Search

Agglomerated multigrid techniques used in unstructured-grid methods are studied critically for a model problem representative of laminar diffusion in the incompressible limit. The studied target-grid discretizations and discretizations used on agglomerated grids are typical of current node-centered formulations. Agglomerated multigrid convergence rates are presented using a range of two- and three-dimensional randomly perturbed unstructured grids for simple geometries with isotropic and stretched grids. Two agglomeration techniques are used within an overall topology-preserving agglomeration framework. The results show that a multigrid with an inconsistent coarse-grid scheme using only the edge derivatives (also referred to in the literature as a thin-layer formulation) provides considerable speedup over single-grid methods, but its convergence can deteriorate on highly skewed grids. A multigrid with a Galerkin coarse-grid discretization using piecewise-constant prolongation and a heuristic correction factor is slower and also can be grid dependent. In contrast, nearly grid-independent convergence rates are demonstrated for a multigrid with consistent coarse-grid discretizations. Convergence rates of multigrid cycles are verified with quantitative analysis methods in which parts of the two-grid cycle are replaced by their idealized counterparts. DOI: 10.2514/1.J050055

Large eddy simulation of flow around a NACA-0012 airfoil at a Reynolds number of 50,000 has been used to study the behavior of a laminar separation bubble near stall The effects of the subgrid-scale model and explicit filtering were studied for a test case in which direct numerical simulation results were available. It was found that a method incorporating a mixed-time-scale model in addition to explicit filtering gave improved results compared with a method with filtering alone. Statistical results as well as snapshots of the flow below stall exhibit good agreement with the direct numerical simulations. For a configuration near stall, the effect of the spanwise domain width was investigated by increasing the spanwise length from 20 to 50% chord. Two-point velocity correlations showed a significant improvement for the wider computational domain, in which the simulation was able to capture a low-frequency flow oscillation, in which intermittent bursting of the bubble was observed. The bubble bursting observed here is more irregular than in experiments at higher Reynolds number. The amplitude and frequency are compared with experimental results and with an unsteady viscons-inviscid interaction method which is shown to be capable of capturing unsteady behavior during stall. DOI: 10.2514/1.44298

The laminar near-wake flow behind a circular cylinder at hypersonic speeds has been examined experimentally and analytically. Surface pressure and heat flux measurements were obtained in a free-piston shock tunnel at a nominal Mach number of 10. The freestream unit Reynolds numbers were 3.02 x [10.sup.5]/m and 11.7 x [10.sup.5]/m at total specific enthalpies of 13.35 and 3.94 MJ/kg, respectively. The experimental data of surface pressure and heat flux showed good agreement with theory based on perfect gas. Unlike surface pressure, the surface heat flux depended strongly on the wall-to-total-temperature ratio, and it increased with increase in the ratio. The surface pressure, however, depended on the Reynolds number, although this dependency was found to be weak. The flow separation angles behind the cylinder showed an inverse of the square root of Reynolds number dependence similar to the low-speed laminar flow separation behind a circular cylinder. DOI: 10.2514/1.44167

In this experimental study, the pressure dependence of the extinction strain rate of flames of jet fuel and other hydrocarbons was measured and quantified. Laminar nonpremixed opposed-jet flames of fuel/nitrogen mixtures versus oxygen-enriched air were progressively strained to extinction by lowering pressure over the pressure range 0.1 to 0.68 atm. The fuels investigated were methane; ethylene; Jet-A; n-decane; 1, 2, 4-trimethyl benzene; and blends of n-decane and 1, 2, 4-trimethyl benzene. All liquid fuels were vaporized and diluted to a mass fraction of 21.5% in nitrogen gas; the gaseous fuels were not diluted. The oxidizer was a 50/50% molar mixture of oxygen and nitrogen. The global strain rate at extinction was seen to monotonieaHy increase with pressure in the subatmospheric pressure range explored. Overall reaction orders calculated from density-weighted extinction strain rates were between 1.3 and 2.0. Jet-A flames were extinguished at conditions similar to those for the decane/trimethyl benzene blends, indicating that these blends can serve as a surrogate for Jet-A. DOI: 10.2514/1.42742

We numerically investigate the application of steady blowing to three-dimensional stalled flows around low-aspect-ratio rectangular flat-plate wings at a Reynolds number of 300. The objective of this study is to explore techniques to enhance lift by directly modifying the dynamics of the wake vortices. Out of various combinations of forcing location and direction considered, we identify two configurations that provide significant lift enhancement. In these cases, actuation appears to strengthen the tip vortices for increased downward induced velocity upon the leading-edge vortices. This in turn moves the low-pressure core directly above the top surface of the wing to greatly enhance lift.

This paper describes in-flight measurements in low- and high-speed experiments to investigate laminar-turbulent transition on airfoils. The low-speed experiments were carried out using a laminar wing glove for a sailplane. High-speed experiments on an modified A320 hybrid laminar fin were conducted in close collaboration with Airbus. Different surface sensor measuring techniques (piezofoil, surface hot wires, wall microphones) were used in the low-speed experiments. The piezofoil technique was applied in the high-speed in-flight experiments to prove the operation robustness, the functional capability, durability, and reliability under atmospheric conditions in cruise flight on modern airplanes. All measuring techniques were successfully implemented for the particular task and the laminar-turbulent transition was detected with a high degree of certainty. For the high-speed investigations a complete piezofoil sensor array was glued directly to the fin without causing any interference between the boundary layer flow and the sensor foil. This technique therefore offered the good potential to detect transition in the boundary layer under flight conditions especially in high-speed tests.

The origin of the exact, closed-form, self-similar exponential solution for the laminar decay of an isolated two-dimensional vortex in a viscous incompressible fluid is studied to find a proper name for the function. Two major contributions to the solution are the similarity parameter derived by Boltzmann and the derivation of the form of the solution by Carslaw for the diffusion of heat from a line source, that is, a spark or lightning stroke. Lamb adapted the heat transfer solution derived by Carslaw to the time-dependent diffusion of vorticity from a potential line vortex, and, after publication of his book, has provided a short, complete, and readily available derivation. Oseen's derivation followed about four years later and is not as complete. Various titles for the solution are believed to be appropriate, including a generic name such as exponential vortex solution, or the name of Lamb. The name of Lamb is probably the most appropriate because he was the first in existing literature to put the entire derivation together and because the presentation is compact, complete, and readily available.

An improved low-Reynolds-number k-[epsilon] model is adopted to predict turbulent flows with a nonstationary boundary. The performance of the adopted model is first contrasted with direct numerical simulation data of the turbulent plane Couette-Poiseuille flow. Detailed flow structure is captured accurately by the model, in particular the reduction of the shear stress and, hence, the turbulent kinetic energy due to the presence of the moving wail. The validity of the present model in computing complex flows within rotating disk cavities is further examined. Flows with two different rotational Reynolds numbers are investigated, and the predicted mean and turbulence results are also contrasted with measurements. The influence of rotation on the flowfield and turbulence modeling is investigated by sensitizing the turbulence model coefficient to rotational Richardson number, and the effect is found to be marginal. Because the internal flow structure of the rotating disk cavities is induced by the diffusive transport of the tangential momentum from the rotor into the interior, the predicted thickness of the Ekman layer is found to be critical to the correct predictions. The adopted model reproduces correctly the gradual thickening of the Ekman layers from small to large radii, which is due to the transition from laminar to turbulent regimes, especially on the rotor side within the disk cavities. The elevated level of turbulence on the stator side compared to that on the rotor side is also predicted correctly by the present model.

This paper explores the effects of mild sweep on active separation control at high Reynolds numbers and incompressible Mach numbers. The model, which was tested in a cryogenic pressurized wind tunnel, simulates the upper surface of a 20% thick Glauert-Goldschmied type airfoil at zero angle of attack. The boundary-layer flow is turbulent because the tunnel side-wall boundary layer flows over the model, eliminating laminar-turbulent transition from the problem. Without control the flow separates at the highly convex area, and a large turbulent separation bubble is formed at the lee side of the model. Periodic excitation and steady mass transfer were applied to eliminate the separation bubble gradually. During the test, the Reynolds numbers ranged from 7 x [10.sup.6] to 26 x [10.sup.6], and the Mach numbers were 0.2 and 0.25. The test sweep angles were 0 and 30 deg. It was found that the excitation must be introduced slightly upstream of the separation region regardless of the sweep angle at low Mach numbers, as in the two-dimensional flow. The conventional swept flow scaling is valid for controlled, fully and even partially attached flow, but different scaling is required for the separated three-dimensional flow. The effectiveness of the active control is not reduced by mild sweep, and the effective frequencies do not change.

Interlaminar stress distribution in smart composite shells using a coupled thermal-piezoelectric-mechanical model is investigated. To maintain local accuracy of stress distributions, the trial displacement field is assumed layerwise higher order and Co continuous through the entire laminate thickness, accommodating zigzag in-plane warping and interlaminar shear stress continuity. The temperature and electrical fields are modeled using higher. order descriptions that can satisfy surface flux boundary conditions at structural surfaces and equipotential conditions at electrode surfaces. These assumptions ensure computational efficiency. A variational principle, addressing the interaction between thermal, piezoelectric, and mechanical fields, is used to derive the governing equations of equilibrium. The proposed theory is used to investigate the cylindrical bending problem of simply supported composite host structures with attached piezoelectric actuators, subject to a combination of mechanical, piezoelectric, and thermal loading. The interlaminar stress distributions under comprehensive loading are presented for different geometries and stacking sequences. The effects of two-way piezoelectric and thermal coupling on the stress distributions are investigated. The significance of the thermal mismatch effect on interlaminar stress distribution is also discussed. The results from present theory are validated with available exact elasticity solutions.

The shapes (flame-sheet and luminous-flame boundaries) of steady weakly buoyant round hydrocarbon-fueled laminar-jet diffusion flames in still and coflowing air were studied both experimentally and theoretically. Flamesheet shapes were measured from photographs using a CH optical filter to distinguish flame-sheet boundaries in the presence of blue C[O.sub.2] and OH emissions and yellow continuum radiation from soot. Present experimental conditions included acetylene-, methane-, propane-, and ethylene-fueled flames having initial reactant temperatures of 300 K, ambient pressures of 4-50 kPa, jet-exit Reynolds numbers of 3-54, initial air/fuel velocity ratios of 0-9, and luminous flame lengths of 5-55 mm; earlier measurements for propylene- and 1,3-butadiene-fueled flames for similar conditions were considered as well. Nonbuoyant flames in still air were observed at microgravity conditions; essentially nonbuoyant flames in coflowing air were observed at small pressures to control effects of buoyancy. Predictions of luminous flame boundaries from soot luminosity were limited to laminar smoke-point conditions, whereas predictions of flame-sheet boundaries ranged from soot-free to smoke-point conditions. Flame-shape predictions were based on simplified analyses using the boundary-layer approximations along with empirical parameters to distinguish flame-sheet and luminous-flame (at the laminar smoke point) boundaries. The comparison between measurements and predictions was remarkably good and showed that both flame-sheet and luminous-flame lengths are primarily controlled by fuel flow rates with lengths in coflowing air approaching 2/3 of the lengths in still air as coflowing air velocities are increased. Finally, luminous flame lengths at laminar smoke-point conditions were roughly twice as long as flame-sheet lengths at comparable conditions because of the presence of luminous soot particles in the fuel-lean region of the flames.

Transition characteristics of a supersonic natural laminar flow wing with a sweep angle of more than 60 deg were measured using hot-film sensors and an infrared camera at Mach 2. The pressure falls very rapidly in the vicinity of the leading edge of the wing, such that crossflow instabilities are reduced. The flow slightly accelerates downstream such that streamwise instabilities are stabilized. Tests were conducted in two wind tunnels to estimate the transition location in flight: a quiet tunnel with a low Reynolds number and a moderately quiet tunnel with variable Reynolds number. As a result, the natural laminar flow effect of the wing was confirmed. The unit Reynolds number had no effect on the transition Reynolds number of the wing. The transition Reynolds number was 8 x 10[.sup.5] at the design angle of attack at Mach 2, but there is room for further investigation.

A small trailing-edge flap, often referred to as a cruise flap or camber-changing flap, can be used to extend the low-drag range of a natural-laminar-flow airfoil. Automation of such a cruise flap is likely to result in improved aircraft performance over a large speed range without an increase in the pilot work load. An important step in achieving the automation is to arrive at a simple approach for determination of the optimum flap angle for a given airfoil lift coefficient. This optimum flap angle can then be used in a closed-loop control system to set the flap automatically. Two pressure-based schemes are presented for determining the optimum flap angle for any given airfoil lift coefficient. The schemes use the pressure difference between two pressure sensors on the airfoil surface close to the leading edge. In each of the schemes, for a given lift coefficient, this nondimensionalized pressure difference is brought to a predetermined target value by deflecting the flap. It is shown that the drag bucket is then shifted to bracket the given lift coefficient. This nondimensional pressure difference, therefore, can be used to determine and set the optimum flap angle for a specified lift coefficient. The two schemes differ in the method used for the nondimensionalization. The effectiveness of the two schemes is verified using computational and wind-tunnel results for two NASA laminar flow airfoils. Finally, an aircraft performance simulation approach is used to analyze the potential aircraft performance benefits while addressing trim drag considerations.

A method is presented for estimating the laminar/turbulent transition location in three-dimensional boundary layers for computational fluid dynamics (CFD) applications requiring numerous transition estimates with no user intervention. Given the Reynolds number and the [C.sub.P] distribution, the location of transition is estimated based on the attachment-line state, the potential for relaminarization, the occurrence of laminar separation, and the growth of instabilities. Transition caused by instability is estimated based on N factors calculated for Tollmien-Schlichting waves and for stationary crossflow instabilities. A neural network is used (in place of solving the Orr-Sommerfeld stability equation) for determining the instability growth rates. The current version of the method assumes incompressible flow. The boundary-layer flow and instabilities are calculated based on an infinite-sweep (strip boundary layer) approximation; the instability calculations also employ the parallel-flow approximation. Comparisons with traditional stability codes show good N-factor agreement over a practical range of [C.sub.P] distributions. The method is several hundred times faster than traditional stability calculations, and it is robust enough to function as a simple 'subroutine' in CFD codes. The method is biased toward application efficiency and simplicity as balanced against improvements in the detailed physical modeling.

Even with all of the advances in airfoil and aircraft design, there remains little guidance on how to tailor an airfoil to suit a particular aircraft. A two-pronged approach is presented to tailor an airfoil for an aircraft: 1) an approach in which aircraft performance simulations are used to study the effects of airfoil changes and to guide the airfoil design and 2) an analytical approach to determine expressions that provide guidance in sizing and locating the airfoil low-drag range. The analytical study shows that there is an ideal value for the lift coefficient for the lower corner of the airfoil low-drag range when the airfoil is tailored for aircraft level-flight maximum speed. Likewise, there is an ideal value for the lift coefficient for the upper corner of the low-drag range when the airfoil is tailored for maximizing the aircraft range. These ideal locations are functions of the amount of laminar flow on the upper and lower surfaces of the airfoil and also depend on the geometry, drag, and power characteristics of the aircraft. Comparison of the results from the two approaches for a hypothetical general aviation aircraft are presented to validate the expressions derived in the analytical approach.

The recent progress in compliant-wall designs for aeronautical applications is reviewed, focusing on flow-induced surface instabilities, multiple-panel compliant walls and laminar flow control.

The problem of optimizing suction distribution on multi-panel hybrid laminar flow aircraft to minimize total energy usage is discussed. Experimental results are included.

Laminar flow was measured from the standpoint of occurring coherent structures. Streamwise and normal-to-the-wall velocity was measured with an X-type hot-wire probe, and passage of von Karman vortices were measured with a gradient hot-wire probe.

A study has been conducted to evaluate the mixed-layer models that proposed in an earlier study. Displacement formulations were implemented to compare equation results and solve shell equations for the particular cases of orthotropic lamina cross-ply laminated shells that were loaded by a harmonic distribution of transverse pressure. Findings have revealed that the fulfillment of the transverse shear and normal stress interlaminar equilibria has led to a better description as far as the related theory is concerned.

A study was conducted to examine the stability and transition on a fully three-dimensional configuration and to demonstrate a case in which a crossflow instability had a significant influence on boundary-layer transition. The experiments involved the use of an elliptical cone to induce significant significant crossflow and to closely resemble realistic conditions in a hypersonic vehicle. Findings have revealed that the basic state of laminar flow was relatively complex with highly skewed velocity profiles and a pair of symmetric vortices on the top centerline of the cone.

A new fiber-optic catheter for in vivo blood-flow measurements has been developed. The catheter is designed to measure blood flow in both the forward (toward the catheter tip) and reverse (away from the catheter tip) flow directions. It consists of two multimode optical fibers with core diameter of 50 [[micro]meter] and cladding diameter of 125 [[micro]meter]. One fiber transmits the laser beam into blood and the other receives the backscattered light from the erythrocytes within the probe volume. In the flow experiment, it was found that the flow within the boundary layer is indeed laminar and, hence, the relationship between the Doppler shift frequencies and the flow velocities is linear, thereby making the linear calibration possible for predicting the free stream flow velocity. Plots of the maximum shift frequency (frequency at which the Doppler spectrum disappeared into the noise spectrum) against the flow velocities are found to be more linear in both the forward and reverse flow directions than that of the dominant shift frequency (frequency with the highest amplitude). These results were reaffirmed by the numerical flow simulation along the catheter side wall. Index Terms - Anemometry, boundary layer, dominant shift frequency, Doppler frequency, laminar, maximum shift frequency.

A new design method for reducing drag through the design of natural laminar flow (NLF) airfoils is presented. The method uses proven computational fluid dynamics (CFD) analysis, combined with a new target pressure design method. Its main features are a compressible linear stability analysis code which calculates the N-factors and its ability to calculate a target N-factor distribution.

The capture of fine paramagnetic particles from a fluid suspension in a magnetic filter element of a novel design is analyzed. Unlike the systems previously analyzed, in our model the flow is bounded by two by two parallel planar plates, and the ferromagnetic wires are installed outside these spaces, within planes parallel with the plates. Our analysis is based on the study of particle trajectories, considering the laminar flow of carrier fluid. From these we establish the conditions for the maximum recovery of the particles in suspension. This study is useful in designing magnetic filter batteries with corrosion-protected ferromagnetic wires. Index Terms - Fluid suspension, laminar flow, magnetic filtration.

A comparison of numerical and experimental results of dynamic stall flow over an oscillating airfoil shows the use of transition onset point movements and transition length changes in predicting the extent of laminar separation bubble. The incorporation of these changes results in good agreement between the numerical and experimental data for the pressure and velocity distributions near the leading edge. The thin-layer approximations of the compressible, Reynolds-averaged Navier-Stokes equations give the numerical solutions.

The application of Newton-Krylov (NK) methods to low-Mach-number combustion problems shows that the matrix-free NK method is superior to the modified NK method. Mesh sequencing results in significant computational savings for fine grid calculations of the nonlinear algebraic equations. The nonpremixed laminar diffusion flame model problem is solved by applying an NK algorithm. The domain-based multiplicative Schwarz preconditioner is more effective than the incomplete lower-upper type preconditioning at low Mach numbers.

Experiments are carried out in a low-speed water channel to investigate saddle-point-of-attachment flowfields in laminar horseshoe vortex flows upstream of a cylinder/flat plate. Flow visualization is performed using an argon-ion laser and cylindrical optics. The generated images are then analyzed by means of personal computer. Results indicate that the saddle-point-of-attachment topology exists over a broad range of turbulent and high-speed flows.

The boundary-layer transition on a swept-wing leading-edge model at the NASA Langley Supersonic Low-Disturbance Tunnel was investigated at Mach 5. Specifically, measurements were taken of surface pressure and wall temperature distributions on pressure and thin-skin thermocouple models along with flow visualizations. The results, which were compared with numerical solutions to the thin-layer Navier-Stokes equation and N-factors derived via the envelope e(sup N) method, suggest that travelling crossflow disturbances are the likeliest cause of such transitions.

Research work on the impact of three-dimensional mean flow on the near-wall structure of turbulent boundary layers is assessed. These include studies of flows approaching a wedge, flows over a rotating disk and the development of embedded vortices in wedge flow boundary layers. All were characterized by a reduction in Reynolds shear stress and the presence of quasistream vortices as well as low- and high-speed streaks in the near-wall region.

A new boundary-layer transformation computes the compressible, laminar boundary layers on swept, tapered wings with greater reliability than the Kaups-Cebeci equations. Inclusion of corrected boundary-layer growth in the new transformation causes the minimization of the streamwise derivatives. Solutions from the new transformation overcome the spurious oscillations in second-derivative profiles. Insignificant streamwise differences are observed for transformed boundary-layer thickness.

The feasibility of using the selective suction process in controlling the breakdown of streamwise vortices around aerodynamic structures was evaluated. Experiments were carried out wherein a test model was subjected to simulated turbulence in an open return wind tunnel. Suction was applied pointwise between counter-rotating streamwise vortex pairs at different directions. Results showed the breakdown of the vortices was delayed when the suction was applied in the normal direction.

Analysis of the two-dimensional steady laminar flow of an ideal gas subjected to incipient separation in the region of strong interaction arising due to an impinging shock or a compression corner helps formulate a unified scaling law for moderately hypersonic and supersonic Mach members. The triple-deck theory is modified using the reference temperature concept to suit nonadiabatic flows and utilized for the analysis of compression corner interactions and impinging shocks.

A combination of an Euler/boundary layer method, a second order boundary layer theory known as EUBL, linear stability theory and the Exponential method determined the transition location for a hypersonic, axisymmetric boundary layer from an engineering perspective. EUBL-based analysis of stability behavior and transition location coincided with the results of Navier-Stokes mean flows, but were more efficient and cost-effective in determining laminar mean flows.

Studies of two-dimensional, unsteady, leading-edge, boundary-layer separation of subsonic laminar flow above a pitching airfoil reveal that a clockwise-rotating recirculating region is followed by secondary and tertiary clockwise-rotating recirculating regions. The primary and secondary regions cause the boundary layer separation due to interactions. The flowfield center and saddle points determine the primary recirculating region.

A theoretical and experimental study of the statistics of the received signal from laminar flow, following the transmission of a series of short pulses is detailed to determine the limiting velocity resolution that can be achieved using ultrasound. This also provides a model which can be used to generalize the analysis of distributed flow.

The effects of preferential thermal transport on the characteristics of diffusion flames are studied. The systems important parameters, such as strain rate, total mass density and velocity, are expressedin terms of conservation equations using a multicomponent diffusion model. The flame's temperature and front position and the reactant consumption rates are also considered in the study. Results show that the present model performs better than those using mass transport parameters.

A study was conducted to develop a postprocessor that can calculate interlaminar shear and normal stresses of laminated plates subjected to transverse loads. To calculate the derivative information of in-plane stresses, a weighted least-squares was integrated into the global displacement technique which uses Chebyshev and a class of orthogonal polynomials. The results derived from this method are in good agreement with existing data. Furthermore, the shape of through-the-thickness distribution of interlaminar normal stress depends on the side-to-thickness ratio.

A study was conducted to analyze the process toward three-dimensional separation over an abruptly started prolate spheroid by using a time-accurate Eulerian program. Results show that separation at the physical level in both the steady and unsteady cases steam from the extreme streamwise contraction of a certain fluid packet inside the boundary layer. At a later stage, the lateral distribution of the displacement velocity widens into a crescent-shaped ridge. Therefore, the present Eulerian method produces results that are synchronous to the Lagrangian concept of separation.

The interaction between shock waves and boundary layers existing about a hypersonic vehicle is studied through shock tunnel experiments. Tests are carried out in a free-piston shock tunnel wherein a flat plate with a sharp leading edge is subjected to a simulated shock wave. The plate's pressure responses are then measured using an array pressure transducers and a digital event recorder. Results show that free-piston shock tunnels are useful for the speedy analysis of hypersonic shock-wave/boundary-layer interactions.

A study was conducted to describe pressure measurements made under a back-step model in high enthalpy hypervelocity flow conditions. Results show that the general features of hypervelocity laminar dissociated flow behind a step are qualitatively similar to those of an undissociated flow at moderate velocity. The only difference between these two flows is the presence of the thick shear layer behind the step, which is indicative of reattachment shock.

A numerical study was done on both laminar and turbulent horseshoe vortex systems generated by flow past a cylinder mounted on a flat plate, and the juncture flow topology is also analyzed. Results show that the computed juncture flows are in good agreement with the experimental data. As the freestream Mach number increases, the outermost singular point moves upstream. Moreover, the upstream outermost singular point can be either a saddle point of attachment or separation, depending on flow conditions.

A study was conducted to test the integrity of the laminar mixing theory. The calculations of the flowfield of two laminar, steady coflowing streams are compared with the experimental data. Results show that the calculated parameters are in good agreement with the data. For supersonic and hypersonic flows, laminar mixing causes the increased stability of the upstream boundary layers, thereby turbulent transition is delayed. However, the theory needs further improvement in its analytical forms.

The air drag over an airplane can be reduced by increasing the natural laminar flow (NLF) over the plane's wings during subsonic flights. The design of axisymmetric body shapes such as fuselages, external fuel tanks and nacelles, all of which are non-lifting surfaces, play a significant role in drag reduction in aircrafts. An optimization procedure to design axisymmetric body shapes with increased transition Reynolds number is presented.

Design of gas turbine combustors necessitates a suitable temperature distribution at the outlet and a two-equation turbulence model can precisely predict the mixing parameters at this outlet. This mathematical procedure shows that lack of grid nodes results in underestimation of streamwise vorticity. There is also a proper prediction of general flow pattern and the outlet section exhibits a flow primarily governed by the outer jet. The calculations reveal lower mixing levels than those obtained in the experiments.

A solution-adaptive grid scheme for the three-dimensional parabolized Navier-Stokes (PNS) equations is based on an error equidistributionprinciple. The method employs redistribution of grid points and the solutions are found more efficiently by marching in space instead of time. The adaptive grid algorithm gives better shock resolving properties and can align grid linesbetter than conventional flow algorithms. The prediction of pitot pressure on cones is facilitated by the solution-adaptive method rather than by a fixed grid algorithm.

The advancement of supersonic combustion ramjet engines necessitates enhanced flow mixing conditions and thus, a better understanding of the instability mechanism. Experiments on basic flow structures depend primarily on flow visualizations and numerical simulations. These experiments can deal with more detailed studies on effects of grid resolution and scheme dissipation on the solution quality. High grid density is needed for mixing flow computations. Reynolds stress is also very sensitive to grid resolution and eddy shocklets fail to adhere to the wall for transonic mixing layers. Dissipation via limiting procedure should be minimized to avoid nonphysical overcompression.

Application of the laminar flow control (LFC) technology to subsonic andsupersonic aircraft design necessitates accurate prediction of the boundary- layer transition location. The linear stability code COSAL is used to examine the linear stability of fully three-dimensional boundary layer showing the practicality of both Tollmien-Schlichting and crossflow disturbances in the transition process. The predicted transition location approximates the experimental results of Meier and Kreplin showing that the direction of disturbance propagation depends on disturbance type and dimensional frequency.

A study was conducted to study the physical mechanisms involved in the fluid-wall interaction of transitional and turbulent flows. In the boundary-layer transition, transition delays have primary instability which gives rise to a secondary instability mechanism. Transition-control devices like compliant and rigid walls were used, and both isotropic and nonisotropic compliant walls lead to significant reduced secondary growth rates compared with the rigid wall results. Moreover, using compliant walls to suppress the primary growth rates also give rise to delays in the growth of the secondary instability mechanism.

A Nwewton's method for the calculation of separated supersonic and hypersonic viscous flows is discussed. The method uses a FORTRAN computer code and a matrix inversion technique to generate accurate solutions for the steady, two-dimensional, laminar Navier-Stokes equations governing the flowfield parameters. It provides a cost-effective alternative to conventional marching schemes for the analysis of high-speed viscous turbulent flows.

Research was conducted to evaluate the effectiveness of the periodic injection of momentum in applications involving swept-back wings. Flow visualization experiments performed on a yawed circular cylinder revealed that only 10% of the span was affected by wall interference. Pressure distribution data showed that the effect of forcing did not deteriorate due to the sweep.

A numerical Navier-Stokes laminar flowfield simulation for the cone-derived waverider with multidirectional curvature involves both on-design Mach 4 and off-design conditions. The analysis includes attack angles from 0 to 10 degrees and Mach numbers from 2 to 6. For the on-design conditions, both the inviscid and viscous simulations correlate well with the hypersonic small-disturbance theory. An enhanced volumetric ratio, wider range of flight conditions, and an increased lift-to-drag ratio confirm the merits of a longitudinal curvature.