8/12/2019 Non-Axisymmetric Endwall Contouring in a Compressor Cascade With Tip Gap

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1 Copyright 2014 by ASME

Proceedings of ASME Turbo Expo 2014: Turbine Technical Conference and Expos ition

GT2014

June 16 20, 2014, Dsseldorf , Germany

GT2014-26725

NON-AXISYMMETRIC ENDWALL CONTOURING IN A COMPRESSOR CASCADEWITH TIP GAP

Mahesh K. Varpe and A. M. PradeepDepartment of Aerospace EngineeringIndian Institute of Technology, Bombay

Mumbai, India 400 076Email: ampradeep@aero.iitb.ac.in

ABSTRACT

This paper describes the design of a non-axisymmetric hub

contouring in a shroudless axial flow compressor cascade

operating at near stall condition. Although, an optimum tip

clearance reduces the total pressure loss, further minimization

of the losses using hub contouring was achieved. The design

methodology presented here combines an evolutionary principle

with a three-dimensional CFD flow solver to generate different

geometric profiles of the hub systematically. The total pressure

loss coefficient was used as a single objective function to guide

the search process for the optimum hub geometry. The resulting

three dimensionally complex hub promises considerable

benefits discussed in detail in this paper. A reduction of 15.2%and 16.23% in the total pressure loss and secondary kinetic

energy, respectively, was achieved in the wake. The blade

loading was observed to improve by about 4.53%. Other

complementary benefits are also listed in the paper. The resultsconfirm that non-axisymmetric contouring is an effective method

for reducing the losses and thereby improving the performance of

the cascade.

NOMENCLATUREC Blade chord, m

Cp Static pressure coefficient, = (P2-P1)/(U2/2)

Cp0 Total pressure coefficient, = (P01-P02)/(U2/2)

Cp0, ref Midspan total pressure coefficient in the

wake for t = 0

CSKE Secondary kinetic energy coefficient,

= KE-sec/KE1CFD Computational fluid dynamics

EA Evolutionary algorithm module

h Blade span with TC = 1%, m

H Blade span with no tip gap, m

i Incidence angle, deg.

KE Kinetic energy

KE-sec Kinetic energy of secondary flow

= [M (v2+w

2)] / (M1V1

2)

LE Leading edge

M mass flow rate, kg/s

MUSCL Monotone Upstream-centered Schemes for

Conservation Laws

P.S Pressure surface of the blade

P1,P2 Static pressure at the inlet and wake, Pa

P01, P02 Total pressure at the inlet and wake, Pa

Re Reynolds number based on chord length

s Pitch of blade, m

S.S Suction surface of the blade

SIMPLE Semi-Implicit Method for Pressure-Linked

Equations

SIMPLEC SIMPLE Consistentt Tip gap, m

TC Tip clearance ratio, t/H

TE Trailing edge

TLV Tip leakage vortex

u, v ,w Velocity components in (x,y,z) coordinate

system, m/s

U Mean velocity, m/s

xn, yn, zn Normalized coordinates w.r.t C, s

and corresponding span.

2 Exit flow angle, deg.

2, ref Mid-span exit flow angle in the

wake, at t = 0, deg.

* Deviation from the reference exit flow angle,

(2, - 2, ref), deg.

2, ref Vorticity along 2, ref, 1/s

Subscript

1 Inlet location

2 Downstream location

ref reference

ske Secondary kinetic energy