Comparison of Flow Field Simulation of Liquid Ejector Pump using Standard K-ε and Embedded LES Turbulence Modelling Techniques

Full text

Journal of Applied Fluid Mechanics, Vol. 11, No. 2, pp. 385-395, 2018.
Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645.
DOI: 10.29252/jafm.11.02.28141
Comparison of Flow Field Simulation of Liquid Ejector
Pump using Standard K-ε and Embedded LES
Turbulence Modelling Techniques
Q. Zaheer1† and J. Masud2
1College of Aeronautical Engineering, NUST, Risalpur 24080, Pakistan
2Department of Mechanical and Aerospace Engineering, IAA, Air University, Islamabad 44000, Pakistan
†Corresponding Author Email: qasim1985@cae.nust.edu.pk
(Received June 22, 2017; accepted October 21, 2017)
ABSTRACT
The flow field analysis of a liquid ejector pump is important for its design improvements, performance
estimation and understanding of mixing and entrainment phenomenon. Ejector pumps, due to their simpler
design and ease of maintenance are used in a variety of industrial applications. The subject pump, under
consideration in this study, is used for transferring fuel from one fuel tank to another in a fighter aircraft. To
study the underlying flow field characteristics of subject ejector pump, the fluid domain is simulated using
Embedded LES turbulence modelling technique in Ansys Fluent ® environment. The flow field and
performance parameters of subject pump are then compared with that of previously researched study of same
pump wherein Standard K-ε RANS Turbulence Model was used. It is revealed that the results obtained using
Embedded LES are much closer to experimental data than that of Standard K-ε. The limitations of RANS
turbulence model for accurate simulation of complex flow field of subject pump are then identified, analyzed
and discussed in details by studying the flow characteristics such as Reynolds shear stresses distribution,
Potential Core estimation and turbulent viscosity modelling, obtained using both turbulent models.
Keywords: Ejector pump; Complex flow; Reynolds shear stresses; Potential core; Embedded LES.
NOMENCLATURE
ELES Embedded Large Eddy Simulation
SGS Sub Grid Scale
u’v’ Reynolds stresses
 turbulent stresses
 turbulent Viscosity
 turbulent kinetic energy
 dissipation rate
 fluid density
 integral length scale
1. INTRODUCTION
Ejector pump is a device that transfers the
momentum from a high velocity primary jet flow
(motive flow) to the secondary flow (entrained
flow). The ejector pumps are also referred as
injectors or jet pumps. They can be operated with
the compressible as well as incompressible fluids.
When the ejectors are operated using
incompressible fluids like liquids, they are often
termed as Jet Pumps. One of the most important
feature of these devices is that they provide the use
of any ordinary centrifugal pump with a lower head
but with a higher capacity, thus resulting into 2-3
folds increased mass flow rates. The geometry of
ejector pump is very simple which provides pivotal
advantages like ease of installation, economical
usage, lack of moving parts, lubrication sealing
problems etc. Due to these advantages, these pumps
are extensively used in different industrial
applications as well as in engineering field. In this
study, the subject modeled ejector pump is being
used in the fuel system of a fighter aircraft for
transfer of between the fuel tanks.
The ejector pump flow domain is comprised of
adverse pressure gradient, formation of turbulent
structures due to Kelvin-Helmholtz instabilities in
flow and existence of turbulent shear flows like
mixing layer, free shear layer and turbulent jet flow.
Such field in which various turbulent phenomena
takes place is generally referred to as complex flow
filed. The existence of such complex flow of the
ejector pump makes it difficult to predict its actual

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386
performance analytically. Simplified analytical
models were devised as initial design methodology
of ejector pump, as mentioned in (Royal
Aeronautical Society, December 1985) but these
mathematical models incorporate various
assumptions, hence the prediction of accurate
efficiency and performance of subject pumps is
compromised. Thus, experimentation is carried out
to ascertain the performance and efficiency of
subject pumps but this is not economically feasible
solution. With the advancement in the field of
Computational Fluid Dynamics, the flow field of
ejector pump can be modelled numerically and
selection of suitable turbulence modelling technique
can bring the numerical results closer to the
experimental results.
The literature survey indicates various studies
conducted to analyze the flow field of ejector pump
using different turbulence models. An insight into
the ejector flow phenomena was obtained using
computational and analytical tools and the results
were compared via shadowgraph images of flow
domain (Adrienne et al. 2015). Computationally,
the flow field was simulated using k- RNG and k-
ω SST models, and the results revealed that later
turbulence model predicted the flow features more
accurately. The performance characterization of
“short” ejectors was conducted analytically and
experimentally and it was concluded that proposed
new ejector model for “short” ejectors can
accurately predict its performance (Im and Song,
2015). Experimentally, Laser visualization
technique was utilized to determine and analyze
flow of air inside a supersonic ejector (Desevaux et
al. 2004). In that research work, the phenomena of
choking of flow was studied in details and
experimental data was utilized to authenticate CFD
results. The experimental methodology was also
utilized to visualize the ejector pump flow field
which was integrated with Pulsed Detonation
Engine. The methodology helped in determining the
equivalence ratio which effectively induce
secondary flow (Hoke et al. 2002). The effect of
different geometrical configurations of primary
flow inlets on the turbulent flow regime of jets was
investigated using Reynolds Stress Model and it
was concluded that development of the triangular
jets is stronger than others (Kim and Park, 2013).
To comprehend the mixing and entrainment
mechanism inside the turbulent mixing region of
ejector pump, it is necessary to accurately simulate
the physics of turbulent structures as they are the
prime factor for above mentioned phenomenon. The
literature shows that turbulence models based on
RANS technique have deficiencies in identification
and visualization of these important flow features
(Yodere et al. 2013) as vortical structures are
transient in nature. On the other hand, LES based
turbulence models are more suitable for
visualization of such turbulent structures in
complex flow region like that of ejector pump
(Zaheer and Masud, 2017). The accurate estimation
of turbulent viscosity in such complex flows is also
important as pressure and velocity profiles are
directly linked to flow viscosity. Here again, the
RANS turbulence models lack accuracy in
numerically replicating the flow characteristics
(mass flow rate) (Masud and Imran, 2015) when the
flow field inside the subject pump was simulated
and analyzed using Standard K- family of
turbulence models for closure. The simulated results
once compared to the experimental test data showed
an over predicted mass flow rate due to the complex
nature of flow which is mostly pronounced by the
turbulent shear and mixing layers. The study
showed that to numerically replicate the
experimental data, the model coefficients needed
recalibration (Masud and Javed, 2007). Hence, a
priori simulation of subject pump flow field was
not obtained as the model constants were tweaked
randomly.
In present study, flow domain of subject pump is
first simulated and analyzed using Large Eddy
Simulation based turbulence model and then
comparison is carried out with the experimental
data for validation of results. The underlying
reasons behind why the performance of RANS
turbulence models is much less uniform for
complex flows, like the one of subject pump, are
explored and analyzed by comparing the simulated
flow field characteristics using LES and RANS
based turbulence models.
2. TURBULENCE MODELING
As the performance of RANS based turbulence
models for accurate flow characterization of
complex flows is inadequate (Menter, 2011), hence
the advantages of Large Eddy Simulation based
models are explored in the present study. In LES
based turbulence models, the turbulent kinetic
energy associated with larger vortical structures of
the flow is resolved and only small, isotropic and
homogeneous eddies are modelled (Bouhanguel et
al. 2015). But the high computational power
requirement for performing LES based simulations
makes it tedious and computationally inviable for
engineering problems. Embedded LES, a hybrid
RANS-LES turbulence model, is then utilized to
overcome the computational cost barrier associated
with LES but at the same time taking advantage of
LES based models in region of interest i.e. high
turbulence region is numerically solved using LES
whereas rest of the flow field is solved numerically
using Standard k–ε turbulence model. The proposed
methodology is performed using ANSYS Fluent®
(Cokljat et al. 2009).
Mathematical formulation of Standard K-
turbulence model, which is based on transport
equations for the turbulence kinetic energy (k) and
its dissipation rate (), is given as follows:


ii
ij
ii
t
iki
uu
uu
xx
k
xx
k
k
t






















 (1)
and ‘’ is modeled as

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387
Fig. 1. Various sections of Ejector Pump.
Table 1 Geometrical features of ejector pump
Primary Nozzle
(mm) S- Sec Inlet Dia
(mm)
Mixing Chamber
Dia (mm)
Mixing Chamber
Length (mm)
Diffuser Sectio
n
Length (mm)
Pump Outlet
Diameter (mm
)
Inlet Dia Exit Dia
18 7 50 34 272 271 72


2
12
it
ij j
k
u
txx x
CC
kk


 








 



(2)
The eddy viscosity  is expressed as:
2
tt k
CL k C

 


(3)
The constants carry the default values: C=0.09,
C1=1.44, C2=1.92, k=1.0 and =1.3.
Utilizing the Kolmogorov theory of turbulent flows,
Large Eddy Simulation based turbulence models
explicitly solve the large eddies whereas implicitly
solve for eddies of small sizes by incorporating sub
grid-scale turbulence model. To decompose
resolved and modelled field, a filtering function G
is used which decomposes the subject field into a
resolved and subgrid scale modeled parts. The
function G is generally defined as:
   
i
ux Gx u d 


 
(4)
This result in
iii
uuu

 (5)
Here 
 is the resolved part of velocity vector where
as 
 is modelled subgrid part. The filtering
operator used in LES is the grid cell dimension (box
filter), therefore the resolved length scales of
turbulent flow filed can be estimated by knowing
the maximum grid cell dimension. Once this
filtering function is applied to Navier Stokes
equations, it resulted in nonlinear advection terms.
ij i j i j
uu uu

 (6)
To solve these turbulent stresses term, WALE
subgrid scale model is used in the LES domain of
the flow field. WALE model is based on
Boussinesq hypothesis for calculation of SGS stress
tensor.
3. GEOMETRICAL AND
NUMERICAL SETUP
The under-investigation pump, being a component
of aircraft fuel system, is immersed in fuel
contained in the fuel tanks. To transfer this bulk of
fuel from one tank to another, a high pressure,
known as motive fuel, from fuel pump is injected
into ejector pump through primary fuel nozzle.
Once this stream of high velocity fuel is discharged
from primary nozzle, it creates a low-pressure
region in the near field of primary nozzle, hence
entrains fuel from fuel tank via secondary nozzle.
The pressure of bulk of fuel is thus increased once it
flows out of the ejector pump due to momentum
transfer between primary and secondary fluid
streams. The different components of the subject
ejector pump are displayed in the Fig. 1.
The geometrical details of subject pump are given
in Table 1. The dimensions of subject pump are
rendered into the CAD Model (3D) using Gambit®
software and meshing is also carried out in the same
software.
For analyzing the flow field using Embedded LES,
the complete fluid domain of pump needs to be
divided into RANS and LES zone where respective
turbulence models can operate independently. The
defined fluid zones and accompanying interfaces
are displayed in Fig. 2. The placement of RANS-
LES interfaces is such that they must lie in section
of uninterrupted equilibrium. For conversion of
modelled TKE from RANS zone to LES zone,
Vortex Method is used to generate synthetic

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388
Fig. 2. CAD model of pump displaying fluid zones and interfaces.
Fig. 3. Contours of ILS in LES zone.
turbulence at specified RANS-LES (Mathey et al.
2003) and no perturbation is generated synthetically
at LES-RANS interface.
The quality of LES performed is highly dependent
on fineness of the grid cells. From the Turbulent
Kinetic Energy spectrum analysis, it is evident that
approximately 80 % of total TKE is contained in
eddies of integral length scales. Hence this length
scale must be sufficiently resolved while simulating
flow field using LES. By knowing the distribution
of turbulent structures equivalent to dimensions of
Integral Length Scale (ILS) inside the flow domain
of pump, an estimation to maximum grid cell
dimensions can be ascertained. The length scale ()
is given by the Eq. (7) and its distribution on the
grid using a precursor RANS simulation is shown in
Fig. 3.
3/2
ok
l

 (7)
From Fig. 3, it is evident that a maximum cell
dimension of ×
 m may resolve the turbulent
eddies of integral length scale. The structured mesh
of 2.44 Mil in RANS and 9.8 Mil in LES zones is
generated. The mesh details are shown in Fig. 4.
The time step size of 5µsec is used to satisfy the
CFL~1 requirement for LES. The properties of fuel
(jet A-1) are used and it is treated as incompressible
fluid. Pressure boundary conditions are used at
primary nozzle inlet (three different settings), fuel
tank inlet (hydrostatic pressure corresponding to
fuel height above the ejector pump) and pump
outlet (values corresponding to nozzle inlet
pressures). The values are extracted from previously
used test data (Masud and Javed, 2007).
4. RESULTS AND DISCUSSION
4.1. Quality Estimation of LES
The quality of Large Eddy Simulation performed
for analyzing the flow characteristics of subject
ejector pump is assessed by following methods:
(i) Assessment of Grid Resolution
The qualitative analysis of LES which is embedded
inside a global RANS domain, is carried out using
methodology proposed by Celik et al (2005). The
LES Index of Quality (LES IQ) compares the
turbulent viscosity to that of laminar one using the
following relation.

0.53
1
10.05 sgs
LES IQ








(9)
The constant values used in the above-mentioned
relation are calibrated such that index acts like the
ratio of resolved to total turbulent kinetic energy.
As it is a dimensionless number and varies from 0-
1, the LES IQ greater than 0.8 is representation of a
good LES whereas 0.95 and higher is referred as

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(a)
(b)
Fig. 4. Mesh Details (a) X-sectional view (b) Isometric View at various cross sections of pump.
Fig. 5. LES quality index plot.
DNS (Celik et al. 2005). The distribution of index
over LES zone inside flow domain of pump for one
of the test cases, is shown in Fig. 5. It is apparent
that sufficient grid resolution is incorporated,
satisfying the laid down quality criteria for LES.
(ii) Eddy Viscosity Modeling
The other parameter for estimating the quality of
LES is the extent of modeling of turbulent viscosity
by the subgrid scale model. As per the literature,
subgrid scale turbulent viscosity must be far lesser
than that of RANS turbulence model and if the SGS
viscosity completely vanishes then it is plausible to
assume LES solution as DNS one. In Fig. 6, the
modelled turbulent viscosity by WALE SGS model
in case of LES and that of Standard k–ε RANS
model, is compared at two different cross section of
the ejector pump. The selected locations are the
inlet of S section and the inlet of mixing section. It
is clearly inferred from these plots that the modelled
turbulent viscosity by WALE SGS model is far
smaller than that of Standard k–ε RANS model,
hence ascertaining the better quality of LES
performed in this study.
4.2. Validation of Results
The matrix of the experimental data of subject
ejector pump [9] includes the range of Primary
Nozzle inlet pressure from 0.6 MPa to 2.0 MPa with
the interval of 0.2 MPa. Out of this matrix, three
test cases are selected i.e. primary nozzle inlet
pressure of 0.6 MPa, 1.2 MPa and 1.8 MPa for
numerical simulation of the flow field of ejector
pump. The parameters of ejector pump flow field
which are of paramount importance include
pressures and mass flow rates at pump outlet,
secondary flow inlet and primary nozzle inlet. The
values of these parameters obtained after
performing ELES numerical simulation of ejector
pump flow field are then validated against the
experimental results. The Standard k–ε simulation
results from the previous study are also plotted, Fig.
7, depicting inadequacy of RANS turbulence model
of reproducing experimental results. It is clearly
inferred from the comparison that the results
obtained from high fidelity Embedded LES are
improved than RANS model with default values of
constants used in its mathematical model. Hence the
Embedded LES technique can be utilized to predict
a priori simulation of the under-investigation pump
flow field. It can be inferred from the Fig. 7 that
with the default values of constants, the Standard k–
ε RANS model accurately simulates the pressure at
the boundaries of ejector pump but there is a
variation in results with respect to experimental

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(a)
(b)
(c)
Fig. 6. Comparison of modelled turbulent viscosity at primary nozzle pressures of (a) 0.6 MPa (b) 1.2
MPa (c) 1.8 MPa
values as far as mass flow rate prediction is
concerned. The RANS turbulence model over
predicts the mass flow rate at the ejector pump
outlet. This deficiency of RANS model is overcome
by the ELES simulation as the results for prediction
of both pressures and mass flow rate are closer to
the experimental values.
The performance parameters of the ejector pump
like Mass Flow Ratio M, Pressure Ratio N and the
efficiency η are also calculated based on the results
obtained from Embedded LES simulation. These
results are also validated against the experimental
values, shown in Table 2 and found in better
agreement. Hence the performance of pump is also
validated.
4.3. Flow Field Analysis Using Embedded
LES
The static pressure profiles for three test cases are
shown in Fig. 8. The generation of turbulent

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Table 2 Comparison of ejector pump performance parameters between Embedded LES &
Experimental values
Inlet press(MPa)
Pump Outlet
press (MPa)
Primary
Nozzle MFR
(Qp)
Secondary
Nozzle MFR
(Qs)
MFR ratio
(M) Ef (η)
Pri
Nozz
Sec
Nozz Exp ELES Exp ELES Exp ELES Exp ELES
0.60 0.00224 0.025 1.17 1.15 4.76 4.79 4.06 4.16 0.161 0.164
1.20 0.00224 0.051 1.65 1.63 6.72 6.84 4.06 4.20 0.172 0.178
1.80 0.00224 0.078 1.98 1.98 8.17 8.37 4.12 4.23 0.181 0.185
structures at the primary nozzle exit is the reason
for pulsating behavior of pressure along the flow
path. The low-pressure region is the consequence of
phenomenon of generation of turbulence (Aldas and
Yapici, 2014) (Karimipanah, 1996). As the flow
travels downstream, the primary and secondary
flow streams get mixed and momentum exchange
takes place which recovers the static pressure from
negative peak. The static pressure is further
increased to design outlet pressure in the diffuser
section.
(a)
(b)
Fig. 7. Comparison of Exp, ELES and Standard
K-ε results (a) Pump outlet pressure (b) Pump
outlet Mass flow rate.
Fig. 8. Averaged Static Pressure profile.
The velocity variation along the centerline of pump
is depicted in Fig. 9. The high-speed flow ejects
from exit of primary nozzle and discharges into the
domain of relatively static flow. As this high
velocity flow encounters fluid from secondary
nozzle, it transfers its momentum to the later one,
consequently, its velocity reduces. The distance
downstream of primary nozzle where the velocity
almost remains unchanged is called the “potential
core”. This region of uniform flow vanishes
because of spreading of shear layers. The mixing of
jet flow is characterized by the decrease of the
centerline velocity after potential core.
The mixing and entrainment phenomenon of ejector
pump fluid streams can be accurately computed by
analyzing the distribution of TKE across flow
domain. The profile of Tubulent Kinetic Energy,
Fig. 10, shows where the kinetic energy of turbulent
structures is low, the region is more pronounced by
less turbulence and alongcenterline, it is the region
where potential core exists. Once the uniform
velocity region culminates on the centreline, the
kinetic energy of vortices increases, thereby
increasing the the mixing and entrainment between
the two fluid streams. The crest of Turbulent KE
profile lies in the region where shear layers,
initiated from the lip of primary nozzle, meet each
other. The dissipation of TKE takes place as
momentum exchange between secondary and
primary fluid streams reaches equillibrium state.
The shedding of larger eddies into realtively smaller
eddies decreases the magnitude of TKE further
downstream until it vanishes out.

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(a)
(i)
(ii)
(iii)
(b)
Fig. 9. (a) Variation of Averaged Velocity Profile
(b) Instantaneous Velocity Contours for primary
nozzle pressures of (i)0.6 MPa (ii)1.2 MPa (iii)
1.8 Mpa.
In to visualize the tubulent structures present in the
flow domain of ejector pump, iso contours of Q-
criterion are plotted for each case and are coloured
with instantaneous velocity. The plots are shown in
Fig. 11. The turbulent structures at the exit of the
primary nozzle are indicative shear layer generation
and hence mixing process. The phenomenon of
vortex shedding is also visible as the large vortical
structures break down to the smaller ones as the
fluid flows downstream. Such visualization cannot
be achieved from RANS based models.
Fig. 10. Variation of TKE along flow direction.
(a)
(b)
(c)
Fig. 11. Iso contours of Q-criterion colored by
mean velocity magnitudes at primary nozzle
pressures of (a) 0.6 MPa (b) 1.2 MPa (c) 1.8
Mpa.
4.4. Comparison of Ejector Flow
Characteristics : Embedded LES vs
Standard K-ε
The previous research work (Masud and Imran,
2015) (Masud and Javed, 2007) on utilizing the
RANS turbulence models and selecting the best for
reproducing the experimental results related to the
flow field of subject ejector pump suggests that
with the default values of constants used in the
mathematical modelling of RANS turbulence
models, they are inadequate to reproduce the
experimental mass flow rates. To identify the

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reasoning behind lack of accuracy of Standard k–ε
RANS turbulence model for prediction of complex
flow fields, a comparison of flow characteristics
obtained from Standard k–ε and Embedded LES
simulations of ejector pump flow field, is drawn. As
it is evident that the behavior / trend of flow field of
ejector pump is somewhat similar in all three test
cases, hence the flow field of only first test case i.e.
of primary nozzle pressure of 0.6 MPa, is chosen
for comparison purpose.
(i) Comparison of Potential Core length
To compare the potential core length of subject
ejector pump, the unsteady statistics of the
instantaneous velocity field simulated by Embedded
LES are gathered for a sufficient flow through time.
The mean velocity contours are then plotted on the
cross-sectional view of ejector pump domain. These
results are then compared with that of Standard k–ε
simulation. The contour plots, Fig. 12, and mean
velocity profile plot, Fig. 13, reveal that RANS
based simulation overpredict the length of potential
core as compared to that of Embedded LES.
(a)
(b)
Fig. 12. Comparison of Potential Core prediction
(a) Standard k–ε (b)
Embedded LES.
The reason behind this deficiency of Standard k–ε
RANS model is that it underpredict the initial shear
layer growth rate. The turbulent structures in near
field of jet region, at the end of potential core and
farther downstream are different from each other
due to flow physics. Hence, each region would
require separate calibration of model constants,
however, this has not been the case and a single set
of Standard k–ε model constants are used whose
calibration is based on fully turbulent flow.
Therefore, the turbulence level of eddies is reduced
which slows the shear layer growth rate throughout
the flow field. This poor performance of RANS
model results in weak mixing in shear layers of jet,
yielding potential core length that are longer than
the Embedded LES simulation. As the shear layer
growth rate is largely influenced by structural
details of large coherent structures, the Embedded
LES directly resolves the large turbulent coherent
structures through the use of unsteady Navier
Stokes equations and hence accurate simulation of
potential core length.
Fig. 13. Comparison of Averaged Velocity
Profile.
(ii) Comparison of Jet Flow Spread Rate
For the prediction of primary jet flow spread rate,
the mean velocity profile obtained from Embedded
LES and RANS models are plotted at two different
cross sections i.e inlet of S section and inlet of
Mixing Section, Fig. 14. It is very much evident
from these plots that as the primary flow jet ejects
out of primary nozzle exit and flows downstream,
its outward spread into the secondary fluid due to
generation of shear layers and consequent turbulent
structures, is strongly underpredicted by Standard
k–ε RANS model than that of Embedded LES. A
similar deficiency is also observed by (S. Kubacki
et al. 2010),(Surya et al. 2017) and (Fernandez et
al. 2007). Following are the mean velocity profiles
at said cross sections of ejector pump.
Fig. 14. Comparison of average velocity profiles
at two sections of ejector pump.

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The underprediction of primary jet spread rate by
Standard k–ε RANS model is due to the false
prediction of Reynolds shear stresses (u’v’) close to
the symmetry plane and in shear layers of jet. The
quantitative measure of the Reynolds shear stresses
represents the transports of momenta by coherent
structures’ motion. The evaluation of these stresses
help in estimating of momentum being transported
by the coherent turbulent structures between the
primary and secondary flows. The quantitative
analysis of these Reynolds shear stresses at defined
cross section of ejector pump, Fig. 15, explains that
momentum transfer between the primary and
secondary fluids is underpredicted by Standard k–ε
RANS model as compared to that of Embedded
LES. Due to this deficiency of Standard k–ε RANS
model, the jet spread rate is also underpredicted and
hence the numerically simulated mass flow rate at
the pump outlet is overpredicted than the
corresponding experimental value.
Fig. 15. Comparison of (u’v’) Reynolds Shear
Stress profiles at two cross sections of ejector
pump.
5. CONCLUSION
The analysis of comparison of turbulent flow
characteristics between the Standard k–ε RANS
model and Embedded LES simulations of ejector
pump flow field reveals a strong deficiency in
Standard k–ε model for simulating the complex
flow fields. This deficiency of said model is due to
its reliance on Boussinesq Approximation for
modeling of eddy viscosity μ
t
. The Standard k–ε
RANS model constants are calibrated for spreading
rate of jets in fully developed region and as this
model is based on eddy viscosity, it does not
possess enough freedom to calibrate itself for non-
homogenous, anisotropic region of the flow
domain. As in case of ejector pump flow field, the
primary region of interest is the flow developing
region located in the nearfield of primary nozzle
exit where the turbulence is in non-equilibrium
state. The Standard k–ε RANS model fails to
accurately model this developing region of the flow.
However, the same region is resolved in Embedded
LES simulation to the extent of integral length scale
of turbulent spectrum present in ejector pump flow
field. Hence, the results obtained are in better
approximation to the experimental data. Therefore,
it is concluded that LES based turbulence models
can be used as a priori to estimate ejector pump
performance characteristics.
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