SEARCH · Engineering Papers

Results for “PRANDTL NUMBER”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

All sources NASA NTRS DOE OSTI

NASA NTRS1988

Fingering flow patterns of thermosolutal convection in rectangular enclosures

Convection in rectangular enclosures with combined horizontal temperature and concentration gradients is studied. An electrochemical system is employed to impose the concentration gradients. Due to a large difference between the thermal and solutal diffusion rates the flow possesses double-diffusive characteristics. Very complex fingering flow patterns are observed around the two-phase interfaces. The main objective of the present work is to obtain more information on the flows near the two vertical phase interfaces under various parametric conditions. The fingering flows near the crystal could be one of the most important factors to cause the crystal imperfections. The ranges of the parameters studied are Sc (Schmidt number) = 2200 to 2400, Pr (Prandtl number) = 4.0 to 7.0, Gr sub T (Grashof number) = 2.50 x 10 to the 6th to 5.10 x 10 to the 7th power, Ar (aspect ratio) = 0.61 to 3.0, and N (buoyancy ratio) = 0.05 to 54.8.

Wang, L. W.↗

NASA NTRS1989

Buoyancy effects on the vapor condensation rate on a horizontal liquid surface

The results are presented of a numerical study of the effects of buoyancy on the direct condensation of saturated or nearly saturated vapor on a horizontal liquid surface in a cylindrical tank. The liquid motion beneath the liquid-vapor interface is induced by an axisymmetric laminar jet of subcooled liquid. Analysis and numerical results show that the dominant parameter which determines the influence of buoyancy on the condensation rate is the Richardson number. However, the effect of buoyancy on the condensation rate cannot be quantified in terms of the Richardson number alone. The critical value of the Richardson number below which the condensation rate is not significantly reduced depends on the Reynolds number as well as the Prandtl number.

Hasan, Mohammad M.↗

NASA NTRS1990

Buoyancy effects on the vapor condensation rate on a horizontal liquid surface

Hasan, Mohammad M.↗

NASA NTRS1999

Predicting Buoyant Shear Flows Using Anisotropic Dissipation Rate Models

This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress and Reynolds-heat-flux equations. Several closure models have been investigated-, the emphasis is placed on assessing the effect of modeling the dissipation rate tensor in the Reynolds-stress equation. Three different approaches are considered: one is an isotropic approach while the other two are anisotropic approaches. The isotropic approach is based on Kolmogorov's hypothesis and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for this tensor. In addition, within the former anisotropic approach, two different algebraic representations are examined one is a function of the Reynolds-stress anisotropy tensor, and the other is a function of' the mean velocity gradients. The performance of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows. pure buoyant flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flux in a stratified shear flow can be assessed. At low Ri, the isotropic model performs well in the predictions of stratified shear flows; however, its performance deteriorates as Ri increases. At high Ri, the transport equation model for the dissipation rate tensor gives the best result. Furthermore, the results also lend credence to the algebraic dissipation rate model based on the Reynolds stress anisotropy tensor. Finally, it is found that Pr has an effect on the development of counter-gradient heat flux. The calculations show that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow.

So, R. M. C.↗

DOE OSTI2011

Stochastic flux freezing and magnetic dynamo

Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the ''spontaneous stochasticity'' of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr{sub m}) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr{sub m}=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered.

42 ENGINEERING↗

DOE OSTI2013

Spatio-temporal evolution of the H → L back transition

Since ITER will operate close to threshold and with limited control, the H → L back transition is a topic important for machine operations as well as physics. Using a reduced mesoscale model [Miki et al., Phys. Plasmas 19, 092306 (2012)], we investigate ELM-free H → L back transition dynamics in order to isolate transport physics effects. Model studies indicate that turbulence spreading is the key process which triggers the back transition. The transition involves a feedback loop linking turbulence and profiles. The I-phase appears during the back transition following a slow power ramp down, while fast ramp-downs reveal a single burst of zonal flow during the back transition. The I-phase nucleates at the pedestal shoulder, as this is the site of the residual turbulence in H-mode. Hysteresis in the profile gradient scale length is characterized by the Nusselt number, where Nu=χ{sub i,turb}/χ{sub i,neo}. Relative hysteresis of temperature gradient vs density gradient is sensitive to the pedestal Prandtl number, where Pr{sub ped}=D{sub ped}/χ{sub i,neo}. We expect the H-mode to be somewhat more resilient in density than in temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Diffusive magnetohydrodynamic instabilities beyond the Chandrasekhar theorem

We consider the stability of axially unbounded cylindrical flows that contain a toroidal magnetic background field with the same radial profile as their azimuthal velocity. For ideal fluids, Chandrasekhar had shown the stability of this configuration if the Alfvén velocity of the field equals the velocity of the background flow, i.e., if the magnetic Mach number Mm=1. We demonstrate that magnetized Taylor–Couette flows with such profiles become unstable against non-axisymmetric perturbations if at least one of the diffusivities is finite. We also find that for small magnetic Prandtl numbers Pm the lines of marginal instability scale with the Reynolds number and the Hartmann number. In the limit Pm→0 the lines of marginal instability completely lie below the line for Mm=1 and for Pm→∞ they completely lie above this line. For any finite value of Pm, however, the lines of marginal instability cross the line Mm=1, which separates slow from fast rotation. The minimum values of the field strength and the rotation rate that are needed for the instability (slightly) grow if the rotation law becomes flat. In this case, the electric current of the background field becomes so strong that the current-driven Tayler instability (which also exists without rotation) appears in the bifurcation map at low Hartmann numbers.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Floquet stability analyses of stratified oscillating boundary layers on adiabatic slopes

The presence of a no-slip, impermeable, adiabatic, sloped boundary in an otherwise quiescent, stably stratified, Boussinesq flow generates baroclinic vorticity within a diffusive boundary layer. Such conditions are typical of the oscillating boundary layers on adiabatic abyssal slopes, sloped lake bathymetry and sloped coastal bathymetry in the absence of high-wavenumber internal waves, mean flows, far-field turbulence on larger scales, and resonant tidal–bathymetric interaction. We investigate the linear stability of the oscillating flow within non-dimensional parameter space typical of the $M_2$ tide and hydraulically smooth, middle-latitude abyssal slopes through Floquet linear stability analysis. The flow dynamics depends on three non-dimensional variables: the Reynolds number for Stokes’ second problem, the Prandtl number, and a frequency ratio that accounts for the resonance conditions ($C$, criticality) of the buoyant restoring force and the tidal forcing. The Floquet analysis results suggest that oscillating laminar boundary layers on adiabatic abyssal slopes are increasingly unstable as Reynolds number, criticality parameter and/or spanwise disturbance wavenumber are increased. We also show that the two-dimensional Floquet linear instability necessarily generates three-dimensional baroclinic vorticity, which suggests that the evolution of the gravitational instabilities may be nonlinear as $t→∞$.

42 ENGINEERING↗

DOE OSTI2017

Effects of turbulence, resistivity and boundary conditions on helicoidal flow collimation: Consequences for the Von-Kármán-Sodium dynamo experiment

We present hydrodynamic and magneto-hydrodynamic simulations of a liquid sodium flow using the compressible MHD code PLUTO to investigate the magnetic field regeneration in the Von-Karman-Sodium dynamo experiment. The aim of the study is to analyze influence of the fluid resistivity and turbulence level on the collimation by helicoidal motions of a remnant magnetic field. We use a simplified cartesian geometry to represent the flow dynamics in the vicinity of one cavity of a multi-blades impeller inspired by those used in the Von-Karman-Sodium (VKS) experiment. We perform numerical simulations with kinetic Reynolds numbers up to 1000 for magnetic Prandtl numbers between 30 and 0.1. Our study shows that perfect ferromagnetic walls favour enhanced collimation of flow and magnetic fields even if the turbulence degree of the model increases. More specifically the location of the helicoidal coherent vortex in between the blades changes with the impinging velocity. It becomes closer to the upstream blade and impeller base if the flow incident angle is analogous to the TM73 impeller configuration rotating in the unscooping direction. This result is also obtained at higher kinetic Reynolds numbers when the helicoidal vortex undergoes a precessing motion, leading to a reinforced effect in the vortex evolution and in the magnetic field collimation when using again perfect ferromagnetic boundary conditions. Configurations with different materials used for the impeller blades and impeller base confirm a larger enhancement of the magnetic field when perfect ferromagnetic boundary conditions are used compared with the perfect conductor case, although smaller than with a perfect ferromagnetic impeller, as it was observed in the VKS experiment. We further estimate the efficiency of a hypothetical dynamo loop occurring in the vicinity of the impeller and discuss the relevance of our findings in the context of mean field dynamo theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1975

Modal equations for cellular convection

We expand the fluctuating flow variables of Boussinesq convection in the planform functions of linear theory. Our proposal is to consider a drastic truncation of this expansion as a possible useful approximation scheme for studying cellular convection. With just one term included, we obtain a fairly simple set of equations which reproduces some of the qualitative properties of cellular convection and whose steady-state form has already been derived by Roberts (1966). This set of 'modal equations' is analyzed at slightly supercritical and at very high Rayleigh numbers. In the latter regime the Nusselt number varies with Rayleigh number just as in the mean-field approximation with one horizontal scale when the boundaries are rigid. However, the Nusselt number now depends also on the Prandtl number in a way that seems compatible with experiment. The chief difficulty with the approach is the absence of a deductive scheme for deciding which planforms should be retained in the truncated expansion.

Gough, D. O.↗

NASA NTRS1980

Stellar convection. III - Convection at large Rayleigh numbers

The results of a numerical, three-dimensional study of convection in a self-gravitating sphere of Boussinesq fluid with a Rayleigh number of 10-billion and a Prandtl number of 1 are presented. The velocity and temperature are computed by using spectral methods in the horizontal and finite-differencing in the radial directions. An eddy viscosity and diffusivity are needed to model the subresolution flow. For Rayleigh numbers much less than 10-billion the flows do not have well-defined inertial ranges, and an eddy viscosity and diffusivity cannot be assigned in this self-consistent manner. By computing the energy spectra as well as the detailed energy budgets as a function of wavenumber, it is shown that for Rs = 10-billion there is an inertial range for the modes corresponding to spherical harmonics with l greater than 6.

Marcus, P. S.↗

NASA NTRS1987

Estimation of instantaneous heat transfer coefficients for a direct-injection stratified-charge rotary engine

The main objective of this report was to derive equations to estimate heat transfer coefficients in both the combustion chamber and coolant pasage of a rotary engine. This was accomplished by making detailed temperature and pressure measurements in a direct-injection stratified-charge rotary engine under a range of conditions. For each sppecific measurement point, the local physical properties of the fluids were calculated. Then an empirical correlation of the coefficients was derived by using a multiple regression program. This correlation expresses the Nusselt number as a function of the Prandtl number and Reynolds number.

Lee, C. M.↗

NASA NTRS1988

Regressed relations for forced convection heat transfer in a direct injection stratified charge rotary engine

Currently, the heat transfer equation used in the rotary combustion engine (RCE) simulation model is taken from piston engine studies. These relations have been empirically developed by the experimental input coming from piston engines whose geometry differs considerably from that of the RCE. The objective of this work was to derive equations to estimate heat transfer coefficients in the combustion chamber of an RCE. This was accomplished by making detailed temperature and pressure measurements in a direct injection stratified charge (DISC) RCE under a range of conditions. For each specific measurement point, the local gas velocity was assumed equal to the local rotor tip speed. Local physical properties of the fluids were then calculated. Two types of correlation equations were derived and are described in this paper. The first correlation expresses the Nusselt number as a function of the Prandtl number, Reynolds number, and characteristic temperature ratio; the second correlation expresses the forced convection heat transfer coefficient as a function of fluid temperature, pressure and velocity.

Lee, Chi M.↗

NASA NTRS1988

Regressed relations for forced convection heat transfer in a direct injection stratified charge rotary engine

Lee, Chi M.↗

DOE OSTI2011

Turbulent Transport in Tokamak Plasmas with Rotational Shear

Nonlinear gyrokinetic simulations are conducted to investigate turbulent transport in tokamak plasmas with rotational shear. At sufficiently large flow shears, linear instabilities are suppressed, but transiently growing modes drive subcritical turbulence whose amplitude increases with flow shear. This leads to a local minimum in the heat flux, indicating an optimal ExB shear value for plasma confinement. Local maxima in the momentum fluxes are observed, implying the possibility of bifurcations in the ExB shear. The critical temperature gradient for the onset of turbulence increases with flow shear at low flow shears; at higher flow shears, the dependence of heat flux on temperature gradient becomes less stiff. The turbulent Prandtl number is found to be largely independent of temperature and flow gradients, with a value close to unity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2012

A UNIFYING PICTURE OF HELICAL AND AZIMUTHAL MAGNETOROTATIONAL INSTABILITY, AND THE UNIVERSAL SIGNIFICANCE OF THE LIU LIMIT

The magnetorotational instability (MRI) plays a key role for cosmic structure formation by triggering turbulence in the rotating flows of accretion disks that would be otherwise hydrodynamically stable. In the limit of small magnetic Prandtl number, the helical and the azimuthal versions of MRI are known to be governed by a quite different scaling behavior than the standard MRI with a vertical applied magnetic field. Using the short-wavelength approximation for an incompressible, resistive, and viscous rotating fluid, we present a unified description of helical and azimuthal MRI, and we identify the universal character of the Liu limit 2(1-{radical}2){approx}-0.8284 for the critical Rossby number. From this universal behavior we are also led to the prediction that the instability will be governed by a mode with an azimuthal wavenumber that is proportional to the ratio of axial to azimuthal applied magnetic field, when this ratio becomes large and the Rossby number is close to the Liu limit.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

Transport Properties of Electronically Excited N{sub 2}/N and O{sub 2}/O Mixtures

Chemically non-equilibrium neutral gas mixture flows of N{sub 2}/N and O{sub 2}/O with electronic excitation are studied. The one-temperature model of transport properties taking into account electronic states of both molecules and atoms is developed. The generalized Chapman-Enskog method is applied to derive the closed set of governing equations and to evaluate the transport terms. The transport coefficients of thermal conductivity, diffusion and thermal diffusion, shear and bulk viscosity, as well as the Prandtl number are calculated in the temperature range 500-50000 K for various mixture compositions. Contribution of the electronic degrees of freedom to the transport properties is found to be important, especially for atomic species.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2014

On the abrupt growth dynamics of nonlinear resistive tearing mode and the viscosity effects

The nonlinear evolution of the resistive tearing mode exhibits an abrupt growth after an X-point collapse once the magnetic island exceeds a certain critical width Δ′w{sub c} for large instability parameter Δ′, leading to a current sheet formation [N. F. Loureiro et al., Phys. Rev. Lett. 95, 235003 (2005)]. In this work, we investigate the underlying mechanism of the X-point collapse as well as the current sheet formation including the viscosity effects, based on a secondary instability analysis. The secondary instability is excited due to the quasilinear current modification by the zonal current. In particular, it is identified that the current peaking effect is plausibly responsible for the onset of the X-point collapse and the current sheet formation, leading to the explosive growth of reconnected flux. In the presence of finite viscosity, the Δ′w{sub c} scaling with the resistivity gets modified. A transition behavior is revealed at P{sub r}≈1 for the viscosity dependence of Δ′w{sub c} and the linear tearing instability. However, the explosive growth seems to be independent of the viscosity in the magnetic Prandtl number P{sub r}<1 regime, while large viscosity plays a strong dissipation role.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗