Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Euler flow”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Unsteady transonic flows past airfoils using the Euler equations

An explicit finite difference solver for the Euler equations was developed and used to calculate the flow past two of the AGARD standard aeroelastic configurations, an NACA 64A010 and an NLR 7301. The algorithm employed uses a modified four step Runge-Kutta time stepping scheme, boundary conditions determined from the time-dependent theory of characteristics and an unsteady automatic grid generation procedure. In general, the calculated results are in good agreement with available experiment. Moreover, they demonstrate the importance of using the Euler equations for super-critical airfoils and in situations where the transonic small disturbance theory results in poor agreement with experiment.

Smith, G. E.↗
NASA NTRS1984

Euler and Navier-Stokes solutions for supersonic shear flow past a circular cylinder

Euler and Navier-Stokes solutions of the supersonic shear flow past a circular cylinder are obtained. These solutions are used to study the basic flow structure around the cylinder. Both the inviscid and viscous calculations show the formation of a large recirculating flow region around the front stagnation point. The calculations further show that the overall size of the recirculating region is approximately the same for the Euler and Navier-Stokes solutions but the inside structure is quite different. The inviscid flow shows only one vortex whereas the viscous flow shows two vortices inside the recirculating flow region. The inner vortex in the Navier-Stokes solution is formed primarily due to the viscous effects near the body surface and its size depends upon the Reynolds number. It is found that with increasing Reynolds number, the inner vortex diminishes in size and the Navier-Stokes solution asymptotically approaches the Euler solution. These results indicate that the Euler equations may correctly predict certain high Reynolds number separation phenomenon in flows with natural inviscid vorticity source.

Kumar, A.↗
NASA NTRS1990

Analysis and mitigation of numerical dissipation in inviscid and viscid computation of vortex-dominated flows

The conservative unsteady Euler equations for the flow relative motion in the moving frame of reference are used to solve for the steady and unsteady flows around sharp-edged delta wings. The resulting equations are solved by using an implicit approximately-factored finite volume scheme. Implicit second-order and explicit second- and fourth-order dissipations are added to the scheme. The boundary conditions are explicitly satisfied. The grid is generated by locally using a modified Joukowski transformation in cross flow planes at the grid chord stations. The computational applications cover a steady flow around a delta wing whose results serve as the initial conditions for the unsteady flow around a pitching delta wing about a large angle of attack. The steady results are compared with the experimental data and the periodic solution is achieved within the third cycle of oscillation.

Kandil, Osama A.↗
NASA NTRS1993

Conical Euler analysis and active roll suppression for unsteady vortical flows about rolling delta wings

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling, highly swept delta wings undergoing either forced motions or free-to-roll motions that include active roll suppression. The flow solver of the code involves a multistage, Runge-Kutta time-stepping scheme that uses a cell-centered, finite-volume, spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free to-roll case by simultaneously integrating in time the rigid-body equation of motion with the governing flow equations. Results are presented for a delta wing with a 75 deg swept, sharp leading edge at a free-stream Mach number of 1.2 and at 10 deg, 20 deg, and 30 deg angle of attack alpha. At the lower angles of attack (10 and 20 deg), forced-harmonic analyses indicate that the rolling-moment coefficients provide a positive damping, which is verified by free-to-roll calculations. In contrast, at the higher angle of attack (30 deg), a forced-harmonic analysis indicates that the rolling-moment coefficient provides negative damping at the small roll amplitudes. A free-to-roll calculation for this case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation, which is characteristic of highly swept delta wings. This limit cycle oscillation may be actively suppressed through the use of a rate-feedback control law and antisymmetrically deflected leading-edge flaps. Descriptions of the conical Euler flow solver and the free-to roll analysis are included in this report. Results are presented that demonstrate how the systematic analysis of the forced response of the delta wing can be used to predict the stable, neutrally stable, and unstable free response of the delta wing. These results also give insight into the flow physics associated with unsteady vortical flows about delta wings undergoing forced motions and free-to-roll motions, including the active suppression of the wing-rock type phenomenon. The conical Euler methodology developed is directly extend able to three-dimensional calculations.

Lee-Rausch, Elizabeth M.↗
NASA NTRS2006

Comparison of a Convected Helmholtz and Euler Model for Impedance Eduction in Flow

Impedances educed from a well-tested convected Helmholtz model are compared to that of a recently developed linearized Euler model using two ceramic test liners under the assumed conditions or uniform flow and a plane wave source. The convected Helmholtz model is restricted to uniform mean flow whereas the linearized Euler model can account for the effect or the shear layer. Test data to educe the impedance is acquired from measurements obtained in the NASA Langley Research Center Grazing Incidence Tube for mean flow Mach numbers ranging from 0.0 to 0.5 and source frequencies ranging from 0.5 kHz to 3.0 kHz. The unknown impedance of the liner b educed by judiciously choo~ingth e impedance via an optimization method to match the measured acoustic pressure on the wall opposite the test liner. Results are presented on four spatial grids using three different optimization methods (contour deformation, Davidon-Fletcher Powell, and the Genetic Algorithm). All three optimization methods converge to the same impedance when used with the same model and to nearly identical impedances when used on different models. h anomaly was observed only at 0.5 kHz for high mean flow speeds. The anomaly is likely due to the use of measured data in a flow regime where shear layer effects are important but are neglected in the math models. Consistency between the impedances educed using the two models provides confidence that the linearized Euler model is ready For application to more realistic flows, such as those containing shear layers.

Watson, Willie R.↗
NASA NTRS1979

Internal corner flow fields

A computational procedure has been developed to predict the inviscid super/hypersonic flow field of conical internal corners. The prediction of internal corner flow fields can be important in the design of supersonic 'box' type inlets. The computational procedure utilizes a second order finite difference marching technique to asymptote to the conical corner flow solution of Euler's equations. These flow fields are dominated by complex shock interactions. All discontinuities, shocks and slip surfaces are fitted with the appropriate jump conditions. The 'triple' points (the interaction of two shocks and a slip surface) are also computed exactly. Computed results are compared with experimental data and the computational results of other investigators. In addition, the sensitivity of these flow fields to a number of geometric parameters is studied, and the impact of these flows on inlet performance is assessed.

Marconi, F.↗
NASA NTRS1987

Algorithm developments for the Euler equations with calculations of transonic flows

A new algorithm has been developed for the Euler equations that uses flux vector splitting in combination with the concept of rotating the coordinate system to the local streamwise direction. Flux vector biasing is applied along the local streamwise direction and central differencing is used transverse to the flow direction. The flux vector biasing is switched from upwind for supersonic flow to downwind-biased for subsonic flow. This switching is based on the Mach number; hence the proper domain of dependence is used in the supersonic regions and the switching occurs across shock waves. The theoretical basis and the development of the formulas for flux vector splitting are presented. Then several one-dimensional calculations are presented of steady and unsteady transonic flows, which demonstrate the stability and accuracy of the algorithm. Finally results are shown for unsteady transonic flow over an airfoil. The pressure coefficient plots show sharp transonic shock profiles, and the Mach contour plots show smoothly varying contours.

Goorjian, Peter M.↗
NASA NTRS1982

Application of two-point difference schemes to the conservative Euler equations for one-dimensional flows

An implicit finite difference method is presented for obtaining steady state solutions to the time dependent, conservative Euler equations for flows containing shocks. The method used the two-point differencing approach of Keller with dissipation added at supersonic points via the retarded density concept. Application of the method to the one-dimensional nozzle flow equations for various combinations of subsonic and supersonic boundary conditions shows the method to be very efficient. Residuals are typically reduced to machine zero in approximately 35 time steps for 50 mesh points. It is shown that the scheme offers certain advantages over the more widely used three-point schemes, especially in regard to application of boundary conditions.

Wornom, S. F.↗
NASA NTRS1982

Application of two-point difference schemes to the conservative Euler equations for one-dimensional flows

An implicit finite-difference method is presented for obtaining steady-state solutions to the time-dependent, conservative Euler equations for flows containing shocks. The method uses a two-point central difference scheme with dissipation added at supersonic points via the retarded density concept. Application of the method to the one-dimensional nozzle flow equations for various combinations of subsonic and supersonic boundary conditions show the method to be very efficient. Residuals are typically reduced to machine zero in approximately 35 time steps for 50 mesh points. It is shown that the scheme offers certain advantages over the more widely-used three-point schemes, especially in regard to application of boundary conditions.

Wornom, S. F.↗
NASA NTRS1986

Implicit methods for computing chemically reacting flow

The backward Euler scheme was used to solve a large system of inviscid flow and chemical rate equations in three spatial coordinates. The flow equations were integrated simultaneously in time by a conventional ADI factorization technique, then the species equations were solved by either simultaneous or successive techniques. The methods were evaluated in their efficiency and robustness for a hypersonic flow problem involving an aerobrake configuration. It was found that both implicit methods can effectively reduce the stiffness associated with the chemical production term and that the successive solution for the species was as stable as the simultaneous solution. The latter method is more economical because the computation time varies linearly with the number of species.

Li, C. P.↗
NASA NTRS1987

Euler solution of the transonic flow for a helicopter rotor

A new method is presented for calculating the quasi-steady transonic flow over a lifting or nonlifting rotor blade in both hover and forward flight by using Euler equations. The approach is to solve the Euler equations in a rotor-fixed frame of reference using a finite volume method. A computer program was developed and was then verified by comparison with wind-tunnel data. In all cases considered, good agreement was found with available experimental data.

Chang, I-Chung↗
NASA NTRS1993

A multiblock/multigrid Euler method to simulate 2D and 3D compressible flow

An efficient and flexible multiblock/multigrid Euler solver is described which uses a cell-centered finite-volume method based on a multigrid implementation of the alternating direction implicit algorithm. The fully conservative treatment of the inter-block boundary allows the passage of discontinuities across block boundaries with minimum distortion of the solution. Information is exchanged between blocks by using surface arrays which contain all the data needed to update the inter-block boundary conditions. The proposed multiblock/multigrid approach is considered to be feasible for solving flow problems involving complex geometries.

Wang, Lixia↗
NASA NTRS1985

Applications of variational principles in computing rotational flows

Ecer and Akay (1983) have developed a variational formulation of rotational flow for Euler equations. The present paper provides a summary of these developments. The considered variational formulation provides a transformation of a type considered by Clebsch (1859). In this transformation, a new set of variables replaces the more commonly used primitive variables u(i), rho and p. Here, u(i) denotes the velocity components, while rho is the density, and p the pressure. The employed transformation produces a natural uncoupling of the equations when written in a quasi-linear form. After obtaining the governing equations in terms of the 'Clebsch variables', a solution scheme developed for calculating steady flows is discussed. Attention is given to numerical solutions of Euler equations based on the derived variational principles, and a study of inviscid, separated flows is conducted.

Ecer, A.↗
NASA NTRSDate not supplied

CFD Modeling of Cryogenic Chilldown in a Complex Channel under Normal and Low Gravity Conditions

Future NASA architectures have baselined cryogenic propulsion systems as well as cryogenic fluid management to support lunar missions and ultimately to support future missions to Mars. These missions will require chilling hardware down prior to engine restart as well as chilling lines and tanks prior to transferring and refueling these propulsion elements in orbit. In lieu of expensive tests conducted on-orbit, accurate predictive computational models of these chilldown processes can be used to reduce system and propellant mass as well as mission risk. To gain confidence in these computational models, appropriate anchoring and validation to experimental data in a relevant environment needs to be performed. Recent ground and sub-orbital flight experiments conducted by the Japan Aerospace Exploration Agency (JAXA) investigated chilldown of a complex channel resembling a turbopump bearing cavity at low flow rates. This work presents Computational Fluid Dynamics (CFD) model development of the chilldown experiment employing two-phase flow boiling models available in commercial CFD software STAR-CCM+ using Volume of Fluid (VOF) and the traditional Euler-Euler multiphase flow solvers. Comparisons of the numerical and experimental results under normal and low-gravity conditions are presented. An assessment of solid wall temperatures and phase distribution yielded important insights into multiphase solver choice, dependence on gravity environment, and challenges associated with cryogenic flow boiling prediction and validation.

CFD↗
NASA NTRS1989

Application of unstructured grid methods to steady and unsteady aerodynamic problems

The purpose is to describe the development of unstructured grid methods which have several advantages when compared to methods which make use of structured grids. Unstructured grids, for example, easily allow the treatment of complex geometries, allow for general mesh movement for realistic motions and structural deformations of complete aircraft configurations which is important for aeroelastic analysis, and enable adaptive mesh refinement to more accurately resolve the physics of the flow. Steady Euler calculations for a supersonic fighter configuration to demonstrate the complex geometry capability; unsteady Euler calculations for the supersonic fighter undergoing harmonic oscillations in a complete-vehicle bending mode to demonstrate the general mesh movement capability; and vortex-dominated conical-flow calculations for highly-swept delta wings to demonstrate the adaptive mesh refinement capability are discussed. The basic solution algorithm is a multi-stage Runge-Kutta time-stepping scheme with a finite-volume spatial discretization based on an unstructured grid of triangles in 2D or tetrahedra in 3D. The moving mesh capability is a general procedure which models each edge of each triangle (2D) or tetrahedra (3D) with a spring. The resulting static equilibrium equations which result from a summation of forces are then used to move the mesh to allow it to continuously conform to the instantaneous position or shape of the aircraft. The adaptive mesh refinement procedure enriches the unstructured mesh locally to more accurately resolve the vortical flow features. These capabilities are described in detail along with representative results which demonstrate several advantages of unstructured grid methods. The applicability of the unstructured grid methodology to steady and unsteady aerodynamic problems and directions for future work are discussed.

Batina, John T.↗
NASA NTRS1991

High-Resolution Computations Of Hypersonic Flows

Report discusses extension, to hypersonic flows, of class of implicit, total-variation-diminishing (TVD) algorithms suitable for numerical simulation of transonic and supersonic flows obeying Euler and Navier-Stokes equations. Stabilities and rates of convergence, relative to those of other algorithms discussed. Study complemented by variety of compuations of steady and unsteady viscous and inviscid hypersonic flows about blunt bodies.

Yee, H. C.↗
NASA NTRS2007

Nonlinear Theory and Breakdown

The main points of recent theoretical and computational studies on boundary-layer transition and turbulence are to be highlighted. The work is based on high Reynolds numbers and attention is drawn to nonlinear interactions, breakdowns and scales. The research focuses in particular on truly nonlinear theories, i.e. those for which the mean-flow profile is completely altered from its original state. There appear to be three such theories dealing with unsteady nonlinear pressure-displacement interactions (I), with vortex/wave interactions (II), and with Euler-scale flows (III). Specific recent findings noted for these three, and in quantitative agreement with experiments, are the following. Nonlinear finite-time break-ups occur in I, leading to sublayer eruption and vortex formation; here the theory agrees with experiments (Nishioka) regarding the first spike. II gives rise to finite-distance blowup of displacement thickness, then interaction and break-up as above; this theory agrees with experiments (Klebanoff, Nishioka) on the formation of three-dimensional streets. III leads to the prediction of turbulent boundary-layer micro-scale, displacement-and stress-sublayer-thicknesses.

Smith, Frank↗
DOE OSTI2026

Optimization techniques in self-similar compressible flow

We investigate the one-dimensional (1D) inviscid compressible flow equations for an ideal gas through the lens of optimization techniques. It is the case that, to our knowledge, optimization analysis applied to the so-called “linear velocity” solutions of the Euler compressible flow equations has not been previously conducted. Through both gradient-based and variational techniques, new variants of well-studied flow scenarios, i.e., self-similar, 1D, linear velocity solution class to idealized inviscid compressible flow equations, are determined, as encoded in both the kinematic and thermodynamic properties of this self-similar solution class. With the kinematics of the said solutions being driven by a self-similar “scale radius” and the thermodynamics being driven separately through the appearance of an arbitrary function, a myriad of new solution classes is possible. Acting as a guide to more realistic physical circumstances as well as discovery, it is the hope that the presented cases serve as the framework for future investigations into the intersection of self-similarity and optimization techniques. Fields of study that may find this work to be of interest include aerodynamic design, flow control, inertial confinement fusion, physics-informed neural networks, and other related areas of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗