Simulation of Engine Flow with Swirl Using Re-Stress Turbulence Model in KIVA Code

The objective of this paper is to present recent research on the use of a Reynolds Stress Closure Model (RSCM) for a Lean Direct Injection (LDI) combustor with swirlers. This paper will provide comparisons between RSCM results, k-ε turbulence model results, and experimental data for chemically nonreactive swirling flows. The results show that, for high degree swirl flow, the RSCM can provide predictions in favorable agreement with the experimental data, and that the RSCM predicts recirculations and high velocity gradients better than the k-ε turbulence model. Through a parametric study, the results also show that the choice of swirler has a significant influence on the combustor flow field. Introduction A key characteristic of gas turbine combustor performance is the emission of NOx. Although the emissions of unburned hydrocarborns and carbon monoxide have been greatly reduced through the design process, the problem of NOx emission still requires significant improvements in combustor design [Koff, 1994]. Combustion at near stoichiometric fuel-air ratios produces high combustion temperatures which are the main cause of high thermal NOx emissions. As a result, combustor designs have sought non-stoichiometric fuelair ratios in both rich and lean ranges. Rich burn combustion reduces NOx by limiting the amount of oxygen present for high temperature combustion. Combustors like these are often labeled Rich-burn Quick-quench Lean-burn (RQL). Here, a rich burn primary zone is followed by a quick quench zone where the combustion gases are diluted before combustion is completed in a cooler lean burn zone. This design concept has been the subject of several studies [Cline et al., 1995; Micklow et al., 1993; Talpallikar et al., 1992; Yang et al., 1992]. An alternative to RQL is LeanPremixed combustion in which a lean combination of fuel and air is premixed and prevaporized prior to introduction into the combustor. It has also been studied by several researchers [Cowell and Smith, 1993; Kumakura et al., 1993; Leonard and Stegmaier, 1994], although low NOx emissions required uniform fuel-air mixtures. Tacina [1990] found that a lean premixed combustor produced less NOx in comparison with the RQL. A third approach is called Lean Direct Injection (LDI). Instead of injecting a lean premixed quantity of fuel and air into the combustor, fuel is injected into the airflow entering the combustor. Such a combustor depends on fuel injectors which can produce a spray of very small droplets that quickly atomize and vaporize. Furthermore, the mixing process is also a key issue for the LDI. Several studies have pursued Computational Fluid Dynamics techniques to predict the flow field inside the combustor. Successful predictions of turbulent reactive flows depend highly on successful prediction of the turbulent fluid flow [Gran et al., 1997]. A popular choice for the turbulence model has been the two equation k-ε eddy viscosity turbulence model (EVTM). Such calculations have been performed [Cline et al., 1995; McGuirk and Palma, 1993; Relation et al., 1998; Rizk and Mongia, 1993]. Despite its popularity and low computational overhead, the standard k-ε model suffers from several deficiencies. It is not suited well for modeling swirling flows [Sloan et al., 1986] which are often present and desired in combustors. Therefore, ad hoc modifications to the turbulent energy dissipation equation are necessary to provide satisfactory results. It also tends to incorrectly predict recirculation regions [Gran et al., 1997]. Prediction of these flow structures is important since the location of recirculation regions can influence the residence time involved in NOx production [Micklow et al., 1993] and/or can increase the residence time for liquid fuel evaporation. Finally, the standard kε model often underpredicts large velocity gradients because of the more diffusive nature of this model [Relation et al., 1998]. * Associate Professor, Dept. of Mechanical Engineering-Engineering Mechanics, Michigan Technological University. † Ph.D. Candidate, Dept. of Mechanical Engineering-Engineering Mechanics, Michigan Technological University. ‡ Aerospace Engineer, Combustion Technology Branch, NASA John H. Glenn Research Center. In contrast, the Reynolds Stress Closure Model (RSCM) provides hope for better accuracy in predicting the complex swirling flow, which may also contain recirculation. Unlike the standard EVTM, the RSCM is able to capture the anisotropy caused by complex flow, flow rotation (swirl flow), and wall effects. This is achieved naturally since each Re-stress component has its own transport equation. As a result, the RSCM is needed to properly address these flow issues. Re-stress calculations have been performed on combustors [Lin and Lu, 1994; Tsao and Lin, 1999] for cases with low and high inlet swirl. In each study the Gibson and Launder [1978] RSCM was used with a modified ε equation. Promising results were observed in a RSCM study by Yang et al. [2000] when applying the SSG model of Speziale et al. [1991] to reciprocating engines and to a lean premixed combustor. The purpose of this study is to expound upon Yang et al. [2000] by implementing, investigating, and validating the SSG Reynolds Stress Closure model for cold flow calculation of a LDI combustor using the KIVA-3V computer code. The study is to substantiate the RSCM as a preferred turbulence model by presenting evaluations and comparisons of the results with experimental data and k-ε turbulence model results. It is also desired to show that, unlike two-equation models, a RSCM does not require ad hoc modification, while being capable of capturing the complex characteristics of turbulent swirling flow. Due to space limitation, the Re-stress model equations, their derivation and implementation, and the numerical method will not be presented here. Detailed explanation can be found in Yang et al. [2000]. Axial Swirlers and Computational Domain Inlet swirl can increase combustor performance by aiding in the fuel-air mixing process and by producing recirculation regions which can act as flame holders. As mentioned earlier, recirculation can influence residence time and, as a result, NOx production. Therefore, proper selection of a swirler is needed to reduce NOx. Two different helical swirlers were used based on blade angle inclination from the direction of air flow. One swirler had a 45° angle, and the other had a 60° angle. These angles refer to the outermost vane twisting angle of the helical swirler. Due to confidentiality agreements, the swirlers cannot be shown in any figures at this time. The modeled LDI combustor includes inlets at 9 inflow locations, which are attached to a single primary combustion zone shown in Fig. 1. The inlets are atop axial swirlers arranged in a 3 by 3 square which lies in the x-y plane. The rotation imparted to the air by each swirler is directed in the negative z-direction. A 3% pressure drop, ∆p, was specified across the height of the combustor along with an outlet pressure of 1.0 atm. The inlet air velocities Vin to the swirlers were determined from the following combination of the continuity equation, inlet air density at 27°C, and the Bernoulli equation with a discharge coefficient, CD, obtained from experiment: Vin=CD√(2(∆p)/ρ) (1) After air exits a swirler it passes through a venturi. At the center of the venturi circle, a fuel injector nozzle can inject liquid fuel. This arrangement is used since the combination of swirler and venturi were found to have a significant influence on the liquid atomization and droplet distribution [Im et al., 1998]. A short divergent cone, acting like a diffuser, follows and ends at the primary zone inlet plane. Three cutting planes each for the y=constant planes and for the z=constant planes were defined for postprocessing, and these locations are shown in Fig. 1. Three computational meshes with different grid densities, namely 113793, 173829, and 254853 grid points were used. Results from the three grids are consistent with each other. The medium density grid was used in the following presentations. Results The purpose of this study was to investigate the success in predicting the mean fluid flow within the combustor. Therefore, the spray and ignition options were turned off. Calculations were performed with the SSG RSCM and also with the k-ε model. The two predictions were compared with the available experimental data. Predictions were obtained for the k-ε and for the SSG turbulence models for both a 45° swirler and a 60° swirler. A distinct difference between these swirlers, as will be shown in the following subsections, is that the 60 swirler can produce higher degree of swirl flow than can the 45 swirler. Since the computational domain was three-dimensional, results of these predictions are presented at the cutting planes indicated by Fig. 1. Experimental data of the axial velocity component is available only for a 60° swirler and only for display on the x-y planes. Discussion of the results and comparisons follow. Results for 60° Swirler Observations of the results on the x-y planes shows that the RSCM predicts stronger velocity variations. Although the -w velocity contour structures and the vector orientations shown in Fig. 2 show similarities, the magnitude of the velocities differ greatly between the RSCM and the k-ε model. Comparison with experimental data in Fig. 2 shows that the reversed flow at the center of the circles is better predicted by the RSCM. The contour legend shows that the RSCM velocity levels vary over a greater range. Similar observations are found further downstream at the z=18mm surface in Fig. 3. Again, contour structures look alike between the two models, but the RSCM magnitude extremes are greater. Forward flow between swirlers from the RSCM is in better agreement with experiment. Reversed velocity magnitude at the circle centers also agrees better between the RSCM and experiments. It appears that the RSCM can better predict the reversed flow associated with swirl. The contrast between the recirculations of the two models can be further displayed by viewing the velocity on the x-z planes, such as along the y0-y0 cutting plane shown in Fig. 4. Reversed flow is much stronger below the swirlers with the RSCM. For example, the RSCMpredicted reverse flow reaches up to the venturi while the k-ε prediction falls far short. Concurrently, the forward flow regions predicted by the RSCM are also stronger. Since much of the cross section of the combustor has a reversed mass flux, the forward mass flux regions must be stronger to satisfy overall mass conservation. From these plots, the k-ε model results appear more diffuse than those of the RSCM. This is due to the overestimated eddy viscosity which is a general characteristic of the k-ε model. This set of results also indicates that without ad hoc modification, the k-ε model is simply unable to predict the essence of flow recirculation from the large longitudinal pressure gradient created by the high degree of swirl [Gupta et al., 1984]. Results for 45° Swirler The predictions obtained with the 45° swirler primarily display the significant difference between swirlers. The magnitude of the inlet velocity is the same as the 60° swirler case. As Figs. 5 and 6 indicate, there is no reversed flow at the center of the circles. Since the swirler diverts the upstream air at a smaller angle, a strong and solid forward flow jet enters the combustor and does not permit recirculation as did the more conical jet from the 60° swirlers. Due to the lower degree of swirl, the two models produce results almost identical to each other; however, weak recirculation regions were captured by the RSCM. Since the 45 swirler produces such weak swirl flow, these results show that both RSCM and k-ε models can predict the flow field equally well. The velocity profiles in Fig. 6 would suggest that the atomization, vaporization, and mixing processes would occur less effectively with the 45° swirler. Fuel and air are injected directly downward into the primary zone, reducing the time for the three processes. Fuel-air jets around the perimeter are directed toward the wall and could lead to fuel droplet impingement on the walls. The lack of recirculation could reduce the amount of shear which aids in fuel atomization, and it could also reduce the degree of mixing which aids in uniform lean combustion. Results for 60 cw+ccw Swirler Comparisons are also made for 60 swirlers where the center swirler twists in the counter-clockwise direction, while the outer eight remain clockwise. The results show a quite distinctive swirling profile compared to the two swirler types presented above. The counter-rotation causes much higher velocity in the combustor around the central circle, as shown in Fig. 7. These two plots also show that the RSCM consistently predicts a more intense and vigorous velocity profile in comparison to the k−ε model. The reversed twisting of the central swirler also brings about stronger and deeper recirculations, as evident in Fig. 8 where reversed flow can still be observed below the z=18mm plane. An apparent outcome of this arrangement is that reversing the central swirler rotation enhances the strength of swirl flow, not only in the vicinity of the central circle, but for the entire region inside the combustor. Conclusion The SSG Reynolds Stress Closure model was implemented into the KIVA-3V computer code and simulations were produced of the cold flow within an LDI combustor. The RSCM performed better than the standard k-ε model when comparisons were made with experiment for 60 co-rotating swirlers. The primary improvements were the capture of recirculation regions and the accompanying reversed flow. These flow characteristics were predicted to be stronger and more distinct with the RSCM. The results reaffirm that the RSCM can out-perform the k-ε model when swirling flows and recirculations are present. The results from the 45 swirler type indicated that the choice of swirler also plays an important role in the production of swirl and recirculation. It was shown that the 60 configuration is able to produce much stronger swirling profile than the 45 swirler. The results from 60 swirlers with reversed rotation at the center were also studied. The results clearly demonstrated the advantage the RSCM has over the k−ε model for parametric studies. Since in the RSCM each component of the Restresses is computed individually, no ad hoc modification is required when the problem geometry or flow condition is altered. 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J. for Numerical Methods in Fluids, Vol. 15, 1992, pp. 865881.Yang, S. L., Peschke, B. D., and Hanjalic, K., “Second-Moment Closure Model for IC Engine Flow SimulationUsing KIVA Code,” to appear in the ASME J. of Engineering for Gas Turbines and Power, 2000. Fig. 1 Computational grid of combustor. Fig. 2 Results for 60 swirler at z=5mm cutting plane: a) RSCM, b) k-ε, c) experiment. Fig. 3 Results for 60 swirler at z=18mm cutting plane: a) RSCM, b) k-ε, c) experiment. Fig. 4 Velocity on y0-y0 plane for 60° swirler: a) RSCM, b) k-ε.a)b)c)