Xiaodan Cai

Turbulence spectra characteristics of high order schemes for direct and large eddy simulation

Abstract The comparative resolution of the high wavenumber portion of compressible turbulence energy spectrum by some high order numerical schemes is presented in this paper. Included in this are the essentially nonoscillatory (ENO) schemes, the weighted essentially nonoscillatory schemes (WENO), and the compact differencing schemes. The governing equations are the Navier–Stokes equations and the objective is to identify the numerical scheme that best represents the physics of compressible turbulence. Mach numbers M 1 values of 0.1, 0.5 and 0.7 are studied. The compact differencing schemes need filters for numerical stability. It is found in this work that a parameter in the filter scheme provides some flexibility for controlling the physical turbulence energy transfer rate at high wavenumbers, vis-a-vis the numerical dissipation at those scales. Although the ENO schemes do not require filters for numerical stability, the present study shows that the addition of filters improves the energy transfer process at high wavenumbers. Without filtering, with relatively coarse grids, numerical turbulence caused by stencil adaptation persists. This limits the useful wavenumber resolution range of the ENO schemes. The WENO schemes do not require the stabilizing filters but the results tend to be slightly more dissipative. Finally, at low Mach numbers, the current compact differencing and filter scheme formulation gives better results but as the Mach number increases the relative suitability of the ENO method increases.

The First High-Order CFD Simulation of Aircraft: Challenges and Opportunities

The textbook advantages of high-order differencing schemes in computational fluid dynamics (CFD) are well documented. They have also been demonstrated in the literature, albeit for canonical problems. The objective of the work described in this paper is to provide a robust implementation of high-order schemes to permit high fidelity and routine simulation of realistic aerospace systems which usually involve very complex geometries and flow behaviors. The two high-order schemes we have implemented are the compact and weighted essentially non-oscillatory (WENO) schemes. Some challenges were encountered in our efforts to accomplish the foregoing objective. Detailed illustrations of the various challenges are provided, as are some remedies that we have proposed and successfully implemented. This then allows us to illustrate some of the potential advantages of high-order methods for the simulation of realistic aerospace applications. The roles that the authors envision for high-order methods in CFD simulation of realistic aerospace systems are also discussed.

Performance of WENO Scheme in Generalized Curvilinear Coordinate Systems

The weighted-essentially non-oscillatory (WENO) schemes have been used to calculate the shock-embedded compressible fluid flow ([9]). The potential high-fidelity qualities of this approach make it attractive for jet noise simulation. However, in its present form, the WENO procedure has many drawbacks that prevent direct applications to jet noise simulations. In this paper, various WENO procedures are evaluated in generalized curvilinear coordinate systems. In addition, freestream preservation and boundary treatment are discussed. It has been verified in this paper that the original WENO procedure drafted by Jiang and Shu ([9]) is too dissipative for shock/entropy wave interactions. It has also been found that the ghost-point boundary treatment suggested in [9] does not perform well for shock-boundary interaction problems and more general problems with solid walls. Furthermore, it is demonstrated that the modifications suggested by Martin et al. ([11], [12]) are susceptible to numerical oscillations in non-homogeneous compressible flows. A modified WENO scheme that is more robust and less dissipative is proposed and tested in this paper.

Level-Set Flamelet/Large-Eddy Simulation of a Premixed Augmentor Flame Holder

The objective of the current study is to combine a high-fidelity large eddy simulation (LES) flow solver with a level-set flamelet algorithm for the prediction of premixed turbulent combustion. The same level of high accuracy is implemented for simulation at all speeds. The goal of this work is to accurately predict the unsteady turbulence-flame interaction for realistic industrial combustors with complex geometries. The numerical issues related to the numerical implementation of the LES equations, flamelet model and level-set algorithm are presented in detail. The accuracy of the numerical implementation is verified through comparisons with experimental data for an augmentor flame holder and a turbulent Bunsen burner flame.

A parallelized Eno procedure for direct numerical simulation of compressible turbulence

In this paper, a finite-difference based ENO (essentially nonoscillatory) procedure has been chosen for the direct numerical simulation (DNS) of compressible turbulence. The implementation of the ENO scheme follows the relatively efficient procedure in Shuet al. (1992), but the latter has been modified in the present paper to admit scalar conservation equations and to run on the iPSC/860 Paragon parallel supercomputer. DNS results with our procedure are in excellent agreement with pseudo-spectral and Padé approximation calculations in two and three dimensions. This is the case for a variety of initial conditions for compressible turbulence. The parallel algorithms presented are simple but quite efficient for DNS, with a speedup that approaches the theoretical value. Some of the attractive features include 1) minimum communication whereby a processor only communicates with two neighbors, 2) almost one hundred percent load balancing, 3) a checker-board approach to solve the Poisson equation reduces communication by a factor of approximately 2, and, 4) obtaining turbulence statistics is based on a ‘global collect’ approach, which is implemented to ensure that a single number, rather than a large matrix of numbers, is communicated between processors. The ENO code presented in this paper should be quite useful in its own right, while the parallel implementation should allow the simulation of fairly realistic problems.

A Combined Level-Set/Mixture Fraction/Progress-Variable Approach for Partially-Premixed Turbulent Reacting Flows

*† ‡ § An approach to predict partially-premixed turbulent reacting flows is presented in this paper within the context of large-eddy simulation (LES). A high-order, fully compressible LES flow solver is combined with a level-set/mixture fraction flamelet formulation to predict combustion in premixed and partially-premixed turbulent reacting flows. The results for a lean premixed dump combustor are compared with available experimental results and previous numerical studies. A good agreement between the numerical results and the experimental data is observed. Future validation will include comparisons with experimental data obtained in realistic engineering configurations such as augmentors.

On the Connection between Near-field and Far-field Solutions of High-Speed Jet Noise

Recent computational aero-acoustics development for high speed jet noise has focused on advanced LES methods. Validation efforts have largely been directed at comparisons in the acoustic far-field. While these results have shown encouraging levels of agreement, they bypass direct comparison on the basis of jet source characteristics. Thus, the current study aims to compare LES on the basis of multi-point statistics of jet near-field hydrodynamic pressure. A key advantage of the study is the provision for an intermediate check on the “beginning to end” simulation methodology by way of the near field measurements. Highfidelity simulations using improved low dissipation and low dispersion high-order numerical (CFD) schemes were carried out for flows from a round nozzle, with the inclusion of the nozzle in the model. Experimental measurements for the subsonic jet near-field noise assessments were obtained from a prior study led by Bridges at NASA using an array design by Suzuki and Colonius 19 with jet flows corresponding to test cases reported by Tanna 1 . Supersonic shock free near field jet noise measurements were acquired at UTRC using a novel rotating phased array system reported here for the first time. The simulated near-field results were generated directly from the RANS/LES calculations, whereas the far-field results follow from the Ffowcs Williams-Hawkings (FW-H) projection of the near-field results. Our results have shown a consistent over-prediction of the jet spreading rate. Despite this, salient qualitative features of the near-field source characteristics are captured in the simulations. Detailed analysis and resolution of the sources of discrepancy are currently in progress.

A Hybrid LES/RANS Calculation of Subsonic, Supersonic Hot Jet Noise

In this paper, pure RANS and hybrid LES/RANS procedures have been investigated for the simulation of jet noise from subsonic and supersonic, hot jets. The aerodynamic predictions from the RANS calculations agree well with experimental measurements. It is emphasized that the RANS-based acoustic analogy method used is incapable of capturing the sound characteristics at small jet angles, which are dominated by the sound radiated from large-scale turbulent structures. The hybrid LES/RANS approach investigated by Shur et al is examined. The preliminary results for a subsonic, hot jet (Set Point 46 in Tanna’s experiment) have shown that this method can capture, satisfactorily, the near-filed velocity and pressure signatures induced by large-scale turbulent structures. It is our goal to establish the feasibility and advantages of using a high-fidelity tool for predicting both small scale and large-scale supersonic jet noise with arbitrary complex geometries and under realistic flight conditions.Copyright

Towards Predicting Supersonic, Hot Jet Noise

The noise from supersonic jet aircraft during landing and taking-off poses serious environmental challenge to military bases. Two RANS-based acoustic source models have been used to calculate the noise signature from a supersonic, hot jet flow, one is based on the MGBK method from Khavaran et al. [12] and the other one is from Tam and Auriault . The aerodynamic predictions from our RANS calculation with high-order numerical schemes and modified k-ε models agree well with experimental data. However, it is found that both acoustic models have only limited success in predicting the far-field sound spectrum especially for shallow aft-angles, while the MGBK method has a slightly better performance over Tam’s method for the prediction of overall sound pressure levels. The large-eddy simulation approach is suggested to use for predicting supersonic, hot jet noise.

Flamelet Studies of Reduced and Detailed Kinetic Mechanisms for Methane/Air Diffusion Flames

We adopt a steady-state flamelet model in this paper to study the performance of reduced and detailed kinetic mechanisms for methane/air diffusion flames. Through the numerical calculations, we investigate the sensitivity of the main and intermediate species mass fractions to the mixture fraction dissipation rate, χ. Our results seem to suggest a weak to moderate effect of χ on the calculated species mass fraction. It has also been shown in this paper that the current flamelet calculations fail to predict the extinction strain rate.Copyright