Question

Explain the design complexity in axial flow turbine and compressor and their solution in brief.

Answer 1

DESIGN METHODOLOGY:

Primary design calculations were carried out using isentropic relations, later the obtained parameters were used

for mean-line design through a commercial 2D design tool. Preliminary flow path is established using inlet total

pressure, temperature, flow angle, total-to-static pressure ratio, mass flow, reference radius, flow and load

coefficients. The compressor flow path is evolved by varying hub and tip end wall which can be seen in the figure

1. Koch & Smith loss model is used for the prediction of performance and stalling conditions of the rotor. Multiple

Circular Arch (MCA) profiles for rotor blades and Double Circular Arc (DCA) profiles for stator blades are used

for all the three stages. 3D blade design is also carried out using commercial tool dedicated for turbomachinery

design. Flow path contour refinement, flow angle adjustment, blade profile corrections and managing the gap

between each stage is done through the same design tool. A 3D model of the compressor stage is depicted in the

figure 2.

Figure 1: Flow path of the compressor stage 2D.

Figure 2: 3D model of the compressor stage.

COMPUTATIONAL METHODOLOGY:

Grid generation: ANSYS Turbogrid has been used for grid generation. O-H topology was chosen for

generating structured hexahedral grid. Spacing between the end-wall and first cell was maintained small enough

to meet y plus (y+) requirement. For assuring the reliability of the solution, grid independent study was carried

out for coarse, medium and fine mesh sizes (1, 1.5 and 2 Million) keeping total pressure ratio as monitoring

parameter. Deviation of the coarse and medium grid was 1.8 % and 0.6 % from the fine grid as can be seen in

figure 3, therefor analysis was continued for the medium grid size. Grid generated for three stages is presented in

the figure 4.

Figure 3: Peak total PR deviation with

respect to grid size.

Figure 4: Computational grid generate for three stage compressor.

Boundary conditions: Single blade row 3D passage for all the three stages was considered for the analysis, as

given in the figure 5. All the solid boundaries were treated as wall with no slip and non-heat transfer. Side walls

of the domain were imposed with periodic boundaries. Inlet of the compressor stage was enforced with total

pressure and total temperature assuming the flow normal to the boundary. Exit boundary of the last stage was

defined with static pressure at mid location having pressure averaging over the entire face.

Flow solver: Steady state density based RANS (Reynolds Averaged Navier Stoke) solver including viscous

work was adapted in ANSYS CFX to perform the computational analysis for all the three stages together. SST

(Shear stress transport) k-ω model with 5% turbulence intensity at inlet, was considered for turbulence closure.

Rotor stator interaction plane was defined as mixing plane which does circumferential averaging of the flow

parameter for transferring information at the interface.

Figure 5: Computational domain with boundary conditions.

RESULT AND DISCUSSION:

Stage performance: Performance plots are generated from chock to stall conditions by varying the back pressure

at the exit. In the beginning of computation, solution had violent fluctuations in the convergence which is

attributed to the rear stage operating at extremely off design conditions thereby making the solution unstable.

Near the onset of stall, convergence of fluxes begins to fluctuate and finally it fails to converge, this point is

considered as numerical stall (NS). Performance of all three stages is evaluated in terms of pressure ratio and

efficiency at 80 %, 90 % and 100 % which is given in the figure 6 (a) and 6 (b). At design speed, PR of 2.32 and

efficiency of 81.2 % is achieved with respect to targeted value.

(a): Stage total PR Vs non-dimensional mass flow.

(b): Stage isentropic efficiency Vs non-dimensional

mass flow.

Figure 6: Compressor performance map.

Stream-wise flow physics: Variation of static pressure (normalized by Pst_max at DP) throughout the compressor

stages is given in figure 7 for CP, DP and NS conditions. At the entry to R1, pressure rise is nearly constant over

the 50% of the chord for CP, DP and NS due to rapid acceleration of the flow which can be seen in figure 8 in

terms of Mrel contours as well. Again at the entry to R2 and R3 there is a sudden dip in the pressure (Indicated by

circle) due to rotor LE acceleration followed by steep diffusion in rest of the rotor part for DP and NS. Static

pressure rise through S1, S2 and S3 is very gradual compared to rotor which indicates relatively high loading of

the rotor blades. At CP, rise in the static pressure from R2 to R3 is very marginal due to relatively high acceleration

over 80 % of the rotor blade suction surface which is clear from Mrel contours as well. A sudden drop indicated

by arrow in the S3 at CP is observed. This is mainly due to CP having the highest mass flow and all the stages

operating at very low PR with marginal density changes therefore in order to balance the inlet and exit mass, flow

encounters rapid acceleration in the rear stages as depicted by Mrel contour in the S3.

Figure 7: Stream-wise static pressure built up at CP, DP and NS for all the three stages.

Figure 8: Tip relative Mach number contours across all the stages at CP, DP and NS.

Span-wise variation of the flow: Figure 9 (a), 9 (b) and 9 (c) show the span-wise variation of the total pressure

(Normalized by S3 exit Po_max at DP) at rotor (R1, R2, R3) and (S1, S2, S3) exit for CP, DP and NS conditions.

As we move along the rear stages, there is increase in the total pressure radially and axially. From the rotor exit

profiles, it can be seen that R1 has huge flow reversal till 60% span for CP and DP which increases at NS almost

till 85 % span with spike in total pressure near the blade tip region. R2 exit profiles have similar distribution over

the entire span for all three conditions with flow reversal up to 75% of span. R3 exit has almost uniform total

pressure distribution for CP except end-wall region however it does have flow reversal over 40% of the span for

DP and NS which is less compared to R1 and R2. S1 and S2 exit profiles are almost same at all the three points

(CP, DP and NS) having flow reversal till 40% of span on the other hand, S3 exit profile for all the conditions

remains uniform over the entire span except end-wall regions.

Normalized total pressure (Po/Po_max)

Normalized total pressure (Po/Po_max)

Figure 9 (a): R1 and S1 Span-wise variation of Po/Po_max for all three conditions.

Normalized total pressure (Po/Po_max)

Normalized total pressure (Po/Po_max)

Figure 9 (b): R2 and S2 Span-wise variation of Po/Po_max for all three conditions.

Normalized total pressure (Po/Po_max)

Normalized total pressure (Po/Po_max)

Figure 9 (c): R3 and S3 Span-wise variation of Po/Po_max for all three conditions.

Blade passage flow behavior: Figure 10 (a), 10 (b), 10 (c) and 10 (d) show the stream line pattern along the rotor

(R1, R2, R3) and stator (S1, S2, S3) blades at DP and NS. In the rotor passage, along with stream-wise pressure

gradient, a radial pressure gradient does exist due to the centrifugal force acting on the fluid partial causing them

to move towards the casing which can be seen in the figure 10 (a) and 10 (c) for rotor flow. At DP and NS, due

to radial pressure gradient, flow in the R1 is subjected to reversal near hub TE causing the streamlines to drift

radially upwards. Tip leakage flow (TLF) coming from the pressure side to suction side then interacts with this

upward moving flow forming a spiral cortex (SV) which can be seen in R1 for DP and NS. However, the intensity

and extent of SV formation deepens on the presence of adverse pressure gradient. SV in R1 at DP forms around

40 % of the chord penetrating core flow over 20 % of the blade span. On the other hand, at NS, strong SV forms

almost form the LE of the R1 penetrating core flow over the 30 % of blade span. Similar flow pattern can be see

for the R2 at DP and NS. Towards the rear stages, adverse pressure gradient increases which causes the flow

incidence to change and consequently early flow separation from the blade surface. Unlike R1 and R2, R3 does

not have flow drifting upwards form the hub surface in both the cases however it does have strong SV and high

flow incidence. This is probably due to the flow essentially being dominated by BL and TLV in R3 and fluid

particles experiencing relatively lower centrifugal force in the low aspect ratio blade passage. S1 is observed to

have separation near the tip at DP which is attributed to the intense SV being conveyed from the R1. This probably

indicates that stalling begins from the first stage at DP. This phenomenon is not observed at NS since the SV

formed in R1 is more dominant radially than stream wise. Similarly, at DP, S2 also have separation bubble near

the tip due to SV carried from the R2, however the severity of the separation is more at NS. S3 seems to have no

separation at DP but does have strong separation bubble spanning around 20 % of the blade chord. This probably

attributes to stalling from the rear stages at NS.

Figure 10 (a): Rotor streamlines at DP.

Figure 10 (b): Stator streamlines at DP.

Figure 10 (c): Rotor streamlines at NS.

Figure 10 (d): Stator streamlines at NS.

CONCLUSIONS:

A three stage axial flow compressor design and CFD analysis have been carried out which is mainly aligned with

small gas turbine (SGT) applications. At design speed, PR of 2.32 and efficiency of 81.2 % is achieved with

respect to targeted value. Detailed flow physics is investigated to analyze the interaction of all the stages together

at CP, DP and NS conditions. During the simulation it was observed that convergence of the solution was very

difficult at all three operating speeds for low pressure ratios with high fluctuations in the fluxes. This was mainly

due to the rear stages operating at far off design conditions. SV is formed in the R1 and R2 due to interaction of

TLV and upward drifting flow acted by centrifugal force. SV is found to be axially more dominant at DP and

radially at NS. Unlike R1 and R2, R3 does not have upward moving flow due to low aspect ratio passage having

lower centrifugal force being acted on the fluid particles. Designed multistage compressor under predict the

pressure ratio and efficiency marginally. There is a need to fine tune the design and CFD aspects in future course

of action.