CFD Large-Eddy Simulation of a Round Jet in Crossflow.pdf

Large-Eddy Simulation of a Round Jet in Crossflow J¨org Ziefle 1 Ph. D. student, Institute of Fluids Dynamics 2 , ETH Zurich, Switzerland Leonhard Kleiser Full professor, Institute of Fluids Dynamics, ETH Zurich, Switzerland Abstract A numerical simulation of a compressible round turbulent jet issuing perpendicu- larly into a laminar boundary layer (jet in crossflow, JICF) is performed at a jet-to- crossflow momentum ratio of 3.3 (defined with the bulk momentum of the jet and the free-stream momen
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  Large-Eddy Simulation of a Round Jet in Crossflow J¨org Ziefle 1 Ph.D. student, Institute of Fluids Dynamics 2 , ETH Zurich, Switzerland Leonhard Kleiser Full professor, Institute of Fluids Dynamics, ETH Zurich, Switzerland Abstract A numerical simulation of a compressible round turbulent jet issuing perpendicu-larly into a laminar boundary layer (jet in crossflow, JICF) is performed at a jet-to-crossflow momentum ratio of 3.3 (defined with the bulk momentum of the jet and the  free-stream momentum of the boundary layer) and a Reynolds number of 2100 (based on the free-stream momentum, jet diameter and dynamic viscosity at the wall). To be able to compare the results with incompressible reference data while still allowing for an efficient time integration, a Mach number of 0.2 is chosen. The mixing behaviour of the JICF is investigated by computing the evolution of a passive scalar at a Schmidt number that equals the Prandtl number of the flow.The spatial discretisation of the computational domain consists of a block-structured multi-block grid with 58 blocks and a total of 8.9 million cells. The simulation code NSMB uses a finite-volume discretisation with a skew-symmetric fourth-order central scheme and a second-order Runge-Kutta method for time integration. To account  for the subgrid scales, the approximate deconvolution model (ADM) is employed in a multiblock formulation.Of special interest in this investigation are the mixing behaviour of the jet with the crossflow and the complex vortex systems in the mixing region. Results are compared with incompressible LES data at similar flow parameters as mentioned above. The evolution of a jet under the influence of a crossflow (jet in crossflow,JICF) has been subject to extensive research for more than half a century [ ? ].While many earlier investigations have focussed on aerospace applications suchas vertical and/or short take-off and landing (V/STOL) aircraft, steering of rockets, film cooling of turbine blades or fuel injection into combustors, inmore recent times ecological aspects such as plumes of smokestacks, volcanoesor (tunnel) fires have also gained attention.The goals of our study of a jet in crossflow are threefold. In the course of therecent work, the approximate-deconvolution subgrid-scale model (ADM) [ ? ,  ? , ? ] has been implemented into a semi-industrial flow solver, supporting domaindecomposition and parallel computing. After a validation study using a sim-pler configuration [ ? ], the complex JICF case provides a means to validate thedomain-decomposition features of the new model code. Additionally, we wantto assess the suitability of ADM for separated flows in a low-order numeri-cal code. Finally, the experience and infrastructure developed with this flowcase is applicable for the simulation of a flow configuration of great industrialinterest, namely film-cooling of turbine-blades, a work currently in progress. 1 Email: 2 WWW:  htp:// 1  We selected the experimental JICF setup of Sherif and Pletcher [ ? ], whichwas also thoroughly investigated numerically by LES in the Ph.D. thesis of Yuan [ ? ]. In contrast to many other works, the Reynolds number is quite lowhere, rendering well-resolved incompressible LES possible even with the com-pressible simulation approach we used. The two investigated jet-to-crossflowvelocity ratios of 2 and 3.3 are low enough for a rather small vertical size of the computational domain, but still large enough for a highly complex and inboth cases differing flow structure. The specific flow case, see figure  ?? , con-sists of a turbulent jet issuing perpendicularly into a laminar boundary layer.All relevant flow parameters and geometric dimensions are listed in table  ?? .  L z L x L upstream L nozzle L pipe D Figure 1: Schematic of the jet in crossflow configuration.    Pipe simulation,   nozzle and    boundary layer of main JICF simulation.   /   Data transferbetween pipe and main JICF simulations (see text).The jet nozzle consists of two independent parts, marked    and    in fig-ure  ?? . The upper part  , which ends at the boundary layer, obtains its inflowdata from the lower part    by the usual block coupling interface, symbolisedby connection  . The lower part of the nozzle, however, is not coupled to theupper one but assumes streamwise-periodic boundary conditions (connection  ). In these so-called “blind blocks”, an independent simulation of turbulentpipe flow is carried out concurrently with the main JICF simulation. Thisone-way block-coupling mechanism in conjunction with the simultaneous in-flow data generation is a convenient and easy-to-implement way of providing2  Table 1: Geometric and calculation parameters. Unless otherwise noted, allboundary-layer quantities refer to the hypothetical laminar flow state in thecentre of the jet nozzle ( x  = 0) without the presence of a jet. L x  = 16  R  = ( ρ ˜ w ) V  b / ( ρ ˜ u ) ∞ , BL  = 3.3 L y  = 10 Re JICF  = ( ρ ˜ u ) ∞ , BL D/ ˇ µ wall  = 2100 L z  = 10 Re  jet  = ( ρ ˜ w ) V  b D/ ˇ µ wall  = 6930 L upstream  = 5.5 Re BL  = ( ρ ˜ u ) ∞ , BL δ  99% , BL / ˇ µ wall  = 1050 L nozzle  = 5 Re δ ∗ , BL | inlet  = 309.28 L pipe  = 5 Ma ∞  = 1 /   γR gas  = 0.2 D  = 1  δ  99% , BL /D  = 0.5unsteady turbulent inflow data.The current computational grid was generated with the commercial meshgenerator ICEM CFD Hexa. Its topology consists of 58 structured blockswith matching interfaces, of which five blocks comprise the pipe region (blindblocks) and another five blocks are used for the pipe nozzle. The total numberof cells is approximately 8 . 9 million, of which 4 . 5% each belong to the pipesimulation and the jet nozzle.A complete simulation cycle consists of the following steps. First solelythe pipe flow simulation is run, until a statistically stationary flow state isobtained. During this stage, no simulation takes place in the blocks of themain JICF simulation domain (   and   ). When the pipe flow simulationreaches a stationary state, the full JICF simulation setup is turned on. Aftera sufficiently long time, in which the jet penetrates the crossflow and the char-acteristic vortex systems have evolved, statistical sampling is started. Thesimulation is continued until the statistics have converged to the desired de-gree.Time-averaging was performed by sampling the instantaneous flow field ev-ery 30 time-steps during a period of more than 250 time units  L/ ˜ u ∞ , BL . Thisaveraging time is significantly longer than in the reference computation[ ? ],where available computational resources limited sampling to 80 time units.However, our statistics were still found to be not perfectly symmetric, es-pecially in the far-field downstream of the jet exit, where the flow is highlyunsteady and irregular.The computation was carried out on four processors of the NEC SX/8vector machine at HLRS, using more than 3000 CPU hours (including initialtransients). During time-averaging, 12GB of memory were necessary. One in-stantaneous flow field (including mesh and restart data) consumes 1.4GB diskspace, while the time-averaged flow field (73 quantities) requires 5.9GB diskspace. The total accumulated data (including a series of instantaneous flowfields for animation and frequency analysis purposes) comprises approximately700GB.3  In the following a few sample results are shown. More details are found inthe corresponding publication [ ? ]. The jet trajectory is one of the most impor-tant characteristics of a JICF. Naturally, its determination is to some extenta matter of definition. Here we compute the jet trajectory in three differentways that are commonly used in literature [ ? ]. As the first possibility, seefigure  ?? , the streamline of the mean flow field through the centre of the jetnozzle (( x,y,z ) = 0) marks the jet trajectory. Additionally, the streamlinesstarting at the upstream and downstream edges of the jet nozzle are shownas an approximation of the jet boundary in the centre plane. Secondly, asdepicted in figure  ?? , the trajectory can be defined as the locus through allpoints with maximum scalar concentration in the centre plane  y  = 0. Alter-natively, the maximum velocity magnitude can be used as defining quantity,as shown in figure  ?? . All trajectories exhibit generally good agreement withthe computational results of Yuan [ ? ] (experimental results were not avail-able for comparison), even though the sensitivity to the particular method of determination is quite strong for the latter two methods.To allow for a more quantitative comparison of our LES results with theincompressible reference simulation [ ? ] and experiment [ ? ], vertical profilesof the mean flow field in the symmetry plane are depicted at four differentstreamwise positions in figure  ?? . The first series of pictures, figures  ?? - ?? ,shows the average velocity magnitude  | ˜ u | . The overall agreement with thereference data is quite good. The first local minimum fits the experimentaldata better in our LES than in the one of Yuan. In the next row of figures, ?? - ?? , the normalised rms fluctuations of the velocity magnitude  | ˜ u | rms / | ˜ u | are plotted. Again our LES generally reproduces the comparison results well.The isocontour of the passive-scalar concentration in figure  ??  gives a goodimpression of the unsteady and irregular instantaneous flow state caused bythe mixing of the two streams. The roll-up and breakdown of the jet shearlayer is also observable: the initially smooth contour surface above the jet exitshows a regular pattern of ripples after a distance along the jet trajectory of approximately one jet hole diameter. A few diameters farther downstream thestructure changes to an irregular form, which coincides with the breakup of the shear-layer vortices [ ? ].Figure  ??  depicts an isocontour of the instantaneous vortex-identificationquantity ˇ λ 2 . Similar to the flow around a wall-mounted cylinder, a horseshoevortex wraps around the jet exit hole. The mentioned shedding of shear-layervortices from the upstream edge of the jet nozzle is directly visible. After afew jet diameters along the trajectory they loose their distinct appearance.This marks the location of their breakup which was already observed in theisocontour of the passive-scalar concentration in figure  ?? .In figure  ??  we display three sets of streamlines: two srcinating from the jet nozzle and one from the crossflow. The red streamlines start from withinthe boundary layer upstream of the jet exit at 10% boundary-layer thickness.The green and blue streamlines are seeded across the jet nozzle throughoutthe two spanwise diameters aligned with the  x  and  y  axes.Following the red boundary-layer streamlines, we observe their deflectionaround the jet exit, as the jet obstructs their downstream path, and the cre-ation of a horseshoe vortex. We can clearly recognise the bundling of the outer4
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