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NASA NTRSDate not supplied

Comparison of Pre- and Post-Flight Estimations of Pitch Damping Coefficients for Unguided Entry Vehicles

Introduction: Pre-flight predictions of pitch damping coefficient (𝐶!!+𝐶!"̇)curves are used in entry simulations to determine flight readiness and if any dynamic remediation strategies are required. Accurate characterization of these pitch damping coefficient curves is crucial for mission success. Historically, pre-flight estimations of these curves are derived experimentally either via ballistic range testing or with 1-degree-of-freedom (DOF) free-or forced-oscillation wind tunnel testing. Methodology:With post-flight best-estimated trajectories, a fitting procedure as described in Karlgaard, et. al. [1] is used to compare pre-and post-flight pitch damping coefficients. This technique relies on an assumed analytical form of the trajectory, a limited 3-DOF representation described in Schoenenbergerand Queen [2], which results in anEuler-Cauchy solution form.This solution assumes constant density,thus limited amplitude multi-peak windows of the trajectory are considered to populate the pitch damping-amplitudes pace. Fig. 1 shows preliminary estimations of the pitch damping coefficients estimated using the post-flight best estimated trajectoryfor MER B, using a3-amplitude-peak window. Important to note is that the Euler-Cauchy solution also assumes planar motion, thus coning or 𝛽contribution is not included. Further,the estimated post-flight pitch damping approximations and the pre-flight predictions shown are effective representations of pitch damping, or the integrated effect of the pitch damping coefficient over one pitch cycle at the corresponding cycle’s peak amplitude. Effective pitch damping coefficient curves provide more intuitive insights about where the vehicle is stable and permits readily processed comparisons between data-sets. It is important to note that most pitch damping curves, such as those reported in aerodatabases and utilized in flight mechanics trajectory simulations, are represented in instantaneous angle-of-attack space distinct from what is presented in Fig 1. The extracted post-flight pitch damping coefficient points show a wide range of values across a narrow band of amplitudes (Fig.1a), albeit centered on the published pre-flight approximation. This also applies to the prediction as a function of Mach in Fig1b, where the post-flight scatter points are centered around the pre-flight predictions, but the pre-flight predictions notably lack data aboveMach 5.Further tuning of the technique, such as changing the number of peaks considered in each stencil, resolving density in higher resolution, and employing more accurate fitting procedures (beyond scipy.curve_fit()), will be performed. PosterFocus:This study will apply this reconstruction method to the as-flown trajectories for the following unguided entry vehicles: MER A, MER B, IRVE3, Phoenix, Insight, Pathfinder, and SIAD. The pitch damping coefficient will be derived from these trajectories and compared with the pre-flight predictions. Comparing across different missions, entry environments, and vehicle geometries can inform where our pre-flight testing methodologies accurately capture the flight dynamics. Results will provide valuable insight into the accuracy of pre-flight predicted pitch damping curves. Beyond that, this method can shed light on how accurate these curves need to be, which can inform uncertainty ranges applied to pre-flight curves for other missions.

pitch damping coefficient↗

NASA NTRS1974

The dyadic diffraction coefficient for a curved edge

A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edge formed by perfectly conducting curved or plane surfaces is obtained. This diffraction coefficent remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. The method is on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresnel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved edge.

Kouyoumjian, R. G.↗

NASA NTRS1978

Effect of concentration dependence of the diffusion coefficient on homogenization kinetics in multiphase binary alloy systems

Diffusion calculations were performed to establish the conditions under which concentration dependence of the diffusion coefficient was important in single, two, and three phase binary alloy systems. Finite-difference solutions were obtained for each type of system using diffusion coefficient variations typical of those observed in real alloy systems. Solutions were also obtained using average diffusion coefficients determined by taking a logarithmic average of each diffusion coefficient variation considered. The constant diffusion coefficient solutions were used as reference in assessing diffusion coefficient variation effects. Calculations were performed for planar, cylindrical, and spherical geometries in order to compare the effect of diffusion coefficient variations with the effect of interface geometries. In most of the cases considered, the diffusion coefficient of the major-alloy phase was the key parameter that controlled the kinetics of interdiffusion.

Tenney, D. R.↗

NASA NTRS1993

Application of neural network to remote sensing of soil moisture using theoretical polarimetric backscattering coefficients

This paper investigates the potential application of neural network to inversion of soil moisture using polarimetric remote sensing data. The neural network used for the inversion of soil parameters is multi-layer perceptron trained with the back-propagation algorithm. The training data include the polarimetric backscattering coefficients obtained from theoretical surface scattering models together with an assumed nominal range of soil parameters which are comprised of the soil permittivity and surface roughness parameters. Soil permittivity is calculated from the soil moisture and the assumed soil texture based on an empirical formula at C-, L-, and P-bands. The rough surface parameters for the soil surface, which is described by the Gaussian random process, are the root-mean-square (rms) height and correlation length. For the rough surface scattering, small perturbation method is used for the L-band frequency, and Kirchhoff approximation is used for the C-band frequency to obtain the corresponding backscattering coefficients. During the training, the backscattering coefficients are the inputs to the neural net and the output from the net are compared with the desired soil parameters to adjust the interconnecting weights. The process is repeated for each input-output data entry and then for the entire training data until convergence is reached. After training, the backscattering coefficients are applied to the trained neural net to retrieve the soil parameters which are compared with the desired soil parameters to verify the effectiveness of this technique. Several cases are examined. First, for simplicity, the correlation length and rms height of the soil surface are fixed while soil moisture is varied. Soil moisture obtained using the neural networks with either L-band or C-band backscattering coefficients for the HH and VV polarizations as inputs is in good agreement with the desired soil moisture. The neural net output matches the desired output for the soil moisture range of 16 to 60 percent for the C-band case. The next case investigated is to vary both soil moisture and rms height while keeping the correlation length fixed. For this case, C-band backscattering coefficients are not sufficient for retrieving two parameters because the Kirchhoff approximation gives the same HH and VV backscattering coefficients. Therefore, the backscattering coefficients at two different frequency bands are necessary to find both the soil moisture and rms height. Finally, the neural nets are also applied to simultaneously invert soil moisture, rms height, and correlation length. Overall, the soil moisture retrieved from the neural network agrees very well with the desired soil moisture. This suggests that the neural network shows potential for retrieval of soil parameters from remote sensing data.

Wang, L.↗

NASA NTRS2006

Measurements and Theoretical Calculations of N2-broadening and N2-shift Coefficients in the v2 band of CH3D

In this paper, we report measured Lorentz N2-broadening and N2-induced pressure-shift coefficients of CH3D in the v2 fundamental band using a multispectrum fitting technique. These measurements were made by analyzing 11 laboratory absorption spectra recorded at 0.0056 cm(exp -1) resolution using the McMath-Pierce Fourier transform spectrometer located at the National Solar Observatory on Kitt Peak, Arizona. The spectra were obtained using two absorption cells with path lengths of 10.2 and 25 cm. The total sample pressures ranged from 0.98 to 402.25 Torr with CH3D volume mixing ratios of 0.01 in nitrogen. We have been able to determine the N2 pressure- broadening coefficients of 368 v2 transitions with quantum numbers as high as J"= 20 and K = 16, where K" = K' equivalent to K (for a parallel band). The measured N2-broadening coefficients range from 0.0248 to 0.0742 cm(exp -1) atm(exp -1) at 296 K. All the measured pressure-shifts are negative. The reported N2-induced pressure-shift coefficients vary from about 0.0003 to 0.0094 cm(exp -1) atm(exp -1). We have examined the dependence of the measured broadening and shift parameters on the J", and K quantum numbers and also developed empirical expressions to describe the broadening coefficients in terms of m (m = -J", J", and J" + 1 in the (sup Q)P-, (sup Q)Q-, and (sup Q)R-branch, respectively) and K. On average, the empirical expressions reproduce the measured broadening coefficients to within 4.7%. The N2-broadening and pressureshift coefficients were calculated on the basis of a semiclassical model of interacting linear molecules performed by considering in addition to the electrostatic contributions the atom atom Lennard-Jones potential. The theoretical results of the broadening coefficients are in good overall agreement with the experimental data (8.7%). The N2-pressure shifts whose vibrational contribution is derived from parameters fitted in the (sup Q)Q-branch of self-induced shifts of CH3D, are also in reasonable agreement with the scattered experimental data (20% in most cases).

Predoi-Cross, A.↗

NASA NTRS2006

Room-temperature Broadening and Pressure-shift Coefficients in the nu(exp 2) Band of CH3D-O2: Measurements and Semi-classical Calculations

We report measured Lorentz O2-broadening and O2-induced pressure-shift coefficients of CH3D in the nu(exp 2) fundamental band. Using a multispectrum fitting technique we have analyzed 11 laboratory absorption spectra recorded at 0.011 cm(exp 1) resolution using the McMath-Pierce Fourier transform spectrometer, Kitt Peak, Arizona. Two absorption cells with path lengths of 10.2 and 25 cm were used to record the spectra. The total sample pressures ranged from 0.98 to 339.85 Torr with CH3D volume mixing ratios of 0.012 in oxygen. We report measurements for O2 pressure-broadening coefficients of 320 nu(exp 2) transitions with quantum numbers as high as J0(sup w) = 17 and K = 14, where K(sup w) = K' is equivalent to K (for a parallel band). The measured O2-broadening coefficients range from 0.0153 to 0.0645 cm(exp -1) atm(exp -1) at 296 K. All the measured pressure-shifts are negative. The reported O2-induced pressure-shift coefficients vary from about -0.0017 to -0.0068 cm(exp -1) atm(exp -1). We have examined the dependence of the measured broadening and shift parameters on the J(sup W), and K quantum numbers and also developed empirical expressions to describe the broadening coefficients in terms of m (m = -J(sup W), J(sup W), and J(sup w) + 1 in the QP-, QQ-, and QR-branch, respectively) and K. On average, the empirical expressions reproduce the measured broadening coefficients to within 4.4%. The O2-broadening and pressure shift coefficients were calculated on the basis of a semiclassical model of interacting linear molecules performed by considering in addition to the electrostatic contributions the atom-atom Lennard-Jones potential. The theoretical results of the broadening coefficients are generally larger than the experimental data. Using for the trajectory model an isotropic Lennard-Jones potential derived from molecular parameters instead of the spherical average of the atom-atom model, a better agreement is obtained with these data, especially for |m| <= 12 values (11.3% for the first calculation and 8.1% for the second calculation). The O2-pressure shifts whose vibrational contribution are either derived from parameters fitted in the QQ-branch of selfinduced shifts of CH3D or those obtained from pressure shifts induced by Xe in the nu(sup 3) band of CH3D are in reasonable agreement with the scattered experimental data (17.0% for the first calculation and 18.7% for the second calculation).

Predoi-Cross, Adriana↗

NASA NTRS2016

Collisional Dissociation of CO: ab initio Potential Energy Surfaces and Quasiclassical Trajectory Rate Coefficients

We have generated accurate global potential energy surfaces for CO+Ar and CO+O that correlate with atom-diatom pairs in their ground electronic states based on extensive ab initio electronic structure calculations and used these potentials in quasi-classical trajectory nuclear dynamics calculations to predict the thermal dissociation rate coefficients over 5000- 35000 K. Our results are not compatible with the 20-45 year old experimental results. For CO + Ar we obtain fairly good agreement with the experimental rate coefficients of Appleton et al. (1970) and Mick and Roth (1993), but our computed rate coefficients exhibit a stronger temperature dependence. For CO + O our dissociation rate coefficient is in close agreement with the value from the Park model, which is an empirical adjustment of older experimental results. However, we find the rate coefficient for CO + O is only 1.5 to 3.3 times larger than CO + Ar over the temperature range of the shock tube experiments (8000-15,000 K). The previously accepted value for this rate coefficient ratio is 15, independent of temperature. We also computed the rate coefficient for the CO + O ex- change reaction which forms C + O2. We find this reaction is much faster than previously believed and is the dominant process in the removal of CO at temperatures up to 16,000 K. As a result, the dissociation of CO is accomplished in two steps (react to form C+O2 and then O2 dissociates) that are endothermic by 6.1 and 5.1 eV, instead of one step that requires 11.2 eV to break the CO bond.

exchange rate coefficient↗

DOE OSTI2024

Determination of the Diffusion Coefficients of Binary CH4 and C2H6 in a Supercritical CO2 Environment (500–2000 K and 100–1000 atm) by Molecular Dynamics Simulations

The self-diffusion coefficients of carbonaceous fuels in a supercritical CO2 environment provide transport information that can help us understand the Allam Cycle mechanism at a high pressure of 300 atm. The diffusion coefficients of pure CO2 and binary CO2/CH4 and CO2/C2H6 at high temperatures (500 K~2000 K) and high pressures (100 atm~1000 atm) are determined by molecular dynamics simulations in this study. Increasing the temperature leads to an increase in the diffusion coefficient, and increasing the pressure leads to a decrease in the diffusion coefficients for both methane and ethane. The diffusion coefficient of methane at 300 atm is approximately 0.012 cm2/s at 1000 K and 0.032 cm2/s at 1500 K. The diffusion coefficient of ethane at 300 atm is approximately 0.016 cm2/s at 1000 K and 0.045 cm2/s at 1500 K. The understanding of diffusion coefficients potentially leads to the reduction in fuel consumption and minimization of greenhouse gas emissions in the Allam Cycle.

Energy & Fuels↗

NASA NTRS1959

Measurements of Heat-Transfer and Friction Coefficients for Helium Flowing in a Tube at Surface Temperatures up to 5900 Deg R

Measurements of average heat transfer and friction coefficients and local heat transfer coefficients were made with helium flowing through electrically heated smooth tubes with length-diameter ratios of 60 and 92 for the following range of conditions: Average surface temperature from 1457 to 4533 R, Reynolds numbe r from 3230 to 60,000, heat flux up to 583,200 Btu per hr per ft2 of heat transfer area, and exit Mach numbe r up to 1.0. The results indicate that, in the turbulent range of Reynolds number, good correlation of the local heat transfer coefficients is obtained when the physical properties and density of helium are evaluated at the surface temperature. The average heat transfer coefficients are best correlated on the basis that the coefficient varies with [1 + (L/D))(sup -0,7)] and that the physical properties and density are evaluated at the surface temperature. The average friction coefficients for the tests with no heat addition are in complete agreement with the Karman-Nikuradse line. The average friction coefficients for heat addition are in poor agreement with the accepted line.

Taylor, Maynard F.↗

NASA NTRS1983

The drag coefficient of cylindrical spacecraft in orbit at altitudes greater than 150 km

The spacecraft of the Geopotential Research Mission (GRM) are cylindrical in form and designed to fly with their longitudinal axes parallel to their direction of flight. The ratio of length to diameter of these spacecraft is roughly equal to 5.0. Other spacecraft previously flown had corresponding ratios roughly equal to 1.0, and therefore the drag produced by impacts on the lateral surfaces of those spacecraft was not as large as it will be on the GRM spacecraft. Since the drag coefficient is essentially the drag force divided by the frontal area in flight, lateral impacts, when taken into account make the GRM drag coefficient significantly larger than the coefficients used before for shorter spacecraft. A simple formula is derived for the drag coefficient of a cylindrical body flying with its long axis along the direction of flight, and it is used to estimate the drag for the GRM. The formula shows that the drag due to lateral surface impacts depends on the ratio of length-to-diameter and on a coefficient C sub LS (lateral surface impact coefficient) which can be determined from previous cylindrical spacecraft flown with the same attitude, or can be obtained from laboratory measurements of momentum accommodation coefficients.

Herrero, F. A.↗

NASA NTRS1998

Pressure Broadening and Pressure Shift Coefficients in the 2nu(sup 0, sub 2) and nu(sub 1) Bands of (16)O(13)C(18)O

In this study we report the first measurements of the pressure broadening and the pressure-induced line shift coefficients due to air and nitrogen for 93 individual rovibrational lines, P(46) to R(46) and P(50) to R(45), respectively, belonging to the 2nu(sup 0, sub 2) and nu(sub 1) bands of (16)O(13)C(18)O. The results were obtained by analyzing ten long path, high-resolution laboratory, absorption spectra using a multispectrum nonlinear least-squares technique. Broadening due to nitrogen was about 4% larger than by air. Similar to broadening coefficients, the pressure-shift coefficients were found to be transition dependent, but different for the P- and R-branch lines with the same rotational quantum number, J. Except for a few R-branch lines, the measured shift coefficients were negative. The shift coefficients varied from + 4 x 10(exp -3)/cm.atm at 296 K to -5.6 x 10(exp -3)/cm.atm at 296 K. Comparisons of the broadening and shift coefficients between the two bands, between the P and R branches, and between the two broadening gases are reported. No significant difference between shift coefficients of the two bands or the two broadening gases was observed. The results obtained were compared with those reported in the literature for the more abundant (12)C(16)O2 species.

Devi, V. Malathy↗

NASA NTRS2000

A Solution Methodology and Computer Program to Efficiently Model Thermodynamic and Transport Coefficients of Mixtures

A solution methodology has been developed to efficiently model multi-specie, chemically frozen, thermally perfect gas mixtures. The method relies on the ability to generate a single (composite) set of thermodynamic and transport coefficients prior to beginning a CFD solution. While not fundamentally a new concept, many applied CFD users are not aware of this capability nor have a mechanism to easily and confidently generate new coefficients. A database of individual specie property coefficients has been created for 48 species. The seven coefficient form of the thermodynamic functions is currently used rather then the ten coefficient form due to the similarity of the calculated properties, low temperature behavior and reduced CPU requirements. Sutherland laminar viscosity and thermal conductivity coefficients were computed in a consistent manner from available reference curves. A computer program has been written to provide CFD users with a convenient method to generate composite specie coefficients for any mixture. Mach 7 forebody/inlet calculations demonstrated nearly equivalent results and significant CPU time savings compared to a multi-specie solution approach. Results from high-speed combustor analysis also illustrate the ability to model inert test gas contaminants without additional computational expense.

Ferlemann, Paul G.↗

NASA NTRS2006

Inter-Comparison of ILAS-II Version 1.4 Aerosol Extinction Coefficient at 780 nm with SAGE II, SAGE III, and POAM III Aerosol Data

The Improved Limb Atmospheric Spectrometer (ILAS) II on board the Advanced Earth Observing Satellite (ADEOS) II observed stratospheric aerosol in visible/near-infrared/infrared spectra over high latitudes in the Northern and Southern Hemispheres. Observations were taken intermittently from January to March, and continuously from April through October, 2003. We assessed the data quality of ILAS-II version 1.4 aerosol extinction coefficients at 780 nm from comparisons with the Stratospheric Aerosol and Gas Experiment (SAGE) II, SAGE III, and the Polar Ozone and Aerosol Measurement (POAM) III aerosol data. At heights below 20 km in the Northern Hemisphere, aerosol extinction coefficients from ILAS-II agreed with those from SAGE II and SAGE III within 10%, and with those from POAM III within 15%. From 20 to 26 km, ILAS-II aerosol extinction coefficients were smaller than extinction coefficients from the other sensors; differences between ILAS-II and SAGE II ranged from 10% at 20 km to 34% at 26 km. ILAS-II aerosol extinction coefficients from 20 to 25 km in February over the Southern Hemisphere had a negative bias (12-66%) relative to SAGE II aerosol data. The bias increased with increasing altitude. Comparisons between ILAS-II and POAM III aerosol extinction coefficients from January to May in the Southern Hemisphere (defined as the non-Polar Stratospheric Cloud (PSC) season ) yielded qualitatively similar results. From June to October (defined as the PSC season ), aerosol extinction coefficients from ILAS-II were smaller than those from POAM III above 17 km, as in the case of the non-PSC season; however, ILAS-II and POAM III aerosol data were within 15% of each other from 12 to 17 km.

Saitoh, Naoko↗

NASA NTRS2015

Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows

The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-w Model, and the Menter Shear-Stress Trans- port Model. The FUN3D code developed by NASA Langley Research Center was used as the flow solver. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows.

Schaefer, John↗

NASA NTRSDate not supplied

Effect of Pressure on Trace Element Activity Coefficients in Metal-Silicate Systems

The partitioning of trace elements between metal and silicate melts serves as the foundation for understanding the differentiation of a planetary body into a metallic core and silicate mantle. Element activity influences metal-silicate partitioning behavior. Activity coefficients are directly dependent on composition and temperature, and can be indirectly dependent on oxygen fugacity and pressure. Distinguishing the effect of pressure from other variables on the activity coefficients and partitioning is important for understanding the chemical evolution of different planetary bodies during differentiation. In this study, we investigated the influence of pressure on the activity coefficients of Cu, Mo, Pd, Pt, As, Sb, and Bi in Fe-Si metallic liquids. All of these elements exhibit moderate to high activity coefficients in Fe-Si liquids at low pressure, which significantly controls their metal-silicate partitioning behavior. Identifying whether this strong dependence persists at higher pressures is critical to modeling and understanding the chemical consequences of core formation. New experiments at 10 GPa were used to derive activity coefficients for these metals which can be compared to activity coefficients determined at 1 GPa. Experiments were conducted at 10 GPa and 2373K using a 10/5 assembly in the 880-ton multi-anvil press at NASA Johnson Space Center. The standard 10/5 COMPRES assembly was slightly modified to accommodate a sample capsule machined from single-crystal MgO that minimizes melt percolation out of the sample volume during the experiment. Experiment starting materials were comprised of 70 wt.% Knippa basalt and 30 wt.% metal. The metal mixture (~85 wt.% Fe) was created by adding the elements of interest (Cu, Mo, Pd, Pt, As, Sb, Bi) to Fe metal powder. Varied amounts of Si metal (0-10 wt.% Si) were added to the metal-silicate mixtures to generate a systematic series of starting materials. For each element, an epsilon interaction parameter in Fe-Si liquid was derived from the results of our 0-10 wt.% Si metal series. To investigate whether pressure influences the trace element activity coefficients in the 1-10 GPa pressure range, we compared our results at 10 GPa to those at 1-4 GPa [1-3]. Our results can also be directly compared to interaction parameters for Au, P, V, Mn, Ga, Zn, Cd, Sn, W, Pb, and Nb previously determined at 10 GPa and 2373K following the same methods [4]. Combined, this suite of interaction parameters will directly inform metal-silicate partitioning between 1 and 10 GPa, and assess whether these values can be extrapolated to modeling differentiation processes at pressures >10 GPa.

Kelsey Prissel↗

DOE OSTI2025

Dynamic response of a freely rotating butterfly valve in the advanced test reactor − dynamic coefficients modeling

Here, in evaluating the water hammer issue pertaining to the primary-coolant-regulating butterfly valve in the Advanced Test Reactor, the dynamic fluid body interaction (DFBI) approach was implemented in the analysis covered in Part I. Although DFBI modeling accurately and simultaneously solved the dynamic motion of the valve’s disk along with the flow field of the surrounding fluid, it shed little light on the reason behind such motion. For Part II, the reacting torque of the fluid on the disk was decomposed into representations of the dynamic coefficients in terms of stiffness, damping, and added mass. These were evaluated via simulations with steady-state static (stiffness), constant angular speed (damping), and variable angular speed (added mass) disks. Substituting the dynamic coefficients into Newton’s second law enabled the response trajectories to be obtained. Stable (by average) and unstable equilibrium positions and thrust tendencies of the valve were determined based on the stiffness coefficient (or static torque), the response amplitude was dampened or enlarged by the damping coefficient (minorly affected by added mass), and the response frequency was altered by the damping and added mass coefficients. Although the dynamic coefficient approach renders slightly different trajectories, due to the averaging effect of the torque in comparison to the DFBI method, the overall trend of the response aligns with the DFBI simulation, thus confirming the conclusion in Part I that a fix to the current butterfly valve is necessary.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2017

Pre-Test Assessment of the Upper Bound of the Drag Coefficient Repeatability of a Wind Tunnel Model

A new method is presented that computes a pre{test estimate of the upper bound of the drag coefficient repeatability of a wind tunnel model. This upper bound is a conservative estimate of the precision error of the drag coefficient. For clarity, precision error contributions associated with the measurement of the dynamic pressure are analyzed separately from those that are associated with the measurement of the aerodynamic loads. The upper bound is computed by using information about the model, the tunnel conditions, and the balance in combination with an estimate of the expected output variations as input. The model information consists of the reference area and an assumed angle of attack. The tunnel conditions are described by the Mach number and the total pressure or unit Reynolds number. The balance inputs are the partial derivatives of the axial and normal force with respect to all balance outputs. Finally, an empirical output variation of 1.0 microV/V is used to relate both random instrumentation and angle measurement errors to the precision error of the drag coefficient. Results of the analysis are reported by plotting the upper bound of the precision error versus the tunnel conditions. The analysis shows that the influence of the dynamic pressure measurement error on the precision error of the drag coefficient is often small when compared with the influence of errors that are associated with the load measurements. Consequently, the sensitivities of the axial and normal force gages of the balance have a significant influence on the overall magnitude of the drag coefficient's precision error. Therefore, results of the error analysis can be used for balance selection purposes as the drag prediction characteristics of balances of similar size and capacities can objectively be compared. Data from two wind tunnel models and three balances are used to illustrate the assessment of the precision error of the drag coefficient.

drag coefficient measurement↗

NASA NTRSDate not supplied

Evaluation of Heat Transfer Coefficient from Velocity Distribution in Boundary Layer

This paper describes a method of evaluating heat transfer coefficient from a velocity distribution in the boundary layer. The power law velocity profile and universal velocity distribution in a smooth pipe have been used to evaluate the wall shear stress, and the heat transfer coefficient was evaluated from the wall shear stress using the Chilton-Colburn analogy. The predicted pressure drop was compared with the pressure drop computed by the Colebrook equation, and the predicted heat transfer coefficient was compared with the heat transfer coefficient calculated by the Dittus-Boelter equation. The accuracy of pressure drop prediction was within 1%, and the accuracy of heat transfer coefficient prediction was within 8%. This method has the potential to use a Navier-Stokes based CFD solution to evaluate the heat transfer coefficient in nodal or network flow codes.

Heat Transfer Coefficient↗