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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Exploring Discretization Error in Simulation-Based Aerodynamic Databases

This work examines the level of discretization error in simulation-based aerodynamic databases and introduces strategies for error control. Simulations are performed using a parallel, multi-level Euler solver on embedded-boundary Cartesian meshes. Discretization errors in user-selected outputs are estimated using the method of adjoint-weighted residuals and we use adaptive mesh refinement to reduce these errors to specified tolerances. Using this framework, we examine the behavior of discretization error throughout a token database computed for a NACA 0012 airfoil consisting of 120 cases. We compare the cost and accuracy of two approaches for aerodynamic database generation. In the first approach, mesh adaptation is used to compute all cases in the database to a prescribed level of accuracy. The second approach conducts all simulations using the same computational mesh without adaptation. We quantitatively assess the error landscape and computational costs in both databases. This investigation highlights sensitivities of the database under a variety of conditions. The presence of transonic shocks or the stiffness in the governing equations near the incompressible limit are shown to dramatically increase discretization error requiring additional mesh resolution to control. Results show that such pathologies lead to error levels that vary by over factor of 40 when using a fixed mesh throughout the database. Alternatively, controlling this sensitivity through mesh adaptation leads to mesh sizes which span two orders of magnitude. We propose strategies to minimize simulation cost in sensitive regions and discuss the role of error-estimation in database quality.

Aftosmis, Michael J.↗
NASA NTRS2011

Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

The proposed paper reports advances in developing a method for high Reynolds number compressible viscous flow simulations using a Cartesian cut-cell method with embedded boundaries. This preliminary work focuses on accuracy of the discretization near solid wall boundaries. A model problem is used to investigate the accuracy of various difference stencils for second derivatives and to guide development of the discretization of the viscous terms in the Navier-Stokes equations. Near walls, quadratic reconstruction in the wall-normal direction is used to mitigate mesh irregularity and yields smooth skin friction distributions along the body. Multigrid performance is demonstrated using second-order coarse grid operators combined with second-order restriction and prolongation operators. Preliminary verification and validation for the method is demonstrated using flat-plate and airfoil examples at compressible Mach numbers. Simulations of flow on laminar and turbulent flat plates show skin friction and velocity profiles compared with those from boundary-layer theory. Airfoil simulations are performed at laminar and turbulent Reynolds numbers with results compared to both other simulations and experimental data

Berger, Marsha↗
NASA NTRS2014

Cart3D Simulations for the First AIAA Sonic Boom Prediction Workshop

Simulation results for the First AIAA Sonic Boom Prediction Workshop (LBW1) are presented using an inviscid, embedded-boundary Cartesian mesh method. The method employs adjoint-based error estimation and adaptive meshing to automatically determine resolution requirements of the computational domain. Results are presented for both mandatory and optional test cases. These include an axisymmetric body of revolution, a 69deg delta wing model and a complete model of the Lockheed N+2 supersonic tri-jet with V-tail and flow through nacelles. In addition to formal mesh refinement studies and examination of the adjoint-based error estimates, mesh convergence is assessed by presenting simulation results for meshes at several resolutions which are comparable in size to the unstructured grids distributed by the workshop organizers. Data provided includes both the pressure signals required by the workshop and information on code performance in both memory and processing time. Various enhanced techniques offering improved simulation efficiency will be demonstrated and discussed.

Predictions↗
NASA NTRS2014

Static Aeroelastic Analysis with an Inviscid Cartesian Method

An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.

Aeroelastic↗
NASA NTRS2017

Cart3D Simulations for the Second AIAA Sonic Boom Prediction Workshop

Simulation results are presented for all test cases prescribed in the Second AIAA Sonic Boom Prediction Workshop. For each of the four nearfield test cases, we compute pressure signatures at specified distances and off-track angles, using an inviscid, embedded-boundary Cartesian-mesh flow solver with output-based mesh adaptation. The cases range in complexity from an axisymmetric body to a full low-boom aircraft configuration with a powered nacelle. For efficiency, boom carpets are decomposed into sets of independent meshes and computed in parallel. This also facilitates the use of more effective meshing strategies - each off-track angle is computed on a mesh with good azimuthal alignment, higher aspect ratio cells, and more tailored adaptation. The nearfield signatures generally exhibit good convergence with mesh refinement. We introduce a local error estimation procedure to highlight regions of the signatures most sensitive to mesh refinement. Results are also presented for the two propagation test cases, which investigate the effects of atmospheric profiles on ground noise. Propagation is handled with an augmented Burgers' equation method (NASA's sBOOM), and ground noise metrics are computed with LCASB.

Prediction↗
NASA NTRS2019

Rapid Prediction of Installed Jet Noise from RANS

A new method of computing jet noise, called mSrc, was developed on the general principles of acoustic analogies. In the method, the problem of translating turbulent flow energy into acoustic energy at a far-field observer is broken into two parts, a calculation of acoustic source strengths and then their propagation. The acoustic sources are related to turbulent quantities in the jet plume in a robust manner. The propagation, which is more properly computed using a Green's function accounting for nonuniform speed of sound and solid surfaces, is instead modeled using commonly observed features of jet acoustic far field directivity, and by diffraction barrier theory for surfaces. The mSrc method does not require gradients of the predicted flow field, allowing it to make use of robust unstructured RANS CFD methods, including embedded boundary codes. Such codes do not require specification of surface meshes, and auto-refine their grid to resolve flow gradients, putting resolution where it is required without a priori user input. The ability of mSrc to use such radically unstructured flow input results in an efficient method of estimating noise from jet flows from complex nozzles installed on aircraft. Many validation cases are presented to demonstrate the accuracy and range of applicability of the mSrc method for representative jet noise applications.

Bridges, James↗
NASA NTRS2019

Rapid Prediction of Installed Jet Noise From RANS

A new method of computing jet noise, called mSrc, was developed on the general principles of acoustic analogies. In the method, the problem of translating turbulent flow energy into acoustic energy at a far-field observer is broken into two parts, a calculation of acoustic source strengths and then their propagation. The acoustic sources are related to turbulent quantities in the jet plume in a robust manner. The propagation, which is more properly computed using a Green's function accounting for nonuniform speed of sound and solid surfaces, is instead modeled using commonly observed features of jet acoustic far field directivity, and by diffraction barrier theory for surfaces. The mSrc method does not require gradients of the predicted flow field, allowing it to make use of robust unstructured RANS CFD methods, including embedded boundary codes. Such codes do not require specification of surface meshes, and auto-refine their grid to resolve flow gradients, putting resolution where it is required without a priori user input. The ability of mSrc to use such radically unstructured flow input results in an efficient method of estimating noise from jet flows from complex nozzles installed on aircraft. Many validation cases are presented to demonstrate the accuracy and range of applicability of the mSrc method for representative jet noise applications.

Bridges, James↗
NASA NTRS1991

The structure and development of streamwise vortex arrays embedded in a turbulent boundary layer

An investigation of the structure and development of streamwise vortices embedded in a turbulent boundary layer was conducted. The vortices were generated by a single spanwise row of rectangular vortex generator blades. A single embedded vortex was examined, as well as arrays of embedded counter rotating vortices produced by equally spaced vortex generators. Measurements of the secondary velocity field in the crossplane provided the basis for characterization of vortex structure. Vortex structure was characterized by four descriptors. The center of each vortex core was located at the spanwise and normal position of peak streamwise vorticity. Vortex concentration was characterized by the magnitude of the peak streamwise vorticity, and the vortex strength by its circulation. Measurements of the secondary velocity field were conducted at two crossplane locations to examine the streamwise development of the vortex arrays. Large initial spacings of the vortex generators produced pairs of strong vortices which tended to move away from the wall region while smaller spacings produced tight arrays of weak vortices close to the wall. A model of vortex interaction and development is constructed using the experimental results. The model is based on the structure of the Oseen Vortex. Vortex trajectories are modelled by including the convective effects of neighbors.

Wendt, Bruce J.↗
NASA NTRS1984

Heat transfer effects of longitudinal vortices embedded in a turbulent boundary layer

The results of tests with five different vortex generators in an open circuit wind tunnel are reported. The tests were performed to enhance the data base on heat transfer effects of an isolated longitudinal vortex in a turbulent boundary layer and the effects of embedded vortex pairs. A heated plate was set in the boundary layer downstream of a tripping mechanism and measurements were made of the free stream and surface temperatures using thermocouples. A four-hole cobra probe assayed the velocity profiles. Trials revealed that vortex pairs with scales larger than the boundary layer thickness induce significant changes in the Stanton number. A 15 percent Stanton number increase was produced by isolated vortices, which swept cool free stream fluid into the near-wall region.

Eibeck, P. A.↗
NASA NTRS1987

An experimental study of the development of longitudinal vortex pairs embedded in a turbulent boundary layer

The mean streamwise development of pairs of longitudinal vortices embedded in an otherwise two-dimensional turbulent boundary layer was studied. Planes of closely spaced measurements of the three components of mean velocity were obtained at several streamwise locations, and the vorticity and circulation were calculated. Skin-friction measurements were also made. It was found that the rate of vorticity spreading in a vortex was greatly increased by close proximity of other vortices. The rate of streamwise circulation decrease was significantly greater for corotating vortices than for counter rotating vortices. Boundary-layer thinning and increased skin friction occured in regions where the secondary flow induced by the pairs was directed toward the wall; the boundary layer was thickened and skin friction reduced where the secondary flow was directed away from the wall.

Pauley, Wayne R.↗
NASA NTRS1992

The structure and development of streamwise vortex arrays embedded in a turbulent boundary layer

The results of an experimental investigation of the structure and development of streamwise vortices embedded in a turbulent boundary layer are presented. Measurements of secondary velocity in the crossplane are used to characterize the vortex array structure. Measurements in the crossplane at two streamwise locations characterize the influence of interactions among the vortices on the array structure when the initial spacing between vortices is varied. Evidence of the merging of counter-rotating cores is found in embedded arrays of closely spaced vortices. A model of vortex interaction and development is constructed from the experimental results. This model is based on the structure of the two dimensional Ossen vortex. The decay of vortex circulation due to the merging of the cores is correlated with the crossplane gradient in streamwise vorticity occurring between an embedded vortex and its adjacent counter-rotating neighbors.

Wendt, Bruce J.↗
NASA NTRS2006

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Nguyen, Nhan↗
NASA NTRS1990

Embedded function methods for supersonic turbulent boundary layers

The development of embedded functions to represent the mean velocity and total enthalpy distributions in the wall layer of a supersonic turbulent boundary layer is considered. The asymptotic scaling laws (in the limit of large Reynolds number) for high speed compressible flows are obtained to facilitate eventual implementation of the embedded functions in a general prediction method. A self-consistent asymptotic structure is derived, as well as a compressible law of the wall in which the velocity and total enthalpy are logarithmic within the overlap zone, but in the Howarth-Dorodnitsyn variable. Simple outer region turbulence models are proposed (some of which are modifications of existing incompressible models) to reflect the effects of compressibility. As a test of the methodology and the new turbulence models, a set of self-similar outer region profiles is obtained for constant pressure flow; these are then coupled with embedded functions in the wall layer. The composite profiles thus obtained are compared directly with experimental data and good agreement is obtained for flows with Mach numbers up to 10.

He, J.↗
NASA NTRS1992

Energetics and structural properties of twist grain boundaries in Cu

Structural and energetics properties of atoms near a grain boundary are of great importance from theoretical and experimental standpoints. From various experimental work it is concluded that diffusion at low temperatures at polycrystalline materials take place near grain boundary. Experimental and theoretical results also indicate changes of up to 70 percent in physical properties near a grain boundary. The Embedded Atom Method (EAM) calculations on structural properties of Au twist grain boundaries are in quite good agreement with their experimental counterparts. The EAM is believed to predict reliable values for the single vacancy formation energy as well as migration energy. However, it is not clear whether the EAM functions which are fitted to the bulk properties of a perfect crystalline solid can produce reliable results on grain boundaries. One of the objectives of this work is to construct the EAM functions for Cu and use them in conjunction with the molecular static simulation to study structures and energetics of atoms near twist grain boundaries in Cu. This provides tests of the EAM functions near a grain boundary. In particular, we determine structure, single vacancy formation energy, migration energy, single vacancy activation energy, and interlayer spacing as a function of distance from grain boundary. Our results are compared with the available experimental and theoretical results from grain boundaries and bulk.

Karimi, Majid↗
NASA NTRS1983

A flexible grid embedding technique with application to the Euler equations

An automated grid embedding procedure for solution of flows about complex geometries is described. The physical domain is subdivided into regions that can accommodate easily generated grids. The grids are organized in a hierarchical structure, and communication among grids is accomplished by interpolation of the flow variables at mesh boundaries. Algorithms for locating embedded boundaries, special treatment of the embedded grids, and the data structures required for manipulating the solution data are described. The method is demonstrated by solution of the Euler equations for transonic flow about a supercritical airfoil and a flapped airfoil.

Benek, J. A.↗
NASA NTRS1989

Interaction of an oscillating vortex with a turbulent boundary layer

An oscillating vortex embedded within a turbulent boundary layer was generated experimentally by forcing a periodic lateral translation of a half-delta wing vortex generator. The objective of the experiment was to investigate the possibility that a natural oscillation, or meander, might be responsible for flattened vortex cores observed in previous work, which could also have contaminated previous turbulence measurements. The effect of this forced oscillation was characterized by comparison of measurements of the mean velocities and Reynolds stresses at two streamwise stations, for cases with and without forcing. The Reynolds stresses were affected significantly by the forced oscillation, mainly through contributions from the individual production terms, provided that the vortex was not too diffuse.

Westphal, R. V.↗