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A Simple Approach for SpecifyingVelocity Inflow Boundary Conditions inSimulations of Turbulent Opposed-JetFlowsRanjith R. Tirunagari, Michael W. A.Pettit, Andreas M. Kempf & StephenB. PopeFlow, Turbulence and CombustionAn International Journal published inassociation with ERCOFTACISSN 1386-6184Volume 98Number 1Flow Turbulence Combust (2017)98:131-153DOI 10.1007/s10494-016-9743-41 23

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Author's personal copyFlow Turbulence Combust (2017) 98:131–153DOI 10.1007/s10494-016-9743-4A Simple Approach for Specifying Velocity InflowBoundary Conditions in Simulations of TurbulentOpposed-Jet FlowsRanjith R. Tirunagari1,4 · Michael W. A. Pettit2 ·Andreas M. Kempf3 · Stephen B. Pope1Received: 3 November 2015 / Accepted: 17 May 2016 / Published online: 28 May 2016 Springer Science Business Media Dordrecht 2016Abstract A new methodology is developed to specify inflow boundary conditions for thevelocity field at the nozzle exit planes in turbulent counterflow simulations. The turbulentcounterflow configuration consists of two coaxial opposed nozzles which emit highlyturbulent streams of varying species compositions depending on the mode considered. Thespecification of velocity inflow boundary conditions at the nozzle exits in the counterflowconfiguration is non-trivial because of the unique turbulence field generated by the turbulence generating plates (TGPs) upstream of the nozzle exits. In the method presented here,a single large-eddy simulation (LES) is performed in a large domain that spans the regionbetween the TGPs of the nozzles, and the time series of the velocity fields at the nozzle exitplanes are recorded. To provide inflow boundary conditions at the nozzle exit planes forsimulations under other conditions (e.g., different stream compositions, bulk velocity, TGPlocation), transformations are performed on the recorded time series: the mean and r.m.s.(root-mean-square) quantities of velocity, as well as the longitudinal integral length scaleon the centerline, at the nozzle exits in simulations are matched to those observed in experiments, thereby matching the turbulent Reynolds number Ret . The method is assessed byimplementing it in coupled large-eddy simulation/probability density function (LES/PDF)simulations on a small cylindrical domain between the nozzle exit planes for three different modes of the counterflow configuration: N2 vs. N2 ; N2 vs. hot combustion products; Ranjith R. [email protected] School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853,USA2Department of Mechanical Engineering, Imperial College London, South Kensington Campus,Exhibition Road, London SW7 2AZ, UK3Institute for Combustion and Gas Dynamics (IVG) and Center for Computational Sciences andSimulation, Universität Duisburg-Essen, Duisburg 47048, Germany4Present address: CD-adapco, 21800 Haggerty Road, Suite 300, Northville, MI 48167, USA

Author's personal copy132Flow Turbulence Combust (2017) 98:131–153and CH4 /N2 vs. O2 . The inflow method is found to be successful as the first and second moments of velocity from the LES/PDF simulations agree well with the experimentaldata on the centerline for all three modes. This simple yet effective inflow strategy can beapplied to eliminate the computational cost required to simulate the flow field upstream ofthe nozzle exits. It is also emphasized that, in addition to the predicted time series data,the availability of experimental data close to the nozzle exit planes plays a key role in thesuccess of this method.Keywords Turbulent counterflow simulations · Velocity inflow boundary conditions ·LES/PDF · Auto-correlation function · Velocity statistics1 IntroductionTurbulent counterflow flames (TCFs) were experimentally studied in the early 1990s interms of their flame structure, fundamental combustion processes and extinction limits innon-premixed and premixed modes, to evaluate the potential of this configuration for combustion research and to establish a foundation for computational investigations [1–3]. Morerecently, TCFs have been considered as an alternative to the well-known jet flames as aconfiguration in which to study fundamental processes in turbulent combustion. It is welldemonstrated and documented in [4–8] that the TCF configuration offers several advantages for the study of turbulence-chemistry interactions in a laboratory arrangement. Someof the key advantages are: (i) the achievement of high Reynolds numbers without pilotflames; (ii) the range of combustion regimes that can be realized, from stable flames tolocal extinction/re-ignition conditions; (iii) the compactness of the domain compared to jetflames; (iv) the ability to explore a variety of fuels, including bio-fuels and fuel blends; and(v) the relevance to practical combustion devices in terms of operating conditions.The main motivation of the collaborative TCF studies has been to test the computationalmodels of mixing [9, 10], turbulence [11] and combustion [4] by performing detailed comparisons to experimental data for flow and scalar fields. The computational work describedin this paper is part of a collaborative project which aims at studying TCFs using bothexperimental and computational techniques. A series of experiments on TCFs, operating innon-reactive, non-premixed and premixed modes, were performed at Yale University and atSandia National Laboratories [12, 13]; and the same flames are being studied computationally using the large-eddy simulation/probability density function (LES/PDF) methodology[14–16].1.1 The turbulent counterflow flame (TCF) configurationThe counterflow configuration shown in Fig. 1 consists of two coaxial opposed nozzles ofdiameter dj et 12.7 mm placed at a variable distance d apart. The nozzles are surroundedby an annular co-flow of N2 with an outer diameter of 29.5 mm. This configuration can beoperated in different modes and we considered three modes in this paper as follows:––Inert/Inert (I/I) mode: both nozzles emit highly-turbulent streams of N2 gas at temperature Tu 294 K and pressure 1 atm., leading to a non-reactive flow with inertmixing.Inert/Burnt (I/B) mode: the top nozzle emits a highly-turbulent stream of N2 at Tu 294K and 1 atm., while the bottom nozzle emits burnt stoichiometric combustion products

Author's personal copyFlow Turbulence Combust (2017) 98:131–153133Fig. 1 The experimental configuration for (a) the I/I and F/O modes, and (b) the I/B mode. The extent ofthe large computational domain used in the single large-domain LES is highlighted by the green box in (a),whereas the extent of the small computational domain used in the small-domain LES/PDF simulations ishighlighted by the red box in (a) and (b). The simulation results are presented such that the bottom stream ison the LHS and the top stream is on the RHS–at Tb 1850 K and 1 atm., leading to an essentially non-reactive flow with mixingbetween the inert gas and hot combustion products.Fuel/Oxidant (F/O) mode: the top nozzle emits a highly-turbulent stream of oxidant inthe form of pure O2 at Tu 294 K and 1 atm. and the bottom nozzle emits a highlyturbulent stream of diluted fuel in the form of CH4 /N2 at a molar ratio of 35:65 atTu 294 K and 1 atm., leading to a non-premixed flame sandwiched between the twonozzles.The experimental configuration for the I/I and F/O modes is shown in Fig. 1a and for the I/Bmode in Fig. 1b. The configuration for the I/B mode is different in that the bottom nozzlehosts a pre-burner which burns a stoichiometric fuel-air mixture (CH4 /O2 /N2 with a molarratio of 26:74 for O2 /N2 ) to completion to generate the stream of hot combustion products.It is important to note that all the streams operated in the above modes are highly-turbulentexcept for the combustion product stream in the I/B mode. The hot stream of combustionproducts has high viscosity and therefore the turbulence generating plate (TGP) is removedfrom the corresponding nozzle. More experimental details of these modes can be found in[12, 13].As highlighted in Fig. 1b, each nozzle (except the bottom nozzle in the I/B mode) housesa high-blockage TGP [17] which generates a high-intensity turbulence field at the nozzleexit. The stream forms a high-speed jet as it passes through the TGP, which breaks up into

Author's personal copy134Flow Turbulence Combust (2017) 98:131–153a complex, highly-turbulent flow with strong re-circulation effects in the contraction zoneprior to exiting the nozzle. The turbulence that is observed in the region between the twonozzles is largely determined by the turbulence generating mechanism of the TGP in thecontraction zone [12].1.2 Choice of LES solution domainThere have been many collaborations in the past involving experimental and numerical studies of the TCF configuration (e.g., [4, 12, 18–20]). One of the underlying aspects in thesestudies is the choice of the computational domain. The two computational domains that havebeen used are, broadly: (i) a large domain that includes the upstream region of the nozzleexits as well as the region between them, as highlighted by the green box in Fig. 1a; and,(ii) a small cylindrical domain that includes only the region between the two nozzle exits,and therefore excludes the upstream region involving the TGP, as depicted by the red box inFig. 1a and b.In many previous studies involving LES of the counterflow configuration (e.g., [4, 12,20]), a large computational domain is chosen, which includes the region upstream of thenozzle exits. The main advantage of choosing such a computational domain is that it facilitates the prediction of the development of the flow and turbulence field downstream of theTGP. Hence, such simulations are predictive. Additionally, the boundary conditions for thevelocity field at the inflow boundaries of the large domain are simpler, i.e., non-turbulent,and we suppose that the conditions at the nozzle exits are insensitive to the details of thesespecified boundary conditions. However, the large computational domain and the complexgeometry make the LES calculations difficult and expensive. Although the prediction ofthe velocity field downstream of the TGP is important, the main focus of the past counterflow studies has been to understand turbulence-chemistry interactions in the region betweenthe two nozzle exit planes, where a turbulent non-premixed/premixed flame is establishednear the mid-plane. It is therefore logical to consider the second choice – a smaller cylindrical computational domain between the two nozzle exits. Due to its simple geometry andsmaller size, this solution domain enables simpler and less expensive high-fidelity LES. Onthe other hand, one major limitation of choosing such a compact domain is the need to specify inflow boundary conditions on the (turbulent) velocity field at the nozzle exit planes. Itwas concluded early on in previous counterflow studies that predicting the turbulent velocity field in the downstream region of the TGP is essential to choosing the correct boundaryconditions at the nozzle exit planes [21].1.3 Objectives and challengesIn this work, we present results from the LES/PDF simulations of the three operatingmodes described in Section 1.1 on a small cylindrical domain that encompasses the volumebetween the two nozzle exit planes as highlighted by the red box in Fig. 1b. The solutiondomain has two inflows in the axial direction for the two opposed streams and an outflowin the radial direction. The coupled LES/PDF simulations are computationally expensiveprimarily due to the Monte-Carlo particle based PDF code, and therefore, it is decided toconsider the small solution domain excluding the nozzles to make the LES/PDF simulationssimpler and less expensive.It then becomes imperative to specify realistic velocity inflow boundary conditions at theexit planes that mimic the conditions observed in the experiments. For example, the velocityfield data generated by simulating the turbulent flow in a simple pipe is not adequate to

Author's personal copyFlow Turbulence Combust (2017) 98:131–153135represent the complex perturbations imposed by the TGP on the turbulence field at thenozzle exit. In particular, the turbulence intensity generated from a pipe flow is much lowerthan that obtained at the nozzle exit when using the TGP inside the nozzle.The main objective of this work is to address the issue of providing velocity boundaryconditions at the inflow boundaries (i.e., nozzle exit planes) of this small computationaldomain to facilitate LES/PDF simulations of turbulent flows/flames in TCFs.The remainder of the paper is organized as follows. In Section 2, we describe the methodology for specifying the velocity inflow boundary conditions and compare it with previousrelated works. In Section 3, the inflow method is applied in the LES/PDF simulations involving the non-reactive and non-premixed modes described in Section 1.1: we describe thecomputational methodology and the key simulation parameters, followed by a discussion onthe comparisons of velocity statistics on the centerline and across the nozzle exits with theexperimental data for all the modes. Finally, conclusions from this study are summarized inSection 4.2 Inflow Boundary Conditions MethodologyWe present a methodology to address the issue of specifying velocity inflow boundary conditions at the nozzle exit planes for the small cylindrical domain used in the LES/PDFsimulations. The three key components of this methodology are:–––A single LES on the large domain, which includes the TGP, as highlighted by the greenbox in Fig. 1a, to obtain and record the time series of the velocity components at thenozzle exit planes.The existing experimental data [12, 13] on the mean and r.m.s. (root-mean-square)axial and radial velocity components, and the longitudinal integral length scale on thecenterline near the nozzle exit planes.A transformation procedure that is used on the recorded exit-plane data to form velocityinflow boundary conditions for use in the LES/PDF simulations on the small domain,shown by the red box in Fig. 1b. The transformations are performed so that key statisticsof the inflowing velocity fields match those measured in the experiments.In the following sub-sections, we describe these three components of the methodology inmore detail.2.1 Single large-domain LESThe non-reactive case of the I/I mode is simulated in the large computational domain (shownin Fig. 1a) in order to collect the time series of the velocity field at the nozzle exit planes.The burner geometry is described using immersed boundary conditions and the computational domain spans the entire region between the two TGPs of the nozzles. As a result, theevolution of the turbulent jet downstream of each TGP nozzle is calculated. The conditionsused in the simulations are listed under the Inert/Inert mode in Table 1. The large-domainLES is performed in Cartesian coordinates using the ‘PsiPhi’ LES/DNS code [12, 22].The uniform grid resolution used in the simulation is h 0.5 mm, corresponding to atotal number of 3.7M grid cells (where 1M 106 ). In comparison, the integral lengthscale atthe nozzle exit is shown to be around 4 mm (for a single nozzle configuration, at least) [12],while the Kolmogorov lengthscale is estimated to be 0.21 mm [23]. The time-step width isadjusted at each step to maintain a Courant-Friedrichs-Lewy (CFL) number of 0.3. It is to

Author's personal copy136Flow Turbulence Combust (2017) 98:131–153Table 1 Simulation parameters in the LES/PDF simulations of the three zzle exit diameter (mm), dj et12.712.712.7Distance between nozzles (mm), d12.71619Computational domain:12.7, 6016, 6019, 60Top streamN2N2O2Bottom streamN2Hot productsCH4 /N2height, diameter (mm)Bulk axial velocity in the streamsa (m/s), Ubulk 6.5811.2; 38.211.2Co-flow bulk velocity (m/s)0.432.11.73Bulk Reynolds number, Re550094009400Bulk strain rate (1/s), Kbulk105014001200Turbulent Reynolds number, Ret6501050750Temperature of the streamsa (K)294294; 1850294Grid size (z r θ )96 96 3296 96 32144 96 32Total number of cells, particles0.3M, 6M0.3M, 6M0.45M, 9MComputational wall-clock time 16 (24 %–76 %) 26 (30 %–70 %) 20 (17 %-83 %)(μs/cell/timestep), (NGA%-HPDF%)a The numerical values in each column are for the top and bottom streams, respectively. Single values arecommon for both the streamsbe pointed out that the large-domain LES is performed on a relatively coarse grid to makethe long sampling times affordable. In particular, the large-domain LES is performed forover 600 ms and used 24 computational processors, for a total cost of around 2000 CPUh.It is found that the simulation (from specified initial conditions) reaches a statisticallystationary state after 100 ms. The time series of the three components of velocity on bothnozzle exit planes are then recorded for 500 ms. Specifically, the velocities are recorded forthe two 26 26 sub-meshes (corresponding to a grid spacing of 0.5 mm) that cover the exitsof the 12.7 mm diameter nozzles.As shown in Fig. 2, the agreement with experiments is reasonable considering that theturbulence evolution in the nozzle must be captured. In [12], we performed large-domainLES at resolutions of 0.5 mm and 0.2 mm. Figure 7 of [12] shows that the mean velocityprofiles are largely consistent between the two resolutions, while the fluctuations differ byaround 10 %. The Smagorinsky constant is reduced from 0.12 at 0.5 mm to 0.065 at 0.2 mm.A ratio of turbulent to laminar viscosity of smaller than 10 and 3 is maintained throughoutthe domain for the simulations at resolutions of 0.5 mm and 0.2 mm, respectively. Basedon the reduction in cell size and time-step width (to maintain the same Courant number)the finer simulation is approximately 40 times more computationally expensive for a givensimulated time.2.2 ExperimentsThe experiments were performed on this counterflow configuration in the three modes atYale University and at Sandia National Laboratories [12, 13]. The radial profiles of the meanand r.m.s. of axial and radial components of velocity, and longitudinal integral length scale

Author's personal copyFlow Turbulence Combust (2017) 98:131–153137on the centerline, are measured at a distance of 0.5 mm downstream of the nozzle exits.Additionally, experimental data are also available for velocity statistics (for all operatingmodes), and for OH mass fraction in the F/O mode, on the centerline connecting the twonozzles.2.3 Transformation procedureThe time series of the velocity fields collected at the nozzle exit planes from the largedomain LES described in Section 2.1 are suitably transformed and used as boundaryconditions at the inflow boundaries of the small cylindrical domain. In the following, wedescribe the treatment at the bottom nozzle exit plane. The treatment at the bottom nozzleexit plane is exactly the same in the I/I and F/O modes, whereas the treatment at the bottomnozzle exit plane in the I/B mode is described in Section 2.5. The procedure involves thefollowing four transformations:1.The velocities from the large-domain LES are transformed to the polar cylindrical coordinates used in the LES/PDF simulations. Thus Ui (r, θ, t) denotes the time series ofthe i th component of the instantaneous velocity in the cylindrical coordinates at thenozzle exit plane obtained from the large-domain LES after this transformation. Theaxial, radial and azimuthal velocities are denoted by i 1, 2 and 3, respectively.2. The axial and radial velocities are subjected to an r-dependent shift to match themeasured mean velocity profiles.3. The fluctuating components of velocity are subjected to an r-dependent scaling tomatch the measured r.m.s. velocities.4. Time is stretched or compressed to match the longitudinal integral length scale on thecenterline.With Uis (r, θ, t) denoting the specified inflow velocities at the nozzle exit planes, thetransformation procedure is as follows: Uis (r, θ, t) Ui (r) m αi (r) Ui (r, θ, βt) Ui (r) .(1)With the above transformation procedure, the statistics of the modified time seriesUis (r, θ, t) are closely matched to the corresponding statistics measured at a distance of 0.5mm downstream of the nozzle exit plane in the experiments. The statistics that are matchedare: – The mean of the modified time series, Uis (r) , is equal to the measured mean in theexperiments, Ui (r) m .– The parameter αi (r) scales the fluctuations so as to closely match the r.m.s. axial andradial velocities of the modified time series to those measured in the experiments. Dueto the lack of experimental data on the r.m.s. velocity in the azimuthal direction, α3 (r)is taken to be equal to α2 (r).– The parameter β stretches time so as to closely match the longitudinal integral lengthscale on the centerline at the nozzle exit plane of the modified time series to that measured on the centerline at a distance of 0.5 mm downstream of the exit plane in theexperiments. Note that the time series of all the velocity components are stretched withthe same scaling factor.Thus Uis (r, θ, t) is the modified time series of velocity at the nozzle exit plane, in cylindrical coordinates, whose mean and r.m.s. axial and radial velocity profiles, and longitudinal

Author's personal copy138Flow Turbulence Combust (2017) 98:131–153integral length scale on the centerline, closely match the corresponding quantities measuredat 0.5 mm downstream of the exit plane in the experiments.In the subsequent exposition, we show how Eq. 1 is applied to the time series data ofthe velocity fields at the bottom nozzle exit plane from the large-domain LES, in order toobtain the modified velocity time series data that can be used in the LES/PDF simulationof the I/I mode in the small domain. It should be noted that although the large-domain LESis performed for the I/I mode, the predicted r.m.s. quantities at the nozzle exit planes donot exactly match the measured values in the experiments. Hence, we apply the transformation procedure to the recorded time series to obtain velocity inflow boundary conditions toperform LES/PDF simulations of all the three modes including the I/I mode.Figure 2 shows the radial profiles of the mean and r.m.s. axial and radial velocity components of the modified velocity time series data at the nozzle exit plane. It is clear fromthis figure that the mean quantities match very well with the experimental data for all valuesof r/R as we directly impose the mean profiles from the experiments. The scaling parameters, α1 (r) and α2 (r) (with α3 (r) α2 (r)), are taken as quadratic and cubic polynomials,respectively. These low-order polynomials are chosen as they provide smooth specificationsof αi (r), which can simply be obtained by solving a linear system of equations. With thescaling parameters αi (r), we are able to match the r.m.s. quantities well with the experimental data for values of r/R up to 0.8 for the axial r.m.s. velocity and up to 0.6 for the g. 2 The radial profiles of the mean (top row) and r.m.s. (bottom row) axial and radial velocities acrossthe nozzle exit plane for the I/I mode; blue line: modified time series data as derived in Section 2.3, greenline: large-domain LES (Section 2.1), red symbols: experimental data at 0.5 mm downstream of the nozzleexit plane [12]

Author's personal copyFlow Turbulence Combust (2017) 98:131–153139r.m.s. velocity. It is important to match the r.m.s. quantities at the centerline (r/R 0) andthe mismatch away from the centerline has little effect on the centerline results from theLES/PDF simulations because the turbulent structures are convected away from the centerline in the radial direction. It is worth noting the significant turbulence intensities onthe centerline of 40 % (axial) and 28 % (radial) that are characteristic of the present TCFconfiguration.2.4 Matching the longitudinal integral length scale of turbulenceIn the experiments, the longitudinal integral length scale is measured on the centerline at adistance of 0.5 mm from the nozzle exit plane. The time series of the velocity at the nozzleexit plane from the large-domain LES (i.e., Ui (r, θ, t)) are stretched (or compressed) inorder to match the longitudinal integral length scale (on the centerline at the nozzle exitplane) of the modified time series to that measured in the experiments. We now describe thestretching method.Consider the axial component of the centerline velocity at the nozzle exit plane from thelarge-domain LES, U1 (0, θ, t). It is noted that this quantity is independent of θ . We thendefine u(t), the velocity fluctuation at this location, by: u(t) U1 (0, θ, t) U1 (0, θ, t) .(2)The longitudinal auto-correlation function (LACF) ρL (s) is defined based on u(t) asfollows: u(t)u(t s) ρL (s) .(3)u(t)2The entire 500 ms of data from the large-domain time series are used to calculate theLACF, which is shown in Fig. 3a for time increments up to 20 ms. From the LACF, thecorresponding time scale τ (t) can be calculated as a function of time as: tρL (s)ds.(4)τ (t) 0110.80.80.60.60.40.40.20.20 0.20510(a)1520005101520(b)Fig. 3 (a) The longitudinal auto-correlation function (LACF) ρL (s) based on the centerline axial velocity atthe nozzle exit plane and (b) the corresponding integral time scale τ (t) as a function of time. The time seriesfrom the large-domain LES (Section 2.1) are used

Author's personal copy140Flow Turbulence Combust (2017) 98:131–153Figure 3b shows τ (t) for time increments up to 20 ms. The time scale τ (t) is subject tostatistical sampling errors which increase with t, as may be evident from Fig. 3a. Whilethe definition of the longitudinal integral time scale is τL τ ( ), a practical means ofestimating τL from a finite time series is needed. Accordingly we estimate τL as the valueof the integral in Eq. 4 at 20 ms, i.e., τL τ (0.02), as the curve reaches a plateau aroundthis time value. Therefore, from Fig. 3b, the value of τL for the large-domain LES velocitydata is taken as 0.75 ms.For the small-domain LES, the fluctuating component of the centerline axial velocity atthe nozzle exit plane is specified (from Eq. 1) as:us (t) α1 (0) u (βt) .(5)It follows that the longitudinal integral time scale of us (t), τLs , is related to that of u(t) byτLs τL /β. Thus, in order to match the measured longitudinal integral time scale, τLm , thestretching factor β is specified as:β τL.τLm(6)The longitudinal integral length scale mL observed in the experiments for the I/I modeis 3.6 mm, which corresponds to a longitudinal integral time scale τLm of 0.55 ms from therelation:m mL U1 (0) m τL .(7)Using the values of τL , τLm and Eq. 6, a value of approximately 1.36 is obtained for β.(This is verified by stretching the large-domain LES time series velocity data by this factorβ and recalculating the longitudinal integral time scale on the centerline at the nozzle exitplane for the modified time series data.)It is noted that the Eulerian time scales of all velocity components are scaled by β 1 ;however only the axial length scales are affected and the two point correlations in the nozzleexit plane are unaltered.The two key quantities that we match through the (fluctuation) scaling and (time) stretching methods are the axial r.m.s. velocity and the longitudinal integral length scale on thecenterline at the nozzle exit plane to those measured at 0.5 mm downstream of the nozzleexit in the experiments. Therefore, we are able to match the turbulent Reynolds number Retin the simulations to that of the experiments for the I/I mode (see Eq. 12, Section 3.2).Note that the above procedure is applied to the time series data from the large-domainLES at the bottom nozzle exit plane; a similar procedure can be followed to obtain themodified time series data at the top nozzle exit plane. Finally, these modified time seriesdata are interpolated both in space and time during the LES/PDF simulations.It is evident that the time series of the velocity field and the experimental data at (or closeto) the nozzle exit planes play key roles in the success of this method. It is also importantto note that the transformations are performed on the recorded data at the exit planes fromthe large-domain LES to obtain the velocity inflow boundary conditions for the LES/PDFsimulations of all the three modes. Therefore, only a single large-domain LES is required forthis method to be applied. Finally we conclude this section by acknowledging that as far asthe velocity and turbulence fields at the inflow boundaries are concerned, the method is notpredictive; however, it enables realistic simulations of these fields so that the combustionbetween the two nozzle exit planes can be studied.

Author's personal copyFlow Turbulence Combust (2017) 98:131–1531412.5 Inflow boundary conditions for the burnt stream of the Inert/Burnt (I/B)modeWith the exception of the bottom nozzle in the I/B mode, the velocity inflow boundaryconditions for all the turbulent streams of the three operating modes are generated

Flow Turbulence Combust (2017) 98:131-153 133 Fig. 1 The experimental configuration for (a) the I/I and F/O modes, and (b) the I/B mode.The extent of the large computational domain used in the single large-domain LES is highlighted by the green box in (a), whereas the extent of the small computational domain used in the small-domain LES/PDF simulations is