IRJET - Characteristics of 90°/90° S-Shaped Diffusing Duct using SST K-O Turbulent Model

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 07 Issue: 04 | Apr 2020 www.irjet.net p-ISSN: 2395-0072
© 2020, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1809
Characteristics of 90°/90° S-Shaped Diffusing Duct using SST k-ω
Turbulent Model
Manideep Roy1
1B.Tech, Department of Mechanical Engineering, National Institute of Technology Durgapur, West Bengal, India
---------------------------------------------------------------------***----------------------------------------------------------------------
Abstract - Characteristics of S-shaped diffusing ducts are
explored using CFD. The characteristics are achieved for
turning angle 900/900 with constant circularcenterlinelength
600 mm, constant outlet cross-sectional area 100x300 mm2
and constant inlet cross-sectional area 50x300mm2.
Incompressible flow analysis has been done using SST k-ω
turbulent model. Flow separation is observed nearthetopand
the bottom wall of the diffuser. Cross-flow velocity vector
shows the formation of a counter rotating vortex pair at the
exit plane. The variations in the total pressure loss coefficient
and static pressure recovery coefficient and are obtained for
different x/c value.
Key Words: CFD, flow separation, S diffusers, SST k-ω
1. INTRODUCTION
Diffusers are utilized in many systems to slow downflow for
the conversion of dynamic pressure into static pressure.
Based on the application, the diffusers areproducedinmany
sizes and shapes. S-shaped diffusing ducts are used as
interconnectors between gas turbine engine components
and as intake manifold for aircraft engines.
The purpose of the diffuser design is to calculate pressure
recovery, losses, and flow uniformity at the outlet.
Characteristics of flow in the diffusers are strongly
dependent on the ratio of the outlet to the inlet area, length
of the centerline, the throat width ratio, the velocity at the
inlet, the turbulence intensity profile and the angle of turn.
Strong secondary motion occurs due to disparity between
radial pressure gradient and centrifugal force resulting in
uneven flow distribution and increased losses.
Nur Hazirah et al. [5] investigated pressure recovery and
flow uniformity of turning diffusers using baffles. Velocity at
the outlet is found to be more uniform withtheuseof baffles.
Saha et al. [7] conducted flow simulation in 22.5°/22.5°
curved diffuser having a constant circular outlet and
changing cross-section at inlet such as elliptic, semicircular,
rectangular, square, thereby elliptical shape has been
obtained as the optimized one.
Gupta et al. [1] performed flow simulation in 15°/15°,
22.5°/22.5°, 30°/30°, 45°/45°, 90°/90°ata constantcircular
centerline length of 600 mm. with an aspect ratio of 2, 4, 6 at
the inlet. It has been observed that as the curvature and
aspect ratio increases, the flow uniformity at the exit
reduces, the in-plane velocity increases and the pressure
recovery coefficient decreases.
Sullery et al. [8] performed a comparison of performancefor
curved and straight diffuser. It has been found that for
straight diffusers, pressurerecoveryisbetterthanforcurved
diffuser and that flow turbulence has a greater influence on
the pressure recovery of bent diffuser.
Paul A R et al. [6] performed comparative studies on flow
control using vortex generators immersed in rectangular S-
duct diffusers. Flow separation was found only for bare S-
duct whereas no flow separation was found in S duct with
the immersed vortex generator
B.Majumdar et al. [4] carried out experimental
measurements to investigate characteristics of flowinthe S-
shaped diffusing duct with area ratio 2.0 and aspect ratio6.0
at the inlet. It was found that the total pressure recovery is
less i.e. 46 percent of the inlet dynamic pressure. The
reversal of the flow in the inflection planeandtheuniformity
of the flow at the outlet were also observed.
Jihyeong Lee et al. [3] studied the effect of boundary layer
suction on flow distortion at the inlet using subsonic S
diffuser. It was found that the flow separationwasimproved
by suction of the boundary layer.
M.A.A Halim et al. [2] investigated the development of k-ω
and k-ε turbulent models in modelling the flow and
performance of S-shaped diffusers. It was found that k-ω
turbulent model gives better results than the k-ε model.
Thenambika V et al. [9] performed a numerical study on
recovery of static pressure and loss of total pressure using a
vortex generator at Mach no 0.6 and 1.0 thereby, obtaining
better flow values for Mach no 0.6 than Mach no 1.0.
The purpose of this study is to analyze the performance
characteristics of 90°/90° S- shaped diffuser using SST k-ω
turbulent model.
2. MATHEMATICAL FORMULATION
Any fluid domain is divided into infinitesimallysmall control
volumes where the equations of fluid flow are written in the
form of partial differential equations. The continuity

equation for incompressible and steady flow (density and
time independent) is as follows:
0
i
i
u
x



The RANS (Reynolds Average Navier Stokes)equationsused
for the present turbulent models are:
2
( )
1 i j
i i i
j
j i j j j
u u
u u p u
u
t x x x x x


 
 
   
    
     
where i j
u u
 

is called the Reynolds stress which is
approximated by Boussinesq Hypothesis as given below:
2
3
j
i
i j t ij
j i
u
u
u u k
x x
 
 


 
   
 
 
 
 
3. GEOMETRY USED
The performance parameters of rectangular S-shaped
diffuser is studied using SST K-ω turbulent model. The
geometrical parameters of thediffuser(asshowninFigure1.
is same as that of Majumdar et al [4].)
1) Cross-sectional area of inlet = 50x300 mm2
2) Cross-sectional area of outlet = 100x300 mm2
3) Centreline length = 600 mm.
4) The angle of turn = 90°/90°
Fig-1. S-shaped diffusing duct used in the present study.
4. CODE VALIDATION
The geometry used for the purpose of validation issimilarto
that of Majumdar et al. [4]. The experimental result showed
that the overall Cp value is 46% of the inlet dynamic
pressure. A numerical investigation is done using SST k-ω
turbulent model. The Cp value obtained is 51.32% of the
inlet dynamic pressure.. The difference in Cp value observed
in the numerical and experimental results may be due to an
error in the input velocity determination as that of
Majumdar [4]. The error can also be caused by the density
and viscosity of air, which are temperature dependent.
Change in the inlet speed showed an improvement in the
results.
5. SOLUTION SCHEME
Second-order upwind discretization scheme is applied to
each equation for greater accuracy. Pressure-velocity
coupling is performed using the SIMPLE algorithm. The
residuals were continuously computed for y-velocity, x
velocity, continuity, z-velocity, ω and, k. The convergence
criteria for the residues were set to 10-5.
6. BOUNDARY CONDITIONS
The velocity at the inlet is taken as 40 m/sec. Atmospheric
pressure was specified at the outlet. The turbulent intensity
is taken as 4% at the inlet and 8% at the outlet for the
purpose of initialization to have faster convergence. No-slip
boundary condition is specified at all walls.
7. RESULTS AND DISCUSSION
Using SST k-ω turbulent models, velocity variation at the
longitudinal mid plane, cross flow velocity vectorsattheexit
plane, wall shear stress and different parameters of
performance such as coefficient of static pressure recovery
and coefficient of total pressure loss have been investigated.
7.1 Velocity variationatthelongitudinalmid-plane
and cross flow velocity vector at the exit:
Figure 2. illustrates the velocity variation at the longitudinal
midplane of the diffuser. Zero or negative values of velocity
indicates flow separation. Flow separation is observed near
the top and the bottom wall.
Figure 3. illustrates the evolution of a pair of vortices
rotating in the opposite direction due to centrifugal forces.
The centrifugal forces try to push theﬂuidawayfromthe top
wall, but the ﬂuid turns due to normal pressure from the
bottom wall, leading to the generation of vortices.

Fig-2. Velocity contour at the longitudinal mid plane of the
diffuser.
Fig.-3. Crossflow velocity vector at the exit
7.2 Effect of variation of x/c on static pressure
recovery coefficient:
Figure 4. illustrates that the coefficient of static pressure
recovery (Cp) first increases, then decreases slightly (at
point 4) after which it increases to the exit plane. It is
obvious from the general trend that the Cp value will
increase with the increase in x/c. Here, the decrease in Cp is
found because of the flowseparationoccurringatthebottom
and the top walls.
Fig-4. Cp versus x/c
7.3 Effect of variation of x/c on total pressure loss
coefficient:
Figure 5. illustrates that the coefficient of total pressure loss
(Cl) increases almost linearly with the increase in x/c. As
distance along centreline length increases, the pressure
increases and the velocity decreases. The increase in
pressure causes a reduction in Cl while decrease in velocity
causes an increase in Cl. However, near the inflection plane
the effect is opposite as the pressure decreases and the
velocity increases. These effects counteract with each other
and thus produces the net effect.
Fig-5. Cp versus x/c

7.4 Effect of wall shear stresses with X- position:
The wall shear stresses are plotted in Figure (6-8) againstX-
position for both the bottom and the top walls for all the
diffusers to show flow separation. Separation of flow occurs
due to adverse pressure gradient which is indicated by the
negative or zero values of X wall shear stress.
Fig- 6. Wall shear stress along X directions versus X
position
Fig-7. Wall shear stress along Y direction versus X position
Fig-8. Wall shear stress along Z direction versus X position
8. CONCLUSIONS
Form the velocity variation and the plot of wall shear
stresses it is found that the flow separation in the diffuser
takes place near the bottom and top wall due to adverse
pressure gradient.
Cross flow velocity vector shows the evolution of a pair of
vortices rotating in the opposite direction.Duetocentrifugal
forces.
The overall Cp value is 51.32% of the dynamic pressure at
the inlet and the overall Cl value is 17.2% of the dynamic
pressure at the entry of the diffuser.
APPENDIX
Cp= total pressure loss coefficient,(Pti – Pt) / ρu2
avi
Cl = static pressure loss coefficient, (Pst – Psti) / ρu2
avi
c = centerline length of the duct
k = turbulent kinetic energy
x = distance along centerline
ω = specific dissipation rate
Subscripts:
t = stagnation property
st = static property
ti = stagnation property at inlet
sti = static property at inlet
i, j = tensor
avi = mass average property at inlet

REFERENCES
[1] Gupta, V., Devpura, R., Singh, S., Seshadri, V., 2001.Effect
of aspect ratio and curvature on characteristics of s-
shaped diffusers.
[2] Halim, M.A., Mohd, N.N., Nasir, M.M., Dahalan, M., 2018.
The evaluation of k-" and k-! turbulence models in
modelling flows and performance of s-shaped diffuser.
International Journal of Automotive and Mechanical
Engineering 15.
[3] Lee, J., Lee, S., Cho, J., 2019. Effect of inlet boundarylayer
suction on flow distortion in subsonic diffusing s-duct.
International Journal of Aeronautical and Space
Sciences, 1–8.
[4] Majumdar, B., Singh, S., Agrawal, D., 1997. Flow
characteristics in the s-shaped diffusing duct.
International Journal of Turbo and Jet Engines 14, 45–
57.
[5] Nohseth, N.H., Nordin, N., Othman, S., Raghavan, V.R.,
2014. Investigation of flow uniformity and pressure
recovery in a turning diffuser by means of baffles, in:
Applied Mechanics and Materials, Trans Tech Publ. pp.
526–530.
[6] Paul, A.R., Ranjan, P., Patel, V.K., Jain, A., 2013.
Comparative studies on flow control in rectangular s-
duct diffusers using submerged vortex generators.
Aerospace Science and Technology 28, 332–343.
[7] Saha, K., Singh, S.N., Seshadri, V., Mukhopadhyay, S.,
2007. Computational analysis onflowthroughtransition
s-diffusers: Effect of inlet shape. Journal of aircraft 44,
187–193.
[8] Sullerey, R., Chandra, B., Muralidhar, V., 1983.
Performance comparison of straight and curved
diffusers. Defence Science Journal 33, 195–203.
[9] Thenambika V, Ponsankar S, P.M.K., 2016. Design and
flow analysis of s duct diffuser with submerged vortex
generators. Jounal of Engineering Research and
Application 6, 79–84.
BIOGRAPHIES
Manideep Roy is pursuing B.Tech.
in Department of Mechanical
EngineeringatNITDurgapur,India.
His interest includes CFD, Fluid
mechanics and Heat Transfer. He
has done research internship at IIT
Madras.

IRJET - Characteristics of 90°/90° S-Shaped Diffusing Duct using SST K-O Turbulent Model

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