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Computational Fluid Dynamics (CFD) was used to investigate the flow in a rotating detonation engine (RDE) with ideal and slot injection of H2-air at stoichiometric conditions. A detailed kinetic mechanism was used to show that a stable, grid independent, rotating detonation traveling at the correct speed could be established for ideal injection. Stable rotating detonation was not sustained when slot injectors were used with an area ratio of 0.2. Numerical experiments showed that a higher area ratio is required to establish a single rotating detonation when using a realistic kinetics model. A one-step kinetic model with longer induction time was used to establish a stable rotating detonation wave within the engine for injectors with an area ratio of 0.2. These studies point to issues with the presence of hot burned gas in the head-end of the RDE affecting the stability of RDE operation.

The Rt turbulence closure (Goldberg 2003) is coupled with an intermittency transport equation, γ, to enable prediction of laminar-to-turbulent flow by-pass transition. The model is not correlation-based and is completely topography-parameter-free, thus ready for use in parallelized Computational Fluid Dynamics (CFD) solvers based on unstructured book-keeping. Several examples compare the R-γ model's performance with experimental data and with predictions by the Langtry–Menter γ-Reθ transition closure (2009). Like the latter, the R-γ model is very sensitive to freestream turbulence levels, limiting its utility for engineering purposes.

The purpose of this article is to offer some insights, suggestions and recommendations on usage of current statistical models of turbulence. The issues discussed have arisen during several decades' worth of combined research experience and through direct support of numerous commercial computational fluid dynamics (CFD) customer projects covering a broad range of aerospace, automotive, marine and manufacturing applications. The discussions and ideas presented pertain to how existing algorithms and phenomenological models of turbulence can best be used with current computer hardware.

Progress toward a general purpose hybrid Reynolds-averaged Navier-Stokes (RANS)/large-eddy simulation (LETS) framework is described, in which large-scale, statistically represented turbulence kinetic energy is converted automatically into resolved-scale velocity fluctuations wherever the local mesh resolution is sufficient to support them. Existing hybrid RANS/LES approaches alter the nature of the local partial differential equations according to the local mesh resolution, but they do not alter the nature of the data on which these equations operate. The implications of this are discussed. Subsequently, a simple mechanism is introduced to transfer statistical kinetic energy into resolved-scale fluctuations in a manner that preserves a given set of space/time correlations and set of second moments. This process, which can appropriately be termed Large-Eddy STimulation (LEST), generates the large-scale eddies needed to form the unsteady boundary conditions at RANS interfaces to LES regions, into which turbulence energy can be deposited either through mean convection or through turbulent transport

Two- and three-dimensional hypersonic flow cases are computed using linear one-equation closures and a nonlinear two-equation model, where the anisotropy tensor is modeled as a cubic function of mean strain and vorticity tensors. The latter is found to excel in predicting bypass transition, whereas the one-equation R t model is very good at heat-transfer prediction. Both closures excel in predicting pressure distributions; however, the nonlinear model is found to overpredict heat-transfer. This suggests that in separated flow regions with simultaneously low mean-flow kinetic energy (and therefore low strain magnitude) and high temperature gradients, overpredicted levels of turbulence length scale can lead to rather small errors in the turbulent shear stress, while at the same time leading to a large overprediction of the turbulent heat fluxes

Chilli-based repellents have shown promise as deterrents against crop-raiding elephants in Africa. We experimented with ropes coated with chilli-based repellent as a cheap alternative to existing elephant cropraid deterrent methods in India. Three locations (Buxa Tiger Reserve, Wyanad Wildlife Sanctuary and Hosur Forest Division) representing varying rainfall regimes from high to low, and with histories of intense elephant-agriculture conflict, were selected for the experiments that were conducted over 2-3 months during the pre-harvest period of the kharif season in late 2006. Chilli and tobacco powder mixed with waste oil was applied to ropes strung around agricultural fields of 1.4-5.5 km perimeter and elephant approaches were monitored. Elephants breached the rope fences a few times at all three study sites. Female-led herds were far more deterred (practically 100% reduction) than were solitary males (c. 50%) by the chilli-tobacco rope. Efficacy of this method as a deterrent was significantly better in the low-rainfall regime relative to medium and high-rainfall regimes. The initial promising results present a case for more rigorous experimentation; these would help determine if the elephants avoiding the rope are responding physiologically to the chilli-tobacco smell or merely reacting cautiously to a novel substance in their environment.

A code validation study has been conducted using four different codes for solving the compressible Navier-Stokes equations. Computations for a series or nominally two-dimensional high-speed laminar separated flows were compared with detailed experimental shock-tunnel results. The shock-wave boundary-layer interactions considered were induced by a compression ramp.

A computational fluid dynamics solution of the Navier-Stokes equations has been applied to the internal and external flow of inert solid-fuel ramjet projectiles. Computational modeling reveals internal flowfield details not attainable by flight or wind tunnel measurements, thus contributing to the current investigation into the flight performance of solid-fuel ramjet projectiles. The present code employs numerical algorithms termed total variational diminishing (TVD). Computational solutions indicate the importance of several special features of the code including the zonal grid framework, the TVD scheme, and a recently developed backflow turbulence model. The solutions are compared with results of internal surface pressure measurements. As demonstrated by these comparisons, the use of a backflow turbulence model distinguishes between satisfactory and poor flowfield predictions.

Several ways of achieving higher order accuracy on arbitrary grids are explored. These include polynomial reconstructions based on point and cell average values and the Discontinuous Galerkin method, in which the solution is expanded within a cell, and evolution equations are derived for the expansion coefficients. The polynomial reconstruction scheme based on cell averages is also extended to deal with unsteady viscous flows to higher order accuracy.

We compare the results obtained with an approximately factored lower-upper triangular solver, an explicit Runge-Kutta scheme, and a point implicit method for a variety of timesteps to assess solver error and timestep issues in computations of unsteady flows

We present a review of studies on elephant social and reproductive behaviour. While the social organization of the African savannah elephant (Loxodonta africana africana) has been intensively studied,that of the African forest elephant (Loxodonta africana cyclotis) and the Asian elephant (Elephas maximus) are poorly understood. Noninvasive molecular methods are useful in combination with behavioural data in understanding social organization and dispersal strategies. The ecological determinants of social organization, and the importance of matriarchal leadership to social groups, and relative importance of different forms of communication under various ecological conditions remain interesting topics that await investigation. Reproductive behaviour also has been examined in detail only in the African savannah elephant, although rigorous chemical analyses continue to be carried out using captive elephants of both species. Improved laboratory techniques may enable future work on reproductive signalling in free-ranging elephants, allowing for comprehensive studies of male-male interactions and mate choice by females.

The use of microsatellite DNA markers in large mammal conservation genetics has been limited by the logistic difficulty in obtaining optimal sources of DNA from free-ranging animals. Here, we show high amplification success of microsatellite DNA from elephant dung samples collected under field conditions. Amplification success depended on how fresh the sample was when collected, and on the sensitivity of primers at individual loci. No significant allelic dropout was observed. We also examined the loci for selective neutrality, independent inheritance of loci, and the probability of identity of individuals to confirm their utility in studies of population genetic structure.

Social organization of the Asian elephant (Elephas maximus) is not well understood in the absence of long-term studies of identified individuals. Adult Asian elephant females and their young offspring of both sexes form matriarchal groups, with pubertal males dispersing from natal groups, but whether these social groups represent families and whether males show locational or social dispersal were unknown. Using nuclear microsatellite loci amplified from dung-extracted DNA of free-ranging elephants in a large southern Indian population, we demonstrate that female-led herds comprise closely related individuals that are indeed families, and that males exhibit non-random locational dispersal.

Selective poaching of Asian elephant (Elephas maximus) males for ivory has resulted in highly female-biased adult sex ratios, necessitating regular monitoring of population structure and demography. We demonstrate that molecular sexing from dung-extracted DNA, based on ZFX-ZFY fragment amplification and ZFY-specific BamHI site restriction, can be applied to estimate sex ratios of free-ranging Asian elephants, in addition to or instead of field demographic methods. The adult sex ratios using molecular sexing in Nagarahole and Mudumalai-Bandipur reserves during May 2001 were 1:3.1, which matched the demography-based sex ratio for the same month, and 1:9.4, respectively.

Some ecological factors that might potentially influence intestinal parasite loads in the Asian elephant (Elephas maximus Linn.) were investigated in the Nilgiris, southern India. Fresh dung samples from identified animals were analysed, and the number of eggs/g of dung used as an index of parasite load. Comparisons across seasons and habitats revealed that parasite loads were significantly higher during the dry season than the wet season, but were not different between the dry-deciduous and dry-thorn forests in either season. After accounting for the effect of age on body condition, there was no correlation between body condition, assessed visually using morphological criteria, and parasite load in either season. Individuals of different elephant herds were not characterized by distinct parasite communities in either season. When intra-individual variation was examined, samples collected from the same individual within a day differed significantly in egg densities, while the temporal variation over several weeks or months (within a season) was much less. Egg densities within dung piles were uniform, enabling a simpler collection method henceforth.

The Asian elephant (Elephas maximus) is believed to number about 45,000 in the wild and is distributed across several populations over South and Southeast Asia. It is an important flagship species for the conservation of biodiversity as well as being a cultural symbol of the people of this region. We analyse a Geographical Information System database of administrative forest divisions constituting four Project Elephant Reserves designated for southern India, in an attempt to prioritize them for specific conservation action and funding allocation. We compute a conservation value for each of these divisions by using five variables characterizing habitat, population and biodiversity attributes. We also compute threat values for each, using two variables which represent the most significant threats. Based on a cluster analysis we demonstrate that divisions with high conservation values have large elephant distribution areas, preferred habitat areas and elephant

The stable carbon and oxygen isotope ratios in cellulose of C3 and C4 plants growing on the surface of a montane peat bog in the Nilgiri hills, southern India, were measured. The mean monthly delta(13)C values in cellulose of both C3 and C4 plants are found to be significantly related to rainfall, while the delta(18)O values are sensitive to changes in maximum temperature and relative humidity of the region. Further, higher delta(18)O values were observed in C4 plants compared to C3 plants, suggesting that C4 plants are probably less sensitive to relative humidity as compared to C3 plants and are able to photosynthesize even during drier conditions. The plant isotope-climate correlations thus established can be used for reconstructing the past temperature and rainfall conditions of the tropics from the isotopic ratios of peat deposits, derived from a mixture of C3 and C4 plants in the region.

The stable carbon and oxygen isotope ratios in cellulose of C3 and C4 plants growing on the surface of a montane peat bog in the Nilgiri hills, southern India, were measured. The mean monthly $\delta^{13}C$ values in cellulose of both C3 and C4 plants are found to be significantly related to rainfall, while the $\delta^{18}O$ values are sensitive to changes in maximum temperature and relative humidity of the region. Further, higher $\delta^{18}O$ values were observed in C4 plants compared to C3 plants, suggesting that C4 plants are probably less sensitive to relative humidity as compared to C3 plants and are able to photosynthesize even during drier conditions. The plant isotope-climate correlations thus established can be used for reconstructing the past temperature and rainfall conditions of the tropics from the isotopic ratios of peat deposits, derived from a mixture of C3 and C4 plants in the region.

Populations of many animal species worldwide are threatened with loss of genetic variation due to substantial reduction in population size.

Stable carbon isotope ratios of peats dated (by C-14) back to 40 kyr BP from the montane region (> 1800 m asl) of the Nilgiris, southern India, reflect changes in the relative proportions of C3 and C4 plant types, which are influenced by soil moisture (and hence monsoonal precipitation), From prior to 40 kyr BP until 28 kyr BP, a general decline in delta(13)C values from about - 14 per mil to - 19 per mil suggests increased dominance of C3 plants concurrent with increasingly moist conditions, During 28-18 kyr BP there seems relatively little change with delta(13) C of - 19 to - 18 per mil, At about 16 kyr BP a sharp reversal in delta(13)C to a peak of - 14.7 per mil indicates a clear predominance of C4 vegetation associated with arid conditions, possibly during or just after the Last Glacial Maximum, A moist phase at about 9 kyr BP (the Holocene Optimum) with dominance of C3 vegetation type is observed, while arid conditions are re-established during 5-2 kyr BP with an overall dominance of C4 vegetation, New data do not support the occurrence of a moist phase coinciding with the Mediaeval Warm Period (at 0.6 kyr BP) as suggested earlier, Overall, the climate and vegetation in the high altitude regions of the southern Indian tropics seem to have responded to past global climatic changes, and this is consistent with other evidences from India and other tropical regions.

Publisher Summary This chapter describes the role of the host-node and client-server programming paradigms in effectively adapting full-fledged computational fluid dynamics (CFD) codes designed for conventional workstations and supercomputers to massively parallel processor (MPP) computers, and in designing new CFD software for them. They permit the various tasks to be encapsulated in an object-oriented fashion and result in the synergistic use of all available computational resources. In the host-node programming model, programs run concurrently on the host as well as on a chosen set of nodes. The programs can communicate with each other by passing messages. The chapter discusses the minimum hardware configuration, including one MPP computer, one or more graphics workstation with X-windows, and disks on the workstation. It is assumed that the amount of main memory available on the MPP computer far exceeds the maximum possible on an individual workstation. The chapter further describes the application domain; geometric domain decomposition and synthesis; functional domain decomposition and synthesis; application domain decomposition and synthesis, along with the benefits of host-node model.

We have evaluated techniques of estimating animal density through direct counts using line transects during 1988-92 in the tropical deciduous forests of Mudumalai Sanctuary in southern India for four species of large herbivorous mammals, namely, chital (Axis axis), sambar (Cervus unicolor), Asian elephant (Elephas maximus) and gaur (Bos gauras). Density estimates derived from the Fourier Series and the Half-Normal models consistently had the lowest coefficient of variation. These two models also generated similar mean density estimates. For the Fourier Series estimator, appropriate cut-off widths for analysing line transect data for the four species are suggested. Grouping data into various distance classes did not produce any appreciable differences in estimates of mean density or their variances, although model fit is generally better when data are placed in fewer groups. The sampling effort needed to achieve a desired precision (coefficient of variation) in the density estimate is derived. A sampling effort of 800 km of transects returned a 10% coefficient of variation on estimate for chital; for the other species a higher effort was needed to achieve this level of precision. There was no statistically significant relationship between detectability of a group and the size of the group for any species. Density estimates along roads were generally significantly different from those in the interior af the forest, indicating that road-side counts may not be appropriate for most species.

Un nouveau logiciel de visualisation scientifique a ete developpe, en utilisant des objets comme unite de base d'affichage. Il gere aussi bien des grilles structurees ou non, des lignes generiques, que des couches en surfaces NURBS, des profils et des textes. Chacun de ces types de donnees est entre comme un objet, defini par son type, sa geometrie, sa fonction et ses attributs. GLIMPSE peut etre considere aussi bien comme un progiciel que comme une librairie de fonctions de haut niveau appelables par des applications voulant profiter d'une flexibilite et d'un controle accru. C'est en fait un environnement graphique qui a ete cree pour fournir un outil performant a un groupe d'utilisateurs.

As part of an international network of large plots to study tropical vegetation dynamics on a long-term basis, a 50-hectare permanent plot was set up during 1988-89 in the deciduous forests of Mudumalai, southern India. Within this plot 25,929 living woody plants (71 species) above 1 cm DBH (diameter at breast height) were identified, measured, tagged and mapped. Species abundances corresponded to the characteristic log-normal distribution. The four most abundant species (Kydia calycina, Lagerstroemia microcarpa, Terminalia crenulata and Helicteres isora) constituted nearly 56% of total stems, while seven species were represented by only one individual each in the plot. Variance/mean ratios of density showed most species to have clumped distributions. The population declined overall by 14% during the first two years, largely due to elephant and fire-mediated damage to Kydia calycina and Helicteres isora. In this article we discuss the need for large plots to study vegetation dynamics.

The ability to predict safe and effective release of air-launched weapons carried internally in a weapon bay or externally on a pylon/rack is required by the Safety Committee before approval is given for a flight test to validate various store separation characterisitics. Because of the novel conditions attendant to test and evaluation (T and E) testing, only limited experimental and flight data are available beforehand to aid in assessing safe weapon release. Computational methods have the potential of resolving, in a timely manner, the store separation problem without these weaknesses. Two areas need to be addressed. First, an accurate computational algorithm is needed to minimize numerical uncertainty as the store is tracked in time. Second, correct physical models must be implemented to model the moving store, including grid capability to provide accurate numerical flowfield predictions for situation of weapon carriage and release from an internal weapons bay. Based on a truly multidimensional unrestricted Essentially Non-oscillatory (ENO) scheme, a new UNIVERSE (Unification of essentially Non-oscillatory Interpolation techniques with a geometrically VERSatilE) series code has been developed at the Rockwell International Science Center. The new ENO concepts are state-of-the-art interpolation schemes that work with arbitrary cell shapes. For example, hexahedral, triangular prism, and tetrahedral elements (conservation cells) can all be covered in a unified manner. This also implies that both structured and unstructured bookkeeping schemes can be employed to conveniently treat complex topologies. A new suite of fully automatic flexible-cell mesh generation methods is also being developed for integration with the new series.

Preface. 1: Accuracy. Progress in Applied Numerical Analysis for Computational Fluid Dynamics M.B. Giles. Examples of Error Propagation from Discontinuities B. Engquist, B. Sjogreen. Accurate Finite Difference Algorithms J.V. Goodrich. Computational Considerations for the Simulation of Discontinuous Flows M. H. Carpenter, J.H. Casper. Space-Time Methods for Hyperbolic Conservation Laws R.B. Lowrie, et al. II: Boundary Conditions and Stiffness Issues. Anisotropic Mesh Adaptation: A Step Towards a Mesh-Independent and User-Independent CFD W.G. Habashi, et al. Artificial Boundary Conditions for Infinite-Domain Problems S.V.Tsynkov. Issues and Strategies for Hyperbolic Problems with Stiff Source Terms M. Arora, P.L. Roe. III: Discontinuities. Numerical Methods for a One-Dimensional Interface Separating Compressible and Incompressible Flows R. Fedkiw, et al. On Some Outstanding Issues in CFD (1996) R. Lohner. Accurate and Robust Methods for Variable Density Incompressible Flows with Discontinuities W.J. Rider, et al. A Variational Approach to Deriving Smeared-Interface Surface Tension Models D. Jacqmin. IV: Other Applications. Compounded of Many Simples: Reflections on the Role of Model Problems in CFD P. Roe. A Unified CFD-Based Approach to a Variety of Problems in Computational Physics R.K. Agarwal. Second Order Godunov Schemes for 2D and 3D MHD Equations and Divergence-Free Condition Wenlong Dai, P.R. Woodward. On Multidimensional Positively Conservative High-Resolution Schemes T. Linde, P.L. Roe. A New Scheme for the Solutions of Multidimensional MHD Equations N. Aslan, T. Kamash . V: Convergence. Local Preconditioning: Who Needs It? B. Van Leer. The Quest for Diagonalization of Differential Systems P. Roe, E. Turkel. Multidimensional Upwinding: Unfolding the Mystery D. Sidilkover.

The Osher algorithm for solving the Euler equations is an upwind finite difference procedure that is derived by combining the salient features of the theory of conservation laws and the mathematical theory of characteristi cs for hyperbolic systems of equations. A first-order accurate version of the numerical method was derived by Osher circa 1980 for the one-dimensional non-isentropic Euler equations in Cartesian coordinates. In this paper, the extension of the scheme to arbitrary two-dimensional geometries is explained. Results are then presented for several example problems in one and two dimensions. Future work will include extension of the method to second-order accuracy and the development of implicit time differencing for the Osher algorithm.

Implicit boundary condition procedures are presented for use with implicit finite difference schemes for the unsteady Euler equations. This new boundary point treatment is based on the mathematical theory of characteristics for hyperbolic systems of equations. Along with the theoretical background, the practical application of the method to several types of boundaries is also explained using several examples. The specific boundary conditions covered include subsonic inflow and outflow, surface tangency, and shock waves. The example problems include one-dimensional Laval nozzle flow, dual-throat rocket engine nozzle flow, and supersonic flow past a sphere. The implicit boundary treatment permits the use of large time steps allowing the finite difference algorithm to converge to the asymptotic steady state much faster than schemes that use explicitly applied boundary conditions. At least an order of magnitude increase in computational speed is demonstrated in the examples shown.' Background T HE growing popularity of solutions to the Euler equations in transonics and their continued application in supersonics have increased the need for quicker solutions. The potential of implicit schemes in this direction has not been fully exploited for want of correct, implicit application of boundary conditions. The predominant use of implicit algorithms for the Navier-Stokes equations has partly been responsible for the neglect of implicit boundary point treatment for the Euler equations. Thus, there is a need for correct and stable procedures for the easy implicit application of boundary conditions. Such methods will serve the two purposes of 1) reaching time-asymptotic steady state faster and 2) permitting a time step for truly unsteady flow that is not necessarily restricted by the CFL stability criterion but is based upon the magnitude of the transients. For clues and information on how to construct such boundary condition procedures, one must turn to the mathematical theory of characteristi cs for hyperbolic systems of equations. The unsteady Euler equations belong to this category. The theory for hyperbolic systems is rich with information on signal propagation directions. The characteristics theory clearly points to the number of boundary conditions that may and need be prescribed without overdetermining the solution. Boundary condition procedures based on this theory have been known and applied for several years by Kentzer, 1 Porter and Coakley,2 de Neef, 3 and others. In earlier work by this author,4'5 easily understood and implementable methods for boundary point treatment were presented. However, all of the above techniques were developed for explicit finite difference schemes. It seems that it must be easy to extend such methodologies based on mathematical theory for hyperbolic systems to implicit finite difference schemes, and indeed, it is simple enough. The rest of this paper describes such implicit boundary condition procedures. The given examples illustrate in detail the application of the proposed methodology to specific types of boundaries and demonstrate the merits of the new scheme.

The flowfield around various axisymmetric afterbody configurations is computed with a finite-volume NavierStokes code, incorporating a total variation diminishing implicit upwind-biased scheme for high accuracy and using alternatively the k-e or the Baldwin-Lomax turbulence model. Computations are done for both solid plume simulators and real jet flows. Results for two geometries at several combinations of jet and freestream conditions are shown. Agreement with the experimental data is very good.

A unified treatment of several upwind shock capturing algorithms is presented. Each algorithm has a Riemann initial value problem as its basis. The treatment of boundaries involves solving the associated Riemann initial-boundary value problem. The first author's algorithm, applied to multidimensional Euler equations in general geometries, is then presented. Its worth is verified by various calculations, which include Mach 8 supersonic flow past a circular cylinder.

Computations on zonal grids - in particular, grids with metric discontinuities resulting from the interspersion of highly clustered regions with coarse regions - are possible using a fully conservative form of the Osher upwind scheme. These zonal grids can result from an abrupt clustering of points near solution discontinuities or near other flow features that require improved resolution. The zonal approach is shown to capture shocks with almost 'shock-fitting' quality but with minimal effort. Results for inviscid flow, including quasi-one-dimensional nozzle flow, supersonic flow over a cylinder, and blast-wave diffraction by a ramp, are presented. These calculations demonstrate the powerful capabilities of the Osher scheme used in conjunction with zonal grids in simulating flow fields with complex shock patterns.

A recently introduced backflow turbulence model for separated flows has been used to calculate the reattaching flow over a backward facing step and the shock-induced separation over an axisymmetric bump. Results are compared with experimental data and with calculations using the k-e turbulence model and the JohnsonKing model. It is concluded that the new backflow turbulence model performs as well as the Johnson-King model and better than the k-e model.

An implicit, finite difference computer code has been developed to solve the incompressible Navier-Stokes equations in a three-dimensional curvilinear coordinate system. The pressure field solution is based on the pseudocompressibility approach in which a time derivative pressure term is introduced into the mass conservation equation. The solution procedure employs an implicit, approximate factorization scheme. The Reynolds Stresses, which are uncoupled from the implicit scheme, are lagged by one time step to facilitate implementing various levels of the turbulence model. Test problems for external and internal flows are computer and the results are compared with existing experimental data. The application of this technique for general three-dimensional problems is then demonstrated.

Conservative upwind schemes for the Euler equations, such as the Osher scheme, accurately resolve flow discontinuities and correctly model the physics of the problem. However, these schemes require many more arithmetic operations per integration step than simple central-difference schemes and hence result in large computing times. An implicit version of the first-order- and second-order-accurate Osher schemes in two spatial dimensions and generalized coordinates is developed in this study. Because implicit schemes permit the use of large integration steps, in many cases they require fewer integration steps to reach steady-state (especially in calculations on grids with widely varying mesh-cell sizes). The implicit scheme developed in this study accelerated convergence speeds by almost an order of magnitude in the problems considered. Test cases include quasi-one-dimensional nozzle flow and supersonic flow past a cylinder.

Nonclassical flutter has been observed during transonic conditions associated with flight and wind tunnel testing of various fighter and bomber aircraft As contrasted with classical flutter the underlying mechanism has been ascribed to a phase lag between lift variations and wing motions Based on the observations that the wing oscillations were restricted to bending mode shapes similar to the free fundamental, the phenomenon was idealized as the lift induced forced oscillation of a Cantilever beam simulating the wing. Coupling with the aerodynamics occurs through the beam equation forcing term, representing the lift, and the tangency boundary condition for the unsteady transonic small disturbance equation for the latter Strip theory has been used with a suitably revised version of LTRAN2 to supply the aerodynamic input The resulting time integration algorithm provides a procedure to determine the destabilizing effects of sweepback Computations with the method closely predict flutter frequencies observed for the HiMAT canard during wind tunnel testing, as well as for the B-l wing in flight tests in two out of three cases Qualitative behavior of the oscillation agrees for these conditions For the third case, damped oscillations are predicted rather than the amplified ones observed Reasons for the discrepancy are provided, involving the second bending mode of these oscillations in contrast to the fun damental assumed by the current approach Specific recommendations for refinements of the procedure in volving inclusion of modal coupling analysis of limit cycle aspects and three dimensional phenomena are given

A new finite-difference scheme has been developed to solve efficiently the unsteady Euler equations for three-dimensional inviscid supersonic flows with subsonic pockets. The technique utilizes planar Gauss-Seidel relaxation in the marching direction and approximate factorization n the crossflow plane. An 'infinitely large' time step is used in parts of the flowfield where the component of velocity in the marching direction is supersonic - here the Gauss-Seidel sweeps are restricted to the forward direction only, and the procedure reduces to simple space-marching; a finite time step is used in parts of the flowfield where the marching component of velocity is subsonic - here, backward and forward Gauss-Seidel sweeps are employed to allow for upstream and downstream propagation of signals, and a time-asymptotic steady state is obtained. The discretization formulas are based on finite-volume implementation of high accuracy (up to third-order) total variation diminishing formulations. Numerical solutions are obtained for an analytically defined forebody, a realistic fighter configuration, and the Space Shuttle. The results are in very good agreement with available experimental data and numerical solutions of the full-potential equation.

A new hybrid one-equation k-L /backflow model has been used to compute several turbulent flow problems involving detached flow regions. The model incorporates algebraic near-wall treatments for the kinetic energy of turbulence fc, the length scale L, and the eddy viscosity /*,. The near-wall formulation depends on whether the flow is attached or detached. This approach obviates the need to use wall functions. Agreement between predictions and experimental data is generally very good throughout the Mach number range.