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DOE OSTI2020

Ultra-thin passivation layers in Cu(In,Ga)Se 2 thin-film solar cells: full-area passivated front contacts and their impact on bulk doping

In the search for highly transparent and non-toxic alternative front layers replacing state-of-the-art CdS in Cu(In,Ga)Se 2 thin-film solar cells, alternatives rarely exceed reference devices in terms of efficiency. Full-area ultra-thin aluminium oxide tunnelling layers do not require any contact patterning and thus overcome the main drawback of insulating passivation layers. Even a few monolayers of aluminium oxide can be deposited in a controlled manner by atomic layer deposition, they show excellent interface passivation properties, low absorption, and suitable current transport characteristics on test devices. Depositing a ZnO-based transparent front contact, however, results in extremely poor solar cell performance. The issue is not necessarily a low quality of the alternative front layer, but rather the intricate relation between front layer processing and electronic bulk properties in the absorber layer. We identify three challenges critical for the development of novel front passivation approaches:(i) both Cd and Zn impurities beneficially reduce the high native net dopant concentration in the space charge region, (ii) sputter deposition of ZnO damages the passivation layer resulting in increased interface recombination, (iii) thermal treatments of devices with ZnO layer result in substantial Zn diffusion, which can penetrate the full absorber thickness already at moderate temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Epitaxially Grown Single-Crystalline SrTiO 3 Membranes Using a Solution-Processed, Amorphous SrCa 2 Al 2 O 6 Sacrificial Layer

Water-soluble sacrificial layers based on epitaxially-grown, single crystalline (Ca, Sr, Ba) 3 Al 2 O 6 layer are widely used for creating free-standing perovskite oxide membranes. However, obtaining these sacrificial layers with intricate stoichiometry remains a challenge, especially for molecular beam epitaxy (MBE). In this study, we demonstrate the hybrid MBE growth of epitaxial, single crystalline SrTiO 3 films using a solution processed, amorphous SrCa 2 Al 2 O 6 sacrificial layer onto SrTiO 3 (001) substrates. Prior to the growth, the oxygen plasma exposure was used to first create the crystalline SrCa 2 Al 2 O 6 layer with well-defined surface crystallinity. Utilizing reflection high energy electron diffraction, x-ray diffraction, and atomic force microscopy, we observe an atomic layer-by-layer growth of epitaxial, single crystalline SrTiO 3 film on the SrCa 2 Al 2 O 6 layer with atomically smooth surfaces. The SrCa 2 Al 2 O6 layer was subsequently dissolved in de-ionized water to create free-standing SrTiO3 membranes that were transferred onto a metal-coated Si wafer. Membranes created with Sr-deficiency revealed ferroelectric-like behavior measured using piezo force microscopy whereas stoichiometric films remained paraelectric-like. Furthermore, these findings underscore the viability of using ex-situ deposited amorphous SrCa2Al2O6 for epitaxial, single crystalline growth, as well as the importance of point defects in determining the ferroic properties in membranes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Impact of aqueous solution pH on network structure of corrosion–induced surface layers of boroaluminosilicate glass

Understanding of the long-term stability of vitrified nuclear waste glass is critical to its safe storage, but knowledge gaps remain regarding the corrosion mechanism, especially with respect to surface alteration layers whose presence changes the observed corrosion rates. Here, we report the aqueous corrosion of a model boroaluminosilicate glass at ground water relevant pHs as investigated by vibrational spectroscopy to understand the network structure of the alteration layer that we hypothesize controls the corrosion rates. Both specular reflection infrared spectroscopy and infrared variable angle spectroscopic ellipsometry were used to elucidate details of the structure of the alteration layers formed at pH 7 and pH 9. After 2312 days, the thickness of the alteration layer is found to be ~2000 nm for corrosion at pH 7 and ~300 nm for corrosion at pH 9. Here, the interpretation of the vibrational spectra suggests that alteration layers formed at pH 7 and pH 9 both exhibit a porous network with "silica-like" structures, but with differences in the bond lengths and bond angles in the glass network. Moreover, the relative abundance of the hydrous species within the porous network appears to be dependent on pH. Additionally, the spectroscopic data suggest that the B and Ca trapped in the alteration layer during the secondary corrosion of the pH 9 pre-corroded sample in pH 3 solution are hydrated within the nano-porous layer and not bound to the silicate network. However, the precise chemical form remains to be determined. Based on these findings, we propose that the combination of the network structure of the alteration layer and the relative abundance of hydrous species within the alteration layer act to control the transport of ionic species dissolved from the reaction front to the aqueous solution outside the glass.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Modeling Single and Two-Phase Transport in Thin Porous Layers Using a Composite Continuum-Pore Network Formulation

In this work, a composite continuum-pore network formulation is presented to model single and two-phase transport thin porous layers, such as gas diffusion layers in polymer electrolyte fuel cells (PEFCs) and active electrodes in redox flow batteries (RFBs). The formulation can be integrated into CFD codes, thus combining the ease of implementation of continuum-based modeling and the computational power of pore-network modeling. The composite model includes a control volume (CV) mesh at the layer scale, which embeds a cubic pore network [1,2]. The pore-network model is used to determine analytically local anisotropic effective transport properties (local effective diffusivity and permeability), which are mapped onto the CV mesh to simulate transport in the porous transport layer [3,4]. Good agreement is found between the predicted global effective transport properties (global effective diffusivity and permeability) under dry and wet conditions and previous experimental data reported in the literature for Toray TGP-H series carbon paper. Water saturation distributions are also compared with results obtained using X-ray computed tomography [4]. [1] P.A. García-Salaberri, I.V. Zenyuk, J.T. Gostick, A.Z. Weber, Modeling Gas Diffusion Layer in Polymer Electrolyte Fuel Cells Using a Continuum-Based Pore-Network Formulation, ECS Trans. 97 (2020) 615. [2] P.A. García-Salaberri, Modeling diffusion and convection in thin porous transport layers using a composite continuum-network model: Application to gas diffusion layers in polymer electrolyte fuel cells, Int J. Heat Mass Transf. (2020), submitted. [3] P.A. García-Salaberri, J.T. Gostick, G. Hwang, A.Z. Weber, M. Vera, Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: Effect of local saturation and application to macroscopic continuum models, J. Power Sources 296 (2015) 440–453. [4] P.A. García-Salaberri, G. Hwang, M. Vera, A.Z. Weber, J.T. Gostick, Effective diffusivity in partially-saturated carbon-fiber gas diffusion layers: Effect of through-plane saturation distribution, Int. J. Heat Mass Transf. 86 (2015) 319–333.

Garcia-Salaberri, Pablo↗

DOE OSTI2023

Comparing measurements of the mixing layer height to modeled values

The mixing layer height (MLH) is the top layer of turbulent mixing within the lower atmosphere, above the Earth’s surface. Estimates of the mixing layer height allow us to determine the volume available for the dispersion of pollutants throughout the atmosphere. Our goal is to identify the most suitable mixing layer height input for our dispersion modeling tool (AERMOD). For this project we evaluated two different methods of estimating the local mixing layer height. First, we use 3 estimates of the mixing layer height obtained from a ceilometer, each height estimate corresponds to a different gradient in aerosol backscatter which is used as a proxy for mixing layer height identification. Second, we use AERMET, our AERMOD modeling system preprocessor for meteorological data, which estimates the mixing layer height using several equations combined with measured meteorological data. We evaluate the ceilometer and AERMET estimates over a 5-year period (2015-2019) to see how well aligned the estimated mixing layer heights are. Our results suggest that our model, AERMET, is on average, aligned with ceilometer estimates during the daytime hours. However, daily maximum MLH estimates by AERMET occur earlier in the day than those estimated by the ceilometer. We believe that the ceilometer struggles with accurately measuring the MLH during nighttime hours as a result of sensor limitations.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1980

Density response of the mesospheric sodium layer to gravity wave perturbations

Lidar observations of the mesospheric sodium layer often reveal wavelike features moving through the layer. It is often assumed that these features are a layer density response to gravity waves. Chiu and Ching (1978) described the approximate form of the linear response of atmospheric layers to gravity waves. In this paper, their results are used to predict the response of the sodium layer to gravity waves. These simulations are compared with experimental observations and a good correlation is found between the two. Because of the thickness of the sodium layer and the density gradients found in it, a linear model of the layer response is not always adequate to describe gravity wave-sodium layer interactions. Inclusion of nonlinearities in the layer response is briefly discussed. Experimental data is seen to contain features consistent with the predicted nonlinearities.

Shelton, J. D.↗

NASA NTRS1984

Near-field turbulence properties of single- and two-stream plane mixing layers

Detailed mean-flow and turbulence measurements have been made in the near-field of two plane mixing layers in air with a maximum velocity of 21 m/s. The experimental rig enabled mixing layers of velocity ratios 0 and 0.46 to be generated simultaneously. Cases with both tripped and untripped initial boundary layers were studied. In all cases, it was found that the two-stream layer developed to the self-preserving state in a distance much shorter than the single-stream layer which followed accepted criteria for the development distance. The asymptotic levels of the turbulence quantities in the two-stream layer, and the development of the single-stream layer showed agreement with existing data. The results suggest that the two-stream mixing layer should provide a better test case for the development of turbulence models and calculation methods than the single-stream mixing layer.

Mehta, R. D.↗

NASA NTRS1985

An experimental study of plane mixing layer development

Mean flow and turbulence was measured in the near field of two plane mixing layers in air with a maximum velocity of 21 m/sec. The experimental rig enabled mixing layers of velocity ratios 0 and 0.46 to be generated simultaneously. Gases with both tripped and untripped initial boundary layers were studied. It was found that the two stream layer developed to the self preserving state in a distance much shorter than did the single stream layer which followed accepted criteria for the development distance. The asymptotic levels of the turbulence quantities in the two stream layer and the development of the single stream layer showed agreement with existing data. It is suggested that the two stream mixing layer should provide a better test case for the development of turbulence models and calculation methods than the single stream mixing layer.

Mehta, R. D.↗

NASA NTRS1990

An experimental investigation of nozzle-exit boundary layers of highly heated free jets

An experimental investigation of the effects of nozzle operating conditions on the development of nozzle-exit boundary layers of highly heated air free jets is reported in this paper. The total pressure measurements in the nozzle-exit boundary layer were obtained at a range of jet Mach numbers from 0.1 to 0.97 and jet total temperatures up to 900 K. The analysis of results shows that the nozzle-exit laminar boundary-layer development depends only on the nozzle-exit Reynolds number. For the nozzle-exit turbulent boundary layer, however, it appears that the effects of the jet total temperature on the boundary-layer integral characteristics are independent from the effects of the nozzle-exit Reynolds number. This surprizing finding has not yet been reported. Further, laminar boundary-layer profiles were compared with the Pohlhausen solution for a flat-wall converging channel and an acceptable agreement was found only for low Reynolds numbers. For turbulent boundary layers, the dependence of the shape factor on relative Mach numbers at a distance of one momentum thickness from the nozzle wall resembles Spence's prediction. Finally, the calculated total pressure loss coefficient was found to depend on the nozzle-exit Reynolds number for the laminar nozzle-exit boundary layer, while for the turbulent exit boundary layer this coefficient appears to be constant.

Lepicovsky, J.↗

NASA NTRS1993

The structure of a three-dimensional turbulent boundary layer

The three-dimensional turbulent boundary layer is shown to have a self-consistent two-layer asymptotic structure in the limit of large Reynolds number. In a streamline coordinate system, the streamwise velocity distribution is similar to that in two-dimensional flows, having a defect-function form in the outer layer which is adjusted to zero at the wall through an inner wall layer. An asymptotic expansion accurate to two orders is required for the cross-stream velocity which is shown to exhibit a logarithmic form in the overlap region. The inner wall-layer flow is collateral to leading order but the influence of the pressure gradient, at large but finite Reynolds numbers, is not negligible and can cause substantial skewing of the velocity profile near the wall. Conditions under which the boundary layer achieves self-similarity and the governing set of ordinary differential equations for the outer layer are derived. The calculated solution of these equations is matched asymptotically to an inner wall-layer solution and the composite profiles so formed describe the flow throughout the entire boundary layer. The effects of Reynolds number and cross-stream pressure gradient on the crossstream velocity profile are discussed and it is shown that the location of the maximum cross-stream velocity is within the overlap region.

Degani, A. T.↗

NASA NTRS1943

Determination of general relations for the behavior of turbulent boundary layers

An analysis has been made of a considerable amount of data for turbulent boundary layers along wings and bodies of various shapes in order to determine the fundamental variables that control the development of turbulent boundary layers. It was found that the type of velocity distribution in the boundary layer could be expressed in terms of a single parameter. This parameter was chosen as the ratio of the displacement thickness to the momentum thickness of the boundary layer. The variables that control the development of the turbulent boundary layer apparently are: (1) the ratio of the nondimensional pressure gradient, expressed in terms of the local dynamic pressure outside the boundary layer and boundary-layer thickness, to the local skin-friction coefficient and (2) the shape of the boundary layer. An empirical equation has been developed in terms of these variables that, when used with the momentum equation and the skin-friction relation, makes it possible to trace the development of the turbulent boundary layer to the separation point.

Von Doenhoff, Albert E↗

NASA NTRS1950

The Effect of the Inlet Mach Number and Inlet-boundary-layer Thickness on the Performance of a 23 Degree Conical-diffuser-tail-pipe Combination

An investigation was conducted to determine the effect of the inlet Mach number and entrance-boundary-layer thickness on the performance of a 23 degree 21-inch conical-diffuser - tail-pipe combination with a 2:1 area ratio. The air flows used in this investigation covered an inlet Mach number range from 0.17 to 0.89 and corresponding Reynolds numbers of 1,700,000 to 7,070,000. Results are reported for two inlet-boundary-layer thicknesses. Over the entire range of flows, the mean value of the inlet displacement thickness is about 0.034 inch for the thinner inlet boundary layer and about 0.170 inch for the case of the thicker inlet boundary layer. The performance of the diffuser - tail-pipe combination is presented together with examples of longitudinal static-pressure distribution and the results of boundary-layer pressure surveys made at six points along the diffuser wall. The results indicated a progressive diminution of the static-pressure recovery and a steady increase in the total-pressure losses as the inlet Mach number was increased for both inlet-boundary-layer thicknesses. The ratio of actual static-pressure rise to that theoretically possible was much less and the total-pressure losses were greater for the case of the thicker inlet boundary layer throughout the speed range investigated. With the thinner inlet boundary layer, flow separation occurred at the diffuser exit at all inlet Mach numbers.Unseparated flow alternating with separated flow was observed near the inlet at the higher velocities. For the case of the thicker inlet boundary layer, the origin of the separated region occurred in the vicinity of the inlet-duct-diffuser junction section at all Mach numbers.

Persh, Jerome↗

NASA NTRS1994

Discrete-Layer Piezoelectric Plate and Shell Models for Active Tip-Clearance Control

The objectives of this work were to develop computational tools for the analysis of active-sensory composite structures with added or embedded piezoelectric layers. The targeted application for this class of smart composite laminates and the analytical development is the accomplishment of active tip-clearance control in turbomachinery components. Two distinct theories and analytical models were developed and explored under this contract: (1) a discrete-layer plate theory and corresponding computational models, and (2) a three dimensional general discrete-layer element generated in curvilinear coordinates for modeling laminated composite piezoelectric shells. Both models were developed from the complete electromechanical constitutive relations of piezoelectric materials, and incorporate both displacements and potentials as state variables. This report describes the development and results of these models. The discrete-layer theories imply that the displacement field and electrostatic potential through-the-thickness of the laminate are described over an individual layer rather than as a smeared function over the thickness of the entire plate or shell thickness. This is especially crucial for composites with embedded piezoelectric layers, as the actuating and sensing elements within these layers are poorly represented by effective or smeared properties. Linear Lagrange interpolation polynomials were used to describe the through-thickness laminate behavior. Both analytic and finite element approximations were used in the plane or surface of the structure. In this context, theoretical developments are presented for the discrete-layer plate theory, the discrete-layer shell theory, and the formulation of an exact solution for simply-supported piezoelectric plates. Finally, evaluations and results from a number of separate examples are presented for the static and dynamic analysis of the plate geometry. Comparisons between the different approaches are provided when possible, and initial conclusions regarding the accuracy and limitations of these models are given.

Heyliger, P. R.↗

NASA NTRS1995

Boundary layer transition studies

A small-scale wind tunnel previously used for turbulent boundary layer experiments was modified for two sets of boundary layer transition studies. The first study concerns a laminar separation/turbulent reattachment. The pressure gradient and unit Reynolds number are the same as the fully turbulent flow of Spalart and Watmuff. Without the trip wire, a laminar layer asymptotes to a Falkner & Skan similarity solution in the FPG. Application of the APG causes the layer to separate and a highly turbulent and approximately 2D mean flow reattachment occurs downstream. In an effort to gain some physical insight into the flow processes a small impulsive disturbance was introduced at the C(sub p) minimum. The facility is totally automated and phase-averaged data are measured on a point-by-point basis using unprecedently large grids. The evolution of the disturbance has been tracked all the way into the reattachment region and beyond into the fully turbulent boundary layer. At first, the amplitude decays exponentially with streamwise distance in the APG region, where the layer remains attached, i.e. the layer is viscously stable. After separation, the rate of decay slows, and a point of minimum amplitude is reached where the contours of the wave packet exhibit dispersive characteristics. From this point, exponential growth of the amplitude of the disturbance is observed in the detached shear layer, i.e. the dominant instability mechanism is inviscid. A group of large-scale 3D vortex loops emerges in the vicinity of the reattachment. Remarkably, the second loop retains its identify far downstream in the turbulent boundary layer. The results provide a level of detail usually associated with CFD. Substantial modifications were made to the facility for the second study concerning disturbances generated by Suction Holes for laminar flow Control (LFC). The test section incorporates suction through interchangeable porous test surfaces. Detailed studies have been made using isolated holes in the impervious test plate that used to establish the Blasius base flow. The suction is perturbed harmonically and data are averaged on the basis of the phase of the disturbance, for conditions corresponding to strong suction and without suction. The technique was enhanced by using up to nine multiple probes to reduce the experimental run-time. In both cases, 3D contour surfaces in the vicinity of the hole show highly 3D TS waves which fan out in the spanwise direction forming bow-shaped waves downstream. The case without suction has proved useful for evaluating calculation methods. With suction, the perturbations on the centerline are much stronger and decay less rapidly, while the TS waves in the far field are similar to the case without suction. Downstream, the contour surfaces of the TS waves develop spanwise irregularities which eventually form into clumps. The spanwise clumping is evidence of a secondary instability that could be associated with suction vortices. Designers of porous surfaces use Goldsmith's Criterion to minimize cross-stream interactions. It is shown that partial TS wave cancellation is possible, depending on the hole spacing, disturbance frequency and free-stream velocity. New high-performance Constant Temperature Hot-Wire Anemometers were designed and built, based on a linear system theory analysis that can be extended to arbitrary order. The motivation was to achieve the highest possible frequency reponse while ensuring overall system stability. The performance is equal to or superior to commercially available instruments at about 10% of the cost. Details, such as fabrication drawings and a parts list, have been published to enable the instrument to be construced by others.

Watmuff, Jonathan H.↗

NASA NTRS2000

Mars Secular Obliquity Decrease and the Layered Terrain

Mars may have substantially decreased its average axial tilt over geologic time due to the waxing and waning of water ice caps through the phenomenon of climate friction (also called obliquity-oblateness feedback). Depending upon Mars' climate and internal structure, water caps of the order of 10(exp 17) - 10(exp 18) kg cycling with the obliquity oscillations could have either increased or decreased the average obliquity by possibly tens of degrees over the age of the solar system. Gravity and topography observations by the Mars Global Surveyor indicate that the south polar cap is mostly uncompensated, so that Mars may be largely rigid on the obliquity timescale. Further, Mars may be a water-rich planet, so that there is a large phase angle between insolation forcing and the size of the obliquity-driven water caps. A stiff, water-rich planet implies an obliquity decrease over the eons. Such a decrease might account for the apparent youthfulness of the polar layered terrain. The idea is that fewer volatiles were available to be cycled into and out of the terrain at high mean obliquity, because of the eveness of insolation between equator and pole, and because of small insolation variations as the obliquity oscillated; so that the movement of volatiles and dust produced thin layers or perhaps no layers at all. As the average obliquity decreased, the insolation contrast between high and low latitudes increased, plus the insolation variations over the obliquity cycle grew somewhat bigger, so that more volatiles and dust might have shuttled into and out of the polar regions, forming the observed thick layers late in Mars' history. It may also be that the average tilt has decreased to the point where the climate friction mechanism is starving itself: more and more water has gotten locked up in the polar regions, making less available for cycling with the oscillations. And the layer-forming mechanism may be starving too: not only less water, but also at low average obliquity the atmospheric pressure is lower, so that dust storms become rarer, making less dust available to be deposited in the layers. The rate of water ice sublimation and the atmospheric pressure are both expected to drop sharply for obliquities only slightly lower than the present one. Hence there are qualitative reasons for believing that (a) the mean obliquity may be about as low as it can get, and (b) the mechanism for making the layers may turn off at low average obliquity, so that the layered terrain is a transient phenomenon. Thus the formation of the layered terrain may be intimately connected to a change in the mean axial tilt.

Rubincam, D. P.↗

NASA NTRS1994

Turbulent Heat Transfer Characteristics in the Shear Layer of a Separated Flow

Experiments were performed to study the evolution of the heat transfer structure in a separated free shear layer region of an incompressible separated turbulent boundary layer flow behind a backward-facing step. While there is an abundance of velocity field measurements of separated flows, heat transfer measurements are rather scarce, thus limiting assessment of the heat transfer physics and its accurate modeling. The purpose of the paper is twofold: to improve an understanding of effects of flow separation on heat transfer characteristics, and to provide data for turbulence modeling and computation. The boundary layer upstream of the step was turbulent and fully developed. A constant temperature surface boundary condition was imposed upstream and downstream of the step for the heat transfer study. An internal mixing-layer like flow forms and grows from the step lip within the original boundary layer. The turbulent structure of the flow evolving downstream, however, does not switch immediately to that of a mixing layer over the entire shear layer thickness. Measurements of mean and fluctuating velocity and temperature fields indicate that the internal layer spreads gradually in the transverse direction while the outer part of the original boundary layer is effectively unperturbed. The results in this paper have not been previously reported.

Jovic, S.↗

NASA NTRS1956

Boundary Layer

The fundamental, practically the most important branch of the modern mechanics of a viscous fluid or a gas, is that branch which concerns itself with the study of the boundary layer. The presence of a boundary layer accounts for the origin of the resistance and lift force, the breakdown of the smooth flow about bodies, and other phenomena that are associated with the motion of a body in a real fluid. The concept of boundary layer was clearly formulated by the founder of aerodynamics, N. E. Joukowsky, in his well-known work "On the Form of Ships" published as early as 1890. In his book "Theoretical Foundations of Air Navigation," Joukowsky gave an account of the most important properties of the boundary layer and pointed out the part played by it in the production of the resistance of bodies to motion. The fundamental differential equations of the motion of a fluid in a laminar boundary layer were given by Prandtl in 1904; the first solutions of these equations date from 1907 to 1910. As regards the turbulent boundary layer, there does not exist even to this day any rigorous formulation of this problem because there is no closed system of equations for the turbulent motion of a fluid. Soviet scientists have done much toward developing a general theory of the boundary layer, and in that branch of the theory which is of greatest practical importance at the present time, namely the study of the boundary layer at large velocities of the body in a compressed gas, the efforts of the scientists of our country have borne fruit in the creation of a new theory which leaves far behind all that has been done previously in this direction. We shall herein enumerate the most important results by Soviet scientists in the development of the theory of the boundary layer.

Loitsianskii. L. G.↗

NASA NTRS1949

An Approximate Method for Calculation of the Laminar Boundary Layer with Suction for Bodies of Arbitrary Shape

Various ways were tried recently to decrease the friction drag of a body in a flow; they all employ influencing the boundary layer. One of them consists in keeping the boundary layer Laminar by suction; promising tests have been carried out. Since for large Reynolds numbers the friction drag of the laminar boundary layer is much lower than that of the turbulent boundary layer, a considerable saving in drag results from keeping the boundary layer laminar, even with the blower power required for suction taken into account. The boundary layer is kept laminar by suction in two ways: first, by reduction of the thickness of the boundary layer and second, by the fact that the suction changes the form of the velocity distribution so that it becomes more stable, in a manner similar to the change by a pressure drop. There by the critical Reynolds number of the boundary layer (USigma*/V) (sub crit) becomes considerably higher than for the case without suction. This latter circumstance takes full effect only if continuous suction is applied which one might visualize realized through a porous wall. Thus the suction quantities required for keeping the boundary layer laminar become so small that the suction must be regarded as a very promising auxiliary means for drag reduction.

Schlichting, H.↗