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NASA NTRS1990

Nonlinear spatial evolution of externally excited instability waves in free shear layers

The effects of critical-layer nonlinearity on spatially growing instability waves on shear layers between parallel streams are considered. In the two-dimensional incompressible case, the flow in the critical layer is governed by a nonequilibrium, nonlinear vorticity equation. The initial exponential growth of the instability wave is converted into algebraic growth during the streamwise 'aging' of the critical layer into a quasi-equilibrium state. This leads to a next stage of evolution where the instability-wave growth is affected by both mean-flow-divergence and nonlinear effects and is eventually converted to decay. A uniformly valid composite formula for the instability wave amplitude, accounting for both nonparallel and nonlinear effects, is given and compared to experimental results. The inviscid solutions to these equations always end in a singularity at finite downstream distance.

Hultgren, L. S.↗
NASA NTRS1992

Crossflow effects on the growth rate of inviscid Goertler vortices in a hypersonic boundary layer

The effects of crossflow on the growth rate of inviscid Goertler vortices in a hypersonic boundary layer with pressure gradient are studied. Attention is focused on the inviscid mode trapped in the temperature adjustment layer; this mode has greater growth rate than any other mode. The eigenvalue problem which governs the relationship between the growth rate, the crossflow amplitude, and the wavenumber is solved numerically, and the results are then used to clarify the effects of crossflow on the growth rate of inviscid Goertler vortices. It is shown that crossflow effects on Goertler vortices are fundamentally different for incompressible and hypersonic flows. The neutral mode eigenvalue problem is found to have an exact solution, and as a by-product, we have also found the exact solution to a neutral mode eigenvalue problem which was formulated, but unsolved before, by Bassom and Hall (1991).

Fu, Yibin↗
NASA NTRS1992

Lee waves, benign and malignant

The flow of an incompressible, stratified fluid over an obstacle will produce an oscillation in which buoyancy is the restoring force, called a gravity wave. For disturbances of this scale, the atmosphere may be treated as incompressible; and even the linear approximation will explain many of the phenomena observed in the lee of mountains. However, nonlinearities arise in two ways: (1) through the large (scaled) size of the mountain, and (2) from dynamically singular levels in the fluid field. These produce a complicated array of phenomena that present hazards to aircraft and to lee surface areas. If there is no dynamic barrier, these waves can penetrate vertically into the middle atmosphere (30-100 km attitude), where recent observations show them to be of a length scale that must involve the Coriolis force in any modeling. At these altitudes, the amplitude of the waves is very large, and the waves are studied with a view to their potential impact on the projected National Aerospace Plane. This paper presents the results of analyses and state-of-the-art numerical simulations, validated where possible by observational data.

Wurtele, M. G.↗
NASA NTRS1993

A study of eigenvalue sensitivity for hydrodynamic stability operators

The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.

Schmid, Peter J.↗
NASA NTRS1947

Isolated and cascade airfoils with prescribed velocity distribution

An exact solution of the problem of designing an airfoil with a prescribed velocity distribution on the suction surface in a given uniform flow of an incompressible perfect fluid is obtained by replacing the boundary of the airfoil by vortices. By this device, a method of solution is developed that is applicable both to isolated airfoils and to airfoils in cascade. The conformal transformation of the designed airfoil into a circle can then be obtained and the velocity distribution at any angle of attack computed. Numerical illustrations of the method are given for the airfoil in cascade.

Goldstein, Arthur W↗
NASA NTRS1940

Recent work on airfoil theory

The basic ideas of a new method for treating the problem of the airfoil are presented, and a review is given of the problems thus far computed for incompressible and supersonic flows. Test results are reported for the airfoil of circular plan form and the results are shown to agree well with the theory. As a supplement, a theory based on the older methods is presented for the rectangular of small aspect ratio.

Prandtl, L↗
NASA NTRS1995

Numerical thermal analyses of heat exchangers for the stirling engine application

The Regenerator, Cooler and Heater for the NASA Space Power Research Engine (SPRE) have been analyzed in detail for laminar, incompressible and oscillatory flow conditions. Each component has been analyzed independently and in detail with the regenerator being modeled as two-parallel-plates channel with a solid wall. The ends of the channel are exposed to two reservoir maintained at different temperature thus providing an axial temperature gradient along the channel. The cooler and heater components have been modeled as circular pipes with isothermal walls. Two different types of thermal boundary conditions have been investigated for the cooler and heater, namely, symmetric and asymmetric temperature inflow. In symmetric temperature inflow the flow enters the channel with the same temperature in throughout the velocity cycle whereas, in asymmetric temperature inflow the flow enters with a different temperature in each half cycle. The study was conducted over a wide range of Maximum Reynolds number (RE(max) varying from 75 to 60000, Valensi number (Va) from 2.5 to 800, and relative amplitude of fluid displacement (A(sub r) from 0.357 to 1.34. A two dimensional Finite volume method based on the SIMPLE algorithm was used to solve the governing partial differential equations. Post processing programs were developed to effectively describe the heat transfer mechanism under oscillatory flows. The computer code was validated by comparing with existing analytical solutions for oscillating flows. The thermal field have been studied with the help of temperature contour and three dimensional plots. The instantaneous friction factor, wall heat flux and heat transfer coefficient have been examined. It has been concluded that in general, the frictional factor and heat transfer coefficient are higher under oscillatory flow conditions when the Valensi number is high. Also, the thermal efficiency decreases for lower A(r) values. Further, the usual steady state definition for the heat transfer coefficient does not seem to be valid.

Kannapareddy, Mohan Raj↗
NASA NTRS1997

An NPARC Turbulence Module with Wall Functions

The turbulence module recently developed for the NPARC code has been extended to include wall functions. The Van Driest transformation is used so that the wall functions can be applied to both incompressible and compressible flows. The module is equipped with three two-equation K-epsilon turbulence models: Chien, Shih-Lumley and CMOTR models. Details of the wall functions as well as their numerical implementation are reported. It is shown that the inappropriate artificial viscosity in the near-wall region has a big influence on the solution of the wall function approach. A simple way to eliminate this influence is proposed, which gives satisfactory results during the code validation. The module can be easily linked to the NPARC code for practical applications.

Zhu, J.↗
NASA NTRS1998

Barriers to Achieving Textbook Multigrid Efficiency (TME) in CFD

As a guide to attaining this optimal performance for general CFD problems, the table below lists every foreseen kind of computational difficulty for achieving that goal, together with the possible ways for resolving that difficulty, their current state of development, and references. Included in the table are staggered and nonstaggered, conservative and nonconservative discretizations of viscous and inviscid, incompressible and compressible flows at various Mach numbers, as well as a simple (algebraic) turbulence model and comments on chemically reacting flows. The listing of associated computational barriers involves: non-alignment of streamlines or sonic characteristics with the grids; recirculating flows; stagnation points; discretization and relaxation on and near shocks and boundaries; far-field artificial boundary conditions; small-scale singularities (meaning important features, such as the complete airplane, which are not visible on some of the coarse grids); large grid aspect ratios; boundary layer resolution; and grid adaption.

Brandt, Achi↗
NASA NTRS1997

SWIFT: Multistage Turbomachinery Analysis Code Developed

A new turbomachinery analysis code called SWIFT has been developed at the NASA Lewis Research Center. SWIFT solves thin-layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and an explicit finite-difference scheme. Preconditioning allows the code to be used for all speed ranges, from incompressible to supersonic flows. Multiblock capability allows three types of grids to be patched together to simulate many types of turbomachinery geometries, including hub and tip clearances. In addition, code users can analyze multistage turbomachinery by using a steady averaging-plane approach. This approach uses linearized characteristic boundary conditions to pass information accurately between the stages.

Chima, Rodrick V.↗
NASA NTRS2008

Implementation and Validation of a Laminar-to-Turbulent Transition Model in the Wind-US Code

A bypass transition model has been implemented in the Wind-US Reynolds Averaged Navier-Stokes (RANS) solver. The model is based on the Shear Stress Transport (SST) turbulence model and was built starting from a previous SST-based transition model. Several modifications were made to enable (1) consistent solutions regardless of flow field initialization procedure and (2) fully turbulent flow beyond the transition region. This model is intended for flows where bypass transition, in which the transition process is dominated by large freestream disturbances, is the key transition mechanism as opposed to transition dictated by modal growth. Validation of the new transition model is performed for flows ranging from incompressible to hypersonic conditions.

Denissen, Nicholas A.↗
NASA NTRS2007

Self-Regulating Water-Separator System for Fuel Cells

proposed system would perform multiple coordinated functions in regulating the pressure of the oxidant gas (usually, pure oxygen) flowing to a fuelcell stack and in removing excess product water that is generated in the normal fuel-cell operation. The system could function in the presence or absence of gravitation, and in any orientation in a gravitational field. Unlike some prior systems for removing product water, the proposed system would not depend on hydrophobicity or hydrophilicity of surfaces that are subject to fouling and, consequently, to gradual deterioration in performance. Also unlike some prior systems, the proposed system would not include actively controlled electric motors for pumping; instead, motive power for separation and pumping away of product water would be derived primarily from the oxidant flow and perhaps secondarily from the fuel flow. The net effect of these and other features would be to make the proposed system more reliable and safer, relative to the prior systems. The proposed system (see figure) would include a pressure regulator and sensor in the oxidant supply just upstream from an ejector reactant pump. The pressure of the oxidant supply would depend on the consumption flow. In one of two control subsystems, the pressure of oxidant flowing from the supply to the ejector would be sensed and used to control the speed of a set of a reciprocating constant-displacement pump so that the volumetric flow of nominally incompressible water away from the system would slightly exceed the rate at which water was produced by the fuel cell(s). The two-phase (gas/liquid water) outlet stream from the fuel cell(s) would enter the water separator, a turbinelike centrifugal separator machine driven primarily by the oxidant gas stream. A second control subsystem would utilize feedback derived from the compressibility of the outlet stream: As the separator was emptied of liquid water, the compressibility of the pumped stream would increase. The compressibility would be sensed, and an increase in compressibility beyond a preset point (signifying a decrease in water content below an optimum low level) would cause the outflow from the reciprocating pump to be diverted back to the separator to recycle some water.

Vasquez, Arturo↗
NASA NTRS2015

Multiscale and Multiphysics Modeling of Additive Manufacturing of Advanced Materials

The objective of this proposed project is to research and develop a prediction tool for advanced additive manufacturing (AAM) processes for advanced materials and develop experimental methods to provide fundamental properties and establish validation data. Aircraft structures and engines demand materials that are stronger, useable at much higher temperatures, provide less acoustic transmission, and enable more aeroelastic tailoring than those currently used. Significant improvements in properties can only be achieved by processing the materials under nonequilibrium conditions, such as AAM processes. AAM processes encompass a class of processes that use a focused heat source to create a melt pool on a substrate. Examples include Electron Beam Freeform Fabrication and Direct Metal Deposition. These types of additive processes enable fabrication of parts directly from CAD drawings. To achieve the desired material properties and geometries of the final structure, assessing the impact of process parameters and predicting optimized conditions with numerical modeling as an effective prediction tool is necessary. The targets for the processing are multiple and at different spatial scales, and the physical phenomena associated occur in multiphysics and multiscale. In this project, the research work has been developed to model AAM processes in a multiscale and multiphysics approach. A macroscale model was developed to investigate the residual stresses and distortion in AAM processes. A sequentially coupled, thermomechanical, finite element model was developed and validated experimentally. The results showed the temperature distribution, residual stress, and deformation within the formed deposits and substrates. A mesoscale model was developed to include heat transfer, phase change with mushy zone, incompressible free surface flow, solute redistribution, and surface tension. Because of excessive computing time needed, a parallel computing approach was also tested. In addition, after investigating various methods, a Smoothed Particle Hydrodynamics Model (SPH Model) was developed to model wire feeding process. Its computational efficiency and simple architecture makes it more robust and flexible than other models. More research on material properties may be needed to realistically model the AAM processes. A microscale model was developed to investigate heterogeneous nucleation, dendritic grain growth, epitaxial growth of columnar grains, columnar-to-equiaxed transition, grain transport in melt, and other properties. The orientations of the columnar grains were almost perpendicular to the laser motion's direction. Compared to the similar studies in the literature, the multiple grain morphology modeling result is in the same order of magnitude as optical morphologies in the experiment. Experimental work was conducted to validate different models. An infrared camera was incorporated as a process monitoring and validating tool to identify the solidus and mushy zones during deposition. The images were successfully processed to identify these regions. This research project has investigated multiscale and multiphysics of the complex AAM processes thus leading to advanced understanding of these processes. The project has also developed several modeling tools and experimental validation tools that will be very critical in the future of AAM process qualification and certification.

Liou, Frank↗
NASA NTRS1959

Energy Equation Approximation in Fluid Mechanics

There is some confusion in the literature of fluid mechanics in regard to the correct form of the energy equation for the study of the flow of nearly incompressible fluids. Several forms of the energy equation and their use are therefore discussed in this note.

Goldstein, Arthur W.↗
NASA NTRS2002

Incompressible Navier-Stokes Solvers in Primative Variables and their Applications to Steady and Unsteady Flow Simulations

This paper reviews recent progress made in incompressible Navier-Stokes simulation procedures and their application to problems of engineering interest. Discussions are focused on the methods designed for complex geometry applications in three dimensions, and thus are limited to primitive variable formulation. A summary of efforts in flow solver development is given followed by numerical studies of a few example problems of current interest. Both steady and unsteady solution algorithms and their salient features are discussed. Solvers discussed here are based on a structured-grid approach using either a finite -difference or a finite-volume frame work. As a grand-challenge application of these solvers, an unsteady turbopump flow simulation procedure has been developed which utilizes high performance computing platforms. In the paper, the progress toward the complete simulation capability of the turbo-pump for a liquid rocket engine is reported. The Space Shuttle Main Engine (SSME) turbo-pump is used as a test case for evaluation of two parallel computing algorithms that have been implemented in the INS3D code. The relative motion of the grid systems for the rotorstator interaction was obtained using overact grid techniques. Unsteady computations for the SSME turbo-pump, which contains 114 zones with 34.5 million grid points, are carried out on SCSI Origin 3000 systems at NASA Ames Research Center. The same procedure has been extended to the development of NASA-DeBakey Ventricular Assist Device (VAD) that is based on an axial blood pump. Computational, and clinical analysis of this device are presented.

Kiris, Cetin C.↗
NASA NTRS1998

Numerical Procedures for Inlet/Diffuser/Nozzle Flows

Two primitive variable, pressure based, flux-split, RNS/NS solution procedures for viscous flows are presented. Both methods are uniformly valid across the full Mach number range, Le., from the incompressible limit to high supersonic speeds. The first method is an 'optimized' version of a previously developed global pressure relaxation RNS procedure. Considerable reduction in the number of relatively expensive matrix inversion, and thereby in the computational time, has been achieved with this procedure. CPU times are reduced by a factor of 15 for predominantly elliptic flows (incompressible and low subsonic). The second method is a time-marching, 'linearized' convection RNS/NS procedure. The key to the efficiency of this procedure is the reduction to a single LU inversion at the inflow cross-plane. The remainder of the algorithm simply requires back-substitution with this LU and the corresponding residual vector at any cross-plane location. This method is not time-consistent, but has a convective-type CFL stability limitation. Both formulations are robust and provide accurate solutions for a variety of internal viscous flows to be provided herein.

Rubin, Stanley G.↗
NASA NTRS1997

Computations of Complex Three-Dimensional Turbulent Free Jets

Three-dimensional, incompressible turbulent jets with rectangular and elliptical cross-sections are simulated with a finite-difference numerical method. The full Navier- Stokes equations are solved at low Reynolds numbers, whereas at high Reynolds numbers filtered forms of the equations are solved along with a sub-grid scale model to approximate the effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporary discretization and a fourth-order compact scheme is used for spatial discretization. Although such methods are widely used in the simulation of compressible flows, the lack of an evolution equation for pressure or density presents particular difficulty in incompressible flows. The pressure-velocity coupling must be established indirectly. It is achieved, in this study, through a Poisson equation which is solved by a compact scheme of the same order of accuracy. The numerical formulation is validated and the dispersion and dissipation errors are documented by the solution of a wide range of benchmark problems. Three-dimensional computations are performed for different inlet conditions which model the naturally developing and forced jets. The experimentally observed phenomenon of axis-switching is captured in the numerical simulation, and it is confirmed through flow visualization that this is based on self-induction of the vorticity field. Statistical quantities such as mean velocity, mean pressure, two-point velocity spatial correlations and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stresses are presented. Detailed budgets of the mean momentum and Reynolds stress equations are presented to aid in the turbulence modeling of complex jets. Simulations of circular jets are used to quantify the effect of the non-uniform curvature of the non-circular jets.

Wilson, Robert V.↗
NASA NTRS1974

Application of wave mechanics theory to fluid dynamics problems: Boundary layer on a circular cylinder including turbulence

The application of the elements of quantum (wave) mechanics to some special problems in the field of macroscopic fluid dynamics is discussed. Emphasis is placed on the flow of a viscous, incompressible fluid around a circular cylinder. The following subjects are considered: (1) the flow of a nonviscous fluid around a circular cylinder, (2) the restrictions imposed the stream function by the number of dimensions of space, and (3) the flow past three dimensional bodies in a viscous fluid, particularly past a circular cylinder in the symmetrical case.

Krzywoblocki, M. Z. V.↗