Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

High order accurate weighted essentially nonoscillatory (WENO) schemes are relatively new but have gained rapid popularity in numerical solutions of hyperbolic partial differential equations (PDEs) and other convection dominated problems. The main advantage of such schemes is their capability to achieve arbitrarily high order formal accuracy in smooth regions while maintaining stable, nonoscillatory, and sharp discontinuity transitions. The schemes are thus especially suitable for problems containing both strong discontinuities and complex smooth solution features. WENO schemes are robust and do not require the user to tune parameters. At the heart of the WENO schemes is actually an approximation procedure not directly related to PDEs, hence the WENO procedure can also be used in many non-PDE applications. In this paper we review the history and basic formulation of WENO schemes, outline the main ideas in using WENO schemes to solve various hyperbolic PDEs and other convection dominated problems, and present a collection of applications in areas including computational fluid dynamics, computational astronomy and astrophysics, semiconductor device simulation, traffic flow models, computational biology, and some non-PDE applications. Finally, we mention a few topics concerning WENO schemes that are currently under investigation.

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems

The need for better understanding of the low-frequency unsteadiness observed in shock wave/turbulent boundary layer interactions has been driving research in this area for several decades. We present here a large-eddy simulation investigation of the interaction between an impinging oblique shock and a Mach 2.3 turbulent boundary layer. Contrary to past large-eddy simulation investigations on shock/turbulent boundary layer interactions, we have used an inflow technique which does not introduce any energetically significant low frequencies into the domain, hence avoiding possible interference with the shock/boundary layer interaction system. The large-eddy simulation has been run for much longer times than previous computational studies making a Fourier analysis of the low frequency possible. The broadband and energetic low-frequency component found in the interaction is in excellent agreement with the experimental findings. Furthermore, a linear stability analysis of the mean flow was performed and a stationary unstable global mode was found. The long-run large-eddy simulation data were analyzed and a phase change in the wall pressure fluctuations was related to the global-mode structure, leading to a possible driving mechanism for the observed low-frequency motions.

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Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble

Progress in shock wave/boundary layer interactions

Development of micro power generators – A review

The feasibility of a 100 W class micro-scale gas turbine with a centrifugal impeller of 10 mm diameter has been studied by experimentally verifying the four major component performance requirements found from cycle analysis. The rotor is required to rotate at 870 000 rpm to generate the compressor pressure ratio 3, and it has successfully been achieved by using hydroinertia gas bearings. A compressor efficiency higher than that required by the target cycle has been measured. After correcting the effect of the heat leakage, approximately 65% of the compressor adiabatic efficiency is estimated to be achievable. The combustor has achieved stable self-sustained combustion at a combustion efficiency higher than 99.9%. The heat conduction analysis based on measured data showed that it is possible to keep the compressor below 170 °C when the turbine inlet temperature is 1050 °C. All four requirements are proven to be achievable, and hence, the feasibility of the micro-scale gas turbine at an impeller of 10 mm diameter has successfully been proven at component level.

https://iopscience.iop.org/article/10.1088/0960-1317/16/9/S13/pdf

Experimental verification of the feasibility of a 100 W class micro-scale gas turbine at an impeller diameter of 10 mm

The transition of a boundary layer on a flat plate with an impinging shock wave is studied numerically by compressible large-eddy simulation using a hybrid compact/Roe scheme. The numerical code is verified by comparison with experimental observations of shock wave/turbulent boundary-layer interaction and then applied for the analysis of shock wave/transitional boundary-layer interaction. The simulation provides accurate results with respect to the location of reattachment and the boundary-layer properties downstream of reattachment. Large-scale coherent structures such as longitudinal vortex pairs, low-speed streaks, and hairpin vortices are identified in the transitional region, and it is revealed that these coherent structures play important roles in the transition. Thus, it is important to resolve these structures adequately to obtain an accurate prediction of the reattachment point. The subsequent breakdown of these coherent structures have smaller length scales, and resolving the breakdown requires much finer grid resolution. However, the influence of underresolution of breakdown on the downstream flowfield can be largely ignored under the conditions examined. Large-eddy simulation is, therefore, useful for the qualitative analysis of flowfields involving a supersonic transitional boundary layer.

Large-Eddy Simulation of Transitional Boundary Layer with Impinging Shock Wave

Dynamic stability of a reentry capsule in transonic speeds is discussed. An unsteady flowfield around the capsule under the forced pitching oscillation in the transonic flow of M = 1.3 is numerically simulated based on the three-dimensional thin-layer Navier-Stokes equations. The numerical result reveals that the dynamic instability is caused by the phase delay of the base pressure. It is also found that the base pressure, the recompression shock wave, and the wake behind the recompression shock wave all oscillate with the same delay time. The flow mechanism is proposed based on the idea that the phase delay of the base pressure is caused by a feedback loop of the flowfield behind the capsule. This flow mechanism reasonably explains the features observed in the present numerical simulation, as well as the experimental fact that the dynamic instability occurs at very low reduced frequencies.

Numerical Analysis of Dynamic Stability of a Reentry Capsule at Transonic Speeds

PAYLOAD vibration due to acoustic waves from the exhaust plume is a significant problem during the liftoff of a launch vehicle. These acoustic waves are considered to be caused by jet impingement on the ground or on the flame deflector at the launch pad, as well as being from the free jet region. The ground slope or flame deflector profiles are therefore considered to affect the intensity and characteristics of this acoustic phenomenon, but design principles to suppress acoustic wave generation have not yet been established, because the generation mechanisms of the acoustic waves from the jet impingement have not been sufficiently clarified. Therefore, this study investigates the acoustic phenomena from a correctly expanded supersonic jet impinging on an inclined flat plate, through experiments conducted using a jet facility. The flow field of a supersonic jet impinging on a solid surface has been examined in many previous studies. For example, the fundamental flow structure was described by Donaldson and Snedecker [1]. From their experiments using an underexpanded jet impinging on a perpendicular or inclined plate at various angles, the flow structure was explained as being composed of three regions with different flow regimes: the free jet, impingement, and wall jet regions. The free jet region is minimally affected by the jet impingement, and its flow structure is similar to that of a free jet, as regard the potential core and supersonic shear layers. Next, the jet impinges on the plate, yielding a recirculation flow in the impingement region while, finally, the jet flows along the plate surface in the wall jet region. Carling and Hunt [2] experimentally discussed the flow field of a correctly expanded jet impinging on a perpendicular plate, and observed a series of expansion, recompression, and, in some cases, shock waves on the plate surface. As for an underexpanded jet impinging on an inclined plate, complicated shock structure in the impingement regionwas observed in the experiments of Lamont and Hunt [3], and in the calculations of Kim and Chang [4]. This structure is composed of plate shocks (i.e., standoff shocks) with additional tail shocks around the plate shocks. Nakai et al. [5] experimentally classified this structure into four types under various plate angle, nozzle–plate distance, and pressure ratio conditions. Moreover, a detailed numerical description of this shock structure was given by McIlroy and Fujii [6]. As for the investigation of the related acoustic phenomena, most previous studies have focused on discrete tone noise. The acoustic characteristics and the related perpendicular jet impingement flow phenomena were discussed in experimental studies (e.g., [7,8]) and recent numerical works (e.g., [9,10]), while, also, Risborg and Soria [11] discussed the acoustic feedback loop of an underexpanded jet impinging on an inclined plate by visualizing acoustic waves. As for studies on the acoustic phenomena from a correctly expanded supersonic jet impinging on an inclined plate, the subject that is examined in the present study, several numerical reports can be found, such as [12–14]. These studies were conducted to investigate the acoustic phenomena during the liftoff of a launch vehicle, and also discussed the acoustic and flow fields, which contain complex shock structures in the impingement region. In particular, the results of these studies revealed that there exist two types of acoustic waves: the Mach waves from the supersonic turbulent wall jet, and the acoustic waves propagating in an approximately perpendicular direction to the plate. The acoustic field under various impingement conditions was also calculated by Nonomura et al. [14] and Honda et al. [15] but, on the other hand, only [16] can be found as an experimental study of these phenomena. They measured noise from Mj 1.5 correctly expanded jets impinging on inclined plates at two fixed locations, mainly focusing on the noise environment of an aircraft carrier deck. They successfully revealed the influence of the nozzle–plate distance and the jet temperature on the sound pressure level (SPL), whereas they also noted that further investigations, such as spatial distribution of SPL, localization of the source region, and optical measurements, may be useful to fully characterize the acoustic and flow properties. As described above, these acoustic phenomena have been investigated numerically in detail, but discussion based on experimental data is currently lacking. Detailed experimental results are indispensable to a discussion of acoustic phenomena, because a limitation in the frequency range of the spectra obtained by numerical analyses exists. Therefore, the objective of the present study is to study the characteristics of the acoustic waves from a correctly expanded supersonic jet impinging on the inclined plate experimentally. To achieve this, the acoustic waves from the impinging jet are measured using a microphone at a jet facility. The waves are then visualized using the schlieren method, and their propagation directions, spectra, and the extent of the source region are discussed in this study.After an evaluation of the accuracy of the SPLmeasurement and confirmation of the jet profile (described in Sec. II.D.), an overview of the acoustic field based on the results of the SPL measurements and schlieren visualization is presented inSec. III.A. Then, the spectra of the acoustic waves are discussed in Sec. III.B. Finally, the extent of the source region of the acoustic waves is discussed using the SPL distributions and a schlieren visualization movie analysis, in Sec. III.C. Received 26 September 2014; revision received 4 November 2014; accepted for publication4November 2014; published online 28 January 2015. Copyright© 2014byMasahitoAkamine. Published by theAmerican Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1533-385X/15 and $10.00 in correspondence with the CCC. *Graduate Student, Department of Advanced Energy. Student Member AIAA. Ph.D. Student, Department of Advanced Energy; currently at IHI Corporation. Associate Professor, Department of Advanced Energy. Member AIAA. Associate Professor, Department of Aeronautics and Astronautics. Senior Member AIAA. Senior Engineer, Department of Aeronautics and Astronautics. **Engineer, JAXA’s Engineering Digital Innovation (JEDI) Center. Member AIAA.

Acoustic Phenomena from Correctly Expanded Supersonic Jet Impinging on Inclined Plate

A blunt and short reentry capsule tends to be dynamically unstable at transonic speeds, attributed primarily to the delay of base pressure. In the present study the flowfield around a capsule under forced pitching oscillation is numerically simulated, and the results are compared with that around the capsule at a fixed pitch angle. The two flowfields are found to be essentially the same except for a delay in the base pressure in the oscillating case. Detailed flow analysis reveals that impingement of reverse flow behind the capsule determines the base pressure distribution, and the behavior of the reverse flow is governed by the vortex structure behind the capsule. The vortex structure is composed of a ring vortex and a pair of longitudinal vortices, and the interaction between the longitudinal vortices and the flowfield near the neck point defines the flowfield behind the capsule

Susumu Teramoto

Papers

Experimental verification of the feasibility of a 100 W class micro-scale gas turbine at an impeller diameter of 10 mm

Large-Eddy Simulation of Transitional Boundary Layer with Impinging Shock Wave

Numerical Analysis of Dynamic Stability of a Reentry Capsule at Transonic Speeds

Acoustic Phenomena from Correctly Expanded Supersonic Jet Impinging on Inclined Plate

Mechanism of Dynamic Instability of a Reentry Capsule at Transonic Speeds