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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Topology of three-dimensional, variable density flows

This paper is concerned with the interpretation of unsteady, variable-density flow fields. The topology of the flow is determined by finding critical points and identifying the character of local solution trajectories. The time evolution of the flow is studied by following the paths of the critical points in the three-dimensional space of invariants of the local deformations tensor. The methodology can be applied to any smooth vector field and its associated gradient tensor including the vorticity and pressure gradient fields. This approach provides a framework for describing the geometry of complex flow patterns. Concisely summarizing that geometry in the space of invariants of the local gradient tensor may be a useful way of gaining insight into time-dependent processes described by large computational data bases. Applications to the descriptions of a flickering diffusion flame and a compressible wake are discussed.

Cantwell, Brian↗
DOE OSTI2024

A numerical method for simulating variable density flows in membrane desalination systems

Here, we present a novel method for simulating unsteady, variable density, fluid flows in membrane desalination systems. By assuming the density varies only with concentration and temperature, the scheme decouples the solution of the governing equations into two sequential blocks. The first solves the governing equations for the temperature and concentration fields, which are used to compute all thermophysical properties. The second block solves the conservation of mass and momentum equations for the velocity and pressure. We show that this is computationally more efficient than schemes that iterate over the full coupled equations in one block. We verify that the method achieves second-order spatial-temporal accuracy, and we use the method to investigate buoyancy-driven convection in a desalination process called vacuum membrane distillation. Specifically, we show that with gravity properly oriented, variations in temperature and concentration can trigger a double-diffusive instability that enhances mixing and improves water recovery. We also show that the instability can be strengthened by providing external heating.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Modeling of Fluctuating Mass Flux in Variable Density Flows

The approach solves for both Reynolds and Favre averaged quantities and calculates the scalar pdf. Turbulent models used to close the governing equations are formulated to account for complex mixing and variable density effects. In addition, turbulent mass diffusivities are not assumed to be in constant proportion to turbulent momentum diffusivities. The governing equations are solved by a combination of finite-difference technique and Monte-Carlo simulation. Some preliminary results on simple variable density shear flows are presented. The differences between these results and those obtained using conventional models are discussed.

So, R. M. C.↗
NASA NTRS1974

A new formulation of the conservation equations of fluid dynamics

The computation of time-dependent flows has inspired a new, higher-dimensional formulation of the conservation equations of fluid dynamics in which time is treated as a fourth coordinate. The formulation is derived for a constant-density flow, and then extended to a variable-density flow by introducing a fifth, fictitious coordinate. This new coordinate can also act as a source coordinate, so that external source terms can be included. The analysis is carried out for both incompressible, stratified flow, and compressible equilibrium flow. The results are then extended to non-equilibrium and magnetohydrodynamic flows. Several applications of the new formulation to the computation of time-dependent flows are discussed.

Vinokur, M.↗
NASA NTRS1972

Continuous-flow variable-density wind tunnel facilities

Unique features of wind tunnel facilities at Jet Propulsion Laboratory permit variety of conventional and novel tests to be performed at supersonic and hypersonic speeds. Facilities and operations are described.

Herrera, J. G.↗
NASA NTRS1993

A transport equation for the scalar dissipation in reacting flows with variable density: First results

Although the different regimes of premixed combustion are not well defined, most of the recent developments in turbulent combustion modeling are led in the so-called flamelet regime. The goal of these models is to give a realistic expression to the mean reaction rate (w). Several methods can be used to estimate (w). Bray and coworkers (Libby & Bray 1980, Bray 1985, Bray & Libby 1986) express the instantaneous reaction rate by means of a flamelet library and a frequency which describes the local interaction between the laminar flamelets and the turbulent flowfield. In another way, the mean reaction rate can be directly connected to the flame surface density (Sigma). This quantity can be given by the transport equation of the coherent flame model initially proposed by Marble & Broadwell 1977 and developed elsewhere. The mean reaction rate, (w), can also be estimated thanks to the evolution of an arbitrary scalar field G(x, t) = G(sub O) which represents the flame sheet. G(x, t) is obtained from the G-equation proposed by Williams 1985, Kerstein et al. 1988 and Peters 1993. Another possibility proposed in a recent study by Mantel & Borghi 1991, where a transport equation for the mean dissipation rate (epsilon(sub c)) of the progress variable c is used to determine (w). In their model, Mantel & Borghi 1991 considered a medium with constant density and constant diffusivity in the determination of the transport equation for (epsilon(sub c)). A comparison of different flamelet models made by Duclos et al. 1993 shows the realistic behavior of this model even in the case of constant density. Our objective in this present report is to present preliminary results on the study of this equation in the case of variable density and variable diffusivity. Assumptions of constant pressure and a Lewis number equal to unity allow us to significantly simplify the equation. A systematic order of magnitude analysis based on adequate scale relations is performed on each term of the equation. As in the case of constant density and constant diffusivity, the effects of stretching of the scalar field by the turbulent strain field, of local curvature, and of chemical reactions are predominant. In this preliminary work, we suggest closure models for certain terms, which will be validated after comparisons with DNS data.

Mantel, T.↗
NASA NTRS1989

On the modelling of scalar and mass transport in combustor flows

Results are presented of a numerical study of swirling and nonswirling combustor flows with and without density variations. Constant-density arguments are used to justify closure assumptions invoked for the transport equations for turbulent momentum and scalar fluxes, which are written in terms of density-weighted variables. Comparisons are carried out with measurements obtained from three different axisymmetric model combustor experiments covering recirculating flow, swirling flow, and variable-density swirling flow inside the model combustors. Results show that the Reynolds stress/flux models do a credible job of predicting constant-density swirling and nonswirling combustor flows with passive scalar transport. However, their improvements over algebraic stress/flux models are marginal. The extension of the constant-density models to variable-density flow calculations shows that the models are equally valid for such flows.

Nikjooy, M.↗
NASA NTRS1992

A unified approach for numerical simulation of viscous compressible and incompressible flows over adiabatic and isothermal walls

A new formulation (including the choice of variables, their non-dimensionalization, and the form of the artificial viscosity) is proposed for the numerical solution of the full Navier-Stokes equations for compressible and incompressible flows with heat transfer. With the present approach, the same code can be used for constant as well as variable density flows. The changes of the density due to pressure and temperature variations are identified and it is shown that the low Mach number approximation is a special case. At zero Mach number, the density changes due to the temperature variation are accounted for, mainly through a body force term in the momentum equation. It is also shown that the Boussinesq approximation of the buoyancy effects in an incompressible flow is a special case. To demonstrate the new capability, three examples are tested. Flows in driven cavities with adiabatic and isothermal walls are simulated with the same code as well as incompressible and supersonic flows over a wall with and without a groove. Finally, viscous flow simulations of an oblique shock reflection from a flat plate are shown to be in good agreement with the solutions available in literature.

Hafez, M.↗
NASA NTRS1993

A multilevel adaptive projection method for unsteady incompressible flow

There are two main requirements for practical simulation of unsteady flow at high Reynolds number: the algorithm must accurately propagate discontinuous flow fields without excessive artificial viscosity, and it must have some adaptive capability to concentrate computational effort where it is most needed. We satisfy the first of these requirements with a second-order Godunov method similar to those used for high-speed flows with shocks, and the second with a grid-based refinement scheme which avoids some of the drawbacks associated with unstructured meshes. These two features of our algorithm place certain constraints on the projection method used to enforce incompressibility. Velocities are cell-based, leading to a Laplacian stencil for the projection which decouples adjacent grid points. We discuss features of the multigrid and multilevel iteration schemes required for solution of the resulting decoupled problem. Variable-density flows require use of a modified projection operator--we have found a multigrid method for this modified projection that successfully handles density jumps of thousands to one. Numerical results are shown for the 2D adaptive and 3D variable-density algorithms.

Howell, Louis H.↗
NASA NTRS1972

A review of the Grumman orbiter wind tunnel heat transfer tests

Tests were conducted in the NASA Langley continuous flow, variable density and Mach 20 helium tunnels. The orbiter was tested alone and with various side and tandem mounted tanks. Test conditions spanned a Reynolds number range which resulted in both laminar and turbulent flows. Experimental studies also examined the heat transfer problems associated with integration of the auxiliary propulsion system into the orbiter. Tests in the hypersonic shock tunnel investigated heating to cavities and heating from single and multiple hydrogen-oxygen plumes while tests, run as part of the configuration evaluation, examined the heating to wing pods.

Mendelsohn, A. R.↗
NASA NTRSDate not supplied

Twenty-Five Years of Background-Oriented Schlieren: Advances and Novel Applications

Since its introduction in the year 2000, background-oriented schlieren (BOS) has become acornerstone technique for visualizing variable-density flows. In this review, we provide a rigorousexamination of the optical principles underpinning BOS and related refractive-index-basedtechniques, complemented by an appendix linking schlieren imaging to Maxwell’s equations.The core sections delve into the practical aspects of BOS, with detailed discussions on imageprocessing algorithms and critical considerations for experimental setups. We then explorerecent advancements and innovations, including extensions of BOS with tomography, dataassimilation, and event-based imaging. Finally, we present notable applications of BOS inchallenging and unconventional environments, showcasing the method’s versatility and offerinspiration for future research directions.

Background-Oriented Schlieren↗
NASA NTRSDate not supplied

Considerations for High-Speed Background-Oriented Schlieren Visualization Capability for Ground Test Facilities

Since its introduction in the year 2000, background-oriented schlieren (BOS) has become a cornerstone technique for visualizing variable-density flows. In this review, we provide a rigorous examination of the optical principles underpinning BOS and related refractive-index-based techniques, complemented by an appendix linking schlieren imaging to Maxwell’s equations. The core sections delve into the practical aspects of BOS, with detailed discussions on image processing algorithms and critical considerations for experimental setups. We then explore recent advancements and innovations, including extensions of BOS with tomography, data assimilation, and event-based imaging. Finally, we present notable applications of BOS in challenging and unconventional environments, showcasing the method’s versatility and offer inspiration for future research directions.

Brett Bathel↗
NASA NTRS1983

Gas flow through rotameters

Using data available for small rotameters that use spherical floats in gas flow, a linear relationship is derived. It is noted that the relationship provides a good fit for variable volumetric flow, density, and viscosity at constant flow height. With low Reynolds numbers (Re being less than 1), the product of the variable volumetric flow and the viscosity becomes constant; at high Reynolds numbers (Re being greater than 2000), the product of the variable volumetric flow and the square root of the density becomes constant. It is pointed out that the equation given here can be used to obtain an indirect calibration with any gas of known density and viscosity. The constancy of the product of the variable volumetric flow and viscosity at low variable volumetric flows is seen as suggesting the development of simple, inexpensive gas viscometers using rotameter technology.

Levin, H.↗
NASA NTRS1982

Second order closure for variable density free shear layer

A full second order closure turbulence model for the prediction of free shear flows with variable density is developed. The importance of density fluctuations due to inhomogeneities in fluid composition is emphasized. Some simplicity is achieved by using density weighted averaging to account implicitly for density fluctuation effects. Transport equations for various second order correlations - such as Reynolds stress, turbulent mass fluxes or density velocity correlations - are derived, modelled and solved, together with the mean equations for momentum and species conservation. Solutions of these equations are compared with the two different sets of experimental data for low speed free mixing layers (helium into nitrogen and freon 12 into air).

Vandromme, D.↗
NASA NTRS1973

A provisional analysis of two-dimensional turbulent mixing with variable density

A predictive method for the titled flows based on the Prandtl energy method was developed and assessed by comparing predicted results with experimental results. For constant-density flows, both gross properties such as spreading rate and maximum turbulent kinetic energy and detailed properties such as mean shear stress distributions are shown to be well predicted. For variable-density flows, considerable attention is devoted to the inclusion in the analysis of the added effect of pressure fluctuations and of the variation in the several extant empirical parameters on the turbulent kinetic energy. It is found that a variation with Mach number of the characteristic Reynolds number for turbulent transport is needed to account for the observed decrease in spreading rate. The predictions which result from these considerations are compared with the limited experimental data presently available for the two crucial cases: compressible adiabatic mixing and low-speed isothermal mixing of two dissimilar gases.

Libby, P. A.↗
NASA NTRS1990

Numerical investigation of the spreading of self-excited stratified jets

The structure and evolution of self-excited subsonic periodic arrays of jets of constant and variable density are studied using spectral-element direct numerical simulations. The governing equation of motion is presented, and a method based on spectral element discretizations appropriate for simulating arbitrarily complex geometry jets and large density variations for subsonic flows is developed. Variable density fields are found to be more unstable than the corresponding uniform density fields with much higher rms values; as a result, their spreading is also considerably larger. There is a dramatic increase in spreading after a few pairings occur. Findings presented for low and high side-momentum flux reveal a shifting of the origin of instability from the near-field to the far-field, respectively, and suggest possible routes of stabilization.

Batcho, P. F.↗
NASA NTRS1988

Nongradient diffusion in premixed turbulent flames

Recent theoretical and experimental results demonstrating the interaction between force fields and density inhomogeneities as they arise in premixed turbulent flames are discussed. In such flames, the density fluctuates between two levels, the high density in reactants rho sub r and the low density in products rho sub p, with the ratio rho sub r/rho sub p on the order of five to ten in flows of applied interest. The force fields in such flames arise from the mean pressure drop across the flame or from the Reynolds shear stresses in tangential flames with constrained streamlines. The consequence of the interaction is nongradient turbulent transport, countergradient in the direction normal to the flame and nongradient in the tangential direction. The theoretical basis for these results, the presently available experimental support therefore and the implications for other variable density turbulent flows are discussed.

Libby, Paul A.↗