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Aerodynamic Design Optimization for Natural Laminar Flow Airfoils

Natural laminar flow technology is a passive laminar flow control (LFC) strategy that seeks to delay the onset of boundary-layer transition (BLT) through shape optimization to reduce the drag of the aerodynamic vehicle. Adjoint-based design optimization for LFC is proposed in an integrated multidisciplinary framework, which includes the computational fluid dynamics (CFD), geometry and grid deformation, and linear stability analysis (LSA) for transition prediction. In particular, the BLT location is predicted using the dual N-factor method that is based on a linear stability theory (LST) eigenvalue problem. The dual N-factor criterion accounts for the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) boundary-layer instabilities to predict the transition location in three-dimensional boundary-layer flows. The adjoint-based shape optimization procedure is based on an iteratively coupled CFD and LSA methodology to converge the transition location and flow solutions, as well as to calculate the sensitivities of the aerodynamic metrics of interest with respect to the flow and shape design parameters. The RAE 2822 airfoil at 0 and 30 degrees yaw angles, an angle of attack of 0.72 degrees, and subsonic conditions (M∞ = 0.19, Rec = 5.6 × 106 ) are used as baseline configurations for design optimization. The angle of attack and the vertical displacement of free-form-deformation control points are used as design variables to reduce the drag coefficient while reaching a specified lift coefficient. The optimized unswept airfoil designs achieve a 30% drag reduction accompanied by a downstream shift of the transition locations over both suction and pressure sides of the airfoil. The initial design iterations for the swept case also show a favorable trend in the drag reduction with transition delay over both sides.

Transition↗
NASA NTRS1989

Curvature effects on the stability of three-dimensional laminar boundary layers

The linear stability equations for compressible, three-dimensional laminar boundary layer flow are derived in an orthogonal curvilinear coordinate system. The system of equations is solved using a finite difference scheme in order to study the effects of streamline and surface curvature and compressibility on the stability of the flow past a swept wing. It is known that convex surface curvature can have a stabilizing effect on the laminar boundary layer. Conversely, concave surface curvature can be destabilizing. The magnitude of these effects for swept wings is determined. Results indicate that amplification rates and hence, N-factors, for the flow over the convex upper surface of a swept wing can be reduced by about 15 to 45 percent when curvature effects are included in the linear stability analysis. The results of the calculations show that concave curvature destabilizes crossflow type disturbances with a significant increase in amplification rate. In addition, comparisons are made with some experimental results on a swept concave-convex surface. Calculated velocity vector plots show good agreement with observed disturbances in the laminar boundary layer over the concave surface.

Collier, F. S., Jr.↗
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 NTRS1986

A diagnostic study of baroclinic disturbances in polar air streams

Quasi-Lagrangian budgets of mass, vorticity and heat are calculated following disturbances that form within polar air streams. Observed cases are extracted from the European Centre for Medium-range Weather Forecasts analyses during the First GARP Global Experiment. Model-generated cases are extracted from the simulations of extratropical cyclogenesis by Sandgathe. These polar lows grow primarily through basic baroclinic instability processes and exhibit many features of larger maritime extratropical cyclones. Polar lows that originate on the poleward (or Cyclonic - Type C) side of the jet and have considerable midtropospheric positive vorticity advection at formation time are contrasted with lows that form on the equatorward (or Anticyclonic - Type A) side of a nearly straight upper-level jet. The midtropospheric positive vorticity advection must be present to enhance the vertical circulation when the large surface fluxes that are associated with strong outbreaks act to damp the thermal wave amplification. Although latent heat release is an important factor in both types, it is an essential energy source for the Type A low developments on the equatorward side. Although the vorticity balance is initially different for the two types of polar lows, the vorticity budgets during later stages are similar. The heat budget and the thickness tendency equation demonstrated that the self-development process that is present in larger maritime cyclones is also important for polar low intensification. The absence of favorable coupling to a jet stream is the missing factor in a model-generated Type A polar low that failed to develop. Consequently, the mid- and upper-tropospheric wind fields determine which polar lows will intensify to significant amplitudes.

Sinclair, Mark R.↗
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 NTRS2012

Feedback Augmented Sub-Ranging (FASR) Quantizer

This innovation is intended to reduce the size, power, and complexity of pipeline analog-to-digital converters (ADCs) that require high resolution and speed along with low power. Digitizers are important components in any application where analog signals (such as light, sound, temperature, etc.) need to be digitally processed. The innovation implements amplification of a sampled residual voltage in a switched capacitor amplifier stage that does not depend on charge redistribution. The result is less sensitive to capacitor mismatches that cause gain errors, which are the main limitation of such amplifiers in pipeline ADCs. The residual errors due to mismatch are reduced by at least a factor of 16, which is equivalent to at least 4 bits of improvement. The settling time is also faster because of a higher feedback factor. In traditional switched capacitor residue amplifiers, closed-loop amplification of a sampled and held residue signal is achieved by redistributing sampled charge onto a feedback capacitor around a high-gain transconductance amplifier. The residual charge that was sampled during the acquisition or sampling phase is stored on two or more capacitors, often equal in value or integral multiples of each other. During the hold or amplification phase, all of the charge is redistributed onto one capacitor in the feedback loop of the amplifier to produce an amplified voltage. The key error source is the non-ideal ratios of feedback and input capacitors caused by manufacturing tolerances, called mismatches. The mismatches cause non-ideal closed-loop gain, leading to higher differential non-linearity. Traditional solutions to the mismatch errors are to use larger capacitor values (than dictated by thermal noise requirements) and/or complex calibration schemes, both of which increase the die size and power dissipation. The key features of this innovation are (1) the elimination of the need for charge redistribution to achieve an accurate closed-loop gain of two, (2) a higher feedback factor in the amplifier stage giving a higher closed-loop bandwidth compared to the prior art, and (3) reduced requirement for calibration. The accuracy of the new amplifier is mainly limited by the sampling networks parasitic capacitances, which should be minimized in relation to the sampling capacitors.

Guilligan, Gerard↗
NASA NTRS1986

Incompressible boundary-layer stability analysis of LFC experimental data for sub-critical Mach numbers

An incompressible boundary-layer stability analysis of Laminar Flow Control (LFC) experimental data was completed and the results are presented. This analysis was undertaken for three reasons: to study laminar boundary-layer stability on a modern swept LFC airfoil; to calculate incompressible design limits of linear stability theory as applied to a modern airfoil at high subsonic speeds; and to verify the use of linear stability theory as a design tool. The experimental data were taken from the slotted LFC experiment recently completed in the NASA Langley 8-Foot Transonic Pressure Tunnel. Linear stability theory was applied and the results were compared with transition data to arrive at correlated n-factors. Results of the analysis showed that for the configuration and cases studied, Tollmien-Schlichting (TS) amplification was the dominating disturbance influencing transition. For these cases, incompressible linear stability theory correlated with an n-factor for TS waves of approximately 10 at transition. The n-factor method correlated rather consistently to this value despite a number of non-ideal conditions which indicates the method is useful as a design tool for advanced laminar flow airfoils.

Berry, S. A.↗
NASA NTRS1987

Elastic interaction of a crack with a microcrack array. I - Formulation of the problem and general form of the solution. II - Elastic solution for two crack configurations (piecewise constant and linear approximations)

The elastic interactions of a two-dimensional configuration consisting of a crack with an array of microcracks located near the tip are studied. The general form of the solution is based on the potential representations and approximations of tractions on the microcracks by polynomials. In the second part, the technique is applied to two simple two-dimensional configurations involving one and two microcracks. The problems of stress shielding and stress amplification (the reduction or increase of the effective stress intensity factor due to the presence of microcracks) are discussed, and the refinements introduced by higher order polynomial approximations are illustrated.

Chudnovsky, A.↗
NASA NTRS1992

The magnetic field in the heliosheath

The interplanetary magnetic field (IMF) behaves in a reasonably well-understood manner between the Sun and the heliospheric termination shock. At the shock, the azimuthal field is amplified by a factor of four (for a strong shock) and undergoes secular amplification in the heliosheath until the flow is fully turned into the downstream direction and has reached its asymptotic state in the distant heliotail. This amplification may lead to important MHD effects that can cause the shock to be closer to the Sun than otherwise expected. Here we further examine whether there are important MHD effects in the heliosheath. We do this by calculating the kinematic compression of the magnetic field in the heliosheath using an analytic incompressible flow model of the dynamics downstream of the shock. We conclude that it is likely that MHD effects are important in the heliosheath in a narrow cone about the upstream direction.

Suess, S. T.↗
NASA NTRS1989

Parametric amplification in AgGaSe2

AgGaSe2 has been grown, annealed, and characterized for the mid-IR. Characterization includes measurement of the average power-limiting factors including absorption and the variation of the refractive indices with temperature. Using specially annealed crystals 20 mm long and a Ho:YAG pump, parametric amplification at 3.39 microns has achieved a gain of 2.9 with a peak power input of only 8 MW/sq cm.

Barnes, Norman P.↗
NASA NTRS1993

Simulated high speed flight effects on supersonic jet noise

A free jet is utilized to investigate the changes in the noise received from supersonic jets in high speed subsonic flight. Flight Mach numbers to 0.9 are simulated for supersonic jets with fully expanded Mach numbers between 1 and 2. Plume pressure measurements show only minor changes in the shock structure of off-design jets up to a Mach number of 0.6. Correspondingly, far-field noise measurements indicate little change to the broadband shock noise emitted at right angles to the jet. However, measurements within the free jet show that convection effects on the noise are substantial, and that the point source convective amplification that is proportional to the fourth power of the Doppler factor may apply for broadband shock noise in flight. Measurements of jet mixing noise for an on-design supersonic jet show that the current predictions of mixing noise in flight can be extended to flight Mach numbers of at least 0.5.

Norum, Thomas D.↗
NASA NTRS2017

Chapter 12: Sea Level Rise

Global mean sea level (GMSL) has risen by about 7-8 inches (about 16-21 cm) since 1900, with about 3 of those inches (about 7 cm) occurring since 1993. Human-caused climate change has made a substantial contribution to GMSL rise since 1900, contributing to a rate of rise that is greater than during any preceding century in at least 2,800 years. Relative to the year 2000, GMSL is very likely to rise by 0.3-0.6 feet (9-18 cm) by 2030, 0.5-1.2 feet (15-38 cm) by 2050, and 1.0-4.3 feet (30-130 cm) by 2100. Future pathways have little effect on projected GMSL rise in the first half of the century, but significantly affect projections for the second half of the century. Emerging science regarding Antarctic ice sheet stability suggests that, for high emission scenarios, a GMSL rise exceeding 8 feet (2.4 m) by 2100 is physically possible, although the probability of such an extreme outcome cannot currently be assessed. Regardless of pathway, it is extremely likely that GMSL rise will continue beyond 2100. Relative sea level (RSL) rise in this century will vary along U.S. coastlines due, in part, to changes in Earth's gravitational field and rotation from melting of land ice, changes in ocean circulation, and vertical land motion (very high confidence). For almost all future GMSL rise scenarios, RSL rise is likely to be greater than the global average in the U.S. Northeast and the western Gulf of Mexico. In intermediate and low GMSL rise scenarios, RSL rise is likely to be less than the global average in much of the Pacific Northwest and Alaska. For high GMSL rise scenarios, RSL rise is likely to be higher than the global average along all U.S. coastlines outside Alaska. Almost all U.S. coastlines experience more than global mean sea level rise in response to Antarctic ice loss, and thus would be particularly affected under extreme GMSL rise scenarios involving substantial Antarctic mass loss. As sea levels have risen, the number of tidal floods each year that cause minor impacts (also called "nuisance floods") have increased 5- to 10-fold since the 1960s in several U.S. coastal cities. Rates of increase are accelerating in over 25 Atlantic and Gulf Coast cities. Tidal flooding will continue increasing in depth, frequency, and extent this century. Assuming storm characteristics do not change, sea level rise will increase the frequency and extent of extreme flooding associated with coastal storms, such as hurricanes and nor'easters. A projected increase in the intensity of hurricanes in the North Atlantic could increase the probability of extreme flooding along most of the U.S. Atlantic and Gulf Coast states beyond what would be projected based solely on RSL rise. However, there is low confidence in the projected increase in frequency of intense Atlantic hurricanes, and the associated flood risk amplification and flood effects could be offset or amplified by such factors as changes in overall storm frequency or tracks.

Sweet, W. V.↗
NASA NTRS2003

Fidelity and enhanced sensitivity of differential transcription profiles following linear amplification of nanogram amounts of endothelial mRNA

Although mRNA amplification is necessary for microarray analyses from limited amounts of cells and tissues, the accuracy of transcription profiles following amplification has not been well characterized. We tested the fidelity of differential gene expression following linear amplification by T7-mediated transcription in a well-established in vitro model of cytokine [tumor necrosis factor alpha (TNFalpha)]-stimulated human endothelial cells using filter arrays of 13,824 human cDNAs. Transcriptional profiles generated from amplified antisense RNA (aRNA) (from 100 ng total RNA, approximately 1 ng mRNA) were compared with profiles generated from unamplified RNA originating from the same homogeneous pool. Amplification accurately identified TNFalpha-induced differential expression in 94% of the genes detected using unamplified samples. Furthermore, an additional 1,150 genes were identified as putatively differentially expressed using amplified RNA which remained undetected using unamplified RNA. Of genes sampled from this set, 67% were validated by quantitative real-time PCR as truly differentially expressed. Thus, in addition to demonstrating fidelity in gene expression relative to unamplified samples, linear amplification results in improved sensitivity of detection and enhances the discovery potential of high-throughput screening by microarrays.

Evaluation Studies↗
NASA NTRS1977

Mass flow requirements for LFC wing design

The problem of determining optimum suction mass flow requirements for LFC wings is addressed. Some previous methods for predicting the extent of laminar flow over swept wings with suction are briefly reviewed. These range from the purely empirical to those utilizing tabulated linear stability computations. The present method is described. This method solves the linear, incompressible stability equations by spectral techniques. The maximum temporal amplification of boundary layer crossflow and 2-D disturbances is determined for waves of a given frequency. Group velocities are used to integrate these amplification rates along the wing to yield the logarithmic amplitude ratio or 'N factor' of the disturbance. The 'N factor' calibration of a computer code utilizing this method is described, using experimentally determined transition data. The method is shown to be as consistent as previously used 'fixed wavelength' methods.

Srokowski, A. J.↗
NASA NTRS1989

Some characteristics of bypass transition in a heated boundary layer

Experimental measurements of both mean and conditionally sampled characteristics of laminar, transitional and low Reynolds number turbulent boundary layers on a heated flat plate are presented. Measurements were obtained in air over a range of freestream turbulence intensities from 0.3 percent to 6 percent with a freestream velocity of 30.5 m/s and zero pressure gradient. Conditional sampling performed in the transitional boundary layers indicate the existence of a near-wall drop in intermittency, especially pronounced at low intermittencies. Nonturbulent intervals were observed to possess large levels of low-frequency unsteadiness, and turbulent intervals had peak intensities as much as 50 percent higher than were measured at fully turbulent stations. Heat transfer results were consistent with results of previous researchers and Reynolds analogy factors were found to be well predicted by laminar and turbulent correlations which accounted for unheated starting length. A small dependence of the turbulent Reynolds analogy factors on freestream turbulence level was observed. Laminar boundary layer spectra indicated selective amplification of unstable frequencies. These instabilities appear to play a dominant role in the transition process only for the lowest freestream turbulence level studied, however.

Sohn, K. H.↗
NASA NTRS1989

Some characteristics of bypass transition in a heated boundary layer

Experimental measurements of both mean and conditionally sampled characteristics of laminar, transitional and low Reynolds number turbulent boundary layers on a heated flat plate are presented. Measurements were obtained in air over a range of freestream turbulence intensities from 0.3 percent to 6 percent with a freestream velocity of 30.5 m/s and zero pressure gradient. Conditional sampling performed in the transitional boundary layers indicate the existence of a near-wall drop in intermittency, especially pronounced at low intermittencies. Nonturbulent intervals were observed to possess large levels of low-frequency unsteadiness, and turbulent intervals had peak intensities as much as 50 percent higher than were measured at fully turbulent stations. Heat transfer results were consistent with results of previous researches and Reynolds analogy factors were found to be well predicted by laminar and turbulent correlations which accounted for unheated starting length. A small dependence of the turbulent Reynolds analogy factors on freestream turbulence level was observed. Laminar boundary layer spectra indicated selective amplification of unstable frequencies. These instabilities appear to play a dominant role in the transition process only for the lowest freestream turbulence level studied, however.

Sohn, K. H.↗
NASA NTRS2021

A Computational Analysis of Boundary Layer Instability over the BOLT Configuration

The complex boundary layer flow over the BOLT flight configuration is known to exhibit multiple and potentially interacting instability mechanisms. This paper represents a continuation of our numerical investigation of the flow instabilities over the main test surface of the BOLT configuration by using state-of-the-art tools in multidimensional instability analysis. Specifically, the paper extends our previous computations by considering the separate effects of a nonzero angle-of-attack and a nonzero yaw on the modal instability characteristics of the boundary layer streaks adjacent to the minor-axis symmetry plane. At a selected condition from the ascent part of the anticipated flight trajectory, either type of departure from the design condition is shown to have a considerable impact on the structure of the laminar basic state and, hence, also on the amplification characteristics of the instability waves. A broader set of computations, including N-factor predictions for the relevant instabilities, will be presented in the final paper.

Boundary layer transition↗
NASA NTRS1994

Sqeezing generated by a nonlinear master equation and by amplifying-dissipative Hamiltonians

In the first part of this contribution we show that the master equation derived from the generalized version of the nonlinear Doebner-Goldin equation leads to the squeezing of one of the quadratures. In the second part we consider two familiar Hamiltonians, the Bateman- Caldirola-Kanai and the optical parametric oscillator; going back to their classical Lagrangian form we introduce a stochastic force and a dissipative factor. From this new Lagrangian we obtain a modified Hamiltonian that treats adequately the simultaneous amplification and dissipation phenomena, presenting squeezing, too.

Dodonov, V. V.↗