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Comparative study of Non-premixed and Partially-premixed combustion

simulations in a realistic Tay model combustor

Article in Applied Thermal Engineering · January 2017

DOI: 10.1016/j.applthermaleng.2016.08.223

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 Comparative study of Non-premixed and Partially-premixed combustion
simulations in a realistic Tay model combustor
K. Zhang * · A. Ghobadian · J. M. Nouri
School of Mathematics, Computer Science and Engineering, Department of Mechanical Engineering, City University
London, Northampton Square, London EC1V 0HB, UK.

Keywords: CFD; Combustion Modelling; Gas Turbine Combustor; Non-Premixed Flame; Partially-Premixed
Flame

Abstract
A comparative study of two combustion models based on non-premixed assumption and partially premixed
assumptions using the overall models of Zimont Turbulent Flame Speed Closure Method (ZTFSC) and Extended
Coherent Flamelet Method (ECFM) are conducted through Reynolds stress turbulence modelling of Tay model gas
turbine combustor for the first time. The Tay model combustor retains all essential features of a realistic gas
turbine combustor. It is seen that the non-premixed combustion model fails to predict the combustion completely
due to an incorrect assumption of diffusion flame scenario invoking infinitely fast chemistry in complicated flow
environments while the two partially premixed combustion models accurately predict the flame pattern in the
primary region of the combustor. The ZTFSC model outperformed the ECFM model by producing a better
temperature agreement with the experimental result. The latter model predicts lower temperature due to the
underestimation of reaction progress. Additionally, a cross-comparison of the present RSM prediction invoking
ZTFSC model with LES prediction reported in the literature is conducted. The former produces more accurate
species concentration and flame pattern than the latter. This is mainly due to the incorrect assumption of non-
premixed combustion used in LES prediction reported in the literature. It is interesting to find that when non-
premixed combustion model is used for both RSM and LES predictions, the LES predicts higher temperature
closer to the injection nozzle of combustor than the RSM model, though the flame shape in both cases is incorrect.
This is mainly due to the fact that the traditional RANS model dissipates the energy of swirling flow too fast in the
primary region of the combustor. The weaker centre recirculation zone (CRZ) created by vortex breakdown
recirculate less air to the area near the injection nozzle resulting in fuel rich combustion. It indicates that the
temperature difference between predicted results using RSM in conjunction with ZTFC model and experimental
results can be improved by using less energy dissipating turbulence models such as scale resolving simulation
(SRS).

1. Introduction

The advent of Gas-Turbine for military purposes tracks back to 1940s, and it is subsequently used for aviation and
later for ground level power [1]. The main challenge of aviation industries nowadays is the efficiency, stability of
combustion and pollutant control, such as the emission of carbon dioxide (CO2), nitrogen oxide, sulphur dioxide
and etc. In order to design combustors with desired features and meet with relevant criteria, improved
understanding of turbulent combustion through both realistic experimental observation and numerical simulation
and validation is required. The former alone is expensive for industries before a more cost-effective numerical
prediction is performed. However, the accuracy of the numerical simulation is doubtful as it is highly dependent on
the turbulence and combustion models, i.e. the mixing and chemical reactions. To improve the reliability of
simulations, turbulence models which are able to resolve the majority of turbulence features together with the
combustion models which can incorporate detailed chemical reactions are developed under more realistic
assumptions.

Due to the complexity of a realistic gas turbine combustor, most researchers focused on performing CFD
simulation in a combustor-like burner where fuel and oxidizers are injected separately and no additional oxidizers
are injected from other inlets [2-6]. The non-premixed combustion models which employ the infinitely fast
chemistry assumptions are commonly used to predict such diffusion flames and are presumed to be an effective
model in more complicated flow configuration. While, in a realistic gas turbine combustor, two major complexities
make the non-premixed combustion model incorrect: the primary jets which introduce extra oxidizer to premixed
mixtures and the extended flame residence time dominated by the strong swirling flow. Hence, the non-premixed
combustion models are incorrect propositions when they are used in realistic gas turbine combustors where
partially premixed flame occurs due to extra reactants from other inlets.

In a realistic gas turbine combustor, when primary jets introduce extra oxidizers into the premixed mixtures, the
local status of premixed mixtures is assumed to be fully burnt if infinitely fast chemistry is assumed. However, in
reality, chemical reactions are never infinitely fast. The local reactions amongst mixtures/reactants are only
partially progressed which is tracked through the so-called progress variable. Besides, other than the extra oxidizer
introduced by primary jets, the cooling airs from porous walls of realistic combustor further reduce the confidence
of using non-premixed models. Although the flow rate from the porous wall is relatively low compared to the
mainstream, and is commonly assumed not to be involved in any reactions, it is argued that part of these flow is
actually brought into self-ignition region by the strong centre recirculation, and they do influence the reactions due
to the extended flame residence time. It might be concluded that the more complex the flow configuration is, i.e.,
with the strong swirling flow and multiple inlet jets, the worse the performance of non-premixed combustion
models will be due to the infinitely fast chemistry assumption.

In the past, many researchers have employed non-premixed combustion models to interpret the reactions in
realistic gas turbine combustors where partially premixed flame occur. Although some predictions employing non-
premixed assumptions are seen in reasonable agreement with experimental results particularly those using large
eddy simulation (LES), the flame pattern predicted is incorrect mainly in the primary region where two side flames
near the combustor walls are predicted which is inconsistent with experimental result [7-9]. Besides, the use of
LES requires huge computational power and is unaffordable for most industrial problems. On the other hand, the
far less computational power required Reynolds average Navier-Stoke (RANS) method fails to predict the reacting
flow in realistic gas turbine combustors accurately [10]. The principle cause is attributed to the use of the
unsuitable non-premixed combustion model rather than the problem of widely used RANS models. In a simple
burner, both scale resolving simulation (SRS) and RANS methods are seen to provide acceptable results with the
former showing a better agreement [11, 12].

Within the partially premixed combustion model, the status of local mixtures: either burnt, unburnt or partially
burnt, is determined by tracking the propagation of the flame front. The burnt mixtures behind the flame front are
treated similarly as in a diffusion (or non-premixed) flame, while the unburnt regions ahead of flame front are
represented by cold mixtures. To track the flame front propagation, a transport equation of progress variable C is
solved. The model has been applied to many simple combustor-like burners [2, 13-18], but far less attention has
been paid on the performance of this model in a realistic combustor. In addition, there is a lack of comparative
studies on the performance of partially premixed combustion and non-premixed models in complicated flow
configurations and most comparisons are only performed in a simplified burner which provides limited confidence
for applying these models to realistic gas turbine combustors.

To compensate for these gaps, a realistic Tay gas turbine combustor which includes complicated features such as
fuel injector, swirler, primary holes, dilution holes, discharge nozzle, and porous wall is simulated in this paper.
The objectives of the current paper are first to investigate and provide remedies to the deficiencies that have been
observed in past simulation [7] of realistic gas turbine combustors, and second to demonstrate an effective and
efficient combustion model for predicting realistic gas turbine combustors by comparing the performance of the
widely used non-premixed with partially premixed combustion models. The Reynolds stress turbulence model is
chosen to solve the mixing problem, and steady laminar flamelet modelling (SLFM) is chosen to simplify chemical
reactions. Pre-PDF (probability density function) method is employed for turbulent combustion interaction. To
reduce the uncertainties that might be induced by chemistries, 247 chemical reactions and 50 species are employed
to represent the full chemistries involved in the combustion of propane [19]. The flame front propagation in the
partially premixed combustion model is tracked by solving a transport equation for the density weighted mean
reaction progress variable.

2. Mathematical model

In this study, to predict the turbulent combustion in a realistic gas turbine combustor, the Reynolds Stress Model
(RSM) is used to describe the mixing problem. The model is seen to provide better performance in simulating the
strong swirling flow by abandoning the Boussinesq approximation for 2nd order moments and solving six Reynolds
stress of 𝜏𝑖𝑗 appearing in 3D RANS momentum equations directly. As the main objective of this study is to
investigate the performance of different combustion models in gas turbine combustor where stationary flow
assumption can be utilized, the RSM model is chosen for the very fast turn-around and far less computational
resources requirements compared to inherently transient methodologies such as LES, DES, and etc.

Non-premixed combustion: In the non-premixed flame, fuel and oxidizer are injected into the combustion
chamber separately. The reaction rate is mainly controlled by the rate of mixing of fuel and oxidizer, and therefore,
the generated flame due to this process is also called diffusion flame. The non-premixed combustion is said to be
rate limiting process as the regimes of modelling this combustion requires the consideration of both reaction time
and mixing time, and which is described by Damkohler number Da = 𝜏𝑡 /𝜏𝑐 . Poinsot et al. [20] introduced a
regime diagram for non-premixed flame according to the Damkohler number and the turbulence Reynolds number
𝑅𝑒𝑡 = 𝑢′ 𝑙𝑡 /𝜈 shown in Fig 1.

Fig. 1 Regime diagram for non-premixed combustion. [20]

The figure divides the turbulent non-premixed combustion problem into three regimes.

A) When the chemical reaction time is much smaller than mixing time, i.e. for fast chemistry, the reactive layer of
the flame is assumed to be thinner than the diffusion layer. The smallest Kolmogorov size which is equal to the
diffusion layer has no effect on the inner reactive layer, and the turbulent flame is assumed to be composed of
laminar flamelets. The flamelet regions are bounded by the flame Damkohler number and the Damkohler number
of laminar flamelet assumption (LFA), Da 𝑓𝑙 = 𝐷𝑎𝐿𝐹𝐴 . The flame Damkohler number is defined by the ratio of
flow time scale to chemical time scale, the former can be estimated using the averaged scalar dissipation.

B) For slightly larger chemical time scale, the reactive layer is thickened to the size of Kolmogorov length scale,
the LFA is no longer valid, and unsteadiness effect is expected.

C) When the chemical reaction is too slow, the too fast diffusion of the mixture into the reactive layer is not
combusted and flame tends to extinguish. The extinction region is bounded by Da = 𝐷𝑎𝑒𝑥𝑡 .

In the present paper, the fast chemistry assumption made in regime A and the steady laminar flamelet method
(SLFM) is employed not only in non-premixed combustion but also in partially premixed combustion. The
thermochemistry involved in non-premixed combustion is reduced to a single scalar variable, the mixture fraction,
denoted by Z. Complete chemical state information can be derived from Z through chemical state relationship, ∅ =
∅(Z) where ∅ can be quantities such as species mass fraction, temperature and density. The presumed probability
density function (PDF) is used to account for turbulence–chemistry interaction and is to be discussed in the
following sections as well as the discussion on SLFM method.

Partially-premixed Combustion: In the majority of engineering applications, neither pure premixed nor non-
premixed combustion occurs individually. Especially in a realistic gas turbine combustor, the pure consideration of
non-premixed combustion has vital defects though the fuel and oxidizer are usually injected to the combustor
individually and behaves like diffusion jets. To overcome this problem, a partially premixed combustion model is
employed by combining the premixed and non-premixed combustion models. The injected fuel and oxidizers in
the combustor are only classified by their two statuses, either combusted or not combusted. For the combusted
burnt mixtures, the regime A in non-premixed combustion model can be employed to decide the properties of the
flame. For unburnt mixtures, the simple mixing problem can be easily solved without reactions. The only question
is how to solve the status of local mixtures. An extra transport equation for the so-called reaction progress variable
can be employed to track the position of the flame front. The method has been used in premixed combustion
models for many years.

In partially premixed combustion mode, the progress variable is essentially used to compensate the deficiencies of
mixture fraction theory as the mixture fraction does not contain any intrinsic information about the progress of
chemical reactions. The local status of the mixtures is mainly distinguished by the amount of reactions progressed.
The transport equations of the progress variable and mixture fraction are shown in equation 1.

𝜕𝜌𝑍
+ ∇ ∙ (𝜌𝑢𝑘 𝑍) = ∇ ∙ (ρ𝛼𝑧 ∇𝑍)
𝜕𝑡
{𝜕𝜌𝐶 (1)
+ ∇ ∙ (𝜌𝑢𝑘 𝐶) = ∇ ∙ (ρ𝛼𝑐 ∇𝐶) + 𝜌𝜔𝑐
𝜕𝑡

Where 𝛼𝑧 = 𝜇𝑡 /𝜎𝑡 , and the turbulent Prandtl number 𝜎𝑡 takes the value of 0.85, 𝛼𝒄 = 𝜇𝑡 /𝑆𝑐𝑡 and the turbulent
Schmidt number 𝑆𝑐𝑡 takes the value of 0.7. The density weighted scalar quantities such as species mass fractions in
a thin flame can then be calculated as in equation 2.

1 1
∅ = C ∫0 ∅𝑏 (𝑍)𝑝(𝑍)𝑑𝑍 + (1 − 𝐶) ∫0 ∅𝑢 (𝑍)𝑝(𝑍)𝑑𝑍 (2)

Where 𝑝(𝑍) represents the presumed PDF (see equation 25). When C=1, mixtures are burnt so that the regime A in
non-premixed combustion is adopted, when C=0, purely mixing problem is solved using mixture fraction theory.
While, when mixture is fully burnt (C=1), as the strained steady laminar flamelet method has been used for current
study, the density weighted scalar quantities are not only a function of mixture fraction, but also a function of
scalar dissipation/strain rate as shown in equation 8. Besides, in order to solve the progress variable in equation 1,
modelling must be provided to the reaction progress term 𝜔𝑐 (which is also called mean reaction rate).

Five regimes as shown in Fig 2 have been proposed to describe the behaviour of the flame front under the impact
of turbulence and chemical reactions. In this paper, two regimes are employed to provide closure to the term 𝜔𝑐 ,
the Zimont Turbulent Flame Speed Closure Method and extended coherent flamelet method.

Fig. 2 Regime diagram for premixed combustion. [21]

Zimont Turbulent Flame Speed Closure (ZTFSC) Method: The mean reaction rate in equation 1 can be modelled
as [22]:

𝜌𝜔𝑐 = 𝜌𝑢 𝑈𝑡 |∇𝐶| (3)

Where 𝜌𝑢 is the density of unburnt mixture and 𝑈𝑡 is the turbulent flame speed which must be evaluated. The
ZTFSC model belongs to the group of turbulent flame speed (TFS) methods. There are many other models to
decide the TFS, but are not used here [23].

The ZTFSC method computes the turbulent flame speed by considering the wrinkled and thickened flame front
and the regime used locates in the region of thin reaction zones in Figure 2. The thin reaction zone regime assumes
that the smallest Kolmogorov size is smaller than the diffusion layer and penetrates to the flame zone, but is still
larger than the reactive layer, so the theory of laminar flamelet still applies. The thin reaction zone is quantified by
Karlovitz number, Ka, larger than unity and Ka is defined as the ratio between the flame time scale and
Kolmogorov time scale. The ZTFSC method computes the turbulent flame speed by:

3/4 1/2 −1/4 1/4

𝑈𝑡 = 𝐴𝑢′ 𝑈𝑙 𝛼 𝑙𝑡 = A𝑢′ (𝜏𝑡 /𝜏𝑐 )1/4 (4)
Where A takes the value of 0.52 recommended in [22], 𝑢′ represents root mean square (RMS) velocity. 𝑈𝑙 , the
laminar flame speed can be calculated either based on the proposed correlation by Metghachi and Keck [24] or
from fitted curve achieved from the simulation of the laminar flame speed [25]. The latter is used in the present
paper. The α in the equation 4 is the molecular heat transfer coefficient of the unburnt mixture, and 𝑙𝑡 is the
turbulent length scale calculated from 𝑙𝑡 = 𝐶𝐷 𝑘 3/2 /𝜀 where 𝐶𝐷 equals 0.37, 𝑘 represents turbulent kinetic energy
and 𝜀 represents turbulence dissipation rate. The regime used by ZTFSC model is also called Intermediate Steady
Propagation (ISP) combustion regime that the flame front consumes fuel at the speed proportional to the ratio
between turbulent time scale 𝜏𝑡 = 𝑙𝑡 /𝑢′ and chemical time scale 𝜏𝑐 = α/𝑈𝑙2 . The stretch effect is considered by
ZTFSC model by multiplying 𝜌𝜔𝑐 , the mean reaction term with a probability stretch factor G and details are not
discussed here, but could be found in [26].

Extended Coherent Flamelet Method (ECFM): Having discussed the thin reaction zone regime used in ZTFSC
model, it is interesting to consider the region where Ka is smaller than unity in Fig 2. Two regimes of wrinkled and
corrugated flamelets exist in this region and ECFM model is used to account for flame front corrugation by
involving a transport equation of flame area density, denoted by Σ. For wrinkled flamelets regime, the ratio of the
local turbulence velocity fluctuation to laminar flame speed is smaller than unity, indicating that turbulent eddies
are unable to deform the flame front, and only slight wrinkling could occur. While this is not practical as in most
engineering applications, the turbulent intensity is relatively large. The ratio of local turbulence velocity
fluctuation to laminar flame speed is larger than one and the flame front is corrugated. In both of the two regimes,
the smallest eddies are assumed to be larger than flame front thickness so the effect of turbulence is to wrinkle or
corrugate the laminar flame sheet. As the reactive layer of the flame is not perturbed by the smallest eddies, the
flame is quasi-laminar and theory of laminar flamelets applies.

The increased flame area due to wrinkling increases the fuel assumption rate and flame speed, so a transport
equation of flame area density in equation 5 is needed to track their effect [27].

𝜕𝜌Σ
+ ∇ ∙ (𝜌𝑢𝑘 Σ) = ∇ ∙ (ρ𝛼Σ ∇Σ) + 𝑆Σ (5)
𝜕𝑡

Where 𝛼Σ = 𝜇𝑡 /𝑆𝑐𝑡 and the turbulent Schmidt number 𝑆𝑐𝑡 takes the value of 0.7. The 𝑆Σ is composed of four
production terms and one dissipation term but the details are not provided here. Various models are proposed to
close these terms, and the closure method provided by Colin et al. [28] is employed in this paper. The computed
flame area density is then used to provide closure to the reaction progress term 𝜔𝑐 in equation 1:

𝜌𝜔𝑐 = 𝜌𝑢 𝑈𝑙 Σ (6)

Steady Laminar Flamelet Method (SLFM): As it has been discussed above, the SLFM is suitable for both the
ECFM and ZTFSC models. The basic concept of this method views the turbulent flames as an ensemble of 1D-
thin, laminar flamelets embedded in the turbulent flow field [23, 29-30]. Therefore, the concept is only applicable
when the smallest Kolmogorov eddies in the flow field are assumed to be larger than the reactive layer of the
flame.
The most often used laminar flame type can be represented by the geometry which consists of opposed,
axisymmetric fuel and oxidizer jets. When the velocity of jet increases or the distance between the two jet inlets
decreases, the flame is said to be strained and departs away from chemical equilibrium. An increasing high speed
of jets extinguishes the flame as in ‘wood fire blows off’ case, the high-speed wind which introduces oxidizers into
the flame does not enhance the flame but blow the flame off as the diffusion rate is much higher than reaction rate.
The strain rate can be defined as 𝑎𝑠 = 𝑣/2𝑑, but is often replaced by the scalar dissipation represented as:

X = 2D|∇Z|2 (7)

Where D is the diffusion coefficient. The equation defines the scalar dissipation as a function of diffusion rate and
gradient of mixture fraction. A zero scalar dissipation represents the status of chemical equilibrium. The general
laminar counterflow diffusion flame equations can be described in the mixture fraction space transformed from the
physical space by:

𝜕𝑌𝑖 1 𝜕2 𝑌𝑖
𝜌 = 𝜌𝑋 + 𝜔̇ 𝑖
𝜕𝑡 2 𝜕𝑍2
{ 𝜕𝑇 1 𝜕2 𝑇 1 1 𝜕𝐶𝑝 𝜕𝑇 1 𝜕𝑌𝑖 𝜕𝑇 (8)
𝜌 − 𝜌𝑋 − ∑𝑖 𝐻𝑖 𝜔̇ 𝑖 − 𝜌𝑋 − 𝜌𝑋 ∑𝑖 𝐶𝑝,𝑖 =0
𝜕𝑡 2 𝜕𝑍2 𝐶𝑝 2𝐶𝑝 𝜕𝑍2 2𝐶𝑝 𝜕𝑍2

Where 𝑌𝑖 is the ith species mass fraction, 𝐶𝑝,𝑖 and 𝐶𝑝 are the specific heat of ith species and the mixtures. 𝐻𝑖 and 𝜔̇ 𝑖
are the specific enthalpy and species reaction rate for the ith species.

In an SLFM approach, the first term on the L.H.S. of equation 8 disappears. The approach is strictly applicable to
fast chemical reactions and turbulence induced chemical non-equilibrium is mainly due to aerodynamic strain. By
employing this approach, the 247 chemical reactions and 50 species detailed chemical reactions [19] employed in
this study can be used to calculate the laminar opposed-flow diffusion flame in the mixture fraction space. The
steady laminar flamelets are tabulated beforehand considering the full scalar dissipation rate from chemical
equilibrium of 0/s to flame extinction of 58/s for accuracy purpose and to avoid high computational power required
in solving species in physical space.

Presumed Probability Density Function (Presumed-PDF):

In order to account for the turbulence-chemistry interaction, a Presumed-PDF method is employed. The method
considers the fluctuation of local mixture fraction by the turbulence through the mixture variance 𝑍′2 by employing
analytical solution of Beta-function:

Γ(𝑎+𝑏)𝑍𝑎−1 (1−𝑍)𝑏−1
P(Z) = (9)
Γ(a)Γ(b)

Where Γ is the gamma function, a and b are PDF parameters expressed as:

𝑍(1−𝑍)
𝑎 = 𝑍[ − 1]
𝑍′2
{ 𝑍(1−𝑍)
(10)
𝑏 = (1 − 𝑍)[ 2 − 1]
𝑍′

2
To determine the probability function, an additional transport equation for mixture fraction variance 𝑍 ′ must be
given:

𝜕 2 2 2
(𝜌𝑍 ′ ) + ∇ ∙ (𝜌𝑢𝑘 𝑍 ′ ) = ∇ ∙ (𝛼z′ ∇𝑍 ′ ) + 𝐶𝑔 𝜇𝑡 (∇Z)2 − 𝜌𝑋 (11)
𝜕𝑡

Where 𝛼z′ = 𝜇𝑡 /𝜎𝑡 and model constants 𝜎𝑡 (Prandtl number), 𝐶𝑔 are defined to be 0.85 and 2.86. 𝑋 = 𝐶𝑑 𝑍′2 𝜀/𝑘
defines the scalar dissipation rate and 𝐶𝑑 =2.0 [31].
3. Solution methods

In this study, the segregated semi-implicit algorithm simple method is used for pressure-velocity coupling scheme.
Transport equations, which are density weighted, are solved by commercial CFD code, Ansys Fluent 14.5 (Finite
volume method based) [32]. Hexahedral rather than tetrahedral mesh is constructed through Ansys ICEM to
improve the accuracy of prediction. Grid independence is checked by mesh refinement strategy and three mesh
densities of 0.7, 1.2 and 2 million are tested that the last one of 2 million meshes is chosen for present study to
ensure the highest accuracy. Second order upwind is applied to the momentum, progress variable, mean mixture
fraction, mixture fraction variance as spatial discretization method [33].

Experiment Simulated:

Fig. 3 shows the configuration of the model can type combustor described in Bicen, Tse and Whitelaw [34]. It
represents a realistic industrial Tay combustor retaining the essential components of the hemispherical head (blue),
cylindrical barrel (green), circular to rectangular discharge nozzle (cyan), swirler (yellow), fuel device, primary
holes (black) and secondary/dilution holes (purple). The wall of the combustor including head, barrel, and
discharge nozzle are made of ‘Transply’, a kind of porous material.

According to the experiment, six primary holes and six dilution holes are equally distributed around the cylindrical
barrel with the former having a diameter of 10mm, and the latter 20mm. However, it was shown that the radial
velocity profile of flow through primary holes has a tremendous impact on the flow field in the primary region.
Different peak values instead of the plug flow assumptions of radial velocity in the hole affect the central part of
combustor by promoting a stronger penetration of the jets. It was recommended by McGuirk and Palma [35] that
an artifice such as the reduction of the hole diameter by 14% corresponding to the discharge coefficient C D of 0.74
seems to be a good compromise in case no reasonable guess can be made about the shape of the profile. The use of
reduced diameter from 10mm to 8.6mm decreases the maximum axial velocity at a position closer to injection
nozzle and provides better velocity agreement with the experimental data. The swirler, mounted on the
hemispherical head, comprises 18 curved vanes and each of them was originally designed with a thickness of
0.56mm. To reduce the complexity of meshing, swirler vanes are not created. Instead, annular shape of swirler
(yellow) is used that the effective area at the swirler exit is computed and axial velocity component is determined
from the datum swirler exit area. The tangential velocity is obtained by taking into account of turning efficiency of
the vanes and blockage effects following the procedures of determining swirler boundary conditions suggested in
[36, 37]:

𝑊𝑠𝑤
ω=η 𝑡𝑎𝑛𝛼 (12)
𝐴𝑠𝑒 𝜌𝐶𝑑 (1−𝑏)

Where the blockage factor is taken as 0.1, and the turning efficiency is 0.92. Value of 0.75 is assigned to the
discharge coefficient, 𝐶𝑑 . The flow characteristics of the swirler used in the original experiment and this prediction
is available in the technical paper of Bicen and Palma [38].

The propane fueling device has 10, 1.7mm diameter holes equally distributed on a central cone section shown in
Fig 3. Preliminary experiments report the importance of the distribution of fuel holes around the cone section to
the symmetry of flow, but the effect of them has to be neglected here due to the insufficient information about their
exact positioning.
 (a) Isometric view (b) Left View

Fig. 3 Configuration of model can type combustor

A summary of the experimental conditions used in this prediction is given in Table 1. According to the
experiment, 6.9% of total air was injected through swirler, 13.6% through primary holes and 53.3% through
dilution holes into the combustor. To simplify the porous media problem, fixed mass flow rate of 6.6% of total air
is assigned to the hemispherical head (blue), 13.8% to the cylindrical barrel (green), and 5.8% to circular to the
rectangular discharge nozzle (cyan).

Table 1 Experimental condition

Exp ma mg Swirler P Tinlet AFR

(g/s) (g/s) Vane (atm) (K)
Angle
1 100 1.76 45 1 315 57

The computation of the current study was carried out on a 20 processing element solon cluster at City University
London. The steady RSM model based simulation greatly reduces the computational time that total wall clock time
of around 10 hours are spent for one prediction (2 million mesh). The past prediction based on LES requires total
wall clock time of 26,432 hours using 64 processing elements of Cray T3E at the University of Manchester is
unaffordable by most industries (1 million mesh) though the prediction is done in 2004 [7].

4. Result and Discussion

4.1 Behaviour of flow field and scalar variables

The streamlines of the velocity field coloured by mixture fraction are provided in Fig 4, showing the distribution of
mixture fraction under the impact of centre recirculation zone (CRZ). The black lines display the position of
stoichiometric mixture fraction. All three results show clearly the centre recirculation zone inside the combustor
resulting from the phenomenon of vortex breakdown. The CRZ tends to move to the downstream of combustor but
is prevented by jets from primary holes. In realistic gas turbine combustors, the primary jets are mainly used to
shorten the flame length and improve flame stability by reducing axial momentum and enhancing the intensity of
CRZ. The intensive CRZ returns hot products to the upstream of combustor where cold reactants are then self-
ignited to improve the stability of flame. Other than the big CRZ, the narrower and thinner corner wall
recirculation zone (WRZ) is also captured simply due to the sudden expansion of flow configuration.
 (a) (b)

(c)

Fig. 4 Streamline of flow field coloured by mixture fraction. (a) ZTFSC model, (b) Non-premixed model, (c)
ECFM model. Black solid line: stoichiometric mixture fraction=0.0639.

Although two results from the partially premixed combustion models of ZTFSC and ECFM show a similar
distribution of mixture fraction in the primary region, differences between them are noticed as well. The predicted
size of CRZ using ECFM model is seen to be much smaller than the one predicted by ZTFSC model. As the energy
trapped in the CRZ is initially generated by swirling jets, smaller CRZ may indicate higher angular momentum but
lower axial momentum. With lower axial momentum, the CRZ is not penetrating to the downstream and stopped
by primary jets. Instead, two smaller vortices are formed just after the CRZ due to the high lateral momentum of
primary jets. On the other hand, with higher angular momentum, the increased intensity of CRZ has trapped more
fuels in the primary region leading to a lower mixture fraction in the secondary zone (Disappear of the black solid
line). The intensity of CRZ in the primary region is simply represented by the vorticity of the flow shown in Fig 5.
The highly swirling core (HSC) is broken up for the prediction using ZTFSC model, while the result from ECFM
preserves the HSC indicating higher angular momentum. The preserved HSC from ECFM model is believed to
have increased the stability of flame.

In addition, as the main objective of this paper is to demonstrate the performance of different combustion models
in a realistic combustor, more focuses are put on the performance of non-premixed combustion model in Fig 4b
that the model performs completely different from the other two partially premixed models. A large amount of fuel
penetrates to the secondary zone of the combustor without being recirculated back to the upstream for re-ignition.
The difference must be caused by the fact that the non-premixed assumption overestimates the reaction rate in the
primary region while the partially premixed models employ a progress variable C to limit the reaction rate.
 (a) (b)

Fig. 5 Intensity of CRZ in primary region represented by vorticity = 9776.83/s for (a) ZTFSC model, (b) ECFM model.

Fig 6 shows the progress variable (reaction progress) contour for all three combustion models. The reaction
progress of unity indicates the local mixtures are fully combusted while the reaction progress of zero represents no
reaction. In non-premixed combustion, whenever the fuel meets with the oxidizer, combustion completed
immediately within the flammability limit. The reactions are said to be fully progressed under this condition and
the progress variable is assigned to be unity implicitly. While, the prediction by ZTFSC model has limited the
reaction progress in the region closer to the porous wall where cold jets extinguish the flame. Attentions are given
to the performance of ECFM model that the reactions in the primary region are greatly limited probably due to the
underprediction of the strength of turbulence.

(a) (b)

(c)

Fig. 6 Progress variable (reaction progress) contour. (a) ZTFSC model, (b) Non-premixed model, (c) ECFM model.

The temperature contours at several planes of the combustor are presented in Fig 7 to clearly show the impact of
different combustion models. The predicted flame by ZTFSC model is mainly preserved in the primary region of
the combustor with part of the flame near the sidewall of the secondary region for further combustion. No reaction
processes reach the liner/combustor walls, which is isolated by the cooling film formed by the cold injected air
from porous walls. While predicted flame by non-premixed combustion penetrate to the downstream of the
combustor that the flame temperature near the secondary holes is much higher than the temperature in the primary
zone (incomplete combustion in the primary zone). Not surprised that due to the limited reaction progressed
predicted by ECFM model, the combustion is not properly captured though the highest temperature occurs in the
primary region of combustor shown in Fig 7c.

(a)

(b)

(c)
Fig. 7 Temperature contours at axial position of 20mm, 50mm, 80mm, 130mm, and exit of combustor 210mm. (a)
ZTFSC model, (b) Non-premixed model, (c) ECFM model.
In Fig 8, the predicted temperature by Di Mare et al. [7] using large eddy simulation (LES) and non-premixed
combustion model is compared with the result by using partially premixed and RSM model in this study. Although
large temperature difference near the combustor walls is observed that Fig 8b has two side flames compared to Fig
8a, the flame of highest temperature is similar. Regardless of the turbulence models used, the main reason for this
differences can only be caused by the combustion models chosen.

(a) (b)

Fig. 8 Temperture in the primary zone: horizontal midplane. (a) ZTFSC & RSM model, (b) LES & Non-premixed
model, Colour scale: five levels between pink = 2200K and blue = 315K [7].

By observing Fig 6a and b at the position where two side flames occur, the ZTFSC model presents much lower
progress variable of around 0.20.3 compared to the non-premixed combustion model. Such a low value of
progress variable indicates the unburnt or partially burnt nature of local mixtures. The statistical comparisons of
the temperature and species concentration with experimental results are presented in the following section. The
two side flames are confirmed to be non-existent illustrating the importance of employing partially premixed
assumptions in complicated flow environment.

4.2 Statistical Results

In this section, the statistical results of the computation are discussed and compared with measurement [33], as
well as the prediction by Di Mare et al. [7]. Because of limited information about the shape of circular to
rectangular part at downstream of the combustor, only statistical result in the primary region is used for
comparison. The flame in the primary region is of the most interest to most researchers due to the complicated
multi-jets, highly swirling flow condition. The proper prediction of the flame in this region will usually indicate a
good estimation in the downstream of the combustor.

In Fig 9a, it can be clearly seen that the ZTFSC model predicts the temperature profile and thus the flame shape in
reasonable agreement with experimental result, though the temperature difference is noticeable. The two partially
premixed models show similar shapes while flame shape achieved by using the non-premixed model in our
prediction and from Di Mare et al. [7] are seen to be same. The non-premixed model has obviously failed in this
complicated flow configuration due to the fact that it is unable to capture the status of local mixtures where all
mixtures are implicitly assumed to have been burnt (progress variable=1, shown in Fig 6). On the other hand, the
partially premixed model is able to track the status of local mixtures to limit reaction rate and therefore, the two
side flames in Fig 8b are not formed as also indicated by measurements. In one word, the superior performance of
partially premixed model compared to the non-premixed model in complicated flow configuration is mainly
attributed to its ability to account for the imperfect/slow mixing of fuel and swirler air as well as the addition of air
through other routes such as porous wall and primary holes.

By comparing the result from Di Mare et al. [7] and the non-premixed prediction from our result, the temperature
difference can only be attributed to the different turbulence models employed in the predictions. It is widely
accepted that LES model is less dissipative and less energy of CRZ will be dissipated compared to RANS model
used in our prediction. It is believed that the more intensive CRZ allows the unburned fuel to be recirculated back
to upstream for further combustion and will certainly improve the local temperature.

(a) (b)

(c)

Fig. 9 Profile of temperature and mixture fraction in the horizontal midplane of the combustor.

Due to the fact that the CRZ predicted by RANS model is less intensive due to over prediction of mixing, more
fuel is held near the primary holes without being recirculated to the upstream of the combustor. This extra amount
of fuel mixes with oxidizers thoroughly allowing the combustion to happen at approximately stoichiometric
mixture fraction. Meanwhile, insufficient oxidizers from primary holes are recirculated to the upstream of primary
region resulting in fuel rich combustion at x=20mm. Therefore, the temperature predicted by RANS model is seen
to be higher than the one by LES [7] shown in Fig 9b. In addition, in Fig 9c, the mean mixture fraction predicted
by the two partially premixed combustion models are seen to be the same, the temperature differences predicted
can only be caused by the underestimation of progress variable by ECFM model shown in Fig 6.

The profile of various species mole fractions are presented in the following figures, improvements by using
partially premixed combustion models compared to the non-premixed combustion model can be clearly observed
in Fig 10c that the mole fraction of propane is in very good agreement with the experimental result. While, when
non-premixed combustion model invoking either LES or RANS model is employed, large differences between
predictions and experimental results are observed indicating the inapplicability of non-premixed combustion
model in such complicated flow configuration. The benefits of using partially premixed combustion models can
also be observed in Fig 10a that a realistic profile is predicted by ZTFSC model compared to non-premixed
combustion model.
 (a) (b)

(c) (d)

Fig. 10 Profile of species mole fraction in the horizontal midplane of combustor (x=20mm).

Although the prediction of oxygen mole fraction is seen to be far from experimental result, with more consumption
of propane at a radial position of 0.0225m, the mole fraction of oxygen will be in reasonable agreement with
experimental result, i.e. there is an underprediction of combustion near the injection nozzle, shown in Fig 6a.

Finally, the prediction of carbon monoxide in Fig 10b is problematic that none of the available models properly
captures its profile. It was concluded by Di Mare et al. [7] that the CO level may not be well represented by steady
laminar flamelet method due to its slower reaction rate. All the other species other than carbon monoxide are less
sensitive to this and are more strongly influenced by transport effects. As 247 chemical reaction, 50 species and
full scalar dissipation rate are employed in our prediction, it confirms the conclusion made in Di Mare et al. [7]
that more detailed reaction mechanism and the consideration of strain effects have little influence on the prediction
of CO concentration.

5. Conclusions:

Comparative studies of the partially premixed and non-premixed combustion models have been presented. The
chosen geometry retained all features of a commercial aviation used can-type combustor and provides an excellent
test case to illustrate the effectiveness of using well coupled partially premixed combustion model in complicated,
three-dimensional, multi-jets swirling flow environment. The RSM model is used to solve the mixing problem.
Tabulated chemistry and SLFM are chosen to simplify the employed detailed chemical reactions and to reduce the
computational time. Pre-PDF method is used for turbulent combustion interaction. The main findings of the
present papers are:

 For the first time, the partially premixed combustion model has been applied to a Tay model combustor
and the performance is seen to be completely different from that predicted by non-premixed combustion

model. The performance of the two models is usually seen to be similar in simple flow structures such as
 in a simple burner, far less attention has been focused on the performance of two models in complicated
flow structures.

 It is noticed that although the use of RSM and non-premixed combustion model fails to predict the
combustion in complicated flow configuration completely, the use of LES does improve the result at the

position closer to the primary jets of combustor. However, both LES and RSM models fail to predict
flame pattern and species concentration based on non-premixed combustion model near the injection

nozzle.

 For the first time, the comparative study of two partially combustion models of ZTFSC and ECFM is
performed in the Tay model combustor. The predicted mixture fraction by ZTFSC model is similar with
that predicted by ECFM in the primary region of the combustor, while the latter model predicts much

lower temperature due to the underprediction of reaction progress. Both models predict the flame shape
reasonably more accurate in the primary region as compared to the non-premixed combustion

predictions regardless of whether RANS or LES is used.

 The temperature and species concentration predicted by the RSM model in conjunction with ZTFSC
model are in reasonable agreement with the experimental result. Although there is still temperature
difference between the prediction and the experimental result, the flame pattern is accurately captured.

The use of SRS models such as LES will compensate for this defects though not presented in this paper.

 The predicted species concentration of fuel, O2 and CO2 are in reasonable agreement with experimental
results while CO concentration may not be well captured by SLFM method. All the other species other
than CO are less sensitive to SLFM method and are more strongly influenced by transport effects. More

detailed reaction mechanism and the full consideration of strain effects have little influence on the
prediction of CO concentration.

Finally, it is concluded that a more realistic assumption based on partially premixed combustion model must be
properly coupled with either RANS or SRS turbulence models in order to predict the combustion in a complicated
flow environment (such as Tay combustor) efficiently and accurately. In current study, for the first time, the
coupling of a RSM turbulence model with ZTFSC combustion model invoking tabulated chemistry successfully
predicts the combustion in the Tay model combustor within 10 hours by a 20 processing elements of Solon cluster
at City University London (2 million mesh), while the excessive time of 26,432 hours by coupling LES with a
non-premixed combustion model using 64 processing elements of Cray T3E at University of Manchester is
unaffordable by most industries (1 million mesh) [7].

Acknowledgements The authors would like to thank the City University London for partial financial support for
this research.

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