20th Annual CFD Symposium CFD Division, Aeronautical Society of India

09 - 10 August, 2018Bangalore

DESIGN AND ANALYSIS OF A HIGH PRESSURE RATIO AND HIGH MASS FLOWCENTRIFUGAL COMPRESSOR

Lakshya KumarScientist, Propulsion Division

CSIR - National Aerospace LaboratoriesBengaluru, Karnataka, India

R Senthil Kumarana

Senior Scientist, Propulsion DivisionCSIR - National Aerospace Laboratories

Bengaluru, Karnataka, India

ABSTRACT

There has been continuous effort world-wide to improve the performance of centrifugal compressors in terms of efficiency, pressure ratio and operational stability. Advent of advanced 3D computational tools have definitely made study of flow physics across the compressors far easier. Aerodynamic design and analysis of a single stage centrifugal compressor meant for high pressure ratio and mass flow is presented in this paper. Though this centrifugal compressor has been designed with the conventional approach, the operating zone of this compressor has been stretched to its limits. Mean-line design of the centrifugal compressor was carried out and the meridional flow path with the annulus dimensions were arrived at. Three dimensional design of the compressor was carried out for speed of 40,000 rpm, pressure ratio of 4.0 and mass flow of 5.45 kg/s. The compressor consisted of an impeller with 19 blades and a diffuser with 35 vanes. Detailed 3D stage CFD analysis was carried out and the performance characteristics at design and off-design speeds were obtained. Details of the aerodynamic design, 3D CFD analysis and the performance maps of the compressor are presented here. Though the compressor was designed for operating at its limits, it seemed to deliver the required pressure ratio at the desired mass flow with a decent stall margin at the design speed. Efficiency at the design condition was on the lower side at 76%.

Keywords: Centrifugal compressor, diffuser, impeller, lean, pressure ratio, stall margin, sweep.

INTRODUCTION Centrifugal compressors have existed for over 100 years and have been widely used in gas turbine engines, turbochargers, turbo-expanders, refrigeration, gas compression systems and other industrial applications. The extensive use of centrifugal compressor in the gas turbine engine and industry has drawn consistent attention to improve its performance over the years. A typical centrifugal compressor used in the HP spool or the gas generator of a turbofan engine [1] is shown in the Fig.1. Though centrifugal compressors are heavy and occupy larger frontal area, many small gas turbine engines use them as the source for building pressure ratio mainly due to their wide stable operating range and better tolerance against foreign object damage. Another major disadvantage is; multi-staging of centrifugal compressor is not preferred due to the inherent loses associated with it as discussed in [2] and [3].

In a centrifugal compressor stage, impeller and diffuser both play vital roles in building the pressure ratio and passing mass flow in an efficient manner. Hence, the geometric parameters contributing to the performance of individual components have

aR Senthil Kumaran.Email: rsk@nal.res.in

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been extensively analyzed and optimized over the years like by Krain [4].

Figure 1: Cross-section of a turbofan engine [1].

Detailed investigations have been made to optimize the impeller performance by using splitters, 3D blade profiling, sweep, lean, blade tip skewness, inverse blade design etc. Pampreen [5] investigated the effect of splitter blades on aerodynamic loading and reported that impeller with splitter reduces the aerodynamic loading and also the size of the impeller. A 3D inverse design, based on specified circulation method, with splitter and full impeller blade was carried out by Zangeneh [6]. Significant improvement in the flow physics was observed compared to the conventional impeller. Influence of splitter blades on the velocity and pressure field in a hydraulic centrifugal pump was investigated by the Kergourlay et al [7]. They found that, addition of splitter blades helped to rise the head due to increased slip factor however efficiency was lower due to more hydrodynamic loses. Nakagawa et al [8] carried out experimental investigation of a tandem centrifugal compressor to improve HCFC123 refrigerant compression performance. It was reported that the performance of the machine significantly improved in terms of volume flow rate and efficiency. A detailed experimental and numerical study of a tandem bladed impeller was carried out by Danish [9] et al. Enhancement in surge margin was noticed to the tune of 25%. It was also proposed to use thinner blades for further improvement in the performance. Ariga et al [10] analyzed the effect of impeller blade exit rake angle on the leakage through shroud side clearance. This analysis revealed improved performance at an appropriate rake angle at low mass flow range and reduction in the leakage through the shroud side clearance. Flow physics of a backward curved aerofoil was numerically simulated by Huang et al [11]. It was reported that flow was more stable with this kind of aerofoil and the efficiency improved significantly. Ganesh et al [12] carried out numerical analysis to study the effect of LE sweep (-25° to +20°) on the performance of a back swept impeller. It was

noticed that, 20o LE sweep offered higher stall margin, acceptable peak pressure ratio and increased efficiency. Several researchers investigated the impeller diffuser interactions. Schreier [13] experimentally studied the flow in a vanless diffuser. Analysis was based on simplified assumptions that the flow was inviscid, incompressible and 2D. However, the analysis was good enough to find the expression for the pressure, velocity and thrust on the diffuser due to the flow. Jansen [14] analyzed the theoretical and experimental aspects of the unsteady flow in a radial vaneless diffuser under specifically self-excited oscillations of large amplitudes. It was proposed that, unsteady waves in the flow aroused due to the interaction of 3D boundary layer and free stream near the side wall. Unsteady flow of this kind can be linked to unstable operation of centrifugal pump, blower and compressor. Johnston et al. [15] developed two simple methods for predicting the losses in vaneless diffuser of centrifugal compressor: (1) One-dimensional, axisymmetric frictional loss and (2) sudden-expansion mixing to account for losses in the diffuser caused by wakes of separated flows from impeller. This study also demonstrated the utility of these methods in the design process. The flow field development in a splitter bladed impeller coupled with vaned and vaneless diffuser was investigated by Krain [16] using advanced laser velocimetry. Similar internal flow patterns for both the diffusers were observed. But, flow at the entrance of vaned diffuser was periodically fluctuating. Simulations of a single row and stage centrifugal compressor were conducted by Sato et al [17] using a 3D thin layer Navier-Stokes solver. This study illustrated the effect of tip leakage flow on the overall impeller flow field. They also reported that impeller downstream flow conditions influenced the overall performance considerably. Ljevar et al [18] performed numerical analysis of vaneless diffuser core flow instability to understand the rotating stall mechanism. Their analysis revealed that the instability was strongly influenced by diffuser geometry as well as inlet and outlet conditions.

In the present study, a centrifugal compressor stage is designed for high pressure ratio of 4 and high mass flow rate of 5.45 kg/s to work at its extreme limit in terms of specific speed and diameter. While this imposes serious geometrical and flow constraints, reasonable performance is desired nevertheless. Based on the specific speed and diameter plotted on the Cordier diagram shown in Fig.2, compressor design falls in the region of mixed flow type machine which would offer a slightly lower stall margin. But centrifugal compressor is a more robust machine capable of delivering high pressure ratio per stage with wider stall margin. Hence, a centrifugal type design is attempted here. This study also helps in understanding if other performance parameters suffer due the machine type selected.

COMPRESSOR DESIGN PARAMETERS

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The design specifications are well justified by the general functional relationship among N, Z, β1 and Mrel.. The present compressor design is for high mass flow of 5.45 kg/s, high pressure ratio of 4 and rotational speed of 40,000 rpm. The compressor is designed for the ISA SLS condition of P0 = 101.325 kPa and T0 = 288 K. A conservative efficiency level of 80% is targeted for the design. The specific speed and specific diameter of the centrifugal compressor are calculated as shown below:

H ad=γ

(γ−1)R T1[( Po 2

Po 1 )γ−1

γ −1](1)

Had = 155500 m

Q=mρ

(2)

Q = 4.56 m3/s

N s=N √Q

( g Had ) (3)

Ns = 1.015

Ds=N (g H ad)

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√Q(4)

Ds = 3.85

In order to ensure the feasibility of the above specifications, it was analytically compared with correlations available in the literature for mass flow coefficient (ϕ), pressure coefficient (µ0) and work coefficient (µy) as defined below:

Flow coefficient ϕ= mρ01 D2

2U2 (5)

Pressure coefficient μy=C pT 01(π

γ−1γ −1)

U 22

(6)

Work coefficient μ0=C p(T 02−T01)

U 22 (7)

Under the given input conditions, the value of the flow coefficient and pressure coefficient obtained are 0.55 and 0.61, which is well within the range for this kind of compressor.

Another important criterion in the centrifugal compressor design is the slip factor which is considered to be around 0.9 and is given as:

σ=1−0.63 πn

(8)

¿ = 3.1416, n = 19)Specific speed (Ns) and specific diameter Ds of the impeller calculated around 1.015 and 3.85 which is plotted in the Cordier diagram shown in Fig 2. Although the position of the point for the current application falls slightly in the mixed flow zone, a good centrifugal machine can be designed with better stall margin.

Figure 2: Cordier diagram.

This is an aggressive design as the centrifugal compressor operates at its extreme limits in terms of speed, pressure ratio, mass flow and power absorption with severe geometrical constraints. The compressor design parameters are given in Table.1. Initially a mean line design was carried out to fix the basic flow, performance and geometrical parameters. The mean-line parameters of the impeller and diffuser are given in Table.2.

Table 1: Compressor design parameters

Inlet total pressure (Po1) (kPa) 101.325

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Inlet total temperature (To1) (K) 288

Pressure ratio (π) 4.0

Mass flow rate (m) (kg/s) 5.45

Power required (P) (kw) 1162.5

Efficiency ηt-t 80%

Rotational speed (N) (rpm) 40,000

Stage diameter (D) (mm) 310

Hub to Tip Ratio 0.38

Rotor Tip Clearance 0.5 mm

Stage exit Mach number (M2) 0.55

Stage exit angle (αex) 25o

Flow coefficient (ϕ) 0.4

Work coefficient (μy) 0.7

Table 2: Summary of the mean-line parameters

Parameter Impeller Diffuser

Inlet Mach number (Mrel) 0.91 0.97

Inlet absolute angle α1 9.2o 66.6o

Inlet relative angle β1 -50.7o -

Inlet Blade speed (U1) (m/s) 356 -

Exit Mach number (Mrel,ex) 0.65 0.55

Exit absolute angle α2 73.6o 54.1o

Exit relative angle β2 -50.5o -

Exit Blade speed (U2) (m/s) 523 -

Pressure recovery

coefficient (Cp)

- 0.2

Specific speed (Ns) 1.01 -

Figure 3: Meridional view of the plow path

Subsequently detailed three dimensional blading of the impeller (with sweep & lean) and the diffuser was carried out. Meridional view of the flow path is shown in the Fig.3. The Compressor stage consisted of 19 impeller blades with 30o back sweep and a diffuser with 35 vanes. 3D CAD models of the impeller and diffuser are shown in Fig.4.

Figure 4: 3D CAD Model of the impeller and diffuser

3D CFD ANALYSIS

3D computational domain of the compressor stage was modelled for a single blade channel flow passage with tip clearance. A multi-block structured O-H type mesh was created with hexahedral cells in the computational domain. The mesh was created to cater for Y+ <10. Pressure inlet and pressure outlet boundary conditions were imposed at the inlet and outlet of the stage domain respectively. The hub, shroud and blade surfaces were set as no slip wall. The sides were set as periodic and a mixing plane was imposed at the rotor-stator interface which circumferentially averages the flow parameters at the

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interface. The computational domain with different boundary conditions are shown in the Fig.5.

Figure 5: Computational domain with boundary conditions.

The multi-block structured grid developed is shown in Fig.6 and the Y+ contour is shown in the Fig.7.

Figure 6: Grid generated on impeller and diffuser surfaces (fluid domain is hidden).

Figure 7: Y+ contour across the stage

CFD analysis was carried out using a commercial finite volume and pressure based RANS solver. SST k-ω turbulence model without transition was used for modelling the turbulence parameters. Inlet total pressure and temperature were mentioned; flow direction was set as axial entry. 5% free stream turbulence intensity was imposed at the inlet with 1% of the impeller chord as the length scale and exit static pressure was mentioned. The details of numerical analysis are given in Table.3.

Table 3: Details of numerical analysis

Inlet Total pressure, total temperature

Outlet Static pressureSolver Pressure based RANS

Turbulence model SST-K-ωTurbulence intensity 5%

Y+ <10Analysis type Steady

Grid size 1.8 millionGrid topology O-H-Type

Reference pressure 0

In order to ensure the reliability of the computational results, grid independence analysis was carried out with the grid size of

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0.9, 1.8 and 2.4 million. Total pressure profile across the mean line of the compressor stage is shown for the three grids in Fig.8.

Figure 8: Total pressure profile across the mean line of the compressor stage

The gross mass flow and efficiency of the compressor obtained from the simulations using the three grids are given in Table.4. As observed in Fig.8 and Table.4 the results of the 1.8 and 2.4 million grids remained the same, the 1.8 million grid was used for all further computations.

Table 4: Grid independence study

Grid size (Million)

Mass flow(kg/s)

Efficiency

0.9 5.47 75.82

1.8 5.45 75.64

2.4 5.45 75.63

For the computations, a RMS of residuals of 1e-6 is specified as convergence criteria for the mass, momentum, energy and the turbulence quantities. The simulation is taken as converged when the mass flow imbalance (between inlet and outlet) vanishes and RMS value of residuals reach 1e-6. Through CFD analysis compressor performance map in terms of pressure ratio and efficiency are generated at design as well as off-design conditions. The flow field across the full compressor stage is investigated using the Mach number contours.

RESULTS AND DISCUSSION

The relative Mach number contours of the compressor stage at hub (10% span away from hub), mean and tip (10% span away from tip) sections are shown in Figs.9a, 9b and 9c respectively. Clean flow pattern can be observed near the hub surface. As the blade speed and fluid velocity increase radially, a shock wave can be seen forming near the leading edge of the impeller blade at the mean section. This shock further grows strong near the tip region due to increased blade speed and fluid velocity in the radial direction. Stronger shock will cause higher losses and drop in efficiency. A clear low velocity zone arising due to tip clearance flow can be seen close to the trailing edge of the tip section. The effect of tip clearance flow near the trailing edge can also be felt at the mean section as the blade span is very less near the trailing edge.

(a) Hub section

(b) Mean section

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(c) Tip sectionFigure 9: Relative Mach number contour across the

compressor stage

The compressor performance maps of total pressure ratio and efficiency at the design speed are plotted in Figs.10 and 11 respectively. The design pressure ratio of 4 can be attained at the design speed at mass flow of 5.45 kg/s as marked and shown in Fig.10. Mass flow of 5.15 kg/s is a near stall point and 5.7 kg/s is the choke limit of the compressor. Compressor may actually stall at mass flows lesser than 5.15 kg/s but computations could not be made in that zone as the solutions diverged.

Stall margin of the compressor is calculated as shown below:

SM=¿(9)

A stall margin of 18.52% could be achieved at 100% speed which is quite decent for this kind of a design.

Figure 10: Pressure ratio Vs mass flow at design speed.

Figure 11: Efficiency Vs mass flow at design speed.

Efficiency of the compressor is calculated as shown below:

η=( T1

∆ T [( P2

P1)

γ−1γ −1])×100(10)

Efficiency of 76% could be achieved at the design point (design speed and mass flow rate) as shown in Fig.11. The efficiency will definitely be on the lower side given that the compressor is designed to operate at extreme limits and geometric constraints.

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It is because of the high blade and fluid velocities that the shocks and associated losses are profound as seen in this compressor.

Pressure ratio (P02/P01) and efficiency for different speed parameter (N/√T01) are plotted w.r.t mass flow parameter (m√T01/P01) in Figs.12 and 13 respectively.

Figure 12: Pressure ratio Vs mass flow parameter.

Figure 13: Efficiency Vs mass flow parameter.

It can be seen from Figs.12 and 13 that between 80 to 100% speeds, the compressor is exhibiting good performance

characteristics. For this kind of compressor working at its limit, 110% speed corresponding to 44,000 rpm is very high. Hence the tip speed and fluid velocities would be high contributing to massive shock losses and very low peak efficiency of 70%.

Stall margin is plotted w.r.t different speeds of the compressor in Fig.14.

Figure 14: Stall margin at different speeds.

It can be observed that maximum stall margin of 18.52% is available at the design speed and reasonably good stall margin is available at other speeds investigated. This feature definitely lies in favor of the centrifugal compressor to be selected for this operating condition.

CONCLUSIONS

A single stage centrifugal compressor was designed for mass flow rate of 5.45 kg/s and pressure ratio of 4.0 at speed of 40,000 rpm. The specific speed and diameter suggested that this compressor would operate at its extreme limits under severe geometrical and flow constraints. Though a mixed flow compressor would have been a better option in terms of mass flow, pressure ratio and efficiency, a centrifugal design was attempted to gauge the overall performance and to take advantage of the stall margin. Detailed 3D CFD analysis was carried out from choke to stall point to study the flow physics in the compressor. Computational analysis confirmed that, the designed compressor stage met the basic requirements of mass flow and pressure ratio at the design point. Very reasonable stall margin of 18.52% was predicted at the design speed from the

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analysis. However, strong shocks were observed near the impeller tip region due to high blade speed and fluid velocity. Due to the shock and stringent operating conditions, efficiency of the compressor was found to be on the lower side of the order of 76% against the targeted value of 80%. CFD analysis at off-design speeds of 80% and 90% revealed good overall performance. However, at 110% speed the efficiency dropped to a very low value of 70% due to high blade and fluid velocities which led to severe shock losses.

ACKNOWLEDGEMENTS

The authors thank Director CSIR-NAL, for permitting to carry out this work and for allowing it to be published. Authors are grateful to Head & Joint Head Propulsion Division for their encouragement. Authors express sincere gratitude to the other members of the project team for their support while doing this work.

NOMENCLATURE

Symbols

M - Mach Number π, PR - Pressure ratio α - Absolute flow angle β - Relative flow angle φ - Flow coefficientσ - Slip factorμy - Pressure coefficient for impeller μo - Work coefficient for impeller Cp - Specific heat at constant pressure /

pressure recovery coefficient Had - Pressure headg - Acceleration due to gravity U - Blade speed ρ - Density T - Temperature P - Pressure / Power R - Gas constant m - Mass flow rate R - Radius D - Diameter Z - Axial distanceQ - Volume flow rateɳ - Efficiency γ - Ratio of specific heats n - Number of blades N - Rotational speedY+ - Dimensionless wall distance

Abbreviations

CSIR - Council of Scientific and Industrial ResearchNAL - National Aerospace LaboratoriesISA - International Standard AtmosphereSLS - Sea Level StaticSM - Stall MarginCFD - Computational Fluid Dynamics. RANS - Reynolds Averaged Navier StokesRMS - Root Mean Square rpm - Revolutions Per Minute DP - Design Point

Super and Sub scripts

0 - Total 1 - Inlet station 2 - Exit station d - Designs - Specific / Stall h - hub rel - Relativeref - Referencet-t - Total to Total

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