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NASA NTRS2010

Roles of Engineering Correlations in Hypersonic Entry Boundary Layer Transition Prediction

Efforts to design and operate hypersonic entry vehicles are constrained by many considerations that involve all aspects of an entry vehicle system. One of the more significant physical phenomenon that affect entry trajectory and thermal protection system design is the occurrence of boundary layer transition from a laminar to turbulent state. During the Space Shuttle Return To Flight activity following the loss of Columbia and her crew of seven, NASA's entry aerothermodynamics community implemented an engineering correlation based framework for the prediction of boundary layer transition on the Orbiter. The methodology for this implementation relies upon the framework of correlation techniques that have been in use for several decades. What makes the Orbiter boundary layer transition correlation implementation unique is that a statistically significant data set was acquired in multiple ground test facilities, flight data exists to assist in establishing a better correlation and the framework was founded upon state of the art chemical nonequilibrium Navier Stokes flow field simulations. The basic tenets that guided the formulation and implementation of the Orbiter Return To Flight boundary layer transition prediction capability will be reviewed as a recommended format for future empirical correlation efforts. The validity of this approach has since been demonstrated by very favorable comparison of recent entry flight testing performed with the Orbiter Discovery, which will be graphically summarized. These flight data can provide a means to validate discrete protuberance engineering correlation approaches as well as high fidelity prediction methods to higher confidence. The results of these Orbiter engineering and flight test activities only serve to reinforce the essential role that engineering correlations currently exercise in the design and operation of entry vehicles. The framework of information-related to the Orbiter empirical boundary layer transition prediction capability will be utilized to establish a fresh perspective on this role, to illustrate how quantitative statistical evaluations of empirical correlations can and should be used to assess accuracy and to discuss what the authors' perceive as a recent heightened interest in the application of high fidelity numerical modeling of boundary layer transition. Concrete results will also be developed related to empirical boundary layer transition onset correlations. This will include assessment of the discrete protuberance boundary layer transition onset data assembled for the Orbiter configuration during post-Columbia Return To Flight. Assessment of these data will conclude that momentum thickness Reynolds number based correlations have superior coefficients and uncertainty in comparison to roughness height based Reynolds numbers, aka Re(sub k) or Re(sub kk). In addition, linear regression results from roughness height Reynolds number based correlations will be evaluated, leading to a hypothesis that non-continuum effects play a role in the processes associated with incipient boundary layer transition on discrete protuberances.

Campbell, Charles H.↗

NASA NTRS2006

Silicon-Based Optical Modulator with Ferroelectric Layer

According to a proposal, a silicon dioxide layer in a high-speed, low-power, silicon- based electro-optical modulator would be replaced by a layer of lead zirconate titanate or other ferroelectric oxide material. The purpose of this modification is to enhance the power performance and functionality of the modulator. In its unmodified form, the particular silicon- based electro-optical modulator is of an advanced design that overcomes the speed limitation of prior silicon-based electro- optical modulators. Whereas modulation frequencies of such devices had been limited to about 20 MHz, this modulator can operate at modulation frequencies as high as 1 GHz. This modulator can be characterized as a silicon-waveguide-based metal oxide/semiconductor (MOS) capacitor phase shifter in which modulation of the index of refraction in silicon is obtained by exploiting the free-charge-carrier-plasma dispersion effect. As shown in the figure, the modulator includes an n-doped crystalline silicon slab (the silicon layer of a silicon- on-insulator wafer) and a p-doped polycrystalline silicon rib with a gate oxide layer (the aforementioned silicon dioxide layer) sandwiched between them. Under accumulation conditions, the majority charge carriers in the silicon waveguide modify the index of refraction so that a phase shift is induced in the optical mode propagating in the waveguide. The advantage of using an MOS capacitor phase shifter is that it is possible to achieve high modulation speed because there are no slow carrier-generation or -recombination processes involved in the accumulation operation. The main advantage of the proposed substitution of a ferroelectric oxide layer for the silicon dioxide layer would arise from the spontaneous polarization effect of the ferroelectric layer: This spontaneous polarization would maintain accumulation conditions in the absence of applied voltage. Consequently, once the device had been switched to a given optical state, it would remain in that state, even in the absence of applied voltage (in other words, even with power turned off). A secondary advantage is that because the ferroelectric layer would have an index of refraction larger than that of silicon dioxide, there could be some reduction of optical losses attributable to fabrication of the modulator

Sheldon, Douglas↗

NASA NTRS2011

Hypersonic Boundary Layer Transition Measurements Using NO2 approaches NO Photo-dissociation Tagging Velocimetry

Measurements of instantaneous and mean streamwise velocity profiles in a hypersonic laminar boundary layer as well as a boundary layer undergoing laminar-to-turbulent transition were obtained over a 10-degree half-angle wedge model. A molecular tagging velocimetry technique consisting of a NO2 approaches?NO photo-dissociation reaction and two subsequent excitations of NO was used. The measurement of the transitional boundary layer velocity profiles was made downstream of a 1-mm tall, 4-mm diameter cylindrical trip along several lines lying within a streamwise measurement plane normal to the model surface and offset 6-mm from the model centerline. For laminar and transitional boundary layer measurements, the magnitudes of streamwise velocity fluctuations are compared. In the transitional boundary layer the fluctuations were, in general, 2-4 times larger than those in the laminar boundary layer. Of particular interest were fluctuations corresponding to a height of approximately 50% of the laminar boundary layer thickness having a magnitude of nearly 30% of the mean measured velocity. For comparison, the measured fluctuations in the laminar boundary layer were approximately 5% of the mean measured velocity at the same location. For the highest 10% signal-to-noise ratio data, average single-shot uncertainties using a 1 ?Es and 50 ?Es interframe delay were ~115 m/s and ~3 m/s, respectively. By averaging single-shot measurements of the transitional boundary layer, uncertainties in mean velocity as low as 39 m/s were obtained in the wind tunnel. The wall-normal and streamwise spatial resolutions were 0.14-mm (2 pixel) and 0.82-mm (~11 pixels), respectively. These measurements were performed in the 31-inch Mach 10 Air Wind Tunnel at the NASA Langley Research Center.

Bathel, Brett F.↗

NASA NTRS2009

Optimization of Layer Densities for Spacecraft Multilayered Insulation Systems

Numerous tests of various multilayer insulation systems have indicated that there are optimal densities for these systems. However, the only method of calculating this optimal density was by a complex physics based algorithm developed by McIntosh. In the 1970's much data were collected on the performance of these insulation systems with many different variables analyzed. All formulas generated included number of layers and layer density as geometric variables in solving for the heat flux, none of them was in a differentiable form for a single geometric variable. It was recently discovered that by converting the equations from heat flux to thermal conductivity using Fourier's Law, the equations became functions of layer density, temperatures, and material properties only. The thickness and number of layers of the blanket were merged into a layer density. These equations were then differentiated with respect to layer density. By setting the first derivative equal to zero, and solving for the layer density, the critical layer density was determined. Taking a second derivative showed that the critical layer density is a minimum in the function and thus the optimum density for minimal heat leak, this is confirmed by plotting the original function. This method was checked and validated using test data from the Multipurpose Hydrogen Testbed which was designed using McIntosh's algorithm.

Johnson, W. L.↗

NASA NTRS1992

Effect of Index of Refraction on Radiation Characteristics in a Heated Absorbing, Emitting, and Scattering Layer

The index of refraction can considerably influence the temperature distribution and radiative heat flow in semitransparent materials such as some ceramics. For external radiant heating, the refractive index influences the amount of energy transmitted into the interior of the material. Emission within a material depends on the square of its refractive index, and hence this emission can be many times that for a biackbody radiating into a vacuum. Since radiation exiting through an interface into a vacuum cannot exceed that of a blackbody, there is extensive reflection at the internal surface of an interface, mostly by total internal reflection. This redistributes energy within the layer and tends to make its temperature distribution more uniform. The purpose of the present analysis is to show that, for radiative equilibrium in a gray layer with diffuse interfaces, the temperature distribution and radiative heat flux for any index of refraction can be obtained very simply from the results for an index of refraction of unity. For the situation studied here, the layer is subjected to external radiative heating incident on each of its surfaces. The material emits, absorbs, and isotropically scatters radiation. For simplicity the index of refraction is unity in the medium surrounding the layer. The surfaces of the layer are assumed diffuse. This is probably a reasonable approximation for a ceramic layer that has not been polished. When transmitted radiation or radiation emitted from the interior reaches the inner surface of an interface, the radiation is diffused and some of it thereby placed into angular directions for which there is total internal reflection. This provides a trapping effect for retaining energy within the layer and tends to equalize its temperature distribution. An analysis of temperature distributions in absorbing-emitting layers, including index of refraction effects, was developed by Gardon (1958) to predict cooling and heat treating of glass plates. The interfaces were optically smooth; the resulting specular reflections were computed from the Fresnel reflection laws. This provides a somewhat different behavior than for diffuse interfaces. A similar application was for heating that occurs in a window of a re-entry vehicle (Fowle et al., 1969). A number of recent papers (Rokhsaz and Dougherty, 1989; Ping and Lallemand, 1989; Crosbie and Shieh, 1990) further examined the effects of Fresnel boundary reflections and nonunity refractive index. Other examples of analyses of both steady and transient heat transfer to single or multiple plane layers (Amlin and Korpela, 1979; Tarshis et al., 1969) have used diffuse assumptions at the interfaces as in the present study

Siegel, R.↗

NASA NTRS2019

Multi-Layer Wireless Sensor Construct for Use at Electrically-Conductive Material Surfaces

A multi-layer wireless sensor construct is provided. The construct includes a first dielectric layer adapted to be attached to a portion of a first surface of an electrically-conductive material. A layer of mu metal is provided on the first dielectric layer. A second dielectric layer is provided on the layer of mu metal. An electrical conductor is provided on the second dielectric layer wherein the second dielectric layer separates the electrical conductor from the layer of mu metal. The electrical conductor has first and second ends and is shaped to form an unconnected open-circuit that, in the presence of a time-varying magnetic field, resonates to generate a harmonic magnetic field response having a frequency, amplitude and bandwidth.

Dudley, Kenneth L.↗

NASA NTRS2019

The Impact of Stable Layers on Downdrafts in Tropical Convection

While the idea that downdraft vertical velocity is influenced by thermodynamic stability may seem obvious, there remains a gap in the scientific literature surrounding the interaction between downdrafts and stable layers. A number of questions remain unanswered. Can a stable layer stop the downward progression of a downdraft or merely slow its velocity? Related to this, can a stable layer stop the injection of low entropy air into the boundary layer? Do downdrafts modify the environment in a way that removes pre-existing stable layers (limiting the influence of the stable layer)? Is it possible for evaporative cooling to generate and maintain a stable layer that is sufficiently strong to stop the downward progression of downdrafts?The present study aims to answer these questions using a combination of high-altitude airborne radar and dropsonde observations, both collected within four tropical cyclones (Gaston, Hermine, Karl, and Matthew) during the 2016 NOAA SHOUT field campaign, as well as idealized simulations of tropical deep convection. This presentation will focus on the potential for a stable layer to halt the downward progression of a downdraft (and the associated low entropy air) with particular attention given to conditions and processes that might enhance or mitigate the influence of the stable layer.

Helms, Charles N.↗

NASA NTRS2019

Modeling of the Influence of a Damaged Thermally Grown Oxide (TGO) Layer in an Environmental Barrier Coating System

Environmental barrier coatings (EBC) are an enabling technology for the successful application of ceramic matrix composites (CMCs) in air-breathing gas turbine engines. EBCs are susceptible to a number of failure modes including oxidation/delamination, recessions, chemical attack and dissolution, thermomechanical degradation, erosion, and foreign object impact damage in a combustion environment. Spallation of environmental barrier coating (EBC), induced by a thermally grown oxide (TGO) layer, is a key EBC failure mode. The TGO layer, resulting from steam oxidation, grows either from a silicon bond coat layer (if present) or from a silicon carbide (SiC) based substrate itself. The TGO layer evolves (i.e., thickness increases with time) as water vapor and oxygen gradually diffuse through the EBC, and the EBC spalls off once the TGO layer reaches some critical thickness. The critical thickness of the TGO layer for failure is in the range of 20-30 microns, but it can vary due to exposure temperature, microstructure etc. Current work at NASA Glenn Research Center, under the Revolutionary Tools and Methods (RTM) subproject is aimed at addressing associated failure modes in EBC systems and developing robust analysis tools to aid in the design/analysis of these systems. The objective of the current work is to conduct a sensitivity study to examine the influence of uniformly and non-uniformly grown oxide layers on the associated driving forces leading to spallation of the EBC when subjected to isothermal loading. The effect of damage in the TGO layer on the resulting stress states is also assessed both in uniform and non-uniform TGO layers.

Mital, Subodh K.↗

NASA NTRS2020

Investigation of Atmospheric Boundary-Layer Effects on Launch-Vehicle Ground Wind Loads

A launch vehicle ground-wind-loads program is underway at the NASA Langley Transonic Dynamics Tunnel. The objectives are to quantify key aerodynamic and structural characteristics that impact the occurrence of large wind-induced oscillations of a launch vehicle when exposed to ground winds prior to launch. Of particular interest is the dynamic response of a launch vehicle when a von Kármán vortex street forms in the wake of the vehicle resulting in quasiperiodic lift and drag forces. Vehicle response to these quasiperiodic forces can become quite large when the frequency of vortex shedding nears that of a lowly-damped structural mode thereby exciting a resonant response. Wind approaching the vehicle can be characterized by a varying speed with height and turbulence content. The combination of both the varying speed and turbulence content is referred to herein as the atmospheric boundary-layer. The importance of the atmospheric boundary-layer upon launch vehicle wind-induced oscillation response has long been questioned, and its effects are not well understood. Although there are several facilities around the world dedicated to replicating atmospheric boundary layers, the development of such a boundary layer in a wind tunnel capable of producing flight-representative Reynolds numbers for aeroelastically-scaled launch vehicle models has only recently been accomplished. The NASA Langley Transonic Dynamics Tunnel is capable of simulating flight-representative Reynolds numbers of launch vehicles on the pad and is uniquely capable of replicating many fluid-structure scaling parameters typical of aeroelastic tests. Recent test efforts successfully developed representative atmospheric boundary-layers for three launch sites in the Transonic Dynamics Tunnel, thereby allowing all known aerodynamic and fluid-structure coupling parameters to be simultaneously simulated for those sites. Dynamic aeroelastically-scaled models representative of typical large launch vehicles were constructed for testing. Aeroelastic scaling includes matching geometry, mode shapes, reduced frequencies, damping, running mass ratios, and running stiffness ratios. The models were tested in smooth uniform flow and then immersed in the atmospheric boundary-layer for comparison of these effects. Dynamic data were acquired measuring unsteady pressure, acceleration, and base bending moment. It was discovered that peak dynamic loads resulting from resonant wind-induced oscillation response are similar when acquired in either smooth uniform flow or an atmospheric boundary-layer. This indicates that resonant lock-in events are minimally impacted by representative turbulence and/or wind profile. Alternately, nonresonant wind-induced oscillation response events are stronger when acquired in an atmospheric boundary-layer. This indicates that a lowly-damped structural response will increase when exposed to an increased magnitude of random excitation, which is consistent with historical comparisons. Loads created by the resonant response events were substantially stronger than those from the nonresonant response events. Therefore, if testing is done to simply identify worst-case conditions and load magnitude, then smooth uniform flow is likely an adequate test technique. However, if nonresonant response loads are of primary interest, then atmospheric boundary-layer simulation is required.

Thomas G Ivanco↗

NASA NTRS2021

Modeling of the Influence of Thermally Grown Oxide (TGO) Layers on the Driving Forces in Environmental Barrier Coating Systems

Environmental barrier coatings (EBC) are an enabling technology for the successful application of ceramic matrix composites (CMCs) in air-breathing gas turbine engines. EBCs are susceptible to several failure modes including oxidation/delamination, recession, chemical attack and dissolution, thermomechanical degradation, erosion, and foreign object impact damage in a combustion environment. Spallation of environmental barrier coating (EBC), induced by a thermally grown oxide (TGO) layer, is a key EBC failure mode. The TGO layer, resulting from steam oxidation, grows either from a silicon bond coat layer (if present) or from a silicon carbide (SiC) based substrate itself. The TGO layer evolves (i.e., thickness increases with time) as water vapor and oxygen gradually diffuse through the EBC, and the EBC spalls off once the TGO layer reaches some critical thickness. The critical thickness of the TGO layer for failure is in the range of 20-30 microns, with the actual value depending upon exposure temperature, microstructure, etc. Current work at NASA Glenn Research Center, under the Transformative Tools and Technology (TTT) subproject is aimed at addressing associated failure modes in EBC systems and developing robust analysis tools to aid in the design/analysis of these systems. The objective of the current work is to conduct a sensitivity study to examine the influence of uniformly and non-uniformly grown oxide layers on the associated driving forces leading to spallation of the EBC when subjected to isothermal loading. The effect of damage in the TGO layer on the resulting stress states is also assessed both in uniform and non-uniform TGO layers.

Coatings↗

NASA NTRS1972

Characteristics of the unsteady shock-induced laminar boundary layer on a flat plate.

The unsteady shock-induced laminar boundary layer on a flat plate is theoretically studied for shock speeds ranging from 1.12 to 9 km/sec. Boundary layer flows for real air, assumed to be in thermochemical equilibrium, are analyzed by extending Lam's work on shock-induced laminar boundary layers to equilibrium dissociated and ionized flows. A complete description of the unsteady nature of the boundary layer is presented in terms of heat transfer and several boundary layer thickness quantities as functions of a single time-position variable. Boundary layer development is considered for two points of view. Time-dependent boundary layer development and approach to steady state for any fixed position on the plate is described, as is the configuration of the boundary layer with position on the plate at any point in time.

Cook, W. J.↗

NASA NTRS1976

Radiative behavior of a gas layer seeded with soot

Gaseous film or transpiration cooling may be used to reduce the heat flux reaching the wall of a container or other structures. Such a protective film, however, is usually not effective for reducing radiative heat transfer as most gases are transparent in the temperature range for which solid walls can exist. Therefore, heat transfer was examined for a gaseous layer seeded with radiation-absorbing carbon particles (soot) and flowing along a surface. The layer was subjected to an external high temperature source of blackbody radiation. The radiative behavior was found to depend on a parameter containing particle concentration, layer thickness and source temperature. Only a very small particle volume concentration, in the range of .0001, was required to obtain high absorption in a 1-cm-thick layer for typical conditions. The results provide the distance along the surface for which the heat transfer to the wall remains within an acceptable limit and the particles remain below a temperature at which they will melt or vaporize. The wall protection by the layer lasts only until the particles vaporize or the layer becomes so hot that it reradiates substantially to the wall. Depending on the layer mass velocity the protection may be effective for a distance along the wall of only a few layer thickness. Hence, to protect greater wall lengths, it will be necessary to introduce the suspension through multiple slots or holes along the wall.

Siegel, R.↗

NASA NTRS1979

A prediction method for velocity and temperature profiles in a two-dimensional nominally steady turbulent boundary layer

This paper describes a recently developed boundary-layer prediction method for a variable property compressible flow, in which heat transfer takes place primarily by forced convection and for which the mainstream Mach number is small. The leading order terms, in asymptotic expansions for large Reynolds numbers, are obtained for the mean velocity and temperature distribution in both the inner and outer layer of the turbulent boundary layer. Closure in the inner layer is achieved using an analytical model for the mean profiles which is based on the observed coherent structure of the time-dependent inner layer flow. For the outer layer, simple eddy viscosity and conductivity models are developed without recourse to the Reynolds analogy. In the prediction method a numerical solution of the outer layer equations is matched to the analytical inner layer profiles as the computation procedes downstream. Calculations are presented for a range of adverse and favorable pressure gradient flows and the predicted results compare well with existing data.

Weigand, G. G.↗

NASA NTRS1981

Turbulent boundary layer heat transfer experiments - A separate effects study on a convexly-curved wall

Surface heat transfer rates have been measured for several different flows on an isothermal, convexly curved surface. The freestream velocity, boundary layer thickness, acceleration parameter, and unheated starting length were varied systematically, and both turbulent and transitional boundary layers were studied. The effect of convex curvature on heat transfer rates is significant with Stanton numbers reduced 20-25% below flat wall values for the same enthalpy thickness Reynolds number. Heat transfer rates recovered slowly on a flat wall downstream of the curved wall, and after 60 cm, the Stanton numbers were still 15-20% below flat wall values. The behavior of the boundary layer suggests the existence of an asymptotic condition. Boundary layer thickness, freestream velocity, and boundary layer maturity affect the initial response to the introduction of curvature and the rate at which the asymptotic state is approached. Convex curvature appears to increase the boundary layer's sensitivity to acceleration; it also delays and retards transition. Near-laminar or early-transitional boundary layers recover from curvature rapidly, whereas late-transitional and mature boundary layers recover slowly.

Simon, T. W.↗

NASA NTRS1985

The boundary layers as the primary transport regions of the earth's magnetotail

A comprehensive survey of ISEE and IMP LEPEDEA plasma measurements in the earth's magnetotail reveals that the magnetospheric boundary layer and the plasma sheet boundary layer are the primary transport regions there. These plasma measurements also reveal various components of the plasma sheet, including the central plasma sheet and plasma sheet boundary layer. A significant new result reported here is that of cold- and hot-plasma components that are spatially co-present within the central plasma sheet. Such plasma components cannot be explained merely by temporal variations in spectra involving the entire plasma sheet. Contributions to a low temperature component of the plasma sheet enter directly from the boundary layer located along the magnetotail flanks. Field-aligned flows predominate within the plasma sheet boundary layer which is almost always present and is located near the high- and low-latitude border of the plasma sheet. The plasma sheet boundary layer comprises highly anisotropic ion distributions, including counter-streaming ion beams, that evolve into the hot, isotropic component of the plasma sheet. Tailward acceleration regions generate these ion beams with plasma input from the magnetospheric boundary layer. Antisunward-flowing ion beams, at E/q less than 1 kV and of ionospheric composition, are frequently observed in the plasma sheet boundary layer and in tail lobes. These ion beams are likely accelerated at low altitude over the polar cap and especially along auroral field lines.

Eastman, T. E.↗

NASA NTRS1986

Double layers and circuits in astrophysics

As the rate of energy release in a double layer with voltage delta V is P approx I delta V, a double layer must be treated as a part of a circuit which delivers the current I. As neither double layer nor circuit can be derived from magnetofluid models of a plasma, such models are useless for treating energy transfer by means of double layers. They must be replaced by particle models and circuit theory. A simple circuit is suggested which is applied to the energizing of auroral particles, to solar flares, and to intergalactic double radio sources. Application to the heliospheric current systems leads to the prediction of two double layers on the Sun's axis which may give radiations detectable from Earth. Double layers in space should be classified as a new type of celestial object (one example is the double radio sources). It is tentatively suggested in X-ray and Gamma-ray bursts may be due to exploding double layers (although annihilation is an alternative energy source). A study of how a number of the most used textbooks in astrophysics treat important concepts like double layers, critical velocity, pinch effects and circuits is made.

Alfven, Hannes↗

NASA NTRS1988

Structure and growth of the mixing layer over the Amazonian rain forest

The structure and growth of the atmospheric mixed layer over the Amazonian rain forest were examined using measurements obtained during the NASA Amazon Boundary Layer Experiment. Measurements of temperature, moisture, and horizontal wind were carried out in and above the mixed layer by means of a tethered balloon, rawinsonde, and aircraft; fluxes of sensible and latent heat were measured at the top of the canopy. It was found that the mixing layer grows rapidly, at 5-8 cm/sec, soon after sunrise to a mean maximum height of 1200 m by 1300 LT; during undisturbed conditions, mixed layer heights of 1000 are common between 1000 and 1600 LT. No horizontal inhomogeneities in the mixed layer structure or depth were found over large distances. A simple mixed layer model was applied to show how fluxes of species might be estimated using only quantities measured at the surface and prescribing an initial condition and boundary condition for the mixed layer.

Martin, Charles L.↗

NASA NTRS1991

Numerical investigation of an internal layer in turbulent flow over a curved hill

A numerical investigation of incompressible and compressible turbulent flows over strongly curved surfaces is presented. The turbulent flow equations are solved by a pressure based Navier-Stokes equations solver. In the method, the conservation of mass equation is replaced by a pressure correction equation applicable for both compressible and incompressible flows. The turbulence is described by a multiple time scale turbulence model supplemented with a near-wall turbulence model. The numerical results show that the internal layer is a strong turbulence field which is developed beneath the external boundary layer and is located very close to the wall. The development of the internal layer is attributed to the enormous mean flow strain rate caused by the streamline curvature. The external boundary layer flow responds rather slowly to the streamline curvature. Thus, the turbulence field of the forward corner of the curved hill is characterized by two turbulence fields interacting with each other. The turbulence intensity of the internal layer is much stronger than that of the external boundary layer, so that the development of a new boundary layer in the downstream region of the curved hill depends mostly on the internal layer. These numerical results are in good agreement with the measured data, and show that the turbulence model can resolve the turbulence field subjected to the strong streamline curvature.

Kim, S.-W.↗