mass flow rate for impeller with CT-1 (Figure

Relative Mach number distribution on streamwise planes of CT-1 impeller at stall mass flow rate.

Figures

Relative Mach number distribution on spanwise planes of baseline and CT-1 impellers at 90% span from hub at stall mass flow rate of baseline compressor.

Baseline impeller

Impeller with CT-1

Entropy distribution on spanwise planes of baseline and CT-1 impellers at 90% span from hub at stall mass flow rate of baseline compressor.

Baseline impeller

Impeller with CT-1

The effect of inducer casing treatment on the tip leakage flow is depicted in Figure

Relative velocity vectors on spanwise planes of baseline and CT-1 impellers near tip at stall mass flow rate of baseline compressor.

Baseline impeller

Impeller with CT-1

As discussed earlier in Section

Circumferentially mass averaged relative Mach number distribution in meridional plane at respective choke flow rates of baseline and CT-1 impellers.

Baseline impeller

Impeller with CT-1

Relative Mach number distribution on a spanwise plane 90% from hub at respective choke flow rates of baseline and CT-1 impellers.

Baseline impeller

Impeller with CT-1

Referring to Figures

Numerical investigations have been carried out on a high speed centrifugal compressor of design pressure ratio 4 : 1 to determine the effectiveness of casing treatment technique in enhancing the compressor aerodynamic performance. Three casing treatment geometries, differing in inlet configuration and respective lengths (upstream of the inducer leading edge), were incorporated in the shroud over the inducer. The treatment slots of identical porosity were designed to follow the profile of the inducer tip section. The CFD simulations were carried out at 100% design speed from choke to stall mass flow rate. The major conclusions drawn from this study are presented below:

All three casing treatment configurations tend to improve stall margin of the centrifugal compressor with slight reduction in isentropic efficiency. The configuration CT-1 with a larger inlet diameter gives highest stall margin improvement of 18%, whereas for the other two configurations CT-2 and CT-3 the stall margin improvement is relatively much smaller. Peak efficiency of the impeller with CT-1 is reduced by 0.8% and with CT-2 and CT-3 by 1% compared to the baseline impeller.

The casing treatment CT-1 with its outer diameter aligned with the diameter of the compressor inlet duct is able to push the incoming flow straight through the slots, thus energizing the low momentum fluid at the compressor shroud. The recirculating flow region is weakened and pushed downstream. The resulting reduction in flow blockage is responsible for lowering of stall mass flow rate.

The casing treatments CT-2 and CT-3, on the other hand, have slots whose inner diameter is aligned with the compressor inlet diameter. The flow through the slots is not strong enough to weaken the recirculating flow region of baseline impeller. Also, there is reverse flow in the vicinity of the inducer tip. Hence, these two CT configurations are not effective in reducing the flow blockage and the improvement in stall margin is marginal.

The choke mass flow rate of impellers with all three casing treatment configurations is higher than that of the baseline impeller. This is attributed to additional flow area through casing treatment slots available at the compressor inlet.

Overall, the stable operating range from choke to stall mass flow rate is improved by all three casing treatment configurations investigated.

Mach number

Speed, rpm

Static pressure,

Total pressure,

Total temperature,

Mass flow rate, kg/s

Ratio of compressor inlet total pressure to sea level total pressure

Ratio of specific heats

Isentropic efficiency

Ratio of compressor inlet total temperature to sea level total temperature.

Impeller inlet, impeller exit

Absolute

Relative.

Computational Fluid Dynamics

Computer Aided Design

Casing treatment

Leading Edge

National Aeronautics and Space Administration

Pressure surface

Suction surface

Trailing edge.

V. V. N. K. Satish Koyyalamudi is currently working at GE, Oil & Gas, Bangalore, India.

The authors declare that there are no competing interests regarding the publication of this paper.

The authors are thankful to the authorities of M. S. Ramaiah University of Applied Sciences, Bangalore, India, for providing all support to carry out this research work and for granting permission to publish the same in the form of this paper.