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NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the non-local, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, as roughness elements, steps, gaps, or corners. To solve the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 107 to 108. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear system. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE.

Boundary Layer Stability↗

NASA NTRS2003

The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary layers.

Chang, Chau-Lyan↗

NASA NTRS2022

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the nonlocal, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, such as those in the vicinity of roughness elements, steps, gaps, or corners. To compute the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 10^(7) to 10^(8) even in relatively simple flows. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear systems. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE. Additionally, inflow-resolvent analysis based on the HLNSE for discrete-roughness-induced disturbances in the nose tip of a blunt cone at Mach 6 demonstrates the importance of including the disturbance amplification along the near vicinity of the roughness element and separation region.

Boundary Layer Stability↗

NASA NTRS1995

Effect of Far-Field Boundary Conditions on Boundary-Layer Transition

The effect of far-field boundary conditions on the evolution of a finite-amplitude two-dimensional wave in the Blasius boundary layer is assessed. With the use of the parabolized stability equations (PSE) theory for the numerical computations, either asymptotic, Dirichlet, Neumann or mixed boundary conditions are imposed at various distances from the wall. The results indicate that asymptotic and mixed boundary conditions yield the most accurate mean-flow distortion and unsteady instability modes in comparison with the results obtained with either Dirichlet or Neumann conditions.

Bertolotti, Fabio P.↗

NASA NTRS1994

Effect of Far-Field Boundary Conditions on Boundary-Layer Transition

Bertolotti, Fabio P.↗

NASA NTRS1989

The Kelvin-Helmholtz instability at the magnetopause and inner boundary layer surface

Observations by the vector electron spectrometer on the ISEE 1 spacecraft are used to directly check the incompressible hydromagnetic stability condition given by Hasegawa (1975), which indicates how stability is influenced by the velocity shear, density ratio, magnetic field, and the direction of the wave vector of the unstable wave mode. The magnetopause is generally found to be stable, by a large margin. In contrast, many cases of marginal stability or instability are found across density transitions in, and at the inner edge of, the boundary layer for wave vectors in plausible directions. It thus appears that the Kelvin-Helmholtz instability is of importance at the inner edge of the magnetospheric boundary layer, as predicted by MHP theory.

Ogilvie, Keith W.↗

NASA NTRS1994

Numerical simulation of supersonic boundary layer transition

The present contribution reviews some of the recent progress obtained at our group in the direct numerical simulation (DNS) of compressible boundary layer transition. Elements of the different simulation approaches and numerical techniques employed are surveyed. Temporal and spatial simulations, as well as comparisons with results obtained from Parabolized Stability Equations, are discussed. DNS results are given for flat plate boundary layers in the Mach number range 1.6 to 4.5. A temporal DNS at Mach 4.5 has been continued through breakdown all the way to the turbulent stage. In addition results obtained with a recently developed extended temporal DNS approach are presented, which takes into account some nonparallel effects of a growing boundary layer. Results from this approach are quite close to those of spatial DNS, while preserving the efficiency of the temporal DNS.

Guo, Y.↗

NASA NTRS1982

Theoretical analyses of Baroclinic flows

A stability analysis of a thin horizontal rotating fluid layer which is subjected to arbitrary horizontal and vertical temperature gradients is presented. The basic state is a nonlinear Hadley cell which contains both Ekman and thermal boundary layers; it is given in closed form. The stability analysis is based on the linearized Navier-Stokes equations, and zonally symmetric perturbations in the form of waves propagating in the meridional direction are considered. Numerical methods were used for the stability problem. It was found that the instability sets in when the Richardson number is close to unity and that the critical Richardson number is a non-monotonic function of the Prandtl number. Further, it was found that the critical Richardson number decreases with increasing Ekman number until a critical value of the Ekman number is reached beyond which the fluid is stable.

Antar, B.↗

DOE OSTI2026

The Spatial and Temporal Variability of the Clear Convective Boundary Layer at the ARM SGP Supersite

The convective boundary layer (CBL), also known as the mixing layer, constitutes the critical lower segment of the atmosphere that significantly influences daily human activities. The growing demand for precise weather forecasts is driven by the requirements of agriculture, transportation, and routine societal functions. Here, to enhance understanding of the CBL, this study investigates the spatiotemporal variability in the CBL and its controlling factors using four-year Doppler lidar, surface flux, and profiling measurements at five ARM Southern Great Plains sites within a 100 km radius. This investigation utilizes data collected exclusively under clear-sky conditions or scattered low-cloud conditions. Results reveal significant spatial differences in CBL evolutions. Daily mixing layer heights (MLHs) vary up to 1 km (30% of the mean) in late afternoon. There is a clear east–west contrast: western sites (C1, E32, E37) exhibit higher summer MLH (1.9–2.1 km) and vertical velocity variances (1.0–1.2 m 2 s −2 ) than eastern sites (1.6–1.8 km), reversing in winter. Temporally, the MLH peaks at 70% of the sunrise–sunset interval, the lagging heat flux (HF) peaks at 50%; and the seasonal MLH maxima lag the HF by approximately one month, influenced by nighttime PBL (planetary boundary layer) properties. The HF and lower tropospheric stability are the main factors of influence for the CBL, but site-specific dependencies highlight the critical roles of local factors, underscoring the need for including them in CBL modeling.

ARM SGP site↗

DOE OSTI2021

Boundary Layer Climatology at ARM Southern Great Plains

Operational since 1992, the Atmospheric Radiation Measurement (ARM) southern great plains (SGP) site at Oklahoma, USA has become a reference research site for meteorological studies. Due to an open data policy the ARM data are used by researchers all over the world. In this report, we review the long-term climatology of the atmospheric boundary layer, SGP instrumentations, the site and some site-specific atmospheric conditions which potentially effect wind turbines within the region. As the atmospheric boundary layer is bounded and influenced by the surface, observations of surface radiation components and heat fluxes are crucial in understanding land-atmosphere interactions. The entrainment of air, updrafts, downdrafts and boundary layer height characteristics is needed for understanding the structure and growth of the atmospheric boundary layer. Therefore, measurements from both surface in-situ and remote sensing observations at SGP provide an overall climatology and their interactions from surface up to the boundary layer. Measurements from a 60 m meteorological tower, surface flux stations, disdrometers, soil temperature and moisture flux plates, coherent Doppler lidar, Raman lidar, radiosondes, and satellite data at SGP central facility were analyzed. All the measurements were generally within a few square kilometers of each other at the central facility. This report focuses on data from January 2010 to June 2020 at SGP central facility. The various sections describe the ARM SGP site and surrounding wind turbines; in-situ and remote sensing instrumentation used in the report; provides mathematical equations to analyze fluxes, turbulence and other boundary layer parameters; a climatological analysis of surface winds, fluxes and thermodynamic parameters for several years; an analysis of observed winds in the framework of Monin-Obukhov Similarity Theory; an analysis of the boundary layer winds and direction from a Doppler lidar; multi-year turbulence estimates through the boundary layer from a Doppler lidar; atmospheric boundary layer water vapor and relative humidity profiles from Raman lidar; cloud base height and boundary layer height from multiple sensors and satellite data; and finally site specific atmospheric conditions, such as nocturnal low-level jets. Diurnal, seasonal and yearly variations of surface, sub-surface and boundary layer quantities, such as wind speed, direction, temperature, atmospheric stability, soil temperature, and various atmospheric fluxes at SGP showed distinct trends useful for focused modeling studies. The applicability of surface similarity theory on ARM SGP data is also evaluated, which showed northerly flows are aligned with MO theory estimates compared to southerly flows. Boundary layer winds and direction profiles for several years from a Doppler lidar shows a consistent presence of a nocturnal low-level jet and predominant southerly wind directions through the boundary layer at SGP. The inter-annual variability at SGP is low (<3.5%), with a mean annual wind speed of approximately 7 m s -1 at 100 m above ground level. Boundary layer turbulence and moisture transport from Doppler and Raman lidars are evaluated, which provides evidence of increased water vapor mass flux into the great plains during nocturnal low-level jets. The moisture flux from nocturnal low-level jets is observed to be maximum during summer periods. A novel machine learning algorithm is implemented to accurately estimate the planetary boundary layer height, providing further insights into growth and destruction of the convective boundary layer height during various seasons and land-atmosphere conditions. The high frequency of low-level clouds during winter, spring and fall seasons is validated using the multi-sensor array and satellite estimates of cloud top height. Satellite vegetative fraction data provides insight into seasonal surface roughness and vegetation variability around SGP site.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1989

Goertler vortices in supersonic and hypersonic boundary layers

The problem of Goertler vortices in compressible boundary layers over concave walls is considered. At O(1) wavelengths, the instability is governed by parabolic partial differential equations that are solved numerically to determine the effect of various initial conditions on the development of Goertler vortex instability in compressible boundary layers. The results show that both the velocity and temperature fluctuations may lead to a Goertler vortex. The vortex growth rates determined from the present method are found to differ somewhat from those given by a normal mode solution. At both the supersonic and hypersonic Mach numbers, cooling has a small destabilizing effect. In addition, the most unstable disturbances shift toward lower wavelengths because of thinning of the boundary layer. The results also show that compressibility has a stabilizing effect on the Goertler instability, while the effect of an adverse pressure gradient is found to be destabilizing. The behavior of the Goertler vortex structure with Mach number is also examined. At hypersonic Mach numbers, vortices are located near the edge of the boundary layer for adiabatic wall conditions. However, the entire boundary layer is affected when the wall is cooled.

Spall, R. E.↗

NASA NTRS1990

Numerical simulation of particle-wave interaction in boundary layers

The effects of wall injection and particle motion on the spatial stability of two-dimensional plane channel flow are investigated. For this purpose, an accurate Navier-Stokes solver to simulate the space-time evolution of disturbances in three-dimensional flows has been developed. The code is operational on the NASA Langley CRAY2 and can be ported to any other supercomputer. The code has been tested extensively in tracking the spatial evolution of two-dimensional disturbances in plane channel flow and provided excellent agreement with the linear theory including at the inflow/outflow boundaries. Preliminary calculations have been performed to investigate the effects of stationary and moving sources of vortical disturbances simulating a particle traveling in the flow field. Results suggest that even at very low amplitudes, vortical disturbances act as amplifiers on the Tollmien-Schlichting waves promoting rapid instability. It is also found that slow moving particles are more dangerous than both stationary and fast moving particles for the same disturbance levels.

Biringen, S.↗

NASA NTRS1982

Thermal stability of the surface layer and its relation to the dispersion of primary pollutants in St. Louis

The present investigation is concerned with the applicability of the vertical temperature gradient, DT, as a dispersion parameter for urban area sources. Data on DT were tabulated from temperature measurements at 5 m and 30 m obtained on 30 m towers at 12 stations. DT was obtained by subtracting the value at 5 m from that at 30 m. Positive DT values represent an inversion. Accuracy of the DT data is 0.1 K. Hourly measurements of DT along with concentrations of the primary pollutants, CO, NO, and total hydrocarbons (THC), are available from the 1976 RAPS data base for St. Louis. Linear correlations between a given pollutant species concentration and DT are developed from that data set. It could be confirmed that a strong positive correlation exists at night between the thermal stability of the lowest part of the boundary layer and the urban concentration of the primary pollutants CO, NO, and hydrocarbons.

Remsberg, E. E.↗

NASA NTRS2015

Receptivity of Hypersonic Boundary Layers to Acoustic and Vortical Disturbances (Invited)

Boundary-layer receptivity to two-dimensional acoustic and vortical disturbances for hypersonic flows over two-dimensional and axi-symmetric geometries were numerically investigated. The role of bluntness, wall cooling, and pressure gradients on the receptivity and stability were analyzed and compared with the sharp nose cases. It was found that for flows over sharp nose geometries in adiabatic wall conditions the instability waves are generated in the leading-edge region and that the boundary layer is much more receptive to slow acoustic waves as compared to the fast waves. The computations confirmed the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundary layer transition. The receptivity coefficients in flows over blunt bodies are orders of magnitude smaller than that for the sharp cone cases. Wall cooling stabilizes the first mode strongly and destabilizes the second mode. However, the receptivity coefficients are also much smaller compared to the adiabatic case. The adverse pressure gradients increased the unstable second mode regions.

Balakumar, P.↗

NASA NTRS1981

Viscous-inviscid interaction for transonic wing-body configurations including wake effects

An existing three-dimensional compressible integral boundary-layer method was modified to account for mean dilatation effects, to model transition properly, and to provide better numerical stability near computational boundaries. Results of this method were compared against those from a three-dimensional finite-difference boundary-layer method on a difficult test case. An interaction procedure was developed to couple this integral method with a number of wing-alone and wing-body transonic potential codes to account for viscous effects. A strip wake model, including thickness and curvature effects, was developed and incorporated into this interaction procedure. Results from this procedure were compared against experimental data and results from previous procedures, on test cases where viscous effects were large.

Streett, C. L.↗

NASA NTRS1990

The inviscid stability of supersonic flow past a sharp cone

The laminar boundary layer which forms on a sharp cone in a supersonic freestream, where lateral curvature plays a key role in the physics of the problem is considered. This flow is then analyzed from the point of view of linear, temporal, inviscid stability. The basic, non-axisymmetric disturbance equations are derived for general flows of this class, and a so called triply generalized inflexion condition is found for the existence of subsonic neutral modes of instability. This condition is analogous to the well-known generalized inflexion condition found in planar flows, although in the present case the condition depends on both axial and aximuthal wavenumbers. Extensive numerical results are presented for the stability problem at a freestream Mach number of 3.8, for a range of streamwise locations. These results reveal that a new mode of instability may occur, peculiar to flows of this type involving curvature. Additionally, asymptotic analyses valid close to the tip of the cone, far downstream of the cone are presented, and these give a partial (asymptotic) description of this additional mode of instability.

Duck, Peter W.↗

NASA NTRSDate not supplied

Modeling Boundary-Layer Transition in Subsonic Flow over a Swept Wing

Predicting the onset of boundary-layer transition is often more accurate using physics-based models that directly compute disturbance growth rather than phenomenological models often implemented into industrial CFD codes. The aim of this ongoing study is to calibrate linear, physics-based computations of transition in subsonic flows over swept wings against a large set of experimental data. Advancing the calibration of linear models of transition contributes to the CFD-Vision-2030 goal of automated boundary-layer transition prediction. This progress report uses the dual N-factor method to model transition over the swept NACA 64-2-015A wing. The flow conditions match selected test conditions from an extensive experimental dataset acquired from the NASA Ames 12-ft Pressure Tunnel. The OVERFLOW 2.4b flow solver is used to obtain laminar basic states based on an infinite-span assumption. Stability analyses are performed on 365 distinct configurations with linear stability theory (LST) and parabolized stability equations (PSE) from the Langley Stability and Transition Analysis Codes (LASTRAC), modeling the growth of Tollmien-Schlichting (TS) and stationary crossflow (SCF) disturbances. From a total of 67 data points for unswept, i.e., TS-dominant configurations, the critical N-factor based on PSE is found to be N_TS = 9. The SCF critical N-factor is found to be near 8 for the highly swept, SCF-dominant configurations. Dual N-factor curves for both LST and PSE computations demonstrate a high level of interaction between TS and SCF. It may be worthwhile to investigate an alternate metric to visualize maximal SCF amplification upstream of the transition location to account for the growth of SCF modes near the leading edge, which is not considered in the conventional applications of the dual N-factor criterion.

boundary-layer transition↗

DOE OSTI2022

Current state and future trends in boundary layer control on lifting surfaces

Successful flow control may bring numerous benefits, such as flow stabilization, flow reattachment, separation delay, drag reduction, lift increase, aerodynamic performance improvement, energy efficiency increase, shock delay or weakening, noise reduction, etc. For these purposes, many different flow control devices, which can be classified as passive, semi-active and active, have been designed and tested. This review paper aims to highlight the most promising and commonly employed boundary layer control methods as well as outline their potential in specific applications in aerospace and energy engineering. Referenced studies, performed on various geometries (flat plates, channels, airfoils, wings, blades, cylinders), are primarily numerical or experimental. Although enhanced aerodynamic performance is achieved in many cases, further research is required to draw general conclusions. This paper aims to demonstrate that, in the future, we may expect further developments of flow control actuators, as well as their increased application.

42 ENGINEERING↗