Radial static pressure distributions in confined compressible vortex flow fields
Effects of fluid mass flow rate and exit orifice diameter on radial static pressure distribution in compressible vortex flow field
VORTEX FLOW↗
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Magentically actuated compressor
A vibration free fluid compressor particularly adapted for Stirling cycle cryogenic refrigeration apparatus comprises a pair of identical opposing ferromagnetic pistons located in a housing and between a gas spring including a sealed volume of a working fluid such as gas under pressure. The gas compresses and expands in accordance with movement of the pistons to generate a compression wave which can be vented to other apparatus, for example, a displacer unit in a Stirling cycle engine. The pistons are urged outwardly due to the pressure of the gas; however, a fixed electromagnetic coil assembly located in the housing adjacent the pistons, is periodically energized to produce a magnetic field which interlinks the pistons in such a fashion that the pistons are mutually attracted to one another. The mass of the pistons, in conjunction with the compressed gas between them, form a naturally resonant system which, when the pistons are electromagnetically energized, produces an oscillating compression wave in the entrapped fluid medium.
Evans, J.↗
Wrinkling phenomenon in structures. II - Wrinkling criteria
The wrinkling phenomenon in elasticity is mathematically defined and described as a special type of instability associated with the loss of hyperbolicity of the governing equations when some of the characteristic speeds of elastic wave propagation become imaginary. The developed criteria of wrinkling are applied to such structural elements as membranes, strings, soft shells, soft rods, and laminated material. The cause of wrinkling in these elements is due to compression in longitudinal directions that exceeds the through-the-thickness shear modulus. For elements with internal fluid flow the critical compression is reduced due to the destabilizing effect of the flow. The most effective mathematical analysis technique is a combination of tensor analysis and index notations.
Zak, M.↗
Compressibility effects in turbulence modeling
Numerical turbulence modeling is discussed with attention given to fluid property variations caused by compressibility in an adiabatic flow. The models are considered in terms of integral quantities expressed by ordinary differential equations and by those formulated as partial differential equations. Compressibility corrections for both integral and partial differential methods are reviewed. Eddy-viscosity models are explored for their capability to characterize the mass-weighted Reynolds stress, which can be accounted for with primitive and/or mass-weighted variables. Compressible flow simulations are currently constrained to low Re and zero mean dilation. The effects of compressibility are defined in wave number space by resolving the Fourier transforms of the velocity vectors into components which are perpendicular and parallel to the wave number vector. Statistical correlations then permit obtaining a value for each contribution.
Rubesin, M. W.↗
Fluid-Thermal-Structural Interactions Induced by an Asymmetric Shock-Wave/Boundary-Layer Interaction in a Mach-6 Compression Corner
An experimental study is conducted of the fluid-thermal-structural interaction of a clamped compliant panel exposed to a three dimensional shock-wave/boundary-layer interaction (SWBLI) induced by a Mach-6 compression ramp with a spanwise nonuniform incoming boundary layer. The nonuniform boundary layer was produced by placing trips on one side of the upstream flat plate, resulting in largely turbulent flow on the tripped side and transitional flow on the untripped side. Measurements of the flowfield confirmed that the tripped boundary layer contained elevated levels of unsteadiness, and the SWBLI was observed to vary from attached to fully separated as the ramp angle was increased from 10◦ to 38◦; the separation region on the tripped side of the panel was noticeably smaller, showing the elevated turbulence levels of the tripped-side flow to remain relatively localized rather than diffusing across the whole model. Full-field, time-resolved panel deformations were measured using high-speed photogrammetry and the vibrational response at each compression angle was characterized. Although the measured modes conformed largely to those from classical clamped-plate theory, some skewing of the mode shapes was observed. IR thermography highlighted regions of the compliant region where elevated temperatures were likely to promote thermal softening effects to the transient panel response. The quasi-static deformation and stress field was used to characterize the internal stress factor of each mode and showed a meaningful relationship between transient panel response and stress contained within each mode: modes with antinodes lying in high-stress areas of the plate tended to exhibit increases in vibrational frequency and decreases in vibrational power, whereas the opposite was true for modes with antinodes in low-stress areas.
Spectral Proper Orthogonal Decomposition↗
Two fluid model for thermal stratification in the Apollo cryogenic oxygen tanks
It is observed on Apollo flights that for oxygen densities greater than 42 lb/cu ft the heater operation time to achieve a desired pressure rise is half that which would be required if the energy were uniformly dispersed. A two fluid model was developed to describe this effect of stratification on the tank's pressurization behavior. The increase in pressure rise rate is attributed to compression of the bulk fluid in response to expansion of the heated fluid adjacent to the heater. It is assumed that during the heating operation the adjacent fluid retains nearly all the heater energy and has no mass interaction with the bulk fluid. The hot fluid temperatures predicted by the model are in reasonable correspondence with the observed heater temperatures. The model indicates that the fraction of the fluid interacting with the heater increases with decreasing density, from less than 0.1% at full tank to roughly 1% at 50% quantity, the lowest quantity at which stratification effects on pressure are observed.
Saxton, J. A.↗
Effects of Gravity on Supercritical Water Oxidation (SCWO) Processes
The effects of gravity on the fluid mechanics of supercritical water jets are being studied at NASA to develop a better understanding of flow behaviors for purposes of advancing supercritical water oxidation (SCWO) technologies for applications in reduced gravity environments. These studies provide guidance for the development of future SCWO experiments in new experimental platforms that will extend the current operational range of the DECLIC (Device for the Study of Critical Liquids and Crystallization) Facility on board the International Space Station (ISS). The hydrodynamics of supercritical fluid jets is one of the basic unit processes of a SCWO reactor. These hydrodynamics are often complicated by significant changes in the thermo-physical properties that govern flow behavior (e.g., viscosity, thermal conductivity, specific heat, compressibility, etc), particularly when fluids transition from sub-critical to supercritical conditions. Experiments were conducted in a 150 ml reactor cell under constant pressure with water injections at various flow rates. Flow configurations included supercritical jets injected into either sub-critical or supercritical water. Profound gravitational influences were observed, particularly in the transition to turbulence, for the flow conditions under study. These results will be presented and the parameters of the flow that control jet behavior will be examined and discussed.
aqueous solutions↗
Mixing and non-equilibrium chemical reaction in a compressible mixing layer
The effects of compressibility, chemical reaction exothermicity, and non-equilibrium chemical modeling in a reacting plane mixing layer were investigated by means of two dimensional direct numerical simulations. The chemical reaction was irreversible and second order of the type A + B yields Products + Heat. The general governing fluid equations of a compressible reacting flow field were solved by means of high order finite difference methods. Physical effects were then determined by examining the response of the mixing layer to variation of the relevant non-dimensionalized parameters. The simulations show that increased compressibility generally results in a suppressed mixing, and consequently a reduced chemical reaction conversion rate. Reaction heat release was found to enhance mixing at the initial stages of the layer growth, but had a stabilizing effect at later times. The increased stability manifested itself in the suppression or delay of the formation of large coherent structures within the flow. Calculations were performed for a constant rate chemical kinetics model and an Arrhenius type kinetic prototype. The choice of the model was shown to have an effect on the development of the flow. The Arrhenius model caused a greater temperature increase due to reaction than the constant kinetic model. This had the same effect as increasing the exothermicity of the reaction. Localized flame quenching was also observed when the Zeldovich number was relatively large.
Steinberger, Craig J.↗
Analytic Modeling of the Hydrodynamic, Thermal, and Structural Behavior of Foil Thrust Bearings
A simulation and modeling effort is conducted on gas foil thrust bearings. A foil bearing is a self acting hydrodynamic device capable of separating stationary and rotating components of rotating machinery by a film of air or other gaseous lubricant. Although simple in appearance these bearings have proven to be complicated devices in analysis. They are sensitive to fluid structure interaction, use a compressible gas as a lubricant, may not be in the fully continuum range of fluid mechanics, and operate in the range where viscous heat generation is significant. These factors provide a challenge to the simulation and modeling task. The Reynolds equation with the addition of Knudsen number effects due to thin film thicknesses is used to simulate the hydrodynamics. The energy equation is manipulated to simulate the temperature field of the lubricant film and combined with the ideal gas relationship, provides density field input to the Reynolds equation. Heat transfer between the lubricant and the surroundings is also modeled. The structural deformations of the bearing are modeled with a single partial differential equation. The equation models the top foil as a thin, bending dominated membrane whose deflections are governed by the biharmonic equation. A linear superposition of hydrodynamic load and compliant foundation reaction is included. The stiffness of the compliant foundation is modeled as a distributed stiffness that supports the top foil. The system of governing equations is solved numerically by a computer program written in the Mathematica computing environment. Representative calculations and comparisons with experimental results are included for a generation I gas foil thrust bearing.
Bruckner, Robert J.↗
A note on compressibility and energy cascade in turbulent molecular clouds
Observed velocity-size correlations are reexamined in the light of an improved theory of turbulent energy cascade that is developed. It is shown that observed velocity-size correlations cannot be compared with the Kolmogorov law, which is based on incompressible turbulent flow. The fact that the log v-log(l/rho) scaling law (v the turbulent velocity, l the associated region size, and rho the fluid density) predicted for compressible energy cascade is always steeper than that observed in molecular clouds indicates the injection rather than the dissipation of mechanical energy at smaller scales of motion. It is also shown that the concept of strict energy cascade may not be generally applicable in the interstellar medium. The agreement between theory and observation turns out to be best for small cool clouds and cloud cores, suggesting that, for these regions at least, the dominant process in establishing the observed v-l-rho correlation is a turbulent energy cascade.
Fleck, R. C., Jr.↗
Investigation of two and three parameter equations of state for cryogenic fluids
Two-phase flows are a common occurrence in cryogenic engines and an accurate evaluation of the heat-transfer coefficient in two-phase flow is of significant importance in their analysis and design. The thermodynamic equation of state plays a key role in calculating the heat transfer coefficient which is a function of thermodynamic and thermophysical properties. An investigation has been performed to study the performance of two- and three-parameter equations of state to calculate the compressibility factor of cryogenic fluids along the saturation loci. The two-parameter equations considered here are van der Waals and Redlich-Kwong equations of state. The three-parameter equation represented here is the generalized Benedict-Webb-Rubin (BWR) equation of Lee and Kesler. Results have been compared with the modified BWR equation of Bender and the extended BWR equations of Stewart. Seven cryogenic fluids have been tested; oxygen, hydrogen, helium, nitrogen, argon, neon, and air. The performance of the generalized BWR equation is poor for hydrogen and helium. The van der Waals equation is found to be inaccurate for air near the critical point. For helium, all three equations of state become inaccurate near the critical point.
Jenkins, Susan L.↗
On the dynamical buoyancy of vortices
In this paper we consider the effect of dynamical buoyancy (Parker) on the motion of stratified fluid vortex tubes. We find that the dynamical buoyancy force does not necessarily lead to a buoyant rise if there exists a flow field external to a tube. In particular, the vortex tubes presented in our previous work are shown to have a pressure force exactly canceling the buoyancy force so that they do not move vertically (i.e., parallel to gravity) at all. Moreover, we construct a more general class of vortex tubes and find that their vertical motion can be either up or down, depending on the detailed vorticity distribution, regardless of the fact that they are all dynamically buoyant. We find that the vertical motion is intimately related to the horizontal self-motion of stratified fluid vortex tubes. Finally, we note that the presence of dynamical buoyancy implies that steady state compressible flow solutions for isolated fluid regions in a gravitational field do not exist. These results may have relevance to astrophysical convection.
Arendt, Steve↗
Development of High Speed Imaging and Analysis Techniques Compressible Dynamics Stall
Dynamic stall has limited the flight envelope of helicopters for many years. The problem has been studied in the laboratory as well as in flight, but most research, even in the laboratory, has been restricted to surface measurement techniques such as pressure transducers or skin friction gauges, except at low speed. From this research, it became apparent that flow visualization tests performed at Mach numbers representing actual flight conditions were needed if the complex physics associated with dynamic stall was to be properly understood. However, visualization of the flow field during compressible conditions required carefully aligned and meticulously reconstructed holographic interferometry. As part of a long-range effort focused on exposing of the physics of compressible dynamic stall, a research wind tunnel was developed at NASA Ames Research Center which permits visual access to the full flow field surrounding an oscillating airfoil during compressible dynamic stall. Initially, a stroboscopic schlieren technique was used for visualization of the stall process, but the primary research tool has been point diffraction interferometry(PDI), a technique carefully optimized for use in th is project. A review of the process of development of PDI will be presented in the full paper. One of the most valuable aspects of PDI is the fact that interferograms are produced in real time on a continuous basis. The use of a rapidly-pulsed laser makes this practical; a discussion of this approach will be presented in the full paper. This rapid pulsing(up to 40,000 pulses/sec) produces interferograms of the rapidly developing dynamic stall field in sufficient resolution(both in space and time) that the fluid physics of the compressible dynamic stall flowfield can be quantitatively determined, including the gradients of pressure in space and time. This permits analysis of the influence of the effect of pitch rate, Mach number, Reynolds number, amplitude of oscillation, and other parameters on the dynamic stall process. When interferograms can be captured in real time, the potential for real-time mapping of a developing unsteady flow such as dynamic stall becomes a possibility. This has been achieved in the present case through the use of a high-speed drum camera combined with electronic circuitry which has resulted in a series of interferograms obtained during a single cycle of dynamic stall; images obtained at the rate of 20 KHz will be presented as a part of the formal presentation. Interferometry has been available for a long time; however, most of its use has been limited to visualization. The present research has focused on use of interferograms for quantitative mapping of the flow over oscillating airfoils. Instantaneous pressure distributions can now be obtained semi-automatically, making practical the analysis of the thousands of interferograms that are produced in this research. A review of the techniques that have been developed as part of this research effort will be presented in the final paper.
Chandrasekhara, M. S.↗
Transient heating in the upper atmosphere
The time-dependent response of the upper atmosphere to transient heat sources is considered. The basic problem is that of heating a compressible, heat-conducting fluid, which is described in the one-dimensional case by an analytic solution. Comparisons with satellite drag data of such first-order solutions are shown to be useful in determining energy requirements and in determining some constraints on the spatial distribution of the heating. Recent OGO-6 mass spectrometer and interferometric temperature measurements show that atmospheric disturbances during geomagnetic storms are much more prominent in the auroral zones. These results suggest that joule dissipation of auroral currents are important contributors to orbital perturbations of satellites.
Thomas, G. E.↗
A finite element solution algorithm for the Navier-Stokes equations
A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame.
Baker, A. J.↗
COMOC: a finite-element algorithm for the Navier-Stokes equations
Finite-element algorithm devised to facilitate solution of two-dimensional Navier-Stokes equations governing kinematics and thermodynamics of variable-viscosity, compressible, multiple-species fluid. Algorithm has been implemented into existing computer program system.
Baker, A. J.↗
FORTRAN program for calculating coolant flow and metal temperatures of a full-coverage-film-cooled vane or blade
A computer program that calculates the coolant flow and the metal temperatures of a full-coverage-film-cooled vane or blade was developed. The analysis was based on compressible, one-dimensional fluid flow and on one-dimensional heat transfer and treats the vane or blade shell as a porous wall. The calculated temperatures are average values for the shell outer-surface area associated with each film-cooling hole row. A thermal-barrier coating may be specified on the shell outer surface, and centrifugal effects can be included for blade calculations. The program is written in FORTRAN 4 and is operational on a UNIVAC 1100/42 computer. The method of analysis, the program input, the program output, and two sample problems are provided.
Meitner, P. L.↗
Energetic particle transport in relativistic flows
A discussion is given of pitch angle dependent and diffusive transport equations for cosmic rays applicable for both special relativistic and general relativistic flows, derived from the relativistic Boltzmann equation. As an example of particle transport in a curved spacetime we give a pitch angle dependent transport equation appropriate for radial accretion onto a Schwarzschild black hole. The roles of fluid shear, acceleration and compression on the energy changes of particles in the diffusive transport equations are emphasized. Also discussed are special flows (e.g. rigidly rotating flows) associated with a Killing vector for which a constant of the motion of the particles can be identified, and for which simplified transport equations can be constructed.
Webb, G. M.↗