In Search of Grid Converged Solutions

Assessing solution error continues to be a formidable task when numerically solving practical flow problems. Currently, grid refinement is the primary method used for error assessment. The minimum grid spacing requirements to achieve design order accuracy for a structured-grid scheme are determined for several simple examples using truncation error evaluations on a sequence of meshes. For certain methods and classes of problems, obtaining design order may not be sufficient to guarantee low error. Furthermore, some schemes can require much finer meshes to obtain design order than would be needed to reduce the error to acceptable levels. Results are then presented from realistic problems that further demonstrate the challenges associated with using grid refinement studies to assess solution accuracy

Summary of the Tandem Cylinder Solutions from the Benchmark Problems for Airframe Noise Computations-I Workshop

Fifteen submissions in the tandem cylinders category of the First Workshop on Benchmark problems for Airframe Noise Computations are summarized. Although the geometry is relatively simple, the problem involves complex physics. Researchers employed various block-structured, overset, unstructured and embedded Cartesian grid techniques and considerable computational resources to simulate the flow. The solutions are compared against each other and experimental data from 2 facilities. Overall, the simulations captured the gross features of the flow, but resolving all the details which would be necessary to compute the noise remains challenging. In particular, how to best simulate the effects of the experimental transition strip, and the associated high Reynolds number effects, was unclear. Furthermore, capturing the spanwise variation proved difficult

Two-Dimensional Ffowcs Williams/Hawkings Equation Solver

FWH2D is a Fortran 90 computer program that solves a two-dimensional (2D) version of the equation, derived by J. E. Ffowcs Williams and D. L. Hawkings, for sound generated by turbulent flow. FWH2D was developed especially for estimating noise generated by airflows around such approximately 2D airframe components as slats. The user provides input data on fluctuations of pressure, density, and velocity on some surface. These data are combined with information about the geometry of the surface to calculate histories of thickness and loading terms. These histories are fast-Fourier-transformed into the frequency domain. For each frequency of interest and each observer position specified by the user, kernel functions are integrated over the surface by use of the trapezoidal rule to calculate a pressure signal. The resulting frequency-domain signals are inverse-fast-Fourier-transformed back into the time domain. The output of the code consists of the time- and frequency-domain representations of the pressure signals at the observer positions. Because of its approximate nature, FWH2D overpredicts the noise from a finite-length (3D) component. The advantage of FWH2D is that it requires a fraction of the computation time of a 3D Ffowcs Williams/Hawkings solver

Assessment of Hybrid RANS/LES Turbulence Models for Aeroacoustics Applications

Predicting the noise from aircraft with exposed landing gear remains a challenging problem for the aeroacoustics community. Although computational fluid dynamics (CFD) has shown promise as a technique that could produce high-fidelity flow solutions, generating grids that can resolve the pertinent physics around complex configurations can be very challenging. Structured grids are often impractical for such configurations. Unstructured grids offer a path forward for simulating complex configurations. However, few unstructured grid codes have been thoroughly tested for unsteady flow problems in the manner needed for aeroacoustic prediction. A widely used unstructured grid code, FUN3D, is examined for resolving the near field in unsteady flow problems. Although the ultimate goal is to compute the flow around complex geometries such as the landing gear, simpler problems that include some of the relevant physics, and are easily amenable to the structured grid approaches are used for testing the unstructured grid approach. The test cases chosen for this study correspond to the experimental work on single and tandem cylinders conducted in the Basic Aerodynamic Research Tunnel (BART) and the Quiet Flow Facility (QFF) at NASA Langley Research Center. These configurations offer an excellent opportunity to assess the performance of hybrid RANS/LES turbulence models that transition from RANS in unresolved regions near solid bodies to LES in the outer flow field. Several of these models have been implemented and tested in both structured and unstructured grid codes to evaluate their dependence on the solver and mesh type. Comparison of FUN3D solutions with experimental data and numerical solutions from a structured grid flow solver are found to be encouraging

The Variation of Slat Noise with Mach and Reynolds Numbers

The slat noise from the 30P30N high-lift system has been computed using a computational fluid dynamics code in conjunction with a Ffowcs Williams-Hawkings solver. By varying the Mach number from 0.13 to 0.25, the noise was found to vary roughly with the 5th power of the speed. Slight changes in the behavior with directivity angle could easily account for the different speed dependencies reported in the literature. Varying the Reynolds number from 1.4 to 2.4 million resulted in almost no differences, and primarily served to demonstrate the repeatability of the results. However, changing the underlying hybrid Reynolds-averaged-Navier-Stokes/Large-Eddy-Simulation turbulence model significantly altered the mean flow because of changes in the flap separation. However, the general trends observed in both the acoustics and near-field fluctuations were similar for both models

The Effect of Cross Flow on Slat Noise

This paper continues the computational examination (AIAA Journal, Vol. 45, No. 9, 2007, pp. 2174-2186) of the unsteady flow within the slat cove region of a multi-element high-lift airfoil configuration. Two simulations have been performed to examine the effect of cross flow on the near-field fluctuations and far-field acoustics. The cross flow was imposed by changing the free-stream velocity vector and modifying the Reynolds number. The cross flow does appear to alter the dynamics in the cove region, but the impact on the noise seems to be more dependent on the flow conditions. However, separating out the true effects of the cross flow from those of the Mach and Reynolds number would require additional calculations to isolate those effects

Assessment of Slat Noise Predictions for 30P30N High-Lift Configuration From BANC-III Workshop

This paper presents a summary of the computational predictions and measurement data contributed to Category 7 of the 3rd AIAA Workshop on Benchmark Problems for Airframe Noise Computations (BANC-III), which was held in Atlanta, GA, on June 14-15, 2014. Category 7 represents the first slat-noise configuration to be investigated under the BANC series of workshops, namely, the 30P30N two-dimensional high-lift model (with a slat contour that was slightly modified to enable unsteady pressure measurements) at an angle of attack that is relevant to approach conditions. Originally developed for a CFD challenge workshop to assess computational fluid dynamics techniques for steady high-lift predictions, the 30P30N configurations has provided a valuable opportunity for the airframe noise community to collectively assess and advance the computational and experimental techniques for slat noise. The contributed solutions are compared with each other as well as with the initial measurements that became available just prior to the BANC-III Workshop. Specific features of a number of computational solutions on the finer grids compare reasonably well with the initial measurements from FSU and JAXA facilities and/or with each other. However, no single solution (or a subset of solutions) could be identified as clearly superior to the remaining solutions. Grid sensitivity studies presented by multiple BANC-III participants demonstrated a relatively consistent trend of reduced surface pressure fluctuations, higher levels of turbulent kinetic energy in the flow, and lower levels of both narrow band peaks and the broadband component of unsteady pressure spectra in the nearfield and farfield. The lessons learned from the BANC-III contributions have been used to identify improvements to the problem statement for future Category-7 investigations

Noise Radiation From a Leading-Edge Slat

This paper extends our previous computations of unsteady flow within the slat cove region of a multi-element high-lift airfoil configuration, which showed that both statistical and structural aspects of the experimentally observed unsteady flow behavior can be captured via 3D simulations over a computational domain of narrow spanwise extent. Although such narrow domain simulation can account for the spanwise decorrelation of the slat cove fluctuations, the resulting database cannot be applied towards acoustic predictions of the slat without invoking additional approximations to synthesize the fluctuation field over the rest of the span. This deficiency is partially alleviated in the present work by increasing the spanwise extent of the computational domain from 37.3% of the slat chord to nearly 226% (i.e., 15% of the model span). The simulation database is used to verify consistency with previous computational results and, then, to develop predictions of the far-field noise radiation in conjunction with a frequency-domain Ffowcs-Williams Hawkings solver

The Influence of Realistic Reynolds Numbers on Slat Noise Simulations

The slat noise from the 30P/30N high-lift system has been computed using a computational fluid dynamics code in conjunction with a Ffowcs Williams-Hawkings solver. Varying the Reynolds number from 1.71 to 12.0 million based on the stowed chord resulted in slight changes in the radiated noise. Tonal features in the spectra were robust and evident for all Reynolds numbers and even when a spanwise flow was imposed. The general trends observed in near-field fluctuations were also similar for all the different Reynolds numbers. Experiments on simplified, subscale high-lift systems have exhibited noticeable dependencies on the Reynolds number and tripping, although primarily for tonal features rather than the broadband portion of the spectra. Either the 30P/30N model behaves differently, or the computational model is unable to capture these effects. Hence, the results underscore the need for more detailed measurements of the slat cove flow

Permeable Surface Corrections for Ffowcs Williams and Hawkings Integrals

The acoustic prediction methodology discussed herein applies an acoustic analogy to calculate the sound generated by sources in an aerodynamic simulation. Sound is propagated from the computed flow field by integrating the Ffowcs Williams and Hawkings equation on a suitable control surface. Previous research suggests that, for some applications, the integration surface must be placed away from the solid surface to incorporate source contributions from within the flow volume. As such, the fluid mechanisms in the input flow field that contribute to the far-field noise are accounted for by their mathematical projection as a distribution of source terms on a permeable surface. The passage of nonacoustic disturbances through such an integration surface can result in significant error in an acoustic calculation. A correction for the error is derived in the frequency domain using a frozen gust assumption. The correction is found to work reasonably well in several test cases where the error is a small fraction of the actual radiated noise. However, satisfactory agreement has not been obtained between noise predictions using the solution from a three-dimensional, detached-eddy simulation of flow over a cylinder