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Numerical solution of flow equations for laminar, transitional, and turbulent compressible boundary layers for planar or axisymmetric flows
The end-stage phase of boundary layer transition is characterized by the development of hairpin-like vortices which evolve rapidly into patches of turbulent behavior. In general, the characteristics of the evolution form this hairpin stage to the turbulent stage is poorly understood, which has prompted the present experimental examination of hairpin vortex development and growth processes. Two topics of particular relevance to the workshop focus will be covered: 1) the growth of turbulent spots through the generatio and amalgamation of hairpin-like vortices, and 2) the development of hairpin vortices during transition in an end-wall junction flow. Brief summaries of these studies are described below. Using controlled generation of hairpin vortices by surface injection in a critical laminar boundary layer, detailed flow visualization studies have been done of the phases of growth of single hairpin vortices, from the initial hairgin generation, through the systematic generation of secondary hairpin-like flow structures, culminating in the evolution to a turbulent spot. The key to the growth process is strong vortex-surface interactions, which give rise to strong eruptive events adjacent to the surface, which results in the generation of subsequent hairpin vortex structures due to inviscid-viscuous interactions between the eruptive events and the free steam fluid. The general process of vortex-surface fluid interaction, coupled with subsequent interactions and amalgamation of the generated multiple hairpin-type vortices, is demonstrated as a physical mechanism for the growth and development of turbulent spots. When a boundary layer flow along a surface encounters a bluff body obstruction extending from the surface (such as cylinder or wing), the strong adverse pressure gradients generated by these types of flows result in the concentration of the impinging vorticity into a system of discrete vortices near the end-wall juncture of the obstruction, with the extensions of the vortices engirdling the obstruction to form "necklace" or "horseshoe" vortices. Recent hydrogen bubble and particle image visualization have shown that as Reynolds number is increased for a laminar approach flow, the flow will become critical, and a destabilization of the necklace vortices results in the development of an azimuthal waviness, or "kinks", in the vortices. These vortex kinks are accentuated by Biot-Savart effects, causing portions of a distorted necklace vortex to make a rapid approach to the surface, precipitating processes of localized, three-dimensional surface interactions. These interactions result in the rapid generation, focussing, and ejection of thin tongues of surface fluid, which rapidly roll-over and appear as hairpin vortices in the junction region. Subsequent amalgamation of these hairpin vortices with the necklace vortices produces a complex transitional-type flow. A presentation of key results from both these studies will be done, emphasizing both the ubiquity of such hairpin-type flow structures in manifold transitional-type flows, and the importance of vortex-surface interactions n the development of hairpin vortices.
The principles of two flow control strategies, those of Huebler (Luescher and Huebler, 1989) and of Ott et al. (1990) are discussed, and the two schemes are compared for their ability to control shear flow, using fully developed and transitional solutions of the Ginzburg-Landau equation as models for such flows. It was found that the effectiveness of both methods in obtaining control of fully developed flows depended strongly on the 'distance' in state space between the uncontrolled flow and goal dynamics. There were conceptual difficulties in applying the Ott et al. method to transitional convectively unstable flows. On the other hand, the Huebler method worked well, within certain limitations, although at a large cost in energy terms.
A small-scale wind tunnel previously used for turbulent boundary layer studies has been modified for experiments in laminar flow control. The facility incorporates suction through interchangeable porous test surfaces which are used to stabilize the boundary layer and delay transition to turbulent flow. The thin porous test surfaces are supported by a baffled plenum chamber box which also acts to gather the flow through the surface into tubes which are routed to a high pressure fan. An elliptic leading edge is attached to the assembly to establish a new layer on the test plate. A slot is used to remove the test section flow below the leading edge. The test section was lengthened and fitted with a new ceiling. Substantial modifications were also made to the 3D probe traverse. Detailed studies have been made using isolated holes to explore the underlying instability mechanisms. The suction is perturbed harmonically and data are averaged on the basis of the phase of the disturbance. Conditions corresponding to strong suction and without suction have been studied. In both cases, 3D contour surfaces in the vicinity of the hole show highly three-dimensional T-S waves that fan out away from the hole with streamwise distance. With suction, the perturbations on the centerline are much stronger and decay less rapidly, while the far field is similar to the case without suction. Downstream the contour surfaces of the bow-shaped TS waves develop spanwise irregularities which eventually form into clumps. The contours remain smooth when suction is not applied. Even without suction, the harmonic point source is challenging for CFD; e.g. DNS has been used for streamwise growth. With suction, grid resources are consumed by the hole and this makes DNS even more expensive. Limited DNS results so far indicate that the vortices which emanate from suction holes appear to be stable. The spanwise clumping observed in the experiment is evidence of a secondary instability that could be associated with suction vortices. A typical porous surface for LFC consists of 0.002 inch diameter holes with 0.020 inch grid spacing L, which is too small to resolve disturbances. A 20:1 scale porous test surface has been machined for improved spatial resolution while the L/d is still representative of flight conditions. Designers of porous surfaces use Goldsmith's criterion to minimize crossstream interaction. However nothing is known about the streamwise interactions. Results using two holes, aligned but displaced in the streamwise direction, indicate that partial TS wave cancellation is possible, depending on the hole spacing and disturbance frequency. Using DNS for streamwise interaction studies will be prohibitively expensive if linear superposition cannot be used for the multiple holes.
It is not unusual when comparing CFD data to experimental data to find discrepancies between the results. Sometimes forces and moments compare well, while surface pressures do not, and vice versa. It is commonplace for the researcher to believe that the flow field has been accurately simulated when these types of measurements compare well. However, being able to routinely predict boundary layer transition and separated flows are not guaranteed. In fact accurate simulation of these types of flow physics has been a challenge to the CFD community. In order to improve Navier-Stokes predictions for complex vortical flow fields, more detailed information about the flow physics is necessary. Unfortunately, the many wind-tunnel tests performed in Langley's NTF and 14x22 facilities as well as in the Ames' 12 ft. Tunnel provided little information about the detailed flow physics, and no priority was given to obtaining any CFD measurements. Using the latest experimental techniques, this information can and should be obtained for present and future use.
Using numerical simulations of a model disk system, we demonstrate that a machine learning generated order-parameter-like measure can detect depinning transitions and different dynamic flow phases in systems driven far from equilibrium. Furthermore, we specifically consider monodisperse passive disks with short range interactions undergoing a depinning phase transition when driven over quenched disorder. The machine learning derived order-parameter-like measure identifies the depinning transition as well as different dynamical regimes, such as the transition from a flowing liquid to a phase separated liquid-solid state that is not readily distinguished with traditional measures such as velocity-force curves or Voronoi tessellation. The order-parameter-like measure also shows markedly distinct behavior in the limit of high density where jamming effects occur. Our results should be general to the broad class of particle-based systems that exhibit depinning transitions and nonequilibrium phase transitions.
Efforts of the last six months to computationally model the transition process characteristics of flow over swept wings are described. Specifically, the crossflow instability and crossflow/Tollmien-Schlichting wave interactions are analyzed through the numerical solution of the full 3D Navier-Stokes equations including unsteadiness, curvature, and sweep. This approach is chosen because of the complexity of the problem and because it appears that linear stability theory is insufficient to explain the discrepancies between different experiments and between theory and experiment. The leading edge region of a swept wing is considered in a 3D spatial simulation with random disturbances as the initial conditions.
An efficient scheme for the direct numerical simulation of 3D transitional and developed turbulent flow is presented. Explicit and implicit time integration schemes for the compressible Navier-Stokes equations are compared. The nonlinear system resulting from the implicit time discretization is solved with an iterative method and accelerated by the application of a multigrid technique. Since we use central spatial discretizations and no artificial dissipation is added to the equations, the smoothing method is less effective than in the more traditional use of multigrid in steady-state calculations. Therefore, a special prolongation method is needed in order to obtain an effective multigrid method. This simulation scheme was studied in detail for compressible flow over a flat plate. In the laminar regime and in the first stages of turbulent flow the implicit method provides a speed-up of a factor 2 relative to the explicit method on a relatively coarse grid. At increased resolution this speed-up is enhanced correspondingly.
The principal purposes of the present study were to: (1) observe and develop a fundamental understanding of the flow regimes and their transitions occurring in helical and spiral coils; and (2) obtain pressure drop measurements of such flows, and, if possible, develop a method for predicting pressure drop in these flow geometries. Elaborating upon the above, the general intent is to develop criteria (preferably generalized) for establishing the nature of the flow dynamics (e.g. flow patterns) and the magnitude of the pressure drop in such configurations over a range of flow rates and fluid properties. Additionally, the visualization and identification of flow patterns were a fundamental objective of the study. From a practical standpoint, the conditions under which an annular flow pattern exists is of particular practical importance. In the possible practical applications which would implement these geometries, the working fluids are likely to be refrigerant fluids. In the present study the working fluids were an air-water mixture, and refrigerant 113 (R-113). In order to obtain records of flow patterns and their transitions, video photography was employed extensively. Pressure drop measurements were made using pressure differential transducers connected across pressure taps in lines immediately preceding and following the various test sections.
An experimental study of flow over a two-dimensional flat plate-wedge configuration is presented. The investigation encompasses a range of Reynolds numbers characteristics of conditions encountered by deep submersible oceanic vehicles. Flow separation, similar to that found on high speed aircraft control surfaces, is reported and discussed in light of the laminar or transitional nature of the separated shear layer. As discovered in previous high Mach number studies of plate-wedge or ramp configurations, the dependency of the size of the separated region on free stream Reynolds number is reversed for laminar and transitional types of flow separation.
An experimental investigation was conducted to measure the reverse flow within the transitional separation bubble that forms on an airfoil at low Reynolds numbers. Measurements were used to determine the effect of the reverse flow on integrated boundary-layer parameters often used to model the bubble. Velocity profile data were obtained on an NACA 663-018 airfoil at angle of attack of 12 deg and a chord Reynolds number of 140,000 using laser Doppler and single-sensor hot-wire anemometry. A new correlation is proposed based on zero velocity position, since the Schmidt (1986) correlations fail in the turbulent portion of the bubble.
A variety of numerical simulations of transition and turbulence in incompressible flow are presented to compare the commonly used rotation form with the skew-symmetric (and other) forms of the nonlinear terms. The results indicate that the rotation form is much less accurate than the other forms for spectral algorithms which include aliasing errors. For de-aliased methods the difference is minimal.
Velocity flow fields of a nozzle jet exhausting into a supersonic flow were surveyed. The measurements were obtained with a laser transit anemometer (LTA) system in the time domain with a correlation instrument. The LTA data is transformed into the velocity domain to remove the error that occurs when the data is analyzed in the time domain. The final data is shown in velocity vector plots for positions upstream, downstream, and in the exhaust plane of the jet nozzle.
An ethylene trace gas technique was used to map out fluid transport and mixing within a circular to rectangular transition duct. Ethylene gas was injected at several points in a cross stream plane upstream of the transition duct. Ethylene concentration contours were determined at several cross stream measurement planes spaced axially within the duct. The flow involved a uniform inlet flow at a Mach number level of 0.5. Statistical analyses were used to quantitatively interpret the trace gas results. Also, trace gas data were considered along with aerodynamic and surface flow visualization results to ascertain transition duct flow phenomena. Convection of wall boundary layer fluid by vortices produced regions of high total pressure loss in the duct. The physical extent of these high loss regions is governed by turbulent diffusion.
An ethylene trace gas technique was used to map out fluid transport and mixing within a circular-to-rectangular transition duct. Ethylene gas was injected at several points in a cross stream plane upstream of the transition duct. Ethylene concentration contours were determined at several cross stream measurement planes spaced axially within the duct. The flow involved a uniform inlet flow at a Mach number level of 0.5. Statistical analyses were used to quantitatively interpret the trace gas results. Also, trace gas data were considered along with aerodynamic and surface flow visualization results to ascertain transition duct flow phenomena. Convection of wall boundary layer fluid by vortices produced regions of high total pressure loss in the duct. The physical extent of these high loss regions is governed by turbulent diffusion.
Airspace Technology Demonstration – 3 (ATD-3) is part of NASA’s Airspace Operations and Safety Program (AOSP) – specifically, its Airspace Technology Demonstrations (ATD) Project. ATD-3 is a multi-year research and development effort which proposes to develop and demonstrate automation technologies and operating concepts that enable air navigation service providers and airspace users to continuously assess weather, winds, traffic, and other information to identify, evaluate, and implement workable opportunities for flight plan route corrections that can result in significant flight time and fuel savings in en route airspace. In order to ensure that the products of this tech-transfer are relevant and useful, NASA has created strong partnerships with the FAA and key industry stakeholders. This summary document and accompanying technology artifacts satisfy the third Research Transition Product (RTP) defined in the Applied Traffic Flow Management (ATFM) Research Transition Team (RTT) Plan, which is Dynamic Routes for Arrivals in Weather (DRAW). This technology transfer consists of artifacts for DRAW Arrival Metering (AM) Operations delivered in June 2018, DRAW AM updates, and DRAW Extended Metering (XM) Operations. Blue highlighting indicates the new or modified deliverables. Some of the artifacts in this technology transfer have distribution restrictions that need to be followed. Distribution information is noted in each section. DRAW is a trajectory-based system that combines the legacy Dynamic Weather Routes (DWR) weather avoidance technology with an arrival-specific rerouting algorithm and arrival scheduler to improve traffic flows on weather-impacted arrival routes into major airports. First, DRAW identifies flights that could be rerouted to more efficient Standard Terminal Arrival Routes (STARs) that may have previously been impacted by weather. Second, when weather is impacting the arrival routing, DRAW proposes simple arrival route corrections that enable aircraft to stay on their flight plan while avoiding weather. The DRAW system proposes reroutes early enough to allow Time Based Flow Management (TBFM) to make the necessary schedule adjustments. As a result, metering operations can be sustained longer and more consistently in the presence of weather because the arrival schedule accounts for the dynamic routing intent of arrival flights to deviate around weather. The first DRAW tech transfer in June 2018 focused on arrival metering operations with the DRAW algorithm implemented in the NASA Center TRACON Automation System (CTAS) automation software. This tech transfer delivery includes updates for DRAW implemented in FAA’s TBFM 4.7 automation software and preliminary research into DRAW for XM operations.
Static pressure distributions and dark central ground interferometry are used to document the flow on a flap over a range of Reynolds numbers and deflection angles. The pressure profiles and interferograms are analyzed to distinguish laminar, transitional and turbulent flows in attached, incipient and separated cases. Sideplates are used to compare two and three dimensional effects. Data is also presented for extended flaps used to isolate the effect of the trailing edge expansion. The issues of unsteadiness and hysteresis are also addressed.
Under NASA's Environmentally Responsible Aviation Project, flight experiments are planned with the primary objective of demonstrating the Discrete Roughness Elements (DRE) technology for passive laminar flow control at chord Reynolds numbers relevant to transport aircraft. In this paper, we present a preliminary computational assessment of the Gulfstream-III (G-III) aircraft wing-glove designed to attain natural laminar flow for the leading-edge sweep angle of 34.6deg. Analysis for a flight Mach number of 0.75 shows that it should be possible to achieve natural laminar flow for twice the transition Reynolds number ever achieved at this sweep angle. However, the wing-glove needs to be redesigned to effectively demonstrate passive laminar flow control using DREs. As a by-product of the computational assessment, effect of surface curvature on stationary crossflow disturbances is found to be strongly stabilizing for the current design, and it is suggested that convex surface curvature could be used as a control parameter for natural laminar flow design, provided transition occurs via stationary crossflow disturbances.