Smoothing-Based Relative Navigation & Coded Aperture Imaging: Time-windowed Smoothing for Multi-Satellite State Estimation
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Alvar Saenz-otero↗
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Spline-Based Smoothing of Airfoil Curvatures
Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been extensively tested on a number of supercritical airfoil data sets generated by inverse design and optimization computer programs. All of the smoothing results show that CFACS is able to generate unbiased smooth fits of curvature profiles, trading small modifications of geometry for increasing curvature smoothness by eliminating curvature oscillations and bumps (see figure).
Li, W.↗
Diamond Smoothing Tools
Diamond smoothing tools have been proposed for use in conjunction with diamond cutting tools that are used in many finish-machining operations. Diamond machining (including finishing) is often used, for example, in fabrication of precise metal mirrors. A diamond smoothing tool according to the proposal would have a smooth spherical surface. For a given finish machining operation, the smoothing tool would be mounted next to the cutting tool. The smoothing tool would slide on the machined surface left behind by the cutting tool, plastically deforming the surface material and thereby reducing the roughness of the surface, closing microcracks and otherwise generally reducing or eliminating microscopic surface and subsurface defects, and increasing the microhardness of the surface layer. It has been estimated that if smoothing tools of this type were used in conjunction with cutting tools on sufficiently precise lathes, it would be possible to reduce the roughness of machined surfaces to as little as 3 nm. A tool according to the proposal would consist of a smoothing insert in a metal holder. The smoothing insert would be made from a diamond/metal functionally graded composite rod preform, which, in turn, would be made by sintering together a bulk single-crystal or polycrystalline diamond, a diamond powder, and a metallic alloy at high pressure. To form the spherical smoothing tip, the diamond end of the preform would be subjected to flat grinding, conical grinding, spherical grinding using diamond wheels, and finally spherical polishing and/or buffing using diamond powders. If the diamond were a single crystal, then it would be crystallographically oriented, relative to the machining motion, to minimize its wear and maximize its hardness. Spherically polished diamonds could also be useful for purposes other than smoothing in finish machining: They would likely also be suitable for use as heat-resistant, wear-resistant, unlubricated sliding-fit bearing inserts.
Voronov, Oleg↗
Estimation of Smoothing Error in SBUV Profile and Total Ozone Retrieval
Data from the Nimbus-4, Nimbus-7 Solar Backscatter Ultra Violet (SBUV) and seven of the NOAA series of SBUV/2 instruments spanning 41 years are being reprocessed using V8.6 algorithm. The data are scheduled to be released by the end of August 2011. An important focus of the new algorithm is to estimate various sources of errors in the SBUV profiles and total ozone retrievals. We discuss here the smoothing errors that describe the components of the profile variability that the SBUV observing system can not measure. The SBUV(/2) instruments have a vertical resolution of 5 km in the middle stratosphere, decreasing to 8 to 10 km below the ozone peak and above 0.5 hPa. To estimate the smoothing effect of the SBUV algorithm, the actual statistics of the fine vertical structure of ozone profiles must be known. The covariance matrix of the ensemble of measured ozone profiles with the high vertical resolution would be a formal representation of the actual ozone variability. We merged the MLS (version 3) and sonde ozone profiles to calculate the covariance matrix, which in general case, for single profile retrieval, might be a function of the latitude and month. Using the averaging kernels of the SBUV(/2) measurements and calculated total covariance matrix one can estimate the smoothing errors for the SBUV ozone profiles. A method to estimate the smoothing effect of the SBUV algorithm is described and the covariance matrixes and averaging kernels are provided along with the SBUV(/2) ozone profiles. The magnitude of the smoothing error varies with altitude, latitude, season and solar zenith angle. The analysis of the smoothing errors, based on the SBUV(/2) monthly zonal mean time series, shows that the largest smoothing errors were detected in the troposphere and might be as large as 15-20% and rapidly decrease with the altitude. In the stratosphere above 40 hPa the smoothing errors are less than 5% and between 10 and 1 hPa the smoothing errors are on the order of 1%. We validate our estimated smoothing errors by comparing the SBUV ozone profiles with other ozone profiling sensors.
Kramarova, N. A.↗
Employing Relaxed Smoothness Constraints on Imaginary Part of Refractive Index in AERONET Aerosol Retrieval Algorithm
In the Aerosol Robotic Network (AERONET) retrieval algorithm, smoothness constraints on the imaginary part of the refractive index provide control of retrieved spectral dependence of aerosol absorption by preventing the inversion code from fitting the noise in optical measurements and thus avoiding unrealistic oscillations of retrievals with wavelength. The history of implementation of the smoothness constraints in the AERONET retrieval algorithm is discussed. It is shown that the latest version of the smoothness constraints on the imaginary part of refractive index, termed standard and employed by Version 3 of the retrieval algorithm, should be modified to account for strong variability of light absorption by brown-carbon-containing aerosols in UV through mid-visible parts of the solar spectrum. In Version 3 strong spectral constraints were imposed at high values of the Ångström exponent (440–870 nm) since black carbon was assumed to be the primary absorber, while the constraints became increasingly relaxed as aerosol exponent deceased to allow for wavelength dependence of absorption for dust aerosols. The new version of the smoothness constraints on the imaginary part of the refractive index assigns different weights to different pairs of wavelengths, which are the same for all values of the Ångström exponent. For example, in the case of four-wavelength input, the weights assigned to short-wavelength pairs (440–675, 675–870 nm) are small so that smoothness constraints do not suppress natural spectral variability of the imaginary part of the refractive index. At longer wavelengths (870–1020 nm), however, the weight is 10 times higher to provide additional constraints on the imaginary part of refractive index retrievals of aerosols with a high Ångström exponent due to low sensitivity to aerosol absorption for longer channels at relatively low aerosol optical depths. The effect of applying the new version of smoothness constraints, termed relaxed, on retrievals of single-scattering albedo is analyzed for case studies of different aerosol types: black- and brown-carbon-containing fine mode aerosols, mineral dust coarse mode aerosols, and urban industrial fine mode aerosol. It is shown that for brown-carbon-containing aerosols employing the relaxed smoothness constraints resulted in significant reduction in retrieved single-scattering albedo and spectral residual errors (compared to standard) at the short wavelengths. For example, biomass burning smoke cases showed a reduction in single-scattering albedo and spectral residual error at 380 nm of ∼ 0.033 and ∼ 17 %, respectively, for the Rexburg site and ∼ 0.04 and ∼ 12.7 % for the Rimrock site, both AERONET sites in Idaho, USA. For a site with very high levels of black-carbon-containing aerosols (Mongu, Zambia), the effect of modification in the smoothness constraints was minor. For mineral dust aerosols at small Ångström exponent values (Mezaira site, UAE), the spectral constraint on the imaginary part of the refractive index was already relaxed in Version 3; therefore the new relaxed constraint results in minimal change. In the case of weakly absorbing urban industrial aerosols at the GSFC site, there are significant changes in retrieved single-scattering albedo using relaxed assumption, especially reductions at longer wavelengths: ∼ 0.016 and ∼ 0.02 at 875 and 1020 nm, respectively, for 440 nm aerosol optical depth (AOD) ∼ 0.3. The modification of smoothness constraints on the imaginary part of the refractive index has a minor effect on retrievals of other aerosol parameters such as the real part of the refractive index and parameters of the aerosol size distribution. The implementation of the relaxed smoothness constraints on the imaginary part of the refractive index in the next version of the AERONET inversion algorithm will produce significant impacts at some sites in short wavelength channels (380 and 440 nm) for some biomass burning smoke cases with significant brown carbon content and possibly in mid-visible channels (500 and 675 nm) to near-infrared channels (870 to 1020 nm) for some urban industrial aerosol types. However, most differences in single-scattering albedo retrievals between those applying the new relaxed constraint and the standard constraint will be within the uncertainty of the single-scattering albedo retrievals, depending on the level of aerosol optical depth, Ångström exponent, brown carbon content and wavelength.
Aliaksandr Siniuk↗
On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equation
The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation and related models is considered. Here, this work investigates the underlying Hamiltonian structure of such smoothed particle-based methods for Hamiltonian systems and the small-scale regularization such methods implicitly make in approximating the continuum theory. In the context of the Vlasov–Poisson equation and other mean-field Lie–Poisson systems, of which Vlasov–Poisson is a special case, smoothing amounts to a convolutive regularization of the Hamiltonian. This regularization may be interpreted as a change of the inner product structure used to identify the dual space in the Lie–Poisson Hamiltonian formulation. In particular, the shape function used for spatial smoothing may be identified as the kernel function of a reproducing kernel Hilbert space whose inner product is used to define the Lie–Poisson Hamiltonian structure. It is likewise possible to introduce smoothing in the Vlasov–Maxwell system, but in this case the Poisson bracket must be modified rather than the Hamiltonian. The smoothing applied to the Vlasov–Maxwell system is incorporated by inserting smoothing in the map from canonical to kinematic coordinates. In the filtered system, the Lorentz force law and the current, the two terms coupling the Vlasov equation with Maxwell’s equations, are spatially smoothed.
Hamiltonian mechanics↗
Leiomodin and tropomodulin in smooth muscle
Evidence is accumulating to suggest that actin filament remodeling is critical for smooth muscle contraction, which implicates actin filament ends as important sites for regulation of contraction. Tropomodulin (Tmod) and smooth muscle leiomodin (SM-Lmod) have been found in many tissues containing smooth muscle by protein immunoblot and immunofluorescence microscopy. Both proteins cofractionate with tropomyosin in the Triton-insoluble cytoskeleton of rabbit stomach smooth muscle and are solubilized by high salt. SM-Lmod binds muscle tropomyosin, a biochemical activity characteristic of Tmod proteins. SM-Lmod staining is present along the length of actin filaments in rat intestinal smooth muscle, while Tmod stains in a punctate pattern distinct from that of actin filaments or the dense body marker alpha-actinin. After smooth muscle is hypercontracted by treatment with 10 mM Ca(2+), both SM-Lmod and Tmod are found near alpha-actinin at the periphery of actin-rich contraction bands. These data suggest that SM-Lmod is a novel component of the smooth muscle actin cytoskeleton and, furthermore, that the pointed ends of actin filaments in smooth muscle may be capped by Tmod in localized clusters.
Carrier Proteins/analysis/genetics/metabolism↗
Computer programs for smoothing and scaling airfoil coordinates
Detailed descriptions are given of the theoretical methods and associated computer codes of a program to smooth and a program to scale arbitrary airfoil coordinates. The smoothing program utilizes both least-squares polynomial and least-squares cubic spline techniques to smooth interatively the second derivatives of the y-axis airfoil coordinates with respect to a transformed x-axis system which unwraps the airfoil and stretches the nose and trailing-edge regions. The corresponding smooth airfoil coordinates are then determined by solving a tridiagonal matrix of simultaneous cubic-spline equations relating the y-axis coordinates and their corresponding second derivatives. A technique for computing the camber and thickness distribution of the smoothed airfoil is also discussed. The scaling program can then be used to scale the thickness distribution generated by the smoothing program to a specific maximum thickness which is then combined with the camber distribution to obtain the final scaled airfoil contour. Computer listings of the smoothing and scaling programs are included.
Morgan, H. L., Jr.↗
Interpreting SBUV Smoothing Errors: an Example Using the Quasi-biennial Oscillation
The Solar Backscattered Ultraviolet (SBUV) observing system consists of a series of instruments that have been measuring both total ozone and the ozone profile since 1970. SBUV measures the profile in the upper stratosphere with a resolution that is adequate to resolve most of the important features of that region. In the lower stratosphere the limited vertical resolution of the SBUV system means that there are components of the profile variability that SBUV cannot measure. The smoothing error, as defined in the optimal estimation retrieval method, describes the components of the profile variability that the SBUV observing system cannot measure. In this paper we provide a simple visual interpretation of the SBUV smoothing error by comparing SBUV ozone anomalies in the lower tropical stratosphere associated with the quasi-biennial oscillation (QBO) to anomalies obtained from the Aura Microwave Limb Sounder (MLS). We describe a methodology for estimating the SBUV smoothing error for monthly zonal mean (mzm) profiles. We construct covariance matrices that describe the statistics of the inter-annual ozone variability using a 6 yr record of Aura MLS and ozonesonde data. We find that the smoothing error is of the order of 1percent between 10 and 1 hPa, increasing up to 15-20 percent in the troposphere and up to 5 percent in the mesosphere. The smoothing error for total ozone columns is small, mostly less than 0.5 percent. We demonstrate that by merging the partial ozone columns from several layers in the lower stratosphere/troposphere into one thick layer, we can minimize the smoothing error. We recommend using the following layer combinations to reduce the smoothing error to about 1 percent: surface to 25 hPa (16 hPa) outside (inside) of the narrow equatorial zone 20 S-20 N.
ozone profile retrievals↗
Experimental and numerical investigation of fracture conductivity between non-smooth rock surfaces with and without proppant
The enhancement of fracture conductivity is vital for the efficient recovery of subsurface resources, such as geothermal energy and petroleum hydrocarbons. Proppants, granular materials injected into hydraulic fractures to maintain their conductivity, have been studied primarily in the context of smooth fractures (i.e., fractures between smooth rock surfaces). However, non-smooth fractures (i.e., fractures between rough rock surfaces) are common in geoenergy reservoirs and thus require further investigations. In this study, we conducted laboratory measurements of fracture conductivity on shale slabs with non-smooth surfaces and carried out numerical simulation using the lattice Boltzmann (LB) method, which aimed to investigate the conductivity of non-smooth fractures with and without proppants placement. When ceramic proppant with an areal concentration of 2 lb/ft 2 was placed in the fracture, the conductivity was enhanced by roughly 3-8 times compared to fractures without proppant. In fractures with proppant, gas-measured conductivity was higher than that measured with water due to proppant embedment caused by water. The experiments demonstrate the advantages of using proppant in fractures, even if the rock surface roughness can provide certain fracture conductivity via the self-propping mechanism. For fractures without proppants, high rock surface roughness is not necessarily favorable for enhancing fracture conductivity because the self-propping mechanism requires shear slip along the fracture surface. If there is no shear slip, high rock surface roughness can cause a detrimental effect on the fracture conductivity due to the interlocking effect. Utilizing advanced experimental equipment and LB modeling, this research explores the interplays between proppant placement, fracture geometry, and stress conditions to develop a comprehensive understanding of the productivity in non-smooth fractures. Further, the outcomes of this investigation indicate the importance of creating fractures with surface roughness during hydraulic fracturing and will contribute to the development of more efficient stimulation techniques for subsurface energy extraction.
15 GEOTHERMAL ENERGY↗
A User Guide for Smoothing Air Traffic Radar Data
Matlab software was written to provide smoothing of radar tracking data to simulate ADS-B (Automatic Dependent Surveillance-Broadcast) data in order to test a tactical conflict probe. The probe, called TSAFE (Tactical Separation-Assured Flight Environment), is designed to handle air-traffic conflicts left undetected or unresolved when loss-of-separation is predicted to occur within approximately two minutes. The data stream that is down-linked from an aircraft equipped with an ADS-B system would include accurate GPS-derived position and velocity information at sample rates of 1 Hz. Nation-wide ADS-B equipage (mandated by 2020) should improve surveillance accuracy and TSAFE performance. Currently, position data are provided by Center radar (nominal 12-sec samples) and Terminal radar (nominal 4.8-sec samples). Aircraft ground speed and ground track are estimated using real-time filtering, causing lags up to 60 sec, compromising performance of a tactical resolution tool. Offline smoothing of radar data reduces wild-point errors, provides a sample rate as high as 1 Hz, and yields more accurate and lag-free estimates of ground speed, ground track, and climb rate. Until full ADS-B implementation is available, smoothed radar data should provide reasonable track estimates for testing TSAFE in an ADS-B-like environment. An example illustrates the smoothing of radar data and shows a comparison of smoothed-radar and ADS-B tracking. This document is intended to serve as a guide for using the smoothing software.
Center/Tracon Radar↗
An adaptive data-smoothing routine
An adaptive noise reduction algorithm that can be implemented on a microcomputer is developed. Smoothing polynomials are used where the polynomial coefficients are chosen such that the mean-square-error between the noisy and smoothed data is minimized. This approach is equivalent to the implementation of a low-pass finite impulse response filter. The noise reduction depends on the order of the smoothing polynomial. A whiteness test on the error sequence is incorporated to search for the optimal smoothing. Expansion coefficients may be computed via the fast Fourier transform, and the resulting smoothing process is the equivalent of the implementation of an adaptive ideal low-pass filter. Results are obtained for an analytical signal with added white Gaussian noise. The routine may be applied to any smooth signal with additive random noise.
Taylor, Clayborne D.↗
Comparison of Predictable Smooth Ocular and Combined Eye-Head Tracking Behaviour in Patients with Lesions Affecting the Brainstem and Cerebellum
We compared the ability of eight normal subjects and 15 patients with brainstem or cerebellar disease to follow a moving visual stimulus smoothly with either the eyes alone or with combined eye-head tracking. The visual stimulus was either a laser spot (horizontal and vertical planes) or a large rotating disc (torsional plane), which moved at one sinusoidal frequency for each subject. The visually enhanced Vestibulo-Ocular Reflex (VOR) was also measured in each plane. In the horizontal and vertical planes, we found that if tracking gain (gaze velocity/target velocity) for smooth pursuit was close to 1, the gain of combined eye-hand tracking was similar. If the tracking gain during smooth pursuit was less than about 0.7, combined eye-head tracking was usually superior. Most patients, irrespective of diagnosis, showed combined eye-head tracking that was superior to smooth pursuit; only two patients showed the converse. In the torsional plane, in which optokinetic responses were weak, combined eye-head tracking was much superior, and this was the case in both subjects and patients. We found that a linear model, in which an internal ocular tracking signal cancelled the VOR, could account for our findings in most normal subjects in the horizontal and vertical planes, but not in the torsional plane. The model failed to account for tracking behaviour in most patients in any plane, and suggested that the brain may use additional mechanisms to reduce the internal gain of the VOR during combined eye-head tracking. Our results confirm that certain patients who show impairment of smooth-pursuit eye movements preserve their ability to smoothly track a moving target with combined eye-head tracking.
Grant, Michael P.↗
Radiative Smoothing in Clouds at Transparent and Absorbing Wavelengths
For absorbing and transparent wavelengths, we discuss the effect of horizontal solar radiative fluxes in clouds on the accuracy of a conventional plane-parallel radiative transfer calculations for a single pixel, known as the Independent Pixel Approximation (IPA). We address the question of correlations between horizontal fluxes, IPA accuracies and radiative smoothing. By smoothing we understand a radiative transfer process whereby radiation does not follow the small-scale fluctuations of cloud structure, producing much smoother radiation fields. The scale eta that characterizes this process is called "radiative smoothing scale." We relate radiative smoothing to the photon's horizontal displacement that characterizes a "spot" of reflected light associated with a point source. We generalize the "spot-size" estimate derived for conservative scattering using the diffusion theory to the case of non-conservative scattering. For reflected light, theoretical results are confirmed with numerical simulations. The radiative smoothing scale eta is a critical value where IPA effectively breaks down; for scales smaller than TI, real radiation field are much smoother than their IPA counterparts for the same cloud structure. In addition to the estimate of il for absorbing wavelengths, we show that: (1) with more absorption, the scale break determined by eta in a log-log plot of wavenumber spectra moves towards smaller scales and (2) the smaller eta the flatter the small-scale slope which means less radiative smoothing, thus more accuracy in the IPA reflection.
Marshak, A.↗
A Smoothed Augmented Lagrangian Framework for Convex Optimization with Nonsmooth Constraints
Augmented Lagrangian (AL) methods have proven remarkably useful in solving optimization problems with complicated constraints. The last decade has seen the development of overall complexity guarantees for inexact AL variants. Yet, a crucial gap persists in addressing nonsmooth convex constraints. To this end, we present a smoothed augmented Lagrangian (AL) framework where nonsmooth terms are progressively smoothed with a smoothing parameter $\eta _k$ . The resulting AL subproblems are $\eta _k$ -smooth, allowing for leveraging accelerated schemes. By a careful selection of the inexactness level $\epsilon _k$ (for inexact subproblem resolution), the penalty parameter $\rho _k$ , and smoothing parameter $\eta _k$ at epoch k, we derive rate and complexity guarantees of $\tilde{\mathcal {O}}(1/{\varepsilon }^{3/2})$ and $\tilde{\mathcal {O}}(1/{\varepsilon })$ in convex and strongly convex regimes for computing an ${\varepsilon }$ -optimal solution, when $\rho _k$ increases at a geometric rate, a significant improvement over the best available guarantees for AL schemes for convex programs with nonsmooth constraints. Analogous guarantees are developed for settings with $\rho _k = \rho$ as well as $\eta _k = \eta$ . Preliminary numerics on a fused Lasso problem display promise.
augmented Lagrangian↗
Surface smoothing for laser powder-bed Ti-6Al-4V by a transient liquid phase
Surface roughness is the primary driver of fatigue for additively manufactured metals. To address surface roughness, this work introduces a new method to smooth features beyond line-of-sight without material removal. The method applies a coating that triggers local surface remelting by activating a eutectic reaction during heat treatment. The associated liquid phase then wets and isothermally solidifies into a smoother surface. For Ti-6Al-4V fabricated with laser powder bed fusion, samples with and without TLP smoothing (using a Cu coating) were characterized with a suite of techniques, including mechanical testing, electron backscatter diffraction, synchrotron X-ray tomography, and fractography. TLP smoothing reduced surface roughness by 80% and amplified compressive residual stress at the surface by about 50%. With statistically equivalent virtual microstructures, crystal plasticity scrutinized the roles of phases, porosity, and surface roughness. Although the tensile strain-to-failure was reduced to 1% strain, the TLP smoothing process increased high-cycle fatigue strength by about 20% compared to control samples, pointing to future opportunities to optimize the new process through various coating compositions and heat treatment schedules. Overall, this work establishes a new paradigm for treating surfaces of materials for smoothness and compressive residual stress.
Additive manufacturing↗
Recursive algorithms for two-dimensional smoothing using bicubic hermite polynomial
It is noted that in the past, smoothing splines originated from approximation theory have been successfully applied to data filtering and image smoothing problems. Even though the nonrecursive technique of smoothing splines gives an optimal solution, the amount of computation increases rapidly with the size of the two-dimensional data. A derivation is presented here of quarter-plane filtering algorithms that provide smoothed estimates of function values and their derivatives by fitting two-dimensional smoothing splines in a recursive manner. The derivation procedure sheds light on specific problems encountered in two-dimensional filtering problems. What is more, the amount of computation for this recursive processor increases only linearly with the size of the two-dimensional data. Because of certain approximations introduced in its derivation, this recursive processor becomes suboptimal.
Kim, C. S.↗
The turbulent thermal boundary layer with an abrupt change from a rough to a smooth wall
The work reported here was motivated by concern over the use of smooth heat flux gages for heat transfer measurements on the otherwise rough turbine blades. Stanton number distributions and boundary layer profiles of mean temperature, mean velocity, and turbulence intensity are reported for a surface with a step change from a rough to a smooth surface. In most cases, the Stanton number immediately downstream of the change in roughness drops below the all-smooth-wall data at the same x-Reynolds number. The alignment of the smooth surface between the bases and crests of the roughness elements is shown to have only a weak effect on the Stanton number distribution. It is concluded that the use of smooth heat flux gages on otherwise rough surfaces can cause large errors. It is recommended that heat transfer data collected in this manner be used with caution.
Taylor, Robert P.↗