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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel width, depending on the Reynolds number.

Scott, James R.↗
NASA NTRS1993

Design efficiency evaluation for transonic airfoil optimization - A case for Navier-Stokes design

A constrained-optimization design method which improves the aerodynamic performance of transonic airfoils is evaluated from a design-quality and design-efficiency viewpoint. Design efficiency is a measure of the performance improvement and the design time (CPU time). Total-airfoil design and upper-surface design are performed using the Euler and Navier-Stokes equations with several grids, and are evaluated using the Navier-Stokes equations to determine the anticipated physical design response. Even though the cost of the Euler design is lower than Navier-Stokes design, the Navier-Stokes evaluation indicates that the Euler design does not necessarily improve the aerodynamic performance. Therefore, the design optimization should be based on an accurate flow simulation to achieve an actual performance improvement, and the design time is a secondary concern.

Hager, J. O.↗
NASA NTRS1994

Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

Jiang, Bo-Nan↗
NASA NTRS1995

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Scott, James R.↗
NASA NTRS1993

Cavitation Modeling in Euler and Navier-Stokes Codes

Many previous researchers have modeled sheet cavitation by means of a constant pressure solution in the cavity region coupled with a velocity potential formulation for the outer flow. The present paper discusses the issues involved in extending these cavitation models to Euler or Navier-Stokes codes. The approach taken is to start from a velocity potential model to ensure our results are compatible with those of previous researchers and available experimental data, and then to implement this model in both Euler and Navier-Stokes codes. The model is then augmented in the Navier-Stokes code by the inclusion of the energy equation which allows the effect of subcooling in the vicinity of the cavity interface to be modeled to take into account the experimentally observed reduction in cavity pressures that occurs in cryogenic fluids such as liquid hydrogen. Although our goal is to assess the practicality of implementing these cavitation models in existing three-dimensional, turbomachinery codes, the emphasis in the present paper will center on two-dimensional computations, most specifically isolated airfoils and cascades. Comparisons between velocity potential, Euler and Navier-Stokes implementations indicate they all produce consistent predictions. Comparisons with experimental results also indicate that the predictions are qualitatively correct and give a reasonable first estimate of sheet cavitation effects in both cryogenic and non-cryogenic fluids. The impact on CPU time and the code modifications required suggests that these models are appropriate for incorporation in current generation turbomachinery codes.

Deshpande, Manish↗
NASA NTRS1995

Progress in incompressible Navier-Stokes computations for propulsion flows and its dual-use applications

Development of an incompressible Navier-Stokes solution procedure was performed for the analysis of a liquid rocket engine pump components and for the mechanical heart assist devices. The solution procedure for the propulsion systems is applicable to incompressible Navier-Stokes flows in a steadily rotating frame of reference for any general complex configurations. The computer codes were tested on different complex configurations such as liquid rocket engine inducer and impellers. As a spin-off technology from the turbopump component simulations, the flow analysis for an axial heart pump was conducted. The baseline Left Ventricular Assist Device (LVAD) design was improved by adding an inducer geometry by adapting from the liquid rocket engine pump. The time-accurate mode of the incompressible Navier-Stokes code was validated with flapping foil experiment by using different domain decomposition methods. In the flapping foil experiment, two upstream NACA 0025 foils perform high-frequency synchronized motion and generate unsteady flow conditions for a downstream larger stationary foil. Fairly good agreement was obtained between unsteady experimental data and numerical results from two different moving boundary procedures. Incompressible Navier-Stokes code (INS3D) has been extended for heat transfer applications. The temperature equation was written for both forced and natural convection phenomena. Flow in a square duct case was used for the validation of the code in both natural and forced convection.

Kiris, Cetin↗
NASA NTRS1994

Three-Dimensional Navier-Stokes Method with Two-Equation Turbulence Models for Efficient Numerical Simulation of Hypersonic Flows

A new computational efficient 3-D compressible Reynolds-averaged implicit Navier-Stokes method with advanced two equation turbulence models for high speed flows is presented. All convective terms are modeled using an entropy satisfying higher-order Total Variation Diminishing (TVD) scheme based on implicit upwind flux-difference split approximations and arithmetic averaging procedure of primitive variables. This method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent Navier-Stokes procedures to solve flows with mixed supersonic and subsonic zones, including streamwise separated flows. Its robust stability derives from a combination of conservative implicit upwind flux-difference splitting with Roe's property U to provide accurate shock capturing capability that non-conservative schemes do not guarantee, alternating symmetric Gauss-Seidel 'method of planes' relaxation procedure coupled with a three-dimensional two-factor diagonal-dominant approximate factorization scheme, TVD flux limiters of higher-order flux differences satisfying realizability, and well-posed characteristic-based implicit boundary-point a'pproximations consistent with the local characteristics domain of dependence. The efficiency of the method is highly increased with Newton Raphson acceleration which allows convergence in essentially one forward sweep for supersonic flows. The method is verified by comparing with experiment and other Navier-Stokes methods. Here, results of adiabatic and cooled flat plate flows, compression corner flow, and 3-D hypersonic shock-wave/turbulent boundary layer interaction flows are presented. The robust 3-D method achieves a better computational efficiency of at least one order of magnitude over the CNS Navier-Stokes code. It provides cost-effective aerodynamic predictions in agreement with experiment, and the capability of predicting complex flow structures in complex geometries with good accuracy.

Bardina, J. E.↗
NASA NTRS1981

Numerical Prediction Methods (Reynolds-Averaged Navier-Stokes Simulations of Transonic Separated Flows)

During the past five years, numerous pioneering archival publications have appeared that have presented computer solutions of the mass-weighted, time-averaged Navier-Stokes equations for transonic problems pertinent to the aircraft industry. These solutions have been pathfinders of developments that could evolve into a major new technological capability, namely the computational Navier-Stokes technology, for the aircraft industry. So far these simulations have demonstrated that computational techniques, and computer capabilities have advanced to the point where it is possible to solve forms of the Navier-Stokes equations for transonic research problems. At present there are two major shortcomings of the technology: limited computer speed and memory, and difficulties in turbulence modelling and in computation of complex three-dimensional geometries. These limitations and difficulties are the pacing items of the continuing developments, although the one item that will most likely turn out to be the most crucial to the progress of this technology is turbulence modelling. The objective of this presentation is to discuss the state of the art of this technology and suggest possible future areas of research. We now discuss some of the flow conditions for which the Navier-Stokes equations appear to be required. On an airfoil there are four different types of interaction of a shock wave with a boundary layer: (1) shock-boundary-layer interaction with no separation, (2) shock-induced turbulent separation with immediate reattachment (we refer to this as a shock-induced separation bubble), (3) shock-induced turbulent separation without reattachment, and (4) shock-induced separation bubble with trailing edge separation.

Mehta, Unmeel↗
NASA NTRS1998

Prediction of Unsteady Transitional Layers in Turbomachinery Using Navier Stokes Equations

The objective of the research reported in this presentation is to develop computational techniques for the prediction of unsteady transitional flows associated with the rotor stator interaction in turbomachinery. Three low-Reynolds number turbulence models are incorporated in two unsteady Navier-Stokes codes (one is pressure based and the other is time marching with Runge-Kutta time stepping) and evaluated for accuracy in predicting the onset and the end of unsteady transitional patches due to wake passing. The best model is then used for modification and improvement for the leading edge effect. An existing steady Navier-Stokes code was modified to include pseudo-time stepping, which provided acceleration from 5 to 25 times that of the original code. A systematic validation procedure was implemented to assess the effects of the grid, artificial dissipation, physical, and the pseudo-time step for an accurate prediction of transitional flows resulting from the rotor-stator interaction. The ability of the Navier-Stokes code to predict the unsteady transitional flow on a turbomachinery blade is demonstrated. The unsteady pressure and velocity fields are in good agreement with the experimental data and the prediction from the Euler/boundary layer approach. The numerical solver was able to capture all zones (wake induced transitional strip, wake induced turbulent strip, calmed region, etc.) associated with wake induced transition in a compressor cascade. Another significant step is the assessment of k-epsilon turbulence models, including the leading edge modifications. Best results were obtained from the FLB model. The LB model predicted earlier inception of the transition and shorter transition length. Modification of the k-epsilon model was found to be essential for an accurate prediction of the unsteady transitional flow in a compressor cascade. The CH model failed to predict the unsteady transitional flow. Predicted boundary layer was turbulent from the leading edge, even with the modification of the k-epsilon model near the stagnation point. A comparison of the instantaneous shape factor, the skin friction coefficient, and the momentum thickness indicates that the Navier-Stokes predictions are reasonably good. Interaction between the upstream wake and stator wake results in shedding of unsteady vortices from the trailing edge and increased dissipation in the stator wake and, as a consequence, increased rate of decay of the stator wake. The procedure developed at Penn State should aid the designers of turbomachinery in allowing for the unsteady transitional flows due to rotor-stator interaction.

Lakshminarayana, B.↗
NASA NTRS1999

A Comparison of Three Navier-Stokes Solvers for Exhaust Nozzle Flowfields

A comparison of the NPARC, PAB, and WIND (previously known as NASTD) Navier-Stokes solvers is made for two flow cases with turbulent mixing as the dominant flow characteristic, a two-dimensional ejector nozzle and a Mach 1.5 elliptic jet. The objective of the work is to determine if comparable predictions of nozzle flows can be obtained from different Navier-Stokes codes employed in a multiple site research program. A single computational grid was constructed for each of the two flows and used for all of the Navier-Stokes solvers. In addition, similar k-e based turbulence models were employed in each code, and boundary conditions were specified as similarly as possible across the codes. Comparisons of mass flow rates, velocity profiles, and turbulence model quantities are made between the computations and experimental data. The computational cost of obtaining converged solutions with each of the codes is also documented. Results indicate that all of the codes provided similar predictions for the two nozzle flows. Agreement of the Navier-Stokes calculations with experimental data was good for the ejector nozzle. However, for the Mach 1.5 elliptic jet, the calculations were unable to accurately capture the development of the three dimensional elliptic mixing layer.

Georgiadis, Nicholas J.↗
NASA NTRS1999

Application of an Unstructured Grid Navier-Stokes Solver to a Generic Helicopter Boby: Comparison of Unstructured Grid Results with Structured Grid Results and Experimental Results

An unstructured-grid Navier-Stokes solver was used to predict the surface pressure distribution, the off-body flow field, the surface flow pattern, and integrated lift and drag coefficients on the ROBIN configuration (a generic helicopter) without a rotor at four angles of attack. The results are compared to those predicted by two structured- grid Navier-Stokes solvers and to experimental surface pressure distributions. The surface pressure distributions from the unstructured-grid Navier-Stokes solver are in good agreement with the results from the structured-grid Navier-Stokes solvers. Agreement with the experimental pressure coefficients is good over the forward portion of the body. However, agreement is poor on the lower portion of the mid-section of the body. Comparison of the predicted surface flow patterns showed similar regions of separated flow. Predicted lift and drag coefficients were in fair agreement with each other.

Mineck, Raymond E.↗
NASA NTRS2003

Asymmetric Stokes-V Profiles at the Penumbral Boundary of a Sunspot

We present the spectropolarimetric measurements of a sunspot in the active region NOAA 6958 (15S03W), situated near the central meridian disk passage. The follower polarity sunspot was somewhat symmetrically round shaped with an elongated penumbra. There were several opposite polarity magnetic elements at, and beyond the penumbral boundary. The H-alpha images of the sunspot show the bright emission regions near the penumbral boundary towards the sun-center, which was of opposite polarity with respect to the main spot. The net-circular polarization (NCP) map shows that NCP is negative in the inner part of the spot and positive at the penumbral boundary and near the H-alpha plage. The Doppler velocities were determined by measuring the center-of-gravity (COG) of the Stokes-I profile and zero-crossing (ZC) wavelength of the Stokes-V profiles. The COG velocity map in general agrees with the Evershed flow. In addition, it shows the up flow in the penumbral region. The ZC velocities show the strong down flow at the penumbral boundary. Double-lobed Stokes-V profiles are observed at the locations, where the penumbral fibrils terminate coinciding the H-alpha plage. The Double lobed profiles had an unshifted component similar to the Stokes-V profiles of the sunspot penumbra and a shifted component with a velocity of about 5 km/s. The amplitude of the second component increases along the penumbral fibril as a function of the distance from the center of the sunspot. In this paper we discuss the role of emerging flux in generating the observed double lobed profiles. Based on our present observations, we propose to observe with the Solar-B Spectropolarimeter for understanding the nature of emerging flux near the sunspots.

Choudhary, Debi Prasad↗
NASA NTRS2002

Properties of the Residual Stress of the Temporally Filtered Navier-Stokes Equations

The development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, is of current interest. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. Causal time-domain filters, parameterized by a temporal filter width 0 less than Delta less than infinity, are considered. For several reasons, the differential forms of such filters are preferred to their corresponding integral forms; among these, storage requirements for differential forms are typically much less than for integral forms and, for some filters, are independent of Delta. The behavior of the residual stress in the limits of both vanishing and in infinite filter widths is examined. It is shown analytically that, in the limit Delta to 0, the residual stress vanishes, in which case the Navier-Stokes equations are recovered from the temporally filtered equations. Alternately, in the limit Delta to infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger's equation. Finally, finite filter widths are also considered, and a priori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted.

Pruett, C. D.↗
DOE OSTI2026

Coherent anti-Stokes Raman scattering with squeezed light: CARS for quantum-enhanced spectroscopy and imaging

We theoretically investigate quantum-enhanced coherent anti-Stokes Raman scattering (CARS) using squeezed light to amplify vibrational transition rates at low photon flux. Quantum sensing approaches are needed for nondestructive nanometrology such as in bioimaging where reduced photodamage is desired while retaining resolution and sensitivity. We analyze both single-mode squeezing applied to the pump field and two-mode squeezing between the pump and Stokes fields. We also show that the ordering of displacement and squeezing operations—whether displacement precedes squeezing or squeezing precedes displacement—has an impact on the resulting CARS transition amplitudes due to a difference in the photon number and the quantum-enhancement coefficients, with the latter offering a stronger enhancement in the case of two modes squeezing of the pump and Stokes under experimentally accessible conditions. Furthermore, our calculations capture these quantum enhancements through the intrinsic photon-number correlations of squeezed light, eliminating the need for interferometric detection or higher pump powers that are otherwise required to reach comparable sensitivities in classical CARS. Finally, we outline a quantum plasmonic extension of our model in which local field enhancements caused by surface plasmon excitation in metallic nanoparticles can be incorporated via mode-selective field amplification factors, offering a pathway toward combining squeezed-light quantum optics with surface-enhanced nanoscale spectroscopy and imaging.

Atomic & molecular structure↗
NASA NTRS1972

Ground and flight test program of a Stokes-flow parachute: Packaging, deployment, and sounding rocket integration

The current design and hardware components of the patented 14 sqm Stokes flow parachute are described. The Stokes-flow parachute is a canopy of open mesh material, which is kept deployed by braces. Because of the light weight of its mesh material, and the high drag on its mesh elements when they operate in the Stokes-flow flight regime, this parachute has an extremely low ballistic coefficient. It provides a stable aerodynamic platform superior to conventional nonporous billowed parachutes, is exceptionally packable, and is easily contained within the canister of the Sidewinder Arcas or the RDT and E rockets. Thus, it offers the potential for gathering more meteorological data, especially at high altitudes, than conventional billowed parachutes. Methods for packaging the parachute are also recommended. These methods include schemes for folding the canopy and for automatically releasing the pressurizing fluid as the packaged parachute unfolds.

Niederer, P. G.↗
NASA NTRS1974

Gravitational Stokes parameters

The electromagnetic and gravitational Stokes parameters are defined in the general theory of relativity. The general-relativistic equation of radiative transfer for polarized radiation is then derived in terms of the Stokes parameters for both high-frequency electromagnetic and gravitational waves. The concept of Stokes parameters is generalized for the most general class of metric theories of gravity, where six (instead of two) independent states of polarization are present.

Anile, A. M.↗
NASA NTRS1975

Numerical solution of the Navier-Stokes equations for arbitrary two-dimensional multi-element airfoils

Abstracts are presented on a method of numerical solution of the Navier-Stokes equation for the flow about arbitrary airfoils, using a numerically generated curvilinear coordinate system having a coordinate line coincident with the body contour. Results of continuing research are reported and include: application of the Navier-Stokes solution in the vorticity-stream function formulation to a number of single airfoils at Reynolds numbers up to 2000; programming of the Navier-Stokes solution for multiple airfoils in the primitive variable formulation; testing of the potential flow solution of multiple bodies; and development of a generalized coordinate system program.

Thompson, J. F.↗
NASA NTRS1977

Implications of Navier-Stokes turbulence theory for plasma turbulence

The methodology of Navier-Stokes fluid turbulence theory is reviewed, with emphasis placed on the relevance of the Navier-Stokes concepts for understanding plasma turbulence. After a brief consideration of the three-dimensional case, two-dimensional problems are discussed. In addition, MHD turbulence and turbulence in Vlasov plasmas are treated. In particular, the direct interaction approximation developed by Kraichnan (1959) is generalized from Navier-Stokes turbulence theory to produce a computable set of differentio-integral equations for a Vlasov plasma.

Montgomery, D.↗