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NASA NTRS1996

A Revised Thermosphere for the Mars Global Reference Atmospheric Model (Mars-GRAM Version 3.4)

This report describes the newly-revised model thermosphere for the Mars Global Reference Atmospheric Model (Mars-GRAM, Version 3.4). It also provides descriptions of other changes made to the program since publication of the programmer's guide for Mars-GRAM Version 3.34. The original Mars-GRAM model thermosphere was based on the global-mean model of Stewart. The revised thermosphere is based largely on parameterizations derived from output data from the three-dimensional Mars Thermospheric Global Circulation Model (MTGCM). The new thermospheric model includes revised dependence on the 10.7 cm solar flux for the global means of exospheric temperature, temperature of the base of the thermosphere, and scale height for the thermospheric temperature variations, as well as revised dependence on orbital position for global mean height of the base of the thermosphere. Other features of the new thermospheric model are: (1) realistic variations of temperature and density with latitude and time of day, (2) more realistic wind magnitudes, based on improved estimates of horizontal pressure gradients, and (3) allowance for user-input adjustments to the model values for mean exospheric temperature and for height and temperature at the base of the thermosphere. Other new features of Mars-GRAM 3.4 include: (1) allowance for user-input values of climatic adjustment factors for temperature profiles from the surface to 75 km, and (2) a revised method for computing the sub-solar longitude position in the 'ORBIT' subroutine.

Justus, C. G.↗
NASA NTRS1996

An Experimental Study of a Separated/Reattached Flow Behind a Backward-Facing Step. Re(sub h) = 37,000

An experimental study was carried out to investigate turbulent structure of a two-dimensional incompressible separating/reattaching boundary layer behind a backward-facing step. Hot-wire measurement technique was used to measure three Reynolds stresses and higher-order mean products of velocity fluctuations. The Reynolds number, Re(sub h), based on the step height, h, and the reference velocity, U(sub 0), was 37,000. The upstream oncoming flow was fully developed turbulent boundary layer with the Re(sub theta) = 3600. All turbulent properties, such as Reynolds stresses, increase dramatically downstream of the step within an internally developing mixing layer. Distributions of dimensionless mean velocity, turbulent quantities and antisymmetric distribution of triple velocity products in the separated free shear layer suggest that the shear layer above the recirculating region strongly resembles free-shear mixing layer structure. In the reattachment region close to the wall, turbulent diffusion term balances the rate of dissipation since advection and production terms appear to be negligibly small. Further downstream, production and dissipation begin to dominate other transport processes near the wall indicating the growth of an internal turbulent boundary layer. In the outer region, however, the flow still has a memory of the upstream disturbance even at the last measuring station of 51 step-heights. The data show that the structure of the inner layer recovers at a much faster rate than the outer layer structure. The inner layer structure resembles the near-wall structure of a plane zero pressure-gradient turbulent boundary layer (plane TBL) by 25h to 30h, while the outer layer structure takes presumably over 100h.

Jovic, Srba↗
NASA NTRS1996

Hypersonic Boundary-Layer Stability Experiments on a Flared-Cone Model at Angle of Attack in a Quiet Wind Tunnel

An experimental investigation of the effects of angle of attack on hypersonic boundary-layer stability on a flared-cone model was conducted in the low-disturbance Mach-6 Nozzle-Test Chamber Facility at NASA Langley Research Center. This unique facility provided a 'quiet' flow test environment which is well suited for stability experiments because the low levels of freestream 'noise' minimize artificial stimulation of flow-disturbance growth. Surface pressure and temperature measurements documented the adverse-pressure gradient and transition-onset location. Hot-wire anemometry diagnostics were applied to identify the instability mechanisms which lead to transition. In addition, the mean flow over the flared-cone geometry was modeled by laminar Navier-Stokes computations. Results show that the boundary layer becomes more stable on the windward ray and less stable on the leeward ray relative to the zero-degree angle-of-attack case. The second-mode instability dominates the transition process at a zero-degree angle of attack, however, on the windward ray at an angle of attack this mode was completely stabilized. The less-dominant first-mode instability was slightly destabilized on the windward ray. Non-linear mechanisms such as saturation and harmonic generation are identified from the flow-disturbance bispectra.

Doggett, Glen P.↗
NASA NTRS1994

An Experimental Simulation of Flap Flow on Multielement Airfoils at High Reynolds Number

The design of the high lift system has a major impact on the performance of an aircraft yet our understanding of the physics of this flow is still weak. Flow features include interactions between the wakes shed from the upstream elements and the pressure gradients and boundary layers of the downstream elements. Interaction of the turbulent wake of the main element and the flap can cause (1) separation of the flap boundary layer or (2) 'bursting' of the main airfoil wake. Although the first factor is at least partially understood, even the qualitative aspects of (2) remain to be determined. In order to study these phenomena at Reynolds numbers approaching those of flight, a thick high Reynolds number wake is created using a 24 foot flat plate in the long rectangular test section of a 4 ft. by 6 ft subsonic wind tunnel. The design and construction of this test section, plate, and accompanying flap is described. Results obtained in a quarter-scale model were used for design purposes and are also described. Construction of the full scale facility is complete and preliminary results are presented.

Schneider, S.↗
NASA NTRS1997

Factors Influencing Pitot Probe Centerline Displacement in a Turbulent Supersonic Boundary Layer

When a total pressure probe is used for measuring flows with transverse total pressure gradients, a displacement of the effective center of the probe is observed (designated Delta). While this phenomenon is well documented in incompressible flow and supersonic laminar flow, there is insufficient information concerning supersonic turbulent flow. In this study, three NASA Lewis Research Center Supersonic Wind Tunnels (SWT's) were used to investigate pitot probe centerline displacement in supersonic turbulent boundary layers. The relationship between test conditions and pitot probe centerline displacement error was to be determined. For this investigation, ten circular probes with diameter-to-boundary layer ratios (D/delta) ranging from 0.015 to 0.256 were tested in the 10 ft x 10 ft SWT, the 15 cm x 15 cm SWT, and the 1 ft x 1 ft SWT. Reynolds numbers of 4.27 x 10(exp 6)/m, 6.00 x 10(exp 6)/in, 10.33 x 10(exp 6)/in, and 16.9 x 10(exp 6)/m were tested at nominal Mach numbers of 2.0 and 2.5. Boundary layer thicknesses for the three tunnels were approximately 200 mm, 13 mm, and 30 mm, respectively. Initial results indicate that boundary layer thickness, delta, and probe diameter, D/delta play a minimal role in pitot probe centerline offset error, Delta/D. It appears that the Mach gradient, dM/dy, is an important factor, though the exact relationship has not yet been determined. More data is needed to fill the map before a conclusion can be drawn with any certainty. This research provides valuable supersonic, turbulent boundary layer data from three supersonic wind tunnels with three very different boundary layers. It will prove a valuable stepping stone for future research into the factors influencing pitot probe centerline offset error.

Grosser, Wendy I.↗
NASA NTRS1997

A Unique Test Facility to Measure Liner Performance with a Summary of Initial Test Results

A very ambitious study was initiated to obtain detailed acoustic and flow data with and without a liner in a duct containing a mean flow so that available theoretical models of duct liners can be validated. A unique flow-duct facility equipped with a sound source, liner box, flush-walled microphones, traversable microphones and traversable pressure and temperature probes was built. A unique set of instrumentation boxes equipped with computer controlled traverses were designed and built that allowed measurements of Mach number, temperature, SPLs and phases in two planes upstream of a liner section and two planes downstream at a large number of measurement points. Each pair of planes provided acoustic pressure gradients for use in estimating the particle velocities. Specially-built microphone probes were employed to make measurements in the presence of the flow. A microphone traverse was also designed to measure the distribution of SPLs and phases from the beginning of the liner to its end along the duct axis. All measurements were made with the help of cross-correlation techniques to reject flow noise and/or other obtrusive noise, if any. The facility was designed for future use at temperatures as high as 1500 F. In order to validate 2-D models in the presence of mean flow, the flow duct was equipped with a device to modify boundary layer flow on the smaller sides of a rectangular duct to simulate 2-D flow. A massive amount of data was acquired for use in validating duct liner models and will be provided to NASA in an electronic form. It was found that the sound in the plane-wave regime is well behaved within the duct and the results are repeatable from one run to another. At the higher frequencies corresponding to the higher-order modes, the SPLs within a duct are not repeatable from run to run. In fact, when two or more modes have the same frequency (i.e., for the degenerate modes), the SPLs in the duct varied between 2 dB to 12 dB from run to run. This made the calibration of the microphone probes extremely difficult at the higher frequencies.

Ahuja, K. K.↗
NASA NTRS1997

A Review of Hypersonic Boundary Layer Stability Experiments in a Quiet Mach 6 Wind Tunnel

Three recent experimental studies of transition on cones with adverse pressure gradient produced by a flared afterbody and with the additive stability modifiers of wall cooling, angle of attack and bluntness are reviewed. All tests were conducted in a quiet Mach 6 wind tunnel. The dominant instability was found to be the second mode. For the cases examined with linear stability theory, the N factors at mode saturation were in the range of 8.5 to 11. Evidence of a combined second-mode/Gortler transition process was found. Mean, rms and spectral freestream data for the quiet facility is presented and the role of low frequency freestream noise is discussed.

Wilkinson, Stephen P.↗
NASA NTRS1994

Interaction of Oblique Instability Waves with a Nonlinear Plane Wave

This paper is concerned with the downstream evolution of a resonant triad of initially non-interacting linear Instability waves in a boundary layer with a weak adverse pressure gradient. The triad consists of a two-dimensional fundamental mode and a pair of equal-amplitude oblique modes that form a subharmonic standing wave in the spanwise direction. The growth rates are small and there is a well-defined common critical layer for these waves. As in Goldstein & Lee (1992), the wave interaction takes place entirely within this critical layer and is initially of the parametric-resonance type. This enhances the spatial growth rate of the subharmonic but does not affect that of the fundamental. However, in contrast to Goldstein & Lee (1992), the initial subharmonic amplitude is assumed to be small enough so that the fundamental can become nonlinear within its own critical layer before it is affected by the subharmonic. The subharmonic evolution is then dominated by the parametric-resonance effects and occurs on a much shorter streamwise scale than that of the fundamental. The subharmonic amplitude continues to increase during this parametric-resonance stage - even as the growth rate of the fundamental approaches zero - and the subharmonic eventually becomes large enough to influence the fundamental which causes both waves to evolve on the same shorter streamwise scale.

Wundrow, David W.↗
NASA NTRS1995

Upper Thermosphere Winds and Temperatures in the Geomagnetic Polar Cap: Solar Cycle, Geomagnetic Activity, and Interplanetary Magnetic Field Dependencies

Ground-based Fabry-Perot interferometers located at Thule, Greenland (76.5 deg. N, 69.0 deg. W, lambda = 86 deg.) and at Sondre Stromfjord, Greenland (67.0 deg. N, 50.9 deg. W, lambda = 74 deg.) have monitored the upper thermospheric (approx. 240-km altitude) neutral wind and temperature over the northern hemisphere geomagnetic polar cap since 1983 and 1985, respectively. The thermospheric observations are obtained by determining the Doppler characteristics of the (OI) 15,867-K (630.0-nm) emission of atomic oxygen. The instruments operate on a routine, automatic, (mostly) untended basis during the winter observing seasons, with data coverage limited only by cloud cover and (occasional) instrument failures. This unique database of geomagnetic polar cap measurements now extends over the complete range of solar activity. We present an analysis of the measurements made between 1985 (near solar minimum) and 1991 (near solar maximum), as part of a long-term study of geomagnetic polar cap thermospheric climatology. The measurements from a total of 902 nights of observations are compared with the predictions of two semiempirical models: the Vector Spherical Harmonic (VSH) model of Killeen et al. (1987) and the Horizontal Wind Model (HWM) of Hedin et al. (1991). The results are also analyzed using calculations of thermospheric momentum forcing terms from the Thermosphere-ionosphere General Circulation Model TGCM) of the National Center for Atmospheric Research (NCAR). The experimental results show that upper thermospheric winds in the geomagnetic polar cap have a fundamental diurnal character, with typical wind speeds of about 200 m/s at solar minimum, rising to up to about 800 m/s at solar maximum, depending on geomagnetic activity level. These winds generally blow in the antisunward direction, but are interrupted by episodes of modified wind velocity and altered direction often associated with changes in the orientation of the Interplanetary Magnetic Field (IMF). The central polar cap (greater than approx. 80 magnetic latitude) antisunward wind speed is found to be a strong function of both solar and geomagnetic activity. The polar cap temperatures show variations in both solar and geomagnetic activity, with temperatures near 800 K for low K(sub p) and F(sub 10.7) and greater than about 2000 K for high K(sub p) and F(sub 10.7). The observed temperatures are significantly greater than those predicted by the mass spectrometer/incoherent scatter model for high activity conditions. Theoretical analysis based on the NCAR TIGCM indicates that the antisunward upper thermospheric winds, driven by upstream ion drag, basically 'coast' across the polar cap. The relatively small changes in wind velocity and direction within the polar cap are induced by a combination of forcing terms of commensurate magnitude, including the nonlinear advection term, the Coriolis term, and the pressure gradient force term. The polar cap thennospheric thermal balance is dominated by horizontal advection, and adiabatic and thermal conduction terms.

Killeen, T. L.↗
NASA NTRS1996

Observations of Thermospheric Horizontal Winds at Watson Lake, Yukon Territory (lambda=65 Deg N)

Fabry-Perot interferometer observations of the thermospheric O I (6300 A) emission have been conducted from an airglow observatory at a dark field site in the southeastern Yukon Territory, Canada, for the period November 1991 to April 1993. The experiment operated in unattended, remote fashion, has resulted in a substantial data set from which mean neutral winds have been determined. Dependent upon geomagnetic activity, the nocturnal location of the site is either equatorward of the auroral oval or within oval boundaries. The data set is rich enough to permit hourly binning of neutral winds based upon the K(sub p) geomagnetic disturbance index as well as the season. For cases of low geomagnetic activity the averaged vector horizontal neutral wind exhibits the characteristics of a midlatitude site displaying antisunward pressure-gradient-driven winds. As the geomagnetic activity rises in the late afternoon and evening winds slowly rotate sunward in an anticlockwise direction, initially remaining near 100 m/s in speed but eventually increasing to 300 m/s for K(sub p) greater than 5. For the higher levels of activity the observed neutral wind flow pattern resembles a higher-latitude polar cap pattern characterized by ion drag forcing of thermospheric neutral gases. In addition, rotational Coriolis forcing on the dusk side enhances the ion drag forcing, resulting in dusk winds which trace out the clockwise dusk cell plasma flow. On the dawn side the neutral winds also rotate in an anticlockwise direction as the strength of geomagnetic disturbances increase. Since the site is located at a transition latitude between the midlatitude and the polar cap the data set provides a sensitive test for general circulation models which attempt to parameterize the contribution of magnetospheric processes. A comparison with the Vector Spherical Harmonic (VSH) model indicates several regions of poor correspondence for December solstice conditions but reasonable agreement for the vernal equinox.

Niciejewski, R. J.↗
NASA NTRS1997

Laser Anemometer Measurements of the Flow Field in a 4:1 Pressure Ratio Centrifugal Impeller

A laser-doppler anemometer was used to obtain flow-field velocity measurements in a 4:1 pressure ratio, 4.54 kg/s (10 lbm/s), centrifugal impeller, with splitter blades and backsweep, which was configured with a vaneless diffuser. Measured through-flow velocities are reported for ten quasi-orthogonal survey planes at locations ranging from 1% to 99% of main blade chord. Measured through-flow velocities are compared to those predicted by a 3-D viscous steady flow analysis (Dawes) code. The measurements show the development and progression through the impeller and vaneless diffuser of a through-flow velocity deficit which results from the tip clearance flow and accumulation of low momentum fluid centrifuged from the blade and hub surfaces. Flow traces from the CFD analysis show the origin of this deficit which begins to grow in the inlet region of the impeller where it is first detected near the suction surface side of the passage. It then moves toward the pressure side of the channel, due to the movement of tip clearance flow across the impeller passage, where it is cut by the splitter blade leading edge. As blade loading increases toward the rear of the channel the deficit region is driven back toward the suction surface by the cross-passage pressure gradient. There is no evidence of a large wake region that might result from flow separation and the impeller efficiency is relatively high. The flow field in this impeller is quite similar to that documented previously by NASA Lewis in a large low-speed backswept impeller.

Skoch, G. J.↗
NASA NTRS1997

F-16XL Wing Pressure Distributions and Shock Fence Results from Mach 1.4 to Mach 2.0

Chordwise pressure distributions were obtained in-flight on the upper and lower surfaces of the F-16XL ship 2 aircraft wing between Mach 1.4 and Mach 2.0. This experiment was conducted to determine the location of shock waves which could compromise or invalidate a follow-on test of a large chord laminar flow control suction panel. On the upper surface, the canopy closure shock crossed an area which would be covered by a proposed laminar flow suction panel. At the laminar flow experiment design Mach number of 1.9, 91 percent of the suction panel area would be forward of the shock. At Mach 1.4, that value reduces to 65 percent. On the lower surface, a shock from the inlet diverter would impinge on the proposed suction panel leading edge. A chordwise plate mounted vertically to deflect shock waves, called a shock fence, was installed between the inlet diverter and the leading edge. This plate was effective in reducing the pressure gradients caused by the inlet shock system.

Landers, Stephen F.↗
NASA NTRS1997

An Experimental Study of the Near Field Region of a Free Jet with Passive Mixing Tabs

An experimental study was performed to determine the flow characteristics of a tabbed free jet. Results were acquired in the near field (nominally 2 tab widths upstream to 2 tab widths downstream of the exit plane) of a tabbed jet. Upstream pressure results showed static pressure distributions in both the x-and y-directions along the top surface of the tunnel. Hot-wire measurements showed rapid expansion of the core fluid into the ambient region. Two counter rotating regions of streamwise vorticity were shown on each side of the primary tab. An enhancement of the tabbed jet concept was proposed and tested. Specifically, two tabs, half the scale of the primary tab, were added to the primary tab to provide attachment surfaces for the normally occurring ejection of fluid. The secondary tabs caused a slight increase in the streamwise vorticity created from the upstream static pressure gradient while significantly increasing the re-oriented boundary layer vorticity. The combined pumping effect of the two counter rotating regions of vorticity caused a significant increase in the transport of the jet core fluid into the surrounding region.

Bohl, D. G.↗
NASA NTRS1998

Swept-Wing Receptivity Studies Using Distributed Roughness

This paper reviews the important recent progress in three-dimensional boundary-layer transition research. The review focuses on the crossflow instability that leads to transition on swept wings with a favorable pressure gradient. Following a brief overview of swept-wing instability mechanisms and the crossflow problem, a summary of the important findings of the 1990s is given. The discussion is presented from the experimental viewpoint, highlighting the ITAM work of Kachanov and co-workers, the DLR experiments of Bippes and co-workers, and the Arizona State University (ASU) investigations of Saric and co-workers. Where appropriate, relevant comparisons with CFD are drawn. The recent (last 18 months) research conducted by the ASU team is described in more detail in order to underscore the latest developments concerning nonlinear effects and transition control.

Saric, William S.↗
NASA NTRS1998

Effects of Suction on Swept-Wing Transition

Stability experiments are conducted in the Arizona State University Unsteady Wind Tunnel on a 45 deg swept airfoil. The pressure gradient is designed to provide purely crossflow-dominated transition; that is, the boundary layer is subcritical to Tollmien-Schlichting disturbances. The airfoil surface is hand polished to a 0.25 microns rms finish. Under these conditions, stationary crossflow disturbances grow to nonuniform amplitude due to submicron surface irregularities near the leading edge. Uniform stationary crossflow waves are produced by controlling the initial conditions with spanwise arrays of micron-sized roughness elements near the attachment line. Hot-wire measurements provide detailed maps of the crossflow wave structure, and accurate spectral decompositions isolate individual-mode growth rates for the fundamental and harmonic disturbances. Roughness spacing, roughness height, and Reynolds number are varied to investigate the growth of all amplified wavelengths. The measurements show early nonlinear mode interaction causing amplitude saturation well before transition. Comparisons with nonlinear parabolized stability equations calculations show excellent agreement in both the disturbance amplitude and the mode-shape profiles.

Saric, William S.↗
NASA NTRS1997

Toward Understanding Wake Vortices and Atmospheric Turbulence Interactions Using Large-Eddy Simulation

The vortices produced by an aircraft in flight are a complex phenomena created from a 'sheet of vorticity' leaving the trailing edge of the aircraft surfaces. This sheet tends to roll-up into two counter-rotating vortices. After a few spans downstream of the aircraft, the roll-up process is complete and the vortex pair may be characterized in a simple manner for modeling purposes. Our research will focus on what happens to these post roll-up vortices in the vicinity of an airport terminal. As the aircraft wake vortices descend, they are transported by the air mass which they are embedded and are decayed by both internal and external processes. In the vicinity of the airport, these external influences are usually due to planetary boundary layer (PBL) turbulence. Using large-eddy simulation (LES), one may simulate a variety of PBL conditions. In the LES method, turbulence is generated in the PBL as a response to surface heat flux, horizontal pressure gradient, wind shear, and/or stratification, and may produce convective or unstably stratified, neutral, or stably stratified PBL's. Each of these PBL types can occur during a typical diurnal cycle of the PBL. Thus it is important to be able to characterize these conditions with the LES method. Once this turbulent environment has been generated, a vortex pair will be introduced and the interactions are observed. The objective is to be able to quantify the PBL turbulence vortex interaction and be able to draw some conclusions of vortex behavior from the various scale interactions. This research is ongoing, and we will focus on what has been accomplished to date and the future direction of this research. We will discuss the model being used, show results that validate its use in the PBL, and present a nested-grid method proposed to analyze the entire PBL and vortex pair simultaneously.

DeCroix, David↗
NASA NTRS1998

The NASA Low-Pressure Turbine Flow Physics Program

An overview of the NASA Lewis Low-Pressure Turbine (LPT) Flow Physics Program will be presented. The program was established in response to the aero-engine industry's need for improved LPT efficiency and designs. Modern jet engines have four to seven LPT stages, significantly contributing to engine weight. In addition, there is a significant efficiency degradation between takeoff and cruise conditions, of up to 2 points. Reducing the weight and part count of the LPT and minimizing the efficiency degradation will translate into fuel savings. Accurate prediction methods of LPT flows and losses are needed to accomplish those improvements. The flow in LPT passages is at low Reynolds number, and is dominated by interplay of three basic mechanisms: transition, separation and wake interaction. The affecting parameters traditionally considered are Reynolds number, freestream turbulence intensity, wake frequency parameter, and the pressure distribution (loading). Three-dimensional effects and additional parameters, particularly turbulence characteristics like length scales, spectra and other statistics, as well as wake turbulence intensity and properties also play a role. The flow of most interest is on the suction surface, where large losses are generated as the flow tends to separate at the low Reynolds numbers. Ignoring wakes, a common flow scenario, there is laminar separation, followed by transition on the separation bubble and turbulent reattachment. If transition starts earlier the separation will be eliminated and the boundary layer will be attached leading to the well known bypass transition issues. In contrast, transition over a separation bubble is closer to free shear layer transition and was not investigated as well, particularly in the turbine environment. Unsteadiness created by wakes complicates the picture. Wakes induce earlier transition, and the calmed regions trailing the induced turbulent spots can delay or eliminate separation via shear stress modification. Three-dimensional flow physics and geometry will have strong effects. Altogether a very complex and challenging problem emerges. The objective of the program is to provide improved models and physical understanding of the complex flow, which are essential for accurate prediction of flow and losses in the LPT. Experimental, computational and analytical work as complementing and augmenting approaches are used. The program involves industry, universities and research institutes, and other government laboratories. It is characterized by strong interaction among participants, quick dissemination of results, and responsiveness to industry's needs. The presentation will describe the work elements. Highlighting some activities in progress are experiments on simulated blade suction surface in low-speed wind tunnels, on curved wall, and on a flat-plate, both with pressure gradient. In the area of computation, assessment of existing models is performed using RANS (Reynolds Averaged Navier Stokes) simulations. Laminar flow DNS was completed. Analytical studies of instability and receptivity in attached and separated flows were started. In the near future the program is moving to include wake effects and development of improved modeling. Experimental work in preparation stages are: (1) Addition of wakes to the curved tunnel experiment; (2) Low-speed rotating rig experiment on GE90 engine LPT; and (3) Transonic cascade. In the area of computation, it is expected to move from model assessment towards development of improved models. In addition, a new project of Large Eddy Simulation (LES) of LPT is to begin and will provide numerical data bases. It is planned to implement the emerging improved models in a multistage turbomachinery code and to validate against the GE90 engine LPT.

Ashpis, David E.↗
NASA NTRS1959

Skin-Friction Measurements in Incompressible Flow

Experiments have been conducted to measure the local surface-shear stress and the average skin-friction coefficient in Incompressible flow for a turbulent boundary layer on a smooth flat plate having zero pressure gradient. Data were obtained for a range of Reynolds numbers from 1 million to 45 million. The local surface-shear stress was measured by a floating-element skin-friction balance and also by a calibrated total head tube located on the surface of the test wall. The average skin-friction coefficient was obtained from boundary-layer velocity profiles.

Smith, Donald W.↗