Results for “Euler characteristic” — Page 7

NASA NTRS2014

Modeling the Deterioration of Engine and Low Pressure Compressor Performance During a Roll Back Event Due to Ice Accretion

The main focus of this study is to apply a computational tool for the flow analysis of the engine that has been tested with ice crystal ingestion in the Propulsion Systems Laboratory (PSL) of NASA Glenn Research Center. A data point was selected for analysis during which the engine experienced a full roll back event due to the ice accretion on the blades and flow path of the low pressure compressor. The computational tool consists of the Numerical Propulsion System Simulation (NPSS) engine system thermodynamic cycle code, and an Euler-based compressor flow analysis code, that has an ice particle melt estimation code with the capability of determining the rate of sublimation, melting, and evaporation through the compressor blade rows. Decreasing the performance characteristics of the low pressure compressor (LPC) within the NPSS cycle analysis resulted in matching the overall engine performance parameters measured during testing at data points in short time intervals through the progression of the roll back event. Detailed analysis of the fan-core and LPC with the compressor flow analysis code simulated the effects of ice accretion by increasing the aerodynamic blockage and pressure losses through the low pressure compressor until achieving a match with the NPSS cycle analysis results, at each scan. With the additional blockages and losses in the LPC, the compressor flow analysis code results were able to numerically reproduce the performance that was determined by the NPSS cycle analysis, which was in agreement with the PSL engine test data. The compressor flow analysis indicated that the blockage due to ice accretion in the LPC exit guide vane stators caused the exit guide vane (EGV) to be nearly choked, significantly reducing the air flow rate into the core. This caused the LPC to eventually be in stall due to increasing levels of diffusion in the rotors and high incidence angles in the inlet guide vane (IGV) and EGV stators. The flow analysis indicating compressor stall is substantiated by the video images of the IGV taken during the PSL test, which showed water on the surface of the IGV flowing upstream out of the engine, indicating flow reversal, which is characteristic of a stalled compressor.

Veres, Joseph P.↗

NASA NTRS2014

Modeling the Deterioration of Engine and Low Pressure Compressor Performance During a Roll Back Event Due to Ice Accretion

The main focus of this study is to apply a computational tool for the flow analysis of the engine that has been tested with ice crystal ingestion in the Propulsion Systems Laboratory (PSL) of NASA Glenn Research Center. A data point was selected for analysis during which the engine experienced a full roll back event due to the ice accretion on the blades and flow path of the low pressure compressor. The computational tool consists of the Numerical Propulsion System Simulation (NPSS) engine system thermodynamic cycle code, and an Euler-based compressor flow analysis code, that has an ice particle melt estimation code with the capability of determining the rate of sublimation, melting, and evaporation through the compressor blade rows. Decreasing the performance characteristics of the low pressure compressor (LPC) within the NPSS cycle analysis resulted in matching the overall engine performance parameters measured during testing at data points in short time intervals through the progression of the roll back event. Detailed analysis of the fan-core and LPC with the compressor flow analysis code simulated the effects of ice accretion by increasing the aerodynamic blockage and pressure losses through the low pressure compressor until achieving a match with the NPSS cycle analysis results, at each scan. With the additional blockages and losses in the LPC, the compressor flow analysis code results were able to numerically reproduce the performance that was determined by the NPSS cycle analysis, which was in agreement with the PSL engine test data. The compressor flow analysis indicated that the blockage due to ice accretion in the LPC exit guide vane stators caused the exit guide vane (EGV) to be nearly choked, significantly reducing the air flow rate into the core. This caused the LPC to eventually be in stall due to increasing levels of diffusion in the rotors and high incidence angles in the inlet guide vane (IGV) and EGV stators. The flow analysis indicating compressor stall is substantiated by the video images of the IGV taken during the PSL test, which showed water on the surface of the IGV flowing upstream out of the engine, indicating flow reversal, which is characteristic of a stalled compressor.

Jorgenson, Philip C. E.↗

NASA NTRS1991

Spectral methods for the Euler equations - The blunt body problem revisited

The present use of the Chebyshev spectral collocation method, in conjunction with shock-fitting, to solve the blunt-body problem gives attention to the boundary and the shock-acceleration equations. The crux of these procedures is the use of the characteristic compatibility relations to compute the body pressure and shock velocity. It is shown that converged solutions are obtainable without artificial smoothing, and that spectral accuracy is achieved.

Kopriva, David A.↗

NASA NTRS1985

A convergent series expansion for hyperbolic systems of conservation laws

The discontinuities piecewise analytic initial value problem for a wide class of conservation laws is considered which includes the full three-dimensional Euler equations. The initial interaction at an arbitrary curved surface is resolved in time by a convergent series. Among other features the solution exhibits shock, contact, and expansion waves as well as sound waves propagating on characteristic surfaces. The expansion waves correspond to he one-dimensional rarefactions but have a more complicated structure. The sound waves are generated in place of zero strength shocks, and they are caused by mismatches in derivatives.

Harabetian, E.↗

NASA NTRS1987

Computation of non-linear acoustics in two-dimensional blade-vortex interactions

The propagation characteristics of the interaction between a vortex and a helicopter airfoil are investigated by a variety of methods, and a comparison is made between solutions to the linearized transonic small disturbance equation, transonic small disturbance equation, Euler equations, and Navier-Stokes equations. Although the first two methods are able to accurately predict the propagation of acoustic waves, they are unable to accurately describe the initial formation of acoustic waves. The Euler and Navier-Stokes equations are shown to be well suited to the investigation of acoustic waves and give approximately the same results.

Baeder, J. D.↗

NASA NTRS1991

Effect of a multi-dimensional flux function on the monotonicity of Euler and Navier-Stokes computations

A limiting method has been devised for a grid-independent flux function for use with the two-dimensional Euler and Navier-Stokes equations. This limiting is derived from a monotonicity analysis of the model and allows for solutions with reduced oscillatory behavior while still maintaining sharper resolution than a grid-aligned method. In addition to capturing oblique waves sharply, the grid-independent flux function also reduces the entropy generated over an airfoil in an Euler computation and reduces pressure distortions in the separated boundary layer of a viscous-flow airfoil computation. The model has also been extended to three dimensions, although no angle-limiting procedure for improving monotonicity characteristics has been incorporated.

Rumsey, Christopher L.↗

NASA NTRS1995

Supersonic Transport Analysis on the IBM Parallel System SP2

Several studies of supersonic transport (SST) configurations have been undertaken by members of the High Speed Aerodynamics branch at NASA Ames. These computational investigations involved the analysis of shapes to study the sonic boom signatures, aerodynamic performance characteristics, as well as studies of nacelle/airframe integration. A variety of different computer codes were employed including both structured and unstructured codes. The AIRPLANE code has been used extensively in these investigations. This computer code solves the Euler equations for inviscid flow by exploiting an explicit finite volume method on a mesh of tetrahedral cells. AIRPLANE is capable of handling complete aircraft configurations including nacelles and diverters. An example of a generic SST configuration is shown and a comparison of computed and experimental force coefficients is presented. Most of the computations in support of the SST investigations have been run on the YMP and C-90 computers currently installed at NASA Ames. Additional information is contained in the original extended abstract.

Jameson, Antony↗

NASA NTRS1981

A diagonal form of an implicit approximate-factorization algorithm

A modification of an implicit approximate-factorization finite-difference algorithm applied to partial differential equations is presented. This algorithm is applied to the two- and three-dimensional Euler equations in general curvilinear coordinates. The modification transforms the coupled system of equations into an uncoupled diagonal form that requires less computational work. For steady-state applications, the resulting diagonal algorithm retains the stability and accuracy characteristics of the original algorithm. The diagonal algorithm reduces the storage requirement of the implicit solution process and therefore has an important effect on the application of implicit finite-difference schemes to vector processors. Results are presented for realistic two-dimensional transonic flow fields about airfoils. Computation costs are reduced to 24-34%.

Pulliam, T. H.↗

NASA NTRS1981

A Diagonal Form of an Implicit Approximate-Factorization Algorithm

A modification of an implicit approximate-factorization finite-difference algorithm applied to partial differential equations is presented. This algorithm is applied to the two- and three-dimensional Euler equations in general curvilinear coordinates. The modification transforms the coupled system of equations into an uncoupled diagonal form that requires less computational work. For steady-state applications, the resulting diagonal algorithm retains the stability and accuracy characteristics of the original algorithm. The diagonal algorithm reduces the storage requirement of the implicit solution process and therefore has an important effect on the application of implicit finite-difference schemes to vector processors. Results are presented for realistic two-dimensional transonic flow fields about airfoils. Computation costs are reduced 24-34%.

Pulliam, T. H.↗

NASA NTRS1988

The effects of rotational flow, viscosity, thickness, and shape on transonic flutter dip phenomena

The transonic flutter dip phenomena on thin airfoils, which are employed for propfan blades, is investigated using an integrated Euler/Navier-Stokes code and a two degrees of freedom typical section structural model. As a part of the code validation, the flutter characteristics of the NACA 64A010 airfoil are also investigated. In addition, the effects of artificial dissipation models, rotational flow, initial conditions, mean angle of attack, viscosity, airfoil thickness and shape on flutter are investigated. The results obtained with a Euler code for the NACA 64A010 airfoil are in reasonable agreement with published results obtained by using transonic small disturbance and Euler codes. The two artificial dissipation models, one based on the local pressure gradient scaled by a common factor and the other based on the local pressure gradient scaled by a spectral radius, predicted the same flutter speeds except in the recovery region for the case studied. The effects of rotational flow, initial conditions, mean angle of attack, and viscosity for the Reynold's number studied seem to be negligible or small on the minima of the flutter dip.

Reddy, T. S. R.↗

NASA NTRS1988

The effects of rotational flow, viscosity, thickness, and shape on transonic flutter dip phenomena

The transonic flutter dip phenomena on thin airfoils, which are employed for propfan blades, is investigated using an integrated Euler/Navier-Stokes code and a two degrees of freedom typical section structural model. As a part of the code validation, the flutter characteristics of the NACA 64A010 airfoil are also investigated. In addition, the effects of artificial dissipation models, rotational flow, initial conditions, mean angle of attack, viscosity, airfoil thickness, and shape on flutter are investigated. The results obtained with an Euler code for the NACA 64A010 airfoil are in reasonable agreement with published results obtained by using transonic small disturbance and Euler codes. The two artifical dissipation models, one based on the local pressure gradient scaled by a common factor and the other based on the local presure gradient scaled by a spectral radius, predicted the same flutter speeds except in the recovery region for the case studied. The effects of rotation flow, initial conditions, mean angle of attack, and viscosity for the Reynolds number studied seem to be negligible or small on the minima of the flutter dip.

Reddy, T. S. R.↗

NASA NTRS1992

Liquid rocket spray combustion stability analysis

A computational approach to the analysis of spray combustion stability in liquid rocket combustors is proposed which is based on the unsteady quasi-two-dimensional Euler equations with interphase source terms derived from a Lagrangian treatment of the combusting spray. Based on a preliminary evaluation, the computational methodology presented here is a promising research tool and a potential design/development aid for investigating the stability characteristics of liquid rocket engines. The method is characterized by low numerical noise; the Lagrangian treatment of the spray offers improved flexibility for the direct modeling of spray combustion.

Litchford, Ron J.↗

NASA NTRS2004

BASS Code Development

The BASS computational aeroacoustic code solves the fully nonlinear Euler equations in the time domain in two-dimensions. The acoustic response of the stator is determined simultaneously for the first three harmonics of the convected vortical gust of the rotor. The spatial mode generation, propagation and decay characteristics are predicted by assuming the acoustic field away from the stator can be represented as a uniform flow with small harmonic perturbations superimposed. The computed field is then decomposed using a joint temporal-spatial transform to determine the wave amplitudes as a function of rotor harmonic and spatial mode order. This report details the following technical aspects of the computations and analysis. 1) the BASS computational technique; 2) the application of periodic time shifted boundary conditions; 3) the linear theory aspects unique to rotor-stator interactions; and 4) the joint spatial-temporal transform. The computational results presented herein are twofold. In each case, the acoustic response of the stator is determined simultaneously for the first three harmonics of the convected vortical gust of the rotor. The fan under consideration here like modern fans is cut-off at +, and propagating acoustic waves are only expected at 2BPF and 3BPF. In the first case, the computations showed excellent agreement with linear theory predictions. The frequency and spatial mode order of acoustic field was computed and found consistent with linear theory. Further, the propagation of the generated modes was also correctly predicted. The upstream going waves propagated from the domain without reflection from the in ow boundary. However, reflections from the out ow boundary were noticed. The amplitude of the reflected wave was approximately 5% of the incident wave. The second set of computations were used to determine the influence of steady loading on the generated noise. Toward this end, the acoustic response was determined with three steady loading conditions: design, low-loading, high-loading. The overall trend showed significant (approximately 10 dB) increases in the generated noise for the highly loaded stator.

Sawyer, Scott↗

NASA NTRS1990

Grid generation and flow computation about a Martian entry vehicle

A number of vehicles are currently being proposed for a manned mission to Mars. One of these vehicles has a modified blunt-nosed cone configuration. Experimental results were obtained for this vehicle in 1968. They show lift-over-drag ratios comparable to those needed for Mars entry. Computations are performed to verify the earlier results and to further describe the flight characteristics of this vehicle. An analytical method is used to define the surface of this vehicle. A single-block volume grid is generated around the vehicle using the algebraic Two-Boundary Grid Generation algorithm (TBGG) and transfinite interpolation. Euler solutions are then obtained from a Langley Aerodynamic Upward Relaxation Algorithm (LAURA) at Mach 6.0 and angles of attack of 0, 6, and 12 deg. The lift coefficient determined from the LAURA code agree very well with the experimental results. The drag and pitching moment coefficients, however, are underestimated by the code since viscous effects are not considered. Contour plots of the flowfield show no evidence of separation for angles of attack up to 12 deg.

Stewart, J. E.↗

NASA NTRS2017

Aeroelastic Uncertainty Quantification Studies Using the S4T Wind Tunnel Model

This paper originates from the joint efforts of an aeroelastic study team in the Applied Vehicle Technology Panel from NATO Science and Technology Organization, with the Task Group number AVT-191, titled "Application of Sensitivity Analysis and Uncertainty Quantification to Military Vehicle Design." We present aeroelastic uncertainty quantification studies using the SemiSpan Supersonic Transport wind tunnel model at the NASA Langley Research Center. The aeroelastic study team decided treat both structural and aerodynamic input parameters as uncertain and represent them as samples drawn from statistical distributions, propagating them through aeroelastic analysis frameworks. Uncertainty quantification processes require many function evaluations to asses the impact of variations in numerous parameters on the vehicle characteristics, rapidly increasing the computational time requirement relative to that required to assess a system deterministically. The increased computational time is particularly prohibitive if high-fidelity analyses are employed. As a remedy, the Istanbul Technical University team employed an Euler solver in an aeroelastic analysis framework, and implemented reduced order modeling with Polynomial Chaos Expansion and Proper Orthogonal Decomposition to perform the uncertainty propagation. The NASA team chose to reduce the prohibitive computational time by employing linear solution processes. The NASA team also focused on determining input sample distributions.

Nikbay, Melike↗

NASA NTRS1977

The design and reconstruction of the Viking Lander descent trajectories

The success of the Viking Mission is truly a major milestone in this country's planetary exploration program. This paper deals with the trajectory characteristics of the Viking Lander descent trajectories, beginning with the imposed requirements and constraints, the final preflight design based on the final hardware and operational capability, and ending with the actual performance achieved. A comparison between the predicted and actual trajectory characteristics is made to indicate the achieved accuracy and modeling fidelity. Also, estimates of the Martian environment derived from the entry-trajectory reconstruction process are presented.

Euler, E. A.↗

NASA NTRS1983

Symposium on Numerical and Physical Aspects of Aerodynamic Flows, 2nd, California State University, Long Beach, CA, January 17-20, 1983, Proceedings

The present conference covers topics concerning the measurement and calculation of interactive flows, together with problems posed by subsonic and transonic wings, missiles, and ships. Discussions are presented on the time-dependent finite difference simulation of unsteady interactive flows, Navier-Stokes equation methods, numerical solutions for spatially periodic boundary layers, the application of unsteady laminar tripple deck theory to viscous-inviscid interaction, the coupling of boundary layer and Euler equation solutions, and viscous-inviscid flow interactions. Also discussed are leading and trailing edge flows, three-dimensional wing flows, small disturbance calculations including entropy corrections, an inviscid computational method for tactical missiles, and boundary layer and flow separation characteristics of bodies of revolution at incidence.

Source record↗

NASA NTRS1993

Surface boundary conditions for the numerical solution of the Euler equations

We consider the implementation of boundary conditions at solid walls in inviscid Euler solutions by upwind, finite-volume methods. We review some current methods for the implementation of surface boundary conditions and examine their behavior for the problem of an oblique shock reflecting off a planar surface. We show the importance of characteristic boundary conditions for this problem and introduce a method of applying the classical flux-difference splitting of Roe as a characteristic boundary condition. Consideration of the equivalent problem of the intersection of two (equal and opposite) oblique shocks was very illuminating on the role of surface boundary conditions for an inviscid flow and led to the introduction of two new boundary-condition procedures, denoted as the symmetry technique and the curvature-corrected symmetry technique. Examples of the effects of the various surface boundary conditions considered are presented for the supersonic blunt body problem and the subcritical compressible flow over a circular cylinder. Dramatic advantages of the curvature-corrected symmetry technique over the other methods are shown, with regard to numerical entropy generation, total pressure loss, drag and grid convergence.

Dadone, A.↗