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AIAA SciTech Forum, Grapevine, Texas, 9-13 January 2017, 55th AIAA Aerospace Sciences Meeting
MVP-Workshop Contribution: Modeling of Volvo bluff body flame experiment
Hao Wu, Peter C. Ma, Yu Lv and Matthias Ihme∗
Department of Mechanical EngineeringStanford UniversityStanford, CA 94305
AbstractThe Volvo burner features the canonical configuration of a bluff-body stabilized premixed flame. Thisconfiguration was studied experimentally under the Volvo Flygmotor AB program. Two cases are consideredin this study: a non-reacting case with an inlet flow speed of 16.6 m/s and a reacting case with equilibriumratio of 0.65 and inflow speed of 17.3 m/s. The characteristic vortex shedding in the wake behind thebluff body is present in the non-reacting case, while two oscillation modes are intermittently present inthe reacting case. A series of large-eddy simulations are performed on this configuration using two solvers,one using a high-resolution finite-volume (FV) scheme and the other featuring a high-order discontinuous-Galerkin (DG) discretization. The FV calculations are conducted on hexahedral meshes with three differentresolution (4mm, 2mm, and 1mm). The DG calculations are performed using two different polynomial orderson the same tetrahedral mesh. For the non-reacting cases, good agreement with respect to the experimentaldata is achieved by both solvers at high numerical resolution. The reacting cases are calculated using atwo-step global mechanism in combination with the thickened-flame model. Reasonable agreement withexperiments is obtained by both solvers at higher resolution. Models for combustion-turbulence interactionare necessary for the reacting case as it contains the length scale of the flame, which is smaller than the gridresolution in all calculations. The impact of such models on the flame stability and flow/flame dynamics isthe subject of future research.
∗Corresponding Author: [email protected]
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1 Introduction
The pressing need of propulsion systems withhigher efficiency drives the development of lean com-bustion. However, this combustion mode faces chal-lenges in terms of flame stabilization [1]. The inher-ent unsteadiness related to flame stabilization callsfor high-fidelity numerical modeling techniques suchas Large Eddy Simulations (LES). Although, it hasbeen widely accepted that significant improvementcan be achieved in the predictability of turbulent re-acting flow simulations through the adoption of LESfrom RANS [2], many issues around the usage ofLES remain unclear, largely due to the vast varietyof methods that may be applied by LES.
For reacting flow LES, the modeling choices thatmay impact the simulation results include the nu-merical schemes, modeling of sub-grid scale (SGS)turbulence, representation of combustion chemistry,and modeling of turbulence-chemistry interaction.The solution of LES can be affected by the inter-play between numerical schemes and turbulence SGSmodels, because in common practices of LES, theeffects of the turbulence SGS model and the gridresolution occur at the same scale [3]. The choiceof combustion chemistry models can also affect theLES solution as they are usually constructed by sim-plifying the detailed chemistry process for the pur-pose of reducing computational cost [4]. The pro-cess of simplification introduces many assumptions,whose impact and limitations under different cir-cumstances are often not fully understood even byexpert users [5, 6, 7]. In addition, the interactionbetween the combustion process and the turbulentfluid motion at the sub-grid-scale level also needs tobe modeled. This is a particularly challenging is-sue if the Karlovitz number is below order unity, inwhich case the small-scale structure is affected bysuch interaction.
To better understand the effectiveness and pre-dictability of LES in face of the aforementioned chal-lenges, this paper carries out a series of simulationsusing the configuration of the bluff-body stabilizedpremixed flame. This is a canonical reacting flowconfiguration that was experimentally investigatedunder the Volvo Flygmotor AB program [8, 9, 10].The simplistic set-up resembles many aspects ofpractical combustion devises and presents a combi-nation of interesting physical phenomena, such ascombustion instabilities and lean blowout (LBO).In addition, extensive measurements are made avail-able by the experimentalists, which include statisticsof both velocity and scalars in the form of first andsecond moments.
The Volvo configuration has also been ex-
tensively studied numerically by other researchersthrough LES over the past two decades. Among themore recent efforts, the investigation on the effectof numerical methods include the series of simula-tions performed by Cocks et al. [11, 12], in whichthe results produced by four FV-based solvers us-ing different numerics are compared against eachother and experimental data, and the work of Liet al. [13], which studies the effect of reflecting andnon-reflecting inlets on combustion dynamics. Theself-excited combustion instabilities in this configu-ration were studied by Ghani et al. [14]. The ef-fects of chemical kinetics are studied by Sardesh-mukh et al. [15], Fureby [16], and Manickam etal. [17]. The impacts of more sophisticated treat-ment of turbulence-combustion interaction are alsoinvestigated using LES/PDF method [18] as well asEulerian stochastic field method [19].
Among the many aforementioned issues, thisstudy primarily focuses on the effect of numeri-cal methods in this study. Specifically, we will in-vestigate the behavior and performance of a high-resolution finite-volume (FV) scheme, which is theprevailing approach in the LES community, as wellas a particular implementation of a discontinuousGalerkin (DG) scheme, which is particularly suitablefor achieving higher-order accuracy for convection-dominant flows. Both methods will be tested andvalidated by performing a series of reacting andnon-reacting calculations at different levels of nu-merical resolution, while using similar approachesin the modeling of combustion chemistry and theturbulence-chemistry interaction.
The rest of the paper is organized as follows:Section 2 presents the description of the case set-up, including the experimental configuration andthe computational domain. Section 3 describes thefinite-volume and the discontinuous-Galerkin dis-cretization schemes employed by the two solvers.The combustion model and the computational gridsare also briefly summarized. The results of both re-acting and non-reacting simulations produced by thetwo solvers are presented and discussed in Section 4.The paper is concluded in Section 5.
2 Case Description
2.1 Volvo test rig
A schematic of the Volvo test rig is shown inFig. 1. The configuration consists of a 1.5 m longrectangular duct which is 0.24 m wide by 0.12 mhigh with a choked air inlet. The apparatus is di-vided into the inlet and combustor sections, whichare 0.5 m and 1.0 m in length, respectively. Theinlet section is responsible for fueling, seeding, and
2
flow conditioning. A multi-orifice critical flow injec-tor is utilized for the injection of gaseous propaneupstream of the inlet section for the reacting cases.Honeycombs located in the inlet section are used tocontrol the turbulence level and mixture homogene-ity. A 0.04 m equilateral triangle is mounted 0.682 mupstream from the exit spanning the width of theduct, and acts as the bluff-body flameholder. Theflow exits the rectangular duct through a circularoutlet.
Experimental measurements available for theVolvo test rig includes velocity data from LaserDoppler Anemometry (LDA) [8], and temperatureand species data from Coherent Anti-Stokes RamanScattering (CARS) technique [10]. Mean and rootmean square (RMS) velocity data are available foraxial profiles along the center-line and transverseprofiles across the height of the combustor section atseveral axial locations, downstream the flameholder.
The operating conditions under considerationare summarized in Table 1. An air mass flow rateof 0.6 kg/s is considered. The Reynolds number of48,000 is defined using the characteristic length ofthe bluff body (D = 0.04 m) and bulk inlet veloc-ity and viscosity at the temperature of 288 K. Forthe reacting case the equivalence ratio is 0.65, whichgives an adiabatic flame temperature of 1784 K.
2.2 Computational domain
The computational domain considered in thisstudy is shown in Fig. 2, with a depth twice thewidth of the bluff body, corresponding to one thirdof the channel in the experiment. The full combus-tor section downstream of the flameholder is con-sidered. The bluff body is placed 0.2 m from theinlet. Periodic boundary conditions are applied inthe spanwise direction. A fixed mass flow rate of0.2083 kg/s is employed at the inlet through char-acteristic boundary conditions applied by velocity,temperature and species. No turbulence profile is in-cluded for the inlet velocity and a plug-flow profile isadopted. Pressure of 1 bar is specified through char-acteristic boundary conditions at the outlet. No-slipadiabatic wall boundary conditions are employed atthe flameholder and top and bottom walls, followingthe recommendation of the workshop.
3 Numerical Setup
3.1 Governing equations
The fully compressible Navier-Stokes equationsare considered as the governing equations in thisstudy. The Favre-averaged conservation equationsof mass, momentum, total energy, and species, are
written as follows:
∂ρ
∂t+∂ρuj∂xj
= 0 , (1a)
∂ρui∂t
+ρuiuj∂xj
= − ∂p
∂xi
+∂
∂xj
[(µ+ µt)
(∂ui∂xj
+∂uj∂xi− 2
3δij∂uk∂xk
)],
(1b)
∂ρE
∂t+ρujE
∂xj=
∂
∂xj
[(λ
cp+
µt
Prt
)∂h
∂xj− uj p+ ui(τij + τRij )
]
+∂
∂xj
[N∑
k=1
(ρDk −
λ
cp
)hk∂Yk∂xj
],
(1c)
∂ρYk∂t
+ρuj Yk∂xj
=∂
∂xj
[(ρDk +
µt
Sct
∂Yk∂xj
)]+ ¯ωk ,
(1d)
where ui is the i-th component of the velocity vec-tor, E is the total energy including the chemical en-ergy, C is the progress variable, µ and µt are thelaminar and turbulent viscosity, λ is the thermalconductivity, Dk is the diffusion coefficient for thespecies k, ωk is the source term for species k, τij andτRij are the viscous and subgrid-scale stresses, Prt isthe turbulent Prandtl number, and Sct is the turbu-lent Schmidt number. An appropriate subgrid-scalemodel is needed for the computation of the turbu-lent viscosity. The system is closed by the ideal-gaslaw as the equation of state. The sub-grid terms as-sociated with the equation of state are neglected inthis study.
3.2 Finite-volume discretization
The massively paralleled CharLES x, developedat Center for Turbulence Research, Stanford Univer-sity, is used in this study as the finite-volume solver.CharLES x has been applied to studies of severaldifferent flow problems including aeroacoustics [21],supercritical flows [22], supersonic combustion [23],and aerodynamic flows [24]. A brief summary of thenumerical schemes is provided here, and for more de-tails the interested readers are referred to the workby Ham et al. [25] and Khalighi et al. [26].
A control-volume based FV approach is utilizedfor the discretization of the system of Eq. (1):
∂U
∂tVcv +
∑f
F eAf =∑f
F vAf + S∆cv , (2)
3
Figure 1. Schematic of the Volvo test rig (adapted from Sjunnesson et al. [10]).
Case Re Ubulk [m/s] φ Tin [K] Tad [K]
Non-reacting 48,000 16.6 0.0 288 -Reacting 48,000 17.3 0.65 288 1784
Table 1. Operating conditions.
Figure 2. Computational domain and boundary conditions [20].
where U is the vector of conserved variables, F e isthe face-normal Euler flux vector, F v is the face-normal viscous flux vector, which corresponds to ther.h.s of Eq. (1), S is the source term vector, ∆cv isthe volume of the control volume, and Af is the face
area. A strong stability preserving 3rd-order Runge-Kutta (SSP-RK3) scheme [27] is used for time ad-vancement. CharLES x was developed based on areconstruction-based FV scheme. Polynomials withmaximum third-order accuracy are used to recon-
4
(a) 4 mm
(b) 2 mm
(c) 4 mm (top half flameholder) (d) 2 mm (top half flameholder)
Figure 3. Computational grids for the FV solver.
struct the left- and right-biased face centroid val-ues of the flow variables, and a blending between acentral flux and a Riemann flux is computed basedon the local grid quality. This flux computationprocedure yields formally second-order accuracy andhas maximum fourth-order accuracy on a perfectlyuniform Cartesian mesh, without numerical dissipa-tion. For computations of shock-related problemsand cases where large gradients of flow variablesare present, CharLES x utilizes a sensor-based hy-brid Central-ENO scheme to minimize the numericaldissipation while stabilizing the simulation. For re-gions where shocks and large gradients are present,a second-order ENO reconstruction is used at theleft- and right-biased face values, followed by anHLLC Riemann flux computation. A number of dif-ferent hybrid sensors/switches are available. For thisstudy, a relative solution” (RS) sensor is used whichis based on the solution and reconstruction values ofdensity [26, 28]. An entropy-stable flux correctiontechnique [29] is used to ensure the physical real-izability of the numerical solution and to dampennon-linear instabilities.
Following Pope’s criterion [30], Cocks et al. [11]showed that a resolution of 3 mm is required so that80% of the turbulent kinetic energy can be fully re-solved by the LES, although the criterion may not
be sufficient for reacting cases. Based on this ar-gument, three grids with increasing resolutions of4 mm, 2 mm, and 1 mm are generated. The 4 mmand 2 mm grids are shown in Fig. 3 along withzoomed-in regions near the flameholder. The gridsare clustered near the wall, with a minimum wallspacing of 0.3 mm, and the mesh is nearly isotropicin the rest of the domain. A uniform grid is em-ployed in the spanwise direction. The three gridsamount to a total of 0.54, 4.17, and 24.6 millioncells, respectively.
A Vreman SGS model [31] is used for the sug-grid terms. The sub-grid scale eddy viscosity is cal-culated as
µt = ρC∆2/3cv(
β11β22 − β212 + β11β33 − β2
13 + β22β33 − β223
αijαij
)1/2
,
(3)where αij = ∂uj/∂xi, βij = αmiαmj , and ∆cv is thelocal cell volume. The model constant C is set to avalue of 0.07 in this study.
The combustion process in the FV simulations isdescribed by a two-step kinetic scheme as mentionedin the workshop document [20], which is adaptedfrom Ghani et al. [14]. The laminar flame speedand the adiabatic flame temperature obtained bythis mechanism are listed in Table 2 in comparison
5
with those from the GRI 3.0 mechanism [32]. Thedifference in the flame speed is 11% and the flametemperature is virtually identical.
The thickness of the flame is estimated to be0.6 mm, which cannot be resolved by the meshesused in this study. Therefore, a dynamic thickenedflame model [33, 34] is used to describe the flameturbulence interactions with the model of Charletteet al. [35] for the sub-grid efficiency.
3.3 Discontinuous-Galerkin discretization
For notational convenience, the governing equa-tions of Eq. (1) are written in vector form as:
∂
∂tU +∇ · F = ∇ · Q + S , (4)
in which U, F, Q, and S refer to the solution vector,the convective flux, the viscous flux, and the sourceterm, respectively. To discretize Eq. (4) with a vari-ational approach, a broken space is used as the testspace
Vph = φ ∈ L2(Ω) : φe ≡ φ|Ωe ∈ Pp,∀Ωe ∈ Ω , (5)
in which a polynomial space with order p is definedon each individual element Ωe resulting from the do-main partition. The test function φ is then multi-plied to Eq. (4) and integrated to derive the weakform. The left-hand-side of Eq. (4) is the classicalEuler equations, and the corresponding weak formscan be written as:∫
Ω
φ(∂tU +∇ · F)dx
=∑e
(∫Ωe
(φe∂tU−∇φe · F)dx+
∫∂Ωe
φ+e F · nds
)≈∑e
(∫Ωe
φeφTe dtUe,i(t)dx−
∫Ωe
∇φe · F (Ue)dx
+
∫∂Ωe
φ+e F ds
),
(6)
in which the superscript “+” refers to interior quan-tity on the element edge and the discretized solu-tion U (together with Ue and Ue,i), following theGalerkin method, takes the form
U ' U = ⊕Nee=1Ue , (7a)
Ue(t, x) =
Np∑i=1
Ue,i(t)φe,i(x) . (7b)
To complete the discretization, the Riemann flux Fin Eq. (6) needs to be specified. We consider the pre-conditioned Roe scheme [36] for the current study.
Since Q involves multi-entries, here we only con-sider a general form for each of them to simplifythe explanation. Qi denotes the diffusion flux ofNavier-Stokes equations for the ith solution variable.This can be further represented using a linearizationQi =
∑j Dij ∇Uj , where refers to Hadamard
product. Because the discretization is subject to thedistributive property of addition, the problem canbe further simplified by discretizing Dij ∇Uj ≡ Qij
taking the following form
∑e
∫Ωe
φ∇ · Qijdx
=∑e
(−∫Ωe
(Dij ∇Uj) · ∇φedx +
∫∂Ωe
φeQij · nds)
=∑e
(∫Ωe
Uj∇ · (Dij ∇φe)dx −∫∂Ωe
Uj(Dij ∇φe) · nds +
∫∂Ωe
φeQij · nds)
≈∑e
(∫Ωe
Uj∇ · (Dij ∇φe)dx −∫∂Ωe
Uj(Dij ∇φe)+ · nds +
∫∂Ωe
φ+e Qijds
)
=∑e
(−∫Ωe∇φe · (Dij ∇Uj)dx +
∫∂Ωe
(U+j− Uj)(Dij ∇φe)
+ · nds +
∫∂Ωe
φ+e Qijds
).
With this, the discretization of ∇·Qi can be writtenas ∑
e
∫Ωe
φ∇ · Qidx ≈
−∑e
∫Ωe
∇φe · ([Di]T∇U)dx
+∑e
∫∂Ωe
([D+i ]
T (U+ − U) ∇φe) · nds
+∑e
∫∂Ωe
φ+e Qids ,
(8)
where the diffusion Jacobian [Di] has Ns rows com-posed of Dij with j = i · · ·Ns. The three termson the right-hand side account for interior diffu-sion, dual consistency and inter-element diffusion.U and Q can be selected in various ways, result-ing different diffusion-discretization schemes. In thisstudy, we consider the standard interior penalty(SIP) method [37] and U is chosen to be U where· = ((·)+ + (·)−)/2, then we have
Qi = [Di]T∇U+ σSIP
(max
x∈∂Ω±e
µ(x)
)JUK/h , (9)
where J·K = (·)+n+ + (·)−n− and σ refers to con-stant parameters to ensure numerical stability. Asfor σSIP, we use the suggested values of [38]. The
stabilization term for Qi in Eq. (9), having a con-sistent form of that in the Riemann solvers, alwaysbehaves as a dissipation term.
For the present study, the DG-based predictionis carried out on an unstructured mesh that is dis-cretized with about 25,000 tetrahedral elements, asshown in Fig. 4. Two DG schemes, namely DGP1
6
Mechanism Sl [m/s] Tb [K]
2-step 0.194 1805.8GRI30 0.218 1806.6
Table 2. Laminar flame speed and the adiabatic flame temperature obtained by the two-step mechanismfor the FV simulations in comparison to GRI30 [32].
and DGP2, are considered, which represent element-wise solutions using linear and quadratic polynomi-als, respectively. DGP1 and DGP2 schemes con-sists of four and ten polynomial coefficients to besolved in each element. This corresponds to 1.0 and2.5 millions total degrees of freedom for DGP1 andDGP2 predictions, respectively. A standard five-stage fourth-order Runge-Kutta scheme is employedfor time integration. The prediction of reacting flowsrequires consideration of variable thermal properties(i.e., heat capacity as a function of temperature).Without proper treatment, the standard numericalprocedure might produce spurious pressure oscilla-tion. To avoid this issue, a Double-Flux model pro-posed by Billet and Ryan [39] is used [40].
For the present study, no explicit turbulencemodel is employed, which is instead accommodatedusing inherent numerical dissipation [41]. An at-tempt of using a similar strategy to the heat andmass transfer in the reacting simulations shows thatinsufficient numerical dissipation. As a result, athickened flame model is used with a constant thick-ening factor of 20 for DGP1 and 10 for DGP2. TheSGS efficiency is modeled using a constant efficiencyfactor of 5.
4 Results and Discussions
In this section, the reacting and non-reactingsimulations are conducted by two solvers, one usingthe FV discretization and the other using the DGdiscretization. The results are presented in compar-ison with the experimental data.
4.1 Non-reacting simulations: finite-volume dis-cretization
The non-reacting case is simulated with theFV solver using three different resolutions, namely4 mm, 2 mm, and 1 mm. For the sake of validatingthe sub-grid scale models utilized and establishinggrid convergence study. Figure 5 shows the vor-tical structures exhibited downstream of the bluffbody from the simulation using the 1 mm grid. Iso-surfaces of vorticity magnitude of 4000 s−1 coloredby the spanwise velocity are displayed. It can beseen that the von-Karman type shedding is gener-ated behind the flameholder due to the instabilitiesproduced by the flow separations. The large vor-
tices then break up into smaller vortices and theflow becomes more turbulent further downstream.It is also important to observe the interactions be-tween the vortices and the wall. It has been pointedout by Cocks et al. [11] that the wall vortices playa major role inestablishing three-dimensional vortexbreakdown further downstream of the domain.
Figures 6 to 8 show the results of the velocitystatistical profiles for the three different grids used.The simulations are averaged for about 300 ms,which corresponds to about six flow-through timesover the entire computational domain. Five differentaxial locations are considered for comparison withthe experimental measurements. Mean and root-mean-square (RMS) axial and transverse velocityprofiles are shown in Figs. 6 and 7, and the Reynoldsstress profiles are shown in Fig. 8. It can be seen thatgrid convergence is achieved already with the 2 mmgrid for both the first and second moment statistics,and the simulation with the 1 mm grid confirms theconvergence. Excellent agreement can be observedfor all the quantities compared with the measure-ments, except for the transverse velocity at the ax-ial location x/D = 1.53, where the experiments havelarger magnitude.
To further compare the simulation results withthe experimental data quantitatively, two morequantities are considered together with the axialvelocity at the centerline of the domain down-stream the flameholder. The anisotropy and thefluctuation level are defined as URMS/VRMS and√U2
RMS + V 2RMS/Ubulk, respectively. Figure 9 shows
the results from simulations using the three grids.It be seen that although the results from three gridresolutions exhibits little difference for the axial ve-locity and fluctuation level. The 4 mm results for theanisotropy shows behavior quite different to that ob-tained for the other two grids. This shows that the2 mm grid resolution is sufficient for the prediction ofthe instabilities and turbulence for the non-reactingcase.
It can be seen from Fig. 9 that, althoughthe anisotropy and fluctuation levels show excellentagreement with the experimental measurements, theaxial velocity shows 20% to 30% underprediction foraxial locations after x/D = 2. This discrepancy
7
Figure 4. Computational grids for the DG solver.
Figure 5. Iso-surfaces of vorticity magnitude of 4000 s−1 colored by the spanwise velocity on the 1 mm gridfor the non-reacting case from the FV solver.
U/Ubulk
-1 0 1 2
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.375
U/Ubulk
-1 0 1 2-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.95
U/Ubulk
-1 0 1 2-1.5
-1
-0.5
0
0.5
1
1.5x/D = 1.53
U/Ubulk
-1 0 1 2-1.5
-1
-0.5
0
0.5
1
1.5x/D = 3.75
U/Ubulk
-1 0 1 2-1.5
-1
-0.5
0
0.5
1
1.5x/D = 9.4
URMS
/Ubulk
-0.5 0 0.5 1
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.375
URMS
/Ubulk
-0.5 0 0.5 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.95
URMS
/Ubulk
-0.5 0 0.5 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 1.53
URMS
/Ubulk
-0.5 0 0.5 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 3.75
URMS
/Ubulk
-0.5 0 0.5 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 9.4
Figure 6. Normalized mean (left) and RMS (right) axial velocity profiles on three grids (solid line – 4 mm,dashed line – 2 mm, dash-dotted line – 1 mm) in comparison with measurements (dots), at several axiallocations for the non-reacting case from the FV solver.
from the experimental measurements may be dueto the different boundary conditions employed inthe current simulation to that in the experiments,e.g. the flow is assumed to be laminar at the inlet.Similar underprediction of the axial velocity can befound in numerical simulations using other solverswith similar computational domain and boundaryconditions [11]. Overall, the non-reacting simula-tions from the FV solver show very good agreement
with the experiments for the available data consid-ered.
4.2 Reacting simulations: finite-volume discretiza-tion
The reacting flow simulations with the FV dis-cretization is carried out using the 4mm-resolution,2mm-resolution, and 1mm-resolution grids. Bothsimulations use the same combustion model as dis-
8
V/Ubulk
-1 0 1
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.375
V/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.95
V/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 1.53
V/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 3.75
V/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 9.4
VRMS
/Ubulk
-0.5 0.5 1.5
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.375
VRMS
/Ubulk
-0.5 0.5 1.5-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.95
VRMS
/Ubulk
-0.5 0.5 1.5-1.5
-1
-0.5
0
0.5
1
1.5x/D = 1.53
VRMS
/Ubulk
-0.5 0.5 1.5-1.5
-1
-0.5
0
0.5
1
1.5x/D = 3.75
VRMS
/Ubulk
-0.5 0.5 1.5-1.5
-1
-0.5
0
0.5
1
1.5x/D = 9.4
Figure 7. Normalized mean (left) and RMS (right) transverse velocity profiles on three grids (solidline – 4 mm, dashed line – 2 mm, dash-dotted line – 1 mm) in comparison with measurements (dots),at several axial locations for the non-reacting case from the FV solver.
RS/Ubulk
2-0.3 0 0.3
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.375
RS/Ubulk
2-0.3 0 0.3
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.95
RS/Ubulk
2-0.3 0 0.3
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 1.53
RS/Ubulk
2-0.3 0 0.3
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 3.75
RS/Ubulk
2-0.3 0 0.3
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 9.4
Figure 8. Normalized mean Reynolds stress profiles on three grids (solid line – 4 mm, dashed line – 2 mm,dash-dotted line – 1 mm) in comparison with measurements (dots), at several axial locations for the non-reacting case from the FV solver.
cussed in Sec. 3.The elevated temperature in the reacting case as
well as the density ratio significantly alter the flowfield characteristics. The flow is less turbulent dueto the higher viscosity and the large density ratiosuppresses sinuous instability mode, which is char-acteristic for non-reacting flow in the wake of a bluff-body. The laminar flame speed of the mixture withφ = 0.65 is estimated to be 0.2 m/s and the corre-sponding flame thickness is 0.6 mm. Therefore, noneof the three FV meshes calculations can resolve theflame and the impact of the flame thickening modelon the simulation result is not negligible.
The instantaneous temperature fields of the4mm and 2mm simulations are shown in Fig. 10.Vortex shedding is not present in either simulation.The instability of the shear layer at the near field
of the wake is very symmetric. Intermittent sinuousmodes can be observed at locations that are furtherdownstream. A stronger effect of flame wrinklingcan be observed in the 2mm case, which is not sur-prising given the higher resolution.
As part of the validation, the mean and RMSaxial and transverse velocities across the flame arepresented in Fig. 11 and Fig. 12. Reasonable agree-ment is obtained by both cases in terms of the meanvelocity profiles. The fluctuations are better cap-tured by the higher-resolution case. The achieve-ment of grid convergence cannot be observed fromthe two cases presented.
The mean mean axial velocity, anisotropy, andfluctuation along the centerline are shown in Fig 14.The cases with finer mesh shows the improvementover all three quantities, but the overall agreement
9
x/D0 2 4 6 8 10
U/U
bulk
-1
-0.5
0
0.5
1
1.5
4 mm2 mm1 mmExperiment
(a) Axial velocity
x/D0 2 4 6 8 10
VR
MS
/UR
MS
0
0.5
1
1.5
2
2.5
3
4 mm2 mm1 mmExperiment
(b) Anisotropy
x/D0 2 4 6 8 10
(UR
MS
2+
VR
MS
2)1
/2/U
bulk
0
0.2
0.4
0.6
0.8
1
1.2
1.4
4 mm2 mm1 mmExperiment
(c) Fluctuation
Figure 9. Centerline profiles for (a) mean axial velocity, (b) anisotropy, and (c) fluctuation level on threegrids (solid line – 4 mm, dashed line – 2 mm, dash-dotted line – 1 mm) in comparison with measurements(dots) for the non-reacting case from the FV solver.
with the experimental data is worse in comparisonto the non-reacting case. Grid convergence has notbeen reached for the series of reacting calculations.The 2 mm case shows overall best agreement withrespect to the experimental data among the threecases.
4.3 Non-reacting simulations: discontinuous-Galerkin discretization
Figure 15 shows DG simulation results for thenon-reacting case. The axial velocity profile shows anoticeable recirculation zone behind the bluff body.The DG solutions capture the mean-flow profilesalong the transverse direction, especially for theDGP2 solution. However, DGP1 method predicts alarger recirculation zone, showing considerable dis-crepancy from the measurement. As for the profile
of the transverse velocity, both DGP1 and DGP2solutions shows insufficient agreement with experi-mental data. That is likely due to the simplifica-tion made on inflow condition (no consideration ofinflow turbulence) and the size reduction of the do-main along the spanwise direction. Comparativelyspeaking, DGP2 solution is still able to provide abetter representation of the variation of the trans-verse velocity along wall-normal direction, comparedto the DGP1 solution. Velocity RMS predictionsare presented in Figs. 15(b) and 15(d). Both DGP1and DGP2 simulations are able to provide reason-able representation of the RMS of streamwise ve-locity. At the upstream location very close to thebluff body, DGP2 solution shows considerably bet-ter agreement with the measured RMS of streamwise
10
Figure 10. Instantaneous temperature contours of 4mm (top), 2mm (middle) and 1mm (bottom) casesfrom the FV solver.
U/Ubulk
-1 1 3
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.375
U/Ubulk
-1 1 3-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.95
U/Ubulk
-1 1 3-1.5
-1
-0.5
0
0.5
1
1.5x/D = 1.53
U/Ubulk
-1 1 3-1.5
-1
-0.5
0
0.5
1
1.5x/D = 3.75
U/Ubulk
-1 1 3-1.5
-1
-0.5
0
0.5
1
1.5x/D = 9.4
URMS
/Ubulk
-0.5 0 0.5 1
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.375
URMS
/Ubulk
-0.5 0 0.5 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.95
URMS
/Ubulk
-0.5 0 0.5 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 1.53
URMS
/Ubulk
-0.5 0 0.5 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 3.75
URMS
/Ubulk
-0.5 0 0.5 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 9.4
Figure 11. Normalized mean (left) and RMS (right) axial velocity profiles on three grids (solid line – 4 mm,dashed line – 2 mm in comparison with measurements (dots), dash-dotted line – 1 mm), at several axiallocations for the non-reacting case from the FV solver.
velocity, compared to the DGP1 solution. As for theRMS of the transverse velocity, DGP2 prediction isconsistently better than that of DGP1 at all mea-surement locations.
4.4 Reacting simulations: discontinuous-Galerkindiscretization
Figure 16 shows DG prediction of the mean-flowprofile for the reacting case. Compared to the non-reacting case in Fig. 15(a), sharper gradients appearin the axial velocity profile between the forward andbackward flows due to the presence of the premixedflame. Both DGP1 and DGP2 solutions show rea-sonably good agreement with the experimental data.Comparatively, DGP2 solution is superior in termsof representing near-body flow profiles and preserv-
ing the velocity gradient at downstream locations.Both DGP1 and DGP2 methods, however, predict aslightly weaker back-flow in the recirculation zonecompared to the experimental data. As for theprediction of the transverse velocity, results fromDGP1 and DGP2 show difficulties near the bluff-body. DGP1 solution has large discrepancy fromthe measurement. This problem is likely due to thelack of numerical resolution to represent the interac-tion between the flame and the flow field. The lackof resolution in the DGP1 simulation might lead to apoor representation of chemical source terms, whichcould explain the consistent over-prediction of thecenterline temperature. In contrary, DGP2 simula-tion can accurately predict the equilibrium temper-ature along the centerline. The measurement shows
11
V/Ubulk
-1 0 1
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.375
V/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.95
V/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 1.53
V/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 3.75
V/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 9.4
VRMS
/Ubulk
-0.5 0.5 1.5
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.375
VRMS
/Ubulk
-0.5 0.5 1.5-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.95
VRMS
/Ubulk
-0.5 0.5 1.5-1.5
-1
-0.5
0
0.5
1
1.5x/D = 1.53
VRMS
/Ubulk
-0.5 0.5 1.5-1.5
-1
-0.5
0
0.5
1
1.5x/D = 3.75
VRMS
/Ubulk
-0.5 0.5 1.5-1.5
-1
-0.5
0
0.5
1
1.5x/D = 9.4
Figure 12. Normalized mean (left) and RMS (right) transverse velocity profiles on three grids (solidline – 4 mm, dashed line – 2 mm, dash-dotted line – 1 mm) in comparison with measurements (dots), atseveral axial locations for the non-reacting case from the FV solver.
T [K]200 800 1400 2000
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 3.75
T [K]200 800 1400 2000
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 8.75
T [K]200 800 1400 2000
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 13.75
Figure 13. Mean temeparture profiles on three grids (solid line – 4 mm, dashed line – 2 mm, dash-dottedline – 1 mm) in comparison with measurements (dots), at several axial locations for the non-reacting casefrom the FV solver.
a thick flame brush compared to the numerical pre-dictions by the DG methods.
5 Conclusions
A series of LES simulations were performed forthe Volvo bluff-body stabilized combustion configu-ration using two solvers featuring a high-resolutionfinite-volume method as well as a high-order DGdiscretization. Both the non-reacting and react-ing cases are calculated. For the non-reactingcases, good agreement with the experimental datais achieved by solvers at high numerical resolution(2mm case for FV and DGP2 for DG). The reactingcases are more challenging due to the small lengthscale of the flame and the suppression of sinuousmode of absolute instability by the density ratio.Improvements over the results of higher-resolutioncases were observed for both solvers. Grid conver-
gence is not achieved by either solver. The impact ofthe models for turbulence-combustion interaction isimportant at the current resolutions for both solvers.A closer investigation of this aspect is the subject offuture research.
Acknowledgments
This work was funded by NASA Transforma-tional Tools and Technologies Project with AwardNo. NNX15AV04A.
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x/D0 2 4 6 8 10
U/U
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4 mm2 mm1 mmExperiment
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U/Ubulk
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U/Ubulk
-1 0 1 2-1.5
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U/Ubulk
-0.5 0 0.5 1
y/D
-1.5
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U/Ubulk
-0.5 0 0.5 1-1.5
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U/Ubulk
-0.5 0 0.5 1-1.5
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1
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U/Ubulk
-0.5 0 0.5 1-1.5
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1
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U/Ubulk
-0.5 0 0.5 1-1.5
-1
-0.5
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0.5
1
1.5x/D = 9.4
(b) RMS axial velocity
v/U0
-0.5 0 0.5
y/D
-1.5
-1
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1.5
v/U0
-0.5 0 0.5
v/U0
-0.5 0 0.5
v/U0
-0.5 0 0.5
(c) Mean transverse velocity
vrms/U0
0 0.2 0.4 0.6 0.8
y/D
-1.5
-1
-0.5
0
0.5
1
1.5
vrms/U0
0 0.2 0.4 0.6 0.8
vrms/U0
0 0.2 0.4 0.6 0.8
vrms/U0
0 0.2 0.4 0.6 0.8
(d) RMS transverse velocity
Figure 15. DG simulation results for the non-reacting case (blue line − DGP1; red line − DGP2; dots −experimental data).
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U/Ubulk
-1 0 1 2 3
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.375
U/Ubulk
-1 0 1 2 3-1.5
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U/Ubulk
-1 0 1 2 3-1.5
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y/D
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-1
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0.5
1
1.5x/D = 0.375
U/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.95
U/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 1.53
U/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 3.75
U/Ubulk
-1 0 1-1.5
-1
-0.5
0
0.5
1
1.5x/D = 9.4
(b) Mean transverse velocity
U/Ubulk
0 500 1000 1500 2000
y/D
-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.375
U/Ubulk
0 500 1000 1500 2000-1.5
-1
-0.5
0
0.5
1
1.5x/D = 0.95
U/Ubulk
0 500 1000 1500 2000-1.5
-1
-0.5
0
0.5
1
1.5x/D = 1.53
(c) Temperature
Figure 16. DG simulation results of the mean-flow profile for the reacting case (blue line − DGP1; red line− DGP2; dots − experimental data).
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