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NASA NTRS2016

Predicting Transition from Laminar to Turbulent Flow over a Surface

A prediction of whether a point on a computer-generated surface is adjacent to laminar or turbulent flow is made using a transition prediction technique. A plurality of instability modes are obtained, each defined by one or more mode parameters. A vector of regressor weights is obtained for the known instability growth rates in a training dataset. For an instability mode in the plurality of instability modes, a covariance vector is determined. A predicted local instability growth rate at the point is determined using the covariance vector and the vector of regressor weights. Based on the predicted local instability growth rate, an n-factor envelope at the point is determined.

Rajnarayan, Dev↗

NASA NTRSDate not supplied

Global Analysis of Nonlinear Second-Mode Development in a Mach-6 Boundary Layer From High-Speed Schlieren Data

The second-mode instability on a 7◦ half-angle sharp cone at Mach 6 is analyzed using high-speed calibrated schlieren imagery at a frame rate near the expected fundamental frequency. Experiments were conducted in the NASA Langley 20-Inch Mach 6 facility at unit Reynolds number between 6.56×106 and 9.71×106 m−1. Time-resolved pixel intensity signals throughout the boundary layer are reconstructed using spatially available data in the schlieren images to recover an effective sampling rate of over 10 MHz; these are then converted to quantitative density gradients using a thin-lens-based calibration technique. A global analysis is performed on the schlieren data to investigate the nonlinear growth of the second-mode fundamental and harmonic content. Point-wise measures of the auto-bicoherence are used to identify specific triadic interactions and the locations of their highest levels of quadratic phase coupling. Significant resonance interactions between the second-mode fundamental and harmonic instabilities were found along with interactions between these and the mean flow. Bispectral mode decomposition is employed to educe the flow structures associated with these interactions. A similar analysis is performed for the power spectrum, with power spectral densities computed for each pixel’s time-series and spectral proper orthogonal decomposition employed to derive the modal structure and energy of the flow at specific frequencies. Comparisons between the bispectral quantities and second-mode power show that nonlinear interactions, particularly resonance interactions, are closely correlated with space-time modulation of disturbances during the nonlinear stage of transition.

boundary layer transition↗

DOE OSTI2020

Variable-density buoyancy-driven turbulence with asymmetric initial density distribution

The effects of different initial density distributions on the evolution of buoyancy-driven homogeneous variable-density turbulence (HVDT) at low (0.05) and high (0.75) Atwood numbers are studied by using high-resolution direct numerical simulations. HVDT aims to mimic the acceleration-driven Rayleigh–Taylor and shock-driven Richtmyer–Meshkov instabilities and reveals new physics that arise from variable-density effects on the turbulent mixing. Here, the initial amounts of pure light and pure heavy flows are altered primarily to mimic the variable-density turbulence at the different locations of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities’ mixing layers where the amounts of the mixing fluids are not equal. It is found that for the low Atwood number cases, the asymmetric initial density distribution has limited effects on both global and local flow evolution for HVDT. However, at high Atwood number, both global flow evolution and the local flow structures are strongly affected by the initial composition ratio. The flow composed of more light fluid reaches higher turbulent levels and the local statistics reach their fully-developed behavior earlier in the time evolution. In contrast, during the late time decay, where most of the flow is well-mixed, all parameters become independent of the initial composition ratio for both low and high Atwood number cases.

42 ENGINEERING↗

NASA NTRS1979

General Theory of Aerodynamic Instability and the Mechanism of Flutter

The aerodynamic forces on an oscillating airfoil or airfoil-aileron combination of three independent degrees of freedom were determined. The problem resolves itself into the solution of certain definite integrals, which were identified as Bessel functions of the first and second kind, and of zero and first order. The theory, based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing section theory relating to the steady case. The air forces being known, the mechanism of aerodynamic instability was analyzed. An exact solution, involving potential flow and the adoption of the Kutta condition, was derived. The solution is of a simple form and is expressed by means of an auxiliary parameter k. The flutter velocity, treated as the unknown quantity, was determined as a function of a certain ratio of the frequencies in the separate degrees of freedom for any magnitudes and combinations of the airfoil-aileron parameters.

Theodorsen, Theodore↗

DOE OSTI2020

Rayleigh-Taylor Instability: A Status Review of Experimental Designs and Measurement Diagnostics

The focus of experiments and the sophistication of diagnostics employed in Rayleigh-Taylor instability (RTI) induced mixing studies have evolved considerably over the past seven decades. The first theoretical analysis by Taylor and the two-dimensional experimental results by Lewis on RTI in 1950 examined single-mode RTI using conventional imaging techniques. Over the next 70 years, several experimental designs have been used to creating an RTI unstable interface between two materials of different densities. These early experiments though innovative, were arduous to diagnose and provided little information on the internal, turbulent structure and initial conditions of the RT mixing layer. Coupled with the availability of high-fidelity diagnostics, the experiments designed and developed in the last three decades allow detailed measurements of various turbulence statistics that have allowed broadly to validate and verify late-time nonlinear models and mix-models for buoyancy-driven flows. Besides, they have provided valuable insights to solve several long-standing disagreements in the field. Herein, this review serves as an opportunity to discuss the understanding of the RTI problem and highlight valuable insights gained into the RTI driven mixing process with a focus on low to high Atwood number (> 0.1) experiments.

42 ENGINEERING↗

NASA NTRS1991

Nonlinear symmetric instability and intraseasonal oscillations in the tropical atmosphere

Symmetric inertial instability (SII) is studied as a mechanism for stratospheric and tropospheric phenomena in the equatorial regions. The linear and nonlinear dynamics of SII in a two-layer, zonally symmetric model on an equatorial beta plane, in the presence of a basic flow with horizontal and vertical shear, with and without dissipative effects are investigated. Linear symmetric instabilities are, in accordance with previously published results, purely exponential, that is, nonoscillatory. Nonlinear SII, studied here for the first time on a planetary scale, can produce finite-amplitude oscillatory behavior, periodic or chaotic. The period of oscillations in the inviscid case depends on the initial data. In the presence of dissipative effects, all solutions tend to a limit cycle or to a strange attractor. The dominant period in this case, over a wide range of parameters and whether vertical shear is present or not, is in the intraseasonal, 20-30-day range. It appears therefore that nonlinear SII might be a contributing mechanism to low-frequency oscillations in the tropical atmosphere.

Zhao, J.-X.↗

NASA NTRS1978

Thickening of axisymmetric accretion disks and flows

A study is made to determine whether or not hot plasma flowing from the inner edge of an accretion disk around a black hole can thicken out of the disk plane with the onset of a Pringle-Rees thermal instability. The instability is caused by the density thinning caused by the sharp increase in radial infall velocity near the radius of the marginally stable circular orbit, or by abrupt variations in viscosity or Lightman-Eardly secular instabilities. An estimate of the thickening timescale is given. Various physically realistic situations involving radial steady-state flow and where significant disk thickening can occur in the region of the radius of the marginally stable circular orbit are identified. It is noted that its evolution into a large spherical cloud would require large velocities of the viscosity parameter and the amount of energy dissipated in the unstable region.

Stoeger, W. R.↗

NASA NTRS1987

An experimental evaluation of slots versus porous strips for laminar-flow applications

Detailed mean velocity and disturbance amplitude measurements were conducted in a Blasius boundary-layer flow with wall suction applied at three downstream locations. The main emphasis was a direct comparison of the growth rate of the instability wave with discrete spanwise slots versus wide porous strips. The results demonstrate that the local effects of suction through slots or very narrow porous strips have a greater beneficial effect on the stability of the boundary-layer flow relative to the suction influence of a wide porous strip. Codes which use continuous suction for the growth rates of the instability waves to determine the suction quantities for a multiple series of slots will be quite conservative in the estimation of the suction quantity. Guidelines were provided for suction-chamber design and flow rates to minimize internal oscillations which propagate into the boundary-layer flow.

Cornelius, Kenneth C.↗

NASA NTRS1988

Dynamical criterion for a marginally unstable, quasi-linear behavior in a two-layer model

A two-layer quasi-geostrophic flow forced by meridional variations in heating can be in regimes ranging from radiative equilibrium to forced geostrophic turbulence. Between these extremes is a regime where the time-mean (zonal) flow is marginally unstable. Using scaling arguments, it is concluded that such a marginally unstable state should occur when a certain parameter, measuring the strength of wave-wave interactions relative to the beta effect and advection by the thermal wind, is small. Numerical simulations support this proposal. A transition from the marginally unstable regime to a more nonlinear regime is then examined through numerical simulations with different radiative forcings. It is found that transition is not caused by secondary instability of waves in the marginally unstable regime. Instead, the time-mean flow can support a number of marginally unstable normal modes. These normal modes interact with each other, and if they are of sufficient amplitude, the flow enters a more nonlinear regime.

Ebisuzaki, W.↗

NASA NTRS1998

Experimental Study of Transitional Flow Behavior in a Simulated Low Pressure Turbine

A detailed investigation of the flow physics occurring on the suction side of a simulated Low Pressure Turbine (LPT) blade was performed. A contoured upper wall was designed to simulate the pressure distribution of an actual LPT airfoil onto a flat lower plate. The experiments were carried out for the Reynolds numbers of 35,000, 70,000, 100,000 and 250,000 with four levels of freestream turbulence ranging from 1% to 4%. For the three lower Reynolds numbers, the boundary layer on the flat plate was separated and formed a bubble. The size of laminar separation bubble was measured to be inversely proportional to the freestream turbulence levels and Reynolds numbers. However, no separation was observed for the Re = 250,000 case. The transition on a separated flow was found to proceed through the formation of turbulent spots in the free shear layer as evidenced in the intermittency profiles for Re = 35,000, 70,000 and 100,000. Spectral data show no evidence of Kelvin-Helmholtz or Tollmien-Schlichting instability waves in the free shear layer over a separation bubble (bypass transition). However, the flow visualization revealed the large vortex structures just outside of the bubble and their development to turbulent flow for Re = 50,000, which is similar to that in the free shear layer (separated-flow transition). Therefore, it is fair to say that the bypass and separated-flow transition modes coexist in the transitional flows over the separation bubble for certain conditions. Transition onset and end locations and length determined from intermittency profiles decrease as Reynolds number and freestream turbulence levels increase.

Sohn, Ki Hyeon↗

NASA NTRS2007

Experimental Study of Transitional Flow Behavior in a Simulated Low Pressure Turbine

A detailed investigation of the flow physics occurring on the suction side of a simulated Low Pressure Turbine (LPT) blade was performed. A contoured upper wall was designed to simulate the pressure distribution of an actual LPT airfoil onto a flat lower plate. The experiments were carried out for the Reynolds numbers of 35,000, 70,000, 100,000, and 250,000 with four levels of freestream turbulence ranging from 1 to 4 percent. For the three lower Reynolds numbers, the boundary layer on the flat plate was separated and formed a bubble. The size of laminar separation bubble was measured to be inversely proportional to the freestream turbulence levels and Reynolds numbers. However, no separation was observed for the Re = 250,000 case. The transition on a separated flow was found to proceed through the formation of turbulent spots in the free shear layer as evidenced in the intermittency profiles for Re = 35,000, 70,000, and 100,000. Spectral data show no evidence of Kelvin-Helmholtz of Tollmien-Schlichting instability waves in the free shear layer over a separation bubble (bypass transition). However, the flow visualization revealed the large vortex structures just outside of the bubble and their development to turbulent flow for Re = 50,000, which is similar to that in the free shear layer (separated-flow transition). Therefore, it is fair to say that the bypass and separated-flow transition modes coexist in the transition flows over the separation bubble of certain conditions. Transition onset and end locations and length determined from intermittency profiles decreased as Reynolds number and freestream turbulence levels increase.

Sohn, Ki Hyeon↗

DOE OSTI2023

Nonlinear mode coupling and energetics of driven magnetized shear-flow turbulence

To comprehensively understand the saturation of two-dimensional (2D) magnetized Kelvin–Helmholtz-instability-driven turbulence, energy transfer analysis is extended from the traditional interaction between scales to include eigenmode interactions, by using the nonlinear couplings of linear eigenmodes of the ideal instability. While both kinetic and magnetic energies cascade to small scales, a significant fraction of turbulent energy deposited by unstable modes in the fluctuation spectrum is shown to be re-routed to the conjugate-stable modes at the instability scale. They remove energy from the forward cascade at its inception. The remaining cascading energy flux is shown to attenuate exponentially at a small scale, dictated by the large-scale stable modes. Guided by a widely used instability-saturation assumption, a general quasi-linear model of instability is tested by retaining all nonlinear interactions except those that couple to the large-scale stable modes. These complex interactions are analytically removed from the magnetohydrodynamic equations using a novel technique. Observations are an explosive large-scale vortex separation instead of the well-known merger of 2D, a dramatic enhancement in turbulence level and spectral energy fluxes, and a reduced small-scale dissipation length scale. These show the critical role of the stable modes in instability saturation. Possible reduced-order turbulence models are proposed for fusion and astrophysical plasmas, based on eigenmode-expanded energy transfer analyses.

Physics↗

NASA NTRS1977

Transition and laminar instability

The linear stability theory was applied to the problem of boundary layer transition in incompressible flow. The theory was put into a form suitable for three-dimensional boundary layers; both the temporal and spatial theories were examined; and a generalized Gaster relation for three-dimensional boundary layers was derived. Numerical examples include the stability characteristics of Falkner-Skan boundary layers, the accuracy of the two-dimensional Gaster relation for these boundary layers, and the magnitude and direction of the group velocity for oblique waves in the Blasius boundary layer. Available experiments which bear on the validity of stability theory and its relation to transition are reviewed and the stability theory is applied to transition prediction. The amplitude method is described in which the wide band disturbance amplitude in the boundary layer is estimated from stability theory and an interaction relation for the initial amplitude density of the most unstable frequency.

Mack, L. M.↗

NASA NTRS1985

Disturbance-wave interactions in flows with crossflow

The leading-edge region of swept wings is dominated by the crossflow instability, resulting in vortices that all rotate in the same sense. The effect of these possibly unsteady vortices on the behavior of other disturbances is examined, and a strong interaction between these and disturbances of half the dominating crossflow wavelength is predicted. According to theory, the interaction is of crossflow-crossflow type. The effect explains the anomalies found in the experimental observations of Saric and Yeates. Visually, they observe vortices at the wavelength predicted by linear theory; however, in their hot-wire measurements they find that the superharmonic dominates disturbance growth, eventually having three times the amplitude of the primary wave. In this case, the usual transition prediction methods would fail, clearly indicating the importance of studying interactions of this sort.

Reed, H. L.↗

NASA NTRS1992

Instability and transition in three-dimensional supersonic boundary layers

Linear stability of three-dimensional flow past a 5 deg semi-vertex sharp cone at 2 deg incidence in Mach 3.5 free-stream is studied. Computed laminar mean flow profiles along the leeward line of symmetry are highly inflectional and, hence, much more unstable than the profiles along the windward line of symmetry. Accordingly, transition occurs much earlier along the leeward line both in the present calculations (based upon eN approach) and in the experiments of King (1991) performed in NASA Langley 'quiet' tunnel. Boundary-layer transition in the region between the two symmetry lines is influenced by the crossflow generated due to the angle of attack and, as a consequence, it progressively moves upstream with increasing azimuthal angle measured from the windward line. The computed transition front is qualitatively similar to the experimental results, although some differences remain.

Malik, M. R.↗

NASA NTRS2000

Quantifying Instability Sources in Liquid Rocket Engines

Computational fluid dynamics methodology to predict the effects of combusting flows on acoustic pressure oscillations in liquid rocket engines (LREs) is under development. 'Me intent of the investigation is to develop the causal physics of combustion driven acoustic resonances in LREs. The crux of the analysis is the accurate simulation of pressure/density/sound speed in a combustor which when used by the FDNS-RFV CFD code will produce realistic flow phenomena. An analysis of a gas generator considered for the Fastrac engine will be used as a test validation case.

Farmer, Richard C.↗

NASA NTRS1990

Ballooning mode instability at the plasmapause

The ballooning mode instability, which can excite hydromagnetic waves at the plasmapause, is studied in the presence of azimuthal plasma flows induced during geomagnetically disturbed periods. A general sufficient criterion for the ballooning mode stability is derived, for a change in the potential energy greater than or equal to 0, which involves the integration over an entire field line. A local stability analysis at the equatorial plasmapause region shows that the ballooning modes could be spontaneously generated via instability under at least two conditions: one is similar to the usual interchange condition, and the second to the quasi-interchange modes. Both of these local instability conditions can be derived from the general stability criterion. Finally an exact solution for the equilibrium state with flow is derived analytically, and the change in the potential energy is computed numerically. It is found that, in the cases studied, the flow does not spontaneously excite the ballooning modes; it only further stabilizes (or destabilizes) the ballooning spectrum if originally the system is stable (or unstable). The analysis would be useful for the interpretation of some of the low-frequency modes observed at the ground and near the equatorial plasmapause.

Lakhina, G. S.↗

NASA NTRS1988

Rotating disk transition due to isolated roughness with intense acoustic irradiation

The low transition Reynolds numbers associated with boundary-layers which exhibit crossflow instability have made them an important area of study in fluid mechanics. An excellent test bed for the study of this flow is a flat disk rotating in still fluid. An experimental investigation of stability and transition of a rotating disk boundary-layer has been conducted. The effects of isolated roughness elements and acoustic forcing, both alone and in combination, were considered. The flow showed no receptivity to intense monochromatic acoustic forcing except in the presence of sizable roughness. A case was investigated where the growth of the primary instability, seeded by an isolated roughness element, was positively altered in the presence of sound, leading to a downstream movement of transition. In agreement with the work of several investigators, the results of this study suggest that receptivity to long wavelength phenomena, such as traveling sound waves, is contingent upon the presence of strong localized pressure gradients (such as those introduced by roughness) to reduce the length scales of the disturbance to those which are consistent with unstable wavelengths in the flow field.

Waitz, Ian A.↗