SEARCH · Search NASA

Results for “coefficients”

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 91 records · Page 5

All sources NASA NTRS DOE OSTI

NASA NTRS1921

Effect of the Reversal of Air Flow upon the Discharge Coefficient of Durley Orifices

Experiments were conducted to obtain information on the relationship between the coefficients for flow in two directions through thin plate orifices at low velocities. The results indicate that the ratio of the orifice discharge coefficient from standard orifice C(sub s)(sup 1) to the discharge coefficient from the reverse flow C(sub s) is always less than unity with increasing ratio of box area to orifice area. Even for areas as low as twenty, the ratios of the coefficients are not much less than unity. It is probable, however, that when the ratio of box area is less than twenty, the ratio of discharge coefficients would be greatly reduced. Specific results are given for the case of an apparatus for the laboratory testing of superchargers.

Ware, Marsden↗

NASA NTRS1954

Lift and moment coefficients expanded to the seventh power of frequency for oscillating rectangular wings in supersonic flow and applied to a specific flutter problem

Linearized theory for compressible unsteady flow is used to derive the velocity potential and lift and moment coefficients in the form of oscillating rectangular wing moving at a constant supersonic speed. Closed expressions for the velocity potential and lift and moment coefficients associated with pitching and translation are given to seventh power of the frequency. These expressions extend the range of usefulness of NACA report 1028 in which similar expressions were derived to the third power of the frequency of oscillation. For example, at a Mach number of 10/9 the expansion of the potential to the third power is an accurate representation of the potential for values of the reduced frequency only up to about 0.08; whereas the expansion of the potential to the seventh power is an accurate representation for values of the reduced frequency up to about 0.2. The section and total lift and moment coefficients are discussed with the aid of several figures. In addition, flutter speeds obtained in the Mach number range from 10/9 to 10/6 for a rectangular wing of aspect ratio 4.53 by using section coefficients derived on the basis of three-dimensional flow are compared with flutter speeds for this wing obtained by using coefficients derived on the basis of two-dimensional flow.

Nelson, Herbert C↗

NASA NTRS1924

The Inertial Coefficients of an Airship in a Frictionless Fluid

This report deals with the investigation of the apparent inertia of an airship hull. The exact solution of the aerodynamical problem has been studied for hulls of various shapes and special attention has been given to the case of an ellipsoidal hull. In order that the results for this last case may be readily adapted to other cases, they are expressed in terms of the area and perimeter of the largest cross section perpendicular to the direction motion by means of a formula involving a coefficient K which varies only slowly when the shape of the hull is changed, being 0.637 for a circular or elliptic disk, 0.5 for a sphere, and about 0.25 for a spheroid of fineness ratio 7. For rough purposes it is sufficient to employ the coefficients, originally found for ellipsoids, for hulls otherwise shaped. When more exact values of the inertia are needed, estimates may be based on a study of the way in which K varies with different characteristics and for such a study the new coefficient possesses some advantage over one which is defined with reference to the volume of fluid displaced. The case of rotation of an airship hull has been investigated also and a coefficient has been defined with the same advantages as the corresponding coefficient for rectilinear motion.

Bateman, H↗

NASA NTRS1926

An Investigation of the Coefficient of Discharge of Liquids Through Small Round Orifices

The work covered by this report was undertaken in connection with a general investigation of fuel injection engine principles as applied to engines for aircraft propulsion, the specific purpose being to obtain information on the coefficient of discharge of small round orifices suitable for use as fuel injection nozzles. Values for the coefficient were determined for the more important conditions of engine service such as discharge under pressures up to 8,000 pounds per square inch, at temperatures between 80 degrees and 180 degrees F. And into air compressed to pressures up to 1,000 pounds per square inch. The results show that the coefficient ranges between 0.62 and 0.88 for the different test conditions between 1,000 and 8,000 pounds per square inch hydraulic pressure. At lower pressures the coefficient increases materially. It is concluded that within the range of these tests and for hydraulic pressures above 1,000 pound per square inch the coefficient does not change materially with pressure or temperature; that it depends considerably upon the liquid, decreases with increase in orifice size, and increases in the case of discharge into compressed air until the compressed-air pressure equals approximately three-tenths of the hydraulic pressure, beyond which pressure ratio it remains practically constant.

Joachim, W F↗

NASA NTRS1932

Coefficients of discharge of fuel-injection nozzles for compression-ignition engines

This report presents the results of an investigation to determine the coefficients of discharge of nozzles with small, round orifices of the size used with high-speed compression-ignition engines. The injection pressures and chamber back pressures employed were comparable to those existing in compression-ignition engines during injection. The construction of the nozzles was varied to determine the effect of the nozzle design on the coefficient. Tests were also made with nozzles assembled in an automatic injection valve, both with a plain and with a helically grooved stem. It was found that a smooth passage before the orifice is requisite for high flow efficiency. A beveled leading edge before the orifice gave a higher coefficient of discharge than a rounded edge. The results with the nozzles assembled in an automatic injection valve having a plain stem duplicated those with the nozzles assembled at the end of a straight tube of constant diameter. Lower coefficients were obtained with the nozzles assembled in an injection valve having a helically grooved stem. When the coefficients of nozzles of any one geometrical shape were plotted against values of corresponding Reynold's numbers for the orifice diameters and rates of flow tested, it was found that experimental points were distributed along a single curve.

Gelalles, A G↗

NASA NTRS1996

Dynamic model with scale-dependent coefficients in the viscous range

The standard dynamic procedure is based on the scale-invariance assumption that the model coefficient C is the same at the grid and test-filter levels. In many applications this condition is not met, e.g. when the filter-length, delta, approaches the Kolmogorov scale, and C(delta approaches eta) approaches O. Using a priori tests, we show that the standard dynamic model yields the coefficient corresponding to the test-filter scale (alpha delta) instead of the grid-scale (delta). Several approaches to account for scale dependence are examined and/or tested in large eddy simulation of isotropic turbulence: (a) take the limit alpha approaches 1; (b) solve for two unknown coefficients C(Delta) and C(alpha delta) in the least-square-error formulation; (c) the 'bi-dynamic model', in which two test-filters (e.g. at scales 2(delta) and 4(delta) are employed to gain additional information on possible scale-dependence of the coefficient, and an improved estimate for the grid-level coefficient is obtained by extrapolation, (d) use theoretical predictions for the ratio C(alpha delta)/C(delta) and dynamically solve for C(delta). None of these options is found to be entirely satisfactory, although the last approach appears applicable to the viscous range.

Meneveau, C.↗

NASA NTRS1997

Effect of Flow Misalignment and Multi-Hole Interaction on Boundary-Layer Bleed Hole Flow Coefficient Behavior

The effect of flow misalignment on the flow coefficient behavior of a 20 deg. boundary-layer bleed hole and the effect of the interaction between two 90 deg. bleed holes separated by two hole diameters on flow coefficient behavior has been studied experimentally. Both tests were run at freestream Mach numbers of 0.61, 1.62 and 2.49. The flow misalignment study was conducted over a range of 0 to 30 deg. The results show that neither flow misalignment nor hole interaction has much effect on the flow coefficient for the subsonic case. For the supersonic cases, flow misalignment causes significant degradation in the performance of the slant hole. For the supersonic normal hole interaction cases, depending on the hole orientation, either an increase or decrease in overall flow coefficient was observed. The largest change in flow coefficient, 6% increase at near choke conditions, occurred when the holes were oriented in line with the flow direction.

Davis, David O.↗

NASA NTRS1959

Effects of Cross-Sectional Shape, Solidity, and Distribution of Heat-Transfer Coefficient on the Torsional Stiffness of Thin Wings Subjected to Aerodynamic Heating

A study has been made of the effects of varying the shape, solidity, and heat-transfer coefficient of thin wings with regard to their influence on the torsional-stiffness reduction induced by aerodynamic heating. The variations in airfoil shape include blunting, flattening, and combined blunting and flattening of a solid wing of symmetrical double-wedge cross section. Hollow double-wedge wings of constant skin thickness with and without internal webs also are considered. The effects of heat-transfer coefficients appropriate for laminar and turbulent flow are investigated in addition to a step transition along the chord from a lower to a higher constant value of heat-transfer coefficient. From the results given it is concluded that the flattening of a solid double wedge decreases the reduction in torsional stiffness while slight degrees of blunting increase the loss. The influence of chordwise variations in heat-transfer coefficient due to turbulent and laminar boundary-layer flow on the torsional stiffness of solid wings is negligible. The effect of a step transition in heat-transfer coefficient along the chord of a solid wing can, however, become appreciable. The torsional-stiffness reduction of multiweb and hollow double-wedge wings is substantially less than that calculated for a solid wing subjected to the same heating conditions.

Thomson, Robert G.↗

NASA NTRS1959

Maximum Mean Lift Coefficient Characteristics at Low Tip Mach Numbers of a Hovering Helicopter Rotor Having an NACA 64(1)A012 Airfoil Section

An investigation has been conducted on the Langley helicopter test tower to determine experimentally the maximum mean lift-coefficient characteristics at low tip Mach number and a limited amount of drag- divergence data at high tip Mach number of a helicopter rotor having an NACA 64(1)AO12 airfoil section and 8 deg of linear washout. Data are presented for blade tip Mach numbers M(t) of 0.29 to 0.74 with corresponding values 6 6 of tip Reynolds number of 2.59 x 10(exp 6) and 6.58 x 10(exp 6). Comparisons are made between the data from the present rotor with results previously obtained from two other rotors: one having NACA 0012 airfoil sections and the other having an NACA 0009 airfoil tip section. At low tip Mach numbers, the maximum mean lift coefficient for the blade having the NACA 64(1)AO12 section was about 0.08 less than that obtained with the blade having the NACA 0009 tip section and 0.21 less than the value obtained with the blade having the NACA 0012 tip section. Blade maximum mean lift coefficient values were not obtained for Mach number values greater than 0.47 because of a blade failure encountered during the tests. The effective mean lift-curve slope required for predicting rotor thrust varied from 5.8 for the tip Mach nuniber range of 0.29 to 0.55 to a value of 6.65 for a tip Mach number of 0.71. The blade pitching-moment coefficients were small and relatively unaffected by changes in thrust coefficient and Mach number. In the instances in which stall was reached, the break in the blade pitching-moment curve was in a stable direction. The efficiency of the rotor decreased with an increase in tip speed. Expressed as figure of merit, at a tip Mach number of 0.29 the maximum value was about 0.74. Similar measurements made on another rotor having an NACA 0012 airfoil and with a rotor having an NACA 0009 tip section, showed a value of 0.75. Synthesized section lift and profile-drag characteristics for the rotor-blade airfoil section are presented as an aid in predicting the high-tip-speed performance of rotors having similar airfoils.

Powell, Robert D., Jr.↗

NASA NTRS1999

Determination of the Accomodation Coefficient Using Vapor/Gas Bubble Dynamics in an Acoustic Field

Non-equilibrium liquid/vapor phase transformations can occur in superheated or subcooled liquids in fast processes such as in evaporation in a vacuum, in processing of molten metals, and in vapor explosions. The rate at which such a phase transformation occurs, Xi, can be described by the Hertz-Knudsen-Langmuir formula. More than one century of the history of the accommodation coefficient measurements shows many problems with its determination. This coefficient depends on the temperature, is sensitive to the conditions at the interface, and is influenced by small amounts of impurities. Even recent measurements of the accommodation coefficient for water (Hagen et al, 1989) showed a huge variation in Beta from 1 for 1 micron droplets to 0.006 for 15 micron droplets. Moreover, existing measurement techniques for the accommodation coefficient are complex and expensive. Thus development of a relatively inexpensive and reliable technique for measurement of the accommodation coefficient for a wide range of substances and temperatures is of great practical importance.

Gumerov, Nail A.↗

NASA NTRS2001

Viscosity Coefficient Curve Fits for Ionized Gas Species Grant Palmer

Viscosity coefficient curve fits for neutral gas species are available from many sources. Many do a good job of reproducing experimental and computational chemistry data. The curve fits are usually expressed as a function of temperature only. This is consistent with the governing equations used to derive an expression for the neutral species viscosity coefficient. Ionized species pose a more complicated problem. They are subject to electrostatic as well as intermolecular forces. The electrostatic forces are affected by a shielding phenomenon where electrons shield the electrostatic forces of positively charged ions beyond a certain distance. The viscosity coefficient for an ionized gas species is a function of both temperature and local electron number density. Currently available curve fits for ionized gas species, such as those presented by Gupta/Yos, are a function of temperature only. What they did was to assume an electron number density. The problem is that the electron number density they assumed was unrealistically high. The purpose of this paper is two-fold. First, the proper expression for determining the viscosity coefficient of an ionized species as a function of both temperature and electron number density will be presented. Then curve fit coefficients will be developed using the more realistic assumption of an equilibrium electron number density. The results will be compared against previous curve fits and against highly accurate computational chemistry data.

Palmer, Grant↗

NASA NTRS2001

Nonlinearity Effects of Lateral Density Diffusion Coefficient on Gain-Guided VCSEL Performance

Electron and hole diffusions in the plane of semiconductor quantum wells play an important part in the static and dynamic operations of semiconductor lasers. In this paper, we apply a hydrodynamic model developed from the semiconductor Bloch equations to numerically study the effects of nonlinearity in the diffusion coefficient on single mode operation and direct modulation of a gain-guided InGaAs/GaAs multiple quantum well laser, operating not too far from threshold. We found that a small diffusion coefficient is advantageous for lowering the threshold current and increasing the modulation bandwidth. Most importantly, the effects of nonlinearity in the coefficient can be approximately reproduced by replacing the coefficient with an effective constant diffusion coefficient, which corresponds roughly to the half height density of the density distribution.

Li, Jian-Zhong↗

NASA NTRS1947

Summary of Available Data Relating to Reynolds Number Effects on the Maximum Lift Coefficients of Swept-Back Wings

The available foreign and American data relating to Reynolds number effects on the maximum lift coefficients of swept-back wings are summarized and discussed. The data show that at low Reynolds numbers (below about 2.0 x 10(exp 6)) higher maximum lift coefficients were measured in most cases for moderately swept-back wings than for unswept wings of similar plan form; at high Reynolds numbers, however, increasing sweepback resulted in decreasing maximum lift coefficients. A smaller rate of increase of the maximum lift coefficient with Reynolds number was measured for the swept-back wings than for similar unswept wings in the critical range of Reynolds number. Increasing the Reynolds number resulted in decreases in the maximum lift coefficients of the two wings of approximately triangular plan form that were investigated.

Sweberg, Harold H.↗

NASA NTRS1958

Statistical Study of Turbulence: Spectral Functions and Correlation Coefficients

In reading the publications on turbulence of different authors, one often runs the risk of confusing the various correlation coefficients and turbulence spectra. We have made a point of defining, by appropriate concepts, the differences which exist between these functions. Besides, we introduce in the symbols a few new characteristics of turbulence. In the first chapter, we study some relations between the correlation coefficients and the different turbulence spectra. Certain relations are given by means of demonstrations which could be called intuitive rather than mathematical. In this way we demonstrate that the correlation coefficients between the simultaneous turbulent velocities at two points are identical, whether studied in Lagrange's or in Euler's systems. We then consider new spectra of turbulence, obtained by study of the simultaneous velocities along a straight line of given direction. We determine some relations between these spectra and the correlation coefficients. Examining the relation between the spectrum of the turbulence measured at a fixed point and the longitudinal-correlation curve given by G. I. Taylor, we find that this equation is exact only when the coefficient is very small.

Frenkiel, Francois N.↗

NASA NTRS2008

Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter s performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Miller, Bard A.↗

NASA NTRS2008

Identifying Bearing Rotordynamic Coefficients using an Extended Kalman Filter

Miller, Brad A.↗

NASA NTRS1943

Preliminary Investigation of the Effect of Compressibility on the Maximum Lift Coefficient, Special Report

Preliminary data are presented on the variation of the maximum lift coefficient with Mach number. The data were obtained from tests in the 8-foot high-speed tunnel of three NACA 16-series airfoils of 1-foot chord. Measurements consisted primarily of pressure-distribution measurements in order to illustrate the nature of the phenomena. It was found that the maximum lift coefficient of airfoils is markedly affected by compressibility even at Mach numbers as low as 0.2. At high Mach numbers pronounced decrease of the maximum lift coefficient was found. The magnitude of the effects of compressibility on the maximum lift coefficient and the low speeds at which these effects first appear indicate clearly that consideration of the take-off thrust for propellers will give results seriously in error if these considerations are based on the usual low-speed maximum-lift-coefficient data generally used.

Stack, John↗

NASA NTRS2008

Identifying Bearing Rotodynamic Coefficients Using an Extended Kalman Filter

An Extended Kalman Filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates for the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates for the cross-coupled damping coefficients were the least accurate.

Miller, Brad A.↗