1 Introduction

MGT engines are extensively used in both civilian and military applications. Military applications include Unmanned Aerial Vehicles (UAVs), long-range Stand-off Weapons (SOWs) and target drones. Produced thrust values vary between 50 and 800 N. Due to ease of manufacturing, economic restrictions and higher per stage pressure ratio requirements inherent to MGT engine applications, single-stage centrifugal compressors are traditionally preferred [1]. Radial compressors do, however, deliver lower mass flow rates when compared to similar sized axial compressors [2]. Mixed flow compressor configurations provide a hybrid solution, being able to pass higher mass flow rates, while still producing high single-stage pressure ratios [3]. An added advantage of the mixed flow design is a reduced frontal engine area, which contributes to a reduced platform total drag value with associated performance increases [4].

In an ideal scenario, air will leave the impeller blade along the blade exit angle (\(\beta_{2}\)—defined from vertical, see Fig. 1). Due to the relative circulation in the blade passage and pressure differences between the suction and pressure side of the impeller blade, the flow leaves the impeller along a relative velocity exit angle (\(\beta_{2}^{\prime }\)) such that \(\beta_{2}\) < \(\beta_{2}^{\prime }\). This phenomenon is defined as slip, which manifests itself in a reduced outlet tangential velocity component (\(C_{U2}\)) by a magnitude of \(\Delta C_{U2}\). Slip has a considerable influence on the impeller exit flow conditions and consequently also on the total compressor performance. In mixed flow impellers, slip decreases when the meridional exit angle (\(\alpha_{C2}\)—see Fig. 1) is reduced. This is attributed to the reduction in the Coriolis force [5]. An advantage of a mixed flow configuration, therefore, is that the reduction in slip has the effect that \(C_{U2}\) increases relative to a pure radial exit flow case. Assuming a constant rotational velocity and radial exit velocity, the effect is a higher impeller exit velocity. This, in conjunction with the increased axial velocity component inherent to a mixed flow configuration, increases the mass flow capacity of a mixed flow design. Higher associated thrust levels are, therefore, possible [6].

Fig. 1
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Impeller Blade Exit Angle (β2) and Impeller Meridional Exit Angle (αC2) Definition

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MGT compressor performance is largely dictated by diffuser performance. The limited space afforded to the diffuser section in a radial and mixed flow MGT engine, necessitates the use of a vaned diffuser section. A crossover diffuser is particularly well suited for this function, due to superior performance compared to similar vaneless and legacy type diffusers [7]. This is especially true when geometric restrictions are enforced. Additionally, crossover diffusers gradually re-align the flow towards the axial direction enroute to the combustor. Consequently, the requirement for an additional de-swirler section is eliminated. A disadvantage of a crossover diffuser is limited operating range, with both the onset of stall and choke typically occurring in the vaned diffuser section of the compressor stage.

The operating range of a compressor is defined as the mass flow range between the stall and choke points at operating speed. This is an important parameter, especially in airborne platforms, since engine intake conditions can vary dramatically in a dynamic environment. These sudden disturbances in intake airflow can lead to sudden mass flow changes at a specific engine speed. A compressor with a limited operating range could therefore easily encounter stall or choke conditions during such dynamic flight conditions. A wider operating range is, therefore, an important design requirement for MGT engines. Compressor operating range is quantified by means of choke margin (\(CM\)) and stall margin (\({{SM}}\)):

$${\text{CM}}\, = \,\frac{{\dot{m}_{c} - \dot{m}_{o} }}{{\dot{m}_{o} }},$$
(1)
$${\text{SM}} = \frac{{\dot{m}_{o} - \dot{m}_{s} }}{{\dot{m}_{o} }},$$
(2)

where, \(\dot{m}_{c}\) Mass flow rate at choke point. \(\dot{m}_{s}\) Mass flow rate at stall point. \(\dot{m}_{o}\) Mass flow rate at design (operating) point.

Impeller blade tip clearance is defined as the shortest distance between the rotating impeller blade tip and the stationary shroud casing. In a rotating impeller, the pressure difference that exists between the suction and pressure side of the impeller blade creates a blade tip vortex, due to the presence of the blade tip clearance. This 3D vortex flow is not aligned with the mean flow direction in the impeller, and the mixing leads to losses in the compressor [8]. These losses are primarily a function of the size of the blade tip clearance gap. Murray [8] found that a 1% increase in tip clearance approximately resulted in a 1% reduction in efficiency for a compressor stage fitted with a vaneless diffuser.

Ramesh Rajakumar et al. [9] studied the effect of impeller blade tip clearance on the performance of a mixed flow impeller. They found that the impeller performance (pressure ratio and efficiency) reduced approximately linearly with an increasing tip gap. They also found that the impeller tip clearance did not have a significant impact on the impeller blade loading. Ramesh Rajakumar et al. [10] explored the effect of a constant impeller tip clearance gap versus a varying tip clearance gap on the performance of a mixed flow compressor. For the latter case, the tip clearance gap (between blade tip and shroud casing) was increased from impeller inlet to outlet. They found that the constant tip clearance provided better performance results compared to the varying tip gap configuration.

Shum et al. [11] conducted a study on impeller-diffuser interaction in a centrifugal compressor. They found that the most influential aspect leading to unsteady impeller-diffuser interaction was the impeller tip clearance leakage flow. A change in impeller tip clearance induces a change in three different impeller exit flow parameters, namely slip, blockage and viscous losses.

The effect of impeller tip clearance on the performance of a mixed flow compressor equipped with a crossover diffuser is numerically evaluated in this study. Three compressor performance aspects are evaluated, namely design point performance (total-to-total pressure ratio and efficiency), choke margin and stall margin. These evaluations are conducted by designing three baseline test compressors. The impeller tip clearance of each are modified and the resultant performance are compared to the baseline test compressors.

2 Baseline Test Compressor Design and CFD Validation

The evaluation methodology used in this study entails the design of three baseline test compressors (Comp1, Comp2, and Comp3) covering a range of design mass flow rates, velocities, and mixed flow angles. The three test compressors are designed using the 1D App as developed by Van Eck et al. [12, 13]. The design process followed are described in Van Eck et al. [12, 13]. A logical set of rotational speeds, mass flow rates and meridional exit angles are selected for the test compressors (see Table 1). The impeller compressor diameter for all three test compressors is selected such that the impeller exit Mach number does not exceed M0.92 at design point. This also ensures numeric stability of the 1D App, which is also used to perform the preliminary performance prediction results of the three baseline compressors. The three baseline test compressors feature a splitter bladed impeller and single vane crossover diffuser. Comp1 and Comp2 are designed with an impeller blade thickness of 2 mm and 1.5 mm at the hub and shroud, respectively. In the case of Comp3, the impeller blade thickness is 1.5 mm and 1 mm at the hub and shroud, respectively. For this study, the impeller tip clearance is modified for each of the test compressors. The modified compressor performance results are numerically analyzed and compared to the baseline configurations. For each design, the 1D App produces a compressor geometry text file for export to Numeca/FINE™ Turbo computational fluid dynamics (CFD) software, which is used to verify all performance results.

Table 1 Test compressor basic design parameters
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Meridional views and 3D schematics of the three test compressors are provided in Figs. 2 and 3.

Fig. 2
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Test Compressor Meridional Views—a Comp1 b Comp2 c Comp3

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Fig. 3
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Test Compressor 3D Schematics—a Comp1 b Comp2 c Comp3

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CFD mesh creation is performed using NUMECA AutoGrid5™. AutoGrid5™ creates meshes in three grid levels (000, 111 and 222) of increasing coarseness. This allows the flow solver (FINE Turbo™) to commence a simulation at a courser grid level, using the result as an initial solution for the next finer grid level, increasing initial robustness. It also allows the user to select the maximum required grid level for a flow simulation, which has a major impact on simulation time and computer resources. For the purpose of the current study, the 111 grid level is selected as the grid level of choice for all of the flow simulations conducted. To ensure satisfactory accuracy of the 111 grid level, a mesh independence check is conducted on Comp3. These include conducting a simulation on both the 111 and 000 grid level and comparing performance results and y+ values. For Comp3, two configurations are evaluated. These include the baseline configuration, designed with an impeller tip clearance of 0.3 mm, as well as a 0.1 mm impeller tip clearance configuration. No difference in stall prediction is observed between the fine and medium grid. Minor differences in design point (DP) performance (total-to-total efficiency \(\left( {{\text{DP}}\left( {\Delta \eta_{{{\text{TT}},1 - 4}} } \right)} \right)\) and pressure ratio (DP \(\left( {{\text{DP}}\left( {\Delta {\text{PR}}_{{{\text{TT}},1 - 4}} } \right)} \right)\) and choke mass flow rate \(\left( {\Delta \dot{m}_{{{\text{choke}}}} } \right)\) are observed. These are summarized in Tables 2 and 3.

Table 2 Medium (111) vs fine (000) mesh comparison—Comp3-0.3 mm
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Table 3 Medium (111) vs fine (000) mesh comparison—Comp3-0.1 mm
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For the purpose of this study, the minor differences encountered between the medium and fine mesh is deemed insignificant if weighed against the substantial (up to 8 times longer) additional computational time required for conducting a fine mesh simulation. The use of the medium grid level is further justified when comparing the y+ values of the medium and fine mesh. For both the medium and fine grid levels, the y+ values are found to be below the maximum recommended value of 10 as specified for the Spalart–Allmaras turbulence model. All generated meshes are imported into FINE™/Turbo for 3D flow simulation. The inlet boundary conditions are kept constant at standard atmospheric conditions, namely 101,325 Pa and 288 K. The various operating curve points are determined by altering the mass flow rate [in kg/s] as an outlet boundary condition. All other simulation flow settings are set as presented by Van Eck et al. [12, 13]. The Spalart–Allmaras turbulence model is used, as recommended by Numeca™ for centrifugal compressors. The model is a one-equation model and provides economical computations in boundary layers, especially for external aerodynamic scenarios where adverse pressure gradients are encountered [14].

To evaluate the effect of impeller tip clearance, it is varied for each of the three baseline test compressors. This is done during mesh creation (NUMECA Autogrid5™) to ensure that all other compressor design parameters remain unchanged. The baseline test compressors feature a design 0.3 mm impeller tip gap. In this evaluation, impeller tip gaps of 0.1 mm and 0.6 mm are additionally evaluated for each test compressor. The resulting performance curves for all three test compressors are provided in Figs. 4, 5, 6 below.

Fig. 4
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Impeller tip clearance performance comparison—Comp1

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Fig.5
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Impeller tip clearance performance comparison—Comp2

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Fig.6
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Impeller tip clearance performance comparison—Comp3

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From Figs. 4, 5, 6, it is immediately apparent that the 0.6 mm tip clearance configurations for both Comp2 and Comp3 reach a choked condition at a mass flow rate lower than the original design point mass flow rates of 0.5 kg/s and 0.2 kg/s, respectively. Therefore, for the purpose of this study, a comparative design point of 0.48 kg/s and 0.19 kg/s is chosen for Comp2 and Comp3, respectively. Detailed result discussions follow in the next sections.

3 Design Point Performance

A summary of the design point (DP) performance of Comp1, 2 and 3 for the various impeller tip clearances is provided in Table 4.

Table 4 Varying tip gap design point performance comparison
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As expected, design point performance (pressure ratio and efficiency) increases with a reduction in impeller tip clearance for all three baseline compressors (compare Figs. 4, 5, 6). To visualize this relationship, plots of design point pressure ratio vs impeller tip clearance for all three test compressors are provided in Fig. 7.

Fig. 7
figure 7

Effect of impeller tip clearance on pressure ratio

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From Fig. 7, it is evident that the design point pressure ratio for all three test compressors decreases approximately linearly with an increase in impeller tip clearance. This result compares well with the conclusion of Ramesh Rajakumar et al. [9]. An increase in impeller tip clearance leads to an increase in leakage losses [15]. The reduced performance is therefore attributed to the increase in losses. Leakage losses occur in the rotating impeller tip clearance gap (between the blade tips and shroud casing) due to spill-over from the pressure side to the suction side of the blade [15]. This pressure difference creates a blade tip vortex, which is not aligned with the mean flow in the impeller. This mixing flow leads to the impeller tip clearance losses [16] (see Fig. 8).

Fig. 8
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Comp1 Meridional Streamlines: Impeller Shroud Recirculation at DP—a 0.1 mm, b 0.3 mm, c 0.6 mm

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From Fig. 8, it is evident that the leakage flow manifests itself as two distinct recirculation zones. These recirculation zones appear inside the impeller section (midway, adjacent to shroud surface) and at the impeller outlet (shroud side of vaneless gap). It is observed that the size of the recirculation bubble at the impeller exit is not significantly affected by the variation in tip clearance at the design speed. The recirculation zone inside the impeller is however affected with an increase in tip clearance. Impeller tip clearance, therefore, has a significant influence on impeller performance, which directly affects compressor stage performance.

It is important to note that the observed recirculation inside the impeller is not actually a function of the magnitude of the tip clearance, but rather a function of the tip clearance relative to the impeller meridional width (shroud-to-hub distance). Therefore, a relative tip clearance value is more appropriate for use as reference. To this end, the impeller tip clearance ratio is defined as the ratio of the impeller tip clearance (\({s}_{CL}\)) relative to the impeller exit width (\(b_{2}\)):

$$TCR\left[ \% \right] = \frac{{s_{CL} }}{{b_{2} }} \times 100.$$
(3)

During the design of the test compressors, it was found that the 1D App provided satisfactory performance prediction results for compressors with an impeller tip clearance ratio of ~ 4%. It was found that the 1D App over-predicted the performance of compressors with a \(TCR > 4\%\) and under-predicted the performance of compressors with a \(TCR < 4\%\). In the 1D App, impeller tip clearance leakage losses is determined using the equation proposed by Aungier [15]:

$$\overline{\omega }_{{{\text{CL}}}} = \frac{{2\dot{m}_{{{\text{CL}}}} \Delta p_{{{\text{CL}}}} }}{{\dot{m}\overline{\rho }_{1} \overline{W}_{1}^{2} }},$$
(4)

where, \(\dot{m}_{{{\text{CL}}}}\) Blade clearance gap leakage mass flow. \(\Delta p_{{{\text{CL}}}}\) Average pressure difference across clearance gap. \(\dot{m}\) Mass flow rate. \(\overline{\rho }_{1}\) Impeller inlet mean density. \(\overline{W}_{1}\) Impeller inlet mean relative velocity.

Although Eq. 4 takes the impeller tip clearance value into account \(\left( {\dot{m}_{{{\text{CL}}}} = f\left( {s_{{{\text{CL}}}} } \right)} \right)\), it does not take the relative tip clearance into account. To cater for the \({\text{TCR}}\), an updated equation is proposed:

$$\overline{\omega }_{{{\text{CL}}}} = \frac{{2\dot{m}_{{{\text{CL}}}} \Delta p_{{{\text{CL}}}} }}{{\dot{m}\overline{\rho }_{1} \overline{W}_{1}^{2} }}F_{{{\text{TCR}}}} \frac{{s_{{{\text{CL}}}} }}{{b_{2} }}.$$
(5)

The updated formula for tip clearance leakage loss includes a constant (\(F_{{{\text{TCR}}}}\)) and the \({\text{TCR}}\). Values for \(F_{{{\text{TCR}}}}\) are evaluated at various \({\text{TCR}}\) s and the impeller performance prediction results of the 1D App are compared to the CFD results. Empirical results indicate that an approximate linear relationship exists between the factor \(F_{{{\text{TCR}}}} \frac{{s_{{{\text{CL}}}} }}{{b_{2} }}\) and the \({\text{TCR}}\) [%]. This implies that \(F_{{{\text{TCR}}}}\) is an approximate constant. Figure 9 below presents the test points of the three Comp1 modified configurations at 1.34%, 4.03% and 8.06% \({\text{TCR}}\).

Fig. 9
figure 9

Comp1 impeller leakage loss evaluation

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The analysis provides a nearly linear relationship between impeller tip clearance ratio and leakage losses. A value of \(F_{{{\text{TCR}}}} \approx 25\) is obtained. Equation 5 can therefore be written as:

$$\overline{\omega }_{{{\text{CL}}}} = \frac{{50\dot{m}_{{{\text{CL}}}} \Delta p_{{{\text{CL}}}} }}{{\dot{m}\overline{\rho }_{1} \overline{W}_{1}^{2} }}\frac{{s_{{{\text{CL}}}} }}{{b_{2} }}.$$
(6)

A similar linear behavior is observed for Comp 2 and Comp3 (see Fig. 10). The leakage loss discussed above is primarily attributed to the recirculation zone inside the impeller. Due to the similar behavior displayed by all three test compressors, the conclusion is made that the effect of impeller tip clearance on the impeller internal recirculation zone is not influenced by the impeller meridional exit angle.

Fig. 10
figure 10

Impeller leakage loss evaluation—a Comp2 b Comp3

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The effect of impeller tip clearance on the performance of a mixed flow compressor fitted with a crossover diffuser is evaluated. It is shown that the overall performance (compressor efficiency and pressure ratio) across the entire operating range increases with a decrease in impeller tip clearance, regardless of impeller meridional exit angle (mixed flow angle).

4 Choke Performance

From Figs. 4, 5, 6, it is evident that the impeller tip clearance has a marked influence on choke margin. The choke margin results for the various tip clearances for all three test compressors are provided in Table 5 below.

Table 5 Choke margin comparison
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To better understand the manifestation of choke at the various tip clearances, the flow fields in the impeller–diffuser interaction region (vaneless gap) is analyzed. As an example, a schematic of these meridional flow fields at choke mass flow rate for each tip clearance of Comp2 is provided in Fig. 11. A 3D schematic of the diffuser throat position is provided in Fig. 12.

Fig. 11
figure 11

Comp2 meridional streamlines and relative Mach number color chart: choke analysis—a 0.1 mm, b 0.3 mm, c 0.6 mm

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Fig. 12
figure 12

Choke position inside diffuser throat—Comp2 (0.3 mm)

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In all three cases presented in Fig. 11, the position of choke in the diffuser throat is clearly visible (see also Fig. 12). It is also evident that an increased impeller tip clearance results in a lower choke mass flow rate. This phenomenon is attributed to the size increase of the impeller exit recirculation zone (see Fig. 11). The recirculation zone settles at the shroud side of impeller exit, immediately downstream of the impeller tip clearance termination point. The shroud-to-hub extent of the recirculation zone is a function of the magnitude of the tip clearance. It is observed that the shroud-to-hub width of the recirculation zone increases from 0.1 mm to 0.6 mm tip clearance. The recirculation zone shroud-to-hub width expansion increases the effective blockage area in the vaneless gap. This has the effect that the effective flow area in the vaneless gap decreases with an increase in impeller tip clearance. The reduced effective vaneless gap area leads to an acceleration of the flow through the vaneless gap, which leads to earlier choke in the diffuser throat.

In the 1D App, diffuser choke prediction is conducted using the mean line theory proposed by Aungier [15]. During this study, it was found that the 1D App choke prediction was satisfactory for impeller tip clearance ratios \({\text{TCR}} < 9\%\). It was found that above this value, the 1D App over-predicted the choke point. Aungier [15] defines a contraction ratio (\(C_{r}\)) to quantify the diffuser throat area blockage attributed to viscous effects. He estimates this value based on the diffuser inlet area (\(A_{3}\)), the diffuser inlet vane angle (\(\beta_{3}\)) and diffuser throat area (\(A_{{{\text{th}}}}\)):

$$C_{r} = \sqrt {A_{3} \frac{{{\text{cos}}\beta_{3} }}{{A_{{{\text{th}}}} }}} .$$
(7)

It is clear from the above equation that impeller tip clearance is not considered in the contraction ratio calculation. As indicated before, if \(TCR < 9\%\), this is adequate. However, at higher values of \(TCR\), the effective increase in blockage due to the size increase of the impeller tip recirculation zone cannot be ignored anymore. To cater for this, the following modification to the contraction ratio formula is proposed:

$$C_{r} = \left\{ {\begin{array}{*{20}c} {\sqrt {A_{3} \frac{{{\text{cos}}\beta_{3} }}{{A_{{{\text{th}}}} }}} ; {\text{TCR}} \le 9\% } \\ {K_{{{\text{TCR}}}} \sqrt {A_{3} \frac{{{\text{cos}}\beta_{3} }}{{A_{{{\text{th}}}} }}} ; {\text{TCR}} > 9\% } \\ \end{array} } \right..$$
(8)

Values for \(K_{{{\text{TCR}}}}\) vs \({\text{TCR}}\) are evaluated for the cases where \({\text{TCR}} > 9\%\) (see Table 5). These results indicated that an approximate linear relationship exists between \(K_{{{\text{TCR}}}}\) and \({\text{TCR}}\) for values of \({\text{TCR}} > 9\%\) (see Fig. 13).

Fig. 13
figure 13

Crossover diffuser choke contraction ratio evaluation for \(TCR>9\%\)

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The linear relationship \(K_{{{\text{TCR}}}} = f\left( {{\text{TCR}}} \right)\) depicted in Fig. 13 is quantified and implemented in the 1D App, which provides improved choke prediction. For the Comp2 0.6 mm configuration, the 1D App choke prediction error is reduced from 6.8% to 0.41%. For the Comp3 0.6 mm configuration, the 1D App choke prediction error is reduced from 11.2 to 0.15%.

The effect of impeller tip clearance on choke behavior of a mixed flow compressor fitted with a crossover diffuser is observed for all three test compressors. The conclusion, therefore, is that the meridional exit angle (mixed flow angle) does not affect this behavior.

5 Stall Performance

The prediction and understanding of stall in a compressor stage is probably one of the most challenging aspects for a designer. This notion is echoed in no uncertain terms by Day [17]: “…, after 75 years of research, we are still unable to predict the stalling behaviour of a new compressor or to contribute much to the design of a more stall-resistant machine.” The fundamental driver of stall is flow separation, either in a stationary location (diffuser vaned channel) or in a dynamic situation (rotating impeller channels). Diffuser type (vaneless vs vaned) affects compressor stall to a large extent. In a compressor equipped with a vaneless diffuser, compressor stall is clearly dictated by impeller stall. Conversely, in a compressor fitted with a vaned diffuser, compressor stall is typically dictated by diffuser stall [18].

During the pre-manufacture design phase and numeric modeling of a MGT compressor, designers face a real challenge in determining the stall/surge point for a specific speed curve. Researchers have recommended various methods for predicting stall, but even the best of these do not always provide accurate stall prediction results. For the purpose of this study, a simple, conservative stall prediction method is employed. It is based on the stability criteria of Japikse and Baines [19]:

$$\begin{gathered} \frac{{\partial {\text{PR}}}}{{\partial \dot{m}}} = 0 \left[ {\text{Metastable conditions}} \right],{ } \hfill \\ \frac{{\partial {\text{PR}}}}{{\partial \dot{m}}}\, < \,\,0\,\,\,\left[ {\text{Stable conditions}} \right], \hfill \\ \frac{{\partial {\text{PR}}}}{{\partial \dot{m}}}\, > \,0 \left[ {\text{Unstable conditions}} \right]. \hfill \\ \end{gathered}$$
(9)

The gradient of the total-to-total pressure ratio performance curve is used to ascertain the stall/surge point. A positive gradient indicates the onset of unstable conditions and is used as the criteria for stall/surge point prediction. In the CFD simulation environment, a compressor performance curve is constructed by simulating a series of operating points at a constant rotational velocity. Each operating point is defined by either a mass flow rate or exit pressure (amongst other methods). In this study, performance curves are constructed by defining exit mass flow rates, starting at the design point. The only exception is the choke point, where an unrealistic low exit pressure is selected. Suitable mass flow rates are selected between the design point and choke point to form a proper locus on the choke side of the operating point. On the stall side, suitable operating points (mass flow rates) are selected, starting at the design point, and moving left towards stall. Consecutive points are selected until stall is reached.

In the CFD simulation environment, the feasibility of an operating point is indicated by convergence. Convergence is established by a suitably reduced residual, as well as inlet vs outlet mass flow convergence. Near the stalling point, it is often observed in FINE Turbo™ that mass flow displays oscillatory behavior towards convergence. Often, convergence is still reached, which technically confirms the feasibility of the simulated operating point. Often, the next lower operating point displays the same behavior but requires more iterations to reach convergence. Again, if convergence is reached, the operating point is technically feasible. This might continue for several additional points, all requiring more iterations to converge. Considering this, the question is raised: how many iterations still suggest a feasible solution? To avoid this dilemma, the stall point is fixed using the Japikse and Baines [19] stability criterion. The total-to-total pressure ratio of each simulated operating point in the direction of stall is compared with each previous point. Once a reduction in pressure ratio occurs (gradient change), the process is terminated, and the previous point is fixed as the stall point. It often happens that simulations at mass flow rates below the fixed stall point converge within a reasonable number of iterations. This is an indication that the Japikse and Baines [19] stall stability criterion is reasonably conservative in many cases.

With the stall point prediction method fixed, the stall performance of the three test compressors at various impeller tip clearances is analyzed. It is interesting to note that the meridional extent of the impeller exit recirculation zone is hampered by the commencement of the diffuser vaned section. To confirm this notion, a vaneless diffuser configuration of Comp1 is evaluated. The meridional geometry of the baseline Comp1 diffuser is maintained, with the diffuser vanes merely removed. The extent of the recirculation zone in the vaneless diffuser configuration of Comp1 at design point is clearly evident in Fig. 14.

Fig. 14
figure 14

Comp1 meridional streamlines: meridional extent of impeller exit recirculation zone—a vaneless diffuser b crossover diffuser

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In the vaned diffuser test compressor configurations, the diffuser vanes, therefore, have the effect of re-aligning the flow and suppressing the meridional extent of the recirculation zone. This is visualized in Fig. 15. In Fig. 15a, the meridional extent of the recirculation zone is indicated by the flow vectors pointing away from the shroud surface. In Fig. 15b, the presence of the diffuser vane has the effect that the flow is re-aligned along the meridional direction much sooner when compared to the vaneless diffuser case. This does, however, imply that the recirculated flow approaching the diffuser vane leading edge is not aligned with the inlet vane angle, especially closer to the shroud side. This is also depicted in Fig. 15b where the flow vectors are not well aligned with the diffuser vane at the leading edge, especially towards the shroud side. A fair assumption would, therefore, be that the recirculation zone will affect the stall performance of the diffuser, and that it would be dependent on the size of the recirculation zone.

Fig. 15
figure 15

Effect of diffuser vanes of flow alignment—a Comp1 vaneless b Comp1

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From Figs. 4, 5, 6, it is observed that an increase in tip clearance leads to an increase in stall margin. This observation is in contradiction to what is observed for choke margin and design point performance. The difference in stall mass flow rate between the three tip clearance configurations is however smaller than the difference in choke mass flow rate. A reduced tip clearance, therefore, still provides a better operating range (more is gained on the choke side than is lost on the stall side).

Figures 16 and 17 provide a schematic of the meridional streamlines at stall for the three vaneless gap configurations of Comp1 and Comp2. It is evident that the impeller exit recirculation zone has increased in size compared to the size of the recirculation zone at the operating point (compare with Fig. 8). The size of the impeller exit recirculation area, therefore, increases as stall is approached. When studying Figs. 16 and 17, it is also interesting to observe that the upstream extent of the recirculation zone (back into the impeller) increases with an increase in tip clearance (see black oval area sizes in Figs. 16 and 17). The conclusion is made that the further the recirculation zone extends back into the impeller (due to an increased impeller tip clearance), the less effect it has on the diffuser vane inlet. This would explain the increase in stall margin with an increase in tip clearance.

Fig. 16
figure 16

Comp1 meridional streamlines: stall analysis—a 0.1 mm, b 0.3 mm, c 0.6 mm

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Fig. 17
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Comp2 meridional streamlines: stall analysis—a 0.1 mm, b 0.3 mm, c 0.6 mm

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The effect of impeller tip clearance on stall behavior of a mixed flow compressor fitted with a crossover diffuser is observed for all three test compressors. The conclusion, therefore, is that the meridional exit angle (mixed flow angle) does not affect this behavior.

6 Conclusion

In this study, it is shown that impeller tip clearance has a marked influence on performance and operating range of a MGT mixed flow compressor stage fitted with a crossover diffuser. To evaluate this, three test compressors (Comp1, Comp2 and Comp3) are designed using the 1D App. Performance results are validated using Numeca/FINE™ CFD software. It is shown that a smaller impeller tip clearance leads to better performance (compressor efficiency and pressure ratio) across the entire operating range, regardless of the impeller meridional exit angle.

An updated mean line impeller leakage loss model is proposed. The 1D App utilizes the impeller leakage loss model as proposed by Aungier [15]. This model provides good results for impellers with a tip clearance ratio (\({\text{TCR}}\)) of ~ 4%, but over-predicts performance of impellers with \(TCR\) > 4%, and under-predicts performance for \(TCR\) < 4%. The analysis shows that a nearly linear relationship between \(TCR\) and leakage losses exist. The leakage loss model of Aungier [15] used in the 1D App is updated to include this linear relationship.

In terms of choke performance, it is shown that a smaller impeller tip clearance leads to an increased choke margin. The increased choke margin is attributed to the decrease in size of the impeller tip recirculation zone with a decrease in impeller tip clearance. Consequently, the effective vaneless gap flow area reduces and increases the flow blockage prior to entering the diffuser vaned section. This smaller area leads to accelerated flow, which in turn leads to earlier choke. An updated mean line diffuser choke prediction model is proposed for mixed flow compressor stages featuring an impeller \({\text{TCR}} > 9\%\). The 1D App choke prediction error is reduced from 6.8 to 0.41% and 11.2 to 0.15% for the Comp2 0.6 mm configuration and the Comp3 0.6 mm configuration, respectively.

Compared to design point and choke margin performance, an opposite response is observed for stall margin. It is shown that stall margin increases with an increasing impeller tip clearance. This is attributed to the impeller exit recirculation zone being “push back” into the impeller with an increase in impeller tip clearance. The recirculation zone, therefore, has less effect on the diffuser vane inlet, which explains the increase in stall margin.

In terms of total operating range, the gain in choke margin is larger than the loss in stall margin with a reduction in impeller tip clearance. The net effect of a reduced impeller tip clearance is therefore a larger operating range and better design point performance. A smaller tip clearance is therefore always preferable. In practice, however, a minimum tip clearance will be dictated by the achievable tolerances in the manufacturing process.