1 Introduction
The stabilisation of premixed flames in the wake of obstacles is a key phenomenon in the field of combustion. Bluff bodies are commonly used as ‘flame holders’ to create a low-pressure recirculation zone that allows the flame to anchor in a low-speed region (Williams, Hottel & Scurlock Reference Williams, Hottel and Scurlock1951; Longwell Reference Longwell1952; Williams & Shipman Reference Williams and Shipman1953; Penner & Williams Reference Penner and Williams1957) where incoming fresh gases mix with hot recirculated gases and ignite (Zukoski & Marble Reference Zukoski and Marble1956; Chen et al. Reference Chen, Driscoll, Kelly, Namazian and Schefer1990; Correa & Gulati Reference Correa and Gulati1992; Masri, Barlow & Carter Reference Masri, Dally, Barlow and Carter1994; Smith et al. Reference Smith, Nickolaus, Leach, Kiel and Garwick2007; Nair & Lieuwen Reference Nair and Lieuwen2007). Various bluff-body geometries can be used: cylinder, triangle, square, closed cone, closed and open V-gutter, plate, etc. (Zukoski & Marble Reference Zukoski and Marble1955; Ballal & Lefebvre Reference Ballal and Lefebvre1979; Sanquer, Bruel & Deshaies Reference Sanquer, Bruel and Deshaies1998). The fundamental mechanisms involved in flame stabilisation are numerous. Heat transfer between flame holders and the flow, low-temperature chemistry and recirculating gases influence the flame root location (where chemical reactions begin) and determine the ability of a flame to be stabilised (Plee & Mellor Reference Plee and Mellor1979; Glassman Reference Glassman1996; Shanbhogue, Husain & Lieuwen Reference Shanbhogue, Husain and Lieuwen1997; Chen et al. Reference Chen, Chang, Pan and Yang1998; Kedia, Altay & Ghoniem Reference Kedia, Altay and Ghoniem2011; Mejia et al. Reference Mejia, Selle, Bazile and Poinsot2015).
Since flame holders are usually obstacles placed in the flow, they also trigger hydrodynamic instabilities that can lead to situations where the flame is ‘stabilised’ (i.e. anchored on the flame holder) but ‘unstable’ (i.e. showing strong fluctuations of heat-release rate coupled with the unsteady flow created by the flame holder). One specific example of such instabilities is thermoacoustic modes where fluctuations in heat-release rate lead to self-excited instabilities due to a constructive coupling between acoustics and combustion (Rayleigh Reference Rayleigh1878; Culick Reference Culick1988; Candel Reference Candel2002; Lieuwen & Yang Reference Lieuwen and Yang2005). These instabilities can restrict the range of operating conditions and yield unacceptable pollutant emissions (Rhee, Talbot & Sethian Reference Rhee, Talbot and Sethian1995; Huang & Yang Reference Huang and Yang2009; Stohr et al. Reference Stohr, Boxx, Carter and Meier2012; Kwong, Geraedts & Steinberg Reference Kwong, Geraedts and Steinberg2016). Even if hydrodynamic modes are not the sole driver of thermoacoustic instabilities, their role in these instability loops has been largely documented (Poinsot & Veynante Reference Poinsot and Veynante2011; Lieuwen Reference Lieuwen2012; Terhaar, Oberleithner & Paschereit Reference Terhaar, Oberleithner and Paschereit2015). For example, vortex generation behind obstacles is one typical mechanism leading to thermoacoustic activity (Poinsot et al. Reference Poinsot, Trouve, Veynante, Candel and Esposito1987; Ducruix et al. Reference Ducruix, Schuller, Durox and Candel2003; Ghani et al. Reference Ghani, Poinsot, Gicquel and Staffelbach2015) which has been identified for a very long time (Reynst Reference Reynst and Thring1961). Therefore, our capacity to mitigate these hydrodynamic instabilities is of great importance as it could improve flame stabilisation.
One method to suppress or control these hydrodynamic instabilities is to implement an active or passive control to modify the flow field: micro-jets, vibrating/moving parts, plasma or morphing actuators have been reported (Viets, Piatt & Ball Reference Viets, Piatt and Ball1981; Gelzer & Amitay Reference Gelzer and Amitay2002; Moreau Reference Moreau2007; Dong, Triantafyllou & Karniadakis Reference Dong, Triantafyllou and Karniadakis2008; Godoy-Diana et al. Reference Godoy-Diana, Marais, Aider and Wesfreid2009; Cattafesta & Sheplak Reference Cattafesta and Sheplak2011; Chinaud et al. Reference Chinaud, Rouchon, Duhayon, Scheller, Cazin, Marchal and Braza2014). Controlling flows around objects has been extensively used in the aerodynamic community to reduce drag or to modify the global flow topology (Roshko Reference Roshko1993; Leweke, Provansal & Boyer Reference Leweke, Provansal and Boyer1993; Mittal & Balachandar Reference Mittal and Balachandar1995; Cimbala, Nagib & Roskho Reference Cimbala, Nagib and Roskho1988; Prasad & Williamson Reference Prasad and Williamson1997).
A canonical example to illustrate these hydrodynamic flow instabilities is a laminar flow around a cylinder (
$Re\leqslant 2000$
, based on the cylinder diameter). Kelvin–Helmholtz (KH) instabilities develop in shear layers where velocity gradients induce coherent structures whereas Bénard–von Kármán (BVK) instabilities lead to an asymmetric vortex shedding in the wake of the obstacle (Cantwell & Coles Reference Cantwell and Coles1983; Monkewitz Reference Monkewitz1988; Plaschko, Berger & Peralta-Fabi Reference Plaschko, Berger and Peralta-Fabi1993; Kelso, Lim & Perry Reference Kelso, Lim and Perry1996). The transition to observe such instabilities does not depend only on the Reynolds number
$Re$
(Rao, Thompson & Hourigan Reference Rao, Thompson and Hourigan2016), but also on the blockage ratio determined by the ratio of the cylinder diameter to the width of the flow passage (Sahin & Owens Reference Sahin and Owens2004), or the position of the cylinder with respect to walls (Rao et al.
Reference Rao, Leontini, Thompson and Hourigan2013). One method to cancel the KH or BVK instabilities is to rotate the cylinder along its axis. Rotation can be used for symmetry breaking and wake control. Depending on the rotation rate (defined as the ratio of the cylinder boundary velocity to the incoming velocity), the usual von Kármán vortex street observed for a fixed cylinder can be suppressed (Badr et al.
Reference Badr, Coutanceau, Dennis and Menard1990; Schumm, Berger & Monkewitz Reference Schumm, Berger and Monkewitz1994; Modi Reference Modi1997; Coutanceau & Menard Reference Coutanceau and Menard1998; Rao et al.
Reference Rao, Leontini, Thompson and Hourigan2013; Bourguet & Jacono Reference Bourguet and Jacono2014). An example of the vorticity field obtained by direct numerical simulation (DNS) for a non-rotating and a rotating cylinder (figure 1) shows that rotation can be used to control vortex shedding by creating an asymmetric flow field and when the rotation rate is high enough (figure 1
b), the vortex street observed for a fixed cylinder totally disappears. Flow control around an obstacle in reactive conditions has received less attention (Mejia et al.
Reference Mejia, Bauerheim, Xavier, Ferret, Selle and Poinsot2016) and many questions arise regarding flame stabilisation in these conditions.
Therefore, the general aim of the present work is to better understand the stabilisation mechanisms of laminar methane/air premixed flames in the wake of a rotating cylinder. Based on existing non-reacting flow studies, it is expected that rotation will change the flow field, the flame roots location and thus the mean flame topology. Note that this study only deals with steady flames even though the cylinder is rotating. Another goal of this study is that it is a novel technique to create original steady laminar flame structures that differ from the usual laminar premixed flame configurations: planar, cylindrical (Kitano, Kobayashi & Otsuka Reference Kitano, Kobayashi and Otsuka1989; Groot & Goey Reference Groot and De Goey2002) or spherical (Dowdy, Smith & Taylor Reference Dowdy, Smith, Taylor and Williams1991; Chen Reference Chen2011; Bonhomme, Selle & Poinsot Reference Bonhomme, Selle and Poinsot2013).
Figure 1. Iso-contours of vorticity, coloured by vorticity in the case of a non-reacting flow around (a) a non-rotating cylinder and (b) a rotating cylinder (
$\unicode[STIX]{x1D6FC}=4.10$
,
$\unicode[STIX]{x1D6FC}$
is the rotation rate, see (2.3)).
The specific objectives of the paper are to: (i) analyse the stabilisation of a laminar premixed flame behind a rotating flame holder and compare experimental to numerical results; (ii) analyse the different flame structures in order to understand the key mechanisms leading to the observed flames; and (iii) determine the effects of heat transfer between the flow and the cylinder. This investigation is conducted with both experimental and numerical approaches. The paper first describes the experimental and numerical methods used to study flame stabilised on rotating cylinders (§ 2). Next, flame topologies are presented as a function of the rate of rotation of the cylinder and experimental results are compared to DNS data (§ 3). Third, the structure of each flame branch is analysed using DNS data, taking into account non-adiabadicity in the vicinity of the cylinder: effects of stretch, dilution and cooling will be studied (§ 4). Finally, the distribution of heat transfer on the cylinder wall is studied to examine the interaction between the flame fronts and the rotating cylinder (§ 5).
2 Experimental and numerical methods
2.1 Experimental set-up
Figure 2. (a) Schematic of the rotating cylinder in the present configuration. (b) Experimental field of view (EFOV) and definition of the controlling parameters. The shaded area corresponds to the computed domain.
The experimental set-up consists of a rectangular cross-section combustion chamber (
$h=34$
mm by
$l=94$
mm), operated at atmospheric pressure, in which a stainless steel cylinder with a diameter
$d=8$
mm, serves as the flame holder (figure 2
a). The cylinder is connected to a brushless direct current electric motor with rotational speed ranging from 600 to 20 000 revolutions per minute (RPM). During experiments, the motor experienced low frequency rotation fluctuations so that the uncertainty on the rotation speed was
$\pm$
100 RPM. The flame shape is however weakly sensitive to these fluctuations so that it remains steady. The combustion chamber is equipped with three planar quartz windows allowing optical access. The lean air–methane mixture is injected in a plenum through six injectors. The flow is then laminarised by a bed of 1 mm glass balls and two honeycombs. The upper part of the plenum is water cooled to ensure a constant temperature for the fresh mixture (
$T_{in}=288.15$
K). The velocity field is measured with particle image velocimetry (PIV). A double cavity Nd:YAG laser (Quantel Big Sky), operating at 532 nm, fires two laser beams, with a delay of
$200~\unicode[STIX]{x03BC}\text{s}$
. The laser beam is expanded through a set of fused silica lenses (spherical and diverging). Since the flow is not symmetric when the cylinder is rotating, a tilted mirror is inserted to lighten the cylinder shadow region with a reflection of the incoming laser sheet (figure 2
a). The laser sheet thickness is measured to
$500~\unicode[STIX]{x03BC}\text{m}$
. Olive oil particles of
$1~\unicode[STIX]{x03BC}\text{m}$
are seeded through two injection systems located just before the glass balls bed (venturi seeder). Mie scattering is collected on a Imager Intense camera (Lavision), operating at a repetition rate of 1 Hz and a resolution of 1376
$\times$
1040 pixels. A f/16 182 mm telecentric lens (TC4M64, Opto-engineering) is used to reduce parallax displacements occurring with classical lenses and obtain more accurate velocity vector fields in the vicinity of the cylinder. A narrow band-pass optical filter, centred at
$\unicode[STIX]{x1D706}_{c}=532\pm 10$
nm is inserted in front of the camera sensor to record only Mie scattering of olive oil particles. PIV images are processed with a cross-correlation multi-pass algorithm (Davis 8.2.3), resulting in a final window of 16
$\times$
16
$\text{pix}^{2}$
and a 50 % overlap. Ninety images are collected for each operating condition, with a spatial vector spacing of 0.2 mm.
The flame is also visualised thanks to a second Imager Intense camera (Lavision), equipped with a similar telecentric lens as the PIV system. The exposure time is set to 500 ms and a band-pass optical filter, centred at
$\unicode[STIX]{x1D706}_{c}=430\pm 10$
nm, is placed in front of the camera to record spontaneous
$\text{CH}^{\ast }$
emission.
A
$50/50$
beam splitter is inserted between the two cameras to simultaneously record PIV and
$\text{CH}^{\ast }$
signals, with only one optical access for visualisation. The experimental field of view (EFOV) shown in figure 2(b) captures a part of the combustion chamber section (36 mm
$\times$
26 mm) and the origin is taken at the centre of the cylinder.
The inlet temperature of fresh gases
$T_{in}$
and the ambient pressure
$P_{0}$
are systematically checked prior to measurements, and images are recorded when thermal equilibrium of the combustion chamber is reached (measured with a K-thermocouple fixed on the burner structure). During experiments, the flame started to slightly flicker for certain operating conditions (pressure fluctuations less than 2 Pa). These effects contribute to the slight flame thickening observed in the experiments.
2.2 Direct numerical simulations
The reactive multi-species Navier–Stokes equations are solved using a fully compressible unstructured solver called AVBP (Schonfeld & Rudgyard Reference Schonfeld and Rudgyard1999; Moureau et al.
Reference Moureau, Lartigue, Sommerer, angelberger, Colin and Poinsot2005). A major advantage of the configuration of figure 2 is that it is almost perfectly two-dimensional so that a two-dimensional DNS with detailed chemistry can be used. Chemical kinetics are described by the ‘Lu 19’ analytical mechanism of Lu & Law (Reference Lu and Law2008) for methane/air combustion. This mechanism involves
$19$
transported species and
$11$
quasi-steady state (QSS) species. The viscosity is modelled with a power law, each species has its own Lewis number and a constant Prandtl number is assumed. It was validated for a large range of equivalence ratio (
$\unicode[STIX]{x1D719}=0.5{-}1.5$
), pressure (
$P_{0}=1{-}30$
atm) and correctly predicts auto-ignition times as well as CO levels. It was implemented in the DNS code and validated by comparison with GRI-MECH3.0 computations using the Cantera open source solver (Smith et al.
Reference Smith, Golden, Frenklach, Moriarty, Eiteneer, Goldenberg, Bowman, Hanson, Song and Gardiner1999; Goodwin Reference Goodwin2002). Laminar flame speeds and adiabatic temperatures are correctly reproduced (figure 3
b). In addition, properties of flame/wall interactions were validated by running one-dimensional flames. For the canonical head-on quenching scenario, the maximum normalised wall heat flux is 0.35 and the corresponding Peclet number is 3, being in agreement with the literature (Huang, Vosen & Greif Reference Huang, Vosen and Greif1988; Jarosinski Reference Jarosinski1988; Wichman & Bruneaux Reference Wichman and Bruneaux1995). The laminar flame thickness for the
$\unicode[STIX]{x1D719}=0.7$
equivalence ratio flame studied here is
$0.680$
mm while the mesh resolution in the flame zone is
$0.06$
mm so that at least
$12$
points are used to resolve the flame front. Mesh sensitivity was verified by testing a finer mesh, with a cell resolution of
$25~\unicode[STIX]{x03BC}\text{m}$
(instead of
$60~\unicode[STIX]{x03BC}\text{m}$
in this study), leading to negligible modifications in flame position and velocity field.
The two-step Taylor–Galerkin convection scheme (Colin & Rudgyard Reference Colin and Rudgyard2000) used for DNS provides third-order accuracy in time and space. This scheme is characterised by a high spectral resolution, excellent dispersion and dissipation properties. Navier–Stokes characteristic boundary conditions (NSCBC) (Poinsot & Lele Reference Poinsot and Lele1992; Moureau et al.
Reference Moureau, Lartigue, Sommerer, angelberger, Colin and Poinsot2005) are applied at inlet and outlet. Lateral walls were modelled as no-slip and isothermal (
$T_{w}=288$
K). In order to account for the rotation of the cylinder, the velocity of its wall is set at
$u_{\unicode[STIX]{x1D703}}=\unicode[STIX]{x1D714}/2$
in the frame of the burner, where
$\unicode[STIX]{x1D714}$
is the angular rotation speed. The temperature
$T_{c}$
is imposed at the cylinder external face (see § 2.2.1). The computational domain extends from
$z=-35$
to
$z=45$
mm, which corresponds to the shaded zone in figure 2(b). The velocity profile at the inlet (figure 3
a) is imposed by fitting experimental velocity data.
Figure 3. (a) Experimental inlet velocity profile (hot-wire anemometry) measured at
$z/d=-4.6$
and fit used in the simulation (figure 2
a). (b) Laminar burning velocities for air–methane mixtures. Comparison between different solvers, chemical schemes and the experiment of Varea et al. (Reference Varea, Modica, Vandel and Renou2012).
2.2.1 Cylinder temperature
Many recent studies emphasise the importance of the flame holder temperatures on the flame structure and dynamics (Duchaine et al.
Reference Duchaine, Boudy, Durox and Poinsot2011; Kedia & Ghoniem Reference Kedia and Ghoniem2013, Reference Kedia and Ghoniem2015; Miguel-Brebion et al.
Reference Miguel-Brebion, Mejia, Xavier, Duchaine, Bedat, Selle and Poinsot2016). The temperature of the flame holder modifies the quenching distance which is the minimum distance between flame front and wall. This distance then controls the flame dynamics so that an accurate DNS of this flame requires a precise determination of the cylinder temperature. This does not necessarily require a full coupled simulation of heat transfer between the cylinder and the flow. An estimation of the Biot number
$Bi$
is 0.01, so that very small temperature gradients are expected in the cylinder. Moreover, a one-dimensional model of the wall temperature, considering a periodic and unsteady wall heat flux (related to the rotation speed) gives penetration depths of around 1 mm with negligible temperature fluctuations in the bluff body itself. This proves that the cylinder responds to an average heat flux and thus its temperature is constant when steady state is reached. The temperature within the cylinder can be assumed to be homogeneous and constant so that a simplified lumped model is used to evaluate its temperature, starting from the unsteady heat equation, integrated over the cylinder:
$$\begin{eqnarray}\displaystyle \unicode[STIX]{x1D70C}C_{p}V\frac{\text{d}T_{c}}{\text{d}t}=\int _{S}\boldsymbol{q}\boldsymbol{\cdot }\boldsymbol{n}\,\text{d}S, & & \displaystyle\end{eqnarray}$$
where
$T_{c}$
is the cylinder temperature,
$S$
is its surface,
$V$
its volume and
$\boldsymbol{q}$
the energy flux at the fluid–solid interface. Thus the cylinder temperature
$T_{c}$
is:
$$\begin{eqnarray}\displaystyle \frac{\text{d}T_{c}}{\text{d}t}=\frac{S}{\unicode[STIX]{x1D70C}C_{p}V}(\unicode[STIX]{x1D6F7}_{cond}-\unicode[STIX]{x1D6F7}_{rad}), & & \displaystyle\end{eqnarray}$$
where radiative
$\unicode[STIX]{x1D6F7}_{rad}$
and convective
$\unicode[STIX]{x1D6F7}_{cond}$
fluxes are considered at the cylinder boundary. The radiative flux
$\unicode[STIX]{x1D6F7}_{rad}=\unicode[STIX]{x1D70E}\unicode[STIX]{x1D716}(T_{c}^{4}-T_{ext}^{4})$
is assumed to be absorbed by the combustion chamber walls at temperature
$T_{ext}=T_{w}$
. Additionally, gases are considered as transparent and do not radiate to the cylinder. In the present configuration,
$S/(\unicode[STIX]{x1D70C}C_{p}V)=0.003~\text{m}^{2}~\text{KJ}^{-1}$
and the emissivity of the cylinder is set to
$\unicode[STIX]{x1D716}=0.9$
, corresponding to an unpolished used surface. Equation (2.2) is solved at run time and provides the value of the equilibrium wall temperature
$T_{c}$
used as boundary condition for the DNS. The value of
$S/(\unicode[STIX]{x1D70C}C_{p}V)$
is only relevant for the resolution of the transient evolution of
$T_{c}$
. Since we are only interested in the steady state, in practice this value is increased in order to speed up the transient phase. Depending on the operating conditions, the radiative heat flux accounts from 12 % to 25 % of the total heat flux. Neglecting its contribution would result in incorrect cylinder temperature and wrong flame stabilisation pattern (Miguel-Brebion et al.
Reference Miguel-Brebion, Mejia, Xavier, Duchaine, Bedat, Selle and Poinsot2016).
2.3 Operating conditions
A large range of operating conditions have been tested in order to determine the stability map of the burner. Based on these observations, the bulk velocity taken in the plenum was set to
$u_{b}=1.07~\text{m}~\text{s}^{-1}$
and the equivalence ratio of the air–methane mixture to
$\unicode[STIX]{x1D719}=0.70$
. The Reynolds number
$Re$
of the incoming flow is
$580$
(based on the cylinder diameter
$d$
). To characterise the rate of rotation of the cylinder, the normalised parameter
$\unicode[STIX]{x1D6FC}$
is introduced as:
$$\begin{eqnarray}\displaystyle \unicode[STIX]{x1D6FC}=\frac{\unicode[STIX]{x1D714}d}{2u_{b}}. & & \displaystyle\end{eqnarray}$$
This parameter compares the radial velocity at the cylinder to the bulk flow velocity
$u_{b}$
, and is the control parameter for non-reactive flows around rotating cylinders. The fresh gas temperature is
$T_{in}=288.15$
K and the outlet pressure
$P_{0}=0.99$
bar. In this study, all parameters are kept constant except for
$\unicode[STIX]{x1D6FC}$
whose variations are reported in table 1 together with the corresponding cylinder temperature.
Table 1. Operating conditions investigated in the present study. The last column gives the temperature of the cylinder (
$T_{c}$
) obtained with (2.2).
Figure 4. Comparison between experimental and DNS flame fronts for increasing rotation rates
$\unicode[STIX]{x1D6FC}$
. CH* traces from experiments are shown in grey scale and red dashed lines are an iso-contour of the heat release rate from the DNS (20 % of the maximum). (a)
$\unicode[STIX]{x1D6FC}=0.00$
; (b)
$\unicode[STIX]{x1D6FC}=1.16$
; (c)
$\unicode[STIX]{x1D6FC}=2.30$
; (d)
$\unicode[STIX]{x1D6FC}=3.07$
; (e)
$\unicode[STIX]{x1D6FC}=4.10$
. The temperatures of the cylinder are given in table 1.
3 Experimental and numerical results: flame classification
Figure 4 shows the normalised time averaged CH* signal (grey scale) and an iso-contour of the heat-release rate extracted from the DNS (20 % of the maximum, dashed lines) when the flames have reached steady state. Even though CH* traces do not match exactly reaction rate zones, they are a good indicator of the flame position. The flame roots location obtained in the experiments is well reproduced with the DNS. However, some differences on the flame angle are observed for
$z/d>2$
. This latter effect is caused by the chemical scheme that overestimates the laminar burning velocity
$s_{l}^{0}$
(figure 3
b), resulting in a slightly wider flame angle. A V-shape symmetric flame is observed when there is no rotation, i.e.
$\unicode[STIX]{x1D6FC}=0.00$
(figure 4
a). The flame intensity decreases when approaching the cylinder due to the flame/wall interaction. During the transient period, the cylinder temperature increases due to the presence of burned gases in the wake of the cylinder and flame roots move closer to the cylinder. When thermal equilibrium is reached, the flame roots stabilise at
$z/d=0.66$
.
Profiles of axial velocity
$u$
(normalised by the bulk velocity upstream of the cylinder,
$u_{b}=1.07~\text{m}~\text{s}^{-1}$
) without rotation (
$\unicode[STIX]{x1D6FC}=0$
, figure 5, first row) show that the flow speed upstream of the cylinder (
$z/d=-0.9$
) is affected by the presence of the cylinder. At
$z/d=0.0$
, the axial velocity exceeds the bulk velocity
$u_{b}$
by a factor of
${\approx}$
1.7 because of the area restriction (figure 5
b, top). Negative
$u$
values at
$z/d=0.9$
(figure 5
c, top) reveal a weak symmetric recirculation zone in the wake of the cylinder.
Figure 5. Experimental (circles) and DNS (line) mean axial velocity profiles (
$u/u_{b}$
) at three axial locations (columns) and for three different
$\unicode[STIX]{x1D6FC}$
(rows). The dashed line corresponds to
$u/u_{b}=0.0$
. (a)
$z/d=-0.9$
; (b)
$z/d=0.0$
; (c)
$z/d=0.9$
.
When the cylinder has a moderate rotation rate, the flame becomes asymmetric (figure 4
b:
$\unicode[STIX]{x1D6FC}=1.16$
and c:
$\unicode[STIX]{x1D6FC}=2.30$
). Indeed, the lower branch stabilises close to the cylinder and the flame root is more curved when the rotation rate is increased, thus leading to a L-shape flame (figure 4
c). This branch exhibits a maximum intensity near the cylinder, and decreases along the flame. In contrast, the upper branch is not anchored to the cylinder any more and it is located far downstream of the cylinder. Its intensity is very low and this flame branch is virtually quenched over a large region downstream of the flame holder.
Velocity profiles (figure 5, middle row) show an asymmetric flow at the cylinder and downstream. The cylinder rotation locally increases the flow velocity by a factor of 2, and the recirculation region is affected, being shifted in the direction of the cylinder rotation.
When
$\unicode[STIX]{x1D6FC}$
is increased to higher values (figure 4
d:
$\unicode[STIX]{x1D6FC}=3.07$
and 4
e:
$\unicode[STIX]{x1D6FC}=4.10$
), the lower branch is distorted in the direction of rotation by the high velocities induced by the cylinder. A clear L-shape is observed and the lower flame root location is still close to the cylinder while its intensity remains high. The upper branch is now located closer to the cylinder with higher reactivity, almost leading to an asymmetric U-shape flame.
The velocity profile upstream of the cylinder is affected (figure 5
a bottom) as it shows a slight asymmetric shape. Finally for larger rotation speeds, the flame topology changes suddenly and it stabilises upstream of the cylinder, a situation which is not discussed in this study. The effect of rotation is visible on the flow streamlines, as shown in figure 6 which displays the flow and temperature fields for
$\unicode[STIX]{x1D6FC}=1.16$
and 4.10. For the moderate rotation rate (figure 6
a), the streamlines are deflected in the direction of the cylinder rotation. When the rotation rate is increased (figure 6
b), flow streamlines wrap around the cylinder and also shift the temperature iso-contours in the direction of rotation. Moreover, the induced cylinder shear flow may be sufficiently high to continuously carry burned gases to the leading edge of the cylinder.
Figure 6. Temperature iso-contours (black lines) and flow streamlines (grey lines) for cases: (a)
$\unicode[STIX]{x1D6FC}=1.16$
and (b)
$\unicode[STIX]{x1D6FC}=4.10$
. The flame location is marked by the heat release crest (red dashed line).
The five flames of figure 4 exhibit non-trivial stabilisation mechanisms. At moderate rotation rates, the upper branch of the flame is quenched over a long distance so that it is anchored far downstream of the cylinder. In contrast, the lower branch exhibits higher reaction rates in the vicinity of the cylinder (figure 4 b,c).
Figure 7. Schematic representation of flame stabilisation mechanisms on a rotating cylinder.
Figure 8. Scatter plot of mass fraction
$Y_{k}$
with the progress variable
$c$
of different species. Two zones are selected along the upper branch: A (black dots) and C (grey dots). The case corresponds to
$\unicode[STIX]{x1D6FC}=1.16$
.
Figure 7 depicts the different mechanisms involved in this configuration. When the cylinder is rotating, burned gases are carried towards the upper branch while they transfer their energy to heat up the cylinder (
$\unicode[STIX]{x1D6F7}_{bg-c}$
). In parallel, the warm cylinder also heats up the incoming fresh gases (
$\unicode[STIX]{x1D6F7}_{c-ug}$
). As a consequence, the flame roots location and the flame structures are conditioned by heat transfer between the cylinder and the surrounding flow. Moreover, the flow induced by the cylinder rotation mixes fresh and burned gases, and that is dependent on the level of rotation. Figure 8 shows how this mixing affects chemistry. It compares scatter plots of
$\text{CH}_{4}$
,
$\text{CO}_{2}$
,
$\text{CH}_{3}$
and CO mass fractions versus the progress variable
$c$
in two regions of the upper branch: zone A is far away from the cylinder (black dots) whereas region C is located in the quenched zone of the upper flame (grey dots). Flame structures in region A are all similar and collapse on a single curve, showing that, far from the cylinder, there is a unique flame structure (which could be tabulated for example). However, the scatter plots in region C reveal multiple flame structures. Burned gases recirculation and subsequent dilution lead to higher
$\text{CO}_{2}$
and lower
$\text{CH}_{4}$
mass fractions. In turn, formation of radicals and intermediates (
$\text{CH}_{3}$
and CO) is inhibited. In this zone, low-temperature chemistry plays a major role, which is captured by the ‘Lu 19’ scheme and would not be correctly predicted using tabulation of a global mechanism.
The aim of the next sections is to analyse the two branches of figure 7 in terms of flame structure and flame/wall interaction when the wall (here the cylinder) moves.
4 Analysis of the flame structures
4.1 Excess or defect of flow enthalpy
As shown in figure 7, the flow is not adiabatic in the vicinity of the cylinder because of heat transfer with the flame holder. The proper quantity to measure the departure from adiabadicity is the reduced enthalpy defect/excess
${\mathcal{L}}$
given by:
$$\begin{eqnarray}\displaystyle {\mathcal{L}}=\frac{h_{t}-h_{t}^{in}}{QY_{F}^{in}}, & & \displaystyle\end{eqnarray}$$
where
$h_{t}$
is the total chemical enthalpy taking into account sensible, chemical and kinetic energies.
$h_{t}^{in}$
is a reference enthalpy, taken in the fresh gases. The normalizing term
$QY_{F}^{in}$
in (4.1) is the heat of the reaction. Positive values of
${\mathcal{L}}$
correspond to sensible or chemical energy given to the fresh gases: the flame is therefore superadiabatic. Conversely, negative values of
${\mathcal{L}}$
correspond to an enthalpy loss and a subadiabatic flame. Figure 9 presents reduced enthalpy fields for different rotation rates
$\unicode[STIX]{x1D6FC}$
. Far away from the cylinder and the flame fronts, the flow is adiabatic and
${\mathcal{L}}=0$
. When the cylinder is not rotating (
$\unicode[STIX]{x1D6FC}=0$
, figure 9
a),
${\mathcal{L}}$
is negative in the wake of the cylinder because hot gases loose energy to the cylinder through conductive heat transfer. Conversely,
${\mathcal{L}}$
is positive upstream of the cylinder because incoming gases are heated by the cylinder. The latter trend is still valid for moderate values of
$\unicode[STIX]{x1D6FC}$
and even prominent as
${\mathcal{L}}$
goes up to 0.2. However, this region of reduced enthalpy gain narrows and eventually vanishes for larger rotation rates (figure 9
e). The distribution of
${\mathcal{L}}$
around the cylinder is shown in figure 10 (
$\unicode[STIX]{x1D703}$
is defined in figure 7). When the cylinder is at rest or has a low rotation rate (i.e.
$\unicode[STIX]{x1D6FC}=0.00$
or 1.16),
${\mathcal{L}}$
is negative in the wake of the cylinder where burned gases are located, and it is positive on the upstream part where fresh gases impact the hot cylinder. Increasing the rotation rate reduces
${\mathcal{L}}$
all along the cylinder so that it is almost negative at all angles for the higher rotation rate (
$\unicode[STIX]{x1D6FC}=4.10$
). Therefore, it is speculated that the flow induced by the rotation (figure 6) may explain this trend.
Figure 9. Field of enthalpy loss
${\mathcal{L}}$
for different rotation rates
$\unicode[STIX]{x1D6FC}$
. Iso-contour lines of
${\mathcal{L}}$
are shown in black. The red thick lines are the heat-release rate crest of each branch. (a)
$\unicode[STIX]{x1D6FC}=0.00$
; (b)
$\unicode[STIX]{x1D6FC}=1.16$
; (c)
$\unicode[STIX]{x1D6FC}=2.30$
; (d)
$\unicode[STIX]{x1D6FC}=3.07$
; (e)
$\unicode[STIX]{x1D6FC}=4.10$
.
Figure 10. Enthalpy loss
${\mathcal{L}}$
around the cylinder (
$\unicode[STIX]{x1D703}$
).
4.2 Dilution effect at high rotation rates
Figure 11 displays the field of
$\text{CO}_{2}$
mass fraction at
$\unicode[STIX]{x1D6FC}=1.16$
(a) and
$\unicode[STIX]{x1D6FC}=4.10$
(b). For
$\unicode[STIX]{x1D6FC}=4.10$
,
$\text{CO}_{2}$
is found all around the cylinder. This recirculation of burned gases, also observed in figure 6(b), changes the local composition by diluting incoming fresh gases and diminish
${\mathcal{L}}$
to negative values (figure 10).
Figure 11. Reduced carbon dioxide mass fraction
$c_{co_{2}}$
field for (a)
$\unicode[STIX]{x1D6FC}=1.16$
and (b)
$\unicode[STIX]{x1D6FC}=4.10$
. Black lines are iso-contour of
$c_{co_{2}}$
.
To separate preheating and dilution effects,
${\mathcal{L}}$
can be written as:
$$\begin{eqnarray}\displaystyle {\mathcal{L}}=\underbrace{\frac{1}{QY_{F}^{in}}\left[\int _{T_{0}}^{T}C_{p}\,\text{d}T\right]}_{{\mathcal{L}}_{s}}+\underbrace{\frac{1}{QY_{F}^{in}}\left[\mathop{\sum }_{k}\unicode[STIX]{x0394}h_{f,k}^{0}(Y_{k}-Y_{in})\right]}_{{\mathcal{L}}_{c}}+\underbrace{\frac{1}{2QY_{F}^{in}}[(u_{i}^{2}-u_{i}^{in^{2}})]}_{{\mathcal{L}}_{k}}, & & \displaystyle\end{eqnarray}$$
where
${\mathcal{L}}_{s}$
measures gas preheating by the cylinder while
${\mathcal{L}}_{c}$
measures the effect of dilution and
${\mathcal{L}}_{k}$
accounts for the kinetic effect. Because the Mach number is 0.003,
${\mathcal{L}}_{k}$
can be neglected. Figure 12 plots the reduced sensible
${\mathcal{L}}_{s}$
(black line) and reduced chemical
${\mathcal{L}}_{c}$
enthalpies (dashed line) contributing to
${\mathcal{L}}$
, for two rotation rates
$\unicode[STIX]{x1D6FC}=1.16$
(figure 12
a) and 4.10 (figure 12
b). The shape or the amplitude of
${\mathcal{L}}_{s}$
is similar in both cases because gases near the wall receive energy from the hot cylinder. However, the contribution of
${\mathcal{L}}_{c}$
differs from the two cases. At a moderate rotation rate (figure 12
a), the reduced chemical enthalpy parameter
${\mathcal{L}}_{c}$
is null on the upstream part of the cylinder, meaning that only fresh unburned gases are found at this location. In contrast, when the rotation rate is increased (figure 12
b),
${\mathcal{L}}_{c}$
is negative on the leading edge of the cylinder. Therefore, the dilution observed in figure 11(b) is the parameter that decreases
${\mathcal{L}}$
at high rotation rates.
In summary, the excess or defect of the reduced enthalpy
${\mathcal{L}}$
around the cylinder evolves due to the competition between two effects. First, the warmer cylinder heats up near-wall gases that results in positive values of
${\mathcal{L}}_{s}$
for all rotation rates investigated. Second, the induced flow created by the cylinder carries burned gases that diminish the reduced chemical enthalpy
${\mathcal{L}}_{c}$
. This latter effect is prominent when the rotation rate exceeds a certain threshold (
$\unicode[STIX]{x1D6FC}_{c}\approx 3$
).
Figure 12. Sensible (
${\mathcal{L}}_{s}$
) and chemical (
${\mathcal{L}}_{c}$
) enthalpy loss contributions versus position on the cylinder
$\unicode[STIX]{x1D703}$
. (a)
$\unicode[STIX]{x1D6FC}=1.16$
; (b)
$\unicode[STIX]{x1D6FC}=4.10$
.
4.3 Super- and subadiabatic flame structure
This section focuses on the differences between the two flame branches observed in figure 4 and their link with the reduced enthalpy field (figure 9). Figure 13 shows two flame profiles extracted from the DNS (
$\unicode[STIX]{x1D6FC}=1.16$
and
$z/d=1.25$
). The comparison between the overdriven lower branch (dashed lines with symbols) and an adiabatic unstrained flame (lines) in figure 13(a,b) shows a good agreement for the species profiles but the maximum heat-release rate is much higher for the flame of the DNS. This observation is also verified with the reduced enthalpy parameter as this branch is located in a superadiabatic flow (
${\mathcal{L}}>0$
, figure 13
b). In contrast, the upper branch (figure 13
c,d) presents smoother species profiles and a heat-release rate profile quite low. Similarly, as the upper branch stabilises in a subadiabatic flow, no self-sustained or weak flame can exist at this location (
${\mathcal{L}}<0$
, figure 13
d). Figure 14 presents the evolutions of the maximum heat release rate along the lower flame branch for different rotation rates. The location of maximum heat-release rate is detected with a crest sensor, for both flames and these maximum values are plotted along the curvilinear abscissa
$s$
normalised by the flame thickness of a planar unstretched adiabatic flame
$\unicode[STIX]{x1D6FF}_{L}^{0}=(T_{b}-T_{u})/\max (\text{d}T/\text{d}x)$
(0.680 mm for the
$\unicode[STIX]{x1D719}=0.7$
equivalence ratio studied here).
Figure 13. Flame profiles extracted from the DNS at
$z/d=1.25$
for the case
$\unicode[STIX]{x1D6FC}=1.16$
.
$n$
is an axis normal to the flame front. Solid lines correspond to an adiabatic unstrained flame. Dashed lines with markers represent the overdriven and cooled branches. (a) Species profiles on the overdriven branch. (b) Reduced heat-release rate profiles on the overdriven branch. (c) Species profiles on the cooled branch. (d) Reduced heat-release rate profiles on the cooled branch.
Figure 14. Normalised maximum heat-release rate along the lower flame front (overdriven) branch, for rotation rates
$\unicode[STIX]{x1D6FC}$
from 0.00 to 4.10.
When the cylinder is not rotating (figure 14, solid line), the heat-release rate monotonically increases to reach the value obtained in an adiabatic flame. Close to the cylinder (
$s/\unicode[STIX]{x1D6FF}_{L}^{0}<10$
) the reduced heat-release rate drops, due to the heat losses to the cylinder and the recirculation zones. The zone over which the cylinder inhibits chemical reactions is about
$10\unicode[STIX]{x1D6FF}_{l}^{0}$
, being larger in comparison to canonical head-on quenching scenarios (Baum et al.
Reference Baum, Poinsot, Haworth and Darabiha1994; Poinsot & Veynante Reference Poinsot and Veynante2011). When the cylinder is rotating at a moderate level (
$\unicode[STIX]{x1D6FC}=1.16$
, 2.30), the quenching zone narrows to about
$\unicode[STIX]{x1D6FF}_{l}^{0}$
, and the heat-release rate increases near the wall, being locally twice as intense as in an adiabatic flame. When the rate of rotation is much higher (
$\unicode[STIX]{x1D6FC}=3.07$
, 4.10), the flame intensity starts to decrease, and it is even lower than in the non-rotating case when
$\unicode[STIX]{x1D6FC}=4.10$
. This behaviour is an indicator of the dilution effect mentioned previously.
Figure 15 presents the reduced heat-release rate along the upper flame. In contrast with the lower superadiabatic flame branch, all cases exhibit heat-release rates lower than adiabatic conditions. The zone over which the flame is quenched becomes very large. For the case
$\unicode[STIX]{x1D6FC}=2.30$
, the flame has not recovered its adiabatic structure after
$40\unicode[STIX]{x1D6FF}_{l}^{0}$
. However, beyond a critical rotation rate (
$\unicode[STIX]{x1D6FC}_{c}\approx 3$
), as dilution of burned gases shield the cylinder with burned gases, the flame starts to retrieve its adiabatic behaviour.
Figure 15. Normalised maximum heat-release rate along the curvilinear abscissa of the upper flame (subadiabatic) branch, for various rotation rates
$\unicode[STIX]{x1D6FC}$
.
At this point,
${\mathcal{L}}$
may be an adequate parameter explaining the flame topologies near the cylinder. In other words, could the two flame structures be explained by considering only local values of
${\mathcal{L}}$
? It is therefore relevant to compute non-adiabatic stretched planar flame with a one-dimensional solver and to compare the local flame structures obtained with DNS flame profiles.
Figure 16. Schematic illustration of two Cantera prototypes. (a) Overdriven lower branch with preheating; (b) cooled upper branch with cold burned gases. Dashed lines mark the heat-release rate crest used to define the curvilinear abscissa
$s$
.
Two different counterflow flame prototypes are considered to mimic the two flame branches only with the reduced enthalpy parameter
${\mathcal{L}}$
. The lower branch corresponds to a superadiabatic flame where fresh gases have been preheated (figure 16
a) whereas the upper branch corresponds to a flame where fresh gases interact with burned gases that have lost energy to the cylinder (figure 16
b). However, the computation of a one-dimensional counterflow flame also introduces a strain effect. The range of strain rates to be used for the Cantera computations is evaluated by post-processing the DNS. Figure 17 shows the probability density functions of strain rate
$\unicode[STIX]{x1D705}$
for the two branches for
$\unicode[STIX]{x1D6FC}=0$
to 4.1. For all rotation rates, strain rate values are quite low and the possible mechanism of flame extinction due to an important strain rate is not supported here (Vagelopoulos & Egolfopoulous Reference Vagelopoulos and Egolfopoulous1994; Williams Reference Williams2000; Shanbhogue et al.
Reference Shanbhogue, Sanusi, Taamallah, Habib, Mokheimer and Ghoniem2016). A small value
$\unicode[STIX]{x1D705}=300~\text{s}^{-1}$
is therefore used in the Cantera calculations and only the reduced enthalpy parameter
${\mathcal{L}}$
is varied to reproduce the flame structures observed in figures 13–15.
Figure 17. Probability density functions of the strain rate
$\unicode[STIX]{x1D705}$
for different rotation rates. (a) Lower branch; (b) upper branch.
Figure 18. Evolution of the reduced maximum heat release
$\dot{\unicode[STIX]{x1D714}}/\dot{\unicode[STIX]{x1D714}}_{adia}$
with the enthalpy loss
${\mathcal{L}}$
, and for different rotation rates. The Cantera results (solid black line) are given with the methodology given in figure 16.
Figure 19. Evolution of the reduced consumption speed
$S_{c}/S_{c}^{adia}$
versus enthalpy loss
${\mathcal{L}}$
, for various rates of rotation. Planar unstretched flames computed with Cantera are plotted for comparison (solid black line).
Figures 18 and 19 present plots of the reduced heat-release rate and consumption speed versus the reduced enthalpy
${\mathcal{L}}$
. The consumption speed is evaluated locally by integrating the heat release rate on profiles normal to
$s$
:
$$\begin{eqnarray}\displaystyle S_{c}=\frac{1}{\unicode[STIX]{x1D70C}Y_{F}^{0}}\int _{-\infty }^{+\infty }\dot{\unicode[STIX]{x1D714}}_{F}\,\text{d}n, & & \displaystyle\end{eqnarray}$$
where
$\dot{\unicode[STIX]{x1D714}}_{F}$
,
$\unicode[STIX]{x1D70C}$
and
$Y_{F}^{0}$
are the fuel source term, density and fuel mass fraction in the fresh gases, respectively. Data from the DNS have been obtained from profiles taken at
$s/\unicode[STIX]{x1D6FF}_{L}^{0}=0.7$
, 4.7 and 40 for the overdriven branch, and
$s/\unicode[STIX]{x1D6FF}_{L}^{0}=0.1$
, 5.0 and 40 for the cooled branch, and for different rotation rates. The corresponding Cantera results for the two counterflow flame prototypes are shown with the black line. The agreement between the one-dimensional and DNS flame properties is very good, showing that the flame structures observed locally in the DNS can be described to first order by the reduced enthalpy loss parameter
${\mathcal{L}}$
. However, some discrepancies are observed for the lower, superadiabatic branch where curvature effects could modify the flame structure (label 3). This comparison with one-dimensional flames proves that
${\mathcal{L}}$
is a robust and adequate parameter to describe the behaviour of the observed flames. Another approach to study this peculiar flame stabilisation is to look at the details of chemical kinetics, as for example done by Michaels & Ghoniem (Reference Michaels and Ghoniem2016). This analysis for the rotating cylinder is left to a further study.
5 Flame/moving wall interaction
Flame–wall interaction (FWI) is a classical topic in combustion (Ezekoye, Greif & Lee Reference Ezekoye, Greif and Sawyer1992; Poinsot, Haworth & Bruneaux Reference Poinsot, Haworth and Bruneaux1993; Wichman & Bruneaux Reference Wichman and Bruneaux1995; Bruneaux, Poinsot & Ferziger Reference Bruneaux, Poinsot and Ferziger1997). In all these studies, the wall is fixed and the main objective is to determine the maximum heat flux it must sustain during FW interaction. Reproducing numerically flame/wall interactions is dependent on the chemical scheme, that needs to mimic the exothermic zero-activation-energy radical recombination, and the chemical reactivity of the wall (Popp, Smooke & Baum Reference Popp, Smooke and Baum1996; Popp & Baum Reference Popp and Baum1997; Gruber et al.
Reference Gruber, Sankaran, Hawkes and Chen2010; Poinsot & Veynante Reference Poinsot and Veynante2011). The present experiment allows to investigate an interaction between a flame and a moving wall (FMW), which is not the case for classical FWI. For instance, in side wall quenching (SWQ), a flame propagates along a fixed wall (figure 20
b) and the maximum flux to the wall (scaled by the flame power
$\unicode[STIX]{x1D70C}s_{l}^{0}QY_{F}$
) is of the order of 0.15. In the case of head-on quenching (HOQ) where a flame impinges normal to the wall, It can go up to 0.35 (figure 20
a) on fixed walls.
Figure 20. Two different types of flame/wall interaction. (a) Head-on quenching; (b) side wall quenching.
Figure 21. Reduced wall heat flux
$F$
(scaled by the flame power) along the cylinder, for different rotation rates
$\unicode[STIX]{x1D6FC}$
. The locations of the lower and upper flame roots are marked with a circle and a square, respectively. The flux is considered as positive when it transfers energy to the cylinder.
Figure 21 presents the reduced wall heat flux
$F$
along the cylinder (
$\unicode[STIX]{x1D703}$
is the angular position), for different rotation rates. All fluxes are scaled by the flame power
$\unicode[STIX]{x1D70C}s_{l}^{0}QY_{F}$
, and the azimuthal locations of the lower and upper flame roots are marked with a circle and a square, respectively. When the cylinder is at rest (
$\unicode[STIX]{x1D6FC}=0$
), the wall heat flux is symmetric. As the cylinder heats up gases, negative reduced fluxes are found on the upstream part of the cylinder. In contrast, the positive bump in the centre denotes the flux from burned gases to the downstream face of the cylinder. The maximum reduced wall heat flux is found to be approximately 0.20, which agrees with a typical SWQ flame wall/interaction (Lu et al.
Reference Lu, Ezekoye, Greif and Sawyer1991; Poinsot & Veynante Reference Poinsot and Veynante2011). When the cylinder is rotating with moderate rotation rates (
$\unicode[STIX]{x1D6FC}=1.16$
or 2.30), the profile of the wall heat flux becomes asymmetric. A maximum is visible in the vicinity of the lower flame root (circles). The maximum flux obtained at this location reaches a value of 1.1 for
$\unicode[STIX]{x1D6FC}=2.30$
, which exceeds values for SWQ (0.15) or HOQ (0.35) cases (Wichman & Bruneaux Reference Wichman and Bruneaux1995; Poinsot & Veynante Reference Poinsot and Veynante2011). This shows that the flow induced by the rotating cylinder leads to a more intense flame/wall interaction than found in usual flames. It also indicates that the maximum flux which can be reached in a combustion chamber with moving parts (Labarrere et al.
Reference Labarrere, Poinsot, Dauptain, Duchaine, Bellenoue and Boust2016) can exceed SWQ or HOQ values by almost a factor of three. After the maximum reached at the lower branch location, the local wall heat flux decays in the direction of the cylinder rotation, and the upper flame root does not create a new local flame maximum as this flame is subadiabatic and stabilises far downstream of the cylinder.
For higher rotation rates (
$\unicode[STIX]{x1D6FC}$
${>}$
3), the maximum heat flux decreases, even if it remains higher than for classical FW interaction. This trend can be explained by the dilution effect seen in figures 10 and 12. The flow induced by the cylinder creates a layer of burned gases that insulate the cylinder from the flame roots. This leads to a thermal shielding and explains that the cylinder temperature
$T_{c}$
does not increase any more (table 1).
6 Conclusion
The stabilisation of a lean premixed laminar methane/air flame on a rotating cylindrical bluff body was investigated with experiments and DNS to obtain more insights on flame stabilisation. All flames studied were steady both in the experiment and in the DNS. Computations were carried out on a two-dimensional grid with an analytically chemical scheme that could accurately capture flame/wall interactions scenarios and low-temperature chemistry in the wake of the cylinder. In addition, a lumped model was implemented to adapt the cylinder temperature with an energy balance coupled to the DNS. An excellent agreement is found between DNS and experiments over a wide range of rotation rates (ratio of the cylinder’s surface speed to the incoming cold flow) and results show that the bluff-body rotation breaks the symmetry of the flow and creates two distinct flame branches. Surprisingly, a bifurcation takes place at high rotation rates. Beyond a certain rotation rate, the flow induced by the rotation of the cylinder circulates burned gases all around the cylinder, thus creating a layer of gases that changes locally the gas composition. As a result, it reduces the wall heat flux and the cylinder temperature does not increase any more.
DNS results show that the reduced enthalpy defect/gain
${\mathcal{L}}$
is an appropriate control parameter to describe the structure of the two branches. Strain remains small and does not contribute to the flame stabilisation. The superadiabatic branch (positive
${\mathcal{L}}$
) burns fresh gases that have been preheated while flowing along the hot cylinder. In contrast, the subadiabatic branch (negative
${\mathcal{L}}$
) interacts with combustion products that have lost their enthalpy while being convected by the flow induced by the cylinder rotation. The local structures of the two branches can be predicted in terms of maximum heat-release rate and consumption speed using planar unstretched non-adiabatic flames (computed with Cantera) and considering only the local value of the reduced enthalpy parameter
${\mathcal{L}}$
.
This study also unveiled a configuration to investigate FMW (flame/moving wall), something that was not studied before. The wall heat fluxes generated by the interaction of the subadiabatic flame with the moving walls of the cylinder are lower than what is observed when a premixed flame hits a wall in head-on (HOQ) or side-wall quenching (SWQ) configurations. However, the superadiabatic flame creates a wall heat flux to the cylinder that exceeds HOQ by a factor of almost three, showing that the interaction between a flame and a moving wall can be very different and more intense than it is in classical HOQ or SWQ situations.
Acknowledgements
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement ERC-AdG 319067-INTECOCIS. This work was granted access to the high-performance computing resources of IDRIS under the allocation x20162b7036 made by Grand Equipement National de Calcul Intensif. Access to the PIV/CH* acquisition system was obtained through the Toulouse Fermat Federation. The CFD team at Cerfacs is acknowledged for its support on the AVBP code.
The authors wish also to thank M. Marchal and S. Cazin from IMFT for their precious help with the experimental diagnostics, and G. Daviller (Cerfacs), C. Lapeyre (IMFT), C. Kraus (IMFT) and B. Bedat (IMFT) for useful discussions.
