The Effect of Vane Number in Casing Treatment of an Axial-Flow Compressor

Abstract

Improvement of the operating range of compressors will help the power and energy plant to work more flexibly to integrate with other energy generation systems. The stall, rotating stall, and resulting surge are the most dominant limiting phenomenon in axial compressor operating envelop. Several active and passive methods have been employed to eliminate occurring of these phenomena and to extend compressors’ stable range. Among these, casing treatment is one of the most useful methods. This study aims to investigate the effect of the number of stationary blades on the performance and stall margin of an axial compressor through numerical simulation. Casing treatments in two different configurations of 33.3 and 53.5% of rotor blade tip exposure and with six different numbers of vanes, 30, 40, 60, 80, 90, and 120, are simulated with computational fluid dynamics in ANSYS software. The numerical simulation is validated with available experimental data. The results reveal that in a high rotor exposure configuration, the highest number of vanes provides the best performance for the compressor. However, in a low exposure configuration, the optimum number of the vanes, 90 for the 33.3% exposure, can be found with the proposed numerical procedure based on stall margin improvement.

32.1 Introduction

The sustainable supply of energy and electricity is still challenging and the development of efficient, flexible, and low-cost energy systems can contribute significantly to several social, industrial, and economical aspects in certain areas of the world [1]. The gas turbine is considered one of the main solutions to generate reliable power on land, sea and air. High flexibility and availability of the GTs regarding fuel type and short start-up time, respectively, have made them capable to combine with other energy sources to compensate for inherent intermittencies of renewable energy sources [2]. The stable operation range of axial flow compressors is limited by the onset of stall and surge instabilities. These phenomena occur due to the disturbances such as variation in rotor speed, change in upcoming flow angle and airfoil flow separation due to geometry anomaly. The challenge that compressor designers often deal with is finding solutions in order to prevent the occurrence of stall and surge phenomena. A variety of active and passive methods have been applied to extend the stable operating range. Using bleed valves, air injection systems and variable inlet guide vanes are the most common examples of active methods. Passive methods include using different types of casing treatments. One of the interesting approaches in the design of improving walls is the use of the concept of recirculation flow. In this approach, the mass flow resulting from the vortices of the tip leakage flow as well as the low-pressure region resulting from the flow separation on the rotor blade is directed into the empty space in the improving wall and injected into the flow upstream of a preceding rotor blade row. Gourdain and Leboeuf [3] performed a numerical investigation of a casing treatment with non-axisymmetric slots. The method showed a good ability to control the tip leakage flow but failed to reduce the boundary layer separation on the suction side. An increase in the operability range was observed but with a penalty in efficiency. Yang et al. [4] performed an unsteady numerical simulation to study the effect of multiple cylindrical holes casing treatment (MHCT) with pre-swirl blowing. Parametric studies of the total extraction holes area and their axial locations show that the compressor performance deteriorates as the area ratio increases but the stall margin is extended. He also concluded that there is an optimum extraction hole axial location for stall margin extending. Guinet et al. [5] carried out a numerical parametric study using the URANS method on a recirculating tip blowing casing treatment configuration (TBCT) to drive design rules. The wall treatment geometry consists of a recirculating channel with an air off-take above the rotor and an injection nozzle in front of the rotor. A variation of the geometry of the tip blowing, more specifically the nozzle aspect ratio, the axial position, or the tangential orientation of the injection port, was investigated. Kendall-Torry and Gümmer [6] presented the aerodynamic design of 3.5 stage axial compressor. The application and development of axial slot casing treatments (CT) into the smooth casing is performed, aimed at improving the local stage and overall stall margin with particular emphasis on avoiding efficiency penalties within stages. Ahmad et al. [7] designed two models of single groove casing treatment and tested them numerically to improve the performance and stable range of NASA rotor 37. Both models consisted of a single rectangular groove which was located from 10 to 90% of the axial chord. Their work showed that the single rectangular groove structure can enhance the stall margin but reduce the adiabatic efficiency. Chen et al. [8] proposed a coupled casing treatment (CCT), which was built with an injector, a bridge, a plenum chamber, and several slots for a recirculating loop. They carried out a parametric study on the slot axial location, skewed and lean angle and also number of slots and optimized the geometry parameters to enhance the stability of the compressor. The optimized CCT improves the compressor stability and efficiency under the design condition by 75.8% and 0.71%, respectively. Akhlaghi [9] investigated the effect geometric parameters in a casing treatment consists of a cavity with and 120 vanes skewed vanes which directed the recirculated flow toward the main flow. They studied the influences of rotor blade tip exposure and cavity path curve. Other geometric parameters such as vane profile and the number of vanes have not investigated in the introduced casing treatment so far. The objective of this work is to numerically investigate the effect of the vane numbers in the casing treatment wall with semi-circular flow path and recessed vanes in two values of rotor—casing treatment exposure. In the first step, he computational model of the research compressor has been developed and validated against experimental data from Akhlaghi [9]. In the second step, the casing treatment configuration for the vane numbers of 30, 40, 60, 80, 90 and 120 were modelled and applied on the compressor to find the optimum geometry in the rotor blade tip exposure of 33.3 and 53.3%.

32.2 Numerical Methodology

The first stage of a low-speed research compressor rig was used to study casing treatment geometric parameters. The flow path consists of a bellmouth entrance region, inlet guide vanes row, rotary blades row, stator vanes row, the outlet region and the casing treatment which is described in detail in Ref. [3]. The compressor characteristics are presented in Table 32.1. The computational domain has been constructed using a single passage of each blade row and the corresponding inlet and outlet region using rotational periodic boundary conditions as shown in Fig. 32.1.

Table 32.1 Characteristics of the compressor test rig

Fig. 32.1

Geometry modelling of compressor first stage with casing treatment

The CAD modelling of the inlet guide vane and stator vane has been performed using ANSYS BladeGen. The casing treatment is made up of an outer cover ring, a tubular passage inside and a set of curved vanes which are fixed on an inner ring. The configuration of the casing treatment and the dimensions of the tubular passage for two rotor tip exposure values is shown in Fig. 32.2.

Fig. 32.2

a Configuration of casing treatment with 80 vanes and 33.3% rotor exposure, b dimension of casing treatment tubular passage for 33.3% rotor exposure and c 53.5% rotor exposure

ANSYS TurboGrid is used to generate the mesh of inlet guide vane and rotor blade components. The computational grid for the rotor blade, bellmouth and outlet section are generated using the structured mesh method and for the casing treatment, the unstructured mesh method of ANSYS ICEM is applied. As shown in Fig. 32.3a casing treatment recessed vanes direct the recirculated flow toward the upstream main flow to preserve appropriate mixing conditions. In order to model the interference region, a part of the computational domain of the rotor passage is removed and this volume is added to the casing treatment computational domain (Fig. 32.3b). The blocking strategy and the mesh created for the rotor are presented in Fig. 32.3c.

Fig. 32.3

a Rotor and casing treatment positioning, b CAD modelling of rotor and casing treatment, c rotor blocking and meshing strategy

Mesh independence study has been performed for the integrated CFD domain. The result which is presented in Table 32.2 shows that for the 2.5 million elements or more, the solution is dependent on the number of meshes.

Table 32.2 Result of mesh independency study

The numerical solution of the flow has been done using the Reynolds-Averaged Navier–Stokes equations via $SST\,k - \omega$ turbulence model. In order to serve the requirements of the selected turbulence model, the setting of the boundary layer mesh has been tuned to reach the $y^{ + } < 1$ which results in the value of $3 \times 10^{ - 6}$ for the first node height from the wall. To consider the effects of compressibility and temperature changes along the compressor, the energy equation is also solved along with the RANS equations.

Since the inlet flow of the compressor is at subsonic speed, the total pressure and total temperature profiles are considered as the inlet boundary conditions. The turbulence intensity of the flow at the inlet of the current model, which is considered a low-pressure compressor, is 2% and the turbulence viscosity coefficient is 10. The boundary condition at the compressor outlet at lower pressure ratios is considered to be the static pressure, but as the compressor pressure ratio increases and the compressor approaches the stall starting point, the mass flow rate is used as the outlet boundary condition. The adiabatic temperature and no-slip condition are used for all rotary and stationary walls. As mentioned earlier, the rotational periodic boundary condition for a single passage has been used to simulate a full annular blade row. The frozen rotor model is used in the interfaces of IGV to the rotor, rotor to the stator and casing treatment to the rotor to simulate the changes in the coordinate system, the connection of two areas with non-homogeneous grids and the change in the flow scale between the two areas. The general connection interface model is used for the inlet to IGV and stator to outlet interfaces. The characteristics maps of the compressor are presented in the form of the total to total pressure ratio and isentropic efficiency against corrected mass flow rate which are defined in Eqs. (32.1), (32.2) and (32.3), respectively.

$$ PR_{stage} = P_{03} /P_{01} $$

(32.1)

$$ \eta_{{t - t\left( {isentropic} \right)}} = \left( {h_{03ss} - h_{01} } \right)/\left( {h_{03} - h_{01} } \right) $$

(32.2)

$$ \dot{m}_{{corrected}} = {{\left( {\dot{m}\sqrt {\frac{{T_{{amb}} }}{{T_{{std}} }}} } \right)} \mathord{\left/ {\vphantom {{\left( {\dot{m}\sqrt {\frac{{T_{{amb}} }}{{T_{{std}} }}} } \right)} {\left( {\frac{{P_{{amb}} }}{{P_{{std}} }}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\frac{{P_{{amb}} }}{{P_{{std}} }}} \right)}} $$

(32.3)

The performance Enhancement due to applying different casing treatment configurations is compared using Stall Margin Improvement parameters (SMI) for pressure ratio and corrected mass flow rate which quantifies the amount of increment in the operating range (Eqs. 32.4 and 32.5) and the penalty in efficiency (Eq. 32.6).

$$ SMI_{{\dot{m}_{corrected} }} = \frac{{\left( {\dot{m}_{corrected} } \right)_{SC} - \left( {\dot{m}_{corrected} } \right)_{TC} }}{{\left( {\dot{m}_{corrected} } \right)_{SC} }} $$

(32.4)

$$ SMI_{PR} = \frac{{\left( {PR} \right)_{SC} - \left( {PR} \right)_{TC} }}{{\left( {PR} \right)_{SC} }} $$

(32.5)

$$ \Delta \eta = \eta_{peak - CT} - \eta_{peak - NC} $$

(32.6)

32.3 CFD Validation

Compressor characteristics for the 33.3% rotor blade tip exposure and 120 CT vanes have been compared against experimental data of the same model from [9] (Fig. 32.4a, b). The conducted simulations predict the corrected mass flow rate at the point corresponding to the beginning of stall phenomena and at the maximum opening of the discharge valve with an error of 5.17% and 4.95% respectively. The error of total to total pressure ratio at these operating points is predicted 6.6% and 7.8% respectively. The trend of the pressure ratio graphs obtained from the numerical solution is completely consistent with the experimental results and both the total to total and total to statics show a lower value than the experimental data. Figure 32.4b shows the experimental data for the total to total and total to static efficiency and the corresponding numerical simulation. The behaviour of the graphs obtained from the numerical solution is in good agreement with experimental data. The total to total efficiency predicted by numerical simulation, in arbitrarily modified mass flow, shows a higher value and the total to static efficiency shows a lower value than the experimental data. The comparison with experimental results demonstrates the validity of the simulation in the prediction of trends and less than 10% error in stall initiation mass flow rate.

Fig. 32.4

Comparison of numerical simulation with experimental data for casing treatment with 120 vanes and 33.3% rotor exposure a $P_{03} /P_{01}$, b $\eta_{iso}$ versus $\dot{m}_{c}$

32.4 Results and Discussion

The streamlines through the compressor model are shown in Fig. 32.5. The low energy fluid flow of the blade tip has been sucked into the casing treatment cavity and replaced by the high energy fluid of the lower span which results in an improvement in the rotor performance.

Fig. 32.5

Streamlines of the compressor model with casing treatment—33.3% rotor exposure

The results obtained from the numerical simulation of the casing treatment with the rotor blade tip exposure of 33.3% are presented in Table 32.3. The results show that there is no clear upward or downward trend between the number of blades and the compressor performance improvement. The best performance is for the casing treatment with 120 blades.

Table 32.3 Characteristics of 33.3% rotor exposure casing treatment

Figure 32.6 shows the graphs of the total to total efficiency and total-to-total pressure ratio for 33.3% rotor blade tip exposure and the number of 120, 90, 80, 60, 40 and 30 CT vanes, respectively. For higher mass flow rates, close to the maximum opening of the discharge valve, both graphs have similar behaviours and values with insignificant differences, while with the decrease of the mass flow rate and approaching the conditions of the stall initiation point, the effect of the casing treatment on the compressor performance is increased and the number of different blades shows different behaviours. Despite no casing treatment case, in the compressor with casing treatment, graphs of pressure ratio in Fig. 32.6a have an extremum which means the maximum pressure ratio occurs in the mass flow rates greater than the mass flow rate of the stall initiation point.

Fig. 32.6

Comparison of a $P_{03} /P_{01}$, b $\eta_{t - t,iso}$ for casing treatment with 120, 90, 80, 60, 40, 30 vanes and 33.3% rotor exposure

The results obtained from the numerical solution of the casing treatment with 53.5% rotor blade tip exposure are presented in Table 32.4. As with the casing treatment with 33.3% rotor blade tip exposure, there is no clear upward or downward trend between the number of blades and improvement in compressor performance. The best performance is for the casing treatment with 90 blades.

Table 32.4 Values of stall margin improvement for casing treatment with 53.5% rotor exposure

Figure 32.7 shows the graphs of the total to total pressure ratio and total to total efficiency for the number of 120, 90, 80, 60, 40 and 30 casing treatment vanes. As the rotor blade tip exposure increases, the effect of change in the number of casing treatments vanes on the stall margin improvement becomes more distinct. Unlike the pressure ratio graphs for the casing treatment with 33.3% rotor blade tip exposure, for the value of 53.3% exposure, the maximum pressure ratio occurred at the stall beginning point. The diagram of the total to total efficiency, as in the previous case, has an extremum in the mass flow rates close to the maximum opening of the discharge valve (Fig. 32.7b).

Fig. 32.7

Comparison of a $P_{03} /P_{01}$, b $\eta_{t - t,iso}$ for casing treatment with 120, 90, 80, 60, 40, 30 vanes and 53.5% rotor exposure

32.5 Conclusion

A numerical model has been developed to simulate the performance of a low-speed axial compressor stage with different casing treatment configurations. CFD model using RANS equation and $SST\,k - \omega$ turbulence model has been validated using existing experimental data of the same compressor for the casing treatment with 120 vanes and 33.3% rotor blade tip exposure. The effect of the number of vanes in two values of rotor blade tip exposure has been investigated. Numerical results of casing treatment with vane numbers of 30, 40, 60, 80, 90, 120 and 33.3% rotor blade tip exposure show that there is no clear relation between vane numbers and improvement in performance characteristics and casing treatment with 120 number of vanes has the best performance. For the casing treatment with 53.3% rotor blade tip exposure, and 30, 40, 60, 80, 90 and 120 number of vanes, the variations in compressor map due to applying casing treatment are more distinct and the casing configuration with 90 number of vanes has the best results in stall margin improvement. This simulation procedure and treatment technique make it possible to design an optimum geometry for a more stable compressor that can work in a wider operating range.