THE by means of NACA airfoil. Then, 3D numerical



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          Mahesh Kavimandan, Lasheer Shareef

   Cyient Ltd, India (email:
[email protected])



Supersonic engines
are commonly used in military aircraft. They have not been used in civil
aviation or for transport due to several operational reasons. There are
different concepts, which are being proposed for supersonic civil transport.
One of the concepts that presented in this paper is Variable Cycle Engine
(Adaptive Cycle Engine). Variable cycle engines would be able to vary their
bypass ratios, for optimum efficiency at any combination of speed and altitude
within the aircraft’s operating range, despite traditional engines with fixed
airflow. A
supersonic highly loaded high pressure (HP) compressor was designed for a VCE
in the conditions of both single and double bypass modes in accordance with the
similarity principle. The blade profiles were designed by means of NACA
airfoil. Then, 3D numerical simulations were performed on the HP compressor of
both working conditions with different thermodynamic cycle parameters to
confirm the design methods and results. The one equation turbulence model of
Spalart-Allmaras was applied to solve Reynolds’s averaged Navier-Stokes equations.
The results of simulation indicate that the compressor performances are
satisfactory in both working conditions with high efficiency. Further research
reveals, wave structures in the supersonic compressor, behaviour of tip
clearance flow and the phenomenon of transition flow in boundary layer.


? = mass flow rate

? = reduced mass flow

 = inlet airflow density

A = compressor exit

 = axial velocity component at inlet

 = tip radius

 = root radius

= mean radius

R = gas law constant

 = inlet static pressure

 = inlet static temperature

= blade axial velocity

 = blade rotational speed

H = blade height

 = temperature rise per stage

 = rotor pitch

 = chord length

 = polytropic efficiency of compressor

 = number of blades on rotor/stator

 = dynamic viscosity coefficient

 = pressure coefficient

 = reduced power

 = reduced wheel speed

 = whirl speed component


A Variable Cycle Engine (VCE) can be defined as one
that operates with two or more thermodynamic cycles. It is a type of aero
engine whose thermodynamic cycle can be adjusted by changing some components’
shape, size or position, and the cycle parameters, such as pressure ratio, mass
flow, bypass ratio and thrust. It can be varied between those of a turbojet and
a turbofan, making it to combine the advantages of both. These measures may
enable the engine to obtain the optimal thermodynamic cycle, and to acquire the
good adaptability to various flight envelopes 1.














The engine can work as the turbojet when the
aircraft requires high specific thrust, such as take-off, acceleration and
supersonic cruise. It also can work as the turbofan when the aircraft requires
low fuel consumption, such as

and subsonic cruise. The most important advantage expected from using VCE in
future supersonic transport is a substantial range improvements as compared to
a conventional engine. These range improvements are mainly achieved by reducing
the subsonic specific fuel consumption by around 15% (relative to a Turbojet)
and improving the fuel consumption at off-design by the extensive use of
variable geometry. The future VCE will have a low emission combustor and
afterburner. The noise level at take-off will be met by FAR part 36 requirement.
In other words, the future VCE will be environmentally accepted 2.

The disadvantages are mainly an increase in the
engine weight and a more














control system, therefore the reliability of the engine will be affected. The
performance of any VCE depends critically on the attainment of the predicted
technology level improvements. The purpose of research on VCE is to improve
off-design performances, in order to satisfy the needs of broad flight
envelope, large combat radius and long cruise duration 3.

work mode of VCE discussed in this article is presented in Figure 2:

Single bypass mode: The selector valve
is closed and all air goes through the Core Drive Fan Stage (CDFS). The fan
bypass flow bypasses the core engine through the inner bypass duct and remixes
with the core flow downstream of the low pressure turbine. The nozzle is full
open to shift the loading to the HP shaft to cope with the added work of the
CDFS. At the same time, the expansion ratio and the flow rate rise to increase
the specific thrust with low bypass ratio under supersonic and acceleration











Double bypass mode: The selector valve
is full open and the nozzle is now closed to unload the HP turbine and load the
LP turbine. The bypass ratio increases for best specific fuel consumption for
subsonic cruise and best exhaust velocity conditions for improved noise
suppression on take-off 4.

Axial flow compressor is one of the most important
parts of Gas turbine engine. Axial-flow compressors are used in medium to large
thrust gas turbine and jet engines. The compressor rotates at very high speeds,
adding energy to the airflow while at the same time compressing it into a
smaller space. The design of axial flow compressors is a great challenge, both
aerodynamically and mechanically.

The aerodynamic compressor design process basically
consists of mean line prediction calculation, through flow calculation, and
blading procedures. The mean line prediction is the first step within
compressor design. It is a simple one dimensional calculation of flow
parameters along the mid height line of the compressor where global parameters
as the annulus geometry, the number of stages, and the stage pressure ratios
are scaled 5. It is necessary to design axial flow compressor at preliminary
level and require parameters can be checked at initial level so further
improvement can be made at primary level before start a Detailed design.

It is a challenging job to design appropriate
compressor to meet the demands of VCE, which is the compressor should implement
performance adjustment of the engine and ensure the efficiency being maintained
within a higher range. As described by similarity principle, multiple
conditions can be converted to the same working condition according to the rule
of equality in reduced wheel speed, reduced mass flow and Mach number along
circumferential direction and so on. Then, the compressor performances under
different working conditions are approximately equal to each other. In this
research, a high loaded high-pressure compressor with high compression ratio
and large enthalpy rise was designed for VCE in two operating modes of low
bypass ratio (single bypass mode) and high bypass ratio (double bypass mode)
according to this principle 3.

complexities of a supersonic flow in compressor have been summarized: wave
structures such as expansive waves and compressive waves (even the shocks)
exist in supersonic regions. Due to this, flow parameter changes drastically in
the channel. Compressive waves may be formed by disturbed flow in that regions,
so influence on aerodynamic performances caused by compressive wave-boundary
layer interactions must be considered. The blade boundary layer, influenced by
blade’s geometrical parameters and main-flow aerodynamic parameters, usually
develops from laminar to turbulence. As a result, to capture the boundary layer
development, and estimating the transition position is significant for the
investigation of flow performances in the compressor. Besides, variations of
blade profile, blade stacking and end-wall effects often lead to 3D
characteristics in the flow fields, where secondary flows, separated flows and
complicated vortex structures exist. Indeed, it is important to obtain accurate
flow information and aerodynamic performances during the design process, which
is crucial for supersonic compressor.


The steps
involved in design of axial flow compressor is as shown in Figure 3 6:

By assuming values for the blade tip speed, and the
axial velocity and hub-tip ratio at inlet to the first stage, the required
annulus area at entry is obtained from the specified mass flow, assumed axial
velocity, and ambient conditions, using the continuity equation.



























satisfy continuity equation:

the above equation,

 is considered as hub to tip ratio and density
is calculated from the relation
(3)                         …ficient in both
modesgn phase of compressor.ip of rotor and stator blades.peed()be determined.

From the suitable design point under sea level conditions
(atmospheric pressure and temperature) and from cycle calculations, the
required pressure ration, mass flow rate and compressor inlet temperature can
be determined. These can be useful to calculate the stagnation and static
pressure and temperature at the first stage of compressor.

For the assumed axial velocity, tip radius will be the function
of hub to rip ratio.

speed can be represent as:

                                      ……. (4)

                                       ……. (5)

Therefore, we can iteratively determine the tip radius by
appropriate hub to tip ratio  and rotational speed (n). It is useful to know
the mean radius as,

mean line design methodology, mean radius remain constant for all stages.

In case of exit area:

Blade height:

The radius at exit (final stage) of compressor as
determined as:

                             ……. (9)

                                …….. (10)

The number of stages is found by dividing total temperature
rise in all stages by temperature rise per stage.

temperature rise for a stage is:

whirl components of velocity are determined from the velocity triangles as
shown in Figure 4.

















The chord length of the blade airfoil is calculated
by appropriate selection of aspect ratio  based on the application.

pitch and number of blades for the rotor are determined by the given relations,




The principle of
similarity is a consequence of nature for any physical phenomenon. By making
use of this principle, it becomes possible to predict the performance of one
machine from the results of tests on a geometrically similar machine, and also
to predict the performance of the same machine under conditions different from
the test conditions. If two machines are kinematically similar, the velocity
vector diagrams at inlet and outlet of the rotor of one machine must be similar
to those of the other. Geometrical similarity of the inlet and outlet velocity
diagrams is, therefore, a necessary condition for dynamic similarity 10.

VCE can combine the advantages of turbojet and
turbofan by adjusting its bypass ratio in order to change the Thermodynamic
cycle parameters. When the HP compressor was design, two working conditions
have been taken into account, which one is single bypass mode and the other is
double bypass mode. It means that HP compressor must adapt the bypass ratio
variations which makes the flow rate and compression ratio vary within wider
range than ones of conventional compressor besides the compressor must maintain
high efficiency. Namely, the flow fields in compressor should be reasonable
when the cycle parameters are changed greatly 7.

The outer bypass compress air flows into the inner
bypass when VCE changes its working conditions. Then the mass flow of HP compressor
increases. The change rate of mass flow depends upon the change of the bypass
ratio. There are some different working conditions for VCE matching with
different bypass ratios.

Assume that the
VCE works in n conditions. Then HP compressor must correspond with n series
of parameters as follows:

Condition 1    

Condition 2


Condition i


Condition n

Obviously it is different from the conventional
compressor which is often given only one set of design parameters. It is very
difficult to design the compressor to meet so many series of cycle parameters.

turbo machinery, the total-total efficiency is commonly depended on ten
parameters, namely,

    …… (14)

geometry and gas parameters can be omitted for the same compressor and the same
working fluid. The following equations can be gotten from the similarity
principle in turbo machinery.

                ……… (15)


Compression ratio          

Reduced mass flow rate

Reynolds number

Reduced power

Reduced wheel speed

Both and  are the qualitative
parameters and can be represented into:

            …… (16)

               …… (17)

the efficiency is also represented into:

                         …… (18)

The effect of  can be ignored if Re is
bigger than the second critical Re number in turbo machinery. Equation (18) is
reduced as:


…………… (19)

Therefore, if we make following equations both (20)
and (21) to be established for HP compressor of VCE, the multi-conditions
compressor for VCE can be treated as the conventional compressor to be

As a result, the mass flow rate and inlet parameters
of HP compressor are changed into any kind of condition among n series
of conditions when VCE adjusts its bypass ratio but the variations cannot influence
the efficiency of compressor, which is only influenced by the compression


ANSYS Fluent 16.0, a CFD tool has been employed
within the computations to simulate the 3D steady flows and to validate the
aerodynamic performances of designed HP compressor for VCE. Both operating
conditions of single bypass mode and double bypass mode have been taken into

of design involves following steps:

Creating a geometry/mesh

Defining the physics of the model

Solving the CFD problem

Visualizing the results in post


The traditional approach to axial-flow compressor
aerodynamic design was to use various families of airfoil as the basis for
blade design. American practice was based on various families designed by the
National Advisory Committee for Aeronautics (NACA), the most popular being the
65-series family 8. NACA 65410 9 Airfoil is used here to generate blade
coordinates as in Figure 5.












To create the geometry NX UNIGRAPHICS 9.0 software
is used. NACA 65410 airfoil coordinates are imported to software and this
airfoil is used from entire hub to tip of rotor and stator blades. Meshing (Figure
6) has been carried out by Hyper Mesh. The type of element selected here is











In this step we are defining the physics of Model.
This includes specification of type of fluid, defining the domains, Inlet and
Outlet Boundary conditions, type of analysis, turbulence model, and heat
transfer model etc. The following assumptions are taken for defining physics.

Steady state condition

No leakage losses

Friction between walls and fluid is


solver parameters are specified as follows:

Air as an Ideal gas is taken as Working

The one-equation turbulence model of
Spalart-Allmaras has been applied to solve Reynolds’s averaged N-S equations,
and this model is applicable to the separation flow simulations of viscous
fluid under high pressure gradient.

For the two operating modes, total
temperature, total pressure and turbulent viscosity are prescribed at inlet;
the gas enters the calculation domain in axial direction. Meanwhile, static
pressure is given at outlet as shown in Figure 7.

Two domain interfaces are used. Rotor
domain is rotating and stator domain is stationary (Figure 7).

solver manger the number of iterations and accuracy is specified and results can
be analysed with help of CFD Post.












Static pressure distribution on blades
in two modes

Mach number distribution on the blades

Vortex movement

Pressure coefficient distribution on
blades in two modes.


The results show that the relative errors of mass
flow compared to design value. In generally, the results of simulation indicate
that satisfactory aerodynamic performances are available in both of the two
operating conditions, and the designed HP compressor has achieved the anticipated























From the distribution of static pressure on blade
surface (not shown here), the fluid flows around the vane blade characterized
by pressure fluctuating along the whole blade height, and it is the most severe
near the hub, which is relevant to wave structures in the channel and
compressive wave boundary layer interactions. These influences are inevitable
in the supersonic or transonic compressor. In the stator, static pressure is
fully developed on the pressure surface but in the rotor, static pressure on
the blade presents certain differences in the two modes. It shows the power
requirement variation in two modes of operation.

Isolines distributions of absolute Mach number at
stator outlet in each mode represents the characteristics of supersonic wake
flow as depicted in Figure 8. The high-temperature gas flows through the
channel characterized as uneven at different blade heights because of blade
stacking and end wall effect. Mixing flow of supersonic fluid leads more energy
loss. Moreover, the uneven of flow parameters in the flow fields causes radial
movement from blade bottom to the top and corner vortex (Figure 9) near both
hub and shroud at outlet with secondary flow loss increasing apparently. These
secondary flow is mainly responsible for the aerodynamic loss in a supersonic










Tip clearance flow is to blame for the aerodynamic
loss in both rotor and stator stage, with the proportion to be 45% and 30% in
some working conditions. It is significant to understand the features of
clearance flow for the design of rotor and to minimize the flow loss, so
representation formation of tip clearance flow in the supersonic compressor is analysed
with the aid of 3D streamlines as presented in Figures 10a-10c.










There are three forms of tip vortex, (1) Vortex
forms behind the guide vane, (2) Vortex forms due to the gas entering the top
gap from suction surface relative to high-speed rotating blades, (3) Vortex
formed by pressure gradient from blade pressure surface to suction surface
because of more tip clearance. Among these three, mass flow rate of the third
type of clearance flow is larger than the two previous kinds, and corner vortex
occurs when air current flows out of the suction side. So it is necessary to
control this vortex in design phase of compressor.

























Wave structures of supersonic compressor are
analysed by the variation of absolute Mach number and pressure coefficient at
one particular blade height (Figure 11). Detached
shock forms when the gas flow out the trailing edge along pressure surface.
Intersection on different side occurs among detached shock, primary expansive
waves and reflective expansive waves. By the variations of Mach number and
pressure coefficient, it can be drawn the conclusion that the detached shock is
reduced and dissipated by the set of expansive waves. So, influence of the
detached shock is limited to the flow fields near the trailing edge, while the
expansive wave can occupy most space in the tapered-cut









(b)   Double
bypass mode


Figure 11: Mach number
and pressure coefficient in both modes















In present paper, a high loaded high-pressure
compressor stage with high compression ratio has been designed by NACA profile
based on similarity principle. Three-dimensional calculations have been carried
out under different thermodynamic cycle parameters to simulate flow fields in
the two operating conditions (Single bypass mode and double bypass mode). It
reveals the characteristics of supersonic wake flow in a compressor and the formations
of tip clearance flow. Wave structures in the channel and aerodynamic loss in
the flow fields have been analysed.


Dr. P. Pilidis “Variable cycle propulsion systems for a supersonic civil
transport”, Ph.D. thesis, Cranfield university, 1997.

H. G. Munzberg and J. Kurzke, “The Pros and Cons of Variable Geometry Turbines”-
A GARD-CP-205.

3 Liu Zhigang
etc. “Design and analysis of HP-turbine for variable cycle engine”. ASME GT
2010-22449, 2010.

4 YIN Zhao et al
“Research of design method of variable area nozzle turbine for variable cycle
engine” ASME GT 2011-45166, 2011.

5 Nicallas Falck, “Axial Flow Compressor Mean Line Design”,
Master thesis, Lund University, Sweden, Feb.2008.

6 Saravanamutto, Rogers, Cohen. H, “Gas
Turbine Theory” fifth Edition, Pearson Prentice Hall, 2001.

Fang Changde. “Variable Cycle Engines J”, Gas Turbine Experiment and
Research. 2008, 17 (3):1-6.

Ronald H. Aungier, “Axial Flow Compressor”, 2nd edition, 2003.

UIUC Airfoil Coordinates Database Source datfile,”