Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Dimensionless Numbers”

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.

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

At least 109 records · Page 6

A parametric heat transfer study for cryogenic ball bearings in SSME HPOTP

A numerical modeling is to examine the effects of coolant convective heat transfer coefficient and frictional heating on the local temperature characteristics of a ball element in Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump (HPOTP) bearing. The present modeling uses a control-volume based, finite-difference method to solve the non-dimensionalized heat conduction equation in spherical coordinate system. The dimensionless temperature is found as a function of Biot number, heat flux ratio between the two race contacts, and location in the ball. The current results show that, for a given cooling capability, the ball temperature generally increases almost linearly with the heat input from the race-contacts. This increase is always very high at one of the two contacts. An increase in heat transfer coefficient generally reduces the ball temperature and alleviates the temperature gradient, except for the regions very close to the race contacts. For a 10-fold increase of heat transfer coefficient, temperature decrease is 35 percent for the average over entire ball, and 10 percent at the inner-race contact. The corresponding change of temperature gradient displays opposing trends between the regions immediately adjacent to the contacts and the remaining portion of the ball. The average temperature gradient in the vicinity of both contacts increases approximately 70 to 100 percent. A higher temperature gradient produces excessive thermal stress locally which may be detrimental to the material integrity. This, however, is the only unfavorable issue for an increase of heat transfer coefficient.

Chyu, Mingking K.↗

Thermal Edge-Effects Model for Automated Tape Placement of Thermoplastic Composites

Two-dimensional thermal models for automated tape placement (ATP) of thermoplastic composites neglect the diffusive heat transport that occurs between the newly placed tape and the cool substrate beside it. Such lateral transport can cool the tape edges prematurely and weaken the bond. The three-dimensional, steady state, thermal transport equation is solved by the Green's function method for a tape of finite width being placed on an infinitely wide substrate. The isotherm for the glass transition temperature on the weld interface is used to determine the distance inward from the tape edge that is prematurely cooled, called the cooling incursion Delta a. For the Langley ATP robot, Delta a = 0.4 mm for a unidirectional lay-up of PEEK/carbon fiber composite, and Delta a = 1.2 mm for an isotropic lay-up. A formula for Delta a is developed and applied to a wide range of operating conditions. A surprise finding is that Delta a need not decrease as the Peclet number Pe becomes very large, where Pe is the dimensionless ratio of inertial to diffusive heat transport. Conformable rollers that increase the consolidation length would also increase Delta a, unless other changes are made, such as proportionally increasing the material speed. To compensate for premature edge cooling, the thermal input could be extended past the tape edges by the amount Delta a. This method should help achieve uniform weld strength and crystallinity across the width of the tape.

Costen, Robert C.↗

Non-linear effects on sound propagation in a variable area duct carrying high subsonic Mach number flows

The general one-dimensional non-linear equation for the acoustic velocity potential in a variable area duct carrying high subsonic Mach number flows is presented and solved numerically using an implicit finite difference scheme. For the linearized equation with no flow, the present scheme is compared with the exact solution and the fourth-order Runge-Kutta method with excellent agreement for dimensionless time periods. Non-linear solutions are more sensitive to Mach numbers and exciting amplitudes and less sensitive to exciting frequencies. In general, non-linear effects can be safely neglected for low Mach number flows but must be accounted for when high Mach number flows are encountered.

Lumsdaine, E.↗

Random scattering approach to gravitational microlensing

Small random deflections of a narrow beam of radiation due to gravitational scattering by stars randomly distributed within the deflector plane are considered. Using a Fouriere transform method, the probability of scattering is obtained as a function of scattering angle for an arbitrary number of stars with an arbitrary distribution of masses. The probability density, expressed in proper units, depends on one parameter only: the effective number of stars. At small scattering angles the density is a Gaussian, and at large angles it falls off as the scattering angle to the minus fourth power. The probability distribution for scatterings is simply related to the angular distribution of the surface brightness of a macroimage, averaged over many microimages. The isophotes are ellipses, with the ratio of the major axis to the minor axis, determined by the dimensionless surface mass density and the shear of the lensing system. The number of stars that has to be included in the modeling of microlensing is proportional to the amplification due to the macrolens, and to the square of the dimensionless surface mass density.

Katz, N.↗

Development of thermal stratification and destratification scaling concepts. Volume 2: Stratification

Temperature and pressure data obtained from the saturated Freon 113 PCA closed-tank stratification tests are presented. The data presented in tabular form are the test conditions, sensible heat values, and Freon 113 PCA liquid and ullage (vapor) properties. Also included, are graphical representations of the liquid bulk temperature and pressure histories, and dimensionless liquid-ullage delta-temperature profiles. Modified Grashof numbers and Fourier number-history data are also presented graphically.

Lovrich, T. N.↗

A compact presentation of DSN array telemetry performance

The telemetry performance of an arrayed receiver system, including radio losses, is often given by a family of curves giving bit error rate vs bit SNR, with tracking loop SNR at one receiver held constant along each curve. This study shows how to process this information into a more compact, useful format in which the minimal total signal power and optimal carrier suppression, for a given fixed bit error rate, are plotted vs data rate. Examples for baseband-only combining are given. When appropriate dimensionless variables are used for plotting, receiver arrays with different numbers of antennas and different threshold tracking loop bandwidths look much alike, and a universal curve for optimal carrier suppression emerges.

Greenhall, C. A.↗

Scaling laws for homogeneous turbulent shear flows in a rotating frame

The scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier-Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E star (k star, 0), initial dimensionless shear rate SK sub 0/epsilon sub 0, initial Reynolds number K squared sub 0/nu epsilon sub 0, and the ration of the rotation rate to the shear rate omega/S are identical. Consequently, if universal equilibrium states exist, at high Reynolds numbers, they will only depend on the single parameter omega/S. The commonly assumed dependence of such equilibrium states on omega/S through the Richardson number Ri=-2(omega/S)(1-2 omega/S) is proven to be inconsistent with the full Navier-Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier-Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on omega/S is discussed in detail along with the implications for turbulence modeling.

Speziale, Charles G.↗

Scaling laws for homogeneous turbulent shear flows in a rotating frame

The scaling properties of plane homogeneous turbulent shear flows in a rotating frame are examined mathematically by a direct analysis of the Navier-Stokes equations. It is proved that two such shear flows are dynamically similar if and only if their initial dimensionless energy spectrum E star (k star, 0), initial dimensionless shear rate SK sub 0/epsilon sub 0, initial Reynolds number K squared sub 0/nu epsilon sub 0, and the ration of the rotation rate to the shear rate omega/S are identical. Consequently, if universal equilibrium states exist, at high Reynolds numbers, they will only depend on the single parameter omega/S. The commonly assumed dependence of such equilibrium states on omega/S through the Richardson number Ri = -2(omega/S)(1-2 omega/S) is proven to be inconsistent with the full Navier-Stokes equations and to constitute no more than a weak approximation. To be more specific, Richardson number similarity is shown to only rigorously apply to certain low-order truncations of the Navier-Stokes equations (i.e., to certain second-order closure models) wherein closure is achieved at the second-moment level by assuming that the higher-order moments are a small perturbation of their isotropic states. The physical dependence of rotating turbulent shear flows on omega/S is discussed in detail along with the implications for turbulence modeling.

Speziale, Charles G.↗

Stagnation Region Heat Transfer: The Influence of Turbulence Parameters, Reynolds Number and Body Shape

The effect of velocity gradient on stagnation region heat transfer augmentation by free stream turbulence was investigated. Heat transfer was measured in the stagnation region of four models with elliptical leading edges with ratios of major to minor axes of 1:1, 1.5:1, 2.25:1, and 3:1. Four geometrically similar, square bar, square mesh, biplane grids were used to generate free stream turbulence with different intensities and length. Heat transfer measurements were made for the following ranges of parameters: Reynolds number, based on leading edge diameter, 37,000 to 228,000; dimensionless leading edge velocity gradient, 1.20 to 1.80; turbulence intensity, 1.1 to 15.9%; and length scale to leading edge diameter ratio, 0.05 to 0.30. Stagnation point heat transfer augmentation by free stream turbulence can be predicted using a modified version of a previously developed correlation for a circular leading edge. Heat transfer augmentation was independent of body shape at the stagnation point. The heat transfer distribution down-stream from the stagnation point can be predicted using the normalized laminar heat transfer distribution.

Vanfossen, G. James↗

Two Phase Flow Mapping and Transition Under Microgravity Conditions

In this paper, recent microgravity two-phase flow data for air-water, air-water-glycerin, and air- water-Zonyl FSP mixtures are analyzed for transition from bubbly to slug and from slug to annular flow. It is found that Weber number-based maps are inadequate to predict flow-pattern transition, especially over a wide range of liquid flow rates. It is further shown that slug to annular flow transition is dependent on liquid phase Reynolds number at high liquid flow rate. This effect may be attributed to growing importance of liquid phase inertia in the dynamics of the phase flow and distribution. As a result a new form of scaling is introduced to present data using liquid Weber number based on vapor and liquid superficial velocities and Reynolds number based on liquid superficial velocity. This new combination of the dimensionless parameters seem to be more appropriate for the presentation of the microgravity data and provides a better flow pattern prediction and should be considered for evaluation with data obtained in the future. Similarly, the analysis of bubble to slug flow transition indicates a strong dependence on both liquid inertia and turbulence fluctuations which seem to play a significant role on this transition at high values of liquid velocity. A revised mapping of data using a new group of dimensionless parameters show a better and more consistent description of flow transition over a wide range of liquid flow rates. Further evaluation of the proposed flow transition mapping will have to be made after a wider range of microgravity data become available.

Parang, Masood↗

Bubble Formation on a Wall in Cross-Flowing Liquid and Surrounding Fluid Motion,With and Without Heating

Application of gas-liquid two-phase flow systems for space-based thermal management and for the HEDS program demands a precise control of bubble size distribution in liquid. The necessity of bulk liquid motion for controlling bubble size and frequency in the space environment has been suggested by recent studies on pool, forced convection boiling and bubble formation in flowing liquid. The present work, consisting of two parts, explores bubble generation at wall in a cross-flowing liquid, i.e., in a forced convection boiling configuration. A schematic is shown. The first part looks into the bubble formation process under isothermal conditions in a reduced gravity environment, by injecting gas through a hole in the wall of a flowing liquid channel. In the latter part with channel wall heating, flow and temperature fields near a single bubble are studied under normal (1-g) and micro-gravity (mu-g) conditions. The objective of the isothermal experiments is to experimentally investigate the effects of liquid cross-flow velocity, gas flow rate, and orifice diameter on bubble formation. Data were taken mainly under reduced gravity conditions but some data were taken in normal gravity for comparison. The reduced gravity experiment was conducted aboard the NASA DC-9 Reduced Gravity Aircraft. The results show that the process of bubble formation and detachment depends on gravity, the orifice diameter (D(sub N)), the gas flow rate (Q(sub g)), and the liquid cross-flow velocity (U(sub L)). The reduced gravity data are shown. The data are analyzed based on a force balance, and two different detachment mechanisms are identified. When the gas momentum is large, the bubble detaches from the injection orifice as the gas momentum overcomes the attaching effects of liquid drag and inertia. The surface tension force is much reduced because a large part of the bubble pinning edge at the orifice is lost as the bubble axis is tilted by the liquid flow. When the gas momentum is small, the force balance in the liquid flow direction is important, and the bubble detaches when the bubble axis inclination exceeds a certain angle. With wall heating, liquid motion around an air bubble in cross-flowing 2cs silicone oil is experimentally investigated in 1-g. A spectral element based steady 2D numerical model is also developed. The traces of particles from experimental flow visualization and the corresponding computed streamlines are shown. At the upstream side of the bubble facing the cross-flow, thermocapillary and forced convection create liquid motion away from the wall, up along the surface. At the downstream side, a competing interaction between the two creates a recirculation cell, causing the bulk liquid to stagnate on the surface and separate thereafter. The important dimensionless parameters are - Surface tension and local cross-flow Reynolds numbers R(sub sigma)(U(sub ref)a/v) and Re(sub loc)(U(sub L)a/v), respectively based on reference thermocapillary U(sub ref)(sigma(sub T)Delta.T/mu, Delta T=T(sub wall)-T(sub liquid)) and local cross-flow velocity U(sub L), Prandtl number P(sub r) and Grashoff number Gr(rho.g.beta.DeltaTa(sup 3)/mu.v). Variation of the stagnation point with R(sub sigma) and Re(sub loc) is shown. Also shown are good agreement between experimental and numerical results in 1-g. The computational model is extended to mu-g condition to investigate temperature and velocity on the bubble surface, stagnation and reattachment points of the recirculation cell and wall heat transfer. It is observed that wall heating significantly alters the flow field around the bubble and thus the forces acting on the bubble, which control its detachment. Thus a combination of heating and liquid cross-flow can be utilized to precisely control bubble formation in a mu-g environment.

Bhunia, Avijit↗

Prediction of Turbulent Jet Mixing Noise Reduction by Water Injection

A one-dimensional control volume formulation is developed for the determination of jet mixing noise reduction due to water injection. The analysis starts from the conservation of mass, momentum and energy for the confrol volume, and introduces the concept of effective jet parameters (jet temperature, jet velocity and jet Mach number). It is shown that the water to jet mass flow rate ratio is an important parameter characterizing the jet noise reduction on account of gas-to-droplet momentum and heat transfer. Two independent dimensionless invariant groups are postulated, and provide the necessary relations for the droplet size and droplet Reynolds number. Results are presented illustrating the effect of mass flow rate ratio on the jet mixing noise reduction for a range of jet Mach number and jet Reynolds number. Predictions from the model show satisfactory comparison with available test data on perfectly expanded hot supersonic jets. The results suggest that significant noise reductions can be achieved at increased flow rate ratios.

Kandula, Max↗

Effective Jet Properties for the Prediction of Turbulent Mixing Noise Reduction by Water Injection

A one-dimensional control volume formulation is developed for the determination of jet mixing noise reduction due to water injection. The analysis starts from the conservation of mass, momentum and energy for the control volume, and introduces the concept of effective jet parameters (jet temperature, jet velocity and jet Mach number). It is shown that the water to jet mass flow rate ratio is an important parameter characterizing the jet noise reduction on account of gas-to-droplet momentum and heat transfer. Two independent dimensionless invariant groups are postulated, and provide the necessary relations for the droplet size and droplet Reynolds number. Results are presented illustrating the effect of mass flow rate ratio on the jet mixing noise reduction for a range of jet Mach number and jet Reynolds number. Predictions from the model show satisfactory comparison with available test data on supersonic jets. The results suggest that significant noise reductions can be achieved at increased flow rate ratios.

Kandula, Max↗

Effects of a temperature-dependent rheology on large scale continental extension

The effects of a temperature-dependent rheology on large-scale continental extension are investigated using a thin viscous sheet model. A vertically-averaged rheology is used that is consistent with laboratory experiments on power-law creep of olivine and that depends exponentially on temperature. Results of the calculations depend principally on two parameters: the Peclet number, which describes the relative rates of advection and diffusion of heat, and a dimensionless activation energy, which controls the temperature dependence of the rheology. At short times following the beginning of extension, deformation occurs with negligible change in temperature, so that only small changes in lithospheric strength occur due to attenuation of the lithosphere. However, after a certain critical time interval, thermal diffusion lowers temperatures in the lithosphere, strongly increasing lithospheric strength and slowing the rate of extension. This critical time depends principally on the Peclet number and is short compared with the thermal time constant of the lithosphere. The strength changes cause the locus of high extensional strain rates to shift with time from regions of high strain to regions of low strain. Results of the calculations are compared with observations from the Aegean, where maximum extensional strains are found in the south, near Crete, but maximum present-day strain rates are largest about 300 km further north.

Sonder, Leslie J.↗

Effects of a temperature-dependent rheology on large-scale continental extension

The effects of a temperature-dependent rheology on large-scale continental extension are investigated using a thin viscous sheet model. A vertically-averaged rheology is used that is consistent with laboratory experiments on power-law creep of olivine and that depends exponentially on temperature. Results of the calculations depend principally on two parameters: the Peclet number, which describes the relative rates of advection and diffusion of heat, and a dimensionless activation energy, which controls the temperature dependence of the rheology. At short times following the beginning of extension, deformation occurs with negligible change in temperature, so that only small changes in lithospheric strength occur due to attenuation of the lithosphere. However, after a certain critical time interval, thermal diffusion lowers temperatures in the lithosphere, strongly increasing lithospheric strength and slowing the rate of extension. This critical time depends principally on the Peclet number and is short compared with the thermal time constant of the lithosphere. The strength changes cause the locus of high extensional strain rates to shift with time from regions of high strain to regions of low strain. Results of the calculations are compared with observations from the Aegean, where maximum extensional strains are found in the south, near Crete, but maximum present-day strain rates are largest about 300 km further north.

Sonder, Leslie J.↗

An algebraic model for the turbulent flux of a passive scalar

Direct numerical simulations of the unsteady incompressible Navier-Stokes equations have been performed in order to investigate the behavior of passive-scalar fields resulting from mean scalar gradients in each of three orthogonal directions in homogeneous turbulent shear flow. For all orientations of the mean scalar gradient, the sum of the pressure-scalar gradient and velocity gradient-scalar gradient terms in the turbulent scalar flux balance equation are found to be approximately aligned with the scalar flux vector itself. The simulation results are used to obtain dimensionless model coefficients as a function of the turbulence Reynolds and Peclet numbers.

Rogers, Michael M.↗

Nearly sonic and transsonic convective motions in the solar atmosphere related to the solar wind origin

MHD equations are considered for the solar atmosphere. 15 different simplest MHD regimes are indicated for the momentum transport equation depending on the mutual binary interplay between 6 possible and locally dominant terms: non-stationarity and inhomogeneity of the flow, gas pressure, magnetic tensions, viscous and gravity forces. These regimes are delimited by five physically independent dimensionless parameters, for example, Strouhal, sonic Mach, alfvenic Mach, Reynolds and Froude numbers or their combinations. Another partially overlapping classification of the simplest regimes may be introduced based on the energy conservation equation. There are also 15 independent binary combinations between nonstationary and inhomogeneous convective terms, dissipative energy sinks and sources (viscous, heat-conductive, Joule and radiative ones) in the energy equation. More complicated regimes are considered with multiple dominated terms. All these MHD regimes play their important role somewhere in the solar atmosphere complicated by the tensor transport coefficients in the magnetically dominated regions of the upper atmosphere. Nearly sonic and transsonic nonstationary convective motions with ascending and descending flows are observed in the solar chromosphere. the transition region and the lower pans of the solar corona together with related horizontal velocity components. This convection represents a kind of the 'cocoonery' manufacturing nonstationary vortices generated here and partially connected to the photosphere and to the solar wind. The solar wind originates from this powerful transsonic muddle in the solar atmosphere as a tiny fraction of the streamlines which are temporarily getting detached from the 'cocoons; and going to the infinity. The topologically complicated instantaneous 'runaway surface' around the Sun, i.e., the surface which separates outgoing to the infinity streams from other finite flows in the solar atmosphere was not described in the literature and needs additional investigation. We conclude that a simple one-connected smooth and quasistationary 'critical surface' which is often supposed to be placed somewhere in the solar corona (say, at 4 solar radii) in reality does not exist. Observational and theoretical arguments favor instead of this a highly structured, disordered, patched and time-dependent sonic transition surface in the solar atmosphere permanently fluctuating at positional dependent heights starting sometimes from photospheric (and maybe subphotospheric) levels and more frequently from the chromosphenc network up to several solar radii in the solar corona.

Veselovsky, I. S.↗

Flow boiling with enhancement devices for cold plate coolant channel design

Future space exploration and commercialization will require more efficient heat rejection systems. For the required heat transfer rates, such systems must use advanced heat transfer techniques. Forced two phase flow boiling heat transfer with enhancements falls in this category. However, moderate to high quality two phase systems tend to require higher pressure losses. This report is divided into two major parts: (1) Multidimensional wall temperature measurement and heat transfer enhancement for top heated horizontal channels with flow boiling; and (2) Improved analytical heat transfer data reduction for a single side heated coolant channel. Part 1 summarizes over forty experiments which involve both single phase convection and flow boiling in a horizontal channel heated externally from the top side. Part 2 contains parametric dimensionless curves with parameters such as the coolant channel radius ratio, the Biot number, and the circumferential coordinate.

Boyd, Ronald D.↗