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At least 397 records · Page 22

Gas side heat transfer: 2-D flow

Significant progress was made in advancing the idea of establishing a unified approach for predicting airfoil heat transfer for a wide range of operating conditions and geometries. Preliminary results are encouraging and further mixing length (ml) turbulence modeling ideas will be explored, concentrating on transition behavior. The capability of available modeling techniques to predict airfoil surface heat transfer distributions in a two-dimensional flow field was assessed, experimental data as required for model verification were acquired, and improvements in the analytic models was made and verified.

York, R.↗

Shear flow aerodynamics - Lifting surface theory

A lifting surface theory based on a parallel shear flow model is presented for steady, incompressible flows. The theory is intended to account approximately for the presence of a boundary layer. The method of Fourier transforms is used to calculate the pressure on a surface of infinite extent and arbitrary contour. Immediately above the surface is a region of sheared flow (the boundary layer), outside of which the flow velocity is constant. The Fourier transform of the pressure on this surface is used to derive the shear flow equivalent to the kernel function of classical potential flow lifting surface theory. The kernel function provides an integral relation between the upwash at a given point on the surface and the pressure everywhere on the surface. This relation is treated as an integral equation for the pressure, and is solved numerically. Computations are presented for the lift and pitching moment on a flat plate in two-dimensional flow, and for flat, rectangular wings of aspect ratio 1, 2, and 5. As expected, the shear layer decreases the lift curve slope; however, the shear layer (whose thickness is constant along the wing chord) has little effect on the center of pressure.

Ventres, C. S.↗

An Autonomous Sensor System Architecture for Active Flow and Noise Control Feedback

Multi-channel sensor fusion represents a powerful technique to simply and efficiently extract information from complex phenomena. While the technique has traditionally been used for military target tracking and situational awareness, a study has been successfully completed that demonstrates that sensor fusion can be applied equally well to aerodynamic applications. A prototype autonomous hardware processor was successfully designed and used to detect in real-time the two-dimensional flow reattachment location generated by a simple separated-flow wind tunnel model. The success of this demonstration illustrates the feasibility of using autonomous sensor processing architectures to enhance flow control feedback signal generation.

Humphreys, William M, Jr.↗

The Analysis of Turbulent Flow by Hot Wire Signals

When measuring velocities in turbulent gas flow, approximation signal analysis with hot wire anemometers having one and two wire probes are used. A numeric test of standard analyses shows the resulting systemmatic error increases quickly with increasing turbulent intensity. Since it also depends on the turbulence structure, it cannot be corrected. The use of such probes is thus restricted to low turbulence. By means of three wire probes (in two dimensional flows with X wire probes) in principle, instantaneous values of velocity can be determined, and an asymmetric arrangement of wires has a theoretical advantage.

Bartenwerfer, M.↗

Flow Measurements of Methane-Fueled Rotating Detonation Combustion

Time-resolved particle image velocimetry (PIV) is applied to the flow field at the immediate exit of a rotating detonation combustor (RDC) operating on methane fuel and oxygen-enriched air. The detailed experimental results, which allow for the quantification of the periodic flow field, are believed to be the first such measurements acquired for a RDC. A thorough understanding of the velocity flow field exiting the combustor is important to develop future rotating detonation engine (RDE) design, as well as to successfully implement the flow conditioning devices to power generating turbine hardware located downstream. In this study, multiple PIV tests were conducted and a test case with over 16,000 consecutive image pairs acquired at a PIV framing rate of 30 kHz is analyzed in detail, and is supplemented with another test case to verify the repeatability of the measurements. Results are discretized into a two-dimensional flow field to reveal the significant insights to characterize the cyclical velocity fluctuations. While the flow field is primarily axial, a significant circumferential velocity component is also present. Key attributes of the velocity flow field are observed to be repeated from cycle-to-cycle. The codependency of the fluctuations in axial and circumferential velocity components are investigated, as is the relationship between velocity magnitude and flow orientation. At discrete measurement locations, the Fourier analysis of PIV data is used to reconstruct the cyclical variation of velocity components with respect to the phase angle.

03 NATURAL GAS↗

Least-squares solution of incompressible Navier-Stokes equations with the p-version of finite elements

A p-version of the least squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady state incompressible viscous flow problems. The resulting system of symmetric and positive definite linear equations can be solved satisfactorily with the conjugate gradient method. In conjunction with the use of rapid operator application which avoids the formation of either element of global matrices, it is possible to achieve a highly compact and efficient solution scheme for the incompressible Navier-Stokes equations. Numerical results are presented for two-dimensional flow over a backward facing step. The effectiveness of simple outflow boundary conditions is also demonstrated.

Jiang, Bo-Nan↗

Stability of three-dimensional boundary layers

The present evaluation of three-dimensional flows notes that the presence of such disturbance sources as roughness could favor the stationary mode, and that end-conditions may inhibit traveling disturbances in the experiments reported; alternatively, the theory could be inadequate. In general, uncertainties remain as to the definition of transition in three dimensions. It remains important to ascertain whether the formation of three-dimensional structures and characteristic stages will occur, as in two-dimensional flow transition. The possibilities and mechanisms for secondary instabilities also remain to be determined.

Reed, Helen L.↗

On the theory of oscillating airfoils of finite span in subsonic compressible flow

The problem of oscillating lifting surface of finite span in subsonic compressible flow is reduced to an integral equation. The kernel of the integral equation is approximated by a simpler expression, on the basis of the assumption of sufficiently large aspect ratio. With this approximation the double integral occurring in the formulation of the problem is reduced to two single integrals, one of which is taken over the chord and the other over the span of the lifting surface. On the basis of this reduction the three-dimensional problem appears separated into two two-dimensional problems, one of them being effectively the problem of two-dimensional flow and the other being the problem of spanwise circulation distribution. Earlier results concerning the oscillating lifting surface of finite span in incompressible flow are contained in the present more general results.

Reissner, Eric↗

Notes on aerodynamic forces 1 : rectilinear motion

The study of the motion of perfect fluids is of paramount importance for the understanding of the chief phenomena occurring in the air surrounding an aircraft, and for the numerical determination of their effects. The author recently successfully employed some simple methods for the investigation of the flow of a perfect fluid that have never been mentioned in connection with aeronautical problems. These methods appeal particularly to the engineer who is untrained in performing laborious mathematical computations, as they do away with these and allow one to obtain many interesting results by the mere application of some general and well-known principles of mechanics. Discussed here are the kinetic energy of moving fluids, the momentum of a body in a perfect fluid, two dimensional flow, three dimensional flow, and the distribution of the transverse forces of very elongated surfaces of revolution.

Munk, Max M↗

Space-Time Conservation Element and Solution Element Method Being Developed

The engineering research and design requirements of today pose great computer-simulation challenges to engineers and scientists who are called on to analyze phenomena in continuum mechanics. The future will bring even more daunting challenges, when increasingly complex phenomena must be analyzed with increased accuracy. Traditionally used numerical simulation methods have evolved to their present state by repeated incremental extensions to broaden their scope. They are reaching the limits of their applicability and will need to be radically revised, at the very least, to meet future simulation challenges. At the NASA Lewis Research Center, researchers have been developing a new numerical framework for solving conservation laws in continuum mechanics, namely, the Space-Time Conservation Element and Solution Element Method, or the CE/SE method. This method has been built from fundamentals and is not a modification of any previously existing method. It has been designed with generality, simplicity, robustness, and accuracy as cornerstones. The CE/SE method has thus far been applied in the fields of computational fluid dynamics, computational aeroacoustics, and computational electromagnetics. Computer programs based on the CE/SE method have been developed for calculating flows in one, two, and three spatial dimensions. Results have been obtained for numerous problems and phenomena, including various shock-tube problems, ZND detonation waves, an implosion and explosion problem, shocks over a forward-facing step, a blast wave discharging from a nozzle, various acoustic waves, and shock/acoustic-wave interactions. The method can clearly resolve shock/acoustic-wave interactions, wherein the difference of the magnitude between the acoustic wave and shock could be up to six orders. In two-dimensional flows, the reflected shock is as crisp as the leading shock. CE/SE schemes are currently being used for advanced applications to jet and fan noise prediction and to chemically reacting flows.

Chang, Sin-Chung↗

Comparison of two- and three-dimensional flow computations with laser anemometer measurements in a transonic compressor rotor

Two and three dimensional inviscid solutions for the flow in a transonic axial compressor rotor at design speed are compared with probe and laser anemometers measurements at near-stall and maximum-flow operating points. Experimental details of the laser anemometer system and computational details of the two dimensional axisymmetric code and three dimensional Euler code are described. Comparisons are made between relative Mach number and flow angle contours, shock location, and shock strength. A procedure for using an efficient axisymmetric code to generate downstream pressure input for computationally expensive Euler codes is discussed. A film supplement shows the calculations of the two operating points with the time-marching Euler code.

Chima, R. V.↗

The piecewise-linear predictor-corrector code - A Lagrangian-remap method for astrophysical flows

We describe a time-explicit finite-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing Eulerian schemes in its use of operator-splitting and artificial viscosity, except that we solve the Lagrangian equations of motion with a predictor-corrector and then remap onto a fixed Eulerian grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector Lagrangian-remap code has great flexibility for application to a variety of astrophysical problems.

Lufkin, Eric A.↗

A multi-temperature TVD algorithm for relaxing hypersonic flows

In this paper, the extension of a multispecies TVD algorithm, second-order accurate for real-gas flows to a multitemperature formulation is described. The convection algorithm is coupled to internal relaxation processes, and the features of the coupling are examined. The first version consists of a three-temperature model, where translational-rotational, vibrational, and electronic energy modes are separately convected. Although several species are present, there is only one vibrational temperature in this model. The second version generalizes to a vibrational temperature for each molecular specie, with additional couplings between species. The algorithms are applied to a generic two-dimensional flow field, and results are compared with experimental observations.

Cambier, Jean-Luc↗

Optimum design of ninety degree bends

An algorithm for the optimum design of an internal flow component to obtain the maximum pressure rise is presented. Maximum pressure rise in a duct with simultaneous turning and diffusion is shown to be related to the control of flow separation on the passage walls. Such a flow is usually associated with downstream conditions that are desirable in turbomachinery and propulsion applications to ensure low loss and stable performance. The algorithm requires the solution of an 'adjoint' problem in addition to the 'direct' equations governing the flow in a body, which in the present analysis are assumed to be the laminar Navier-Stokes equations. The theoretical framework and computational algorithms presented in this study are for the steady Navier-Stokes equations. A procedure is developed for the numerical solution of the adjoint equations. This procedure is coupled with a direct solver in a design iteration loop, that provides a new shape with a higher pressure rise. This procedure is first validated for the design of optimum plane diffusers in two-dimensional flow. The direct Navier-Stokes and the 'adjoint' equations are solved using a finite volume formulation for spatial discretization in an artificial compressibility framework. A simplified version of the above approach is then utilized to design ninety degree diffusing bends. Calculations were carried out for a mean radius ratio at inlet of 2.5 and Reynolds numbers varying from 100 to 500. While at this stage laminar flows is assumed, it is shown that a similar approach can be conceived for turbulent flows.

Modi, Vijay↗

An efficient method for solving the steady Euler equations

An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.

Liou, M. S.↗

Experimental Study of Buoyant-Thermocapillary Convection in a Rectangular Cavity

The problem of buoyant-thermocapillary convection in cavities is governed by a relatively large number of nondimensional parameters, and there is consequently a large number of different types of flow that can be found in this system. Previous results give disjoint glimpses of a wide variety of qualitatively and quantitatively different results in widely different parts of parameter space. In this study, we report experiments on the primary and secondary instabilities in a geometry with equal aspect ratios in the range from 1 to 8 in both the direction along and perpendicular to the applied temperature gradient. We thus complement previous work which mostly involved either fluid layers of large extent in both directions, or consisted of investigations of strictly two-dimensional disturbances. We observe the primary transition from an essentially two-dimensional flow to steady three-dimensional longitudinal rolls. The critical Marangoni number is found to depend on the aspect ratios of the system, and varies from 4.6 x 10(exp 5) at aspect ratio 2.0 to 5.5 x 10(exp 4) at aspect ratio 3.5. Further, we have investigated the stability of the three-dimensional flow at larger Marangoni numbers, and find a novel oscillatory flow at critical Marangoni numbers of the order of 6 x 10(exp 5). We suggest possible mechanisms which give rise to the oscillation, and find that it is expected to be a relaxation type oscillation.

Braunsfurth, Manfred G.↗