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Unsteady flowfields around oscillating Boeing VR7 airfoil with and without a leading-edge slat were numerically investigated by a novel zonal method using a conformal mapping technique. Numerical aero-dynamic hysteresis loops show that the leading-edge slat prevents the airfoil dynamic stall at reduced frequency of 0.15, Reynolds number of 1 million, and the oscillation range of 5 deg to 25 deg.
Paper discusses reliability of time-dependent approach to numerical solution of nonlinear differential equations (DEs) that describe steady-state behaviors of physical systems. Time-dependent approach followed in related study described in "Spurious Numerical Solutions of Differential Equations" (ARC-13209).
Program verified by comparisons with both experimental and numerical studies. GEOSIM implements numerical model simulating geophysical fluid flow for wide range of problems. Allows for more accurate control over experimental conditions and provides complete data source for performing diagnostic studies. Used by experienced and/or professional fluid dynamicists. Written in FORTRAN 77.
The general objective of this effort is to increase understanding of how frontal scale contraction processes may create and sustain intense mesoscale precipitation along intensifying cold fronts. The five-part project (an expansion of the originally proposed two-part project) employed conventional meteorological data, special mesoscale data, remote sensing measurements, and various numerical models. First an idealized hydrostatic modeling study of the scale contraction effects of differential cloud cover on low-level frontal structure and dynamics was completed and published in a peer-reviewed journal. The second objective was to complete and publish the results from a three dimensional numerical model simulation of a cold front in which differential sensible heating related to cloud coverage patterns was apparently crucial in the formation of a severe frontal squall line. The third objective was to use a nonhydrostatic model to examine the nonlinear interactions between the transverse circulation arising from inhomogeneous cloud cover, the adiabatic frontal circulation related to semi-geostrophic forcing, and diabatic effects related to precipitation processes, in the development of a density current-like microstructure at the leading edge of cold fronts. Although the development of a frontal model that could be used to initialize such a primitive equation model was begun, we decided to focus our efforts instead on a project that could be successfully completed in this short time, due to the lack of prospects for continued NASA funding beyond this first year (our proposal was not accepted for future funding). Thus, a fourth task was added, which was to use the nonhydrostatic model to test tentative hypotheses developed from the most detailed observations ever obtained on a density current (primarily sodar and wind profiler data). These simulations were successfully completed, the findings were reported at a scientific conference, and the results have recently been submitted to a peer-reviewed journal. The fifth objective was to complete the analysis of data collected during the Cooperative Oklahoma Profiler Studies (COPS-91) field project, which was supported by NASA. The analysis of the mesoscale surface and sounding data, Doppler radar imagery, and other remote sensing data from multi frequency wind profiler, microwave radiometer, and the Radio Acoustic Sounding System has been completed. This study is a unique investigation of processes that caused the contraction of a cold front to a microscale zone exhibiting an undular bore-like structure. Results were reported at a scientific conference and are being prepared for publication. In summary, considerable progress has been achieved under NASA funding in furthering our understanding of frontal scale contraction and density current - gravity wave interaction processes, and in utilizing models and remotely sensed data in such studies.
Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.
A thin film draining on an inclined plate has been studied numerically using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary Lagrangian Eulerian frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.
It is shown that ionization occurs wherever the field intensity of the pulse exceeds the local breakdown threshold field of the background air. The produced plasma then attenuates the pulse and gives rise to a tail erosion phenomenon that plays the primary role in limiting the energy transfer of the pulse from source to destination. A theoretical model describing the propagation of an intense microwave pulse in an air breakdown environment is developed that includes the possible focusing effect introduced by either using phase array antennas or the other arrangements. The self-consistent description of the propagation process is provided by a set of two modal equations. These include a continuity equation (Poynting's equation) for the energy density of the pulse and a rate equation of the electron density. A forward wave approximation is used to simplify Poynting's equation, and a semiempirical formula is used for the ionization frequency, nu(sub i). This frequency provides the coupling between the two modal equations, and is used to express the electron rate equation explicitly. In terms of the relevant parameters of the atmosphere, these two equations are normalized for numerical analysis of pulse propagation in the atmosphere. The dependencies of the propagation characteristics of the pulse on intensity, frequency, width, and shape of the pulse are determined. The numerical simulations lead to a useful empirical relation p(exp 3)w = alpha = constant, where p and w are the incident power and width of the pulse and alpha depends on the percentage of pulse energy transferred from the source point to a destined position. The density distribution of the pulse's self-generated plasma is also evaluated. The results also show that for ionization caused by a single unfocused microwave pulse transmitted upwards from the ground, the maximum electron density produced at, for example, 50 km altitude is limited by the tail erosion effect to below 10(exp 6) cm(exp -3). Repetitive pulse and focused beam approaches are also examined. Both approaches can increase the maximum electron density by no more than an order of magnitude. A scheme using two obliquely propagating pulses intersecting at the destined height, e.g. 50 km, is considered. It is shown that the electron density generated at the lowest intersecting position can easily reach a value of 6.6 x 10(exp 8) cm(exp -3), which is considered to be high enough for artificial ionospheric mirror (AIM) application.
A multiblock sensitivity analysis method is applied in a numerical aerodynamic shape optimization technique. The Sensitivity Analysis Domain Decomposition (SADD) scheme which is implemented in this study was developed to reduce the computer memory requirements resulting from the aerodynamic sensitivity analysis equations. Discrete sensitivity analysis offers the ability to compute quasi-analytical derivatives in a more efficient manner than traditional finite-difference methods, which tend to be computationally expensive and prone to inaccuracies. The direct optimization procedure couples CFD analysis based on the two-dimensional thin-layer Navier-Stokes equations with a gradient-based numerical optimization technique. The linking mechanism is the sensitivity equation derived from the CFD discretized flow equations, recast in adjoint form, and solved using direct matrix inversion techniques. This investigation is performed to demonstrate an aerodynamic shape optimization technique on a multiblock domain and its applicability to complex geometries. The objectives are accomplished by shape optimizing two aerodynamic configurations. First, the shape optimization of a transonic airfoil is performed to investigate the behavior of the method in highly nonlinear flows and the effect of different grid blocking strategies on the procedure. Secondly, shape optimization of a two-element configuration in subsonic flow is completed. Cases are presented for this configuration to demonstrate the effect of simultaneously reshaping interfering elements. The aerodynamic shape optimization is shown to produce supercritical type airfoils in the transonic flow from an initially symmetric airfoil. Multiblocking effects the path of optimization while providing similar results at the conclusion. Simultaneous reshaping of elements is shown to be more effective than individual element reshaping due to the inclusion of mutual interference effects.
A major difficulty in designing aeropropulsion systems is that of identifying and understanding the interactions between the separate engine components and disciplines (e.g., fluid mechanics, structural mechanics, heat transfer, material properties, etc.). The traditional analysis approach is to decompose the system into separate components with the interaction between components being evaluated by the application of each of the single disciplines in a sequential manner. Here, one discipline uses information from the calculation of another discipline to determine the effects of component coupling. This approach, however, may not properly identify the consequences of these effects during the design phase, leaving the interactions to be discovered and evaluated during engine testing. This contributes to the time and cost of developing new propulsion systems as, typically, several design-build-test cycles are needed to fully identify multidisciplinary effects and reach the desired system performance. The alternative to sequential isolated component analysis is to use multidisciplinary coupling at a more fundamental level. This approach has been made more plausible due to recent advancements in computation simulation along with application of concurrent engineering concepts. Computer simulation systems designed to provide an environment which is capable of integrating the various disciplines into a single simulation system have been proposed and are currently being developed. One such system is being developed by the Numerical Propulsion System Simulation (NPSS) project. The NPSS project, being developed at the Interdisciplinary Technology Office at the NASA Lewis Research Center is a 'numerical test cell' designed to provide for comprehensive computational design and analysis of aerospace propulsion systems. It will provide multi-disciplinary analyses on a variety of computational platforms, and a user-interface consisting of expert systems, data base management and visualization tools, to allow the designer to investigate the complex interactions inherent in these systems. An interactive programming software system, known as the Application Visualization System (AVS), was utilized for the development of the propulsion system simulation. The modularity of this system provides the ability to couple propulsion system components, as well as disciplines, and provides for the ability to integrate existing, well established analysis codes into the overall system simulation. This feature allows the user to customize the simulation model by inserting desired analysis codes. The prototypical simulation environment for multidisciplinary analysis, called Turbofan Engine System Simulation (TESS), which incorporates many of the characteristics of the simulation environment proposed herein, is detailed.
The work in this report was conducted at NASA Ames Research Center during the period from August 1993 to January 1995 deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a heated flat plate in the presence of relatively high freestream turbulence was performed. The geometry and flow conditions were chosen to match earlier experiments. The development of the momentum and thermal boundary layers was documented. Velocity and temperature profiles, as well as distributions of skin friction, surface heat transfer rate, Reynolds shear stress, and turbulent heat flux were shown to compare well with experiment. The numerical method used here can be applied to complex geometries in a straightforward manner.
Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.
The objective is the development of a high-order and high-resolution method for the direct numerical simulation of shock turbulent-boundary-layer interaction. Details concerning the spatial discretization of the convective terms can be found in Adams and Shariff (1995). The computer code based on this method as introduced in Adams (1994) was formulated in Cartesian coordinates and thus has been limited to simple rectangular domains. For more general two-dimensional geometries, as a compression corner, an extension to generalized coordinates is necessary. To keep the requirements or limitations for grid generation low, the extended formulation should allow for non-orthogonal grids. Still, for simplicity and cost efficiency, periodicity can be assumed in one cross-flow direction. For easy vectorization, the compact-ENO coupling algorithm as used in Adams (1994) treated whole planes normal to the derivative direction with the ENO scheme whenever at least one point of this plane satisfied the detection criterion. This is apparently too restrictive for more general geometries and more complex shock patterns. Here we introduce a localized compact-ENO coupling algorithm, which is efficient as long as the overall number of grid points treated by the ENO scheme is small compared to the total number of grid points. Validation and test computations with the final code are performed to assess the efficiency and suitability of the computer code for the problems of interest. We define a set of parameters where a direct numerical simulation of a turbulent boundary layer along a compression corner with reasonably fine resolution is affordable.
Wave rotor cycles which utilize premixed combustion processes within the passages are examined numerically using a one-dimensional CFD-based simulation. Internal-combustion wave rotors are envisioned for use as pressure-gain combustors in gas turbine engines. The simulation methodology is described, including a presentation of the assumed governing equations for the flow and reaction in the channels, the numerical integration method used, and the modeling of external components such as recirculation ducts. A number of cycle simulations are then presented which illustrate both turbulent-deflagration and detonation modes of combustion. Estimates of performance and rotor wall temperatures for the various cycles are made, and the advantages and disadvantages of each are discussed.
The influence of soot radiation on diffusion flames was investigated using both analytical and numerical techniques. Soot generated in diffusion flames dominate the flame radiation over gaseous combustion products and can significantly lower the temperature of the flame. In low gravity situations there can be significant accumulation of soot and combustion products in the vicinity of the primary reaction zone owing to the absence of any convective buoyant flow. Such situations may result in substantial suppression of chemical activities in a flame, and the possibility of a radiative extinction may also be anticipated. The purpose of this work was to not only investigate the possibility of radiative extinction of a diffusion flame but also to qualitatively and quantitatively analyze the influence of soot radiation on a diffusion flame. In this study, first a hypothetical radiative loss profile of the form of a sech(sup 2) was assumed to influence a pure diffusion flame. It was observed that the reaction zone can, under certain circumstances, move through the radiative loss zone and locate itself on the fuel side of the loss zone contrary to our initial postulate. On increasing the intensity and/or width of the loss zone it was possible to extinguish the flame, and extinction plots were generated. In the presence of a convective flow, however, the movement of the temperature and reaction rate peaks indicated that the flame behavior is more complicated compared to a pure diffusional flame. A comprehensive model of soot formation, oxidation and radiation was used in a more involved analysis. The soot model of Syed, Stewart and Moss was used for soot nucleation and growth and the model of Nagle and Strickland-Constable was used for soot oxidation. The soot radiation was considered in the optically thin limit. An analysis of the flame structure revealed that the radiative loss term is countered both by the reaction term and the diffusion term. The essential balance for the soot volume fraction was found to be between the processes of soot convection and soot growth. Such a balance yielded to analytical treatment and the soot volume fraction could be expressed in the form of an integral. The integral was evaluated using two approximate methods and the results agreed very well with the numerical solutions for all cases examined.
A large class of physical phenomena can be modeled by evolution and wave type Partial Differential Equations (PDE). Few of these equations have known explicit exact solutions. Finite-difference techniques are a popular method for constructing discrete representations of these equations for the purpose of numerical integration. However, the solutions to the difference equations often contain so called numerical instabilities; these are solutions to the difference equations that do not correspond to any solution of the PDE's. For explicit schemes, the elimination of this behavior requires functional relations to exist between the time and space steps-sizes. We show that such functional relations can be obtained for certain PDE's by use of a positivity condition. The PDE's studied are the Burgers, Fisher, and linearized Euler equations.
Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.
The nonlinear interfacial instability of a liquid jet in a coflowing compressible airstream is studied numerically. A high-resolution scheme which has second-order accuracy in space and time is coupled with a Lagrangian marker particle algorithm to visualize the large-scale motion of the interfaces in compressible flow. A numerical algorithm based on an approximate equation of state of a compressible liquid is developed to allow this two-fluid system to be governed by the nonlinear unsteady Euler equations in conservative form. The initial growth of small disturbances given by the simulations agrees well with linear theory. The process of jet disruption in compressible flow is demonstrated to consist of the formation of liquid spikes, interweaving of the gas and liquid and stretching and detachment of the liquid main center core.
Direct numerical simulations have been used to examine the effect of the initial disturbance field on the development of three-dimensionality and the transition to turbulence in the incompressible plane wake. The simulations were performed using a new numerical method for solving the time-dependent, three-dimensional, incompressible Navier-Stokes equations in flows with one infinite and two periodic directions. The method uses standard Fast Fourier Transforms and is applicable to cases where the vorticity field is compact in the infinite direction. Initial disturbances fields examined were combinations of two-dimensional waves and symmetric pairs of 60 deg oblique waves at the fundamental, subharmonic, and sub-subharmonic wavelengths. The results of these simulations indicate that the presence of 60 deg disturbances at the subharmonic streamwise wavelength results in the development of strong coherent three-dimensional structures. The resulting strong three-dimensional rate-of-strain triggers the growth of intense fine scale motions. Wakes initiated with 60 deg disturbances at the fundamental streamwise wavelength develop weak coherent streamwise structures, and do not develop significant fine scale motions, even at high Reynolds numbers. The wakes which develop strong three-dimensional structures exhibit growth rates on par with experimentally observed turbulent plane wakes. Wakes which develop only weak three-dimensional structures exhibit significantly lower late time growth rates. Preliminary studies of wakes initiated with an oblique fundamental and a two-dimensional subharmonic, which develop asymmetric coherent oblique structures at the subharmonic wavelength, indicate that significant fine scale motions only develop if the resulting oblique structures are above an angle of approximately 45 deg.