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 37 records · Page 2

Analysis of gas absorption to a thin liquid film in the presence of a zero-order chemical reaction

The paper presents a detailed theoretical analysis of the process of gas absorption to a thin liquid film adjacent to a horizontal rotating disk. The film is formed by the impingement of a controlled liquid jet at the center of the disk and subsequent radial spreading of liquid along the disk. The chemical reaction between the gas and the liquid film can be expressed as a zero-order homogeneous reaction. The process was modeled by establishing equations for the conservation of mass, momentum, and species concentration and solving them analytically. A scaling analysis was used to determine dominant transport processes. Appropriate boundary conditions were used to solve these equations to develop expressions for the local concentration of gas across the thickness of the film and distributions of film height, bulk concentration, and Sherwood number along the radius of the disk. The partial differential equation for species concentration was solved using the separation of variables technique along with the Duhamel's theorem and the final analytical solution was expressed using confluent hypergeometric functions. Tables for eigenvalues and eigenfunctions are presented for a number of reaction rate constants. A parametric study was performed using Reynolds number, Ekman number, and dimensionless reaction rate as parameters. At all radial locations, Sherwood number increased with Reynolds number (flow rate) as well as Ekman number (rate of rotation). The enhancement of mass transfer due to chemical reaction was found to be small when compared to the case of no reaction (pure absorption), but the enhancement factor was very significant when compared to pure absorption in a stagnant liquid film. The zero-order reaction processes considered in the present investigation included the absorption of oxygen in aqueous alkaline solutions of sodiumdithionite and rhodium complex catalyzed carbonylation of methanol. Present analytical results were compared to previous theoretical results for limiting conditions, and were found to have very good agreement.

Rajagopalan, S.↗

Paramagnetic Liquid Bridge in a Gravity-Compensating Magnetic Field

Magnetic levitation was used to stabilize cylindrical columns of a paramagnetic liquid in air between two solid supports. The maximum achievable length to diameter ratio R(sub max) was approx. (3.10 +/- 0.07), very close to the Rayleigh-Plateau limit of pi. For smaller R, the stability of the column was measured as a function of the Bond number, which could be continuously varied by adjusting the strength of the magnetic field. Liquid bridges supported by two solid surfaces have been attracting scientific attention since the time of Rayleigh and Plateau. For a cylindrical bridge of length L and diameter d, it was shown theoretically that in zero gravity the maximum slenderness ratio R (identically = L/d) is pi. The stability and ultimate collapse of such bridges is of interest because of their importance in a number of industrial processes and their potential for low gravity applications. In the presence of gravity, however, the cylindrical shape of an axisymmetric bridge tends to deform, limiting its stability and decreasing the maximum achievable value of R. Theoretical studies have discussed the stability and possible shapes of axisymmetric bridges. Experiments typically are performed in either a Plateau tank, in which the bridge is surrounded by a density-matched immiscible fluid, or in a space-borne microgravity environment. It has been shown, for example, that the stability limit R can be pushed beyond pi by using flow stabilization, by acoustic radiation pressure, or by forming columns in the presence of an axial electric field. In this work, magnetic levitation was used to simulate a low gravity environment and create quasi-cylindrical liquid columns in air. Use of a magnetic field permits us to continuously vary the Bond number B identically equal to (g)(rho)d(exp 2)/4(sigma), where g is the gravitational acceleration, rho is the density of the liquid, and sigma is the surface tension of the liquid in air. The dimensionless Bond number represents the relative importance of external forces acting on the liquid column to those due to surface tension. Our central result is that in a large magnetic field gradient we could create and stabilize columns of mixtures of water and paramagnetic manganese chloride tetrahydrate (MnCl2.4H2O), achieving a length to diameter ratio very close to pi.

Mahajan, Milind P.↗

Experimental investigation of free-convection heat transfer in vertical tube at large Grashof numbers / E. R. G. Eckert, A. J. Diaguila

Local free-convection heat-transfer coefficients and temperature fields in the turbulent flow range were obtained within a vertical, stationary tube closed at the boom, heated along its walls, and having a length-to-diameter ratio of 5. Convective heat-transfer coefficients were correlated by the general relations for free-convection heat transfer. These coefficients, converted to dimensionless Nusselt numbers were 35 percent below known relations for vertical flat plates. Air temperature measurements within the tube indicated a thin boundary layer along the heated wall surface and unstable conditions in the air flow.

HEAT TRANSFER↗

Determination of Thermal State of Charge in Solar Heat Receivers

The research project at Howard University seeks to develop analytical and numerical capabilities to study heat transfer and fluid flow characteristics, and the prediction of the performance of solar heat receivers for space applications. Specifically, the study seeks to elucidate the effects of internal and external thermal radiation, geometrical and applicable dimensionless parameters on the overall heat transfer in space solar heat receivers. Over the last year, a procedure for the characterization of the state-of-charge (SOC) in solar heat receivers for space applications has been developed. By identifying the various factors that affect the SOC, a dimensional analysis is performed resulting in a number of dimensionless groups of parameters. Although not accomplished during the first phase of the research, data generated from a thermal simulation program can be used to determine values of the dimensionless parameters and the state-of-charge and thereby obtain a correlation for the SOC. The simulation program selected for the purpose is HOTTube, a thermal numerical computer code based on a transient time-explicit, axisymmetric model of the total solar heat receiver. Simulation results obtained with the computer program are presented the minimum and maximum insolation orbits. In the absence of any validation of the code with experimental data, results from HOTTube appear reasonable qualitatively in representing the physical situations modeled.

Glakpe, E. K.↗

The Dynamics of Miscible Interfaces: A Space Flight Experiment

Experiments as well as accompanying simulations are described that serve in preparation of a space flight experiment to study the dynamics of miscible interfaces. The investigation specifically addresses the importance of both nonsolenoidal effects as well as nonconventional Korteweg stresses in flows that give rise to steep but finite concentration gradients. The investigation focuses on the flow in which a less viscous fluid displaces one of higher viscosity and different density within a narrow capillary tube. The fluids are miscible in all proportions. An intruding finger forms that occupies a fraction of the total tube diameter. Depending on the flow conditions, as expressed by the Peclet number, a dimensionless viscosity ratio, and a gravity parameter, this fraction can vary between approximately 0.9 and 0.2. For large Pe values, a quasi-steady finger forms, which persists for a time of O(Pe) before it starts to decay, and Poiseuille flow and Taylor dispersion are approached asymptotically. Depending on the specific flow conditions, we observe a variety of topologically different streamline patterns, among them some that leak fluid from the finger tip. For small Pe values, the flow decays from the start and asymptotically reaches Taylor dispersion after a time of O(Pe). Comparisons between experiments and numerical simulations based on the 'conventional' assumption of solenoidal velocity fields and without Korteweg stresses yield poor agreement as far as the Pe value is concerned that distinguishes these two regimes. As one possibility, we attribute this lack of agreement to the disregard of these terms. An attempt is made to use scaling arguments in order to evaluate the importance of the Korteweg stresses and of the assumption of solenoidality. While these effects should be strongest in absolute terms when steep concentration fronts exist, i.e., at large Pe, they may be relatively most important at lower values of Pe. We subsequently compare these conventional simulations to more complete simulations that account for nonvanishing divergence as well as Korteweg stresses. While the exact value of the relevant stress coefficients are not known, ballpark numbers do exist, and their use in the simulations indicates that these stresses may indeed be important. We plan to evaluate these issues in detail by means of comparing a space experiment with corresponding simulations, in order to extract more accurate Korteweg stress coefficients, and to confirm or deny the importance of such stresses.

Maxworthy, Tony↗

Optimization of self-acting step thrust bearings for load capacity and stiffness.

Linearized analysis of a finite-width rectangular step thrust bearing. Dimensionless load capacity and stiffness are expressed in terms of a Fourier cosine series. The dimensionless load capacity and stiffness were found to be a function of the dimensionless bearing number, the pad length-to-width ratio, the film thickness ratio, the step location parameter, and the feed groove parameter. The equations obtained in the analysis were verified. The assumptions imposed were substantiated by comparing the results with an existing exact solution for the infinite width bearing. A digital computer program was developed which determines optimal bearing configuration for maximum load capacity or stiffness. Simple design curves are presented. Results are shown for both compressible and incompressible lubrication. Through a parameter transformation the results are directly usable in designing optimal step sector thrust bearings.

Hamrock, B. J.↗

Tabulation and summary of thermodynamic effects data for developed cavitation on ogive-nosed bodies

Thermodynamic effects data for developed cavitation on zero and quarter caliber ogives in Freon 113 and water are tabulated and summarized. These data include temperature depression (delta T), flow coefficient (C sub Q), and various geometrical characteristics of the cavity. For the delta T tests, the free-stream temperature varied from 35 C to 95 C in Freon 113 and from 60 C to 125 C in water for a velocity range of 19.5 m/sec to 36.6 m/sec. Two correlations of the delta T data by the entrainment method are presented. These correlations involve different combinations of the Nusselt, Reynolds, Froude, Weber, and Peclet numbers and dimensionless cavity length.

Holl, J. W.↗

Heat transfer characteristics for jet array impingement with initial crossflow

Two-dimensional arrays of circular air jets impinging on a heat transfer surface parallel to the jet orifice plate are considered. The jet flow, after impingement, is constrained to exit in a single direction along the channel formed by the jet orifice plate and the heat transfer surface. In addition to the crossflow which originates from the jets following impingement, an initial crossflow is present which approaches the array through an upstream extension of the channel. The temperature of the initial crossflow air may differ from the jet air temperature. The configurations considered are intended to model the impingement cooled midchord region of gas turbine airfoils in cases where an initial crossflow is also present. Nusselt numbers and dimensionless adiabatic wall temperatures resolved to one streamwise jet hole spacing were experimentally determined for ratios of the initial crossflow rate to the total jet flow rate ranging from zero to unity. These are presented and discussed relative to the flow and geometric parameters.

Florschuetz, L. W.↗

Higher-order parabolic approximations for sound propagation in stratified moving media

Asymptotic solutions of order k-n are developed for the equations governing the propagation of sound through a stratified moving medium. Here k is a dimensionless wave number and n is the arbitrary order of the approximation. These approximations are an extension of geometric acoustics theory and provide corrections to that theory in the form of multiplicative functions which satisfy parabolic partial differential equations. These corrections account for the diffraction effects caused by variation of the field normal to the ray path and the interaction of these transverse variations with the variation of the field along the ray. The theory is illustrated by application to simple examples.

Mcaninch, G. L.↗

Higher order parabolic approximations of the reduced wave equation

Asymptotic solutions of order k to the nth are developed for the reduced wave equation. Here k is a dimensionless wave number and n is the arbitrary order of the approximation. These approximations are an extension of geometric acoustics theory, and provide corrections to that theory in the form of multiplicative functions which satisfy parabolic partial differential equations. These corrections account for the diffraction effects caused by variation of the field normal to the ray path and the interaction of these transverse variations with the variation of the field along the ray. The theory is applied to the example of radiation from a piston, and it is demonstrated that the higher order approximations are more accurate for decreasing values of k.

Mcaninch, G. L.↗

Hydrodynamic effects on cell growth in agitated microcarrier bioreactors

The net growth rate of bovine embryonic kidney cells in microcarrier bioreactor is the result of a variable death rate imposed on a cell culture trying to grow at a constant intrinsic growth rate. The death rate is a function of the agitation conditions in the system, and increases at higher agitation because of increasingly energetic interactions of the cell covered microcarriers with turbulent eddies in the fluid. At very low agitation rates bead-bead bridging becomes important; the large clumps formed by bridging can interact with larger eddies than single beads, leading to a higher death rate at low agitation. The growth and death rate were correlated with a dimensionless eddy number which compares eddy forces to the buoyant force on the bead.

Cherry, Robert S.↗

Granular instability in fluidized beds: A small-over-large instability

For different particle diameters arranged in a gas fluidized bed, a new gravitational instability is predicted. The first order stability analysis yields conditions for growth of the most unstable wavenumber both as a function of particle diameter and dimensionless Bond number. Gravity acts to distribute the greater fluid mass associated with smaller particles, while surface tension stabilizes the entire bed against accelerations. The phenomenon, called the 'Small-over-Large' (SL) instability, evolves somewhat akin to a Rayleigh-Taylor mechanism and in addition to fundamental interest, carries implications for predicting solute redistribution and gravitational alignments in particle beds and chemical separation columns.

Noever, David A.↗

Quantifying ataxia: ideal trajectory analysis--a technical note

We describe a quantitative method to assess repeated stair stepping stability. In both the mediolateral (ML) and anterioposterior (AP) directions, the trajectory of the subject's center of mass (COM) was compared to an ideal sinusoid. The two identified sinusoids were unique in each direction but coupled. Two dimensionless numbers-the mediolateral instability index (IML) and AP instability index (IAP)-were calculated using the COM trajectory and ideal sinusoids for each subject with larger index values resulting from less stable performance. The COM trajectories of nine nonimpaired controls and six patients diagnosed with unilateral or bilateral vestibular labyrinth hypofunction were analyzed. The average IML and IAP values of labyrinth disorder patients were respectively 127% and 119% greater than those of controls (p<0.014 and 0.006, respectively), indicating that the ideal trajectory analysis distinguishes persons with labyrinth disorder from those without. The COM trajectories also identify movement inefficiencies attributable to vestibulopathy.

Non-NASA Center↗

Effect of reduced gravity on the preferred walk-run transition speed

We investigated the effect of reduced gravity on the human walk-run gait transition speed and interpreted the results using an inverted-pendulum mechanical model. We simulated reduced gravity using an apparatus that applied a nearly constant upward force at the center of mass, and the subjects walked and ran on a motorized treadmill. In the inverted pendulum model for walking, gravity provides the centripetal force needed to keep the pendulum in contact with the ground. The ratio of the centripetal and gravitational forces (mv2/L)/(mg) reduces to the dimensionless Froude number (v2/gL). Applying this model to a walking human, m is body mass, v is forward velocity, L is leg length and g is gravity. In normal gravity, humans and other bipeds with different leg lengths all choose to switch from a walk to a run at different absolute speeds but at approximately the same Froude number (0.5). We found that, at lower levels of gravity, the walk-run transition occurred at progressively slower absolute speeds but at approximately the same Froude number. This supports the hypothesis that the walk-run transition is triggered by the dynamics of an inverted-pendulum system.

Non-NASA Center↗

Parametric Evaluation of Interstellar Exploration Mission Concepts

One persistent difficulty in evaluating the myriad advanced propulsion concepts proposed over the last 60 years is a true apples to apples comparison of the expected gain in performance. This analysis is complicated by numerous factors including, multiple missions of interest to the advanced propulsion community, the lack of a credible closed form solution to 'medium thrust' trajectories, and lack of detailed design data for most proposed concepts that lend credibility to engine performance estimates. This paper describes a process on how to make fair comparisons of different propulsion concepts for multiple missions over a wide range of performance values. The figure below illustrates this process. This paper describes in detail the process and outlines the status so far in compiling the required data. Parametric data for several missions are calculated and plotted against specific power-specific impulse scatter plots of expected propulsion system performance. The overlay between required performance as defined by the trajectory parametrics and expected performance as defined in the literature for major categories of propulsion systems clearly defines which propulsion systems are the most apt for a given mission. The application of the Buckingham Pi theorem to general parameters for interstellar exploration ( mission time, mass, specific impulse, specific power, distance, propulsion source energy/mass, etc.) yields a number of dimensionless variables. The relationships of these variables can then be explored before application to a particular mission. Like in the fields of fluid mechanics and heat transfer, the use of the Buckingham Pi theorem results in new variables to make apples to apples comparisons.

Adams, Robert B.↗

Do Sub-Mesoscales Inhibit Destruction of PV?

We present the first explicit form of the three components, advective, diabatic and frictional of the PV J fluxes contributed by sub-mesoscales SM. Of particular interest is the surface value of the vertical frictional PV flux which when positive, can induce destruction of PV by down-front winds. The 2005 numerical simulations of Thomas confirmed that this is indeed the case. However, since the 12 km numerical resolution could not account for sub-mesoscales SM (0.1-10) km, the effect of SM on the PV destruction process could not be quantified. The goal of this work is to provide an answer to that question asked in the title. The two SM parameterizations entering the problem, the vertical buoyancy flux and the momentum flux (Reynolds stresses), bring about a new feature, the dependence on the SM kinetic energy (represented by the dimensionless Rossby number Ro), that causes unexpected results. While in the absence of SM, there were no restrictions on where PV destruction could occur, in the presence of SM, the condition of a positive surface vertical frictional flux is restricted to SM regimes with very low Ro<1 and very high Ro>10. Since the SM kinetic energy is location dependent, so is PV destruction. The effect of SM seems to make PV destruction a much rarer occurrence than previously thought.

potential vorticity↗

Airfoil Table Modification for Improved Calculation of Ingenuity Rotor Performance

To better characterize the behavior of the Ingenuity helicopter, multiple test campaigns were conducted. These tests included the Engineering Design Model 1 (EDM1) tests and the Transonic Rotor Test (TRT), both of which assessed Ingenuity rotor performance at various conditions. Using a comprehensive rotorcraft analysis tool, CAMRAD II, test setups of the two different Ingenuity test campaigns were simulated. The EDM1 test used coaxial test stand which focused on varying collective at various feasible Martian atmospheric densities and the TRT test used a single rotor test stand which focused on varying RPM to assess performance at different blade tip Mach numbers. Initial CAMRAD II analyses yielded performance results which differed significantly from experimental results. To reconcile the experimental results and the CAMRAD II analyses, modifications were made to the input airfoil decks for CAMRAD II. After several iterations of modifications, a specific method of modification was found that more accurately predicted experimental behavior at all tested densities for the coaxial rotor. This same modification was less successful for the single rotor test results. There are a number of differences between coaxial and single rotor aerodynamics and between the two test stands (hub and control system); also, there is a small influence of RPM (mainly tip Mach number) on dimensionless performance. These differences may be causing the coaxial rotor modifications not being successful for the single rotor.

Airfoil↗

Low Reynolds number kappa-epsilon and empirical transition models for oscillatory pipe flow and heat transfer

Stirling engine heat exchangers are shell-and-tube type with oscillatory flow (zero-mean velocity) for the inner fluid. This heat transfer process involves laminar-transition turbulent flow motions under oscillatory flow conditions. A low Reynolds number kappa-epsilon model, (Lam-Bremhorst form), was utilized in the present study to simulate fluid flow and heat transfer in a circular tube. An empirical transition model was used to activate the low Reynolds number k-e model at the appropriate time within the cycle for a given axial location within the tube. The computational results were compared with experimental flow and heat transfer data for: (1) velocity profiles, (2) kinetic energy of turbulence, (3) skin friction factor, (4) temperature profiles, and (5) wall heat flux. The experimental data were obtained for flow in a tube (38 mm diameter and 60 diameter long), with the maximum Reynolds number based on velocity being Re(sub max) = 11840, a dimensionless frequency (Valensi number) of Va = 80.2, at three axial locations X/D = 16, 30 and 44. The agreement between the computations and the experiment is excellent in the laminar portion of the cycle and good in the turbulent portion. Moreover, the location of transition was predicted accurately. The Low Reynolds Number kappa-epsilon model, together with an empirical transition model, is proposed herein to generate the wall heat flux values at different operating parameters than the experimental conditions. Those computational data can be used for testing the much simpler and less accurate one dimensional models utilized in 1-D Stirling Engine design codes.

Bauer, Christopher↗